%------------------------------------------------------------------------------
% File     : Princess---230619
% Problem  : ALG156+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp
% Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s

% Computer : n009.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Wed Aug 30 16:38:34 EDT 2023

% Result   : Unsatisfiable 23.38s 3.80s
% Output   : Proof 154.32s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : ALG156+1 : TPTP v8.1.2. Released v2.7.0.
% 0.07/0.12  % Command  : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33  % Computer : n009.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Aug 28 05:18:50 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.18/0.59  ________       _____
% 0.18/0.59  ___  __ \_________(_)________________________________
% 0.18/0.59  __  /_/ /_  ___/_  /__  __ \  ___/  _ \_  ___/_  ___/
% 0.18/0.59  _  ____/_  /   _  / _  / / / /__ /  __/(__  )_(__  )
% 0.18/0.59  /_/     /_/    /_/  /_/ /_/\___/ \___//____/ /____/
% 0.18/0.59  
% 0.18/0.59  A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.18/0.59  (2023-06-19)
% 0.18/0.59  
% 0.18/0.59  (c) Philipp Rümmer, 2009-2023
% 0.18/0.59  Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.18/0.59                Amanda Stjerna.
% 0.18/0.59  Free software under BSD-3-Clause.
% 0.18/0.59  
% 0.18/0.59  For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.18/0.59  
% 0.18/0.59  Loading /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.18/0.61  Running up to 7 provers in parallel.
% 0.66/0.62  Prover 0: Options:  +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.66/0.62  Prover 1: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.66/0.62  Prover 3: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.66/0.62  Prover 2: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.66/0.62  Prover 5: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.66/0.62  Prover 4: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.66/0.62  Prover 6: Options:  -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 5.55/1.48  Prover 4: Preprocessing ...
% 5.55/1.49  Prover 1: Preprocessing ...
% 5.55/1.52  Prover 2: Preprocessing ...
% 5.55/1.52  Prover 5: Preprocessing ...
% 5.55/1.52  Prover 0: Preprocessing ...
% 5.55/1.52  Prover 3: Preprocessing ...
% 5.55/1.52  Prover 6: Preprocessing ...
% 9.31/1.94  Prover 2: Constructing countermodel ...
% 9.31/1.94  Prover 3: Constructing countermodel ...
% 9.31/1.97  Prover 6: Constructing countermodel ...
% 9.31/2.00  Prover 1: Constructing countermodel ...
% 9.99/2.03  Prover 0: Constructing countermodel ...
% 9.99/2.04  Prover 4: Constructing countermodel ...
% 12.25/2.34  Prover 5: Constructing countermodel ...
% 23.38/3.80  Prover 2: proved (3181ms)
% 23.38/3.80  
% 23.38/3.80  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 23.38/3.80  
% 23.38/3.80  Prover 0: stopped
% 23.38/3.80  Prover 5: stopped
% 23.38/3.81  Prover 3: stopped
% 23.70/3.83  Prover 6: stopped
% 23.70/3.86  Prover 7: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 23.70/3.86  Prover 8: Options:  +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 23.70/3.86  Prover 10: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 23.70/3.86  Prover 11: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 23.70/3.87  Prover 13: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 26.02/4.20  Prover 8: Preprocessing ...
% 26.02/4.20  Prover 13: Preprocessing ...
% 26.02/4.20  Prover 11: Preprocessing ...
% 26.02/4.21  Prover 10: Preprocessing ...
% 26.51/4.21  Prover 7: Preprocessing ...
% 26.96/4.32  Prover 8: Constructing countermodel ...
% 27.88/4.39  Prover 10: Constructing countermodel ...
% 27.88/4.41  Prover 7: Constructing countermodel ...
% 28.24/4.43  Prover 13: Constructing countermodel ...
% 28.33/4.45  Prover 11: Constructing countermodel ...
% 67.18/9.38  Prover 13: stopped
% 67.18/9.38  Prover 16: Options:  +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 67.77/9.47  Prover 16: Preprocessing ...
% 68.49/9.58  Prover 16: Constructing countermodel ...
% 112.32/15.25  Prover 16: stopped
% 112.91/15.27  Prover 19: Options:  +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 114.06/15.42  Prover 19: Preprocessing ...
% 114.49/15.51  Prover 19: Constructing countermodel ...
% 118.11/15.96  Prover 1: stopped
% 139.75/18.98  Prover 7: Found proof (size 195851)
% 139.75/18.98  Prover 7: proved (15103ms)
% 139.75/18.99  Prover 10: stopped
% 139.75/18.99  Prover 4: stopped
% 139.75/18.99  Prover 11: stopped
% 139.75/18.99  Prover 8: stopped
% 139.75/18.99  Prover 19: stopped
% 139.75/18.99  
% 139.75/18.99  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 139.75/18.99  
% 141.73/19.54  % SZS output start Proof for theBenchmark
% 142.28/19.64  Assumptions after simplification:
% 142.28/19.64  ---------------------------------
% 142.28/19.64  
% 142.28/19.64    (ax1)
% 142.28/19.69    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 142.28/19.69    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 142.28/19.69      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 142.28/19.69      $i] :  ? [v14: $i] :  ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 142.28/19.69      op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 142.28/19.69      op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 142.28/19.69      op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 142.28/19.69      op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 142.28/19.69      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 142.28/19.69      $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 142.28/19.69        e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 142.28/19.69        v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 142.28/19.69        = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 142.28/19.69        v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 142.28/19.69        v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 142.28/19.69        v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 142.28/19.69      (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 142.28/19.69        = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 142.28/19.69        = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 142.28/19.69  
% 142.28/19.69    (ax10)
% 142.28/19.69    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.28/19.69    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 142.28/19.69          op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 &
% 142.28/19.69          $i(v1))))
% 142.28/19.69  
% 142.28/19.69    (ax11)
% 142.28/19.70    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.28/19.70    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 142.28/19.70          op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 &
% 142.28/19.70          $i(v1))))
% 142.28/19.70  
% 142.28/19.70    (ax12)
% 142.28/19.70    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.28/19.70    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 142.28/19.70          op(e1, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 &
% 142.28/19.70          $i(v1))))
% 142.28/19.70  
% 142.28/19.70    (ax13)
% 142.28/19.70    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.28/19.70    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 142.28/19.70          op(e1, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 &
% 142.28/19.70          $i(v1))))
% 142.28/19.70  
% 142.28/19.70    (ax14)
% 142.28/19.70    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.28/19.70    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 142.28/19.70          op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 &
% 142.28/19.70          $i(v1))))
% 142.28/19.70  
% 142.28/19.71    (ax15)
% 142.28/19.71    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.28/19.71    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 142.28/19.71          op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 &
% 142.28/19.71          $i(v1))))
% 142.28/19.71  
% 142.28/19.71    (ax16)
% 142.28/19.71    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.28/19.71    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 142.28/19.71          op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 &
% 142.28/19.71          $i(v1))))
% 142.28/19.71  
% 142.28/19.71    (ax17)
% 142.28/19.71    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.28/19.71    (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 142.28/19.71          op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 &
% 142.28/19.71          $i(v1))))
% 142.28/19.71  
% 142.28/19.71    (ax18)
% 142.28/19.72    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.28/19.72    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 142.28/19.72          op(e2, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 &
% 142.28/19.72          $i(v1))))
% 142.28/19.72  
% 142.28/19.72    (ax19)
% 142.28/19.72    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.28/19.72    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 142.28/19.72          op(e2, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 &
% 142.28/19.72          $i(v1))))
% 142.28/19.72  
% 142.28/19.72    (ax2)
% 142.64/19.74    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 142.64/19.74    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 142.64/19.74      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 142.64/19.74      $i] :  ? [v14: $i] :  ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 =
% 142.64/19.74          e3 & op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3,
% 142.64/19.74            e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 142.64/19.74          e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v15
% 142.64/19.74          = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 = e2 &
% 142.64/19.74          op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = e2 & op(e3,
% 142.64/19.74            e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2)
% 142.64/19.74        | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1
% 142.64/19.74          & op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & op(e3,
% 142.64/19.74            e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) =
% 142.64/19.74          e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15
% 142.64/19.74          = e0 & op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 142.64/19.74          op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & op(e3,
% 142.64/19.74            e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0)
% 142.64/19.74        | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3
% 142.64/19.74          & op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & op(e0, e2)
% 142.64/19.74          = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 142.64/19.74        (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 142.64/19.74          op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & op(e1, e2)
% 142.64/19.74          = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) |
% 142.64/19.74        (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 &
% 142.64/19.74          op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & op(e2,
% 142.64/19.74            e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) =
% 142.64/19.74          e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 142.64/19.74        (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 142.64/19.74          op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & op(e2, e1)
% 142.64/19.74          = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) |
% 142.64/19.74        (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 &
% 142.64/19.74          op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & op(e2,
% 142.64/19.74            e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3))
% 142.64/19.74      & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 142.64/19.74          op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & op(e3,
% 142.64/19.74            e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1)
% 142.64/19.74        | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0
% 142.64/19.74          & op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1)
% 142.64/19.74          = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) |
% 142.64/19.74        (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 142.64/19.74          op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) =
% 142.64/19.74          e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8
% 142.64/19.74          = e1 & op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 &
% 142.64/19.74          op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & op(e1, e2)
% 142.64/19.74          = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) &
% 142.64/19.74      ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 142.64/19.74          op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0)
% 142.64/19.74          = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0
% 142.64/19.74          = e2 & op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 &
% 142.64/19.74          op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) =
% 142.64/19.74          e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1
% 142.64/19.74          = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 142.64/19.74          op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) =
% 142.64/19.74          e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2
% 142.64/19.74          = e1 & op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 &
% 142.64/19.74          op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & op(e3,
% 142.64/19.74                e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) =
% 142.64/19.74              e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) |
% 142.64/19.74            (v1 = e0 & op(e0, e1) = e0)))))
% 142.64/19.74  
% 142.64/19.74    (ax20)
% 142.64/19.75    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.75    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 142.64/19.75          op(e2, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 &
% 142.64/19.75          $i(v1))))
% 142.64/19.75  
% 142.64/19.75    (ax21)
% 142.64/19.75    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.75    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 142.64/19.75          op(e2, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 &
% 142.64/19.75          $i(v1))))
% 142.64/19.75  
% 142.64/19.75    (ax22)
% 142.64/19.75    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.75    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 142.64/19.75          op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 &
% 142.64/19.75          $i(v1))))
% 142.64/19.75  
% 142.64/19.75    (ax23)
% 142.64/19.75    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.75    (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 142.64/19.75          op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 &
% 142.64/19.75          $i(v1))))
% 142.64/19.75  
% 142.64/19.75    (ax24)
% 142.64/19.75    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.75    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 142.64/19.75          op(e3, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 &
% 142.64/19.75          $i(v1))))
% 142.64/19.75  
% 142.64/19.75    (ax25)
% 142.64/19.75    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.75    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 142.64/19.75          op(e3, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 &
% 142.64/19.75          $i(v1))))
% 142.64/19.75  
% 142.64/19.75    (ax26)
% 142.64/19.75    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.75    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 142.64/19.75          op(e3, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 &
% 142.64/19.75          $i(v1))))
% 142.64/19.75  
% 142.64/19.75    (ax27)
% 142.64/19.76    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.76    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 142.64/19.76          op(e3, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 &
% 142.64/19.76          $i(v1))))
% 142.64/19.76  
% 142.64/19.76    (ax28)
% 142.64/19.76    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.76    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 142.64/19.76          op(e3, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 &
% 142.64/19.76          $i(v1))))
% 142.64/19.76  
% 142.64/19.76    (ax29)
% 142.64/19.76    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.76    (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 142.64/19.76          op(e3, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 &
% 142.64/19.76          $i(v1))))
% 142.64/19.76  
% 142.64/19.76    (ax3)
% 142.64/19.76    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 142.64/19.76    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 142.64/19.76      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 142.64/19.76      $i] :  ? [v14: $i] :  ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~
% 142.64/19.76      (v15 = v12) &  ~ (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 =
% 142.64/19.76        v13) &  ~ (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) & 
% 142.64/19.76      ~ (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12 =
% 142.64/19.76        v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 = v9) &  ~
% 142.64/19.76      (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9) &  ~ (v10 = v8) &
% 142.64/19.76       ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~ (v9 = v5) &  ~ (v9 = v1) &
% 142.64/19.76       ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6) &  ~ (v7 = v5) &  ~ (v7 = v4) & 
% 142.64/19.76      ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6 = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~
% 142.64/19.76      (v5 = v1) &  ~ (v4 = v0) &  ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~
% 142.64/19.76      (v2 = v1) &  ~ (v2 = v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 142.64/19.76      v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 142.64/19.76      v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 142.64/19.76      & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 142.64/19.76      op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 142.64/19.76      $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 142.64/19.76      $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 142.64/19.76  
% 142.64/19.76    (ax4)
% 142.64/19.77     ~ (e3 = e2) &  ~ (e3 = e1) &  ~ (e3 = e0) &  ~ (e2 = e1) &  ~ (e2 = e0) &  ~
% 142.64/19.77    (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 142.64/19.77  
% 142.64/19.77    (ax5)
% 142.64/19.78    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : 
% 142.64/19.78    ? [v3: $i] :  ? [v4: $i] :  ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8:
% 142.64/19.78      $i] :  ? [v9: $i] :  ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13:
% 142.64/19.78      $i] :  ? [v14: $i] :  ? [v15: $i] : (((v15 = e2 & v1 = e3 &  ~ (v14 = e1) & 
% 142.64/19.78          ~ (v3 = e3) & op(e2, e3) = e2 & op(e2, e2) = v3 & op(e1, e3) = v14 &
% 142.64/19.78          op(e1, e1) = e3 & $i(v14) & $i(v3)) | (v15 = e2 & v0 = e3 &  ~ (v13 =
% 142.64/19.78            e0) &  ~ (v3 = e3) & op(e2, e3) = e2 & op(e2, e2) = v3 & op(e0, e3) =
% 142.64/19.78          v13 & op(e0, e0) = e3 & $i(v13) & $i(v3)) | (v14 = e1 & v3 = e3 &  ~
% 142.64/19.78          (v15 = e2) &  ~ (v1 = e3) & op(e2, e3) = v15 & op(e2, e2) = e3 & op(e1,
% 142.64/19.78            e3) = e1 & op(e1, e1) = v1 & $i(v15) & $i(v1)) | (v14 = e1 & v0 = e3 &
% 142.64/19.78           ~ (v13 = e0) &  ~ (v1 = e3) & op(e1, e3) = e1 & op(e1, e1) = v1 &
% 142.64/19.78          op(e0, e3) = v13 & op(e0, e0) = e3 & $i(v13) & $i(v1)) | (v12 = e3 & v1
% 142.64/19.78          = e2 &  ~ (v11 = e1) &  ~ (v5 = e2) & op(e3, e3) = v5 & op(e3, e2) = e3
% 142.64/19.78          & op(e1, e2) = v11 & op(e1, e1) = e2 & $i(v11) & $i(v5)) | (v12 = e3 &
% 142.64/19.78          v0 = e2 &  ~ (v10 = e0) &  ~ (v5 = e2) & op(e3, e3) = v5 & op(e3, e2) =
% 142.64/19.78          e3 & op(e0, e2) = v10 & op(e0, e0) = e2 & $i(v10) & $i(v5)) | (v11 = e1
% 142.64/19.78          & v5 = e2 &  ~ (v12 = e3) &  ~ (v1 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 142.64/19.78          = v12 & op(e1, e2) = e1 & op(e1, e1) = v1 & $i(v12) & $i(v1)) | (v11 =
% 142.64/19.78          e1 & v0 = e2 &  ~ (v10 = e0) &  ~ (v1 = e2) & op(e1, e2) = e1 & op(e1,
% 142.64/19.78            e1) = v1 & op(e0, e2) = v10 & op(e0, e0) = e2 & $i(v10) & $i(v1)) |
% 142.64/19.78        (v9 = e3 & v3 = e1 &  ~ (v8 = e2) &  ~ (v5 = e1) & op(e3, e3) = v5 &
% 142.64/19.78          op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = v8 & $i(v8) & $i(v5)) |
% 142.64/19.78        (v9 = e3 & v0 = e1 &  ~ (v7 = e0) &  ~ (v5 = e1) & op(e3, e3) = v5 &
% 142.64/19.78          op(e3, e1) = e3 & op(e0, e1) = v7 & op(e0, e0) = e1 & $i(v7) & $i(v5)) |
% 142.64/19.78        (v8 = e2 & v5 = e1 &  ~ (v9 = e3) &  ~ (v3 = e1) & op(e3, e3) = e1 &
% 142.64/19.78          op(e3, e1) = v9 & op(e2, e2) = v3 & op(e2, e1) = e2 & $i(v9) & $i(v3)) |
% 142.64/19.78        (v8 = e2 & v0 = e1 &  ~ (v7 = e0) &  ~ (v3 = e1) & op(e2, e2) = v3 &
% 142.64/19.78          op(e2, e1) = e2 & op(e0, e1) = v7 & op(e0, e0) = e1 & $i(v7) & $i(v3)) |
% 142.64/19.78        (v6 = e3 & v3 = e0 &  ~ (v5 = e0) &  ~ (v4 = e2) & op(e3, e3) = v5 &
% 142.64/19.78          op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = v4 & $i(v5) & $i(v4)) |
% 142.64/19.78        (v6 = e3 & v1 = e0 &  ~ (v5 = e0) &  ~ (v2 = e1) & op(e3, e3) = v5 &
% 142.64/19.78          op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = v2 & $i(v5) & $i(v2)) |
% 142.64/19.78        (v5 = e0 & v4 = e2 &  ~ (v6 = e3) &  ~ (v3 = e0) & op(e3, e3) = e0 &
% 142.64/19.78          op(e3, e0) = v6 & op(e2, e2) = v3 & op(e2, e0) = e2 & $i(v6) & $i(v3)) |
% 142.64/19.78        (v5 = e0 & v2 = e1 &  ~ (v6 = e3) &  ~ (v1 = e0) & op(e3, e3) = e0 &
% 142.64/19.78          op(e3, e0) = v6 & op(e1, e1) = v1 & op(e1, e0) = e1 & $i(v6) & $i(v1)) |
% 142.64/19.78        (v4 = e2 & v1 = e0 &  ~ (v3 = e0) &  ~ (v2 = e1) & op(e2, e2) = v3 &
% 142.64/19.78          op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = v2 & $i(v3) & $i(v2)) |
% 142.64/19.78        (v3 = e0 & v2 = e1 &  ~ (v4 = e2) &  ~ (v1 = e0) & op(e2, e2) = e0 &
% 142.64/19.78          op(e2, e0) = v4 & op(e1, e1) = v1 & op(e1, e0) = e1 & $i(v4) & $i(v1)) |
% 142.64/19.78        (op(e0, e0) = v0 & $i(v0) & ((v13 = e0 & v3 = e3 &  ~ (v15 = e2) &  ~ (v0
% 142.64/19.78                = e3) & op(e2, e3) = v15 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 142.64/19.78              $i(v15)) | (v13 = e0 & v1 = e3 &  ~ (v14 = e1) &  ~ (v0 = e3) &
% 142.64/19.78              op(e1, e3) = v14 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(v14)) |
% 142.64/19.78            (v10 = e0 & v5 = e2 &  ~ (v12 = e3) &  ~ (v0 = e2) & op(e3, e3) = e2 &
% 142.64/19.78              op(e3, e2) = v12 & op(e0, e2) = e0 & $i(v12)) | (v10 = e0 & v1 = e2
% 142.64/19.78              &  ~ (v11 = e1) &  ~ (v0 = e2) & op(e1, e2) = v11 & op(e1, e1) = e2
% 142.64/19.78              & op(e0, e2) = e0 & $i(v11)) | (v7 = e0 & v5 = e1 &  ~ (v9 = e3) & 
% 142.64/19.78              ~ (v0 = e1) & op(e3, e3) = e1 & op(e3, e1) = v9 & op(e0, e1) = e0 &
% 142.64/19.78              $i(v9)) | (v7 = e0 & v3 = e1 &  ~ (v8 = e2) &  ~ (v0 = e1) & op(e2,
% 142.64/19.78                e2) = e1 & op(e2, e1) = v8 & op(e0, e1) = e0 & $i(v8))))) & ((v5 =
% 142.64/19.78          e3 & op(e3, e3) = e3 & ((v15 = e2 & op(e2, e3) = e2) | ( ~ (v3 = e3) &
% 142.64/19.78              op(e2, e2) = v3 & $i(v3))) & ((v14 = e1 & op(e1, e3) = e1) | ( ~ (v1
% 142.64/19.78                = e3) & op(e1, e1) = v1 & $i(v1))) & ((v13 = e0 & op(e0, e3) = e0)
% 142.64/19.78            | ( ~ (v0 = e3) & op(e0, e0) = v0 & $i(v0)))) | (v3 = e2 & op(e2, e2)
% 142.64/19.78          = e2 & ((v12 = e3 & op(e3, e2) = e3) | ( ~ (v5 = e2) & op(e3, e3) = v5 &
% 142.64/19.78              $i(v5))) & ((v11 = e1 & op(e1, e2) = e1) | ( ~ (v1 = e2) & op(e1,
% 142.64/19.78                e1) = v1 & $i(v1))) & ((v10 = e0 & op(e0, e2) = e0) | ( ~ (v0 =
% 142.64/19.78                e2) & op(e0, e0) = v0 & $i(v0)))) | (v1 = e1 & op(e1, e1) = e1 &
% 142.64/19.78          ((v9 = e3 & op(e3, e1) = e3) | ( ~ (v5 = e1) & op(e3, e3) = v5 &
% 142.64/19.78              $i(v5))) & ((v8 = e2 & op(e2, e1) = e2) | ( ~ (v3 = e1) & op(e2, e2)
% 142.64/19.78              = v3 & $i(v3))) & ((v7 = e0 & op(e0, e1) = e0) | ( ~ (v0 = e1) &
% 142.64/19.78              op(e0, e0) = v0 & $i(v0)))) | (v0 = e0 & op(e0, e0) = e0 & ((v6 = e3
% 142.64/19.78              & op(e3, e0) = e3) | ( ~ (v5 = e0) & op(e3, e3) = v5 & $i(v5))) &
% 142.64/19.79          ((v4 = e2 & op(e2, e0) = e2) | ( ~ (v3 = e0) & op(e2, e2) = v3 &
% 142.64/19.79              $i(v3))) & ((v2 = e1 & op(e1, e0) = e1) | ( ~ (v1 = e0) & op(e1, e1)
% 142.64/19.79              = v1 & $i(v1))))))
% 142.64/19.79  
% 142.64/19.79    (ax6)
% 142.64/19.79    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.79    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 142.64/19.79          op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 &
% 142.64/19.79          $i(v1))))
% 142.64/19.79  
% 142.64/19.79    (ax7)
% 142.64/19.79    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.79    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 142.64/19.79          op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 &
% 142.64/19.79          $i(v1))))
% 142.64/19.79  
% 142.64/19.79    (ax8)
% 142.64/19.79    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.79    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 142.64/19.79          op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 &
% 142.64/19.79          $i(v1))))
% 142.64/19.79  
% 142.64/19.79    (ax9)
% 142.64/19.79    $i(e3) & $i(e2) & $i(e1) & $i(e0) &  ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :
% 142.64/19.79    (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 142.64/19.79          op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 &
% 142.64/19.79          $i(v1))))
% 142.64/19.79  
% 142.64/19.79    (function-axioms)
% 142.64/19.79     ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~ (op(v3,
% 142.64/19.79          v2) = v1) |  ~ (op(v3, v2) = v0))
% 142.64/19.79  
% 142.64/19.79  Those formulas are unsatisfiable:
% 142.64/19.79  ---------------------------------
% 142.64/19.79  
% 142.64/19.79  Begin of proof
% 142.64/19.80  | 
% 143.02/19.80  | ALPHA: (ax1) implies:
% 143.02/19.80  |   (1)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 143.02/19.80  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 143.02/19.80  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 143.02/19.80  |         ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 143.02/19.80  |          & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 143.02/19.80  |          = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 143.02/19.80  |            e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 143.02/19.80  |          op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 143.02/19.80  |          $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 143.02/19.80  |          $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 143.02/19.80  |            = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 143.02/19.80  |            = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 143.02/19.80  |            v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 143.02/19.80  |            v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 143.02/19.80  |            | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 143.02/19.80  |            = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 143.02/19.80  |            e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 143.02/19.80  |          (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 143.02/19.80  |            e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 143.02/19.80  |            | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 143.02/19.80  |            = e0))
% 143.02/19.80  | 
% 143.02/19.80  | ALPHA: (ax2) implies:
% 143.02/19.82  |   (2)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 143.02/19.82  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 143.02/19.82  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 143.02/19.82  |         ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = e3 & op(e3, e2)
% 143.02/19.82  |              = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, e0) =
% 143.02/19.82  |              e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 143.02/19.82  |              e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3))
% 143.02/19.82  |          & ((v15 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11
% 143.02/19.82  |              = e2 & op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 =
% 143.02/19.82  |              e2 & op(e3, e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 &
% 143.02/19.82  |              op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 &
% 143.02/19.82  |              op(e3, e3) = e1) | (v14 = e1 & op(e3, e2) = e1) | (v11 = e1 &
% 143.02/19.82  |              op(e3, e1) = e1) | (v6 = e1 & op(e3, e0) = e1)) & ((v15 = e1 &
% 143.02/19.82  |              op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = e1) | (v9 = e1 &
% 143.02/19.82  |              op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 = e0 &
% 143.02/19.82  |              op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 143.02/19.82  |              op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 &
% 143.02/19.82  |              op(e3, e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 &
% 143.02/19.82  |              op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 &
% 143.02/19.82  |              op(e3, e2) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v8 = e3 &
% 143.02/19.82  |              op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v14 = e2 &
% 143.02/19.82  |              op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v8 = e2 &
% 143.02/19.82  |              op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 143.02/19.82  |              op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 &
% 143.02/19.82  |              op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 &
% 143.02/19.82  |              op(e3, e2) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 &
% 143.02/19.82  |              op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v13 = e3 &
% 143.02/19.82  |              op(e2, e3) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v10 = e3 &
% 143.02/19.82  |              op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = e3)) & ((v13 = e2 &
% 143.02/19.82  |              op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v10 = e2 &
% 143.02/19.82  |              op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 143.02/19.82  |              op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 &
% 143.02/19.82  |              op(e2, e1) = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 &
% 143.02/19.82  |              op(e2, e3) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 &
% 143.02/19.82  |              op(e2, e1) = e0) | (v5 = e0 & op(e2, e0) = e0)) & ((v11 = e3 &
% 143.02/19.82  |              op(e3, e1) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v7 = e3 &
% 143.02/19.82  |              op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v11 = e2 &
% 143.02/19.82  |              op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 143.02/19.82  |              op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 &
% 143.02/19.82  |              op(e3, e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 &
% 143.02/19.82  |              op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 &
% 143.02/19.82  |              op(e3, e1) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v7 = e0 &
% 143.02/19.82  |              op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v9 = e3 &
% 143.02/19.82  |              op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v7 = e3 &
% 143.02/19.82  |              op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 143.02/19.82  |              op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 &
% 143.02/19.82  |              op(e1, e1) = e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 &
% 143.02/19.82  |              op(e1, e3) = e1) | (v8 = e1 & op(e1, e2) = e1) | (v7 = e1 &
% 143.02/19.82  |              op(e1, e1) = e1) | (v4 = e1 & op(e1, e0) = e1)) & ((v9 = e0 &
% 143.02/19.82  |              op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v7 = e0 &
% 143.02/19.82  |              op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v6 = e3 &
% 143.02/19.82  |              op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 143.02/19.82  |              op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 &
% 143.02/19.82  |              op(e3, e0) = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 &
% 143.02/19.82  |              op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v6 = e1 &
% 143.02/19.82  |              op(e3, e0) = e1) | (v5 = e1 & op(e2, e0) = e1) | (v4 = e1 &
% 143.02/19.82  |              op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v3 = e3 &
% 143.02/19.82  |              op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 &
% 143.02/19.82  |              op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 143.02/19.82  |              op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 &
% 143.02/19.82  |              op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 &
% 143.02/19.82  |              op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 &
% 143.02/19.82  |              op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 &
% 143.02/19.82  |              op(e0, e0) = e0) | (((v6 = e0 & op(e3, e0) = e0) | (v5 = e0 &
% 143.02/19.82  |                  op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v3 = e0 &
% 143.02/19.82  |                  op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 &
% 143.02/19.82  |                  op(e0, e1) = e0)))))
% 143.02/19.82  | 
% 143.02/19.82  | ALPHA: (ax3) implies:
% 143.02/19.82  |   (3)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 143.02/19.82  |        ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] :  ?
% 143.02/19.82  |        [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14: $i] :
% 143.02/19.82  |         ? [v15: $i] : ( ~ (v15 = v14) &  ~ (v15 = v13) &  ~ (v15 = v12) &  ~
% 143.02/19.82  |          (v15 = v11) &  ~ (v15 = v7) &  ~ (v15 = v3) &  ~ (v14 = v13) &  ~
% 143.02/19.82  |          (v14 = v12) &  ~ (v14 = v10) &  ~ (v14 = v6) &  ~ (v14 = v2) &  ~
% 143.02/19.82  |          (v13 = v12) &  ~ (v13 = v9) &  ~ (v13 = v5) &  ~ (v13 = v1) &  ~ (v12
% 143.02/19.82  |            = v8) &  ~ (v12 = v4) &  ~ (v12 = v0) &  ~ (v11 = v10) &  ~ (v11 =
% 143.02/19.82  |            v9) &  ~ (v11 = v8) &  ~ (v11 = v7) &  ~ (v11 = v3) &  ~ (v10 = v9)
% 143.02/19.82  |          &  ~ (v10 = v8) &  ~ (v10 = v6) &  ~ (v10 = v2) &  ~ (v9 = v8) &  ~
% 143.02/19.82  |          (v9 = v5) &  ~ (v9 = v1) &  ~ (v8 = v4) &  ~ (v8 = v0) &  ~ (v7 = v6)
% 143.02/19.82  |          &  ~ (v7 = v5) &  ~ (v7 = v4) &  ~ (v7 = v3) &  ~ (v6 = v5) &  ~ (v6
% 143.02/19.82  |            = v4) &  ~ (v6 = v2) &  ~ (v5 = v4) &  ~ (v5 = v1) &  ~ (v4 = v0) &
% 143.02/19.82  |           ~ (v3 = v2) &  ~ (v3 = v1) &  ~ (v3 = v0) &  ~ (v2 = v1) &  ~ (v2 =
% 143.02/19.82  |            v0) &  ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 143.02/19.82  |            e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 143.02/19.82  |          op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 143.02/19.82  |          v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 143.02/19.82  |            e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 143.02/19.82  |          $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 143.02/19.82  |          $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 143.02/19.82  | 
% 143.02/19.82  | ALPHA: (ax4) implies:
% 143.02/19.83  |   (4)   ~ (e1 = e0)
% 143.02/19.83  |   (5)   ~ (e2 = e0)
% 143.02/19.83  |   (6)   ~ (e2 = e1)
% 143.02/19.83  |   (7)   ~ (e3 = e0)
% 143.02/19.83  |   (8)   ~ (e3 = e1)
% 143.02/19.83  |   (9)   ~ (e3 = e2)
% 143.02/19.83  | 
% 143.02/19.83  | ALPHA: (ax5) implies:
% 143.02/19.84  |   (10)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] :  ? [v3: $i] :  ? [v4: $i] : 
% 143.02/19.84  |         ? [v5: $i] :  ? [v6: $i] :  ? [v7: $i] :  ? [v8: $i] :  ? [v9: $i] : 
% 143.02/19.84  |         ? [v10: $i] :  ? [v11: $i] :  ? [v12: $i] :  ? [v13: $i] :  ? [v14:
% 143.02/19.84  |           $i] :  ? [v15: $i] : (((v15 = e2 & v1 = e3 &  ~ (v14 = e1) &  ~ (v3
% 143.02/19.84  |                 = e3) & op(e2, e3) = e2 & op(e2, e2) = v3 & op(e1, e3) = v14 &
% 143.02/19.84  |               op(e1, e1) = e3 & $i(v14) & $i(v3)) | (v15 = e2 & v0 = e3 &  ~
% 143.02/19.84  |               (v13 = e0) &  ~ (v3 = e3) & op(e2, e3) = e2 & op(e2, e2) = v3 &
% 143.02/19.84  |               op(e0, e3) = v13 & op(e0, e0) = e3 & $i(v13) & $i(v3)) | (v14 =
% 143.02/19.84  |               e1 & v3 = e3 &  ~ (v15 = e2) &  ~ (v1 = e3) & op(e2, e3) = v15 &
% 143.02/19.84  |               op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = v1 & $i(v15) &
% 143.02/19.84  |               $i(v1)) | (v14 = e1 & v0 = e3 &  ~ (v13 = e0) &  ~ (v1 = e3) &
% 143.02/19.84  |               op(e1, e3) = e1 & op(e1, e1) = v1 & op(e0, e3) = v13 & op(e0,
% 143.02/19.84  |                 e0) = e3 & $i(v13) & $i(v1)) | (v12 = e3 & v1 = e2 &  ~ (v11 =
% 143.02/19.84  |                 e1) &  ~ (v5 = e2) & op(e3, e3) = v5 & op(e3, e2) = e3 &
% 143.02/19.84  |               op(e1, e2) = v11 & op(e1, e1) = e2 & $i(v11) & $i(v5)) | (v12 =
% 143.02/19.84  |               e3 & v0 = e2 &  ~ (v10 = e0) &  ~ (v5 = e2) & op(e3, e3) = v5 &
% 143.02/19.84  |               op(e3, e2) = e3 & op(e0, e2) = v10 & op(e0, e0) = e2 & $i(v10) &
% 143.02/19.84  |               $i(v5)) | (v11 = e1 & v5 = e2 &  ~ (v12 = e3) &  ~ (v1 = e2) &
% 143.02/19.84  |               op(e3, e3) = e2 & op(e3, e2) = v12 & op(e1, e2) = e1 & op(e1,
% 143.02/19.84  |                 e1) = v1 & $i(v12) & $i(v1)) | (v11 = e1 & v0 = e2 &  ~ (v10 =
% 143.02/19.84  |                 e0) &  ~ (v1 = e2) & op(e1, e2) = e1 & op(e1, e1) = v1 &
% 143.02/19.84  |               op(e0, e2) = v10 & op(e0, e0) = e2 & $i(v10) & $i(v1)) | (v9 =
% 143.02/19.84  |               e3 & v3 = e1 &  ~ (v8 = e2) &  ~ (v5 = e1) & op(e3, e3) = v5 &
% 143.02/19.84  |               op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = v8 & $i(v8) &
% 143.02/19.84  |               $i(v5)) | (v9 = e3 & v0 = e1 &  ~ (v7 = e0) &  ~ (v5 = e1) &
% 143.02/19.84  |               op(e3, e3) = v5 & op(e3, e1) = e3 & op(e0, e1) = v7 & op(e0, e0)
% 143.02/19.84  |               = e1 & $i(v7) & $i(v5)) | (v8 = e2 & v5 = e1 &  ~ (v9 = e3) &  ~
% 143.02/19.84  |               (v3 = e1) & op(e3, e3) = e1 & op(e3, e1) = v9 & op(e2, e2) = v3
% 143.02/19.84  |               & op(e2, e1) = e2 & $i(v9) & $i(v3)) | (v8 = e2 & v0 = e1 &  ~
% 143.02/19.84  |               (v7 = e0) &  ~ (v3 = e1) & op(e2, e2) = v3 & op(e2, e1) = e2 &
% 143.02/19.84  |               op(e0, e1) = v7 & op(e0, e0) = e1 & $i(v7) & $i(v3)) | (v6 = e3
% 143.02/19.84  |               & v3 = e0 &  ~ (v5 = e0) &  ~ (v4 = e2) & op(e3, e3) = v5 &
% 143.02/19.84  |               op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = v4 & $i(v5) &
% 143.02/19.84  |               $i(v4)) | (v6 = e3 & v1 = e0 &  ~ (v5 = e0) &  ~ (v2 = e1) &
% 143.02/19.84  |               op(e3, e3) = v5 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 143.02/19.84  |               = v2 & $i(v5) & $i(v2)) | (v5 = e0 & v4 = e2 &  ~ (v6 = e3) &  ~
% 143.02/19.84  |               (v3 = e0) & op(e3, e3) = e0 & op(e3, e0) = v6 & op(e2, e2) = v3
% 143.02/19.84  |               & op(e2, e0) = e2 & $i(v6) & $i(v3)) | (v5 = e0 & v2 = e1 &  ~
% 143.02/19.84  |               (v6 = e3) &  ~ (v1 = e0) & op(e3, e3) = e0 & op(e3, e0) = v6 &
% 143.02/19.84  |               op(e1, e1) = v1 & op(e1, e0) = e1 & $i(v6) & $i(v1)) | (v4 = e2
% 143.02/19.84  |               & v1 = e0 &  ~ (v3 = e0) &  ~ (v2 = e1) & op(e2, e2) = v3 &
% 143.02/19.84  |               op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = v2 & $i(v3) &
% 143.02/19.84  |               $i(v2)) | (v3 = e0 & v2 = e1 &  ~ (v4 = e2) &  ~ (v1 = e0) &
% 143.02/19.84  |               op(e2, e2) = e0 & op(e2, e0) = v4 & op(e1, e1) = v1 & op(e1, e0)
% 143.02/19.84  |               = e1 & $i(v4) & $i(v1)) | (op(e0, e0) = v0 & $i(v0) & ((v13 = e0
% 143.02/19.84  |                   & v3 = e3 &  ~ (v15 = e2) &  ~ (v0 = e3) & op(e2, e3) = v15
% 143.02/19.84  |                   & op(e2, e2) = e3 & op(e0, e3) = e0 & $i(v15)) | (v13 = e0 &
% 143.02/19.84  |                   v1 = e3 &  ~ (v14 = e1) &  ~ (v0 = e3) & op(e1, e3) = v14 &
% 143.02/19.84  |                   op(e1, e1) = e3 & op(e0, e3) = e0 & $i(v14)) | (v10 = e0 &
% 143.02/19.84  |                   v5 = e2 &  ~ (v12 = e3) &  ~ (v0 = e2) & op(e3, e3) = e2 &
% 143.02/19.84  |                   op(e3, e2) = v12 & op(e0, e2) = e0 & $i(v12)) | (v10 = e0 &
% 143.02/19.84  |                   v1 = e2 &  ~ (v11 = e1) &  ~ (v0 = e2) & op(e1, e2) = v11 &
% 143.02/19.84  |                   op(e1, e1) = e2 & op(e0, e2) = e0 & $i(v11)) | (v7 = e0 & v5
% 143.02/19.84  |                   = e1 &  ~ (v9 = e3) &  ~ (v0 = e1) & op(e3, e3) = e1 &
% 143.02/19.84  |                   op(e3, e1) = v9 & op(e0, e1) = e0 & $i(v9)) | (v7 = e0 & v3
% 143.02/19.84  |                   = e1 &  ~ (v8 = e2) &  ~ (v0 = e1) & op(e2, e2) = e1 &
% 143.02/19.84  |                   op(e2, e1) = v8 & op(e0, e1) = e0 & $i(v8))))) & ((v5 = e3 &
% 143.02/19.84  |               op(e3, e3) = e3 & ((v15 = e2 & op(e2, e3) = e2) | ( ~ (v3 = e3)
% 143.02/19.84  |                   & op(e2, e2) = v3 & $i(v3))) & ((v14 = e1 & op(e1, e3) = e1)
% 143.02/19.84  |                 | ( ~ (v1 = e3) & op(e1, e1) = v1 & $i(v1))) & ((v13 = e0 &
% 143.02/19.84  |                   op(e0, e3) = e0) | ( ~ (v0 = e3) & op(e0, e0) = v0 &
% 143.02/19.84  |                   $i(v0)))) | (v3 = e2 & op(e2, e2) = e2 & ((v12 = e3 & op(e3,
% 143.02/19.84  |                     e2) = e3) | ( ~ (v5 = e2) & op(e3, e3) = v5 & $i(v5))) &
% 143.02/19.84  |               ((v11 = e1 & op(e1, e2) = e1) | ( ~ (v1 = e2) & op(e1, e1) = v1
% 143.02/19.84  |                   & $i(v1))) & ((v10 = e0 & op(e0, e2) = e0) | ( ~ (v0 = e2) &
% 143.02/19.84  |                   op(e0, e0) = v0 & $i(v0)))) | (v1 = e1 & op(e1, e1) = e1 &
% 143.02/19.84  |               ((v9 = e3 & op(e3, e1) = e3) | ( ~ (v5 = e1) & op(e3, e3) = v5 &
% 143.02/19.84  |                   $i(v5))) & ((v8 = e2 & op(e2, e1) = e2) | ( ~ (v3 = e1) &
% 143.02/19.84  |                   op(e2, e2) = v3 & $i(v3))) & ((v7 = e0 & op(e0, e1) = e0) |
% 143.02/19.84  |                 ( ~ (v0 = e1) & op(e0, e0) = v0 & $i(v0)))) | (v0 = e0 &
% 143.02/19.84  |               op(e0, e0) = e0 & ((v6 = e3 & op(e3, e0) = e3) | ( ~ (v5 = e0) &
% 143.02/19.84  |                   op(e3, e3) = v5 & $i(v5))) & ((v4 = e2 & op(e2, e0) = e2) |
% 143.02/19.84  |                 ( ~ (v3 = e0) & op(e2, e2) = v3 & $i(v3))) & ((v2 = e1 &
% 143.02/19.84  |                   op(e1, e0) = e1) | ( ~ (v1 = e0) & op(e1, e1) = v1 &
% 143.02/19.84  |                   $i(v1))))))
% 143.02/19.84  | 
% 143.02/19.84  | ALPHA: (ax6) implies:
% 143.02/19.84  |   (11)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 143.02/19.84  |           ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e0, e1) = v1 &
% 143.02/19.84  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 & $i(v1))))
% 143.02/19.84  | 
% 143.02/19.84  | ALPHA: (ax7) implies:
% 143.02/19.84  |   (12)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 143.02/19.84  |           ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e0, e1) = v1 &
% 143.02/19.84  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 & $i(v1))))
% 143.02/19.84  | 
% 143.02/19.84  | ALPHA: (ax8) implies:
% 143.02/19.84  |   (13)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 143.02/19.84  |           ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e0, e2) = v1 &
% 143.02/19.84  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 & $i(v1))))
% 143.02/19.84  | 
% 143.02/19.84  | ALPHA: (ax9) implies:
% 143.02/19.84  |   (14)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 143.02/19.84  |           ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e0, e2) = v1 &
% 143.02/19.84  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 & $i(v1))))
% 143.02/19.84  | 
% 143.02/19.84  | ALPHA: (ax10) implies:
% 143.02/19.84  |   (15)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 143.02/19.84  |           ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e0, e3) = v1 &
% 143.02/19.84  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 & $i(v1))))
% 143.02/19.84  | 
% 143.02/19.84  | ALPHA: (ax11) implies:
% 143.02/19.85  |   (16)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e0, e3) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax12) implies:
% 143.02/19.85  |   (17)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e1, e0) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax13) implies:
% 143.02/19.85  |   (18)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e1, e0) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax14) implies:
% 143.02/19.85  |   (19)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e1, e2) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax15) implies:
% 143.02/19.85  |   (20)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e1, e2) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax16) implies:
% 143.02/19.85  |   (21)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e1, e3) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax17) implies:
% 143.02/19.85  |   (22)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e1, e3) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax18) implies:
% 143.02/19.85  |   (23)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e2, e0) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax19) implies:
% 143.02/19.85  |   (24)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e2, e0) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax20) implies:
% 143.02/19.85  |   (25)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e2, e1) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax21) implies:
% 143.02/19.85  |   (26)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e2, e1) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax22) implies:
% 143.02/19.85  |   (27)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e2, e3) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax23) implies:
% 143.02/19.85  |   (28)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 143.02/19.85  |           ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e2, e3) = v1 &
% 143.02/19.85  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 & $i(v1))))
% 143.02/19.85  | 
% 143.02/19.85  | ALPHA: (ax24) implies:
% 143.02/19.86  |   (29)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 143.02/19.86  |           ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e3, e0) = v1 &
% 143.02/19.86  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 & $i(v1))))
% 143.02/19.86  | 
% 143.02/19.86  | ALPHA: (ax25) implies:
% 143.02/19.86  |   (30)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 143.02/19.86  |           ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e3, e0) = v1 &
% 143.02/19.86  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 & $i(v1))))
% 143.02/19.86  | 
% 143.02/19.86  | ALPHA: (ax26) implies:
% 143.02/19.86  |   (31)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 143.02/19.86  |           ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e3, e1) = v1 &
% 143.02/19.86  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 & $i(v1))))
% 143.02/19.86  | 
% 143.02/19.86  | ALPHA: (ax27) implies:
% 143.02/19.86  |   (32)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 143.02/19.86  |           ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e3, e1) = v1 &
% 143.02/19.86  |               $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 & $i(v1))))
% 143.02/19.86  | 
% 143.02/19.86  | ALPHA: (ax28) implies:
% 143.02/19.86  |   (33)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 143.02/19.86  |           ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e3, e2) = v1 &
% 143.02/19.86  |               $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 & $i(v1))))
% 143.02/19.86  | 
% 143.02/19.86  | ALPHA: (ax29) implies:
% 143.02/19.86  |   (34)   ? [v0: $i] :  ? [v1: $i] :  ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 143.02/19.86  |           ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e3, e2) = v1 &
% 143.02/19.86  |               $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 & $i(v1))))
% 143.02/19.86  | 
% 143.02/19.86  | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 143.02/19.86  |   (35)  op(e1, e1) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e2) | ( ~ (all_4_0
% 143.02/19.86  |               = e0) & op(all_4_1, e1) = all_4_0 & op(e1, e2) = all_4_1 &
% 143.02/19.86  |             $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e3) & op(e1, e2) =
% 143.02/19.86  |             all_4_1 & $i(all_4_1)))
% 143.02/19.86  | 
% 143.02/19.86  | ALPHA: (35) implies:
% 143.02/19.86  |   (36)  op(e1, e1) = all_4_2
% 143.02/19.86  |   (37)   ~ (all_4_2 = e2) | ( ~ (all_4_0 = e0) & op(all_4_1, e1) = all_4_0 &
% 143.02/19.86  |           op(e1, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 =
% 143.02/19.86  |             e3) & op(e1, e2) = all_4_1 & $i(all_4_1))
% 143.02/19.86  | 
% 143.02/19.86  | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 143.02/19.86  |   (38)  op(e2, e2) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e3) | ( ~ (all_6_0
% 143.02/19.86  |               = e1) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 143.02/19.86  |             $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e2, e3) =
% 143.02/19.86  |             all_6_1 & $i(all_6_1)))
% 143.02/19.86  | 
% 143.02/19.86  | ALPHA: (38) implies:
% 143.02/19.86  |   (39)  op(e2, e2) = all_6_2
% 143.02/19.86  |   (40)   ~ (all_6_2 = e3) | ( ~ (all_6_0 = e1) & op(all_6_1, e2) = all_6_0 &
% 143.02/19.86  |           op(e2, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 =
% 143.02/19.86  |             e0) & op(e2, e3) = all_6_1 & $i(all_6_1))
% 143.02/19.86  | 
% 143.02/19.86  | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 143.02/19.86  |   (41)  op(e1, e1) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e3) | ( ~ (all_8_0
% 143.02/19.86  |               = e2) & op(all_8_1, e1) = all_8_0 & op(e1, e3) = all_8_1 &
% 143.02/19.86  |             $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e1, e3) =
% 143.02/19.86  |             all_8_1 & $i(all_8_1)))
% 143.02/19.86  | 
% 143.02/19.86  | ALPHA: (41) implies:
% 143.02/19.86  |   (42)  op(e1, e1) = all_8_2
% 143.02/19.86  |   (43)   ~ (all_8_2 = e3) | ( ~ (all_8_0 = e2) & op(all_8_1, e1) = all_8_0 &
% 143.02/19.86  |           op(e1, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 =
% 143.02/19.86  |             e0) & op(e1, e3) = all_8_1 & $i(all_8_1))
% 143.02/19.86  | 
% 143.02/19.87  | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 143.02/19.87  |        gives:
% 143.02/19.87  |   (44)  op(e0, e0) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e1) | ( ~
% 143.02/19.87  |             (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 & op(e0, e1) =
% 143.02/19.87  |             all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) &
% 143.02/19.87  |             op(e0, e1) = all_10_1 & $i(all_10_1)))
% 143.02/19.87  | 
% 143.02/19.87  | ALPHA: (44) implies:
% 143.02/19.87  |   (45)  op(e0, e0) = all_10_2
% 143.02/19.87  |   (46)   ~ (all_10_2 = e1) | ( ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0
% 143.02/19.87  |           & op(e0, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 143.02/19.87  |           (all_10_1 = e2) & op(e0, e1) = all_10_1 & $i(all_10_1))
% 143.02/19.87  | 
% 143.02/19.87  | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 143.02/19.87  |        gives:
% 143.02/19.87  |   (47)  op(e1, e1) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e3) | ( ~
% 143.02/19.87  |             (all_12_0 = e0) & op(all_12_1, e1) = all_12_0 & op(e1, e3) =
% 143.02/19.87  |             all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) &
% 143.02/19.87  |             op(e1, e3) = all_12_1 & $i(all_12_1)))
% 143.02/19.87  | 
% 143.02/19.87  | ALPHA: (47) implies:
% 143.02/19.87  |   (48)  op(e1, e1) = all_12_2
% 143.02/19.87  |   (49)   ~ (all_12_2 = e3) | ( ~ (all_12_0 = e0) & op(all_12_1, e1) = all_12_0
% 143.02/19.87  |           & op(e1, e3) = all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 143.02/19.87  |           (all_12_1 = e2) & op(e1, e3) = all_12_1 & $i(all_12_1))
% 143.02/19.87  | 
% 143.02/19.87  | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 143.02/19.87  |        gives:
% 143.02/19.87  |   (50)  op(e3, e3) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e0) | ( ~
% 143.02/19.87  |             (all_14_0 = e2) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 143.02/19.87  |             all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e1) &
% 143.02/19.87  |             op(e3, e0) = all_14_1 & $i(all_14_1)))
% 143.02/19.87  | 
% 143.02/19.87  | ALPHA: (50) implies:
% 143.02/19.87  |   (51)  op(e3, e3) = all_14_2
% 143.02/19.87  |   (52)   ~ (all_14_2 = e0) | ( ~ (all_14_0 = e2) & op(all_14_1, e3) = all_14_0
% 143.02/19.87  |           & op(e3, e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 143.02/19.87  |           (all_14_1 = e1) & op(e3, e0) = all_14_1 & $i(all_14_1))
% 143.02/19.87  | 
% 143.02/19.87  | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1, all_16_2
% 143.02/19.87  |        gives:
% 143.02/19.87  |   (53)  op(e2, e2) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e0) | ( ~
% 143.02/19.87  |             (all_16_0 = e3) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 143.02/19.87  |             all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) &
% 143.02/19.87  |             op(e2, e0) = all_16_1 & $i(all_16_1)))
% 143.02/19.87  | 
% 143.02/19.87  | ALPHA: (53) implies:
% 143.02/19.87  |   (54)  op(e2, e2) = all_16_2
% 143.02/19.87  |   (55)   ~ (all_16_2 = e0) | ( ~ (all_16_0 = e3) & op(all_16_1, e2) = all_16_0
% 143.02/19.87  |           & op(e2, e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~
% 143.02/19.87  |           (all_16_1 = e1) & op(e2, e0) = all_16_1 & $i(all_16_1))
% 143.02/19.87  | 
% 143.02/19.87  | DELTA: instantiating (24) with fresh symbols all_18_0, all_18_1, all_18_2
% 143.02/19.87  |        gives:
% 143.02/19.87  |   (56)  op(e2, e2) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e0) | ( ~
% 143.02/19.87  |             (all_18_0 = e1) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 143.02/19.87  |             all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) &
% 143.02/19.87  |             op(e2, e0) = all_18_1 & $i(all_18_1)))
% 143.02/19.87  | 
% 143.02/19.87  | ALPHA: (56) implies:
% 143.02/19.87  |   (57)  op(e2, e2) = all_18_2
% 143.02/19.87  |   (58)   ~ (all_18_2 = e0) | ( ~ (all_18_0 = e1) & op(all_18_1, e2) = all_18_0
% 143.02/19.87  |           & op(e2, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~
% 143.02/19.87  |           (all_18_1 = e3) & op(e2, e0) = all_18_1 & $i(all_18_1))
% 143.02/19.87  | 
% 143.02/19.87  | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1, all_20_2
% 143.02/19.87  |        gives:
% 143.02/19.87  |   (59)  op(e2, e2) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e1) | ( ~
% 143.02/19.87  |             (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 143.02/19.87  |             all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) &
% 143.02/19.87  |             op(e2, e1) = all_20_1 & $i(all_20_1)))
% 143.02/19.87  | 
% 143.02/19.87  | ALPHA: (59) implies:
% 143.02/19.87  |   (60)  op(e2, e2) = all_20_2
% 143.02/19.87  |   (61)   ~ (all_20_2 = e1) | ( ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0
% 143.02/19.87  |           & op(e2, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~
% 143.02/19.87  |           (all_20_1 = e3) & op(e2, e1) = all_20_1 & $i(all_20_1))
% 143.02/19.87  | 
% 143.02/19.87  | DELTA: instantiating (31) with fresh symbols all_22_0, all_22_1, all_22_2
% 143.02/19.87  |        gives:
% 143.02/19.87  |   (62)  op(e3, e3) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e1) | ( ~
% 143.02/19.87  |             (all_22_0 = e2) & op(all_22_1, e3) = all_22_0 & op(e3, e1) =
% 143.02/19.87  |             all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) &
% 143.02/19.87  |             op(e3, e1) = all_22_1 & $i(all_22_1)))
% 143.02/19.87  | 
% 143.02/19.87  | ALPHA: (62) implies:
% 143.02/19.87  |   (63)  op(e3, e3) = all_22_2
% 143.02/19.87  |   (64)   ~ (all_22_2 = e1) | ( ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0
% 143.02/19.87  |           & op(e3, e1) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 143.02/19.87  |           (all_22_1 = e0) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 143.02/19.87  | 
% 143.02/19.87  | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1, all_24_2
% 143.02/19.88  |        gives:
% 143.02/19.88  |   (65)  op(e0, e0) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e2) | ( ~
% 143.02/19.88  |             (all_24_0 = e3) & op(all_24_1, e0) = all_24_0 & op(e0, e2) =
% 143.02/19.88  |             all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) &
% 143.02/19.88  |             op(e0, e2) = all_24_1 & $i(all_24_1)))
% 143.02/19.88  | 
% 143.02/19.88  | ALPHA: (65) implies:
% 143.02/19.88  |   (66)  op(e0, e0) = all_24_2
% 143.02/19.88  |   (67)   ~ (all_24_2 = e2) | ( ~ (all_24_0 = e3) & op(all_24_1, e0) = all_24_0
% 143.02/19.88  |           & op(e0, e2) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 143.02/19.88  |           (all_24_1 = e1) & op(e0, e2) = all_24_1 & $i(all_24_1))
% 143.02/19.88  | 
% 143.02/19.88  | DELTA: instantiating (28) with fresh symbols all_26_0, all_26_1, all_26_2
% 143.02/19.88  |        gives:
% 143.02/19.88  |   (68)  op(e2, e2) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e3) | ( ~
% 143.02/19.88  |             (all_26_0 = e0) & op(all_26_1, e2) = all_26_0 & op(e2, e3) =
% 143.02/19.88  |             all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) &
% 143.02/19.88  |             op(e2, e3) = all_26_1 & $i(all_26_1)))
% 143.02/19.88  | 
% 143.02/19.88  | ALPHA: (68) implies:
% 143.02/19.88  |   (69)  op(e2, e2) = all_26_2
% 143.02/19.88  |   (70)   ~ (all_26_2 = e3) | ( ~ (all_26_0 = e0) & op(all_26_1, e2) = all_26_0
% 143.02/19.88  |           & op(e2, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 143.02/19.88  |           (all_26_1 = e1) & op(e2, e3) = all_26_1 & $i(all_26_1))
% 143.02/19.88  | 
% 143.02/19.88  | DELTA: instantiating (30) with fresh symbols all_28_0, all_28_1, all_28_2
% 143.02/19.88  |        gives:
% 143.02/19.88  |   (71)  op(e3, e3) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e0) | ( ~
% 143.02/19.88  |             (all_28_0 = e1) & op(all_28_1, e3) = all_28_0 & op(e3, e0) =
% 143.02/19.88  |             all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e2) &
% 143.02/19.88  |             op(e3, e0) = all_28_1 & $i(all_28_1)))
% 143.02/19.88  | 
% 143.02/19.88  | ALPHA: (71) implies:
% 143.02/19.88  |   (72)  op(e3, e3) = all_28_2
% 143.02/19.88  |   (73)   ~ (all_28_2 = e0) | ( ~ (all_28_0 = e1) & op(all_28_1, e3) = all_28_0
% 143.02/19.88  |           & op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~
% 143.02/19.88  |           (all_28_1 = e2) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 143.02/19.88  | 
% 143.02/19.88  | DELTA: instantiating (12) with fresh symbols all_30_0, all_30_1, all_30_2
% 143.02/19.88  |        gives:
% 143.02/19.88  |   (74)  op(e0, e0) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e1) | ( ~
% 143.02/19.88  |             (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 143.02/19.88  |             all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) &
% 143.02/19.88  |             op(e0, e1) = all_30_1 & $i(all_30_1)))
% 143.02/19.88  | 
% 143.02/19.88  | ALPHA: (74) implies:
% 143.02/19.88  |   (75)  op(e0, e0) = all_30_2
% 143.02/19.88  |   (76)   ~ (all_30_2 = e1) | ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0
% 143.02/19.88  |           & op(e0, e1) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~
% 143.02/19.88  |           (all_30_1 = e3) & op(e0, e1) = all_30_1 & $i(all_30_1))
% 143.02/19.88  | 
% 143.02/19.88  | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2
% 143.02/19.88  |        gives:
% 143.02/19.88  |   (77)  op(e1, e1) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e2) | ( ~
% 143.02/19.88  |             (all_32_0 = e3) & op(all_32_1, e1) = all_32_0 & op(e1, e2) =
% 143.02/19.88  |             all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e0) &
% 143.02/19.88  |             op(e1, e2) = all_32_1 & $i(all_32_1)))
% 143.02/19.88  | 
% 143.02/19.88  | ALPHA: (77) implies:
% 143.02/19.88  |   (78)  op(e1, e1) = all_32_2
% 143.02/19.88  | 
% 143.02/19.88  | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1, all_34_2
% 143.02/19.88  |        gives:
% 143.02/19.88  |   (79)  op(e3, e3) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e1) | ( ~
% 143.02/19.88  |             (all_34_0 = e0) & op(all_34_1, e3) = all_34_0 & op(e3, e1) =
% 143.02/19.88  |             all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) &
% 143.02/19.88  |             op(e3, e1) = all_34_1 & $i(all_34_1)))
% 143.02/19.88  | 
% 143.02/19.88  | ALPHA: (79) implies:
% 143.02/19.88  |   (80)  op(e3, e3) = all_34_2
% 143.02/19.88  |   (81)   ~ (all_34_2 = e1) | ( ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0
% 143.02/19.88  |           & op(e3, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~
% 143.02/19.88  |           (all_34_1 = e2) & op(e3, e1) = all_34_1 & $i(all_34_1))
% 143.02/19.88  | 
% 143.02/19.88  | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1, all_36_2
% 143.02/19.88  |        gives:
% 143.02/19.88  |   (82)  op(e3, e3) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e2) | ( ~
% 143.02/19.88  |             (all_36_0 = e1) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 143.02/19.88  |             all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) &
% 143.02/19.88  |             op(e3, e2) = all_36_1 & $i(all_36_1)))
% 143.02/19.88  | 
% 143.02/19.88  | ALPHA: (82) implies:
% 143.02/19.88  |   (83)  op(e3, e3) = all_36_2
% 143.02/19.88  |   (84)   ~ (all_36_2 = e2) | ( ~ (all_36_0 = e1) & op(all_36_1, e3) = all_36_0
% 143.02/19.88  |           & op(e3, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~
% 143.02/19.88  |           (all_36_1 = e0) & op(e3, e2) = all_36_1 & $i(all_36_1))
% 143.02/19.88  | 
% 143.02/19.88  | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2
% 143.02/19.88  |        gives:
% 143.02/19.88  |   (85)  op(e2, e2) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e1) | ( ~
% 143.02/19.88  |             (all_38_0 = e3) & op(all_38_1, e2) = all_38_0 & op(e2, e1) =
% 143.02/19.88  |             all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) &
% 143.02/19.88  |             op(e2, e1) = all_38_1 & $i(all_38_1)))
% 143.02/19.88  | 
% 143.02/19.88  | ALPHA: (85) implies:
% 143.02/19.88  |   (86)  op(e2, e2) = all_38_2
% 143.02/19.88  |   (87)   ~ (all_38_2 = e1) | ( ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0
% 143.02/19.88  |           & op(e2, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 143.02/19.88  |           (all_38_1 = e0) & op(e2, e1) = all_38_1 & $i(all_38_1))
% 143.02/19.88  | 
% 143.02/19.88  | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2
% 143.02/19.88  |        gives:
% 143.02/19.88  |   (88)  op(e0, e0) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e2) | ( ~
% 143.02/19.88  |             (all_40_0 = e1) & op(all_40_1, e0) = all_40_0 & op(e0, e2) =
% 143.02/19.88  |             all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) &
% 143.02/19.88  |             op(e0, e2) = all_40_1 & $i(all_40_1)))
% 143.02/19.88  | 
% 143.02/19.88  | ALPHA: (88) implies:
% 143.02/19.88  |   (89)  op(e0, e0) = all_40_2
% 143.02/19.88  |   (90)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0
% 143.02/19.88  |           & op(e0, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 143.02/19.88  |           (all_40_1 = e3) & op(e0, e2) = all_40_1 & $i(all_40_1))
% 143.02/19.88  | 
% 143.02/19.88  | DELTA: instantiating (15) with fresh symbols all_42_0, all_42_1, all_42_2
% 143.02/19.88  |        gives:
% 143.02/19.89  |   (91)  op(e0, e0) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e3) | ( ~
% 143.02/19.89  |             (all_42_0 = e2) & op(all_42_1, e0) = all_42_0 & op(e0, e3) =
% 143.02/19.89  |             all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e1) &
% 143.02/19.89  |             op(e0, e3) = all_42_1 & $i(all_42_1)))
% 143.02/19.89  | 
% 143.02/19.89  | ALPHA: (91) implies:
% 143.02/19.89  |   (92)  op(e0, e0) = all_42_2
% 143.02/19.89  |   (93)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e2) & op(all_42_1, e0) = all_42_0
% 143.02/19.89  |           & op(e0, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 143.02/19.89  |           (all_42_1 = e1) & op(e0, e3) = all_42_1 & $i(all_42_1))
% 143.02/19.89  | 
% 143.02/19.89  | DELTA: instantiating (34) with fresh symbols all_44_0, all_44_1, all_44_2
% 143.02/19.89  |        gives:
% 143.02/19.89  |   (94)  op(e3, e3) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e2) | ( ~
% 143.02/19.89  |             (all_44_0 = e0) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 143.02/19.89  |             all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) &
% 143.02/19.89  |             op(e3, e2) = all_44_1 & $i(all_44_1)))
% 143.02/19.89  | 
% 143.02/19.89  | ALPHA: (94) implies:
% 143.02/19.89  |   (95)  op(e3, e3) = all_44_2
% 143.02/19.89  |   (96)   ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(all_44_1, e3) = all_44_0
% 143.02/19.89  |           & op(e3, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~
% 143.02/19.89  |           (all_44_1 = e1) & op(e3, e2) = all_44_1 & $i(all_44_1))
% 143.02/19.89  | 
% 143.02/19.89  | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 143.02/19.89  |        gives:
% 143.02/19.89  |   (97)  op(e0, e0) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e3) | ( ~
% 143.02/19.89  |             (all_46_0 = e1) & op(all_46_1, e0) = all_46_0 & op(e0, e3) =
% 143.02/19.89  |             all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e2) &
% 143.02/19.89  |             op(e0, e3) = all_46_1 & $i(all_46_1)))
% 143.02/19.89  | 
% 143.02/19.89  | ALPHA: (97) implies:
% 143.02/19.89  |   (98)  op(e0, e0) = all_46_2
% 143.02/19.89  |   (99)   ~ (all_46_2 = e3) | ( ~ (all_46_0 = e1) & op(all_46_1, e0) = all_46_0
% 143.02/19.89  |           & op(e0, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 143.02/19.89  |           (all_46_1 = e2) & op(e0, e3) = all_46_1 & $i(all_46_1))
% 143.02/19.89  | 
% 143.02/19.89  | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1, all_48_2
% 143.02/19.89  |        gives:
% 143.02/19.89  |   (100)  op(e1, e1) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e0) | ( ~
% 143.02/19.89  |              (all_48_0 = e2) & op(all_48_1, e1) = all_48_0 & op(e1, e0) =
% 143.02/19.89  |              all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e3) &
% 143.02/19.89  |              op(e1, e0) = all_48_1 & $i(all_48_1)))
% 143.02/19.89  | 
% 143.02/19.89  | ALPHA: (100) implies:
% 143.02/19.89  |   (101)  op(e1, e1) = all_48_2
% 143.02/19.89  |   (102)   ~ (all_48_2 = e0) | ( ~ (all_48_0 = e2) & op(all_48_1, e1) =
% 143.02/19.89  |            all_48_0 & op(e1, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | (
% 143.02/19.89  |            ~ (all_48_1 = e3) & op(e1, e0) = all_48_1 & $i(all_48_1))
% 143.02/19.89  | 
% 143.02/19.89  | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2
% 143.02/19.89  |        gives:
% 143.02/19.89  |   (103)  op(e1, e1) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e0) | ( ~
% 143.02/19.89  |              (all_50_0 = e3) & op(all_50_1, e1) = all_50_0 & op(e1, e0) =
% 143.02/19.89  |              all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e2) &
% 143.02/19.89  |              op(e1, e0) = all_50_1 & $i(all_50_1)))
% 143.02/19.89  | 
% 143.02/19.89  | ALPHA: (103) implies:
% 143.02/19.89  |   (104)  op(e1, e1) = all_50_2
% 143.02/19.89  |   (105)   ~ (all_50_2 = e0) | ( ~ (all_50_0 = e3) & op(all_50_1, e1) =
% 143.02/19.89  |            all_50_0 & op(e1, e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | (
% 143.02/19.89  |            ~ (all_50_1 = e2) & op(e1, e0) = all_50_1 & $i(all_50_1))
% 143.02/19.89  | 
% 143.02/19.89  | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2,
% 143.02/19.89  |        all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 143.02/19.89  |        all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives:
% 143.02/19.89  |   (106)   ~ (all_52_0 = all_52_1) &  ~ (all_52_0 = all_52_2) &  ~ (all_52_0 =
% 143.02/19.89  |            all_52_3) &  ~ (all_52_0 = all_52_4) &  ~ (all_52_0 = all_52_8) & 
% 143.02/19.89  |          ~ (all_52_0 = all_52_12) &  ~ (all_52_1 = all_52_2) &  ~ (all_52_1 =
% 143.02/19.89  |            all_52_3) &  ~ (all_52_1 = all_52_5) &  ~ (all_52_1 = all_52_9) & 
% 143.02/19.89  |          ~ (all_52_1 = all_52_13) &  ~ (all_52_2 = all_52_3) &  ~ (all_52_2 =
% 143.02/19.89  |            all_52_6) &  ~ (all_52_2 = all_52_10) &  ~ (all_52_2 = all_52_14) &
% 143.02/19.89  |           ~ (all_52_3 = all_52_7) &  ~ (all_52_3 = all_52_11) &  ~ (all_52_3 =
% 143.02/19.89  |            all_52_15) &  ~ (all_52_4 = all_52_5) &  ~ (all_52_4 = all_52_6) & 
% 143.02/19.89  |          ~ (all_52_4 = all_52_7) &  ~ (all_52_4 = all_52_8) &  ~ (all_52_4 =
% 143.02/19.89  |            all_52_12) &  ~ (all_52_5 = all_52_6) &  ~ (all_52_5 = all_52_7) & 
% 143.02/19.89  |          ~ (all_52_5 = all_52_9) &  ~ (all_52_5 = all_52_13) &  ~ (all_52_6 =
% 143.02/19.89  |            all_52_7) &  ~ (all_52_6 = all_52_10) &  ~ (all_52_6 = all_52_14) &
% 143.02/19.89  |           ~ (all_52_7 = all_52_11) &  ~ (all_52_7 = all_52_15) &  ~ (all_52_8
% 143.02/19.89  |            = all_52_9) &  ~ (all_52_8 = all_52_10) &  ~ (all_52_8 = all_52_11)
% 143.02/19.89  |          &  ~ (all_52_8 = all_52_12) &  ~ (all_52_9 = all_52_10) &  ~
% 143.02/19.89  |          (all_52_9 = all_52_11) &  ~ (all_52_9 = all_52_13) &  ~ (all_52_10 =
% 143.02/19.89  |            all_52_11) &  ~ (all_52_10 = all_52_14) &  ~ (all_52_11 =
% 143.02/19.89  |            all_52_15) &  ~ (all_52_12 = all_52_13) &  ~ (all_52_12 =
% 143.02/19.89  |            all_52_14) &  ~ (all_52_12 = all_52_15) &  ~ (all_52_13 =
% 143.02/19.89  |            all_52_14) &  ~ (all_52_13 = all_52_15) &  ~ (all_52_14 =
% 143.02/19.89  |            all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) = all_52_4 & op(e3,
% 143.02/19.89  |            e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3) = all_52_1 &
% 143.02/19.89  |          op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2, e0) =
% 143.02/19.89  |          all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 & op(e1,
% 143.02/19.89  |            e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) = all_52_3 &
% 143.02/19.89  |          op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0) =
% 143.02/19.89  |          all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3)
% 143.02/19.89  |          & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) &
% 143.02/19.89  |          $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) &
% 143.02/19.89  |          $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15)
% 143.02/19.89  | 
% 143.02/19.89  | ALPHA: (106) implies:
% 143.02/19.89  |   (107)   ~ (all_52_14 = all_52_15)
% 143.02/19.89  |   (108)   ~ (all_52_13 = all_52_15)
% 143.02/19.89  |   (109)   ~ (all_52_13 = all_52_14)
% 143.02/19.89  |   (110)   ~ (all_52_12 = all_52_15)
% 143.02/19.89  |   (111)   ~ (all_52_12 = all_52_14)
% 143.02/19.89  |   (112)   ~ (all_52_12 = all_52_13)
% 143.45/19.89  |   (113)   ~ (all_52_11 = all_52_15)
% 143.45/19.89  |   (114)   ~ (all_52_10 = all_52_14)
% 143.45/19.89  |   (115)   ~ (all_52_10 = all_52_11)
% 143.45/19.89  |   (116)   ~ (all_52_9 = all_52_13)
% 143.45/19.89  |   (117)   ~ (all_52_9 = all_52_11)
% 143.45/19.89  |   (118)   ~ (all_52_9 = all_52_10)
% 143.45/19.89  |   (119)   ~ (all_52_8 = all_52_12)
% 143.45/19.89  |   (120)   ~ (all_52_8 = all_52_11)
% 143.45/19.89  |   (121)   ~ (all_52_8 = all_52_10)
% 143.45/19.89  |   (122)   ~ (all_52_8 = all_52_9)
% 143.45/19.89  |   (123)   ~ (all_52_7 = all_52_15)
% 143.45/19.89  |   (124)   ~ (all_52_7 = all_52_11)
% 143.45/19.89  |   (125)   ~ (all_52_6 = all_52_14)
% 143.45/19.89  |   (126)   ~ (all_52_6 = all_52_10)
% 143.45/19.89  |   (127)   ~ (all_52_6 = all_52_7)
% 143.45/19.89  |   (128)   ~ (all_52_5 = all_52_13)
% 143.45/19.89  |   (129)   ~ (all_52_5 = all_52_9)
% 143.45/19.89  |   (130)   ~ (all_52_5 = all_52_7)
% 143.45/19.89  |   (131)   ~ (all_52_5 = all_52_6)
% 143.45/19.89  |   (132)   ~ (all_52_4 = all_52_12)
% 143.45/19.89  |   (133)   ~ (all_52_4 = all_52_8)
% 143.45/19.89  |   (134)   ~ (all_52_4 = all_52_7)
% 143.45/19.89  |   (135)   ~ (all_52_4 = all_52_6)
% 143.45/19.89  |   (136)   ~ (all_52_4 = all_52_5)
% 143.45/19.89  |   (137)   ~ (all_52_3 = all_52_15)
% 143.45/19.89  |   (138)   ~ (all_52_3 = all_52_11)
% 143.45/19.89  |   (139)   ~ (all_52_3 = all_52_7)
% 143.45/19.89  |   (140)   ~ (all_52_2 = all_52_14)
% 143.45/19.89  |   (141)   ~ (all_52_2 = all_52_10)
% 143.45/19.89  |   (142)   ~ (all_52_2 = all_52_6)
% 143.45/19.89  |   (143)   ~ (all_52_2 = all_52_3)
% 143.45/19.89  |   (144)   ~ (all_52_1 = all_52_13)
% 143.45/19.89  |   (145)   ~ (all_52_1 = all_52_9)
% 143.45/19.89  |   (146)   ~ (all_52_1 = all_52_5)
% 143.45/19.89  |   (147)   ~ (all_52_1 = all_52_3)
% 143.45/19.89  |   (148)   ~ (all_52_1 = all_52_2)
% 143.45/19.89  |   (149)   ~ (all_52_0 = all_52_12)
% 143.45/19.89  |   (150)   ~ (all_52_0 = all_52_8)
% 143.45/19.89  |   (151)   ~ (all_52_0 = all_52_4)
% 143.45/19.89  |   (152)   ~ (all_52_0 = all_52_3)
% 143.45/19.89  |   (153)   ~ (all_52_0 = all_52_2)
% 143.45/19.89  |   (154)   ~ (all_52_0 = all_52_1)
% 143.45/19.89  |   (155)  op(e0, e0) = all_52_15
% 143.45/19.89  |   (156)  op(e0, e1) = all_52_11
% 143.45/19.89  |   (157)  op(e0, e2) = all_52_7
% 143.45/19.89  |   (158)  op(e0, e3) = all_52_3
% 143.45/19.89  |   (159)  op(e1, e0) = all_52_14
% 143.45/19.89  |   (160)  op(e1, e1) = all_52_10
% 143.45/19.89  |   (161)  op(e1, e2) = all_52_6
% 143.45/19.89  |   (162)  op(e1, e3) = all_52_2
% 143.45/19.89  |   (163)  op(e2, e0) = all_52_13
% 143.45/19.89  |   (164)  op(e2, e1) = all_52_9
% 143.45/19.89  |   (165)  op(e2, e2) = all_52_5
% 143.45/19.89  |   (166)  op(e2, e3) = all_52_1
% 143.45/19.89  |   (167)  op(e3, e0) = all_52_12
% 143.45/19.90  |   (168)  op(e3, e1) = all_52_8
% 143.45/19.90  |   (169)  op(e3, e2) = all_52_4
% 143.45/19.90  |   (170)  op(e3, e3) = all_52_0
% 143.45/19.90  | 
% 143.45/19.90  | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2,
% 143.45/19.90  |        all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 143.45/19.90  |        all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 143.45/19.90  |   (171)  op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2
% 143.45/19.90  |          & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) =
% 143.45/19.90  |          all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3)
% 143.45/19.90  |          = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1,
% 143.45/19.90  |            e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 &
% 143.45/19.90  |          op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) &
% 143.45/19.90  |          $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) &
% 143.45/19.90  |          $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) &
% 143.45/19.90  |          $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) &
% 143.45/19.90  |          $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 |
% 143.45/19.90  |            all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 |
% 143.45/19.90  |            all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 |
% 143.45/19.90  |            all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 |
% 143.45/19.90  |            all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 |
% 143.45/19.90  |            all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 |
% 143.45/19.90  |            all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 |
% 143.45/19.90  |            all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 |
% 143.45/19.90  |            all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 |
% 143.45/19.90  |            all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 |
% 143.45/19.90  |            all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 |
% 143.45/19.90  |            all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3
% 143.45/19.90  |            | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 =
% 143.45/19.90  |            e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13
% 143.45/19.90  |            = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) &
% 143.45/19.90  |          (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) &
% 143.45/19.90  |          (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0)
% 143.45/19.90  | 
% 143.45/19.90  | ALPHA: (171) implies:
% 143.45/19.90  |   (172)  op(e0, e0) = all_54_15
% 143.45/19.90  |   (173)  op(e0, e1) = all_54_14
% 143.45/19.90  |   (174)  op(e0, e2) = all_54_13
% 143.45/19.90  |   (175)  op(e0, e3) = all_54_12
% 143.45/19.90  |   (176)  op(e1, e0) = all_54_11
% 143.45/19.90  |   (177)  op(e1, e1) = all_54_10
% 143.45/19.90  |   (178)  op(e1, e2) = all_54_9
% 143.45/19.90  |   (179)  op(e1, e3) = all_54_8
% 143.45/19.90  |   (180)  op(e2, e0) = all_54_7
% 143.45/19.90  |   (181)  op(e2, e1) = all_54_6
% 143.45/19.90  |   (182)  op(e2, e2) = all_54_5
% 143.45/19.90  |   (183)  op(e2, e3) = all_54_4
% 143.45/19.90  |   (184)  op(e3, e0) = all_54_3
% 143.45/19.90  |   (185)  op(e3, e1) = all_54_2
% 143.45/19.90  |   (186)  op(e3, e2) = all_54_1
% 143.45/19.90  |   (187)  op(e3, e3) = all_54_0
% 143.45/19.90  |   (188)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 143.45/19.90  |   (189)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 143.45/19.90  |   (190)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 143.45/19.90  |   (191)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 143.45/19.90  |   (192)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 143.45/19.90  |   (193)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 143.45/19.90  |   (194)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 143.45/19.90  |   (195)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 143.45/19.90  |   (196)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 143.45/19.90  |   (197)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 143.45/19.90  |   (198)  all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 143.45/19.90  |   (199)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 143.45/19.90  |   (200)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 143.45/19.90  |   (201)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 143.45/19.90  |   (202)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 143.45/19.90  |   (203)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 143.45/19.90  | 
% 143.45/19.90  | DELTA: instantiating (2) with fresh symbols all_56_0, all_56_1, all_56_2,
% 143.45/19.90  |        all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 143.45/19.90  |        all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives:
% 143.45/19.90  |   (204)  ((all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 143.45/19.90  |              e3) | (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3,
% 143.45/19.90  |                e0) = e3)) & ((all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 =
% 143.45/19.90  |              e3 & op(e2, e3) = e3) | (all_56_6 = e3 & op(e1, e3) = e3) |
% 143.45/19.90  |            (all_56_12 = e3 & op(e0, e3) = e3)) & ((all_56_0 = e2 & op(e3, e3)
% 143.45/19.90  |              = e2) | (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_4 = e2 &
% 143.45/19.90  |              op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)) &
% 143.45/19.90  |          ((all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 143.45/19.90  |              e2) | (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 &
% 143.45/19.90  |              op(e0, e3) = e2)) & ((all_56_0 = e1 & op(e3, e3) = e1) |
% 143.45/19.90  |            (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_4 = e1 & op(e3, e1) =
% 143.45/19.90  |              e1) | (all_56_9 = e1 & op(e3, e0) = e1)) & ((all_56_0 = e1 &
% 143.45/19.90  |              op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_6
% 143.45/19.90  |              = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)) &
% 143.45/19.90  |          ((all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 143.45/19.90  |              e0) | (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3,
% 143.45/19.90  |                e0) = e0)) & ((all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 =
% 143.45/19.90  |              e0 & op(e2, e3) = e0) | (all_56_6 = e0 & op(e1, e3) = e0) |
% 143.45/19.90  |            (all_56_12 = e0 & op(e0, e3) = e0)) & ((all_56_1 = e3 & op(e3, e2)
% 143.45/19.90  |              = e3) | (all_56_3 = e3 & op(e2, e2) = e3) | (all_56_7 = e3 &
% 143.45/19.90  |              op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)) &
% 143.45/19.90  |          ((all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 143.45/19.90  |              e2) | (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 &
% 143.45/19.90  |              op(e0, e2) = e2)) & ((all_56_1 = e1 & op(e3, e2) = e1) |
% 143.45/19.90  |            (all_56_3 = e1 & op(e2, e2) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 143.45/19.90  |              e1) | (all_56_13 = e1 & op(e0, e2) = e1)) & ((all_56_1 = e0 &
% 143.45/19.90  |              op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) | (all_56_7
% 143.45/19.90  |              = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)) &
% 143.45/19.90  |          ((all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 143.45/19.90  |              e3) | (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 &
% 143.45/19.90  |              op(e2, e0) = e3)) & ((all_56_2 = e2 & op(e2, e3) = e2) |
% 143.45/19.90  |            (all_56_3 = e2 & op(e2, e2) = e2) | (all_56_5 = e2 & op(e2, e1) =
% 143.45/19.90  |              e2) | (all_56_10 = e2 & op(e2, e0) = e2)) & ((all_56_2 = e1 &
% 143.45/19.90  |              op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) | (all_56_5
% 143.45/19.90  |              = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)) &
% 143.45/19.90  |          ((all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 143.45/19.90  |              e0) | (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 &
% 143.45/19.90  |              op(e2, e0) = e0)) & ((all_56_4 = e3 & op(e3, e1) = e3) |
% 143.45/19.90  |            (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_8 = e3 & op(e1, e1) =
% 143.45/19.90  |              e3) | (all_56_14 = e3 & op(e0, e1) = e3)) & ((all_56_4 = e2 &
% 143.45/19.90  |              op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_8
% 143.45/19.90  |              = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)) &
% 143.45/19.90  |          ((all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) =
% 143.45/19.90  |              e1) | (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 &
% 143.45/19.90  |              op(e0, e1) = e1)) & ((all_56_4 = e0 & op(e3, e1) = e0) |
% 143.45/19.90  |            (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_8 = e0 & op(e1, e1) =
% 143.45/19.90  |              e0) | (all_56_14 = e0 & op(e0, e1) = e0)) & ((all_56_6 = e3 &
% 143.45/19.90  |              op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_8
% 143.45/19.90  |              = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)) &
% 143.45/19.90  |          ((all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 143.45/19.90  |              e2) | (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 &
% 143.45/19.90  |              op(e1, e0) = e2)) & ((all_56_6 = e1 & op(e1, e3) = e1) |
% 143.45/19.90  |            (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_8 = e1 & op(e1, e1) =
% 143.45/19.90  |              e1) | (all_56_11 = e1 & op(e1, e0) = e1)) & ((all_56_6 = e0 &
% 143.45/19.90  |              op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_8
% 143.45/19.90  |              = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 143.45/19.90  |          ((all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 143.45/19.90  |              e3) | (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 &
% 143.45/19.90  |              op(e0, e0) = e3)) & ((all_56_9 = e2 & op(e3, e0) = e2) |
% 143.45/19.90  |            (all_56_10 = e2 & op(e2, e0) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 143.45/19.90  |              e2) | (all_56_15 = e2 & op(e0, e0) = e2)) & ((all_56_9 = e1 &
% 143.45/19.90  |              op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 143.45/19.91  |            (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 143.45/19.91  |              e1)) & ((all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 &
% 143.45/19.91  |              op(e0, e2) = e3) | (all_56_14 = e3 & op(e0, e1) = e3) |
% 143.45/19.91  |            (all_56_15 = e3 & op(e0, e0) = e3)) & ((all_56_12 = e2 & op(e0, e3)
% 143.45/19.91  |              = e2) | (all_56_13 = e2 & op(e0, e2) = e2) | (all_56_14 = e2 &
% 143.45/19.91  |              op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)) &
% 143.45/19.91  |          ((all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 143.45/19.91  |              e1) | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 &
% 143.45/19.91  |              op(e0, e0) = e1)) & ((all_56_15 = e0 & op(e0, e0) = e0) |
% 143.45/19.91  |            (((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0)
% 143.45/19.91  |                  = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 =
% 143.45/19.91  |                  e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 143.45/19.91  |                (all_56_14 = e0 & op(e0, e1) = e0))))
% 143.45/19.91  | 
% 143.45/19.91  | ALPHA: (204) implies:
% 143.45/19.91  |   (205)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) =
% 143.45/19.91  |                e0) | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 143.45/19.91  |                op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) |
% 143.45/19.91  |              (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1)
% 143.45/19.91  |                = e0)))
% 143.45/19.91  |   (206)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 143.45/19.91  |            e1) | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0,
% 143.45/19.91  |              e0) = e1)
% 143.45/19.91  |   (207)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 143.45/19.91  |            e2) | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0,
% 143.45/19.91  |              e0) = e2)
% 143.45/19.91  |   (208)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 143.45/19.91  |            e3) | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0,
% 143.45/19.91  |              e0) = e3)
% 143.45/19.91  |   (209)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 143.45/19.91  |            e1) | (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0,
% 143.45/19.91  |              e0) = e1)
% 143.45/19.91  |   (210)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 143.45/19.91  |            e2) | (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0,
% 143.45/19.91  |              e0) = e2)
% 143.45/19.91  |   (211)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 143.45/19.91  |            e3) | (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0,
% 143.45/19.91  |              e0) = e3)
% 143.45/19.91  |   (212)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0)
% 143.45/19.91  |          | (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 143.45/19.91  |            e0)
% 143.45/19.91  |   (213)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1)
% 143.45/19.91  |          | (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 143.45/19.91  |            e1)
% 143.45/19.91  |   (214)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2)
% 143.45/19.91  |          | (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 143.45/19.91  |            e2)
% 143.45/19.91  |   (215)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3)
% 143.45/19.91  |          | (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) =
% 143.45/19.91  |            e3)
% 143.45/19.91  |   (216)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0)
% 143.45/19.91  |          | (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 143.45/19.91  |            e0)
% 143.45/19.91  |   (217)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1)
% 143.45/19.91  |          | (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) =
% 143.45/19.91  |            e1)
% 143.45/19.91  |   (218)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2)
% 143.45/19.91  |          | (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) =
% 143.45/19.91  |            e2)
% 143.45/19.91  |   (219)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3)
% 143.45/19.91  |          | (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 143.45/19.91  |            e3)
% 143.45/19.91  |   (220)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 143.45/19.91  |          | (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 143.45/19.91  |            e0)
% 143.45/19.91  |   (221)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 143.45/19.91  |          | (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 143.45/19.91  |            e1)
% 143.45/19.91  |   (222)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 143.45/19.91  |          | (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 143.45/19.91  |            e2)
% 143.45/19.91  |   (223)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 143.45/19.91  |          | (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 143.45/19.91  |            e3)
% 143.45/19.91  |   (224)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 143.45/19.91  |          | (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 143.45/19.91  |            e0)
% 143.45/19.91  |   (225)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 143.45/19.91  |          | (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 143.45/19.91  |            e1)
% 143.45/19.91  |   (226)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 143.45/19.91  |          | (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 143.45/19.91  |            e2)
% 143.45/19.91  |   (227)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 143.45/19.91  |          | (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 143.45/19.91  |            e3)
% 143.45/19.91  |   (228)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 143.45/19.91  |          | (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 143.45/19.91  |            e0)
% 143.45/19.91  |   (229)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 143.45/19.91  |          | (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 143.45/19.91  |            e0)
% 143.45/19.91  |   (230)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 143.45/19.91  |          | (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 143.45/19.91  |            e1)
% 143.45/19.91  |   (231)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1)
% 143.45/19.91  |          | (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 143.45/19.91  |            e1)
% 143.45/19.91  |   (232)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 143.45/19.91  |          | (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 143.45/19.91  |            e2)
% 143.45/19.91  |   (233)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2)
% 143.45/19.91  |          | (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 143.45/19.91  |            e2)
% 143.45/19.91  |   (234)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 143.45/19.91  |          | (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 143.45/19.91  |            e3)
% 143.45/19.91  |   (235)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3)
% 143.45/19.91  |          | (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 143.45/19.91  |            e3)
% 143.45/19.91  | 
% 143.45/19.91  | DELTA: instantiating (10) with fresh symbols all_57_0, all_57_1, all_57_2,
% 143.45/19.91  |        all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, all_57_9,
% 143.45/19.91  |        all_57_10, all_57_11, all_57_12, all_57_13, all_57_14, all_57_15 gives:
% 143.45/19.92  |   (236)  ((all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 143.45/19.92  |                = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 143.45/19.92  |              all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 143.45/19.92  |            (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 143.45/19.92  |              (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 143.45/19.92  |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 143.45/19.92  |              $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.45/19.92  |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2)
% 143.45/19.92  |              = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.45/19.92  |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.45/19.92  |                e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 143.45/19.92  |              all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.45/19.92  |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &
% 143.45/19.92  |               ~ (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 143.45/19.92  |              & op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 143.45/19.92  |              $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &
% 143.45/19.92  |               ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 143.45/19.92  |              & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.45/19.92  |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &
% 143.45/19.92  |               ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 143.45/19.92  |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 143.45/19.92  |              & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 143.45/19.92  |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 143.45/19.92  |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2
% 143.45/19.92  |              & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1
% 143.45/19.92  |              &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.45/19.92  |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 143.45/19.92  |              all_57_7 & $i(all_57_7) & $i(all_57_10)) | (all_57_6 = e3 &
% 143.45/19.92  |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 = e1) &
% 143.45/19.92  |              op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) = all_57_8
% 143.45/19.92  |              & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7 =
% 143.45/19.92  |              e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.45/19.92  |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12
% 143.45/19.92  |              & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 =
% 143.45/19.92  |              e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 143.45/19.92  |              op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8
% 143.45/19.92  |              & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 =
% 143.45/19.92  |              e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 143.45/19.92  |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 143.45/19.92  |              op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 143.45/19.92  |            (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 143.45/19.92  |              (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.45/19.92  |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 143.45/19.92  |              $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9
% 143.45/19.92  |                = e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 143.45/19.92  |              all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 143.45/19.92  |              $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1
% 143.45/19.92  |              &  ~ (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 143.45/19.92  |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 143.45/19.92  |              & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 143.45/19.92  |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.45/19.92  |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 143.45/19.92  |              all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 143.45/19.92  |              all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 143.45/19.92  |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 143.45/19.92  |              & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0)
% 143.45/19.92  |              = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 & 
% 143.45/19.92  |                  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.45/19.92  |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0))
% 143.45/19.92  |                | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 143.45/19.92  |                  (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 143.45/19.92  |                  op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 143.45/19.92  |                  = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3)
% 143.45/19.92  |                  = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 143.45/19.92  |                  $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 143.45/19.92  |                  (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 143.45/19.92  |                  & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.45/19.92  |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 143.45/19.92  |                  (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 143.45/19.92  |                  op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.45/19.92  |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2)
% 143.45/19.92  |                  = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 143.45/19.92  |                  $i(all_57_7))))) & ((all_57_10 = e3 & op(e3, e3) = e3 &
% 143.45/19.92  |              ((all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 143.45/19.92  |                  op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_1 = e1 &
% 143.45/19.92  |                  op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 143.45/19.92  |                  all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) =
% 143.45/19.92  |                  e0) | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 143.45/19.92  |                  $i(all_57_15)))) | (all_57_12 = e2 & op(e2, e2) = e2 &
% 143.45/19.92  |              ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 143.45/19.92  |                  op(e3, e3) = all_57_10 & $i(all_57_10))) & ((all_57_4 = e1 &
% 143.45/19.92  |                  op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 143.45/19.92  |                  all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) =
% 143.45/19.92  |                  e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 143.45/19.92  |                  $i(all_57_15)))) | (all_57_14 = e1 & op(e1, e1) = e1 &
% 143.45/19.92  |              ((all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 143.45/19.92  |                  op(e3, e3) = all_57_10 & $i(all_57_10))) & ((all_57_7 = e2 &
% 143.45/19.92  |                  op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 143.45/19.92  |                  all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) =
% 143.45/19.92  |                  e0) | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 143.45/19.92  |                  $i(all_57_15)))) | (all_57_15 = e0 & op(e0, e0) = e0 &
% 143.45/19.92  |              ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 143.45/19.92  |                  op(e3, e3) = all_57_10 & $i(all_57_10))) & ((all_57_11 = e2 &
% 143.45/19.92  |                  op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 143.45/19.92  |                  all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) =
% 143.45/19.92  |                  e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 143.45/19.92  |                  $i(all_57_14)))))
% 143.45/19.92  | 
% 143.45/19.92  | ALPHA: (236) implies:
% 143.45/19.92  |   (237)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 143.45/19.92  |                e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 143.45/19.92  |                $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 143.45/19.92  |                (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 143.45/19.92  |            ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 143.45/19.92  |                  e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 & op(e2,
% 143.45/19.92  |              e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 =
% 143.45/19.92  |                  e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) & ((all_57_4 =
% 143.45/19.92  |                e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 143.45/19.92  |                all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) =
% 143.45/19.92  |                e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 143.45/19.92  |                $i(all_57_15)))) | (all_57_14 = e1 & op(e1, e1) = e1 &
% 143.45/19.92  |            ((all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3,
% 143.45/19.92  |                  e3) = all_57_10 & $i(all_57_10))) & ((all_57_7 = e2 & op(e2,
% 143.45/19.92  |                  e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.45/19.92  |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~
% 143.45/19.92  |                (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 143.45/19.92  |          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 143.45/19.92  |                e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 143.45/19.92  |                $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 143.45/19.92  |                (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 143.45/19.92  |            ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 143.45/19.92  |                  e1) = all_57_14 & $i(all_57_14))))
% 143.45/19.92  |   (238)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 143.45/19.92  |              = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 143.45/19.92  |            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 143.45/19.92  |          (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 143.45/19.92  |              = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 143.45/19.92  |            all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 143.45/19.92  |          (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 143.45/19.92  |              = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1
% 143.45/19.92  |            & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 143.45/19.92  |          (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 143.45/19.92  |              = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 143.45/19.92  |            all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) |
% 143.45/19.92  |          (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 143.45/19.92  |              = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 143.45/19.92  |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 143.45/19.92  |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 143.45/19.92  |              = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 143.45/19.92  |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 143.45/19.92  |          (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 143.45/19.92  |              = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1
% 143.45/19.92  |            & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 143.45/19.92  |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 143.45/19.92  |              = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 143.45/19.92  |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 143.45/19.92  |          (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 143.45/19.92  |              = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 143.45/19.92  |            e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)) |
% 143.45/19.92  |          (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 143.45/19.92  |              = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.45/19.92  |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 143.45/19.92  |          (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 143.45/19.92  |              = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 143.45/19.92  |            all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 143.45/19.92  |          (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 143.45/19.92  |              = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 143.45/19.92  |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 143.45/19.92  |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 143.45/19.92  |              = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) =
% 143.45/19.92  |            e0 & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 143.45/19.92  |          (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 143.45/19.92  |              = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 143.45/19.92  |            e0 & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)) |
% 143.45/19.92  |          (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12
% 143.45/19.92  |              = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 143.45/19.92  |            all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 143.45/19.92  |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14
% 143.45/19.92  |              = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 143.45/19.92  |            all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)) |
% 143.45/19.92  |          (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 143.45/19.92  |            (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 143.45/19.92  |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.45/19.92  |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 143.45/19.92  |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 143.45/19.92  |            all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 143.45/19.92  |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 143.45/19.92  |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.45/19.92  |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 143.45/19.92  |                  e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 143.45/19.92  |                all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 143.45/19.92  |                op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 143.45/19.92  |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.45/19.92  |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 143.45/19.92  |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 143.45/19.92  |                all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 143.45/19.92  |                op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 143.45/19.92  |                $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.45/19.92  |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 143.45/19.92  |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 143.45/19.92  |                all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 143.45/19.92  |                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 143.45/19.92  |                $i(all_57_7))))
% 143.45/19.92  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_24_2, all_30_2, e0, e0,
% 143.45/19.93  |              simplifying with (66), (75) gives:
% 143.45/19.93  |   (239)  all_30_2 = all_24_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_30_2, all_40_2, e0, e0,
% 143.45/19.93  |              simplifying with (75), (89) gives:
% 143.45/19.93  |   (240)  all_40_2 = all_30_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_40_2, all_42_2, e0, e0,
% 143.45/19.93  |              simplifying with (89), (92) gives:
% 143.45/19.93  |   (241)  all_42_2 = all_40_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_46_2, all_52_15, e0, e0,
% 143.45/19.93  |              simplifying with (98), (155) gives:
% 143.45/19.93  |   (242)  all_52_15 = all_46_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_42_2, all_52_15, e0, e0,
% 143.45/19.93  |              simplifying with (92), (155) gives:
% 143.45/19.93  |   (243)  all_52_15 = all_42_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_15, all_54_15, e0,
% 143.45/19.93  |              e0, simplifying with (155), (172) gives:
% 143.45/19.93  |   (244)  all_54_15 = all_52_15
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_10_2, all_54_15, e0, e0,
% 143.45/19.93  |              simplifying with (45), (172) gives:
% 143.45/19.93  |   (245)  all_54_15 = all_10_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_11, all_54_14, e1,
% 143.45/19.93  |              e0, simplifying with (156), (173) gives:
% 143.45/19.93  |   (246)  all_54_14 = all_52_11
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_7, all_54_13, e2, e0,
% 143.45/19.93  |              simplifying with (157), (174) gives:
% 143.45/19.93  |   (247)  all_54_13 = all_52_7
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_3, all_54_12, e3, e0,
% 143.45/19.93  |              simplifying with (158), (175) gives:
% 143.45/19.93  |   (248)  all_54_12 = all_52_3
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_14, all_54_11, e0,
% 143.45/19.93  |              e1, simplifying with (159), (176) gives:
% 143.45/19.93  |   (249)  all_54_11 = all_52_14
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_8_2, all_12_2, e1, e1,
% 143.45/19.93  |              simplifying with (42), (48) gives:
% 143.45/19.93  |   (250)  all_12_2 = all_8_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_50_2, all_52_10, e1, e1,
% 143.45/19.93  |              simplifying with (104), (160) gives:
% 143.45/19.93  |   (251)  all_52_10 = all_50_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_4_2, all_52_10, e1, e1,
% 143.45/19.93  |              simplifying with (36), (160) gives:
% 143.45/19.93  |   (252)  all_52_10 = all_4_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_10, all_54_10, e1,
% 143.45/19.93  |              e1, simplifying with (160), (177) gives:
% 143.45/19.93  |   (253)  all_54_10 = all_52_10
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_48_2, all_54_10, e1, e1,
% 143.45/19.93  |              simplifying with (101), (177) gives:
% 143.45/19.93  |   (254)  all_54_10 = all_48_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_32_2, all_54_10, e1, e1,
% 143.45/19.93  |              simplifying with (78), (177) gives:
% 143.45/19.93  |   (255)  all_54_10 = all_32_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_12_2, all_54_10, e1, e1,
% 143.45/19.93  |              simplifying with (48), (177) gives:
% 143.45/19.93  |   (256)  all_54_10 = all_12_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_6, all_54_9, e2, e1,
% 143.45/19.93  |              simplifying with (161), (178) gives:
% 143.45/19.93  |   (257)  all_54_9 = all_52_6
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_2, all_54_8, e3, e1,
% 143.45/19.93  |              simplifying with (162), (179) gives:
% 143.45/19.93  |   (258)  all_54_8 = all_52_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_13, all_54_7, e0, e2,
% 143.45/19.93  |              simplifying with (163), (180) gives:
% 143.45/19.93  |   (259)  all_54_7 = all_52_13
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_9, all_54_6, e1, e2,
% 143.45/19.93  |              simplifying with (164), (181) gives:
% 143.45/19.93  |   (260)  all_54_6 = all_52_9
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_20_2, all_26_2, e2, e2,
% 143.45/19.93  |              simplifying with (60), (69) gives:
% 143.45/19.93  |   (261)  all_26_2 = all_20_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_16_2, all_26_2, e2, e2,
% 143.45/19.93  |              simplifying with (54), (69) gives:
% 143.45/19.93  |   (262)  all_26_2 = all_16_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_38_2, all_52_5, e2, e2,
% 143.45/19.93  |              simplifying with (86), (165) gives:
% 143.45/19.93  |   (263)  all_52_5 = all_38_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_26_2, all_52_5, e2, e2,
% 143.45/19.93  |              simplifying with (69), (165) gives:
% 143.45/19.93  |   (264)  all_52_5 = all_26_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_18_2, all_52_5, e2, e2,
% 143.45/19.93  |              simplifying with (57), (165) gives:
% 143.45/19.93  |   (265)  all_52_5 = all_18_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_20_2, all_54_5, e2, e2,
% 143.45/19.93  |              simplifying with (60), (182) gives:
% 143.45/19.93  |   (266)  all_54_5 = all_20_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_6_2, all_54_5, e2, e2,
% 143.45/19.93  |              simplifying with (39), (182) gives:
% 143.45/19.93  |   (267)  all_54_5 = all_6_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_1, all_54_4, e3, e2,
% 143.45/19.93  |              simplifying with (166), (183) gives:
% 143.45/19.93  |   (268)  all_54_4 = all_52_1
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_12, all_54_3, e0, e3,
% 143.45/19.93  |              simplifying with (167), (184) gives:
% 143.45/19.93  |   (269)  all_54_3 = all_52_12
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_8, all_54_2, e1, e3,
% 143.45/19.93  |              simplifying with (168), (185) gives:
% 143.45/19.93  |   (270)  all_54_2 = all_52_8
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_52_4, all_54_1, e2, e3,
% 143.45/19.93  |              simplifying with (169), (186) gives:
% 143.45/19.93  |   (271)  all_54_1 = all_52_4
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_28_2, all_34_2, e3, e3,
% 143.45/19.93  |              simplifying with (72), (80) gives:
% 143.45/19.93  |   (272)  all_34_2 = all_28_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_34_2, all_36_2, e3, e3,
% 143.45/19.93  |              simplifying with (80), (83) gives:
% 143.45/19.93  |   (273)  all_36_2 = all_34_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_36_2, all_44_2, e3, e3,
% 143.45/19.93  |              simplifying with (83), (95) gives:
% 143.45/19.93  |   (274)  all_44_2 = all_36_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_28_2, all_52_0, e3, e3,
% 143.45/19.93  |              simplifying with (72), (170) gives:
% 143.45/19.93  |   (275)  all_52_0 = all_28_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_22_2, all_52_0, e3, e3,
% 143.45/19.93  |              simplifying with (63), (170) gives:
% 143.45/19.93  |   (276)  all_52_0 = all_22_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_44_2, all_54_0, e3, e3,
% 143.45/19.93  |              simplifying with (95), (187) gives:
% 143.45/19.93  |   (277)  all_54_0 = all_44_2
% 143.45/19.93  | 
% 143.45/19.93  | GROUND_INST: instantiating (function-axioms) with all_14_2, all_54_0, e3, e3,
% 143.45/19.93  |              simplifying with (51), (187) gives:
% 143.45/19.93  |   (278)  all_54_0 = all_14_2
% 143.45/19.93  | 
% 143.45/19.93  | COMBINE_EQS: (277), (278) imply:
% 143.45/19.93  |   (279)  all_44_2 = all_14_2
% 143.45/19.93  | 
% 143.45/19.93  | SIMP: (279) implies:
% 143.45/19.93  |   (280)  all_44_2 = all_14_2
% 143.45/19.93  | 
% 143.45/19.93  | COMBINE_EQS: (266), (267) imply:
% 143.45/19.93  |   (281)  all_20_2 = all_6_2
% 143.45/19.93  | 
% 143.45/19.93  | SIMP: (281) implies:
% 143.45/19.93  |   (282)  all_20_2 = all_6_2
% 143.45/19.93  | 
% 143.45/19.93  | COMBINE_EQS: (254), (256) imply:
% 143.45/19.93  |   (283)  all_48_2 = all_12_2
% 143.45/19.93  | 
% 143.45/19.93  | COMBINE_EQS: (254), (255) imply:
% 143.45/19.94  |   (284)  all_48_2 = all_32_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (253), (254) imply:
% 143.45/19.94  |   (285)  all_52_10 = all_48_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (285) implies:
% 143.45/19.94  |   (286)  all_52_10 = all_48_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (244), (245) imply:
% 143.45/19.94  |   (287)  all_52_15 = all_10_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (287) implies:
% 143.45/19.94  |   (288)  all_52_15 = all_10_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (275), (276) imply:
% 143.45/19.94  |   (289)  all_28_2 = all_22_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (289) implies:
% 143.45/19.94  |   (290)  all_28_2 = all_22_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (263), (265) imply:
% 143.45/19.94  |   (291)  all_38_2 = all_18_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (263), (264) imply:
% 143.45/19.94  |   (292)  all_38_2 = all_26_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (251), (286) imply:
% 143.45/19.94  |   (293)  all_50_2 = all_48_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (251), (252) imply:
% 143.45/19.94  |   (294)  all_50_2 = all_4_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (242), (243) imply:
% 143.45/19.94  |   (295)  all_46_2 = all_42_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (242), (288) imply:
% 143.45/19.94  |   (296)  all_46_2 = all_10_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (293), (294) imply:
% 143.45/19.94  |   (297)  all_48_2 = all_4_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (297) implies:
% 143.45/19.94  |   (298)  all_48_2 = all_4_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (283), (284) imply:
% 143.45/19.94  |   (299)  all_32_2 = all_12_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (284), (298) imply:
% 143.45/19.94  |   (300)  all_32_2 = all_4_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (295), (296) imply:
% 143.45/19.94  |   (301)  all_42_2 = all_10_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (301) implies:
% 143.45/19.94  |   (302)  all_42_2 = all_10_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (274), (280) imply:
% 143.45/19.94  |   (303)  all_36_2 = all_14_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (303) implies:
% 143.45/19.94  |   (304)  all_36_2 = all_14_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (241), (302) imply:
% 143.45/19.94  |   (305)  all_40_2 = all_10_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (305) implies:
% 143.45/19.94  |   (306)  all_40_2 = all_10_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (240), (306) imply:
% 143.45/19.94  |   (307)  all_30_2 = all_10_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (307) implies:
% 143.45/19.94  |   (308)  all_30_2 = all_10_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (291), (292) imply:
% 143.45/19.94  |   (309)  all_26_2 = all_18_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (309) implies:
% 143.45/19.94  |   (310)  all_26_2 = all_18_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (273), (304) imply:
% 143.45/19.94  |   (311)  all_34_2 = all_14_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (311) implies:
% 143.45/19.94  |   (312)  all_34_2 = all_14_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (272), (312) imply:
% 143.45/19.94  |   (313)  all_28_2 = all_14_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (313) implies:
% 143.45/19.94  |   (314)  all_28_2 = all_14_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (299), (300) imply:
% 143.45/19.94  |   (315)  all_12_2 = all_4_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (315) implies:
% 143.45/19.94  |   (316)  all_12_2 = all_4_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (239), (308) imply:
% 143.45/19.94  |   (317)  all_24_2 = all_10_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (317) implies:
% 143.45/19.94  |   (318)  all_24_2 = all_10_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (290), (314) imply:
% 143.45/19.94  |   (319)  all_22_2 = all_14_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (319) implies:
% 143.45/19.94  |   (320)  all_22_2 = all_14_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (261), (310) imply:
% 143.45/19.94  |   (321)  all_20_2 = all_18_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (321) implies:
% 143.45/19.94  |   (322)  all_20_2 = all_18_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (262), (310) imply:
% 143.45/19.94  |   (323)  all_18_2 = all_16_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (282), (322) imply:
% 143.45/19.94  |   (324)  all_18_2 = all_6_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (324) implies:
% 143.45/19.94  |   (325)  all_18_2 = all_6_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (323), (325) imply:
% 143.45/19.94  |   (326)  all_16_2 = all_6_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (326) implies:
% 143.45/19.94  |   (327)  all_16_2 = all_6_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (250), (316) imply:
% 143.45/19.94  |   (328)  all_8_2 = all_4_2
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (328) implies:
% 143.45/19.94  |   (329)  all_8_2 = all_4_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (310), (325) imply:
% 143.45/19.94  |   (330)  all_26_2 = all_6_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (291), (325) imply:
% 143.45/19.94  |   (331)  all_38_2 = all_6_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (263), (331) imply:
% 143.45/19.94  |   (332)  all_52_5 = all_6_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (276), (320) imply:
% 143.45/19.94  |   (333)  all_52_0 = all_14_2
% 143.45/19.94  | 
% 143.45/19.94  | COMBINE_EQS: (254), (298) imply:
% 143.45/19.94  |   (334)  all_54_10 = all_4_2
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (154), (333) imply:
% 143.45/19.94  |   (335)   ~ (all_52_1 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (335) implies:
% 143.45/19.94  |   (336)   ~ (all_52_1 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (153), (333) imply:
% 143.45/19.94  |   (337)   ~ (all_52_2 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (337) implies:
% 143.45/19.94  |   (338)   ~ (all_52_2 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (152), (333) imply:
% 143.45/19.94  |   (339)   ~ (all_52_3 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (339) implies:
% 143.45/19.94  |   (340)   ~ (all_52_3 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (151), (333) imply:
% 143.45/19.94  |   (341)   ~ (all_52_4 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (341) implies:
% 143.45/19.94  |   (342)   ~ (all_52_4 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (150), (333) imply:
% 143.45/19.94  |   (343)   ~ (all_52_8 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (343) implies:
% 143.45/19.94  |   (344)   ~ (all_52_8 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (149), (333) imply:
% 143.45/19.94  |   (345)   ~ (all_52_12 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (345) implies:
% 143.45/19.94  |   (346)   ~ (all_52_12 = all_14_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (146), (332) imply:
% 143.45/19.94  |   (347)   ~ (all_52_1 = all_6_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (141), (252) imply:
% 143.45/19.94  |   (348)   ~ (all_52_2 = all_4_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (137), (288) imply:
% 143.45/19.94  |   (349)   ~ (all_52_3 = all_10_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (136), (332) imply:
% 143.45/19.94  |   (350)   ~ (all_52_4 = all_6_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (131), (332) imply:
% 143.45/19.94  |   (351)   ~ (all_52_6 = all_6_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (351) implies:
% 143.45/19.94  |   (352)   ~ (all_52_6 = all_6_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (130), (332) imply:
% 143.45/19.94  |   (353)   ~ (all_52_7 = all_6_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (353) implies:
% 143.45/19.94  |   (354)   ~ (all_52_7 = all_6_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (129), (332) imply:
% 143.45/19.94  |   (355)   ~ (all_52_9 = all_6_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (355) implies:
% 143.45/19.94  |   (356)   ~ (all_52_9 = all_6_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (128), (332) imply:
% 143.45/19.94  |   (357)   ~ (all_52_13 = all_6_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (357) implies:
% 143.45/19.94  |   (358)   ~ (all_52_13 = all_6_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (126), (252) imply:
% 143.45/19.94  |   (359)   ~ (all_52_6 = all_4_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (123), (288) imply:
% 143.45/19.94  |   (360)   ~ (all_52_7 = all_10_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (121), (252) imply:
% 143.45/19.94  |   (361)   ~ (all_52_8 = all_4_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (118), (252) imply:
% 143.45/19.94  |   (362)   ~ (all_52_9 = all_4_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (115), (252) imply:
% 143.45/19.94  |   (363)   ~ (all_52_11 = all_4_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (363) implies:
% 143.45/19.94  |   (364)   ~ (all_52_11 = all_4_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (114), (252) imply:
% 143.45/19.94  |   (365)   ~ (all_52_14 = all_4_2)
% 143.45/19.94  | 
% 143.45/19.94  | SIMP: (365) implies:
% 143.45/19.94  |   (366)   ~ (all_52_14 = all_4_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (113), (288) imply:
% 143.45/19.94  |   (367)   ~ (all_52_11 = all_10_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (110), (288) imply:
% 143.45/19.94  |   (368)   ~ (all_52_12 = all_10_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (108), (288) imply:
% 143.45/19.94  |   (369)   ~ (all_52_13 = all_10_2)
% 143.45/19.94  | 
% 143.45/19.94  | REDUCE: (107), (288) imply:
% 143.45/19.94  |   (370)   ~ (all_52_14 = all_10_2)
% 143.45/19.94  | 
% 143.45/19.94  | BETA: splitting (37) gives:
% 143.45/19.94  | 
% 143.45/19.95  | Case 1:
% 143.45/19.95  | | 
% 143.45/19.95  | |   (371)   ~ (all_4_2 = e2)
% 143.45/19.95  | | 
% 143.45/19.95  | | BETA: splitting (40) gives:
% 143.45/19.95  | | 
% 143.45/19.95  | | Case 1:
% 143.45/19.95  | | | 
% 143.45/19.95  | | |   (372)   ~ (all_6_2 = e3)
% 143.45/19.95  | | | 
% 143.45/19.95  | | | BETA: splitting (43) gives:
% 143.45/19.95  | | | 
% 143.45/19.95  | | | Case 1:
% 143.45/19.95  | | | | 
% 143.45/19.95  | | | |   (373)   ~ (all_8_2 = e3)
% 143.45/19.95  | | | | 
% 143.45/19.95  | | | | REDUCE: (329), (373) imply:
% 143.45/19.95  | | | |   (374)   ~ (all_4_2 = e3)
% 143.45/19.95  | | | | 
% 143.45/19.95  | | | | BETA: splitting (46) gives:
% 143.45/19.95  | | | | 
% 143.45/19.95  | | | | Case 1:
% 143.45/19.95  | | | | | 
% 143.45/19.95  | | | | |   (375)   ~ (all_10_2 = e1)
% 143.45/19.95  | | | | | 
% 143.45/19.95  | | | | | BETA: splitting (52) gives:
% 143.45/19.95  | | | | | 
% 143.45/19.95  | | | | | Case 1:
% 143.45/19.95  | | | | | | 
% 143.45/19.95  | | | | | |   (376)   ~ (all_14_2 = e0)
% 143.45/19.95  | | | | | | 
% 143.45/19.95  | | | | | | BETA: splitting (55) gives:
% 143.45/19.95  | | | | | | 
% 143.45/19.95  | | | | | | Case 1:
% 143.45/19.95  | | | | | | | 
% 143.45/19.95  | | | | | | |   (377)   ~ (all_16_2 = e0)
% 143.45/19.95  | | | | | | | 
% 143.45/19.95  | | | | | | | REDUCE: (327), (377) imply:
% 143.45/19.95  | | | | | | |   (378)   ~ (all_6_2 = e0)
% 143.45/19.95  | | | | | | | 
% 143.45/19.95  | | | | | | | BETA: splitting (61) gives:
% 143.45/19.95  | | | | | | | 
% 143.45/19.95  | | | | | | | Case 1:
% 143.45/19.95  | | | | | | | | 
% 143.45/19.95  | | | | | | | |   (379)   ~ (all_20_2 = e1)
% 143.45/19.95  | | | | | | | | 
% 143.45/19.95  | | | | | | | | REDUCE: (282), (379) imply:
% 143.45/19.95  | | | | | | | |   (380)   ~ (all_6_2 = e1)
% 143.45/19.95  | | | | | | | | 
% 143.45/19.95  | | | | | | | | BETA: splitting (198) gives:
% 143.45/19.95  | | | | | | | | 
% 143.45/19.95  | | | | | | | | Case 1:
% 143.45/19.95  | | | | | | | | | 
% 143.45/19.95  | | | | | | | | |   (381)  all_54_5 = e3
% 143.45/19.95  | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | COMBINE_EQS: (267), (381) imply:
% 143.45/19.95  | | | | | | | | |   (382)  all_6_2 = e3
% 143.45/19.95  | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | REDUCE: (372), (382) imply:
% 143.45/19.95  | | | | | | | | |   (383)  $false
% 143.45/19.95  | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | CLOSE: (383) is inconsistent.
% 143.45/19.95  | | | | | | | | | 
% 143.45/19.95  | | | | | | | | Case 2:
% 143.45/19.95  | | | | | | | | | 
% 143.45/19.95  | | | | | | | | |   (384)   ~ (all_54_5 = e3)
% 143.45/19.95  | | | | | | | | |   (385)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 143.45/19.95  | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | BETA: splitting (385) gives:
% 143.45/19.95  | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | Case 1:
% 143.45/19.95  | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | |   (386)  all_54_5 = e2
% 143.45/19.95  | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | COMBINE_EQS: (267), (386) imply:
% 143.45/19.95  | | | | | | | | | |   (387)  all_6_2 = e2
% 143.45/19.95  | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | REDUCE: (347), (387) imply:
% 143.45/19.95  | | | | | | | | | |   (388)   ~ (all_52_1 = e2)
% 143.45/19.95  | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | REDUCE: (350), (387) imply:
% 143.45/19.95  | | | | | | | | | |   (389)   ~ (all_52_4 = e2)
% 143.45/19.95  | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | REDUCE: (352), (387) imply:
% 143.45/19.95  | | | | | | | | | |   (390)   ~ (all_52_6 = e2)
% 143.45/19.95  | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | REDUCE: (356), (387) imply:
% 143.45/19.95  | | | | | | | | | |   (391)   ~ (all_52_9 = e2)
% 143.45/19.95  | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | REDUCE: (358), (387) imply:
% 143.45/19.95  | | | | | | | | | |   (392)   ~ (all_52_13 = e2)
% 143.45/19.95  | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | REDUCE: (372), (387) imply:
% 143.45/19.95  | | | | | | | | | |   (393)   ~ (e3 = e2)
% 143.45/19.95  | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | REDUCE: (39), (387) imply:
% 143.45/19.95  | | | | | | | | | |   (394)  op(e2, e2) = e2
% 143.45/19.95  | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | BETA: splitting (64) gives:
% 143.45/19.95  | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | Case 1:
% 143.45/19.95  | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | |   (395)   ~ (all_22_2 = e1)
% 143.45/19.95  | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | REDUCE: (320), (395) imply:
% 143.45/19.95  | | | | | | | | | | |   (396)   ~ (all_14_2 = e1)
% 143.45/19.95  | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | BETA: splitting (67) gives:
% 143.45/19.95  | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | Case 1:
% 143.45/19.95  | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | |   (397)   ~ (all_24_2 = e2)
% 143.45/19.95  | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | REDUCE: (318), (397) imply:
% 143.45/19.95  | | | | | | | | | | | |   (398)   ~ (all_10_2 = e2)
% 143.45/19.95  | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | BETA: splitting (84) gives:
% 143.45/19.95  | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | Case 1:
% 143.45/19.95  | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | |   (399)   ~ (all_36_2 = e2)
% 143.45/19.95  | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | REDUCE: (304), (399) imply:
% 143.45/19.95  | | | | | | | | | | | | |   (400)   ~ (all_14_2 = e2)
% 143.45/19.95  | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | BETA: splitting (203) gives:
% 143.45/19.95  | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | Case 1:
% 143.45/19.95  | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | |   (401)  all_54_0 = e3
% 143.45/19.95  | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | | COMBINE_EQS: (278), (401) imply:
% 143.45/19.95  | | | | | | | | | | | | | |   (402)  all_14_2 = e3
% 143.45/19.95  | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | | REDUCE: (336), (402) imply:
% 143.45/19.95  | | | | | | | | | | | | | |   (403)   ~ (all_52_1 = e3)
% 143.45/19.95  | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | | REDUCE: (342), (402) imply:
% 143.45/19.95  | | | | | | | | | | | | | |   (404)   ~ (all_52_4 = e3)
% 143.45/19.95  | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | | REDUCE: (344), (402) imply:
% 143.45/19.95  | | | | | | | | | | | | | |   (405)   ~ (all_52_8 = e3)
% 143.45/19.95  | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | | REDUCE: (346), (402) imply:
% 143.45/19.95  | | | | | | | | | | | | | |   (406)   ~ (all_52_12 = e3)
% 143.45/19.95  | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | | REDUCE: (51), (402) imply:
% 143.45/19.95  | | | | | | | | | | | | | |   (407)  op(e3, e3) = e3
% 143.45/19.95  | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 143.45/19.95  | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | | Case 1:
% 143.45/19.95  | | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | | |   (408)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.45/19.95  | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.45/19.95  | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.45/19.95  | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.45/19.95  | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.45/19.95  | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.45/19.95  | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.45/19.95  | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.45/19.95  | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.45/19.95  | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.45/19.95  | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.45/19.95  | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.45/19.95  | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.45/19.95  | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.45/19.95  | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.45/19.95  | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.45/19.95  | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 143.45/19.95  | | | | | | | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 143.45/19.95  | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 143.45/19.95  | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 143.45/19.95  | | | | | | | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 143.45/19.95  | | | | | | | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.45/19.95  | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.45/19.95  | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 143.45/19.95  | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 143.45/19.95  | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 143.45/19.95  | | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 143.45/19.95  | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 143.45/19.95  | | | | | | | | | | | | | | |              e2) = e1 & op(e1, e1) = all_57_14 &
% 143.45/19.95  | | | | | | | | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 143.45/19.95  | | | | | | | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 143.45/19.95  | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 143.45/19.95  | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 143.45/19.95  | | | | | | | | | | | | | | |            = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 143.45/19.95  | | | | | | | | | | | | | | |            = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.45/19.95  | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 143.45/19.95  | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 143.45/19.95  | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 143.45/19.95  | | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | | | BETA: splitting (408) gives:
% 143.45/19.95  | | | | | | | | | | | | | | | 
% 143.45/19.95  | | | | | | | | | | | | | | | Case 1:
% 143.45/19.95  | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | |   (409)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.45/19.96  | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.45/19.96  | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.45/19.96  | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.45/19.96  | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.45/19.96  | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.45/19.96  | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.45/19.96  | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.45/19.96  | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.45/19.96  | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.45/19.96  | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.45/19.96  | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.45/19.96  | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.45/19.96  | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.45/19.96  | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.45/19.96  | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.45/19.96  | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 143.45/19.96  | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | BETA: splitting (409) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | |   (410)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.45/19.96  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.45/19.96  | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.45/19.96  | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.45/19.96  | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.45/19.96  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.45/19.96  | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.45/19.96  | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.45/19.96  | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (388), (410), (function-axioms) are
% 143.45/19.96  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 143.45/19.96  | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.96  | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | |   (411)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.45/19.96  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.45/19.96  | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.45/19.96  | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.45/19.96  | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.45/19.96  | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.45/19.96  | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.45/19.96  | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.45/19.96  | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 143.45/19.96  | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | BETA: splitting (411) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (412)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.45/19.96  | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.45/19.96  | | | | | | | | | | | | | | | | | |          all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.45/19.96  | | | | | | | | | | | | | | | | | |          op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.45/19.96  | | | | | | | | | | | | | | | | | |          $i(all_57_14)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | ALPHA: (412) implies:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (413)  op(e2, e2) = e3
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (394), (413), (function-axioms) are
% 143.45/19.96  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (414)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.45/19.96  | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 143.45/19.96  | | | | | | | | | | | | | | | | | |          op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 143.45/19.96  | | | | | | | | | | | | | | | | | |          op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | ALPHA: (414) implies:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (415)   ~ (all_57_14 = e3)
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (416)   ~ (all_57_2 = e0)
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (417)  op(e0, e0) = e3
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (418)  op(e0, e3) = all_57_2
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (419)  op(e1, e1) = all_57_14
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (420)  op(e1, e3) = e1
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e3,
% 143.45/19.96  | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (45), (417) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (421)  all_10_2 = e3
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 143.45/19.96  | | | | | | | | | | | | | | | | | |              all_57_2, e3, e0, simplifying with (158), (418)
% 143.45/19.96  | | | | | | | | | | | | | | | | | |              gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (422)  all_57_2 = all_52_3
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 143.45/19.96  | | | | | | | | | | | | | | | | | |              all_57_14, e1, e1, simplifying with (36), (419)
% 143.45/19.96  | | | | | | | | | | | | | | | | | |              gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (423)  all_57_14 = all_4_2
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 143.45/19.96  | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (420) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (424)  all_52_2 = e1
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (296), (421) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (425)  all_46_2 = e3
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | REDUCE: (416), (422) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (426)   ~ (all_52_3 = e0)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | REDUCE: (148), (424) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (427)   ~ (all_52_1 = e1)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | REDUCE: (143), (424) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (428)   ~ (all_52_3 = e1)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | SIMP: (428) implies:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (429)   ~ (all_52_3 = e1)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | REDUCE: (348), (424) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (430)   ~ (all_4_2 = e1)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | SIMP: (430) implies:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (431)   ~ (all_4_2 = e1)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | REDUCE: (349), (421) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (432)   ~ (all_52_3 = e3)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | REDUCE: (367), (421) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (433)   ~ (all_52_11 = e3)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | REDUCE: (369), (421) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | |   (434)   ~ (all_52_13 = e3)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | |   (435)  all_54_4 = e3
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (435) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | |   (436)  all_52_1 = e3
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | REDUCE: (403), (436) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | |   (437)  $false
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | CLOSE: (437) is inconsistent.
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | |   (438)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | |   (439)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | BETA: splitting (439) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | |   (440)  all_56_12 = e2 & op(e0, e3) = e2
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | ALPHA: (440) implies:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | |   (441)  all_56_12 = e2
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | |   (442)  op(e0, e3) = e2
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | |   (443)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (166), (407), (427), (443), (function-axioms)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1176.
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | |   (444)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (444) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | |   (445)  all_56_6 = e1 & op(e1, e3) = e1
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (445) implies:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | |   (446)  all_56_6 = e1
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (438) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | |   (447)  all_54_4 = e2
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (388), (447) are inconsistent by sub-proof
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | |            #1175.
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | |   (448)   ~ (all_54_4 = e2)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | |   (449)  all_54_4 = e1 | all_54_4 = e0
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (449) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (450)  all_54_4 = e1
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (427), (450) are inconsistent by sub-proof
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | |            #1174.
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (451)  all_54_4 = e0
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (451) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (452)  all_52_1 = e0
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (452) implies:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (453)  all_52_1 = e0
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (453) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (454)   ~ (all_52_3 = e0)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (453) imply:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (455)   ~ (all_52_13 = e0)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (455) implies:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (456)   ~ (all_52_13 = e0)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (457)  all_54_10 = e3
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (457) are inconsistent by sub-proof
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1173.
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (458)   ~ (all_54_10 = e3)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (459)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (460)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (390), (446), (460), (function-axioms)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1170.
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (461)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (461) gives:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (462)  all_56_8 = e2 & op(e1, e1) = e2
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (462) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (463)  op(e1, e1) = e2
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (463), (function-axioms) are
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (464)  all_56_11 = e2 & op(e1, e0) = e2
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (464) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (465)  all_56_11 = e2
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (459) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (466)  all_54_10 = e2
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (466) are inconsistent by sub-proof
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1168.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (467)   ~ (all_54_10 = e2)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (468)  all_54_10 = e1 | all_54_10 = e0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (468) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (469)  all_54_10 = e1
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (431), (469) are inconsistent by sub-proof
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1167.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (470)  all_54_10 = e0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (470) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (471)  all_4_2 = e0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (471) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (472)  all_4_2 = e0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (472) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (473)   ~ (all_52_8 = e0)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (472) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (474)   ~ (all_52_9 = e0)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (472) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (475)   ~ (all_52_11 = e0)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (472) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (476)   ~ (e3 = e0)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (472) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (477)   ~ (e2 = e0)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (431), (472) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (478)   ~ (e1 = e0)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (479)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (394), (404), (479), (function-axioms)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1165.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (480)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (480) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (481)  all_56_7 = e3 & op(e1, e2) = e3
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (481) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (482)  all_56_7 = e3
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (483)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (483) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (484)  all_56_2 = e0 & op(e2, e3) = e0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (484) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (485)  all_56_2 = e0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (486)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (486) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (487)  all_56_4 = e3 & op(e3, e1) = e3
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (487) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (488)  op(e3, e1) = e3
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (405), (488), (function-axioms) are
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (489)  all_56_5 = e3 & op(e2, e1) = e3
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (489) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (490)  all_56_5 = e3
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (99) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (491)   ~ (all_46_2 = e3)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (425), (491) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (492)  $false
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (492) is inconsistent.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (493)  ( ~ (all_46_0 = e1) & op(all_46_1, e0) = all_46_0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e3) = all_46_1 & $i(all_46_0) &
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_46_1)) | ( ~ (all_46_1 = e2) & op(e0, e3)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_46_1 & $i(all_46_1))
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (493) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (494)   ~ (all_46_0 = e1) & op(all_46_1, e0) = all_46_0 &
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e0, e3) = all_46_1 & $i(all_46_0) &
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_46_1)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (494) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (495)   ~ (all_46_0 = e1)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (496)  op(e0, e3) = all_46_1
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (497)  op(all_46_1, e0) = all_46_0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (498)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (498) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (499)  all_56_2 = e1 & op(e2, e3) = e1
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (166), (196), (259), (392), (434), (456),
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (499), (function-axioms) are inconsistent by
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1159.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (500)  all_56_3 = e1 & op(e2, e2) = e1
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (500) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (501)  op(e2, e2) = e1
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (163), (164), (222), (391), (392),
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (485), (501), (function-axioms) are inconsistent
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1154.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (502)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (502) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (503)  all_56_5 = e1 & op(e2, e1) = e1
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (490), (503) are inconsistent by sub-proof
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1153.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (504)  all_56_10 = e1 & op(e2, e0) = e1
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (504) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (505)  op(e2, e0) = e1
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (506)  all_54_1 = e3
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (506) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (507)  all_52_4 = e3
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (404), (507) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (508)  $false
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (508) is inconsistent.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_46_1,
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (442), (496) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (509)  all_46_1 = e2
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_46_0,
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e2, simplifying with (505) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (510)  all_46_0 = e1 |  ~ (op(e2, e0) = all_46_0)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (497), (509) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (511)  op(e2, e0) = all_46_0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (510) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (512)   ~ (op(e2, e0) = all_46_0)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (511), (512) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (513)  $false
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (513) is inconsistent.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (514)  all_46_0 = e1
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (495), (514) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (515)  $false
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (515) is inconsistent.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (516)   ~ (all_46_1 = e2) & op(e0, e3) = all_46_1 &
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_46_1)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (516) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (517)   ~ (all_46_1 = e2)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (518)  op(e0, e3) = all_46_1
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_46_1,
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (442), (518) gives:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (519)  all_46_1 = e2
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (517), (519) imply:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (520)  $false
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (520) is inconsistent.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (521)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (156), (212), (433), (446), (465),
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (482), (521), (function-axioms) are inconsistent
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1146.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (522)  all_56_3 = e0 & op(e2, e2) = e0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (522) implies:
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (523)  op(e2, e2) = e0
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (394), (523), (function-axioms) are
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 143.45/19.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (524)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (524) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (525)  all_56_5 = e0 & op(e2, e1) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (474), (525), (function-axioms) are
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1144.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (526)  all_56_10 = e0 & op(e2, e0) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (526) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (527)  all_56_10 = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (528)  all_56_15 = e0 & op(e0, e0) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (528) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (529)  op(e0, e0) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (417), (529), (function-axioms) are
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (530)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (530) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (531)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (531) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (532)  all_56_12 = e0 & op(e0, e3) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (532) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (533)  op(e0, e3) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (426), (533), (function-axioms) are
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (534)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (534) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (535)  all_56_13 = e0 & op(e0, e2) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (535) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (536)  op(e0, e2) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (537)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (537) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (538)  all_56_4 = e3 & op(e3, e1) = e3
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (538) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (539)  op(e3, e1) = e3
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (405), (539), (function-axioms) are
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (540)  all_56_5 = e3 & op(e2, e1) = e3
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (540) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (541)  all_56_5 = e3
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (542)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e0)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (542) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (543)  all_56_0 = e0 & op(e3, e3) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (543) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (544)  op(e3, e3) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (376), (396), (400), (544),
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1139.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (545)  all_56_2 = e0 & op(e2, e3) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (545) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (546)  all_56_2 = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (547)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (547) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (548)  all_56_2 = e1 & op(e2, e3) = e1
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (166), (196), (259), (392), (434), (456),
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (548), (function-axioms) are inconsistent by
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1159.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (549)  all_56_3 = e1 & op(e2, e2) = e1
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (549) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (550)  op(e2, e2) = e1
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (551)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (388), (550), (551), (function-axioms)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1138.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (552)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (552) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (553)  all_56_5 = e2 & op(e2, e1) = e2
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (553) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (554)  op(e2, e1) = e2
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (223), (527), (546), (550), (554),
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1133.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (555)  all_56_10 = e2 & op(e2, e0) = e2
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (527), (555) are inconsistent by sub-proof
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1132.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (556)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (556) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (557)  all_56_5 = e1 & op(e2, e1) = e1
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (541), (557) are inconsistent by sub-proof
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1153.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (558)  all_56_10 = e1 & op(e2, e0) = e1
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (527), (558) are inconsistent by sub-proof
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1131.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (559)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (559) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (560)  all_56_6 = e0 & op(e1, e3) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (560) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (561)  all_56_6 = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (562)  op(e1, e3) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (563)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (563) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (564)  all_56_4 = e0 & op(e3, e1) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (473), (564), (function-axioms) are
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (565)  all_56_5 = e0 & op(e2, e1) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (474), (565), (function-axioms) are
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1144.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (566)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (566) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (567)  all_56_8 = e0 & op(e1, e1) = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (567) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (568)  all_56_8 = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (569)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (569) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (570)  all_56_6 = e2 & op(e1, e3) = e2
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (561), (570) are inconsistent by sub-proof
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1129.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (571)  all_56_7 = e2 & op(e1, e2) = e2
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (482), (571) are inconsistent by sub-proof
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1128.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (461) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (572)  all_56_8 = e2 & op(e1, e1) = e2
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (572) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (573)  all_56_8 = e2
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (568), (573) imply:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (574)  e2 = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (574) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (575)  e2 = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (575) imply:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (576)  $false
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (576) is inconsistent.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (464) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (577)  op(e1, e0) = e2
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (578)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (578) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (420), (562), (function-axioms) are
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (579)  all_56_7 = e1 & op(e1, e2) = e1
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (482), (579) are inconsistent by sub-proof
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1126.
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (580)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (580) gives:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (581)  all_56_8 = e1 & op(e1, e1) = e1
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (581) implies:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (582)  all_56_8 = e1
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (568), (582) imply:
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (583)  e1 = e0
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (583) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (584)  e1 = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (584) imply:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (585)  $false
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (585) is inconsistent.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (586)  all_56_11 = e1 & op(e1, e0) = e1
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (586) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (587)  op(e1, e0) = e1
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (577), (587), (function-axioms) are
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1125.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (588)  all_56_14 = e0 & op(e0, e1) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (588) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (589)  op(e0, e1) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (475), (589), (function-axioms) are
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1124.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (590)  all_56_12 = e0 & op(e0, e3) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (590) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (591)  op(e0, e3) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (157), (158), (536), (591),
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1123.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (592)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (156), (212), (433), (446), (465),
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (482), (592), (function-axioms) are inconsistent
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1146.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (593)  all_56_14 = e0 & op(e0, e1) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (593) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (594)  op(e0, e1) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (475), (594), (function-axioms) are
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1124.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (595)  all_56_13 = e3 & op(e0, e2) = e3
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (595) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (596)  all_56_13 = e3
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (597)  all_56_15 = e0 & op(e0, e0) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (597) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (598)  op(e0, e0) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (417), (598), (function-axioms) are
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (599)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (599) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (600)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (600) gives:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (601)  all_56_12 = e0 & op(e0, e3) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (139), (157),
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (206), (207), (224), (225), (227), (375),
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (394), (398), (596), (600), (601),
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1095.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (602)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (602) gives:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (603)  all_56_13 = e0 & op(e0, e2) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (603) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (604)  all_56_13 = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (596), (604) are inconsistent by sub-proof
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1094.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (605)  all_56_14 = e0 & op(e0, e1) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (605) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (606)  op(e0, e1) = e0
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (475), (606), (function-axioms) are
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1124.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | |   (607)  all_56_12 = e1 & op(e0, e3) = e1
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (607) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | |   (608)  all_56_12 = e1
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (441), (608) are inconsistent by sub-proof
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | |            #1122.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | |   (609)  all_56_13 = e2 & op(e0, e2) = e2
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (609) implies:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | |   (610)  all_56_13 = e2
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | |            (394), (610), (function-axioms) are inconsistent
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1104.
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | End of split
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | Case 2:
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | 
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | |   (611)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 143.45/19.99  | | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | BETA: splitting (611) gives:
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | |   (612)  all_56_14 = e2 & op(e0, e1) = e2
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (612) implies:
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | |   (613)  op(e0, e1) = e2
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (138), (156), (191), (248), (426), (429), (432),
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | |            (613), (function-axioms) are inconsistent by
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1088.
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | |   (614)  all_56_15 = e2 & op(e0, e0) = e2
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (614) implies:
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | |   (615)  op(e0, e0) = e2
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (417), (615), (function-axioms) are
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | End of split
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | End of split
% 143.90/19.99  | | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | | End of split
% 143.90/19.99  | | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | End of split
% 143.90/19.99  | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | End of split
% 143.90/19.99  | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | Case 2:
% 143.90/19.99  | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | |   (616)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.90/19.99  | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.90/19.99  | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 143.90/19.99  | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 143.90/19.99  | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 143.90/19.99  | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 143.90/19.99  | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 143.90/19.99  | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.90/19.99  | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 143.90/19.99  | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.90/19.99  | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 143.90/19.99  | | | | | | | | | | | | | | | |            = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 143.90/19.99  | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 143.90/19.99  | | | | | | | | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.90/19.99  | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 143.90/19.99  | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 143.90/19.99  | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 143.90/19.99  | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 143.90/19.99  | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.90/19.99  | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 143.90/19.99  | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 143.90/19.99  | | | | | | | | | | | | | | | |            $i(all_57_10))
% 143.90/19.99  | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | BETA: splitting (616) gives:
% 143.90/19.99  | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | Case 1:
% 143.90/19.99  | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | |   (617)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.90/19.99  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.90/19.99  | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 143.90/19.99  | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 143.90/19.99  | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 143.90/19.99  | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 143.90/19.99  | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 143.90/19.99  | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.90/19.99  | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10))
% 143.90/19.99  | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (371), (404), (617),
% 143.90/19.99  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 143.90/19.99  | | | | | | | | | | | | | | | | |            #1086.
% 143.90/19.99  | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | Case 2:
% 143.90/19.99  | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | |   (618)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 143.90/19.99  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 143.90/19.99  | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 143.90/19.99  | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) &
% 143.90/19.99  | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 143.90/19.99  | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 143.90/19.99  | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 143.90/19.99  | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.90/19.99  | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 143.90/19.99  | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.90/19.99  | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 143.90/19.99  | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 143.90/19.99  | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 143.90/19.99  | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | BETA: splitting (618) gives:
% 143.90/19.99  | | | | | | | | | | | | | | | | | 
% 143.90/19.99  | | | | | | | | | | | | | | | | | Case 1:
% 143.90/19.99  | | | | | | | | | | | | | | | | | | 
% 143.90/20.00  | | | | | | | | | | | | | | | | | |   (619)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 143.90/20.00  | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 143.90/20.00  | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 143.90/20.00  | | | | | | | | | | | | | | | | | |            e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 143.90/20.00  | | | | | | | | | | | | | | | | | | 
% 143.90/20.00  | | | | | | | | | | | | | | | | | | ALPHA: (619) implies:
% 143.90/20.00  | | | | | | | | | | | | | | | | | |   (620)  op(e3, e3) = e2
% 143.90/20.00  | | | | | | | | | | | | | | | | | | 
% 143.90/20.00  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (407), (620), (function-axioms) are
% 143.90/20.00  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 143.90/20.00  | | | | | | | | | | | | | | | | | | 
% 143.90/20.00  | | | | | | | | | | | | | | | | | Case 2:
% 143.90/20.00  | | | | | | | | | | | | | | | | | | 
% 143.90/20.00  | | | | | | | | | | | | | | | | | |   (621)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.90/20.00  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 143.90/20.00  | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 143.90/20.00  | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 143.90/20.00  | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 143.90/20.00  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.90/20.00  | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 143.90/20.00  | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 143.90/20.00  | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 143.90/20.00  | | | | | | | | | | | | | | | | | | 
% 143.90/20.00  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (45), (394), (398), (621), (function-axioms)
% 143.90/20.00  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1084.
% 143.90/20.00  | | | | | | | | | | | | | | | | | | 
% 143.90/20.00  | | | | | | | | | | | | | | | | | End of split
% 143.90/20.00  | | | | | | | | | | | | | | | | | 
% 143.90/20.00  | | | | | | | | | | | | | | | | End of split
% 143.90/20.00  | | | | | | | | | | | | | | | | 
% 143.90/20.00  | | | | | | | | | | | | | | | End of split
% 143.90/20.00  | | | | | | | | | | | | | | | 
% 143.90/20.00  | | | | | | | | | | | | | | Case 2:
% 143.90/20.00  | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | |   (622)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.93/20.00  | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.93/20.00  | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.93/20.00  | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.93/20.00  | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.93/20.00  | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.93/20.00  | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.93/20.00  | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.93/20.00  | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 143.93/20.00  | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 143.93/20.00  | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.93/20.00  | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 143.93/20.00  | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 143.93/20.00  | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 143.93/20.00  | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 143.93/20.00  | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 143.93/20.00  | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 143.93/20.00  | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 143.93/20.00  | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 143.93/20.00  | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.93/20.00  | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.93/20.00  | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 143.93/20.00  | | | | | | | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 143.93/20.00  | | | | | | | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 143.93/20.00  | | | | | | | | | | | | | | |            = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 143.93/20.00  | | | | | | | | | | | | | | |            = e2 & $i(all_57_9) & $i(all_57_12)) |
% 143.93/20.00  | | | | | | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 143.93/20.00  | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 143.93/20.00  | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 143.93/20.00  | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 143.93/20.00  | | | | | | | | | | | | | | |          | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 143.93/20.00  | | | | | | | | | | | | | | |              = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.93/20.00  | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 143.93/20.00  | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.93/20.00  | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 143.93/20.00  | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 143.93/20.00  | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.93/20.00  | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 143.93/20.00  | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 143.93/20.00  | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 143.93/20.00  | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 143.93/20.00  | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 143.93/20.00  | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.93/20.00  | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 143.93/20.00  | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.93/20.00  | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 143.93/20.00  | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 143.93/20.00  | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.93/20.00  | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 143.93/20.00  | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 143.93/20.00  | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 143.93/20.00  | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 143.93/20.00  | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 143.93/20.00  | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.93/20.00  | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.93/20.00  | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 143.93/20.00  | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 143.93/20.00  | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.93/20.00  | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 143.93/20.00  | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 143.93/20.00  | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 143.93/20.00  | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | BETA: splitting (622) gives:
% 143.93/20.00  | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | Case 1:
% 143.93/20.00  | | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | |   (623)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.93/20.00  | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.93/20.00  | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.93/20.00  | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.93/20.00  | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.93/20.00  | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.93/20.00  | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.93/20.00  | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.93/20.00  | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 143.93/20.00  | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 143.93/20.00  | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.93/20.00  | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 143.93/20.00  | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 143.93/20.00  | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 143.93/20.00  | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 143.93/20.00  | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 143.93/20.00  | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 143.93/20.00  | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 143.93/20.00  | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 143.93/20.00  | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.93/20.00  | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.93/20.00  | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 143.93/20.00  | | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | | BETA: splitting (623) gives:
% 143.93/20.00  | | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | | Case 1:
% 143.93/20.00  | | | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | | |   (624)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.93/20.00  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.93/20.00  | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.93/20.00  | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.93/20.00  | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.93/20.00  | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.93/20.00  | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.93/20.00  | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.93/20.00  | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 143.93/20.00  | | | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (391), (405), (624),
% 143.93/20.00  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 143.93/20.00  | | | | | | | | | | | | | | | | |            #1083.
% 143.93/20.00  | | | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | | Case 2:
% 143.93/20.00  | | | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | | |   (625)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.93/20.00  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 143.93/20.00  | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 143.93/20.00  | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.93/20.00  | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 143.93/20.00  | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 143.93/20.00  | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.93/20.00  | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.93/20.00  | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 143.93/20.00  | | | | | | | | | | | | | | | | |            & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 143.93/20.00  | | | | | | | | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 143.93/20.00  | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 143.93/20.00  | | | | | | | | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 143.93/20.00  | | | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (375), (406), (625),
% 143.93/20.00  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 143.93/20.00  | | | | | | | | | | | | | | | | |            #1080.
% 143.93/20.00  | | | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | | End of split
% 143.93/20.00  | | | | | | | | | | | | | | | | 
% 143.93/20.00  | | | | | | | | | | | | | | | Case 2:
% 143.93/20.00  | | | | | | | | | | | | | | | | 
% 143.95/20.00  | | | | | | | | | | | | | | | |   (626)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 143.95/20.00  | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 143.95/20.00  | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 143.95/20.00  | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 143.95/20.00  | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 143.95/20.00  | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 143.95/20.00  | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 143.95/20.00  | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 143.95/20.00  | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 143.95/20.00  | | | | | | | | | | | | | | | |            e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 143.95/20.00  | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 143.95/20.00  | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.95/20.00  | | | | | | | | | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 143.95/20.00  | | | | | | | | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 143.95/20.00  | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 143.95/20.00  | | | | | | | | | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 143.95/20.00  | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 143.95/20.00  | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 143.95/20.00  | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 143.95/20.00  | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.00  | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 143.95/20.00  | | | | | | | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 143.95/20.00  | | | | | | | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.95/20.00  | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 143.95/20.00  | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 143.95/20.00  | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.95/20.00  | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 143.95/20.00  | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 143.95/20.00  | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 143.95/20.00  | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 143.95/20.00  | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 143.95/20.00  | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.95/20.00  | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.95/20.00  | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 143.95/20.00  | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 143.95/20.00  | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.95/20.00  | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 143.95/20.00  | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.00  | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 143.95/20.00  | | | | | | | | | | | | | | | | 
% 143.95/20.00  | | | | | | | | | | | | | | | | BETA: splitting (626) gives:
% 143.95/20.00  | | | | | | | | | | | | | | | | 
% 143.95/20.00  | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.00  | | | | | | | | | | | | | | | | | 
% 143.95/20.00  | | | | | | | | | | | | | | | | |   (627)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 143.95/20.00  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 143.95/20.00  | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 143.95/20.00  | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 143.95/20.00  | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 143.95/20.00  | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 143.95/20.00  | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 143.95/20.00  | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 143.95/20.00  | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 143.95/20.00  | | | | | | | | | | | | | | | | | 
% 143.95/20.00  | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (376), (396), (400), (627),
% 143.95/20.00  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 143.95/20.00  | | | | | | | | | | | | | | | | |            #1079.
% 143.95/20.00  | | | | | | | | | | | | | | | | | 
% 143.95/20.00  | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.00  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (628)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 143.95/20.01  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.95/20.01  | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.95/20.01  | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 143.95/20.01  | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 143.95/20.01  | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.95/20.01  | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 143.95/20.01  | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 143.95/20.01  | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 143.95/20.01  | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 143.95/20.01  | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.95/20.01  | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 143.95/20.01  | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 143.95/20.01  | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.95/20.01  | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 143.95/20.01  | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 143.95/20.01  | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 143.95/20.01  | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 143.95/20.01  | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 143.95/20.01  | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.95/20.01  | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.95/20.01  | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 143.95/20.01  | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 143.95/20.01  | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.95/20.01  | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 143.95/20.01  | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.01  | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | BETA: splitting (628) gives:
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | |   (629)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.95/20.01  | | | | | | | | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.95/20.01  | | | | | | | | | | | | | | | | | |          $i(all_57_13)
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | ALPHA: (629) implies:
% 143.95/20.01  | | | | | | | | | | | | | | | | | |   (630)  op(e2, e0) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (392), (630), (function-axioms) are
% 143.95/20.01  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | |   (631)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 143.95/20.01  | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 143.95/20.01  | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 143.95/20.01  | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 143.95/20.01  | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 143.95/20.01  | | | | | | | | | | | | | | | | | |                & $i(all_57_7))))
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | BETA: splitting (631) gives:
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |   (632)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | ALPHA: (632) implies:
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |   (633)  op(e2, e2) = e0
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (394), (633), (function-axioms) are
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |   (634)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |          ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |                e1) = all_57_6 & op(e0, e1) = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_7)))
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | ALPHA: (634) implies:
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |   (635)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (371), (374), (394), (407),
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            (635), (function-axioms) are inconsistent by
% 143.95/20.01  | | | | | | | | | | | | | | | | | | |            sub-proof #1075.
% 143.95/20.01  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | End of split
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | End of split
% 143.95/20.01  | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | End of split
% 143.95/20.01  | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | End of split
% 143.95/20.01  | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | Case 2:
% 143.95/20.01  | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | |   (636)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 143.95/20.01  | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | REF_CLOSE: (278), (376), (396), (400), (636) are inconsistent
% 143.95/20.01  | | | | | | | | | | | | | |            by sub-proof #1140.
% 143.95/20.01  | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | End of split
% 143.95/20.01  | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | Case 2:
% 143.95/20.01  | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | |   (637)  all_36_2 = e2
% 143.95/20.01  | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | COMBINE_EQS: (304), (637) imply:
% 143.95/20.01  | | | | | | | | | | | | |   (638)  all_14_2 = e2
% 143.95/20.01  | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | SIMP: (638) implies:
% 143.95/20.01  | | | | | | | | | | | | |   (639)  all_14_2 = e2
% 143.95/20.01  | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | COMBINE_EQS: (280), (639) imply:
% 143.95/20.01  | | | | | | | | | | | | |   (640)  all_44_2 = e2
% 143.95/20.01  | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | REDUCE: (51), (639) imply:
% 143.95/20.01  | | | | | | | | | | | | |   (641)  op(e3, e3) = e2
% 143.95/20.01  | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | BETA: splitting (218) gives:
% 143.95/20.01  | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | Case 1:
% 143.95/20.01  | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | |   (642)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 143.95/20.01  | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 143.95/20.01  | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (229), (231),
% 143.95/20.01  | | | | | | | | | | | | | |            (235), (391), (641), (642), (function-axioms) are
% 143.95/20.01  | | | | | | | | | | | | | |            inconsistent by sub-proof #1061.
% 143.95/20.01  | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | Case 2:
% 143.95/20.01  | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | |   (643)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 143.95/20.01  | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 143.95/20.01  | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | BETA: splitting (643) gives:
% 143.95/20.01  | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | Case 1:
% 143.95/20.01  | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | |   (644)  all_56_8 = e2 & op(e1, e1) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | ALPHA: (644) implies:
% 143.95/20.01  | | | | | | | | | | | | | | |   (645)  op(e1, e1) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (645), (function-axioms) are
% 143.95/20.01  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 143.95/20.01  | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | Case 2:
% 143.95/20.01  | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | |   (646)  all_56_14 = e2 & op(e0, e1) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | ALPHA: (646) implies:
% 143.95/20.01  | | | | | | | | | | | | | | |   (647)  op(e0, e1) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 143.95/20.01  | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | Case 1:
% 143.95/20.01  | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | |   (648)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 143.95/20.01  | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 143.95/20.01  | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | BETA: splitting (648) gives:
% 143.95/20.01  | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (649)  all_56_6 = e2 & op(e1, e3) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | ALPHA: (649) implies:
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (650)  all_56_6 = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230), (234),
% 143.95/20.01  | | | | | | | | | | | | | | | | |            (641), (650), (function-axioms) are inconsistent
% 143.95/20.01  | | | | | | | | | | | | | | | | |            by sub-proof #1050.
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (651)  all_56_7 = e2 & op(e1, e2) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | ALPHA: (651) implies:
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (652)  op(e1, e2) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (390), (652), (function-axioms) are
% 143.95/20.01  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1171.
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | End of split
% 143.95/20.01  | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | Case 2:
% 143.95/20.01  | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | |   (653)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 143.95/20.01  | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 143.95/20.01  | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | BETA: splitting (653) gives:
% 143.95/20.01  | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (654)  all_56_8 = e2 & op(e1, e1) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | ALPHA: (654) implies:
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (655)  op(e1, e1) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (655), (function-axioms) are
% 143.95/20.01  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (656)  all_56_11 = e2 & op(e1, e0) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | ALPHA: (656) implies:
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (657)  all_56_11 = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (658)  op(e1, e0) = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 143.95/20.01  | | | | | | | | | | | | | | | | |              e2, e1, e0, simplifying with (156), (647) gives:
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (659)  all_52_11 = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 143.95/20.01  | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (159), (658) gives:
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (660)  all_52_14 = e2
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | REDUCE: (124), (659) imply:
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (661)   ~ (all_52_7 = e2)
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | REDUCE: (370), (660) imply:
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (662)   ~ (all_10_2 = e2)
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | REDUCE: (366), (660) imply:
% 143.95/20.01  | | | | | | | | | | | | | | | | |   (663)   ~ (all_4_2 = e2)
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 143.95/20.01  | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | |   (664)   ~ (all_44_2 = e2)
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | REDUCE: (640), (664) imply:
% 143.95/20.01  | | | | | | | | | | | | | | | | | |   (665)  $false
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | | CLOSE: (665) is inconsistent.
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.01  | | | | | | | | | | | | | | | | | | 
% 143.95/20.01  | | | | | | | | | | | | | | | | | |   (666)  ( ~ (all_44_0 = e0) & op(all_44_1, e3) = all_44_0
% 143.95/20.02  | | | | | | | | | | | | | | | | | |            & op(e3, e2) = all_44_1 & $i(all_44_0) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | |            $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e3, e2)
% 143.95/20.02  | | | | | | | | | | | | | | | | | |            = all_44_1 & $i(all_44_1))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | |   (667)   ~ (all_42_2 = e3)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | REDUCE: (302), (667) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | |   (668)   ~ (all_10_2 = e3)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | |   (669)  all_54_15 = e3
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (668), (669) are inconsistent by sub-proof
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | |            #1049.
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | |   (670)   ~ (all_54_15 = e3)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | |   (671)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | BETA: splitting (671) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | |   (672)  all_54_15 = e2
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (398), (672) are inconsistent by sub-proof
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | |            #1048.
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | |   (673)   ~ (all_54_15 = e2)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | |   (674)  all_54_15 = e1 | all_54_15 = e0
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (674) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | |   (675)  all_54_15 = e1
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (375), (675) are inconsistent by sub-proof
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | |            #1047.
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | |   (676)  all_54_15 = e0
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (676) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | |   (677)  all_10_2 = e0
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | SIMP: (677) implies:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | |   (678)  all_10_2 = e0
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (678) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | |   (679)   ~ (all_52_3 = e0)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (678) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | |   (680)   ~ (all_52_7 = e0)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (668), (678) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | |   (681)   ~ (e3 = e0)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (398), (678) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | |   (682)   ~ (e2 = e0)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (678) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | |   (683)   ~ (e1 = e0)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (678) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | |   (684)  op(e0, e0) = e0
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | |   (685)   ~ (all_48_2 = e0)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (298), (685) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | |   (686)   ~ (all_4_2 = e0)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | |   (687)  all_54_10 = e3
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (687) are inconsistent by sub-proof
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | |            #1173.
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | |   (688)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (688) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (689)  all_54_10 = e2
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (689) are inconsistent by sub-proof
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | |            #1168.
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (690)   ~ (all_54_10 = e2)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | |   (691)  all_54_10 = e1 | all_54_10 = e0
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (691) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (692)  all_54_10 = e1
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (692) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (693)  all_4_2 = e1
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (693) implies:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (694)  all_4_2 = e1
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (694) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (695)   ~ (all_52_2 = e1)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (694) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (696)   ~ (all_52_6 = e1)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (694) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (697)   ~ (e2 = e1)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (694) imply:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | |   (698)  op(e1, e1) = e1
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (699)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (699) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (700)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (700) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (701)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (388), (701), (function-axioms) are
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (702)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (162), (684), (695), (702), (function-axioms)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1045.
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (703)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (703) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (704)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (704) gives:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (705)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (705) implies:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (706)  op(e1, e1) = e2
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (698), (706), (function-axioms) are
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (707)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (707) implies:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (708)  op(e0, e0) = e2
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (684), (708), (function-axioms) are
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (709)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 143.95/20.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (709) gives:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (710)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (710) implies:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (711)  op(e1, e2) = e1
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (696), (711), (function-axioms) are
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (712)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (394), (684), (712), (function-axioms)
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1041.
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (713)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_9) & $i(all_57_12)) |
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (713) gives:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (714)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (714) gives:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (715)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (391), (684), (715), (function-axioms)
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1039.
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (716)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (716) gives:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (717)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_12)
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (717) implies:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (718)  op(e0, e0) = e1
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (684), (718), (function-axioms) are
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (719)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (719) gives:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (720)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e0) = all_57_11 & $i(all_57_10) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_11)
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (720) implies:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (721)  op(e2, e2) = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (394), (721), (function-axioms) are
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (722)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_10) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_13)
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (722) implies:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (723)  op(e1, e1) = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (698), (723), (function-axioms) are
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (724)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (724) gives:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (725)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (641), (725), (function-axioms) are
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (726)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (726) gives:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (727)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_13)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (727) implies:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (728)  op(e2, e0) = e2
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (392), (728), (function-axioms) are
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (729)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_7))))
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (729) gives:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (730)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (730) implies:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (731)  op(e1, e0) = e1
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (658), (731), (function-axioms) are
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1125.
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (732)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_6 & op(e0, e1) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_7)))
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (732) implies:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (733)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (733) gives:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (734)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (679), (680), (734),
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1035.
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (735)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (735) gives:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (736)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_4)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (736) implies:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (737)  op(e1, e1) = e2
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (698), (737), (function-axioms) are
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (738)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_7))
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (738) gives:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (739)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_6)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (739) implies:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (740)  op(e0, e1) = e0
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (156), (367), (684), (740),
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1034.
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (741)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_7)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (741) implies:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (742)  op(e2, e2) = e1
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (394), (742), (function-axioms) are
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (743)  all_54_10 = e0
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (686), (743) are inconsistent by sub-proof
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1033.
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | |   (744)  all_48_2 = e0
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (744) imply:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | |   (745)  all_4_2 = e0
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (745) imply:
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | |   (746)   ~ (all_52_6 = e0)
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.04  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (745) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | |   (747)  op(e1, e1) = e0
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |   (748)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_15 & $i(all_57_15)))) |
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_15 & $i(all_57_15))))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (748) gives:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (749)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15)))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (749) implies:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (750)  op(e3, e3) = e3
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (641), (750), (function-axioms) are
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (751)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15)))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (751) implies:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (752)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) & op(e3, e3) = all_57_10 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (157), (161), (169), (224), (394),
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (641), (680), (746), (752), (function-axioms) are
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1027.
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |   (753)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_15 & $i(all_57_15)))) |
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14))))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (753) gives:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (754)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15)))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (754) implies:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (755)  op(e1, e1) = e1
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (747), (755), (function-axioms) are
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (756)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_14)))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (756) implies:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (757)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (757) gives:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (758)  all_57_13 = e1 & op(e1, e0) = e1
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (758) implies:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (759)  op(e1, e0) = e1
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (658), (759), (function-axioms) are
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1125.
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (760)   ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_14)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (760) implies:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (761)   ~ (all_57_14 = e0)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (762)  op(e1, e1) = all_57_14
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (747), (761), (762), (function-axioms) are
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1026.
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | |   (763)  all_42_2 = e3
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (763) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | |   (764)  all_10_2 = e3
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | SIMP: (764) implies:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | |   (765)  all_10_2 = e3
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | REDUCE: (349), (765) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | |   (766)   ~ (all_52_3 = e3)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | REDUCE: (368), (765) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | |   (767)   ~ (all_52_12 = e3)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | REDUCE: (45), (765) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | |   (768)  op(e0, e0) = e3
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | |   (769)   ~ (all_48_2 = e0)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | REDUCE: (298), (769) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | |   (770)   ~ (all_4_2 = e0)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | |   (771)  all_54_10 = e3
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (771) are inconsistent by sub-proof
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | |            #1173.
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | |   (772)   ~ (all_54_10 = e3)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | |   (773)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (773) gives:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | |   (774)  all_54_10 = e2
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (774) are inconsistent by sub-proof
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | |            #1168.
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | |   (775)   ~ (all_54_10 = e2)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | |   (776)  all_54_10 = e1 | all_54_10 = e0
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (776) gives:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | |   (777)  all_54_10 = e1
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (777) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | |   (778)  all_4_2 = e1
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (778) implies:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | |   (779)  all_4_2 = e1
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (779) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | |   (780)   ~ (all_52_2 = e1)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (779) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | |   (781)   ~ (all_52_6 = e1)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (779) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | |   (782)   ~ (e3 = e1)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (779) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | |   (783)   ~ (e2 = e1)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (779) imply:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | |   (784)  op(e1, e1) = e1
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |   (785)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (786)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.95/20.05  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (786) gives:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (787)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (388), (787), (function-axioms) are
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (788)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (780), (788), (function-axioms) are
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1025.
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (789)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (789) gives:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (790)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (768), (784), (790),
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1024.
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (791)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (791) gives:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (792)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (792) implies:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (793)  op(e1, e2) = e1
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (781), (793), (function-axioms) are
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (794)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (394), (768), (794), (function-axioms)
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1023.
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |   (795)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_9) & $i(all_57_12)) |
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |              = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (795) gives:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (796)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (796) gives:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (797)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (391), (768), (797), (function-axioms)
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1021.
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (798)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (767), (768), (798), (function-axioms)
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1020.
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |   (799)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (799) gives:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (800)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (641), (800), (function-axioms) are
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |   (801)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (801) gives:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (802)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_13)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (802) implies:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (803)  op(e2, e0) = e2
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (392), (803), (function-axioms) are
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (804)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_7))))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (804) gives:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (805)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (805) implies:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (806)  op(e1, e0) = e1
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (658), (806), (function-axioms) are
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1125.
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (807)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_6 & op(e0, e1) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_7)))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (807) implies:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (808)  op(e0, e0) = all_57_15
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (809)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (809) gives:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (810)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (810) gives:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (811)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_0)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (811) implies:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (812)   ~ (all_57_15 = e3)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (768), (808), (812), (function-axioms) are
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1019.
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (813)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & $i(all_57_3))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (813) gives:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (814)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_1)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (814) implies:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (815)   ~ (all_57_15 = e3)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (768), (808), (815), (function-axioms) are
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1019.
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (816)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_3)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (816) implies:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (817)  all_57_10 = e2
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (818)   ~ (all_57_3 = e3)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (819)  op(e0, e2) = e0
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (820)  op(e3, e2) = all_57_3
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (821)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_15 & $i(all_57_15)))) |
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_15 & $i(all_57_15))))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (821) gives:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (822)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15)))
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (822) implies:
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (823)  op(e3, e3) = e3
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.07  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (371), (374), (394), (809),
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (823), (function-axioms) are inconsistent by
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1075.
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (824)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15)))
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (824) implies:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (825)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2) & op(e3, e3) = all_57_10 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (817), (818), (825) are inconsistent by sub-proof
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1018.
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (826)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_15 & $i(all_57_15)))) |
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14))))
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (826) gives:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (827)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15)))
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (827) implies:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (828)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12))
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (828) gives:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (829)  all_57_7 = e2 & op(e2, e1) = e2
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (829) implies:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (830)  op(e2, e1) = e2
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (391), (830), (function-axioms) are
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (831)   ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_12)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (831) implies:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (832)   ~ (all_57_12 = e1)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (833)  op(e2, e2) = all_57_12
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (157), (819) gives:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (834)  all_52_7 = e0
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (394), (833)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (835)  all_57_12 = e2
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_3, e2, e3, simplifying with (169), (820)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (836)  all_57_3 = all_52_4
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (834) imply:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (837)   ~ (all_52_4 = e0)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (834) imply:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (838)   ~ (all_52_6 = e0)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (661), (834) imply:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (839)   ~ (e2 = e0)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (840)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (840) gives:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (841)  all_56_1 = e1 & op(e3, e2) = e1
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (841) implies:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (842)  op(e3, e2) = e1
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (161), (212), (657), (666), (784),
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (838), (842), (function-axioms) are inconsistent
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1015.
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (843)  all_56_3 = e1 & op(e2, e2) = e1
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (843) implies:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (844)  op(e2, e2) = e1
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (832), (833), (844), (function-axioms) are
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (845)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (161), (169), (224), (394), (781),
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (837), (838), (845), (function-axioms) are
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1009.
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (846)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_14)))
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (846) implies:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (847)  op(e0, e0) = e0
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (768), (847), (function-axioms) are
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (848)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (848) gives:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (849)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_4)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (849) implies:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (850)  op(e1, e1) = e2
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (784), (850), (function-axioms) are
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (851)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_7))
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (394), (647), (851), (function-axioms)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1007.
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | |   (852)  all_54_10 = e0
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (770), (852) are inconsistent by sub-proof
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | |            #1033.
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | |   (853)  all_48_2 = e0
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (853) imply:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | |   (854)  all_4_2 = e0
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (854) imply:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | |   (855)   ~ (e3 = e0)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (854) imply:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | |   (856)   ~ (e2 = e0)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (854) imply:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | |   (857)  op(e1, e1) = e0
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |   (858)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_15 & $i(all_57_15)))) |
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                  e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_15 & $i(all_57_15))))
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (858) gives:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | |   (859)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | |          ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | |              = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15)))
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (859) implies:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | |   (860)  op(e3, e3) = e3
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (641), (860), (function-axioms) are
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.08  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |   (861)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |          ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |              = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15)))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (861) implies:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |   (862)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |              = e2) & op(e1, e1) = all_57_14 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |   (863)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |              = e2) & op(e3, e3) = all_57_10 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (863) gives:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | |   (864)  all_57_3 = e3 & op(e3, e2) = e3
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (864) implies:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | |   (865)  all_57_3 = e3
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |   (866)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (866) gives:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (867)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (867) gives:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (868)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (388), (868), (function-axioms) are
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (869)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (869) gives:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (870)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = all_57_14 & $i(all_57_0) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_14)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (870) implies:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (871)  op(e2, e2) = e3
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (394), (871), (function-axioms) are
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (872)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (872) implies:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (873)   ~ (all_57_2 = e0)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (874)  op(e0, e3) = all_57_2
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (875)  op(e1, e3) = e1
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_2, e3, e0, simplifying with (158), (874)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (876)  all_57_2 = all_52_3
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (875) gives:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (877)  all_52_2 = e1
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (873), (876) imply:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (878)   ~ (all_52_3 = e0)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (877) imply:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (879)   ~ (all_52_3 = e1)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (879) implies:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (880)   ~ (all_52_3 = e1)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (138), (156), (191), (248), (647), (766), (878),
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (880), (function-axioms) are inconsistent by
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1088.
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (881)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (881) gives:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (882)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (882) gives:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (883)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (883) implies:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (884)  op(e1, e1) = e2
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (857), (884), (function-axioms) are
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (885)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (885) implies:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (886)  op(e0, e0) = e2
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (768), (886), (function-axioms) are
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (887)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (887) gives:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (888)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (888) implies:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (889)  all_57_10 = e2
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (890)   ~ (all_57_3 = e3)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (863), (889), (890) are inconsistent by sub-proof
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1018.
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (891)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (394), (768), (891), (function-axioms)
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1023.
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |   (892)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_9) & $i(all_57_12)) |
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |              = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (892) gives:
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (893)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (893) gives:
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (894)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (391), (768), (894), (function-axioms)
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1021.
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (895)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (767), (768), (895), (function-axioms)
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1020.
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (896)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (896) gives:
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (897)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (641), (897), (function-axioms) are
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (898)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 143.95/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (898) gives:
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (899)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_13)
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (899) implies:
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (900)  op(e2, e0) = e2
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (392), (900), (function-axioms) are
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (901)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_7))))
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (394), (647), (658), (768), (862),
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (865), (901), (function-axioms) are inconsistent
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1002.
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | |   (902)   ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (902) implies:
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | |   (903)   ~ (all_57_10 = e2)
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | |   (904)  op(e3, e3) = all_57_10
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (641), (903), (904), (function-axioms) are
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1031.
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.10  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |   (905)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                  e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                  e0) = all_57_15 & $i(all_57_15)))) |
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14))))
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (768), (857), (905), (function-axioms)
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1001.
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.11  | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | End of split
% 144.36/20.11  | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | End of split
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | End of split
% 144.36/20.11  | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | End of split
% 144.36/20.11  | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | End of split
% 144.36/20.11  | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | End of split
% 144.36/20.11  | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | Case 2:
% 144.36/20.11  | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | |   (906)  all_24_2 = e2
% 144.36/20.11  | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | COMBINE_EQS: (318), (906) imply:
% 144.36/20.11  | | | | | | | | | | | |   (907)  all_10_2 = e2
% 144.36/20.11  | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | SIMP: (907) implies:
% 144.36/20.11  | | | | | | | | | | | |   (908)  all_10_2 = e2
% 144.36/20.11  | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | COMBINE_EQS: (306), (908) imply:
% 144.36/20.11  | | | | | | | | | | | |   (909)  all_40_2 = e2
% 144.36/20.11  | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | REDUCE: (360), (908) imply:
% 144.36/20.11  | | | | | | | | | | | |   (910)   ~ (all_52_7 = e2)
% 144.36/20.11  | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | REDUCE: (367), (908) imply:
% 144.36/20.11  | | | | | | | | | | | |   (911)   ~ (all_52_11 = e2)
% 144.36/20.11  | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | REDUCE: (370), (908) imply:
% 144.36/20.11  | | | | | | | | | | | |   (912)   ~ (all_52_14 = e2)
% 144.36/20.11  | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | REDUCE: (45), (908) imply:
% 144.36/20.11  | | | | | | | | | | | |   (913)  op(e0, e0) = e2
% 144.36/20.11  | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | BETA: splitting (218) gives:
% 144.36/20.11  | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | Case 1:
% 144.36/20.11  | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | |   (914)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 144.36/20.11  | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 144.36/20.11  | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | BETA: splitting (914) gives:
% 144.36/20.11  | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | Case 1:
% 144.36/20.11  | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | |   (915)  all_56_4 = e2 & op(e3, e1) = e2
% 144.36/20.11  | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | ALPHA: (915) implies:
% 144.36/20.11  | | | | | | | | | | | | | |   (916)  all_56_4 = e2
% 144.36/20.11  | | | | | | | | | | | | | |   (917)  op(e3, e1) = e2
% 144.36/20.11  | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 144.36/20.11  | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | Case 1:
% 144.36/20.11  | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | |   (918)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 144.36/20.11  | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 144.36/20.11  | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | BETA: splitting (918) gives:
% 144.36/20.11  | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | Case 1:
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | |   (919)  all_56_6 = e2 & op(e1, e3) = e2
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | ALPHA: (919) implies:
% 144.36/20.11  | | | | | | | | | | | | | | | |   (920)  all_56_6 = e2
% 144.36/20.11  | | | | | | | | | | | | | | | |   (921)  op(e1, e3) = e2
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 144.36/20.11  | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (921) gives:
% 144.36/20.11  | | | | | | | | | | | | | | | |   (922)  all_52_2 = e2
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 144.36/20.11  | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (917) gives:
% 144.36/20.11  | | | | | | | | | | | | | | | |   (923)  all_52_8 = e2
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | REDUCE: (142), (922) imply:
% 144.36/20.11  | | | | | | | | | | | | | | | |   (924)   ~ (all_52_6 = e2)
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | REDUCE: (122), (923) imply:
% 144.36/20.11  | | | | | | | | | | | | | | | |   (925)   ~ (all_52_9 = e2)
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | REDUCE: (344), (923) imply:
% 144.36/20.11  | | | | | | | | | | | | | | | |   (926)   ~ (all_14_2 = e2)
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | SIMP: (926) implies:
% 144.36/20.11  | | | | | | | | | | | | | | | |   (927)   ~ (all_14_2 = e2)
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | REDUCE: (361), (923) imply:
% 144.36/20.11  | | | | | | | | | | | | | | | |   (928)   ~ (all_4_2 = e2)
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 144.36/20.11  | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.11  | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | |   (929)  all_54_0 = e3
% 144.36/20.11  | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (929) imply:
% 144.36/20.11  | | | | | | | | | | | | | | | | |   (930)  all_14_2 = e3
% 144.36/20.11  | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | REDUCE: (342), (930) imply:
% 144.36/20.11  | | | | | | | | | | | | | | | | |   (931)   ~ (all_52_4 = e3)
% 144.36/20.11  | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | REDUCE: (346), (930) imply:
% 144.36/20.11  | | | | | | | | | | | | | | | | |   (932)   ~ (all_52_12 = e3)
% 144.36/20.11  | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | REDUCE: (51), (930) imply:
% 144.36/20.11  | | | | | | | | | | | | | | | | |   (933)  op(e3, e3) = e3
% 144.36/20.11  | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 144.36/20.11  | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | |   (934)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.36/20.11  | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.36/20.11  | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 144.36/20.11  | | | | | | | | | | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 144.36/20.11  | | | | | | | | | | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 144.36/20.11  | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.36/20.11  | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | BETA: splitting (934) gives:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |   (935)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (388), (394), (913), (935),
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            #1000.
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |   (936)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | BETA: splitting (936) gives:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |   (937)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10))
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (371), (931), (937),
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            #1086.
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |   (938)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | BETA: splitting (938) gives:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |   (939)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |            e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | ALPHA: (939) implies:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |   (940)  op(e3, e3) = e2
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (933), (940), (function-axioms) are
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |   (941)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (941) gives:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | |   (942)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | |          op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (942) implies:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | |   (943)   ~ (all_57_5 = e0)
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | |   (944)  op(e0, e2) = all_57_5
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | |   (945)  op(e1, e2) = e1
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | |              all_57_5, e2, e0, simplifying with (157), (944)
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | |   (946)  all_57_5 = all_52_7
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 144.36/20.11  | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (161), (945) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |   (947)  all_52_6 = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (943), (946) imply:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |   (948)   ~ (all_52_7 = e0)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (947) imply:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |   (949)   ~ (all_52_4 = e1)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (947) imply:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |   (950)   ~ (all_52_7 = e1)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | SIMP: (950) implies:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |   (951)   ~ (all_52_7 = e1)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (390), (947) imply:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |   (952)   ~ (e2 = e1)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | |   (953)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (953) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | |   (954)  all_56_0 = e1 & op(e3, e3) = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (954) implies:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | |   (955)  op(e3, e3) = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (167), (169), (235), (916), (931),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | |            (932), (955), (function-axioms) are inconsistent
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #998.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | |   (956)  all_56_1 = e1 & op(e3, e2) = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (956) implies:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | |   (957)  all_56_1 = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (958)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (394), (931), (958), (function-axioms)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1165.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (959)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (959) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (960)  all_56_7 = e3 & op(e1, e2) = e3
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (124), (132), (134), (156), (157),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (167), (169), (190), (202), (208), (224),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (230), (232), (235),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (271), (389), (394), (910), (913), (916),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (920), (932), (933), (948), (949), (951), (960),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            #981.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (961)  all_56_13 = e3 & op(e0, e2) = e3
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (961) implies:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (962)  all_56_13 = e3
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (963)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (963) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (964)  all_56_1 = e0 & op(e3, e2) = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (964) implies:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (965)  all_56_1 = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (957), (965) are inconsistent by sub-proof
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1107.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (966)  all_56_3 = e0 & op(e2, e2) = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (966) implies:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (967)  op(e2, e2) = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (394), (967), (function-axioms) are
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (968)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (968) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (969)  all_56_7 = e0 & op(e1, e2) = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (969) implies:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (970)  all_56_7 = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (132), (167), (202), (225), (229),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (271), (389), (394), (916), (931), (933), (949),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (962), (970), (function-axioms) are inconsistent
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #985.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (971)  all_56_13 = e0 & op(e0, e2) = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (971) implies:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (972)  op(e0, e2) = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (948), (972), (function-axioms) are
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | |   (973)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (973) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | |   (974)  all_56_4 = e1 & op(e3, e1) = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (974) implies:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | |   (975)  all_56_4 = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (916), (975) are inconsistent by sub-proof
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | |            #980.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | |   (976)  all_56_9 = e1 & op(e3, e0) = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (976) implies:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | |   (977)  op(e3, e0) = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (978)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (394), (931), (978), (function-axioms)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1165.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (979)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (979) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (980)  all_56_7 = e3 & op(e1, e2) = e3
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (124), (132), (134), (156), (157),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (167), (169), (190), (202), (208), (224),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (230), (232), (235),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (271), (389), (394), (910), (913), (916),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (920), (932), (933), (948), (949), (951), (980),
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            #981.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (981)  all_56_13 = e3 & op(e0, e2) = e3
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (909), (977), (981), (function-axioms) are
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #979.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |   (982)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (982) implies:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |   (983)  op(e2, e2) = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (394), (983), (function-axioms) are
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.12  | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | |   (984)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.36/20.12  | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.36/20.12  | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.36/20.12  | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_9) & $i(all_57_12)) |
% 144.36/20.12  | | | | | | | | | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 144.36/20.12  | | | | | | | | | | | | | | | | | |          | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 144.36/20.12  | | | | | | | | | | | | | | | | | |              = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.36/20.12  | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.36/20.12  | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.36/20.12  | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | BETA: splitting (984) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |   (985)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.36/20.12  | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (985) gives:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.12  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |   (986)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (391), (913), (986), (function-axioms)
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #977.
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |   (987)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (913), (932), (987), (function-axioms)
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #976.
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |   (988)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | BETA: splitting (988) gives:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |   (989)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (933), (989), (function-axioms) are
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |   (990)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | BETA: splitting (990) gives:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |   (991)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |          $i(all_57_13)
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (991) implies:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |   (992)  op(e2, e0) = e2
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (392), (992), (function-axioms) are
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |   (993)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_7))))
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (993) gives:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |   (994)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (994) implies:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |   (995)  op(e2, e2) = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (394), (995), (function-axioms) are
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |   (996)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |          ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_6 & op(e0, e1) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_7)))
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (996) implies:
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |   (997)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (371), (374), (394), (933),
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            (997), (function-axioms) are inconsistent by
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1075.
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.13  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.13  | | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | End of split
% 144.36/20.13  | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.13  | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | |   (998)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 144.36/20.13  | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (376), (396), (927), (998) are inconsistent
% 144.36/20.13  | | | | | | | | | | | | | | | | |            by sub-proof #1140.
% 144.36/20.13  | | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | End of split
% 144.36/20.13  | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | Case 2:
% 144.36/20.13  | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | |   (999)  all_56_7 = e2 & op(e1, e2) = e2
% 144.36/20.13  | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | ALPHA: (999) implies:
% 144.36/20.13  | | | | | | | | | | | | | | | |   (1000)  op(e1, e2) = e2
% 144.36/20.13  | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | | REF_CLOSE: (161), (390), (1000), (function-axioms) are
% 144.36/20.13  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1171.
% 144.36/20.13  | | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | End of split
% 144.36/20.13  | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | Case 2:
% 144.36/20.13  | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | |   (1001)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 144.36/20.13  | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 144.36/20.13  | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | | REF_CLOSE: (36), (159), (371), (912), (1001),
% 144.36/20.13  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.13  | | | | | | | | | | | | | | |            #973.
% 144.36/20.13  | | | | | | | | | | | | | | | 
% 144.36/20.13  | | | | | | | | | | | | | | End of split
% 144.36/20.13  | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | Case 2:
% 144.36/20.14  | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | |   (1002)  all_56_5 = e2 & op(e2, e1) = e2
% 144.36/20.14  | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | ALPHA: (1002) implies:
% 144.36/20.14  | | | | | | | | | | | | | |   (1003)  op(e2, e1) = e2
% 144.36/20.14  | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | REF_CLOSE: (164), (391), (1003), (function-axioms) are
% 144.36/20.14  | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 144.36/20.14  | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | End of split
% 144.36/20.14  | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | Case 2:
% 144.36/20.14  | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | |   (1004)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 144.36/20.14  | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 144.36/20.14  | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | REF_CLOSE: (36), (156), (371), (911), (1004),
% 144.36/20.14  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.14  | | | | | | | | | | | | |            #972.
% 144.36/20.14  | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | End of split
% 144.36/20.14  | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | End of split
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | Case 2:
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | |   (1005)  all_22_2 = e1
% 144.36/20.14  | | | | | | | | | | |   (1006)  ( ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0
% 144.36/20.14  | | | | | | | | | | |             & op(e3, e1) = all_22_1 & $i(all_22_0) &
% 144.36/20.14  | | | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e1)
% 144.36/20.14  | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | COMBINE_EQS: (320), (1005) imply:
% 144.36/20.14  | | | | | | | | | | |   (1007)  all_14_2 = e1
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | SIMP: (1007) implies:
% 144.36/20.14  | | | | | | | | | | |   (1008)  all_14_2 = e1
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | COMBINE_EQS: (312), (1008) imply:
% 144.36/20.14  | | | | | | | | | | |   (1009)  all_34_2 = e1
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | REDUCE: (338), (1008) imply:
% 144.36/20.14  | | | | | | | | | | |   (1010)   ~ (all_52_2 = e1)
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | REDUCE: (340), (1008) imply:
% 144.36/20.14  | | | | | | | | | | |   (1011)   ~ (all_52_3 = e1)
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | REDUCE: (342), (1008) imply:
% 144.36/20.14  | | | | | | | | | | |   (1012)   ~ (all_52_4 = e1)
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | REDUCE: (344), (1008) imply:
% 144.36/20.14  | | | | | | | | | | |   (1013)   ~ (all_52_8 = e1)
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | REDUCE: (346), (1008) imply:
% 144.36/20.14  | | | | | | | | | | |   (1014)   ~ (all_52_12 = e1)
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | REDUCE: (51), (1008) imply:
% 144.36/20.14  | | | | | | | | | | |   (1015)  op(e3, e3) = e1
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | BETA: splitting (67) gives:
% 144.36/20.14  | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | Case 1:
% 144.36/20.14  | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | |   (1016)   ~ (all_24_2 = e2)
% 144.36/20.14  | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | REDUCE: (318), (1016) imply:
% 144.36/20.14  | | | | | | | | | | | |   (1017)   ~ (all_10_2 = e2)
% 144.36/20.14  | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | BETA: splitting (81) gives:
% 144.36/20.14  | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | Case 1:
% 144.36/20.14  | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | |   (1018)   ~ (all_34_2 = e1)
% 144.36/20.14  | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | REDUCE: (1009), (1018) imply:
% 144.36/20.14  | | | | | | | | | | | | |   (1019)  $false
% 144.36/20.14  | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | CLOSE: (1019) is inconsistent.
% 144.36/20.14  | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | Case 2:
% 144.36/20.14  | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | |   (1020)  ( ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0
% 144.36/20.14  | | | | | | | | | | | | |             & op(e3, e1) = all_34_1 & $i(all_34_0) &
% 144.36/20.14  | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e3, e1)
% 144.36/20.14  | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 144.36/20.14  | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | BETA: splitting (93) gives:
% 144.36/20.14  | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | Case 1:
% 144.36/20.14  | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | |   (1021)   ~ (all_42_2 = e3)
% 144.36/20.14  | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | REDUCE: (302), (1021) imply:
% 144.36/20.14  | | | | | | | | | | | | | |   (1022)   ~ (all_10_2 = e3)
% 144.36/20.14  | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 144.36/20.14  | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | Case 1:
% 144.36/20.14  | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | |   (1023)  all_54_15 = e3
% 144.36/20.14  | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | REF_CLOSE: (245), (1022), (1023) are inconsistent by
% 144.36/20.14  | | | | | | | | | | | | | | |            sub-proof #1049.
% 144.36/20.14  | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | Case 2:
% 144.36/20.14  | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | |   (1024)   ~ (all_54_15 = e3)
% 144.36/20.14  | | | | | | | | | | | | | | |   (1025)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 144.36/20.14  | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | BETA: splitting (1025) gives:
% 144.36/20.14  | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | Case 1:
% 144.36/20.14  | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | |   (1026)  all_54_15 = e2
% 144.36/20.14  | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | REF_CLOSE: (245), (1017), (1026) are inconsistent by
% 144.36/20.14  | | | | | | | | | | | | | | | |            sub-proof #1048.
% 144.36/20.14  | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | Case 2:
% 144.36/20.14  | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | |   (1027)   ~ (all_54_15 = e2)
% 144.36/20.14  | | | | | | | | | | | | | | | |   (1028)  all_54_15 = e1 | all_54_15 = e0
% 144.36/20.14  | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | BETA: splitting (1028) gives:
% 144.36/20.14  | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | |   (1029)  all_54_15 = e1
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (375), (1029) are inconsistent by sub-proof
% 144.36/20.14  | | | | | | | | | | | | | | | | |            #1047.
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | |   (1030)  all_54_15 = e0
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1030) imply:
% 144.36/20.14  | | | | | | | | | | | | | | | | |   (1031)  all_10_2 = e0
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | SIMP: (1031) implies:
% 144.36/20.14  | | | | | | | | | | | | | | | | |   (1032)  all_10_2 = e0
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | REDUCE: (349), (1032) imply:
% 144.36/20.14  | | | | | | | | | | | | | | | | |   (1033)   ~ (all_52_3 = e0)
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | REDUCE: (360), (1032) imply:
% 144.36/20.14  | | | | | | | | | | | | | | | | |   (1034)   ~ (all_52_7 = e0)
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | REDUCE: (367), (1032) imply:
% 144.36/20.14  | | | | | | | | | | | | | | | | |   (1035)   ~ (all_52_11 = e0)
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | REDUCE: (1022), (1032) imply:
% 144.36/20.14  | | | | | | | | | | | | | | | | |   (1036)   ~ (e3 = e0)
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | REDUCE: (1017), (1032) imply:
% 144.36/20.14  | | | | | | | | | | | | | | | | |   (1037)   ~ (e2 = e0)
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | REDUCE: (375), (1032) imply:
% 144.36/20.14  | | | | | | | | | | | | | | | | |   (1038)   ~ (e1 = e0)
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | REDUCE: (45), (1032) imply:
% 144.36/20.14  | | | | | | | | | | | | | | | | |   (1039)  op(e0, e0) = e0
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 144.36/20.14  | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | |   (1040)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.36/20.14  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.36/20.14  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 144.36/20.14  | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 144.36/20.14  | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 144.36/20.14  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.36/20.14  | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | BETA: splitting (1040) gives:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |   (1041)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (1041) gives:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |   (1042)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (388), (1042), (function-axioms) are
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |   (1043)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (162), (1010), (1039), (1043),
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |            #1045.
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |   (1044)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (1044) gives:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |   (1045)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1045) gives:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |   (1046)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1046) implies:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |   (1047)  op(e1, e1) = e2
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (1047), (function-axioms) are
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |   (1048)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1048) implies:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |   (1049)  op(e0, e0) = e2
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1039), (1049), (function-axioms) are
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.14  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |   (1050)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (394), (1015), (1039), (1050),
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |            #971.
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.15  | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | |   (1051)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.36/20.15  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.36/20.15  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.36/20.15  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 144.36/20.15  | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 144.36/20.15  | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 144.36/20.15  | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.36/20.15  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.36/20.15  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.36/20.15  | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | BETA: splitting (1051) gives:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |   (1052)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | BETA: splitting (1052) gives:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |   (1053)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (391), (1039), (1053),
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |            #1039.
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |   (1054)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1054) gives:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |   (1055)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1055) implies:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |   (1056)  op(e0, e0) = e1
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1039), (1056), (function-axioms) are
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |   (1057)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1057) gives:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |   (1058)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1058) implies:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |   (1059)  op(e2, e2) = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (394), (1059), (function-axioms) are
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |   (1060)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1060) implies:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |   (1061)   ~ (all_57_13 = e1)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |   (1062)   ~ (all_57_10 = e0)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |   (1063)  op(e1, e0) = all_57_13
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |   (1064)  op(e1, e1) = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |   (1065)  op(e3, e0) = e3
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | |   (1066)  op(e3, e3) = all_57_10
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |   (1067)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1067) gives:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |   (1068)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1068) implies:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |   (1069)  op(e3, e3) = e3
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1015), (1069), (function-axioms) are
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |   (1070)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1070) implies:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |   (1071)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e0, e0) = all_57_15 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1071) gives:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (1072)  all_57_5 = e0 & op(e0, e2) = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1072) implies:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (1073)  op(e0, e2) = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1034), (1073), (function-axioms) are
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (1074)   ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_15)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1074) implies:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (1075)  op(e0, e0) = all_57_15
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (1039), (1075)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (1076)  all_57_15 = e0
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13, e0, e1, simplifying with (159), (1063)
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (1077)  all_57_13 = all_52_14
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0,
% 144.36/20.15  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (1064) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (1078)  all_4_2 = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (167), (1065) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (1079)  all_52_12 = e3
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (1015), (1066)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (1080)  all_57_10 = e1
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1061), (1077) imply:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (1081)   ~ (all_52_14 = e1)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (1079) imply:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (1082)   ~ (all_52_4 = e3)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1079) imply:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (1083)   ~ (all_52_8 = e3)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1078) imply:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (1084)   ~ (all_52_9 = e0)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1085)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1085) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1086)  all_56_9 = e1 & op(e3, e0) = e1
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1014), (1086), (function-axioms) are
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #970.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1087)  all_56_10 = e1 & op(e2, e0) = e1
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1087) implies:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1088)  all_56_10 = e1
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1089)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (1015), (1082), (1089),
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #999.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1090)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1090) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1091)  all_56_4 = e3 & op(e3, e1) = e3
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1091) implies:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1092)  op(e3, e1) = e3
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1083), (1092), (function-axioms) are
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1093)  all_56_9 = e3 & op(e3, e0) = e3
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1093) implies:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1094)  all_56_9 = e3
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1095)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1095) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1096)  all_56_2 = e0 & op(e2, e3) = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1096) implies:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1097)  op(e2, e3) = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1098)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (169), (389), (1015), (1098),
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #968.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1099)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1099) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1100)  all_56_4 = e2 & op(e3, e1) = e2
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1100) implies:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1101)  op(e3, e1) = e2
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1006), (1020), (1097), (1101), (function-axioms)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #965.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1102)  all_56_9 = e2 & op(e3, e0) = e2
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1102) implies:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1103)  all_56_9 = e2
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1094), (1103) are inconsistent by sub-proof
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #964.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1104)  all_56_3 = e0 & op(e2, e2) = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1104) implies:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1105)  op(e2, e2) = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (394), (1105), (function-axioms) are
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1106)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (1084), (1088), (1106),
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #962.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1107)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (1039), (1081), (1107),
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            #960.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |   (1108)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1061), (1064), (1108), (function-axioms) are
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |   (1109)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (1109) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |   (1110)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1015), (1110), (function-axioms) are
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |   (1111)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1111) gives:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | |   (1112)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1112) implies:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | |   (1113)  op(e2, e0) = e2
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (392), (1113), (function-axioms) are
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.16  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |   (1114)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1114) gives:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |   (1115)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1115) implies:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |   (1116)  op(e2, e2) = e0
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (394), (1116), (function-axioms) are
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |   (1117)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1117) implies:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |   (1118)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1118) gives:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |   (1119)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (158), (1015), (1033), (1119),
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |            #955.
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |   (1120)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1120) gives:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |   (1121)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1121) implies:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |   (1122)  op(e1, e1) = e2
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (1122), (function-axioms) are
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |   (1123)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (156), (394), (1035), (1123),
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | |            #954.
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.17  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.17  | | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | End of split
% 144.36/20.17  | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | End of split
% 144.36/20.17  | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | End of split
% 144.36/20.17  | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | End of split
% 144.36/20.17  | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | Case 2:
% 144.36/20.17  | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | |   (1124)  all_42_2 = e3
% 144.36/20.17  | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | COMBINE_EQS: (302), (1124) imply:
% 144.36/20.17  | | | | | | | | | | | | | |   (1125)  all_10_2 = e3
% 144.36/20.17  | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | SIMP: (1125) implies:
% 144.36/20.17  | | | | | | | | | | | | | |   (1126)  all_10_2 = e3
% 144.36/20.17  | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | REDUCE: (367), (1126) imply:
% 144.36/20.17  | | | | | | | | | | | | | |   (1127)   ~ (all_52_11 = e3)
% 144.36/20.17  | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | REDUCE: (368), (1126) imply:
% 144.36/20.17  | | | | | | | | | | | | | |   (1128)   ~ (all_52_12 = e3)
% 144.36/20.17  | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | REDUCE: (45), (1126) imply:
% 144.36/20.17  | | | | | | | | | | | | | |   (1129)  op(e0, e0) = e3
% 144.36/20.17  | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 144.36/20.17  | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | Case 1:
% 144.36/20.17  | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | |   (1130)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.36/20.17  | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.17  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.36/20.17  | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.36/20.17  | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.36/20.17  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.17  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.36/20.17  | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.36/20.17  | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.17  | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.36/20.17  | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.36/20.17  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.36/20.17  | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.36/20.17  | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.36/20.17  | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.17  | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.36/20.17  | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 144.36/20.17  | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 144.36/20.17  | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 144.36/20.17  | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 144.36/20.17  | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 144.36/20.17  | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.36/20.17  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.17  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 144.36/20.17  | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 144.36/20.17  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 144.36/20.17  | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 144.36/20.17  | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 144.36/20.17  | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.17  | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 144.36/20.17  | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 144.36/20.17  | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 144.36/20.17  | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 144.36/20.17  | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 144.36/20.17  | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.36/20.17  | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.36/20.17  | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.17  | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.36/20.17  | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | BETA: splitting (1130) gives:
% 144.36/20.17  | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | Case 1:
% 144.36/20.17  | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | |   (1131)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.36/20.17  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.17  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.36/20.17  | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.36/20.17  | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.36/20.17  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.17  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.36/20.17  | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.36/20.17  | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.17  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.36/20.17  | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.36/20.17  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.36/20.17  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.36/20.17  | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.36/20.17  | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.17  | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.36/20.17  | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.36/20.17  | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | BETA: splitting (1131) gives:
% 144.36/20.17  | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.17  | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | |   (1132)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.36/20.17  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.17  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.36/20.17  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.36/20.17  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.36/20.17  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.36/20.17  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.36/20.17  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.36/20.17  | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (388), (1132), (function-axioms) are
% 144.36/20.17  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 144.36/20.17  | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.17  | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | |   (1133)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.17  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.36/20.17  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.36/20.17  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.36/20.17  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.36/20.17  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.36/20.17  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.17  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.36/20.17  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.36/20.17  | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1010), (1133), (function-axioms) are
% 144.36/20.17  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1025.
% 144.36/20.17  | | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | | End of split
% 144.36/20.17  | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | Case 2:
% 144.36/20.17  | | | | | | | | | | | | | | | | 
% 144.36/20.17  | | | | | | | | | | | | | | | |   (1134)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.17  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.17  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.36/20.17  | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.36/20.17  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.36/20.17  | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.36/20.17  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.36/20.17  | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.36/20.17  | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 144.36/20.17  | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.36/20.17  | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.36/20.17  | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 144.36/20.17  | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 144.36/20.17  | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.36/20.17  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 144.36/20.18  | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.36/20.18  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.36/20.18  | | | | | | | | | | | | | | | |             $i(all_57_10))
% 144.36/20.18  | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | BETA: splitting (1134) gives:
% 144.36/20.18  | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | |   (1135)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.18  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.36/20.18  | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.36/20.18  | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | BETA: splitting (1135) gives:
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.18  | | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | |   (1136)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.18  | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.36/20.18  | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.36/20.18  | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 144.36/20.18  | | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | | ALPHA: (1136) implies:
% 144.36/20.18  | | | | | | | | | | | | | | | | | |   (1137)  op(e1, e1) = e2
% 144.36/20.18  | | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (1137), (function-axioms) are
% 144.36/20.18  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 144.36/20.18  | | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.18  | | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | |   (1138)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.36/20.18  | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 144.36/20.18  | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 144.36/20.18  | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 144.36/20.18  | | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | | ALPHA: (1138) implies:
% 144.36/20.18  | | | | | | | | | | | | | | | | | |   (1139)  op(e0, e0) = e2
% 144.36/20.18  | | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1129), (1139), (function-axioms) are
% 144.36/20.18  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 144.36/20.18  | | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | End of split
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | |   (1140)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 144.36/20.18  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 144.36/20.18  | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 144.36/20.18  | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.36/20.18  | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.18  | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (394), (1015), (1129), (1140),
% 144.36/20.18  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.18  | | | | | | | | | | | | | | | | |            #953.
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | End of split
% 144.36/20.18  | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | End of split
% 144.36/20.18  | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | Case 2:
% 144.36/20.18  | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | |   (1141)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.18  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.36/20.18  | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.18  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.36/20.18  | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.36/20.18  | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.36/20.18  | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.36/20.18  | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.36/20.18  | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.36/20.18  | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.36/20.18  | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.36/20.18  | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.36/20.18  | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.36/20.18  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.36/20.18  | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.36/20.18  | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.36/20.18  | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.36/20.18  | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.36/20.18  | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.36/20.18  | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 144.36/20.18  | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 144.36/20.18  | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 144.36/20.18  | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 144.36/20.18  | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 144.36/20.18  | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 144.36/20.18  | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 144.36/20.18  | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 144.36/20.18  | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 144.36/20.18  | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 144.36/20.18  | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.36/20.18  | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.36/20.18  | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.36/20.18  | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.36/20.18  | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.36/20.18  | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.36/20.18  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.36/20.18  | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.36/20.18  | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.36/20.18  | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.36/20.18  | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.36/20.18  | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.18  | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.36/20.18  | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.36/20.18  | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.36/20.18  | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.36/20.18  | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.36/20.18  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.36/20.18  | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.36/20.18  | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.36/20.18  | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.36/20.18  | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.36/20.18  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.36/20.18  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.36/20.18  | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.36/20.18  | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.36/20.18  | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.18  | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.36/20.18  | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | BETA: splitting (1141) gives:
% 144.36/20.18  | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | Case 1:
% 144.36/20.18  | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | |   (1142)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.18  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.36/20.18  | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.18  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.36/20.18  | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.36/20.18  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.36/20.18  | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.36/20.18  | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.36/20.18  | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.36/20.18  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.36/20.18  | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.36/20.18  | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 144.36/20.18  | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | BETA: splitting (1142) gives:
% 144.36/20.18  | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | |   (1143)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.18  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.36/20.18  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.36/20.18  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.36/20.18  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (391), (1129), (1143),
% 144.36/20.18  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.18  | | | | | | | | | | | | | | | | |            #1021.
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | |   (1144)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.36/20.18  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 144.36/20.18  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 144.36/20.18  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 144.36/20.18  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 144.36/20.18  | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 144.36/20.18  | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 144.36/20.18  | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (1128), (1129), (1144),
% 144.36/20.18  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.18  | | | | | | | | | | | | | | | | |            #1020.
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | End of split
% 144.36/20.18  | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | Case 2:
% 144.36/20.18  | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | |   (1145)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 144.36/20.18  | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 144.36/20.18  | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 144.36/20.18  | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 144.36/20.18  | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 144.36/20.18  | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 144.36/20.18  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 144.36/20.18  | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.36/20.18  | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 144.36/20.18  | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 144.36/20.18  | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 144.36/20.18  | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 144.36/20.18  | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 144.36/20.18  | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 144.36/20.18  | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 144.36/20.18  | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 144.36/20.18  | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 144.36/20.18  | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.36/20.18  | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.36/20.18  | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.36/20.18  | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.36/20.18  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.36/20.18  | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.36/20.18  | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.36/20.18  | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.36/20.18  | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.36/20.18  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.36/20.18  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.36/20.18  | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.36/20.18  | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.36/20.18  | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.36/20.18  | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.18  | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.36/20.18  | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | BETA: splitting (1145) gives:
% 144.36/20.18  | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | |   (1146)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 144.36/20.18  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 144.36/20.18  | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 144.36/20.18  | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 144.36/20.18  | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 144.36/20.18  | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 144.36/20.18  | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1015), (1146), (function-axioms) are
% 144.36/20.18  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.18  | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.18  | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | |   (1147)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 144.36/20.19  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.36/20.19  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.36/20.19  | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.36/20.19  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.36/20.19  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.36/20.19  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.36/20.19  | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.36/20.19  | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.36/20.19  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.36/20.19  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.36/20.19  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.36/20.19  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.36/20.19  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.36/20.19  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.36/20.19  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.36/20.19  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.36/20.19  | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | BETA: splitting (1147) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | |   (1148)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.36/20.19  | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.36/20.19  | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | ALPHA: (1148) implies:
% 144.36/20.19  | | | | | | | | | | | | | | | | | |   (1149)  op(e2, e0) = e2
% 144.36/20.19  | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (392), (1149), (function-axioms) are
% 144.36/20.19  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 144.36/20.19  | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | |   (1150)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 144.36/20.19  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 144.36/20.19  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 144.36/20.19  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 144.36/20.19  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 144.36/20.19  | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | BETA: splitting (1150) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |   (1151)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | ALPHA: (1151) implies:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |   (1152)  op(e2, e2) = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (394), (1152), (function-axioms) are
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |   (1153)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | ALPHA: (1153) implies:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |   (1154)  op(e0, e0) = all_57_15
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |   (1155)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (1155) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |   (1156)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1015), (1129), (1154), (1156),
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |            #952.
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |   (1157)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1157) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |   (1158)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1158) implies:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |   (1159)  op(e1, e1) = e2
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (1159), (function-axioms) are
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |   (1160)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1160) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |   (1161)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_6)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1161) implies:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |   (1162)   ~ (all_57_15 = e1)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |   (1163)  op(e0, e1) = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (156), (1163) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |   (1164)  all_52_11 = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (1164) imply:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |   (1165)   ~ (all_52_9 = e0)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (1164) imply:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |   (1166)   ~ (all_4_2 = e0)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | SIMP: (1166) implies:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |   (1167)   ~ (all_4_2 = e0)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1127), (1164) imply:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | |   (1168)   ~ (e3 = e0)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | |   (1169)  all_54_10 = e3
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (1169) are inconsistent by sub-proof
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | |            #1173.
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | |   (1170)   ~ (all_54_10 = e3)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | |   (1171)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1171) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | |   (1172)  all_54_10 = e2
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (1172) are inconsistent by sub-proof
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | |            #1168.
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | |   (1173)   ~ (all_54_10 = e2)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | |   (1174)  all_54_10 = e1 | all_54_10 = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (1175)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1175) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1176)  all_56_4 = e2 & op(e3, e1) = e2
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1176) implies:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1177)  all_56_4 = e2
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1178)  op(e3, e1) = e2
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1174) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1179)  all_54_10 = e1
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1179) imply:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1180)  all_4_2 = e1
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1180) implies:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1181)  all_4_2 = e1
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (1181) imply:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1182)   ~ (all_52_14 = e1)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (1181) imply:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1183)   ~ (e3 = e1)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (1181) imply:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1184)   ~ (e2 = e1)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1185)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1185) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1186)  all_56_9 = e1 & op(e3, e0) = e1
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1186) implies:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1187)  all_56_9 = e1
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (233), (235),
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1015), (1177), (1187), (function-axioms) are
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #941.
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1188)  all_56_10 = e1 & op(e2, e0) = e1
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1188) implies:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1189)  all_56_10 = e1
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1190)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1190) gives:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1191)  all_56_2 = e0 & op(e2, e3) = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1191) implies:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1192)  op(e2, e3) = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1006), (1020), (1178), (1192), (function-axioms)
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #965.
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1193)  all_56_3 = e0 & op(e2, e2) = e0
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1193) implies:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1194)  op(e2, e2) = e0
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (394), (1194), (function-axioms) are
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1195)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (1165), (1189), (1195),
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #962.
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1196)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1154), (1162), (1182), (1196),
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #939.
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1197)  all_54_10 = e0
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (1167), (1197) are inconsistent by
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1198)  all_56_5 = e2 & op(e2, e1) = e2
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1198) implies:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1199)  op(e2, e1) = e2
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (391), (1199), (function-axioms) are
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | |   (1200)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1200) gives:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1201)  all_56_8 = e2 & op(e1, e1) = e2
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1201) implies:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1202)  op(e1, e1) = e2
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (1202), (function-axioms) are
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1203)  all_56_14 = e2 & op(e0, e1) = e2
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1203) implies:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1204)  op(e0, e1) = e2
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1163), (1204), (function-axioms) are
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1008.
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | |   (1205)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1205) implies:
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | |   (1206)  op(e2, e2) = e1
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | 
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (394), (1206), (function-axioms) are
% 144.36/20.20  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 144.76/20.20  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | Case 2:
% 144.76/20.20  | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | |   (1207)  all_24_2 = e2
% 144.76/20.20  | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | COMBINE_EQS: (318), (1207) imply:
% 144.76/20.20  | | | | | | | | | | | |   (1208)  all_10_2 = e2
% 144.76/20.20  | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | REDUCE: (360), (1208) imply:
% 144.76/20.20  | | | | | | | | | | | |   (1209)   ~ (all_52_7 = e2)
% 144.76/20.20  | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | REDUCE: (367), (1208) imply:
% 144.76/20.20  | | | | | | | | | | | |   (1210)   ~ (all_52_11 = e2)
% 144.76/20.20  | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | REDUCE: (370), (1208) imply:
% 144.76/20.20  | | | | | | | | | | | |   (1211)   ~ (all_52_14 = e2)
% 144.76/20.20  | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | REDUCE: (45), (1208) imply:
% 144.76/20.20  | | | | | | | | | | | |   (1212)  op(e0, e0) = e2
% 144.76/20.20  | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | BETA: splitting (232) gives:
% 144.76/20.20  | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | Case 1:
% 144.76/20.20  | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | |   (1213)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 144.76/20.20  | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 144.76/20.20  | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | REF_CLOSE: (6), (166), (388), (1015), (1213),
% 144.76/20.20  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.20  | | | | | | | | | | | | |            #938.
% 144.76/20.20  | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | Case 2:
% 144.76/20.20  | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | |   (1214)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 144.76/20.20  | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 144.76/20.20  | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | BETA: splitting (1214) gives:
% 144.76/20.20  | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | Case 1:
% 144.76/20.20  | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | |   (1215)  all_56_6 = e2 & op(e1, e3) = e2
% 144.76/20.20  | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | ALPHA: (1215) implies:
% 144.76/20.20  | | | | | | | | | | | | | |   (1216)  all_56_6 = e2
% 144.76/20.20  | | | | | | | | | | | | | |   (1217)  op(e1, e3) = e2
% 144.76/20.20  | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 144.76/20.20  | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | Case 1:
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | |   (1218)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 144.76/20.20  | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | BETA: splitting (1218) gives:
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | Case 1:
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1219)  all_56_4 = e2 & op(e3, e1) = e2
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | ALPHA: (1219) implies:
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1220)  all_56_4 = e2
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1221)  op(e3, e1) = e2
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 144.76/20.20  | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (1217) gives:
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1222)  all_52_2 = e2
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 144.76/20.20  | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (1221) gives:
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1223)  all_52_8 = e2
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | REDUCE: (143), (1222) imply:
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1224)   ~ (all_52_3 = e2)
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | SIMP: (1224) implies:
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1225)   ~ (all_52_3 = e2)
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | REDUCE: (122), (1223) imply:
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1226)   ~ (all_52_9 = e2)
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | REDUCE: (120), (1223) imply:
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1227)   ~ (all_52_11 = e2)
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | REDUCE: (361), (1223) imply:
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1228)   ~ (all_4_2 = e2)
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.20  | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | |   (1229)   ~ (all_34_2 = e1)
% 144.76/20.20  | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | REDUCE: (1009), (1229) imply:
% 144.76/20.20  | | | | | | | | | | | | | | | | |   (1230)  $false
% 144.76/20.20  | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | CLOSE: (1230) is inconsistent.
% 144.76/20.20  | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.20  | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | |   (1231)  ( ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0
% 144.76/20.20  | | | | | | | | | | | | | | | | |             & op(e3, e1) = all_34_1 & $i(all_34_0) &
% 144.76/20.20  | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e3, e1)
% 144.76/20.20  | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 144.76/20.20  | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | BETA: splitting (1231) gives:
% 144.76/20.20  | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.20  | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | |   (1232)   ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0 &
% 144.76/20.20  | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_34_1 & $i(all_34_0) &
% 144.76/20.20  | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 144.76/20.20  | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | | ALPHA: (1232) implies:
% 144.76/20.20  | | | | | | | | | | | | | | | | | |   (1233)  op(e3, e1) = all_34_1
% 144.76/20.20  | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (45), (124), (127),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (132), (134), (135), (138), (139), (142), (147),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (156), (157), (158), (161), (162), (163), (164),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (166), (167), (169), (189), (191), (193), (202),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (206), (209), (215), (216), (219), (220), (222),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (229), (230), (231),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (237), (238), (246),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (248), (271), (334), (364), (367), (371), (374),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (388), (389), (391), (392), (1006), (1010),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (1011), (1012), (1015), (1209), (1210), (1212),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (1216), (1220), (1221), (1225), (1233),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            #872.
% 144.76/20.20  | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.20  | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | |   (1234)   ~ (all_34_1 = e2) & op(e3, e1) = all_34_1 &
% 144.76/20.20  | | | | | | | | | | | | | | | | | |           $i(all_34_1)
% 144.76/20.20  | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | | ALPHA: (1234) implies:
% 144.76/20.20  | | | | | | | | | | | | | | | | | |   (1235)  op(e3, e1) = all_34_1
% 144.76/20.20  | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (45), (124), (127),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (132), (134), (135), (138), (139), (142), (147),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (156), (157), (158), (161), (162), (163), (164),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (166), (167), (169), (189), (191), (193), (202),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (206), (209), (215), (216), (219), (220), (222),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (224), (225), (227), (228), (229), (230), (231),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (232), (233), (234), (235), (237), (238), (246),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (248), (271), (334), (364), (367), (371), (374),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (388), (389), (391), (392), (1006), (1010),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (1011), (1012), (1015), (1209), (1210), (1212),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (1216), (1220), (1221), (1225), (1235),
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.20  | | | | | | | | | | | | | | | | | |            #872.
% 144.76/20.20  | | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | Case 2:
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1236)  all_56_5 = e2 & op(e2, e1) = e2
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | ALPHA: (1236) implies:
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1237)  op(e2, e1) = e2
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (391), (1237), (function-axioms) are
% 144.76/20.20  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | Case 2:
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | |   (1238)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 144.76/20.20  | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | REF_CLOSE: (36), (156), (371), (1210), (1238),
% 144.76/20.20  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.20  | | | | | | | | | | | | | | |            #972.
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | Case 2:
% 144.76/20.20  | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | |   (1239)  all_56_12 = e2 & op(e0, e3) = e2
% 144.76/20.20  | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | ALPHA: (1239) implies:
% 144.76/20.20  | | | | | | | | | | | | | |   (1240)  all_56_12 = e2
% 144.76/20.20  | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 144.76/20.20  | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | Case 1:
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | |   (1241)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 144.76/20.20  | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | BETA: splitting (1241) gives:
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | Case 1:
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1242)  all_56_6 = e2 & op(e1, e3) = e2
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | ALPHA: (1242) implies:
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1243)  all_56_6 = e2
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (228), (234), (1015),
% 144.76/20.20  | | | | | | | | | | | | | | | |            (1240), (1243), (function-axioms) are inconsistent
% 144.76/20.20  | | | | | | | | | | | | | | | |            by sub-proof #867.
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | Case 2:
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1244)  all_56_7 = e2 & op(e1, e2) = e2
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | ALPHA: (1244) implies:
% 144.76/20.20  | | | | | | | | | | | | | | | |   (1245)  op(e1, e2) = e2
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | | REF_CLOSE: (161), (390), (1245), (function-axioms) are
% 144.76/20.20  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1171.
% 144.76/20.20  | | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | Case 2:
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | |   (1246)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 144.76/20.20  | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | | REF_CLOSE: (36), (159), (371), (1211), (1246),
% 144.76/20.20  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.20  | | | | | | | | | | | | | | |            #973.
% 144.76/20.20  | | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | Case 2:
% 144.76/20.20  | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | |   (1247)  all_54_5 = e1 | all_54_5 = e0
% 144.76/20.20  | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | | REF_CLOSE: (267), (378), (380), (1247) are inconsistent by
% 144.76/20.20  | | | | | | | | | |            sub-proof #866.
% 144.76/20.20  | | | | | | | | | | 
% 144.76/20.20  | | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | | 
% 144.76/20.20  | | | | | | | | End of split
% 144.76/20.20  | | | | | | | | 
% 144.76/20.20  | | | | | | | Case 2:
% 144.76/20.20  | | | | | | | | 
% 144.76/20.20  | | | | | | | |   (1248)  all_20_2 = e1
% 144.76/20.20  | | | | | | | |   (1249)  ( ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 &
% 144.76/20.20  | | | | | | | |             op(e2, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1))
% 144.76/20.20  | | | | | | | |           | ( ~ (all_20_1 = e3) & op(e2, e1) = all_20_1 &
% 144.76/20.20  | | | | | | | |             $i(all_20_1))
% 144.76/20.20  | | | | | | | | 
% 144.76/20.20  | | | | | | | | COMBINE_EQS: (282), (1248) imply:
% 144.76/20.20  | | | | | | | |   (1250)  all_6_2 = e1
% 144.76/20.20  | | | | | | | | 
% 144.76/20.20  | | | | | | | | SIMP: (1250) implies:
% 144.76/20.20  | | | | | | | |   (1251)  all_6_2 = e1
% 144.76/20.20  | | | | | | | | 
% 144.76/20.20  | | | | | | | | COMBINE_EQS: (331), (1251) imply:
% 144.76/20.20  | | | | | | | |   (1252)  all_38_2 = e1
% 144.76/20.20  | | | | | | | | 
% 144.76/20.20  | | | | | | | | REDUCE: (347), (1251) imply:
% 144.76/20.21  | | | | | | | |   (1253)   ~ (all_52_1 = e1)
% 144.76/20.21  | | | | | | | | 
% 144.76/20.21  | | | | | | | | REDUCE: (350), (1251) imply:
% 144.76/20.21  | | | | | | | |   (1254)   ~ (all_52_4 = e1)
% 144.76/20.21  | | | | | | | | 
% 144.76/20.21  | | | | | | | | REDUCE: (352), (1251) imply:
% 144.76/20.21  | | | | | | | |   (1255)   ~ (all_52_6 = e1)
% 144.76/20.21  | | | | | | | | 
% 144.76/20.21  | | | | | | | | REDUCE: (354), (1251) imply:
% 144.76/20.21  | | | | | | | |   (1256)   ~ (all_52_7 = e1)
% 144.76/20.21  | | | | | | | | 
% 144.76/20.21  | | | | | | | | REDUCE: (356), (1251) imply:
% 144.76/20.21  | | | | | | | |   (1257)   ~ (all_52_9 = e1)
% 144.76/20.21  | | | | | | | | 
% 144.76/20.21  | | | | | | | | REDUCE: (358), (1251) imply:
% 144.76/20.21  | | | | | | | |   (1258)   ~ (all_52_13 = e1)
% 144.76/20.21  | | | | | | | | 
% 144.76/20.21  | | | | | | | | REDUCE: (372), (1251) imply:
% 144.76/20.21  | | | | | | | |   (1259)   ~ (e3 = e1)
% 144.76/20.21  | | | | | | | | 
% 144.76/20.21  | | | | | | | | BETA: splitting (221) gives:
% 144.76/20.21  | | | | | | | | 
% 144.76/20.21  | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | 
% 144.76/20.21  | | | | | | | | |   (1260)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 &
% 144.76/20.21  | | | | | | | | |             op(e2, e2) = e1)
% 144.76/20.21  | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | BETA: splitting (1260) gives:
% 144.76/20.21  | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | |   (1261)  all_56_2 = e1 & op(e2, e3) = e1
% 144.76/20.21  | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | ALPHA: (1261) implies:
% 144.76/20.21  | | | | | | | | | |   (1262)  op(e2, e3) = e1
% 144.76/20.21  | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | REF_CLOSE: (166), (1253), (1262), (function-axioms) are
% 144.76/20.21  | | | | | | | | | |            inconsistent by sub-proof #1177.
% 144.76/20.21  | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | Case 2:
% 144.76/20.21  | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | |   (1263)  all_56_3 = e1 & op(e2, e2) = e1
% 144.76/20.21  | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | ALPHA: (1263) implies:
% 144.76/20.21  | | | | | | | | | |   (1264)  all_56_3 = e1
% 144.76/20.21  | | | | | | | | | |   (1265)  op(e2, e2) = e1
% 144.76/20.21  | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | BETA: splitting (64) gives:
% 144.76/20.21  | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | |   (1266)   ~ (all_22_2 = e1)
% 144.76/20.21  | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | REDUCE: (320), (1266) imply:
% 144.76/20.21  | | | | | | | | | | |   (1267)   ~ (all_14_2 = e1)
% 144.76/20.21  | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | BETA: splitting (67) gives:
% 144.76/20.21  | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | |   (1268)   ~ (all_24_2 = e2)
% 144.76/20.21  | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | REDUCE: (318), (1268) imply:
% 144.76/20.21  | | | | | | | | | | | |   (1269)   ~ (all_10_2 = e2)
% 144.76/20.21  | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | BETA: splitting (87) gives:
% 144.76/20.21  | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | |   (1270)   ~ (all_38_2 = e1)
% 144.76/20.21  | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | REDUCE: (1252), (1270) imply:
% 144.76/20.21  | | | | | | | | | | | | |   (1271)  $false
% 144.76/20.21  | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | CLOSE: (1271) is inconsistent.
% 144.76/20.21  | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | Case 2:
% 144.76/20.21  | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | |   (1272)  ( ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0
% 144.76/20.21  | | | | | | | | | | | | |             & op(e2, e1) = all_38_1 & $i(all_38_0) &
% 144.76/20.21  | | | | | | | | | | | | |             $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e2, e1)
% 144.76/20.21  | | | | | | | | | | | | |             = all_38_1 & $i(all_38_1))
% 144.76/20.21  | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | BETA: splitting (84) gives:
% 144.76/20.21  | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | |   (1273)   ~ (all_36_2 = e2)
% 144.76/20.21  | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | REDUCE: (304), (1273) imply:
% 144.76/20.21  | | | | | | | | | | | | | |   (1274)   ~ (all_14_2 = e2)
% 144.76/20.21  | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 144.76/20.21  | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | |   (1275)  all_54_0 = e3
% 144.76/20.21  | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | COMBINE_EQS: (278), (1275) imply:
% 144.76/20.21  | | | | | | | | | | | | | | |   (1276)  all_14_2 = e3
% 144.76/20.21  | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | REDUCE: (336), (1276) imply:
% 144.76/20.21  | | | | | | | | | | | | | | |   (1277)   ~ (all_52_1 = e3)
% 144.76/20.21  | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | REDUCE: (342), (1276) imply:
% 144.76/20.21  | | | | | | | | | | | | | | |   (1278)   ~ (all_52_4 = e3)
% 144.76/20.21  | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | REDUCE: (344), (1276) imply:
% 144.76/20.21  | | | | | | | | | | | | | | |   (1279)   ~ (all_52_8 = e3)
% 144.76/20.21  | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | REDUCE: (346), (1276) imply:
% 144.76/20.21  | | | | | | | | | | | | | | |   (1280)   ~ (all_52_12 = e3)
% 144.76/20.21  | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | REDUCE: (51), (1276) imply:
% 144.76/20.21  | | | | | | | | | | | | | | |   (1281)  op(e3, e3) = e3
% 144.76/20.21  | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 144.76/20.21  | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | |   (1282)   ~ (all_42_2 = e3)
% 144.76/20.21  | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | REDUCE: (302), (1282) imply:
% 144.76/20.21  | | | | | | | | | | | | | | | |   (1283)   ~ (all_10_2 = e3)
% 144.76/20.21  | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 144.76/20.21  | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | |   (1284)  all_54_15 = e3
% 144.76/20.21  | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (1283), (1284) are inconsistent by
% 144.76/20.21  | | | | | | | | | | | | | | | | |            sub-proof #1049.
% 144.76/20.21  | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.21  | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | |   (1285)   ~ (all_54_15 = e3)
% 144.76/20.21  | | | | | | | | | | | | | | | | |   (1286)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 144.76/20.21  | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | BETA: splitting (1286) gives:
% 144.76/20.21  | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | |   (1287)  all_54_15 = e2
% 144.76/20.21  | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (1269), (1287) are inconsistent by
% 144.76/20.21  | | | | | | | | | | | | | | | | | |            sub-proof #1048.
% 144.76/20.21  | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | |   (1288)   ~ (all_54_15 = e2)
% 144.76/20.21  | | | | | | | | | | | | | | | | | |   (1289)  all_54_15 = e1 | all_54_15 = e0
% 144.76/20.21  | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | BETA: splitting (1289) gives:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | |   (1290)  all_54_15 = e1
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (375), (1290) are inconsistent by sub-proof
% 144.76/20.21  | | | | | | | | | | | | | | | | | | |            #1047.
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | |   (1291)  all_54_15 = e0
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1291) imply:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | |   (1292)  all_10_2 = e0
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | SIMP: (1292) implies:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | |   (1293)  all_10_2 = e0
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | REDUCE: (349), (1293) imply:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | |   (1294)   ~ (all_52_3 = e0)
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | REDUCE: (360), (1293) imply:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | |   (1295)   ~ (all_52_7 = e0)
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | REDUCE: (367), (1293) imply:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | |   (1296)   ~ (all_52_11 = e0)
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | REDUCE: (1283), (1293) imply:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | |   (1297)   ~ (e3 = e0)
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | REDUCE: (375), (1293) imply:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | |   (1298)   ~ (e1 = e0)
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | REDUCE: (45), (1293) imply:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | |   (1299)  op(e0, e0) = e0
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |   (1300)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1300) gives:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |   (1301)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1301) gives:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |   (1302)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (374), (1299), (1302),
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |            #865.
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |   (1303)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (1265), (1299), (1303),
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |            #864.
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |   (1304)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1304) gives:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |   (1305)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1278), (1305), (function-axioms) are
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |   (1306)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (168), (1269), (1279), (1281), (1306),
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | |            #861.
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.21  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |   (1307)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1307) gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |   (1308)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1308) gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |   (1309)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (1279), (1281), (1309),
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |            #860.
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |   (1310)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (1280), (1299), (1310),
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |            #859.
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |   (1311)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1311) gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |   (1312)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1281), (1312), (function-axioms) are
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |   (1313)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1313) gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |   (1314)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1314) implies:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |   (1315)   ~ (all_57_12 = e0)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |   (1316)  op(e1, e1) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |   (1317)  op(e2, e0) = e2
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |   (1318)  op(e2, e2) = all_57_12
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0,
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (1316) gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |   (1319)  all_4_2 = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (163), (1317) gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |   (1320)  all_52_13 = e2
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (1265), (1318)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |   (1321)  all_57_12 = e1
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (1319) imply:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |   (1322)   ~ (all_52_6 = e0)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | |   (1323)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1323) gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (1324)  all_56_2 = e3 & op(e2, e3) = e3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1277), (1324), (function-axioms) are
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #917.
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (1325)  all_56_3 = e3 & op(e2, e2) = e3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1325) implies:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (1326)  op(e2, e2) = e3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1265), (1326), (function-axioms) are
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | |   (1327)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1327) gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (1328)  all_56_5 = e3 & op(e2, e1) = e3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1328) implies:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (1329)  op(e2, e1) = e3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1272) gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1330)   ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_38_1 & $i(all_38_0) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_38_1)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1330) implies:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1331)  op(e2, e1) = all_38_1
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (161), (224), (1249), (1295), (1315),
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (1318), (1322), (1329), (1331), (function-axioms)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #855.
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1332)   ~ (all_38_1 = e0) & op(e2, e1) = all_38_1 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_38_1)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1332) implies:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1333)  op(e2, e1) = all_38_1
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (161), (224), (1249), (1295), (1315),
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            (1318), (1322), (1329), (1333), (function-axioms)
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #855.
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (1334)  all_56_10 = e3 & op(e2, e0) = e3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1334) implies:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (1335)  op(e2, e0) = e3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1317), (1335), (function-axioms) are
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #854.
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |   (1336)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1336) gives:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |   (1337)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1337) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |   (1338)  op(e2, e2) = e0
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1265), (1338), (function-axioms) are
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |   (1339)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1339) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |   (1340)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (157), (158), (1281), (1294), (1295),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |            (1296), (1340), (function-axioms) are inconsistent
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #850.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | |   (1341)  all_42_2 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (1341) imply:
% 144.76/20.23  | | | | | | | | | | | | | | | |   (1342)  all_10_2 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | SIMP: (1342) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | |   (1343)  all_10_2 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | REDUCE: (367), (1343) imply:
% 144.76/20.23  | | | | | | | | | | | | | | | |   (1344)   ~ (all_52_11 = e3)
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | REDUCE: (45), (1343) imply:
% 144.76/20.23  | | | | | | | | | | | | | | | |   (1345)  op(e0, e0) = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | |   (1346)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 144.76/20.23  | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | BETA: splitting (1346) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | |   (1347)  all_56_4 = e3 & op(e3, e1) = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | ALPHA: (1347) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | |   (1348)  op(e3, e1) = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1279), (1348), (function-axioms) are
% 144.76/20.23  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | |   (1349)  all_56_5 = e3 & op(e2, e1) = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | ALPHA: (1349) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | |   (1350)  all_56_5 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | |   (1351)  op(e2, e1) = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | |   (1352)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (1265), (1278), (1352),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.23  | | | | | | | | | | | | | | | | | | |            #849.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | |   (1353)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | BETA: splitting (1353) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |   (1354)  all_56_7 = e3 & op(e1, e2) = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | ALPHA: (1354) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |   (1355)  all_56_7 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |   (1356)  op(e1, e2) = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (122), (124), (127),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |            (134), (135), (138), (139), (144), (145), (147),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |            (156), (157), (158), (161), (162), (163), (164),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (190), (199), (202),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |            (205), (206), (208), (209), (211), (212), (214),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |            (216), (218), (220), (224), (226), (228), (229),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (235), (237), (238),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |            (247), (268), (271), (1249), (1253), (1254),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |            (1256), (1257), (1258), (1265), (1272), (1280),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |            (1281), (1344), (1350), (1351), (1355), (1356),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |            #793.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |   (1357)  all_56_13 = e3 & op(e0, e2) = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | ALPHA: (1357) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | |   (1358)  all_56_13 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | |   (1359)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1359) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | |   (1360)  all_56_6 = e3 & op(e1, e3) = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1360) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | |   (1361)  all_56_6 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | |   (1362)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (166), (1253), (1281), (1362),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | |            #1176.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | |   (1363)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1363) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |   (1364)  all_56_6 = e1 & op(e1, e3) = e1
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1361), (1364) are inconsistent by sub-proof
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |            #792.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |   (1365)  all_56_12 = e1 & op(e0, e3) = e1
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1365) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | |   (1366)  all_56_12 = e1
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (1367)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1367) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1368)  all_56_0 = e0 & op(e3, e3) = e0
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1368) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1369)  op(e3, e3) = e0
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1281), (1369), (function-axioms) are
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1370)  all_56_2 = e0 & op(e2, e3) = e0
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1370) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1371)  all_56_2 = e0
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1372)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1372) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1373)  all_56_0 = e2 & op(e3, e3) = e2
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1373) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1374)  op(e3, e3) = e2
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (205), (206),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (228), (230), (234), (375), (1269), (1345),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1358), (1374), (function-axioms) are inconsistent
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #780.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1375)  all_56_2 = e2 & op(e2, e3) = e2
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1371), (1375) are inconsistent by sub-proof
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #994.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1376)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1376) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1377)  all_56_6 = e2 & op(e1, e3) = e2
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1361), (1377) are inconsistent by sub-proof
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #779.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1378)  all_56_12 = e2 & op(e0, e3) = e2
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1378) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1379)  all_56_12 = e2
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1366), (1379) are inconsistent by sub-proof
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1122.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (1380)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1380) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1381)  all_56_6 = e0 & op(e1, e3) = e0
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1361), (1381) are inconsistent by sub-proof
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            #778.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1382)  all_56_12 = e0 & op(e0, e3) = e0
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (166), (230), (232),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            (1281), (1361), (1382), (function-axioms) are
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #777.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | |   (1383)  all_56_7 = e3 & op(e1, e2) = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1383) implies:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | |   (1384)  all_56_7 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (224), (226), (1265),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | |            (1358), (1384), (function-axioms) are inconsistent
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #846.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | |   (1385)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (163),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | |            (205), (209), (210), (374), (1269), (1345),
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | |            (1385), (function-axioms) are inconsistent by
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | |            sub-proof #770.
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | |   (1386)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 144.76/20.23  | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 144.76/20.23  | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (156), (374), (1344), (1386),
% 144.76/20.23  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.23  | | | | | | | | | | | | | | | | |            #883.
% 144.76/20.23  | | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | |   (1387)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 144.76/20.23  | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | REF_CLOSE: (278), (376), (1267), (1274), (1387) are
% 144.76/20.23  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 144.76/20.23  | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | End of split
% 144.76/20.23  | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | |   (1388)  all_36_2 = e2
% 144.76/20.23  | | | | | | | | | | | | | |   (1389)  ( ~ (all_36_0 = e1) & op(all_36_1, e3) = all_36_0
% 144.76/20.23  | | | | | | | | | | | | | |             & op(e3, e2) = all_36_1 & $i(all_36_0) &
% 144.76/20.23  | | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e3, e2)
% 144.76/20.23  | | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 144.76/20.23  | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | COMBINE_EQS: (304), (1388) imply:
% 144.76/20.23  | | | | | | | | | | | | | |   (1390)  all_14_2 = e2
% 144.76/20.23  | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | SIMP: (1390) implies:
% 144.76/20.23  | | | | | | | | | | | | | |   (1391)  all_14_2 = e2
% 144.76/20.23  | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | REDUCE: (336), (1391) imply:
% 144.76/20.23  | | | | | | | | | | | | | |   (1392)   ~ (all_52_1 = e2)
% 144.76/20.23  | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | REDUCE: (342), (1391) imply:
% 144.76/20.23  | | | | | | | | | | | | | |   (1393)   ~ (all_52_4 = e2)
% 144.76/20.23  | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | REDUCE: (346), (1391) imply:
% 144.76/20.23  | | | | | | | | | | | | | |   (1394)   ~ (all_52_12 = e2)
% 144.76/20.23  | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | REDUCE: (51), (1391) imply:
% 144.76/20.23  | | | | | | | | | | | | | |   (1395)  op(e3, e3) = e2
% 144.76/20.23  | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 144.76/20.23  | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | |   (1396)   ~ (all_42_2 = e3)
% 144.76/20.23  | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | REDUCE: (302), (1396) imply:
% 144.76/20.23  | | | | | | | | | | | | | | |   (1397)   ~ (all_10_2 = e3)
% 144.76/20.23  | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 144.76/20.23  | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | Case 1:
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | |   (1398)  all_54_15 = e3
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | | REF_CLOSE: (245), (1397), (1398) are inconsistent by
% 144.76/20.23  | | | | | | | | | | | | | | | |            sub-proof #1049.
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.23  | | | | | | | | | | | | | | | Case 2:
% 144.76/20.23  | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | |   (1399)   ~ (all_54_15 = e3)
% 144.76/20.24  | | | | | | | | | | | | | | | |   (1400)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 144.76/20.24  | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | BETA: splitting (1400) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | |   (1401)  all_54_15 = e2
% 144.76/20.24  | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (1269), (1401) are inconsistent by
% 144.76/20.24  | | | | | | | | | | | | | | | | |            sub-proof #1048.
% 144.76/20.24  | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | |   (1402)   ~ (all_54_15 = e2)
% 144.76/20.24  | | | | | | | | | | | | | | | | |   (1403)  all_54_15 = e1 | all_54_15 = e0
% 144.76/20.24  | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | BETA: splitting (1403) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | |   (1404)  all_54_15 = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (375), (1404) are inconsistent by sub-proof
% 144.76/20.24  | | | | | | | | | | | | | | | | | |            #1047.
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | |   (1405)  all_54_15 = e0
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1405) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | |   (1406)  all_10_2 = e0
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | SIMP: (1406) implies:
% 144.76/20.24  | | | | | | | | | | | | | | | | | |   (1407)  all_10_2 = e0
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | REDUCE: (349), (1407) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | |   (1408)   ~ (all_52_3 = e0)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | REDUCE: (360), (1407) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | |   (1409)   ~ (all_52_7 = e0)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | REDUCE: (367), (1407) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | |   (1410)   ~ (all_52_11 = e0)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | REDUCE: (1397), (1407) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | |   (1411)   ~ (e3 = e0)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | REDUCE: (1269), (1407) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | |   (1412)   ~ (e2 = e0)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | REDUCE: (375), (1407) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | |   (1413)   ~ (e1 = e0)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | REDUCE: (45), (1407) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | |   (1414)  op(e0, e0) = e0
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | |   (1415)   ~ (all_48_2 = e0)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | REDUCE: (298), (1415) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | |   (1416)   ~ (all_4_2 = e0)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | |   (1417)  all_54_10 = e3
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (1417) are inconsistent by sub-proof
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | |            #1173.
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | |   (1418)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1418) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | |   (1419)  all_54_10 = e2
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (1419) are inconsistent by sub-proof
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | |            #1168.
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | |   (1420)   ~ (all_54_10 = e2)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | |   (1421)  all_54_10 = e1 | all_54_10 = e0
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1421) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | |   (1422)  all_54_10 = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1422) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | |   (1423)  all_4_2 = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | SIMP: (1423) implies:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | |   (1424)  all_4_2 = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (1424) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | |   (1425)   ~ (all_52_2 = e1)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (1424) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | |   (1426)   ~ (all_52_14 = e1)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (1424) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | |   (1427)   ~ (e2 = e1)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1424) imply:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | |   (1428)  op(e1, e1) = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | |   (1429)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1429) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | |   (1430)  all_56_9 = e1 & op(e3, e0) = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (1431)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1431) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1432)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1432) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1433)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1392), (1433), (function-axioms) are
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1434)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (162), (1414), (1425), (1434),
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1045.
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1435)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1435) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1436)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (45), (1269), (1428), (1436),
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #769.
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1437)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1437) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1438)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1438) implies:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1439)  op(e1, e2) = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1255), (1439), (function-axioms) are
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1440)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1440) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1441)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1441) implies:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1442)  op(e0, e0) = e2
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1269), (1442), (function-axioms) are
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1443)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1443) implies:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1444)   ~ (all_57_10 = e1)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1445)  op(e3, e3) = all_57_10
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1446)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1446) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1447)  all_56_0 = e1 & op(e3, e3) = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1447) implies:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1448)  op(e3, e3) = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1444), (1445), (1448), (function-axioms) are
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #893.
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1449)  all_56_2 = e1 & op(e2, e3) = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1449) implies:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1450)  op(e2, e3) = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1253), (1450), (function-axioms) are
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1177.
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1451)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1451) gives:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1452)  all_56_6 = e1 & op(e1, e3) = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1452) implies:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1453)  op(e1, e3) = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1425), (1453), (function-axioms) are
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1454)  all_56_12 = e1 & op(e0, e3) = e1
% 144.76/20.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1431) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1455)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1455) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1456)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1392), (1456), (function-axioms) are
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1457)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (162), (1414), (1425), (1457),
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1045.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1435) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1458)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (45), (1269), (1428), (1458),
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #769.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1437) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1459)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1459) implies:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1460)  op(e1, e2) = e1
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1255), (1460), (function-axioms) are
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1440) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1461)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1461) implies:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1462)  op(e0, e0) = e2
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1269), (1462), (function-axioms) are
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1443) implies:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1463)  op(e3, e1) = e3
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1454) implies:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1464)  op(e0, e3) = e1
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1430) implies:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1465)  op(e3, e0) = e1
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e1,
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (158), (1464) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1466)  all_52_3 = e1
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e3, simplifying with (167), (1465) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1467)  all_52_12 = e1
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (1463) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1468)  all_52_8 = e3
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (1468) imply:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1469)   ~ (all_52_4 = e3)
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1470)  all_54_1 = e3
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (1469), (1470) are inconsistent by
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #988.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1471)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1471) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1472)  all_54_1 = e2
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (1393), (1472) are inconsistent by
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #768.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1473)  all_54_1 = e1 | all_54_1 = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1473) gives:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1474)  all_54_1 = e1
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (1474) imply:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1475)  all_52_4 = e1
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1475) implies:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1476)  all_52_4 = e1
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1254), (1476) imply:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1477)  $false
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1477) is inconsistent.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1478)  all_54_1 = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (1478) imply:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1479)  all_52_4 = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1479) implies:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1480)  all_52_4 = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (1480) imply:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1481)  op(e3, e2) = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1389), (1464), (1481), (function-axioms) are
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #767.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1482)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (156), (157), (158), (159),
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1265), (1395), (1408), (1409), (1410), (1414),
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1426), (1428), (1482), (function-axioms) are
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #762.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (1483)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (156), (157), (158), (159),
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |            (1265), (1395), (1408), (1409), (1410), (1414),
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |            (1426), (1428), (1483), (function-axioms) are
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #762.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | |   (1484)  all_56_10 = e1 & op(e2, e0) = e1
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1258), (1484), (function-axioms) are
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | |   (1485)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (1414), (1426), (1485),
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | |            #960.
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.25  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | |   (1486)  all_54_10 = e0
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (1416), (1486) are inconsistent by
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | |   (1487)  all_48_2 = e0
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (1487) imply:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | |   (1488)  all_4_2 = e0
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | REDUCE: (359), (1488) imply:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | |   (1489)   ~ (all_52_6 = e0)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1488) imply:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | |   (1490)  op(e1, e1) = e0
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |   (1491)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (1265), (1395), (1491),
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |            #761.
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |   (1492)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1492) gives:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |   (1493)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1493) implies:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |   (1494)  op(e1, e1) = e1
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1490), (1494), (function-axioms) are
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |   (1495)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1495) implies:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |   (1496)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |   (1497)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1496) gives:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | |   (1498)  all_57_13 = e1 & op(e1, e0) = e1
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1498) implies:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | |   (1499)  all_57_13 = e1
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | |   (1500)  op(e1, e0) = e1
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |   (1501)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1501) gives:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |   (1502)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1502) gives:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (1503)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1392), (1503), (function-axioms) are
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (1504)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (1265), (1414), (1504),
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |            #864.
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |   (1505)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1505) gives:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (1506)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1506) gives:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1507)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1507) implies:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1508)  op(e1, e1) = e2
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1490), (1508), (function-axioms) are
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1509)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1509) implies:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1510)  op(e0, e0) = e2
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1269), (1510), (function-axioms) are
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (1511)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1511) gives:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1512)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1512) implies:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1513)  op(e1, e2) = e1
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1255), (1513), (function-axioms) are
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1514)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1514) gives:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1515)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1515) implies:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1516)  op(e0, e0) = e2
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1269), (1516), (function-axioms) are
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1517)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1517) implies:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1518)  op(e3, e1) = e3
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1519)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1519) gives:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1520)  all_56_1 = e0 & op(e3, e2) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1520) implies:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1521)  op(e3, e2) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (159), (1500) gives:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1522)  all_52_14 = e1
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (1518) gives:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1523)  all_52_8 = e3
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (169), (1521) gives:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1524)  all_52_4 = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (1524) imply:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1525)   ~ (all_52_12 = e0)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1525) implies:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1526)   ~ (all_52_12 = e0)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (1523) imply:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1527)   ~ (all_52_12 = e3)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1527) implies:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1528)   ~ (all_52_12 = e3)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (1522) imply:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1529)   ~ (all_52_12 = e1)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1530)  all_54_3 = e3
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1530) imply:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1531)  all_52_12 = e3
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1528), (1531) imply:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1532)  $false
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1532) is inconsistent.
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1533)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1394), (1526), (1529), (1533) are
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #758.
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1534)  all_56_3 = e0 & op(e2, e2) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1534) implies:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1535)  op(e2, e2) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1265), (1535), (function-axioms) are
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1536)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (161), (1409), (1489), (1536),
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1028.
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |   (1537)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1537) gives:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |   (1538)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1538) gives:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (1539)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1539) gives:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1540)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1540) implies:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1541)  op(e0, e0) = e1
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1414), (1541), (function-axioms) are
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1542)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1542) implies:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1543)  op(e3, e3) = e1
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (45), (140), (156), (159), (162),
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (237), (238), (334), (366), (367), (371),
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (374), (1265), (1500), (1543), (function-axioms)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #757.
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (1544)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1414), (1497), (1499), (1544),
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |            #889.
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |   (1545)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1545) gives:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (1546)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1395), (1546), (function-axioms) are
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (1547)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1547) gives:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1548)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 144.76/20.27  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1548) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1549)   ~ (all_57_13 = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1499), (1549) imply:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1550)  $false
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1550) is inconsistent.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1551)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (156), (157), (158), (1408), (1409), (1410),
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            (1490), (1551), (function-axioms) are inconsistent
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #755.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1552)   ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1552) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1553)   ~ (all_57_14 = e0)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1554)  op(e1, e1) = all_57_14
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1490), (1553), (1554), (function-axioms) are
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1026.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | |   (1555)  all_42_2 = e3
% 144.76/20.28  | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | COMBINE_EQS: (302), (1555) imply:
% 144.76/20.28  | | | | | | | | | | | | | | |   (1556)  all_10_2 = e3
% 144.76/20.28  | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | SIMP: (1556) implies:
% 144.76/20.28  | | | | | | | | | | | | | | |   (1557)  all_10_2 = e3
% 144.76/20.28  | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | REDUCE: (367), (1557) imply:
% 144.76/20.28  | | | | | | | | | | | | | | |   (1558)   ~ (all_52_11 = e3)
% 144.76/20.28  | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | REDUCE: (368), (1557) imply:
% 144.76/20.28  | | | | | | | | | | | | | | |   (1559)   ~ (all_52_12 = e3)
% 144.76/20.28  | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | REDUCE: (45), (1557) imply:
% 144.76/20.28  | | | | | | | | | | | | | | |   (1560)  op(e0, e0) = e3
% 144.76/20.28  | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | |   (1561)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 144.76/20.28  | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 144.76/20.28  | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 144.76/20.28  | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 144.76/20.28  | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 144.76/20.28  | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 144.76/20.28  | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 144.76/20.28  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 144.76/20.28  | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 144.76/20.28  | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 144.76/20.28  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.76/20.28  | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 144.76/20.28  | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 144.76/20.28  | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 144.76/20.28  | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 144.76/20.28  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 144.76/20.28  | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (1265), (1395), (1561),
% 144.76/20.28  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.28  | | | | | | | | | | | | | | | |            #761.
% 144.76/20.28  | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | |   (1562)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 144.76/20.28  | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.76/20.28  | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 144.76/20.28  | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.28  | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 144.76/20.28  | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 144.76/20.28  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 144.76/20.28  | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 144.76/20.28  | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 144.76/20.28  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.76/20.28  | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 144.76/20.28  | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 144.76/20.28  | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 144.76/20.28  | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 144.76/20.28  | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 144.76/20.28  | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | BETA: splitting (1562) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | |   (1563)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 144.76/20.28  | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.76/20.28  | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 144.76/20.28  | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.28  | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 144.76/20.28  | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 144.76/20.28  | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | ALPHA: (1563) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | |   (1564)  op(e1, e1) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | |   (1565)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 144.76/20.28  | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.28  | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 144.76/20.28  | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | BETA: splitting (1565) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1566)  all_57_7 = e2 & op(e2, e1) = e2
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | ALPHA: (1566) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1567)  all_57_7 = e2
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1568)  op(e2, e1) = e2
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 144.76/20.28  | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (1564) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1569)  all_4_2 = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 144.76/20.28  | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (164), (1568) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1570)  all_52_9 = e2
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | REDUCE: (348), (1569) imply:
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1571)   ~ (all_52_2 = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | REDUCE: (117), (1570) imply:
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1572)   ~ (all_52_11 = e2)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | SIMP: (1572) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1573)   ~ (all_52_11 = e2)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | REDUCE: (116), (1570) imply:
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1574)   ~ (all_52_13 = e2)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | SIMP: (1574) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1575)   ~ (all_52_13 = e2)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | REDUCE: (364), (1569) imply:
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1576)   ~ (all_52_11 = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | REDUCE: (366), (1569) imply:
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1577)   ~ (all_52_14 = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | REDUCE: (371), (1569) imply:
% 144.76/20.28  | | | | | | | | | | | | | | | | | |   (1578)   ~ (e2 = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | |   (1579)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | BETA: splitting (1579) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | |   (1580)  all_56_12 = e1 & op(e0, e3) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | ALPHA: (1580) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | |   (1581)  all_56_12 = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | |   (1582)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1582) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1583)  all_56_2 = e3 & op(e2, e3) = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1583) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1584)  all_56_2 = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (124), (157),
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |            (159), (161), (162), (163), (166), (167), (189),
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |            (228), (232), (238), (246), (1255), (1392),
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |            (1395), (1558), (1559), (1560), (1564), (1567),
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |            (1571), (1573), (1575), (1576), (1577), (1581),
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |            (1584), (function-axioms) are inconsistent by
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #750.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1585)  all_56_3 = e3 & op(e2, e2) = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1585) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1586)  op(e2, e2) = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1265), (1586), (function-axioms) are
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | |   (1587)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1587) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1588)  all_56_5 = e3 & op(e2, e1) = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1588) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1589)  op(e2, e1) = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1568), (1589), (function-axioms) are
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1135.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1590)  all_56_10 = e3 & op(e2, e0) = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1590) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1591)  all_56_10 = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1592)  op(e2, e0) = e3
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | |   (1593)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1593) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | |   (1594)  all_56_9 = e1 & op(e3, e0) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1594) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | |   (1595)  all_56_9 = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (45), (163), (205), (210),
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | |            (1269), (1560), (1575), (1591), (1595),
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | |            #747.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | |   (1596)  all_56_10 = e1 & op(e2, e0) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1258), (1596), (function-axioms) are
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | |   (1597)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (205), (210),
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | |            (1269), (1560), (1591), (1592), (1597),
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | |            #742.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | |   (1598)  all_56_13 = e1 & op(e0, e2) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | ALPHA: (1598) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | |   (1599)  all_56_13 = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | |   (1600)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1600) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1601)  all_56_1 = e2 & op(e3, e2) = e2
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1393), (1601), (function-axioms) are
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1602)  all_56_3 = e2 & op(e2, e2) = e2
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1602) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1603)  op(e2, e2) = e2
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1265), (1603), (function-axioms) are
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | |   (1604)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1604) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1605)  all_56_7 = e2 & op(e1, e2) = e2
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1605) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | |   (1606)  all_56_7 = e2
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | |   (1607)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1607) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | |   (1608)  all_56_9 = e1 & op(e3, e0) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1608) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | |   (1609)  all_56_9 = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (1610)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1610) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1611)  all_56_0 = e1 & op(e3, e3) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1611) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1612)  op(e3, e3) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1395), (1612), (function-axioms) are
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1613)  all_56_2 = e1 & op(e2, e3) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1613) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1614)  op(e2, e3) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1253), (1614), (function-axioms) are
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1177.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (1615)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1615) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1616)  all_56_6 = e1 & op(e1, e3) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1616) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1617)  op(e1, e3) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1571), (1617), (function-axioms) are
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1618)  all_56_12 = e1 & op(e0, e3) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1618) implies:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1619)  op(e0, e3) = e1
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.28  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1620)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1620) gives:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1621)  all_56_4 = e3 & op(e3, e1) = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1621) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1622)  all_56_4 = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1623)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1623) gives:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1624)  all_56_1 = e3 & op(e3, e2) = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1624) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1625)  all_56_1 = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (224), (226), (1264),
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1265), (1599), (1625), (function-axioms) are
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #736.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1626)  all_56_3 = e3 & op(e2, e2) = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1626) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1627)  op(e2, e2) = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1265), (1627), (function-axioms) are
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1628)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1628) gives:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1629)  all_56_7 = e3 & op(e1, e2) = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1629) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1630)  all_56_7 = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1606), (1630) imply:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1631)  e3 = e2
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1631) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1632)  e3 = e2
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1622), (1632) imply:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1633)  all_56_4 = e2
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1634)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1389), (1395), (1619), (1634),
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #735.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1635)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1635) gives:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1636)  all_56_4 = e0 & op(e3, e1) = e0
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1636) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1637)  all_56_4 = e0
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1633), (1637) are inconsistent by sub-proof
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #936.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1638)  all_56_9 = e0 & op(e3, e0) = e0
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1638) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1639)  all_56_9 = e0
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1609), (1639) are inconsistent by sub-proof
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #946.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1640)  all_56_13 = e3 & op(e0, e2) = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1640) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1641)  all_56_13 = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (205), (206),
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (228), (230), (234), (375), (1269), (1395),
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1560), (1641), (function-axioms) are inconsistent
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #780.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1642)  all_56_5 = e3 & op(e2, e1) = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1642) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1643)  op(e2, e1) = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1568), (1643), (function-axioms) are
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1135.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1644)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (156), (1558), (1564), (1644),
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #733.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | |   (1645)  all_56_10 = e1 & op(e2, e0) = e1
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1258), (1645), (function-axioms) are
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | |   (1646)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (1560), (1577), (1646),
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | |            #732.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | |   (1647)  all_56_13 = e2 & op(e0, e2) = e2
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1647) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | |   (1648)  all_56_13 = e2
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1599), (1648) are inconsistent by sub-proof
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | |            #1110.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | |   (1649)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 144.76/20.29  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | BETA: splitting (1649) gives:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | Case 1:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | |   (1650)  all_56_14 = e1 & op(e0, e1) = e1
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | ALPHA: (1650) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | |   (1651)  op(e0, e1) = e1
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (189), (246), (1558), (1573), (1576),
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | |            (1651), (function-axioms) are inconsistent by
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | |            sub-proof #731.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | |   (1652)  all_56_15 = e1 & op(e0, e0) = e1
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | ALPHA: (1652) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | |   (1653)  op(e0, e0) = e1
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1560), (1653), (function-axioms) are
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | |   (1654)   ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 144.76/20.29  | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 144.76/20.29  | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | ALPHA: (1654) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | | |   (1655)   ~ (all_57_12 = e1)
% 144.76/20.29  | | | | | | | | | | | | | | | | | |   (1656)  op(e2, e2) = all_57_12
% 144.76/20.29  | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1265), (1655), (1656), (function-axioms) are
% 144.76/20.29  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 144.76/20.29  | | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | |   (1657)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 144.76/20.29  | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 144.76/20.29  | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 144.76/20.29  | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 144.76/20.29  | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 144.76/20.29  | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 144.76/20.29  | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 144.76/20.29  | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 144.76/20.29  | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | ALPHA: (1657) implies:
% 144.76/20.29  | | | | | | | | | | | | | | | | |   (1658)  op(e0, e0) = e0
% 144.76/20.29  | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1560), (1658), (function-axioms) are
% 144.76/20.29  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 144.76/20.29  | | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | End of split
% 144.76/20.29  | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | Case 2:
% 144.76/20.29  | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | |   (1659)  all_24_2 = e2
% 144.76/20.29  | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | COMBINE_EQS: (318), (1659) imply:
% 144.76/20.29  | | | | | | | | | | | |   (1660)  all_10_2 = e2
% 144.76/20.29  | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | REDUCE: (367), (1660) imply:
% 144.76/20.29  | | | | | | | | | | | |   (1661)   ~ (all_52_11 = e2)
% 144.76/20.29  | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | REDUCE: (369), (1660) imply:
% 144.76/20.29  | | | | | | | | | | | |   (1662)   ~ (all_52_13 = e2)
% 144.76/20.29  | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | REDUCE: (370), (1660) imply:
% 144.76/20.29  | | | | | | | | | | | |   (1663)   ~ (all_52_14 = e2)
% 144.76/20.29  | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | REDUCE: (45), (1660) imply:
% 144.76/20.29  | | | | | | | | | | | |   (1664)  op(e0, e0) = e2
% 144.76/20.29  | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | BETA: splitting (84) gives:
% 144.76/20.29  | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | Case 1:
% 144.76/20.29  | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | |   (1665)   ~ (all_36_2 = e2)
% 144.76/20.29  | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | REDUCE: (304), (1665) imply:
% 144.76/20.29  | | | | | | | | | | | | |   (1666)   ~ (all_14_2 = e2)
% 144.76/20.29  | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | BETA: splitting (203) gives:
% 144.76/20.29  | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | Case 1:
% 144.76/20.29  | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | |   (1667)  all_54_0 = e3
% 144.76/20.29  | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | COMBINE_EQS: (278), (1667) imply:
% 144.76/20.29  | | | | | | | | | | | | | |   (1668)  all_14_2 = e3
% 144.76/20.29  | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | SIMP: (1668) implies:
% 144.76/20.29  | | | | | | | | | | | | | |   (1669)  all_14_2 = e3
% 144.76/20.29  | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | REDUCE: (342), (1669) imply:
% 144.76/20.29  | | | | | | | | | | | | | |   (1670)   ~ (all_52_4 = e3)
% 144.76/20.29  | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | REDUCE: (344), (1669) imply:
% 144.76/20.29  | | | | | | | | | | | | | |   (1671)   ~ (all_52_8 = e3)
% 144.76/20.29  | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | REDUCE: (346), (1669) imply:
% 144.76/20.29  | | | | | | | | | | | | | |   (1672)   ~ (all_52_12 = e3)
% 144.76/20.29  | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | REDUCE: (51), (1669) imply:
% 144.76/20.29  | | | | | | | | | | | | | |   (1673)  op(e3, e3) = e3
% 144.76/20.29  | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 144.76/20.29  | | | | | | | | | | | | | | 
% 144.76/20.29  | | | | | | | | | | | | | | Case 1:
% 144.76/20.29  | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | |   (1674)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.29  | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.29  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.29  | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.29  | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.29  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.29  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.29  | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.29  | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.29  | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.29  | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.29  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.29  | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.29  | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.29  | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.29  | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.29  | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 145.15/20.29  | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 145.15/20.29  | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 145.15/20.29  | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 145.15/20.29  | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 145.15/20.29  | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.29  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.29  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.15/20.29  | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.15/20.29  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 145.15/20.29  | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 145.15/20.29  | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 145.15/20.29  | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.29  | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 145.15/20.29  | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 145.15/20.29  | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 145.15/20.29  | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 145.15/20.29  | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 145.15/20.29  | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.29  | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.29  | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.29  | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.15/20.29  | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | BETA: splitting (1674) gives:
% 145.15/20.29  | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | Case 1:
% 145.15/20.29  | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | |   (1675)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.29  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.29  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.29  | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.29  | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.29  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.29  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.29  | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.29  | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.29  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.29  | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.29  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.29  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.29  | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.29  | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.29  | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.29  | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.15/20.29  | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | BETA: splitting (1675) gives:
% 145.15/20.29  | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.29  | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | |   (1676)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.29  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.29  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.29  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.29  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.29  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.29  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.29  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.29  | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | | BETA: splitting (1676) gives:
% 145.15/20.29  | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.29  | | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | | |   (1677)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.29  | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.29  | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.29  | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 145.15/20.29  | | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | | | ALPHA: (1677) implies:
% 145.15/20.29  | | | | | | | | | | | | | | | | | |   (1678)  op(e1, e1) = e3
% 145.15/20.29  | | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (374), (1678), (function-axioms) are
% 145.15/20.29  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 145.15/20.29  | | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.29  | | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | | |   (1679)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.29  | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.29  | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.29  | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 145.15/20.29  | | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | | | ALPHA: (1679) implies:
% 145.15/20.29  | | | | | | | | | | | | | | | | | |   (1680)  op(e0, e0) = e3
% 145.15/20.29  | | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1664), (1680), (function-axioms) are
% 145.15/20.29  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 145.15/20.29  | | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | | End of split
% 145.15/20.29  | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.29  | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | |   (1681)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.29  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.29  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.29  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.29  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.29  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.29  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.29  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.29  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.15/20.29  | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (1265), (1664), (1681),
% 145.15/20.29  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.29  | | | | | | | | | | | | | | | | |            #730.
% 145.15/20.29  | | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | | End of split
% 145.15/20.29  | | | | | | | | | | | | | | | | 
% 145.15/20.29  | | | | | | | | | | | | | | | Case 2:
% 145.15/20.29  | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | |   (1682)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.30  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.15/20.30  | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.15/20.30  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.15/20.30  | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.30  | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.15/20.30  | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 145.15/20.30  | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.30  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.15/20.30  | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.15/20.30  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.15/20.30  | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.15/20.30  | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | BETA: splitting (1682) gives:
% 145.15/20.30  | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | |   (1683)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.30  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.15/20.30  | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1670), (1683), (function-axioms) are
% 145.15/20.30  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | |   (1684)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.15/20.30  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.15/20.30  | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 145.15/20.30  | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.30  | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (161), (168), (1255), (1671), (1673), (1684),
% 145.15/20.30  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.30  | | | | | | | | | | | | | | | | |            #729.
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | End of split
% 145.15/20.30  | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | End of split
% 145.15/20.30  | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | Case 2:
% 145.15/20.30  | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | |   (1685)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.30  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.30  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.30  | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.30  | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.30  | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.30  | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.15/20.30  | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.15/20.30  | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.30  | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.15/20.30  | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.15/20.30  | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.15/20.30  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.15/20.30  | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.15/20.30  | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.30  | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.30  | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.30  | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 145.15/20.30  | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 145.15/20.30  | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 145.15/20.30  | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 145.15/20.30  | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 145.15/20.30  | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 145.15/20.30  | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 145.15/20.30  | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 145.15/20.30  | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 145.15/20.30  | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.30  | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.30  | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.15/20.30  | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.15/20.30  | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.30  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.15/20.30  | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.15/20.30  | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.15/20.30  | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.15/20.30  | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.30  | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.30  | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.30  | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.30  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.30  | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.30  | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.30  | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.30  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.30  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.30  | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.30  | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.30  | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.30  | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | BETA: splitting (1685) gives:
% 145.15/20.30  | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | Case 1:
% 145.15/20.30  | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | |   (1686)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.30  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.30  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.30  | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.30  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.15/20.30  | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.15/20.30  | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.15/20.30  | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.15/20.30  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.15/20.30  | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.15/20.30  | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 145.15/20.30  | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | BETA: splitting (1686) gives:
% 145.15/20.30  | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | |   (1687)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.30  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.30  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.30  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (168), (203), (278), (376), (1267), (1666),
% 145.15/20.30  | | | | | | | | | | | | | | | | |            (1671), (1687), (function-axioms) are inconsistent
% 145.15/20.30  | | | | | | | | | | | | | | | | |            by sub-proof #727.
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | |   (1688)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.30  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 145.15/20.30  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 145.15/20.30  | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 145.15/20.30  | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (1664), (1672), (1688),
% 145.15/20.30  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.30  | | | | | | | | | | | | | | | | |            #976.
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | End of split
% 145.15/20.30  | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | Case 2:
% 145.15/20.30  | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | |   (1689)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.15/20.30  | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.15/20.30  | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.15/20.30  | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.15/20.30  | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.15/20.30  | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.15/20.30  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 145.15/20.30  | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.30  | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 145.15/20.30  | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 145.15/20.30  | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 145.15/20.30  | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 145.15/20.30  | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 145.15/20.30  | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.15/20.30  | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 145.15/20.30  | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 145.15/20.30  | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 145.15/20.30  | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.30  | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.30  | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.30  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.30  | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.30  | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.30  | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.30  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.30  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.30  | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.30  | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.30  | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.30  | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | BETA: splitting (1689) gives:
% 145.15/20.30  | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | |   (1690)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.15/20.30  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.15/20.30  | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.15/20.30  | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.15/20.30  | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.15/20.30  | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (376), (1267), (1666), (1690),
% 145.15/20.30  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.30  | | | | | | | | | | | | | | | | |            #1079.
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | |   (1691)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.15/20.30  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.15/20.30  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.30  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.30  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.30  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.30  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.30  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.30  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.30  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.30  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | | BETA: splitting (1691) gives:
% 145.15/20.30  | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.30  | | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | | |   (1692)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.15/20.30  | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.30  | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.30  | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.30  | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 145.15/20.30  | | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | | | ALPHA: (1692) implies:
% 145.15/20.30  | | | | | | | | | | | | | | | | | |   (1693)  op(e2, e0) = e2
% 145.15/20.30  | | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (1662), (1693), (function-axioms) are
% 145.15/20.30  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 145.15/20.30  | | | | | | | | | | | | | | | | | | 
% 145.15/20.30  | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.30  | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | |   (1694)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 145.15/20.31  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.15/20.31  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 145.15/20.31  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 145.15/20.31  | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 145.15/20.31  | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | BETA: splitting (1694) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |   (1695)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | ALPHA: (1695) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |   (1696)  op(e2, e2) = e0
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1265), (1696), (function-axioms) are
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |   (1697)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | ALPHA: (1697) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |   (1698)  op(e0, e0) = all_57_15
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |   (1699)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (1699) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |   (1700)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1700) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |   (1701)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1701) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |   (1702)  op(e2, e2) = e3
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1265), (1702), (function-axioms) are
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |   (1703)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1703) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |   (1704)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1704) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |   (1705)  op(e1, e1) = e3
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (374), (1705), (function-axioms) are
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |   (1706)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1706) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |   (1707)   ~ (all_57_15 = e2)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1664), (1698), (1707), (function-axioms) are
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #901.
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |   (1708)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1708) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |   (1709)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (1709) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |   (1710)   ~ (all_57_15 = e2)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1664), (1698), (1710), (function-axioms) are
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #901.
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |   (1711)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1711) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |   (1712)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_6)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1712) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |   (1713)  op(e3, e3) = e1
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (376), (1267), (1666), (1713),
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |            #728.
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |   (1714)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1714) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |   (1715)   ~ (all_57_15 = e1)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |   (1716)   ~ (all_57_7 = e2)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |   (1717)  op(e0, e1) = e0
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | |   (1718)  op(e2, e1) = all_57_7
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |   (1719)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1719) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |   (1720)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (1664), (1698)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |   (1721)  all_57_15 = e2
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (156), (1717) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |   (1722)  all_52_11 = e0
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_7, e1, e2, simplifying with (164), (1718)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |   (1723)  all_57_7 = all_52_9
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1716), (1723) imply:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |   (1724)   ~ (all_52_9 = e2)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (1722) imply:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |   (1725)   ~ (all_52_3 = e0)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (1722) imply:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |   (1726)   ~ (all_52_7 = e0)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (1722) imply:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |   (1727)   ~ (all_4_2 = e0)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1727) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |   (1728)   ~ (all_4_2 = e0)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1661), (1722) imply:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | |   (1729)   ~ (e2 = e0)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (1730)  all_54_10 = e3
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (1730) are inconsistent by sub-proof
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | |            #1173.
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (1731)   ~ (all_54_10 = e3)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (1732)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1733)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1733) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1734)  all_56_2 = e2 & op(e2, e3) = e2
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1734) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1735)  all_56_2 = e2
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1736)  all_56_15 = e0 & op(e0, e0) = e0
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1736) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1737)  op(e0, e0) = e0
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (156), (367), (1717), (1737),
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1034.
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1738)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1738) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1739)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1732) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1740)  all_54_10 = e2
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (1740) are inconsistent by sub-proof
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1168.
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1741)   ~ (all_54_10 = e2)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1742)  all_54_10 = e1 | all_54_10 = e0
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1739) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1743)  all_56_12 = e0 & op(e0, e3) = e0
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1743) implies:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1744)  op(e0, e3) = e0
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1725), (1744), (function-axioms) are
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1745)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1745) gives:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1746)  all_56_13 = e0 & op(e0, e2) = e0
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1746) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1747)  op(e0, e2) = e0
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1726), (1747), (function-axioms) are
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1748)  all_56_14 = e0 & op(e0, e1) = e0
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1748) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1749)  all_56_14 = e0
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1750)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1750) gives:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1751)  all_56_4 = e3 & op(e3, e1) = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1751) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1752)  op(e3, e1) = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1671), (1752), (function-axioms) are
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1753)  all_56_5 = e3 & op(e2, e1) = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1753) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1754)  op(e2, e1) = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1755)   ~ (all_38_2 = e1)
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1252), (1755) imply:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1756)  $false
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1756) is inconsistent.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1757)  ( ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = all_38_1 & $i(all_38_0) &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e2, e1)
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_38_1 & $i(all_38_1))
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1757) gives:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1758)   ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0 &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_38_1 & $i(all_38_0) &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_38_1)
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1758) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1759)  op(e2, e1) = all_38_1
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (157), (158), (159), (161),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (167), (168), (169), (214),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (224), (228), (238), (334), (348), (359),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (366), (371), (374), (1249), (1265), (1662),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1663), (1664), (1670), (1671), (1672), (1673),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1724), (1725), (1726), (1728), (1735), (1742),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1754), (1759), (function-axioms) are inconsistent
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #714.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1760)   ~ (all_38_1 = e0) & op(e2, e1) = all_38_1 &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_38_1)
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1760) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1761)  op(e2, e1) = all_38_1
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (36), (157), (158), (159), (161),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (167), (168), (169), (214),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (224), (228), (238), (334), (348), (359),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (366), (371), (374), (1249), (1265), (1662),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1663), (1664), (1670), (1671), (1672), (1673),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1724), (1725), (1726), (1728), (1735), (1742),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1754), (1761), (function-axioms) are inconsistent
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #714.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1762)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1762) gives:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1763)  all_56_8 = e3 & op(e1, e1) = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1763) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1764)  op(e1, e1) = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (374), (1764), (function-axioms) are
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1765)  all_56_14 = e3 & op(e0, e1) = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1765) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1766)  all_56_14 = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1749), (1766) imply:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1767)  e3 = e0
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1767) imply:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1768)  $false
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1768) is inconsistent.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1769)  all_56_3 = e2 & op(e2, e2) = e2
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1769) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1770)  op(e2, e2) = e2
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1265), (1770), (function-axioms) are
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1771)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (1662), (1724), (1771),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1155.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |   (1772)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1772) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |   (1773)  op(e2, e2) = e2
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1265), (1773), (function-axioms) are
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |   (1774)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1774) gives:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |   (1775)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1775) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |   (1776)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1265), (1716), (1776), (function-axioms) are
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #713.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |   (1777)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1777) implies:
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |   (1778)  op(e0, e0) = e0
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (156), (367), (1717), (1778),
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | |            #1034.
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | |   (1779)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 145.15/20.32  | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | | REF_CLOSE: (278), (376), (1267), (1666), (1779) are
% 145.15/20.32  | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 145.15/20.32  | | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | |   (1780)  all_36_2 = e2
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | COMBINE_EQS: (304), (1780) imply:
% 145.15/20.32  | | | | | | | | | | | | |   (1781)  all_14_2 = e2
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | SIMP: (1781) implies:
% 145.15/20.32  | | | | | | | | | | | | |   (1782)  all_14_2 = e2
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | REDUCE: (336), (1782) imply:
% 145.15/20.32  | | | | | | | | | | | | |   (1783)   ~ (all_52_1 = e2)
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | REDUCE: (51), (1782) imply:
% 145.15/20.32  | | | | | | | | | | | | |   (1784)  op(e3, e3) = e2
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (159), (163),
% 145.15/20.32  | | | | | | | | | | | | |            (166), (214), (228), (230), (234), (237), (238),
% 145.15/20.32  | | | | | | | | | | | | |            (1265), (1662), (1663), (1664), (1783), (1784),
% 145.15/20.32  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.32  | | | | | | | | | | | | |            #705.
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | |   (1785)  all_22_2 = e1
% 145.15/20.32  | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | COMBINE_EQS: (320), (1785) imply:
% 145.15/20.32  | | | | | | | | | | |   (1786)  all_14_2 = e1
% 145.15/20.32  | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | SIMP: (1786) implies:
% 145.15/20.32  | | | | | | | | | | |   (1787)  all_14_2 = e1
% 145.15/20.32  | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | REDUCE: (346), (1787) imply:
% 145.15/20.32  | | | | | | | | | | |   (1788)   ~ (all_52_12 = e1)
% 145.15/20.32  | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | REDUCE: (51), (1787) imply:
% 145.15/20.32  | | | | | | | | | | |   (1789)  op(e3, e3) = e1
% 145.15/20.32  | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | BETA: splitting (209) gives:
% 145.15/20.32  | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | Case 1:
% 145.15/20.32  | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | |   (1790)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 145.15/20.32  | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 145.15/20.32  | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | BETA: splitting (1790) gives:
% 145.15/20.32  | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | Case 1:
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | |   (1791)  all_56_9 = e1 & op(e3, e0) = e1
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | ALPHA: (1791) implies:
% 145.15/20.32  | | | | | | | | | | | | |   (1792)  op(e3, e0) = e1
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 145.15/20.32  | | | | | | | | | | | | |              e1, e0, e3, simplifying with (167), (1792) gives:
% 145.15/20.32  | | | | | | | | | | | | |   (1793)  all_52_12 = e1
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | REDUCE: (1788), (1793) imply:
% 145.15/20.32  | | | | | | | | | | | | |   (1794)  $false
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | CLOSE: (1794) is inconsistent.
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | |   (1795)  all_56_10 = e1 & op(e2, e0) = e1
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | ALPHA: (1795) implies:
% 145.15/20.32  | | | | | | | | | | | | |   (1796)  op(e2, e0) = e1
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 145.15/20.32  | | | | | | | | | | | | |              e1, e0, e2, simplifying with (163), (1796) gives:
% 145.15/20.32  | | | | | | | | | | | | |   (1797)  all_52_13 = e1
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | REDUCE: (1258), (1797) imply:
% 145.15/20.32  | | | | | | | | | | | | |   (1798)  $false
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | CLOSE: (1798) is inconsistent.
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | |   (1799)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 145.15/20.32  | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 145.15/20.32  | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | BETA: splitting (1799) gives:
% 145.15/20.32  | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | Case 1:
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | |   (1800)  all_56_11 = e1 & op(e1, e0) = e1
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | ALPHA: (1800) implies:
% 145.15/20.32  | | | | | | | | | | | | |   (1801)  op(e1, e0) = e1
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (45), (140), (156), (159), (162),
% 145.15/20.32  | | | | | | | | | | | | |            (193), (237), (238), (334), (366), (367), (371),
% 145.15/20.32  | | | | | | | | | | | | |            (374), (1265), (1789), (1801), (function-axioms)
% 145.15/20.32  | | | | | | | | | | | | |            are inconsistent by sub-proof #757.
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | |   (1802)  all_56_15 = e1 & op(e0, e0) = e1
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | ALPHA: (1802) implies:
% 145.15/20.32  | | | | | | | | | | | | |   (1803)  op(e0, e0) = e1
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | | REF_CLOSE: (45), (375), (1803), (function-axioms) are
% 145.15/20.32  | | | | | | | | | | | | |            inconsistent by sub-proof #1116.
% 145.15/20.32  | | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | 
% 145.15/20.32  | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | 
% 145.15/20.32  | | | | | | | | |   (1804)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1
% 145.15/20.32  | | | | | | | | |             & op(e2, e0) = e1)
% 145.15/20.32  | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | BETA: splitting (1804) gives:
% 145.15/20.32  | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | Case 1:
% 145.15/20.32  | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | |   (1805)  all_56_5 = e1 & op(e2, e1) = e1
% 145.15/20.32  | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | ALPHA: (1805) implies:
% 145.15/20.32  | | | | | | | | | |   (1806)  op(e2, e1) = e1
% 145.15/20.32  | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | REF_CLOSE: (164), (1257), (1806), (function-axioms) are
% 145.15/20.32  | | | | | | | | | |            inconsistent by sub-proof #704.
% 145.15/20.32  | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | |   (1807)  all_56_10 = e1 & op(e2, e0) = e1
% 145.15/20.32  | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | | REF_CLOSE: (163), (1258), (1807), (function-axioms) are
% 145.15/20.32  | | | | | | | | | |            inconsistent by sub-proof #810.
% 145.15/20.32  | | | | | | | | | | 
% 145.15/20.32  | | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | | 
% 145.15/20.32  | | | | | | | | End of split
% 145.15/20.32  | | | | | | | | 
% 145.15/20.32  | | | | | | | End of split
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | Case 2:
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | |   (1808)  all_16_2 = e0
% 145.15/20.32  | | | | | | |   (1809)  ( ~ (all_16_0 = e3) & op(all_16_1, e2) = all_16_0 &
% 145.15/20.32  | | | | | | |             op(e2, e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)) |
% 145.15/20.32  | | | | | | |           ( ~ (all_16_1 = e1) & op(e2, e0) = all_16_1 &
% 145.15/20.32  | | | | | | |             $i(all_16_1))
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | | COMBINE_EQS: (327), (1808) imply:
% 145.15/20.32  | | | | | | |   (1810)  all_6_2 = e0
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | | COMBINE_EQS: (325), (1810) imply:
% 145.15/20.32  | | | | | | |   (1811)  all_18_2 = e0
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | | REDUCE: (347), (1810) imply:
% 145.15/20.32  | | | | | | |   (1812)   ~ (all_52_1 = e0)
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | | REDUCE: (350), (1810) imply:
% 145.15/20.32  | | | | | | |   (1813)   ~ (all_52_4 = e0)
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | | REDUCE: (352), (1810) imply:
% 145.15/20.32  | | | | | | |   (1814)   ~ (all_52_6 = e0)
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | | REDUCE: (354), (1810) imply:
% 145.15/20.32  | | | | | | |   (1815)   ~ (all_52_7 = e0)
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | | REDUCE: (356), (1810) imply:
% 145.15/20.32  | | | | | | |   (1816)   ~ (all_52_9 = e0)
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | | REDUCE: (372), (1810) imply:
% 145.15/20.32  | | | | | | |   (1817)   ~ (e3 = e0)
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | | REDUCE: (39), (1810) imply:
% 145.15/20.32  | | | | | | |   (1818)  op(e2, e2) = e0
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | | BETA: splitting (58) gives:
% 145.15/20.32  | | | | | | | 
% 145.15/20.32  | | | | | | | Case 1:
% 145.15/20.32  | | | | | | | | 
% 145.15/20.32  | | | | | | | |   (1819)   ~ (all_18_2 = e0)
% 145.15/20.32  | | | | | | | | 
% 145.15/20.32  | | | | | | | | REDUCE: (1811), (1819) imply:
% 145.15/20.32  | | | | | | | |   (1820)  $false
% 145.15/20.32  | | | | | | | | 
% 145.15/20.32  | | | | | | | | CLOSE: (1820) is inconsistent.
% 145.15/20.32  | | | | | | | | 
% 145.15/20.32  | | | | | | | Case 2:
% 145.15/20.32  | | | | | | | | 
% 145.15/20.33  | | | | | | | |   (1821)  ( ~ (all_18_0 = e1) & op(all_18_1, e2) = all_18_0 &
% 145.15/20.33  | | | | | | | |             op(e2, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1))
% 145.15/20.33  | | | | | | | |           | ( ~ (all_18_1 = e3) & op(e2, e0) = all_18_1 &
% 145.15/20.33  | | | | | | | |             $i(all_18_1))
% 145.15/20.33  | | | | | | | | 
% 145.15/20.33  | | | | | | | | BETA: splitting (64) gives:
% 145.15/20.33  | | | | | | | | 
% 145.15/20.33  | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | 
% 145.15/20.33  | | | | | | | | |   (1822)   ~ (all_22_2 = e1)
% 145.15/20.33  | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | REDUCE: (320), (1822) imply:
% 145.15/20.33  | | | | | | | | |   (1823)   ~ (all_14_2 = e1)
% 145.15/20.33  | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | BETA: splitting (67) gives:
% 145.15/20.33  | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | |   (1824)   ~ (all_24_2 = e2)
% 145.15/20.33  | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | REDUCE: (318), (1824) imply:
% 145.15/20.33  | | | | | | | | | |   (1825)   ~ (all_10_2 = e2)
% 145.15/20.33  | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | BETA: splitting (84) gives:
% 145.15/20.33  | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | |   (1826)   ~ (all_36_2 = e2)
% 145.15/20.33  | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | REDUCE: (304), (1826) imply:
% 145.15/20.33  | | | | | | | | | | |   (1827)   ~ (all_14_2 = e2)
% 145.15/20.33  | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | BETA: splitting (203) gives:
% 145.15/20.33  | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | |   (1828)  all_54_0 = e3
% 145.15/20.33  | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | COMBINE_EQS: (278), (1828) imply:
% 145.15/20.33  | | | | | | | | | | | |   (1829)  all_14_2 = e3
% 145.15/20.33  | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | REDUCE: (336), (1829) imply:
% 145.15/20.33  | | | | | | | | | | | |   (1830)   ~ (all_52_1 = e3)
% 145.15/20.33  | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | REDUCE: (342), (1829) imply:
% 145.15/20.33  | | | | | | | | | | | |   (1831)   ~ (all_52_4 = e3)
% 145.15/20.33  | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | REDUCE: (344), (1829) imply:
% 145.15/20.33  | | | | | | | | | | | |   (1832)   ~ (all_52_8 = e3)
% 145.15/20.33  | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | REDUCE: (346), (1829) imply:
% 145.15/20.33  | | | | | | | | | | | |   (1833)   ~ (all_52_12 = e3)
% 145.15/20.33  | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | REDUCE: (51), (1829) imply:
% 145.15/20.33  | | | | | | | | | | | |   (1834)  op(e3, e3) = e3
% 145.15/20.33  | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | BETA: splitting (93) gives:
% 145.15/20.33  | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | |   (1835)   ~ (all_42_2 = e3)
% 145.15/20.33  | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | REDUCE: (302), (1835) imply:
% 145.15/20.33  | | | | | | | | | | | | |   (1836)   ~ (all_10_2 = e3)
% 145.15/20.33  | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | BETA: splitting (238) gives:
% 145.15/20.33  | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | |   (1837)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.33  | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.33  | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.33  | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.33  | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.33  | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.33  | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.33  | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.33  | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 145.15/20.33  | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 145.15/20.33  | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 145.15/20.33  | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.33  | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.15/20.33  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 145.15/20.33  | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 145.15/20.33  | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.33  | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 145.15/20.33  | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 145.15/20.33  | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 145.15/20.33  | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 145.15/20.33  | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.33  | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.15/20.33  | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | BETA: splitting (1837) gives:
% 145.15/20.33  | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | |   (1838)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.33  | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.33  | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.33  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.33  | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.33  | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.33  | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.33  | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.33  | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.33  | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | BETA: splitting (1838) gives:
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | |   (1839)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.33  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.33  | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.33  | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.33  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.33  | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | BETA: splitting (1839) gives:
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | |   (1840)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.33  | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.33  | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | | ALPHA: (1840) implies:
% 145.15/20.33  | | | | | | | | | | | | | | | | |   (1841)  op(e1, e1) = e3
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (374), (1841), (function-axioms) are
% 145.15/20.33  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | |   (1842)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.33  | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.33  | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | | ALPHA: (1842) implies:
% 145.15/20.33  | | | | | | | | | | | | | | | | |   (1843)  op(e0, e0) = e3
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (188), (245), (375), (1825), (1836), (1843),
% 145.15/20.33  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.33  | | | | | | | | | | | | | | | | |            #701.
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | End of split
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | Case 2:
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | |   (1844)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.33  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.33  | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.33  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.33  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.33  | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.33  | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.33  | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.33  | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | BETA: splitting (1844) gives:
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | |   (1845)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.33  | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.33  | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.33  | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.33  | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | | ALPHA: (1845) implies:
% 145.15/20.33  | | | | | | | | | | | | | | | | |   (1846)  op(e2, e2) = e3
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1818), (1846), (function-axioms) are
% 145.15/20.33  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | |   (1847)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.33  | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 145.15/20.33  | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 145.15/20.33  | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | | ALPHA: (1847) implies:
% 145.15/20.33  | | | | | | | | | | | | | | | | |   (1848)  op(e0, e0) = e3
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (188), (245), (375), (1825), (1836), (1848),
% 145.15/20.33  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.33  | | | | | | | | | | | | | | | | |            #701.
% 145.15/20.33  | | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | End of split
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | End of split
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | Case 2:
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | |   (1849)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.33  | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.33  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.15/20.33  | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.15/20.33  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.15/20.33  | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 145.15/20.33  | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.33  | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.15/20.33  | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 145.15/20.33  | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 145.15/20.33  | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.33  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.15/20.33  | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.15/20.33  | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.33  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.15/20.33  | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (45), (169), (1818), (1825), (1831),
% 145.15/20.33  | | | | | | | | | | | | | | |            (1834), (1849), (function-axioms) are inconsistent
% 145.15/20.33  | | | | | | | | | | | | | | |            by sub-proof #699.
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | End of split
% 145.15/20.33  | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | Case 2:
% 145.15/20.33  | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | |   (1850)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.33  | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.33  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.33  | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.33  | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.15/20.33  | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.15/20.33  | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.15/20.33  | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.15/20.33  | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.15/20.33  | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.15/20.33  | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.33  | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 145.15/20.33  | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 145.15/20.33  | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 145.15/20.33  | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 145.15/20.33  | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 145.15/20.33  | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 145.15/20.33  | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 145.15/20.33  | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 145.15/20.33  | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.33  | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.15/20.33  | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.33  | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.15/20.33  | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.15/20.33  | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.15/20.33  | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.15/20.33  | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.15/20.33  | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.33  | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.33  | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.33  | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.33  | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.33  | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.33  | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.33  | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.33  | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.33  | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.33  | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.33  | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.33  | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.33  | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.33  | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.33  | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.33  | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.33  | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.33  | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.33  | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | BETA: splitting (1850) gives:
% 145.15/20.33  | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | |   (1851)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.33  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.33  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.33  | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.33  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.33  | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.33  | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.15/20.33  | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.15/20.33  | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.15/20.33  | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.15/20.33  | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.15/20.33  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.15/20.33  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.15/20.33  | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.15/20.33  | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.33  | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.33  | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | BETA: splitting (1851) gives:
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | Case 1:
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | |   (1852)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.33  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.33  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.33  | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.33  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.33  | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.33  | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.33  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.33  | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (1832), (1834), (1852),
% 145.15/20.33  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.33  | | | | | | | | | | | | | | | |            #860.
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | Case 2:
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | |   (1853)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.33  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 145.15/20.33  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 145.15/20.33  | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.33  | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 145.15/20.33  | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 145.15/20.33  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.33  | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.33  | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 145.15/20.33  | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 145.15/20.33  | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.33  | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 145.15/20.33  | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (375), (1833), (1853),
% 145.15/20.33  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.33  | | | | | | | | | | | | | | | |            #1080.
% 145.15/20.33  | | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | | End of split
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.33  | | | | | | | | | | | | | | Case 2:
% 145.15/20.33  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | |   (1854)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.15/20.34  | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.15/20.34  | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.15/20.34  | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.15/20.34  | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.15/20.34  | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.15/20.34  | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.15/20.34  | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 145.15/20.34  | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.34  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 145.15/20.34  | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.34  | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 145.15/20.34  | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 145.15/20.34  | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 145.15/20.34  | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 145.15/20.34  | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 145.15/20.34  | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.15/20.34  | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 145.15/20.34  | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.34  | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 145.15/20.34  | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 145.15/20.34  | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.34  | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.34  | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.34  | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.34  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.34  | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.34  | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.34  | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.34  | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.34  | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.34  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.34  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.34  | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.34  | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.34  | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.34  | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.34  | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.34  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | BETA: splitting (1854) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | |   (1855)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.15/20.34  | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.15/20.34  | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.15/20.34  | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.15/20.34  | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.15/20.34  | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.15/20.34  | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.15/20.34  | | | | | | | | | | | | | | | |             $i(all_57_14))
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (376), (1823), (1827), (1855),
% 145.15/20.34  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.34  | | | | | | | | | | | | | | | |            #1079.
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | |   (1856)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.15/20.34  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.34  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.34  | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.15/20.34  | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.15/20.34  | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.34  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.15/20.34  | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.15/20.34  | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.15/20.34  | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.15/20.34  | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.34  | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.34  | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.34  | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.34  | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.34  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.34  | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.34  | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.34  | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.34  | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.34  | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.34  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.34  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.34  | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.34  | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.34  | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.34  | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.34  | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | BETA: splitting (1856) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | |   (1857)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.15/20.34  | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.34  | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.34  | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | ALPHA: (1857) implies:
% 145.15/20.34  | | | | | | | | | | | | | | | | |   (1858)   ~ (all_57_12 = e0)
% 145.15/20.34  | | | | | | | | | | | | | | | | |   (1859)  op(e2, e2) = all_57_12
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | REF_CLOSE: (1818), (1858), (1859), (function-axioms) are
% 145.15/20.34  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | |   (1860)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.15/20.34  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 145.15/20.34  | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 145.15/20.34  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 145.15/20.34  | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 145.15/20.34  | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 145.15/20.34  | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.15/20.34  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 145.15/20.34  | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 145.15/20.34  | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 145.15/20.34  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 145.15/20.34  | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | BETA: splitting (1860) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | |   (1861)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | ALPHA: (1861) implies:
% 145.15/20.34  | | | | | | | | | | | | | | | | | |   (1862)  op(e1, e0) = e1
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | |   (1863)  all_54_15 = e3
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1863) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | |   (1864)  all_10_2 = e3
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | REDUCE: (1836), (1864) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | |   (1865)  $false
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | CLOSE: (1865) is inconsistent.
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | |   (1866)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | BETA: splitting (1866) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | |   (1867)  all_54_15 = e2
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1867) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | |   (1868)  all_10_2 = e2
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | REDUCE: (1825), (1868) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | |   (1869)  $false
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | CLOSE: (1869) is inconsistent.
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | |   (1870)  all_54_15 = e1 | all_54_15 = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1870) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1871)  all_54_15 = e1
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1871) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1872)  all_10_2 = e1
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (1872) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1873)  $false
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | CLOSE: (1873) is inconsistent.
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1874)  all_54_15 = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (1874) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1875)  all_10_2 = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (1875) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1876)   ~ (all_52_12 = e0)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |   (1877)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (169), (203), (278), (376), (1813), (1823),
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |            (1827), (1877), (function-axioms) are inconsistent
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #698.
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |   (1878)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1878) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | |   (1879)  all_56_4 = e0 & op(e3, e1) = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1879) implies:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | |   (1880)  op(e3, e1) = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (159), (1862) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | |   (1881)  all_52_14 = e1
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (1880) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | |   (1882)  all_52_8 = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (1882) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | |   (1883)   ~ (all_4_2 = e0)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (193), (334), (366), (371), (374), (1881), (1883)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #697.
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | |   (1884)  all_56_9 = e0 & op(e3, e0) = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (1876), (1884), (function-axioms) are
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | |   (1885)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 145.15/20.34  | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 145.15/20.34  | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | ALPHA: (1885) implies:
% 145.15/20.34  | | | | | | | | | | | | | | | | | |   (1886)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.15/20.34  | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.15/20.34  | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.15/20.34  | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (156), (157), (158), (188),
% 145.15/20.34  | | | | | | | | | | | | | | | | | |            (245), (349), (367), (375), (1815), (1818),
% 145.15/20.34  | | | | | | | | | | | | | | | | | |            (1825), (1834), (1836), (1886), (function-axioms)
% 145.15/20.34  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #693.
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | End of split
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | End of split
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | End of split
% 145.15/20.34  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | End of split
% 145.15/20.34  | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | End of split
% 145.15/20.34  | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | |   (1887)  all_42_2 = e3
% 145.15/20.34  | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | COMBINE_EQS: (302), (1887) imply:
% 145.15/20.34  | | | | | | | | | | | | |   (1888)  all_10_2 = e3
% 145.15/20.34  | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | SIMP: (1888) implies:
% 145.15/20.34  | | | | | | | | | | | | |   (1889)  all_10_2 = e3
% 145.15/20.34  | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | REDUCE: (367), (1889) imply:
% 145.15/20.34  | | | | | | | | | | | | |   (1890)   ~ (all_52_11 = e3)
% 145.15/20.34  | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | REDUCE: (45), (1889) imply:
% 145.15/20.34  | | | | | | | | | | | | |   (1891)  op(e0, e0) = e3
% 145.15/20.34  | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | BETA: splitting (215) gives:
% 145.15/20.34  | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | |   (1892)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 145.15/20.34  | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 145.15/20.34  | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | BETA: splitting (1892) gives:
% 145.15/20.34  | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | |   (1893)  all_56_6 = e3 & op(e1, e3) = e3
% 145.15/20.34  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | ALPHA: (1893) implies:
% 145.15/20.34  | | | | | | | | | | | | | | |   (1894)  all_56_6 = e3
% 145.15/20.34  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (166), (203),
% 145.15/20.34  | | | | | | | | | | | | | | |            (228), (230), (232), (278), (376), (1812), (1823),
% 145.15/20.34  | | | | | | | | | | | | | | |            (1827), (1834), (1894), (function-axioms) are
% 145.15/20.34  | | | | | | | | | | | | | | |            inconsistent by sub-proof #691.
% 145.15/20.34  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | |   (1895)  all_56_7 = e3 & op(e1, e2) = e3
% 145.15/20.34  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | ALPHA: (1895) implies:
% 145.15/20.34  | | | | | | | | | | | | | | |   (1896)  op(e1, e2) = e3
% 145.15/20.34  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | |   (1897)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 145.15/20.34  | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (166), (1818), (1830), (1897),
% 145.15/20.34  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.34  | | | | | | | | | | | | | | | |            #690.
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | |   (1898)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 145.15/20.34  | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | BETA: splitting (1898) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | |   (1899)  all_56_5 = e3 & op(e2, e1) = e3
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | ALPHA: (1899) implies:
% 145.15/20.34  | | | | | | | | | | | | | | | | |   (1900)  all_56_5 = e3
% 145.15/20.34  | | | | | | | | | | | | | | | | |   (1901)  op(e2, e1) = e3
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | |   (1902)   ~ (all_48_2 = e0)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | REDUCE: (298), (1902) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | |   (1903)   ~ (all_4_2 = e0)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | |   (1904)  all_54_10 = e3
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (1904) are inconsistent by sub-proof
% 145.15/20.34  | | | | | | | | | | | | | | | | | | |            #1173.
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | |   (1905)   ~ (all_54_10 = e3)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | |   (1906)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | BETA: splitting (1906) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | |   (1907)  all_54_10 = e2
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (1907) are inconsistent by sub-proof
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | |            #1168.
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | |   (1908)   ~ (all_54_10 = e2)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | |   (1909)  all_54_10 = e1 | all_54_10 = e0
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | BETA: splitting (1909) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1910)  all_54_10 = e1
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (1910) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1911)  all_4_2 = e1
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | SIMP: (1911) implies:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1912)  all_4_2 = e1
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (1912) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1913)   ~ (all_52_2 = e1)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (1912) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1914)   ~ (all_52_14 = e1)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (1912) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1915)   ~ (e3 = e1)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (1912) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1916)   ~ (e2 = e1)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1912) imply:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | |   (1917)  op(e1, e1) = e1
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |   (1918)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.15/20.34  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1918) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |   (1919)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1919) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |   (1920)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1920) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (1921)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1921) implies:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (1922)  op(e1, e1) = e3
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1917), (1922), (function-axioms) are
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (1923)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1923) implies:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (1924)   ~ (all_57_2 = e0)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (1925)  op(e2, e3) = e2
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1926)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1926) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1927)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1927) implies:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1928)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e0, e0) = all_57_15 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1891), (1924), (1928), (function-axioms) are
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #833.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1929)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1929) implies:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1930)  op(e2, e2) = e2
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1818), (1930), (function-axioms) are
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1931)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1931) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1932)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1932) implies:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1933)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1933) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1934)  all_57_7 = e2 & op(e2, e1) = e2
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1934) implies:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1935)  op(e2, e1) = e2
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1901), (1935), (function-axioms) are
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1135.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1936)   ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1936) implies:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1937)   ~ (all_57_12 = e1)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1938)  op(e2, e2) = all_57_12
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1939)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1939) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1940)  all_56_2 = e1 & op(e2, e3) = e1
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1940) implies:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1941)  op(e2, e3) = e1
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (1925), (1941), (function-axioms) are
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #842.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1942)  all_56_3 = e1 & op(e2, e2) = e1
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1942) implies:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1943)  op(e2, e2) = e1
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1937), (1938), (1943), (function-axioms) are
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1944)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1944) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1945)  all_56_5 = e1 & op(e2, e1) = e1
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1900), (1945) are inconsistent by sub-proof
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1153.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1946)  all_56_10 = e1 & op(e2, e0) = e1
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1809), (1821), (1896), (1946), (function-axioms)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #688.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1947)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1947) implies:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1948)  op(e0, e0) = e0
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1891), (1948), (function-axioms) are
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |   (1949)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1913), (1949), (function-axioms) are
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1025.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |   (1950)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (45), (169), (1818), (1825), (1831),
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |            (1834), (1950), (function-axioms) are inconsistent
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #699.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |   (1951)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1951) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |   (1952)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1952) gives:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |   (1953)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (1832), (1834), (1953),
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |            #860.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |   (1954)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (1833), (1891), (1954),
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | |            #1020.
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |   (1955)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1955) gives:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |   (1956)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (376), (1823), (1827), (1956),
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |            #1079.
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |   (1957)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1957) gives:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (1958)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1958) implies:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (1959)  op(e1, e1) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1917), (1959), (function-axioms) are
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (1960)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1960) gives:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1961)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1961) implies:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1962)  op(e1, e0) = e1
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1914), (1962), (function-axioms) are
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1963)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1963) implies:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1964)  op(e0, e0) = all_57_15
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1965)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1965) gives:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1966)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (157), (1815), (1818), (1891), (1964),
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1965), (1966), (function-axioms) are inconsistent
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #825.
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (1967)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (157), (1815), (1818), (1834), (1967),
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #823.
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | |   (1968)  all_54_10 = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (1903), (1968) are inconsistent by
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.36  | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | |   (1969)  all_48_2 = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (1969) imply:
% 145.15/20.36  | | | | | | | | | | | | | | | | | |   (1970)  all_4_2 = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | REDUCE: (361), (1970) imply:
% 145.15/20.36  | | | | | | | | | | | | | | | | | |   (1971)   ~ (all_52_8 = e0)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | REDUCE: (364), (1970) imply:
% 145.15/20.36  | | | | | | | | | | | | | | | | | |   (1972)   ~ (all_52_11 = e0)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | REDUCE: (371), (1970) imply:
% 145.15/20.36  | | | | | | | | | | | | | | | | | |   (1973)   ~ (e2 = e0)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | REDUCE: (36), (1970) imply:
% 145.15/20.36  | | | | | | | | | | | | | | | | | |   (1974)  op(e1, e1) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |   (1975)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (1975) gives:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |   (1976)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | ALPHA: (1976) implies:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |   (1977)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |               = e3) & op(e0, e0) = all_57_15 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |   (1978)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = all_57_14 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |   (1979)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = all_57_12 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | |   (1980)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (169), (203), (278), (376), (1813), (1823),
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | |            (1827), (1980), (function-axioms) are inconsistent
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #698.
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | |   (1981)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1981) gives:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | |   (1982)  all_56_4 = e0 & op(e3, e1) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1971), (1982), (function-axioms) are
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | |   (1983)  all_56_9 = e0 & op(e3, e0) = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1983) implies:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | |   (1984)  all_56_9 = e0
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |   (1985)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1985) gives:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |   (1986)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.36  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1986) gives:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (1987)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1977), (1978), (1987), (function-axioms) are
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #814.
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (1988)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1977), (1979), (1988), (function-axioms) are
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |   (1989)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (45), (169), (1818), (1825), (1831),
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |            (1834), (1989), (function-axioms) are inconsistent
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #699.
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |   (1990)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1990) gives:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |   (1991)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1991) gives:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (1992)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (1832), (1834), (1992),
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |            #860.
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (1993)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (1833), (1891), (1993),
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |            #1020.
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |   (1994)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1994) gives:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (1995)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1995) gives:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1996)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1996) implies:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1997)  op(e3, e3) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (231), (233),
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (1832), (1984), (1997), (function-axioms)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #687.
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1998)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1998) implies:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (1999)  op(e3, e3) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (231), (233),
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (1832), (1984), (1999), (function-axioms)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #687.
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (2000)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2000) gives:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2001)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2001) implies:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2002)   ~ (all_57_12 = e0)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2003)  op(e2, e2) = all_57_12
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1818), (2002), (2003), (function-axioms) are
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2004)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2004) gives:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2005)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2005) implies:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2006)   ~ (all_57_14 = e0)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2007)  op(e1, e1) = all_57_14
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1974), (2006), (2007), (function-axioms) are
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1026.
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2008)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2008) implies:
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2009)  op(e0, e0) = all_57_15
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2010)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (156), (157), (1815), (1818), (1891),
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1972), (2009), (2010), (function-axioms) are
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #802.
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2011)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | ALPHA: (2011) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2012)  op(e2, e2) = e2
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1818), (2012), (function-axioms) are
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |   (2013)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (1891), (1974), (2013),
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |            #1001.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | |   (2014)  all_56_10 = e3 & op(e2, e0) = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | ALPHA: (2014) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | |   (2015)  all_56_10 = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | |   (2016)  op(e2, e0) = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | |   (2017)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (168), (220),
% 145.15/20.38  | | | | | | | | | | | | | | | | | |            (221), (222), (223), (1818), (1832), (2015),
% 145.15/20.38  | | | | | | | | | | | | | | | | | |            (2016), (2017), (function-axioms) are inconsistent
% 145.15/20.38  | | | | | | | | | | | | | | | | | |            by sub-proof #674.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | |   (2018)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | BETA: splitting (2018) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |   (2019)  all_56_8 = e3 & op(e1, e1) = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | ALPHA: (2019) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |   (2020)  op(e1, e1) = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (51), (158), (162), (163),
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |            (188), (203), (221), (222), (228), (237), (245),
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |            (278), (349), (369), (375), (376), (1818), (1823),
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |            (1825), (1827), (2015), (2016), (2020),
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |            #667.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |   (2021)  all_56_14 = e3 & op(e0, e1) = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | ALPHA: (2021) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |   (2022)  op(e0, e1) = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (1890), (2022), (function-axioms) are
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1147.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | |   (2023)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 145.15/20.38  | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 145.15/20.38  | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | BETA: splitting (2023) gives:
% 145.15/20.38  | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | |   (2024)  all_56_8 = e3 & op(e1, e1) = e3
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | ALPHA: (2024) implies:
% 145.15/20.38  | | | | | | | | | | | | | | |   (2025)  op(e1, e1) = e3
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | REF_CLOSE: (36), (374), (2025), (function-axioms) are
% 145.15/20.38  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | |   (2026)  all_56_11 = e3 & op(e1, e0) = e3
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | ALPHA: (2026) implies:
% 145.15/20.38  | | | | | | | | | | | | | | |   (2027)  all_56_11 = e3
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (163), (205),
% 145.15/20.38  | | | | | | | | | | | | | | |            (209), (210), (1825), (1891), (2027),
% 145.15/20.38  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.38  | | | | | | | | | | | | | | |            #771.
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | |   (2028)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 145.15/20.38  | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | REF_CLOSE: (278), (376), (1823), (1827), (2028) are
% 145.15/20.38  | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 145.15/20.38  | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | |   (2029)  all_36_2 = e2
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | COMBINE_EQS: (304), (2029) imply:
% 145.15/20.38  | | | | | | | | | | |   (2030)  all_14_2 = e2
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | SIMP: (2030) implies:
% 145.15/20.38  | | | | | | | | | | |   (2031)  all_14_2 = e2
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | COMBINE_EQS: (280), (2031) imply:
% 145.15/20.38  | | | | | | | | | | |   (2032)  all_44_2 = e2
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | REDUCE: (336), (2031) imply:
% 145.15/20.38  | | | | | | | | | | |   (2033)   ~ (all_52_1 = e2)
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | REDUCE: (342), (2031) imply:
% 145.15/20.38  | | | | | | | | | | |   (2034)   ~ (all_52_4 = e2)
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | REDUCE: (344), (2031) imply:
% 145.15/20.38  | | | | | | | | | | |   (2035)   ~ (all_52_8 = e2)
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | REDUCE: (346), (2031) imply:
% 145.15/20.38  | | | | | | | | | | |   (2036)   ~ (all_52_12 = e2)
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | REDUCE: (51), (2031) imply:
% 145.15/20.38  | | | | | | | | | | |   (2037)  op(e3, e3) = e2
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | BETA: splitting (96) gives:
% 145.15/20.38  | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | |   (2038)   ~ (all_44_2 = e2)
% 145.15/20.38  | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | REDUCE: (2032), (2038) imply:
% 145.15/20.38  | | | | | | | | | | | |   (2039)  $false
% 145.15/20.38  | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | CLOSE: (2039) is inconsistent.
% 145.15/20.38  | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | |   (2040)  ( ~ (all_44_0 = e0) & op(all_44_1, e3) = all_44_0
% 145.15/20.38  | | | | | | | | | | | |             & op(e3, e2) = all_44_1 & $i(all_44_0) &
% 145.15/20.38  | | | | | | | | | | | |             $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e3, e2)
% 145.15/20.38  | | | | | | | | | | | |             = all_44_1 & $i(all_44_1))
% 145.15/20.38  | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | BETA: splitting (93) gives:
% 145.15/20.38  | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | |   (2041)   ~ (all_42_2 = e3)
% 145.15/20.38  | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | REDUCE: (302), (2041) imply:
% 145.15/20.38  | | | | | | | | | | | | |   (2042)   ~ (all_10_2 = e3)
% 145.15/20.38  | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | BETA: splitting (188) gives:
% 145.15/20.38  | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | |   (2043)  all_54_15 = e3
% 145.15/20.38  | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | REF_CLOSE: (245), (2042), (2043) are inconsistent by
% 145.15/20.38  | | | | | | | | | | | | | |            sub-proof #1049.
% 145.15/20.38  | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | |   (2044)   ~ (all_54_15 = e3)
% 145.15/20.38  | | | | | | | | | | | | | |   (2045)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 145.15/20.38  | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | BETA: splitting (2045) gives:
% 145.15/20.38  | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | |   (2046)  all_54_15 = e2
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | REF_CLOSE: (245), (1825), (2046) are inconsistent by
% 145.15/20.38  | | | | | | | | | | | | | | |            sub-proof #1048.
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | |   (2047)   ~ (all_54_15 = e2)
% 145.15/20.38  | | | | | | | | | | | | | | |   (2048)  all_54_15 = e1 | all_54_15 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | BETA: splitting (2048) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | |   (2049)  all_54_15 = e1
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | REF_CLOSE: (245), (375), (2049) are inconsistent by sub-proof
% 145.15/20.38  | | | | | | | | | | | | | | | |            #1047.
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | |   (2050)  all_54_15 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (2050) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | |   (2051)  all_10_2 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | SIMP: (2051) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | |   (2052)  all_10_2 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | REDUCE: (349), (2052) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | |   (2053)   ~ (all_52_3 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | REDUCE: (368), (2052) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | |   (2054)   ~ (all_52_12 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | REDUCE: (369), (2052) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | |   (2055)   ~ (all_52_13 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | REDUCE: (1825), (2052) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | |   (2056)   ~ (e2 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | REDUCE: (45), (2052) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | |   (2057)  op(e0, e0) = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | |   (2058)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (169), (1813), (2037), (2058),
% 145.15/20.38  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.38  | | | | | | | | | | | | | | | | |            #666.
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | |   (2059)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | BETA: splitting (2059) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | |   (2060)  all_56_4 = e0 & op(e3, e1) = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | ALPHA: (2060) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | |   (2061)  all_56_4 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | |   (2062)  op(e3, e1) = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |   (2063)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (2063) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2064)  all_56_0 = e0 & op(e3, e3) = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | ALPHA: (2064) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2065)  op(e3, e3) = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2037), (2065), (function-axioms) are
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2066)  all_56_2 = e0 & op(e2, e3) = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1812), (2066), (function-axioms) are
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #840.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |   (2067)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (2067) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2068)  all_56_6 = e0 & op(e1, e3) = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | ALPHA: (2068) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2069)  all_56_6 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2070)  op(e1, e3) = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (2070) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2071)  all_52_2 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (2062) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2072)  all_52_8 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (2071) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2073)   ~ (all_52_3 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (2071) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2074)   ~ (all_52_14 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | SIMP: (2074) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2075)   ~ (all_52_14 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (2072) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2076)   ~ (all_52_9 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (2072) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2077)   ~ (all_52_11 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | SIMP: (2077) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2078)   ~ (all_52_11 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (2072) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2079)   ~ (all_52_12 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (2072) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2080)   ~ (all_4_2 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | SIMP: (2080) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | |   (2081)   ~ (all_4_2 = e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | |   (2082)  all_54_10 = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (2082) are inconsistent by sub-proof
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | |            #1173.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | |   (2083)   ~ (all_54_10 = e3)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | |   (2084)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2084) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | |   (2085)  all_54_10 = e2
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (2085) are inconsistent by sub-proof
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | |            #1168.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | |   (2086)   ~ (all_54_10 = e2)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | |   (2087)  all_54_10 = e1 | all_54_10 = e0
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2087) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | |   (2088)  all_54_10 = e1
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2088) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | |   (2089)  all_4_2 = e1
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2089) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | |   (2090)  all_4_2 = e1
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (2090) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | |   (2091)   ~ (all_52_6 = e1)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (2090) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | |   (2092)   ~ (all_52_14 = e1)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (2090) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | |   (2093)   ~ (e3 = e1)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (2090) imply:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | |   (2094)   ~ (e2 = e1)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | |   (2095)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (161), (162), (2070), (2091), (2095),
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | |            #665.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | |   (2096)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2096) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (2097)  all_56_8 = e1 & op(e1, e1) = e1
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2097) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (2098)  all_56_8 = e1
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2099)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2099) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2100)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2100) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2101)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2033), (2101), (function-axioms) are
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2102)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2102) gives:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2103)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2103) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2104)  op(e1, e3) = e1
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (2070), (2104), (function-axioms) are
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2105)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2105) implies:
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2106)  op(e0, e0) = e3
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2057), (2106), (function-axioms) are
% 145.15/20.38  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2107)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2107) gives:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2108)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2108) gives:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2109)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2109) implies:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2110)   ~ (all_57_10 = e2)
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2111)  op(e3, e3) = all_57_10
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2037), (2110), (2111), (function-axioms) are
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1031.
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2112)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2112) implies:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2113)  op(e0, e0) = e2
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2057), (2113), (function-axioms) are
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2114)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2114) gives:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2115)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2115) implies:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2116)  op(e1, e2) = e1
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2091), (2116), (function-axioms) are
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2117)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1818), (2057), (2117),
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #664.
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2118)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2118) gives:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2119)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2119) gives:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2120)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2120) gives:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2121)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2121) implies:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2122)  op(e3, e1) = e3
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2062), (2122), (function-axioms) are
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #663.
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2123)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2123) implies:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2124)  op(e3, e3) = e1
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2037), (2124), (function-axioms) are
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2125)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2125) gives:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2126)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2126) implies:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2127)  op(e0, e0) = e1
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2057), (2127), (function-axioms) are
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.15/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2128)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2128) gives:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2129)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2129) implies:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2130)  all_57_12 = e0
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2131)   ~ (all_57_11 = e2)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2132)   ~ (all_57_10 = e0)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2133)  op(e2, e0) = all_57_11
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2134)  op(e3, e0) = e3
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2135)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (1818), (2037), (2135),
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #662.
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2136)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2136) gives:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2137)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2137) implies:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2138)  op(e1, e1) = e1
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2139)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e0, e0) = all_57_15 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2140)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2139) gives:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2141)  all_57_8 = e0 & op(e0, e1) = e0
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2141) implies:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2142)  op(e0, e1) = e0
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (2078), (2142), (function-axioms) are
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1124.
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2143)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_15)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2143) implies:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2144)   ~ (all_57_15 = e1)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2145)  op(e0, e0) = all_57_15
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2140) gives:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2146)  all_57_6 = e3 & op(e3, e1) = e3
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2146) implies:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2147)  op(e3, e1) = e3
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, e3, e1,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (2062), (2147) gives:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2148)  e3 = e0
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (2148) imply:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2149)  $false
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2149) is inconsistent.
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2150)   ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2150) implies:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2151)   ~ (all_57_10 = e1)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2152)  op(e3, e3) = all_57_10
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (2057), (2145)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2153)  all_57_15 = e0
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11, e0, e2, simplifying with (163), (2133)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2154)  all_57_11 = all_52_13
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (167), (2134) gives:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2155)  all_52_12 = e3
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (2037), (2152)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2156)  all_57_10 = e2
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2131), (2154) imply:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2157)   ~ (all_52_13 = e2)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2144), (2153) imply:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2158)   ~ (e1 = e0)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (2155) imply:
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2159)   ~ (all_52_4 = e3)
% 145.55/20.39  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (2155) imply:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2160)   ~ (all_52_13 = e3)
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2160) implies:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2161)   ~ (all_52_13 = e3)
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (2155) imply:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2162)   ~ (all_52_14 = e3)
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2162) implies:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2163)   ~ (all_52_14 = e3)
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2164)  all_54_11 = e3
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (2163), (2164) are inconsistent by
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #661.
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2165)   ~ (all_54_11 = e3)
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2166)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2167)  all_54_7 = e3
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (2161), (2167) are inconsistent by
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1163.
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2168)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2169)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (2037), (2159), (2169),
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #660.
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2170)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2170) gives:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2171)  all_56_4 = e3 & op(e3, e1) = e3
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2171) implies:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2172)  op(e3, e1) = e3
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2062), (2172), (function-axioms) are
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #663.
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2173)  all_56_9 = e3 & op(e3, e0) = e3
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2173) implies:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2174)  all_56_9 = e3
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2175)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2175) gives:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2176)  all_56_9 = e2 & op(e3, e0) = e2
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2176) implies:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2177)  all_56_9 = e2
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (235),
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2037), (2061), (2177), (function-axioms) are
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #651.
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2178)  all_56_10 = e2 & op(e2, e0) = e2
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.55/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2178) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2179)  op(e2, e0) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2157), (2179), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2180)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2180) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2181)  all_56_11 = e2 & op(e1, e0) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2181) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2182)  all_56_11 = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2183)  op(e1, e0) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2166) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2184)  all_54_11 = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (2184) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2185)  all_52_14 = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2185) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2186)  all_52_14 = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (2186) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2187)   ~ (all_52_6 = e2)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2163), (2186) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2188)   ~ (e3 = e2)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2189)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2189) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2190)  all_56_1 = e2 & op(e3, e2) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2034), (2190), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2191)  all_56_3 = e2 & op(e2, e2) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2191) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2192)  op(e2, e2) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1818), (2192), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2193)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2193) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2194)  all_56_7 = e2 & op(e1, e2) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2194) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2195)  op(e1, e2) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2187), (2195), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1171.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2196)  all_56_13 = e2 & op(e0, e2) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2196) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2197)  all_56_13 = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2168) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2198)  all_54_7 = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (2157), (2198) are inconsistent by
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1162.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2199)   ~ (all_54_7 = e2)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2200)  all_54_7 = e1 | all_54_7 = e0
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2201)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2201) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2202)  all_56_12 = e1 & op(e0, e3) = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2202) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2203)  all_56_12 = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2200) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2204)  all_54_7 = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (2204) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2205)  all_52_13 = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2205) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2206)  all_52_13 = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (2206) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2207)   ~ (all_52_1 = e1)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (2206) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2208)   ~ (all_52_9 = e1)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (2206) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2209)  op(e2, e0) = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2210)  all_54_4 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (2210) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2211)  all_52_1 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (2211) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2212)   ~ (all_52_9 = e3)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2212) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2213)   ~ (all_52_9 = e3)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2214)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2214) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2215)  all_56_0 = e3 & op(e3, e3) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2215) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2216)  op(e3, e3) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2037), (2216), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2217)  all_56_2 = e3 & op(e2, e3) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2217) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2218)  all_56_2 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2219)  all_54_6 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2213), (2219) are inconsistent by
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #650.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2220)   ~ (all_54_6 = e3)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2221)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2222)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2222) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2223)  all_56_2 = e2 & op(e2, e3) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2223) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2224)  op(e2, e3) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (166), (260), (1816), (2208), (2221),
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2224), (function-axioms) are inconsistent by
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #648.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2225)  all_56_3 = e2 & op(e2, e2) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2225) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2226)  op(e2, e2) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2197), (2226), (function-axioms) are inconsistent
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1104.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2227)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2227) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2228)  all_56_5 = e2 & op(e2, e1) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2228) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2229)  all_56_5 = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2230)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2230) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2231)  all_56_6 = e3 & op(e1, e3) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2231) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2232)  all_56_6 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2069), (2232) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2233)  e3 = e0
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2218), (2233) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2234)  all_56_2 = e0
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (221), (222),
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (1818), (2213), (2234), (function-axioms)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #646.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2235)  all_56_7 = e3 & op(e1, e2) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2235) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2236)  all_56_7 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2237)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2237) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2238)  all_56_4 = e3 & op(e3, e1) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2238) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2239)  op(e3, e1) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2062), (2239), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #663.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2240)  all_56_5 = e3 & op(e2, e1) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2213), (2240), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2241)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2241) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2242)  all_56_8 = e3 & op(e1, e1) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2242) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2243)  all_56_8 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (2182),
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2236), (2243) are inconsistent by sub-proof #643.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2244)  all_56_14 = e3 & op(e0, e1) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2244) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2245)  all_56_14 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2246)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2246) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2247)  all_56_0 = e1 & op(e3, e3) = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2247) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2248)  op(e3, e3) = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (166), (228), (232), (2033),
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2203), (2218), (2248), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #754.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2249)  all_56_1 = e1 & op(e3, e2) = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2249) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2250)  op(e3, e2) = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2040), (2070), (2250), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #642.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2251)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2251) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2252)  all_56_4 = e1 & op(e3, e1) = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2252) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2253)  all_56_4 = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2061), (2253) are inconsistent by sub-proof
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #657.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2254)  all_56_9 = e1 & op(e3, e0) = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2254) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2255)  all_56_9 = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2174), (2255) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2256)  e3 = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2256) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2257)  e3 = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2245), (2257) imply:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2258)  all_56_14 = e1
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (219), (2061), (2138), (2229),
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2258), (function-axioms) are inconsistent by
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #637.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2259)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2259) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2260)  all_56_8 = e3 & op(e1, e1) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2260) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2261)  op(e1, e1) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2138), (2261), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2262)  all_56_11 = e3 & op(e1, e0) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2262) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2263)  all_56_11 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2264)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2264) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2265)  all_56_9 = e2 & op(e3, e0) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2265) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2266)  all_56_9 = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2267)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (169), (1813), (2037), (2267),
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #666.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2059) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2268)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231),
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2037), (2266), (2268), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #653.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (2061), (2170), (2266) are inconsistent
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #652.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2269)  all_56_9 = e0 & op(e3, e0) = e0
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2266), (2269) are inconsistent by sub-proof
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #746.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2270)  all_56_10 = e2 & op(e2, e0) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2270) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2271)  op(e2, e0) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (2209), (2271), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #904.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (1825), (2180), (2263),
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #774.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2272)  all_56_10 = e2 & op(e2, e0) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2272) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2273)  op(e2, e0) = e2
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (2209), (2273), (function-axioms) are
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #904.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2274)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2274) gives:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2275)  all_56_6 = e3 & op(e1, e3) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2275) implies:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2276)  all_56_6 = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2069), (2276) are inconsistent by sub-proof
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #784.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2277)  all_56_12 = e3 & op(e0, e3) = e3
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2203), (2277) are inconsistent by sub-proof
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #919.
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2278)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (1812), (2033), (2207), (2278) are
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #636.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2279)  all_54_7 = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (2055), (2279) are inconsistent by
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1161.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2280)  all_56_13 = e1 & op(e0, e2) = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2280) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2281)  all_56_13 = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2197), (2281) are inconsistent by sub-proof
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1110.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2282)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2282) gives:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2283)  all_56_14 = e1 & op(e0, e1) = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2283) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2284)  all_56_14 = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2285)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2285) gives:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2286)  all_56_4 = e2 & op(e3, e1) = e2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2286) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2287)  all_56_4 = e2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2061), (2287) are inconsistent by sub-proof
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #936.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2288)  all_56_5 = e2 & op(e2, e1) = e2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2288) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2289)  all_56_5 = e2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (219), (2061), (2138), (2284),
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2289), (function-axioms) are inconsistent by
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #637.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2290)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2290) gives:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2291)  all_56_8 = e2 & op(e1, e1) = e2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2291) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2292)  all_56_8 = e2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2098), (2292) imply:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2293)  e2 = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (2293) imply:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2294)  $false
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2294) is inconsistent.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2295)  all_56_14 = e2 & op(e0, e1) = e2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2295) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2296)  all_56_14 = e2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2284), (2296) are inconsistent by sub-proof
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1099.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2297)  all_56_15 = e1 & op(e0, e0) = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2297) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2298)  op(e0, e0) = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2057), (2298), (function-axioms) are
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2299)   ~ (all_54_11 = e2)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (249), (2299) imply:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2300)   ~ (all_52_14 = e2)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2183), (2300), (function-axioms) are
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2301)  all_56_15 = e2 & op(e0, e0) = e2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2301) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2302)  op(e0, e0) = e2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2057), (2302), (function-axioms) are
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2303)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2303) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2304)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2130), (2131), (2304) are inconsistent by
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #890.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2305)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2305) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2306)  all_57_14 = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2307)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (1818), (2037), (2307),
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #662.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2308)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2308) gives:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2309)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2309) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2310)  all_57_14 = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2306), (2310) imply:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2311)  e1 = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2311) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2312)  e1 = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (2312) imply:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2313)  $false
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2313) is inconsistent.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2314)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2314) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2315)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2315) gives:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2316)  all_57_13 = e1 & op(e1, e0) = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2316) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2317)  op(e1, e0) = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2092), (2317), (function-axioms) are
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2318)   ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2318) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2319)   ~ (all_57_14 = e0)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2306), (2319) imply:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2320)  $false
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2320) is inconsistent.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2321)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2321) gives:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2322)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2037), (2322), (function-axioms) are
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2323)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2323) gives:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2324)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2324) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2325)   ~ (all_57_12 = e0)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2326)  op(e2, e2) = all_57_12
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1818), (2325), (2326), (function-axioms) are
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2327)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2327) gives:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2328)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2328) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2329)  op(e1, e0) = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2092), (2329), (function-axioms) are
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2330)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2330) implies:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2331)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2331) gives:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2332)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (1815), (2053), (2332),
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1035.
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2333)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (157), (1815), (1818), (2078), (2333),
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #803.
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (2334)  all_56_11 = e1 & op(e1, e0) = e1
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2334) implies:
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | |   (2335)  op(e1, e0) = e1
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2092), (2335), (function-axioms) are
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | |   (2336)  all_54_10 = e0
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (2081), (2336) are inconsistent by
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | |   (2337)  all_56_12 = e0 & op(e0, e3) = e0
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | ALPHA: (2337) implies:
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | |   (2338)  op(e0, e3) = e0
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2053), (2338), (function-axioms) are
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.42  | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | |   (2339)  all_56_9 = e0 & op(e3, e0) = e0
% 145.57/20.42  | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2054), (2339), (function-axioms) are
% 145.57/20.42  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 145.57/20.42  | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | Case 2:
% 145.57/20.42  | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | |   (2340)  all_42_2 = e3
% 145.57/20.42  | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | COMBINE_EQS: (302), (2340) imply:
% 145.57/20.42  | | | | | | | | | | | | |   (2341)  all_10_2 = e3
% 145.57/20.42  | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | SIMP: (2341) implies:
% 145.57/20.42  | | | | | | | | | | | | |   (2342)  all_10_2 = e3
% 145.57/20.42  | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | REDUCE: (367), (2342) imply:
% 145.57/20.42  | | | | | | | | | | | | |   (2343)   ~ (all_52_11 = e3)
% 145.57/20.42  | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | REDUCE: (368), (2342) imply:
% 145.57/20.42  | | | | | | | | | | | | |   (2344)   ~ (all_52_12 = e3)
% 145.57/20.42  | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | REDUCE: (45), (2342) imply:
% 145.57/20.42  | | | | | | | | | | | | |   (2345)  op(e0, e0) = e3
% 145.57/20.42  | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | BETA: splitting (237) gives:
% 145.57/20.42  | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | Case 1:
% 145.57/20.42  | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | |   (2346)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 145.57/20.42  | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 145.57/20.42  | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.57/20.42  | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.57/20.42  | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.57/20.42  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 145.57/20.42  | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 145.57/20.42  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.57/20.42  | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 145.57/20.42  | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 145.57/20.42  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.57/20.42  | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.57/20.42  | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.57/20.42  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 145.57/20.42  | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 145.57/20.42  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 145.57/20.42  | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (1818), (2037), (2346),
% 145.57/20.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.57/20.42  | | | | | | | | | | | | | |            #662.
% 145.57/20.42  | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | Case 2:
% 145.57/20.42  | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | |   (2347)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 145.57/20.42  | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 145.57/20.42  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.57/20.42  | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.57/20.42  | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.57/20.42  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 145.57/20.42  | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 145.57/20.42  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.57/20.42  | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 145.57/20.42  | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 145.57/20.42  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.57/20.42  | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.57/20.42  | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.57/20.42  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.57/20.42  | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.57/20.42  | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 145.57/20.42  | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | BETA: splitting (2347) gives:
% 145.57/20.42  | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | Case 1:
% 145.57/20.42  | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | |   (2348)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 145.57/20.42  | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 145.57/20.42  | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.57/20.42  | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.57/20.42  | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.57/20.42  | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 145.57/20.42  | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 145.57/20.42  | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.57/20.42  | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | ALPHA: (2348) implies:
% 145.57/20.42  | | | | | | | | | | | | | | |   (2349)  op(e1, e1) = e1
% 145.57/20.42  | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 145.57/20.42  | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | Case 1:
% 145.57/20.42  | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | |   (2350)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 145.57/20.42  | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 145.57/20.42  | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | BETA: splitting (2350) gives:
% 145.57/20.42  | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2351)  all_56_12 = e3 & op(e0, e3) = e3
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | ALPHA: (2351) implies:
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2352)  all_56_12 = e3
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (157), (205),
% 145.57/20.42  | | | | | | | | | | | | | | | | |            (206), (207), (1815), (1825), (2345), (2352),
% 145.57/20.42  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.57/20.42  | | | | | | | | | | | | | | | | |            #632.
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2353)  all_56_13 = e3 & op(e0, e2) = e3
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | ALPHA: (2353) implies:
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2354)  all_56_13 = e3
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (205), (206),
% 145.57/20.42  | | | | | | | | | | | | | | | | |            (207), (228), (230), (234), (375), (1825), (2037),
% 145.57/20.42  | | | | | | | | | | | | | | | | |            (2345), (2354), (function-axioms) are inconsistent
% 145.57/20.42  | | | | | | | | | | | | | | | | |            by sub-proof #780.
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | End of split
% 145.57/20.42  | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | Case 2:
% 145.57/20.42  | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | |   (2355)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 145.57/20.42  | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 145.57/20.42  | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | BETA: splitting (2355) gives:
% 145.57/20.42  | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2356)  all_56_14 = e3 & op(e0, e1) = e3
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | ALPHA: (2356) implies:
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2357)  op(e0, e1) = e3
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (2343), (2357), (function-axioms) are
% 145.57/20.42  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1147.
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | Case 2:
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2358)  all_56_15 = e3 & op(e0, e0) = e3
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 145.57/20.42  | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (2349) gives:
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2359)  all_4_2 = e1
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | REDUCE: (348), (2359) imply:
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2360)   ~ (all_52_2 = e1)
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | REDUCE: (359), (2359) imply:
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2361)   ~ (all_52_6 = e1)
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | REDUCE: (366), (2359) imply:
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2362)   ~ (all_52_14 = e1)
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | REDUCE: (374), (2359) imply:
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2363)   ~ (e3 = e1)
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | REDUCE: (371), (2359) imply:
% 145.57/20.42  | | | | | | | | | | | | | | | | |   (2364)   ~ (e2 = e1)
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 145.57/20.42  | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.42  | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | |   (2365)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.57/20.42  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.57/20.42  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.57/20.42  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.57/20.42  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.57/20.42  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 145.57/20.42  | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 145.57/20.42  | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.57/20.42  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 145.57/20.42  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.57/20.42  | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.57/20.42  | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | BETA: splitting (2365) gives:
% 145.57/20.42  | | | | | | | | | | | | | | | | | | 
% 145.57/20.42  | | | | | | | | | | | | | | | | | | Case 1:
% 145.57/20.42  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |   (2366)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | BETA: splitting (2366) gives:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |   (2367)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2033), (2367), (function-axioms) are
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |   (2368)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2368) gives:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2369)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2369) implies:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2370)  op(e1, e3) = e1
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2360), (2370), (function-axioms) are
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2371)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2371) implies:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2372)  op(e1, e3) = e1
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (2372) gives:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2373)  all_52_2 = e1
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | REDUCE: (2360), (2373) imply:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2374)  $false
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | CLOSE: (2374) is inconsistent.
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |   (2375)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | BETA: splitting (2375) gives:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |   (2376)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2376) gives:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2377)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2377) implies:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2378)   ~ (all_57_10 = e2)
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2379)  op(e3, e3) = all_57_10
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2037), (2378), (2379), (function-axioms) are
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1031.
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2380)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2380) implies:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2381)  op(e0, e0) = e2
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (1825), (2381), (function-axioms) are
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |   (2382)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2382) gives:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2383)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2383) implies:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2384)  op(e1, e2) = e1
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (2361), (2384), (function-axioms) are
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |   (2385)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (45), (1818), (1825), (2385),
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | |            #700.
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.42  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.42  | | | | | | | | | | | | | | | | | | 
% 145.67/20.42  | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.42  | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | |   (2386)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.67/20.43  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.67/20.43  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 145.67/20.43  | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 145.67/20.43  | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | BETA: splitting (2386) gives:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |   (2387)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | BETA: splitting (2387) gives:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |   (2388)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2388) gives:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |   (2389)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2389) implies:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |   (2390)  op(e0, e0) = e1
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2345), (2390), (function-axioms) are
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |   (2391)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2391) implies:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |   (2392)  op(e3, e3) = e1
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2037), (2392), (function-axioms) are
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |   (2393)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (2344), (2345), (2393),
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |            #1020.
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |   (2394)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | BETA: splitting (2394) gives:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |   (2395)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2037), (2395), (function-axioms) are
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |   (2396)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2396) gives:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |   (2397)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2397) implies:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |   (2398)   ~ (all_57_12 = e0)
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |   (2399)  op(e2, e2) = all_57_12
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1818), (2398), (2399), (function-axioms) are
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |   (2400)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2400) gives:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |   (2401)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2401) implies:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |   (2402)  op(e1, e0) = e1
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2362), (2402), (function-axioms) are
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |   (2403)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2403) implies:
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |   (2404)  op(e0, e0) = all_57_15
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |   (2405)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (157), (1815), (1818), (2037), (2345),
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |            (2404), (2405), (function-axioms) are inconsistent
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #826.
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | Case 2:
% 145.67/20.43  | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | |   (2406)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 145.67/20.43  | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 145.67/20.43  | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.43  | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.67/20.43  | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.67/20.43  | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.67/20.43  | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.67/20.43  | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 145.67/20.43  | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | ALPHA: (2406) implies:
% 145.67/20.43  | | | | | | | | | | | | | | |   (2407)  op(e0, e0) = e0
% 145.67/20.43  | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | REF_CLOSE: (7), (2345), (2407), (function-axioms) are
% 145.67/20.43  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 145.67/20.43  | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | End of split
% 145.67/20.43  | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | Case 2:
% 145.67/20.43  | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | |   (2408)  all_24_2 = e2
% 145.67/20.43  | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | COMBINE_EQS: (318), (2408) imply:
% 145.67/20.43  | | | | | | | | | |   (2409)  all_10_2 = e2
% 145.67/20.43  | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | SIMP: (2409) implies:
% 145.67/20.43  | | | | | | | | | |   (2410)  all_10_2 = e2
% 145.67/20.43  | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | REDUCE: (368), (2410) imply:
% 145.67/20.43  | | | | | | | | | |   (2411)   ~ (all_52_12 = e2)
% 145.67/20.43  | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | REDUCE: (369), (2410) imply:
% 145.67/20.43  | | | | | | | | | |   (2412)   ~ (all_52_13 = e2)
% 145.67/20.43  | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | REDUCE: (370), (2410) imply:
% 145.67/20.43  | | | | | | | | | |   (2413)   ~ (all_52_14 = e2)
% 145.67/20.43  | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | REDUCE: (45), (2410) imply:
% 145.67/20.43  | | | | | | | | | |   (2414)  op(e0, e0) = e2
% 145.67/20.43  | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | BETA: splitting (84) gives:
% 145.67/20.43  | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | Case 1:
% 145.67/20.43  | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | |   (2415)   ~ (all_36_2 = e2)
% 145.67/20.43  | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | REDUCE: (304), (2415) imply:
% 145.67/20.43  | | | | | | | | | | |   (2416)   ~ (all_14_2 = e2)
% 145.67/20.43  | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | BETA: splitting (203) gives:
% 145.67/20.43  | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | Case 1:
% 145.67/20.43  | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | |   (2417)  all_54_0 = e3
% 145.67/20.43  | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | COMBINE_EQS: (278), (2417) imply:
% 145.67/20.43  | | | | | | | | | | | |   (2418)  all_14_2 = e3
% 145.67/20.43  | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | SIMP: (2418) implies:
% 145.67/20.43  | | | | | | | | | | | |   (2419)  all_14_2 = e3
% 145.67/20.43  | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | REDUCE: (336), (2419) imply:
% 145.67/20.43  | | | | | | | | | | | |   (2420)   ~ (all_52_1 = e3)
% 145.67/20.43  | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | REDUCE: (342), (2419) imply:
% 145.67/20.43  | | | | | | | | | | | |   (2421)   ~ (all_52_4 = e3)
% 145.67/20.43  | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | REDUCE: (344), (2419) imply:
% 145.67/20.43  | | | | | | | | | | | |   (2422)   ~ (all_52_8 = e3)
% 145.67/20.43  | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | REDUCE: (346), (2419) imply:
% 145.67/20.43  | | | | | | | | | | | |   (2423)   ~ (all_52_12 = e3)
% 145.67/20.43  | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | REDUCE: (51), (2419) imply:
% 145.67/20.43  | | | | | | | | | | | |   (2424)  op(e3, e3) = e3
% 145.67/20.43  | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | BETA: splitting (102) gives:
% 145.67/20.43  | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | Case 1:
% 145.67/20.43  | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | |   (2425)   ~ (all_48_2 = e0)
% 145.67/20.43  | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | REDUCE: (298), (2425) imply:
% 145.67/20.43  | | | | | | | | | | | | |   (2426)   ~ (all_4_2 = e0)
% 145.67/20.43  | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | BETA: splitting (193) gives:
% 145.67/20.43  | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | Case 1:
% 145.67/20.43  | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | |   (2427)  all_54_10 = e3
% 145.67/20.43  | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (2427) are inconsistent by sub-proof
% 145.67/20.43  | | | | | | | | | | | | | |            #1173.
% 145.67/20.43  | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | Case 2:
% 145.67/20.43  | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | |   (2428)   ~ (all_54_10 = e3)
% 145.67/20.43  | | | | | | | | | | | | | |   (2429)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 145.67/20.43  | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | BETA: splitting (2429) gives:
% 145.67/20.43  | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | Case 1:
% 145.67/20.43  | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | |   (2430)  all_54_10 = e2
% 145.67/20.43  | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (2430) are inconsistent by sub-proof
% 145.67/20.43  | | | | | | | | | | | | | | |            #1168.
% 145.67/20.43  | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | Case 2:
% 145.67/20.43  | | | | | | | | | | | | | | | 
% 145.67/20.43  | | | | | | | | | | | | | | |   (2431)   ~ (all_54_10 = e2)
% 145.67/20.43  | | | | | | | | | | | | | | |   (2432)  all_54_10 = e1 | all_54_10 = e0
% 145.67/20.43  | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (159), (161), (162), (163), (167),
% 145.67/20.44  | | | | | | | | | | | | | | |            (168), (169), (238), (334), (348), (359), (366),
% 145.67/20.44  | | | | | | | | | | | | | | |            (371), (374), (1818), (2412), (2414), (2421),
% 145.67/20.44  | | | | | | | | | | | | | | |            (2422), (2423), (2424), (2426), (2432),
% 145.67/20.44  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.44  | | | | | | | | | | | | | | |            #631.
% 145.67/20.44  | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | End of split
% 145.67/20.44  | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | End of split
% 145.67/20.44  | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | |   (2433)  all_48_2 = e0
% 145.67/20.44  | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | COMBINE_EQS: (298), (2433) imply:
% 145.67/20.44  | | | | | | | | | | | | |   (2434)  all_4_2 = e0
% 145.67/20.44  | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | REDUCE: (361), (2434) imply:
% 145.67/20.44  | | | | | | | | | | | | |   (2435)   ~ (all_52_8 = e0)
% 145.67/20.44  | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | REDUCE: (364), (2434) imply:
% 145.67/20.44  | | | | | | | | | | | | |   (2436)   ~ (all_52_11 = e0)
% 145.67/20.44  | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | REDUCE: (371), (2434) imply:
% 145.67/20.44  | | | | | | | | | | | | |   (2437)   ~ (e2 = e0)
% 145.67/20.44  | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | REDUCE: (36), (2434) imply:
% 145.67/20.44  | | | | | | | | | | | | |   (2438)  op(e1, e1) = e0
% 145.67/20.44  | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | BETA: splitting (237) gives:
% 145.67/20.44  | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | |   (2439)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 145.67/20.44  | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 145.67/20.44  | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.67/20.44  | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.67/20.44  | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.67/20.44  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 145.67/20.44  | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 145.67/20.44  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.67/20.44  | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 145.67/20.44  | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 145.67/20.44  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.44  | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.67/20.44  | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.67/20.44  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 145.67/20.44  | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 145.67/20.44  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 145.67/20.44  | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | BETA: splitting (2439) gives:
% 145.67/20.44  | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | |   (2440)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 145.67/20.44  | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 145.67/20.44  | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.67/20.44  | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.67/20.44  | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.67/20.44  | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 145.67/20.44  | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 145.67/20.44  | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.67/20.44  | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | ALPHA: (2440) implies:
% 145.67/20.44  | | | | | | | | | | | | | | |   (2441)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 145.67/20.44  | | | | | | | | | | | | | | |               = e3) & op(e0, e0) = all_57_15 &
% 145.67/20.44  | | | | | | | | | | | | | | |             $i(all_57_15))
% 145.67/20.44  | | | | | | | | | | | | | | |   (2442)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 145.67/20.44  | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = all_57_14 &
% 145.67/20.44  | | | | | | | | | | | | | | |             $i(all_57_14))
% 145.67/20.44  | | | | | | | | | | | | | | |   (2443)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 145.67/20.44  | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = all_57_12 &
% 145.67/20.44  | | | | | | | | | | | | | | |             $i(all_57_12))
% 145.67/20.44  | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | |   (2444)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.44  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.44  | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.44  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.44  | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.44  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.44  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.44  | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.44  | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 145.67/20.44  | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 145.67/20.44  | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 145.67/20.44  | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.44  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.67/20.44  | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.67/20.44  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 145.67/20.44  | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 145.67/20.44  | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 145.67/20.44  | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 145.67/20.44  | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 145.67/20.44  | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 145.67/20.44  | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 145.67/20.44  | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.44  | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.44  | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.44  | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.67/20.44  | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | BETA: splitting (2444) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | |   (2445)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.44  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.44  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.44  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.44  | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.44  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.44  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.67/20.44  | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | BETA: splitting (2445) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | |   (2446)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.44  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2441), (2442), (2446), (function-axioms) are
% 145.67/20.44  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #814.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | |   (2447)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2441), (2443), (2447), (function-axioms) are
% 145.67/20.44  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | End of split
% 145.67/20.44  | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | |   (2448)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.44  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.67/20.44  | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.44  | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.67/20.44  | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 145.67/20.44  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 145.67/20.44  | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.44  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.67/20.44  | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.67/20.44  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.67/20.44  | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.67/20.44  | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | BETA: splitting (2448) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | |   (2449)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2421), (2449), (function-axioms) are
% 145.67/20.44  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | |   (2450)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.67/20.44  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | BETA: splitting (2450) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |   (2451)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | ALPHA: (2451) implies:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |   (2452)  op(e3, e3) = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2424), (2452), (function-axioms) are
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |   (2453)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | BETA: splitting (2453) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | |   (2454)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | ALPHA: (2454) implies:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | |   (2455)  op(e0, e2) = all_57_5
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | |   (2456)  op(e1, e2) = e1
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | |   (2457)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2457) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | |   (2458)  all_56_0 = e0 & op(e3, e3) = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2458) implies:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | |   (2459)  op(e3, e3) = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2424), (2459), (function-axioms) are
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | |   (2460)  all_56_1 = e0 & op(e3, e2) = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1813), (2460), (function-axioms) are
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1013.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | |   (2461)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2461) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | |   (2462)  all_56_4 = e0 & op(e3, e1) = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2435), (2462), (function-axioms) are
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | |   (2463)  all_56_9 = e0 & op(e3, e0) = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2463) implies:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | |   (2464)  all_56_9 = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | |   (2465)  op(e3, e0) = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | |   (2466)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2466) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | |   (2467)  all_56_0 = e0 & op(e3, e3) = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2467) implies:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | |   (2468)  op(e3, e3) = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (231), (233),
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | |            (235), (2422), (2464), (2468), (function-axioms)
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #687.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | |   (2469)  all_56_2 = e0 & op(e2, e3) = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (1812), (2469), (function-axioms) are
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #840.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | |   (2470)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2470) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | |   (2471)  all_56_6 = e0 & op(e1, e3) = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2471) implies:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | |   (2472)  all_56_6 = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | |   (2473)  op(e1, e3) = e0
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | |   (2474)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2474) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2475)  all_56_6 = e2 & op(e1, e3) = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2475) implies:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2476)  all_56_6 = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2472), (2476) are inconsistent by sub-proof
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | |            #724.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2477)  all_56_7 = e2 & op(e1, e2) = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2477) implies:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2478)  op(e1, e2) = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2444) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2479)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (2441), (2442), (2473), (2479),
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #630.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2448) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2480)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2480) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2481)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2481) implies:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2482)  op(e1, e1) = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (142), (156),
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (157), (161), (162), (163), (166), (167), (168),
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (205), (219), (222), (230), (232), (234),
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (1815), (1818), (2412), (2414),
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2421), (2422), (2423), (2424), (2436), (2438),
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2441), (2442), (2443), (2472), (2473), (2482),
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #618.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2483)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2483) implies:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2484)  op(e3, e2) = e3
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2421), (2484), (function-axioms) are
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1166.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2450) gives:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2485)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2485) implies:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2486)  op(e3, e3) = e2
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2424), (2486), (function-axioms) are
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (1818), (2453), (2478),
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #617.
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2487)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (156), (163), (167), (168),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1818), (2412), (2414), (2422), (2423), (2424),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2436), (2438), (2442), (2443), (2487),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #625.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2488)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2488) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2489)  all_56_8 = e2 & op(e1, e1) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2489) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2490)  op(e1, e1) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (142), (156),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            (157), (161), (162), (163), (166), (167), (168),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (205), (219), (222), (230), (232), (234),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (1815), (1818), (2412), (2414),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2421), (2422), (2423), (2424), (2436), (2438),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            (2441), (2442), (2443), (2472), (2473), (2490),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            #618.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2491)  all_56_11 = e2 & op(e1, e0) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2491) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2492)  op(e1, e0) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2413), (2492), (function-axioms) are
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | |   (2493)  all_56_12 = e0 & op(e0, e3) = e0
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2493) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | |   (2494)  op(e0, e3) = e0
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2495)  all_56_15 = e0 & op(e0, e0) = e0
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2495) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2496)  op(e0, e0) = e0
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2414), (2496), (function-axioms) are
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2497)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2497) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2498)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5, e2, e0, simplifying with (157), (2455)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2499)  all_57_5 = all_52_7
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (158), (2494) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2500)  all_52_3 = e0
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (161), (2456) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2501)  all_52_6 = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e3, simplifying with (167), (2465) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2502)  all_52_12 = e0
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (2501) imply:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2503)   ~ (all_52_2 = e1)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (2500) imply:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2504)   ~ (all_52_7 = e0)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (2500) imply:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2505)   ~ (all_52_11 = e0)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (2501) imply:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2506)   ~ (all_52_14 = e1)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2506) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (2507)   ~ (all_52_14 = e1)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2508)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2508) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2509)  all_56_0 = e1 & op(e3, e3) = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2509) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2510)  op(e3, e3) = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2424), (2510), (function-axioms) are
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2511)  all_56_2 = e1 & op(e2, e3) = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2511) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2512)  op(e2, e3) = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2513)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (166), (1818), (2512), (2513),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #624.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2514)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2514) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2515)  all_56_5 = e2 & op(e2, e1) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2515) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2516)  op(e2, e1) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2517)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2517) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2518)  all_56_9 = e1 & op(e3, e0) = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2464), (2518) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #616.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2519)  all_56_10 = e1 & op(e2, e0) = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2519) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2520)  all_56_10 = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2521)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (166), (1818), (2420), (2521),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #690.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2522)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2522) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2523)  all_56_5 = e3 & op(e2, e1) = e3
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2523) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2524)  op(e2, e1) = e3
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2516), (2524), (function-axioms) are
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1135.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2525)  all_56_10 = e3 & op(e2, e0) = e3
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2525) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2526)  all_56_10 = e3
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2520), (2526) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #677.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2527)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (2414), (2507), (2527),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #615.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2528)  all_56_10 = e2 & op(e2, e0) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2528) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2529)  op(e2, e0) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2412), (2529), (function-axioms) are
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2530)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2530) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2531)  all_56_6 = e1 & op(e1, e3) = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2531) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2532)  op(e1, e3) = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2503), (2532), (function-axioms) are
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2533)  all_56_12 = e1 & op(e0, e3) = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2533) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2534)  all_56_12 = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (157), (1815), (2436), (2498), (2534),
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #798.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | |   (2535)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | ALPHA: (2535) implies:
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | |   (2536)  op(e2, e2) = e1
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1818), (2536), (function-axioms) are
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | |   (2537)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.45  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.45  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.45  | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.45  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.67/20.45  | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.67/20.45  | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.67/20.45  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.67/20.45  | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.67/20.45  | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.67/20.45  | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.45  | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.67/20.45  | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.67/20.45  | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.67/20.45  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.67/20.45  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.67/20.45  | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.67/20.45  | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.67/20.45  | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.45  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.45  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.45  | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 145.67/20.45  | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 145.67/20.45  | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 145.67/20.45  | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 145.67/20.45  | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 145.67/20.45  | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 145.67/20.45  | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 145.67/20.45  | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 145.67/20.45  | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 145.67/20.45  | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 145.67/20.45  | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.67/20.45  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.67/20.45  | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.67/20.45  | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.67/20.45  | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.67/20.45  | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.67/20.45  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.67/20.45  | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.67/20.45  | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.67/20.45  | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.67/20.45  | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.67/20.45  | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.45  | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.67/20.45  | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.67/20.45  | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.67/20.45  | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.67/20.45  | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.67/20.45  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.67/20.45  | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.67/20.45  | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.67/20.45  | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.67/20.45  | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.67/20.45  | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.67/20.45  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.67/20.45  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.67/20.45  | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.67/20.45  | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.67/20.45  | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.67/20.45  | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.45  | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.67/20.45  | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (156), (163), (167), (168),
% 145.67/20.45  | | | | | | | | | | | | | | | |            (1818), (2412), (2414), (2422), (2423), (2424),
% 145.67/20.45  | | | | | | | | | | | | | | | |            (2436), (2438), (2442), (2443), (2537),
% 145.67/20.45  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | | | | | |            #625.
% 145.67/20.45  | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | |   (2538)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 145.67/20.45  | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 145.67/20.45  | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.45  | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.67/20.45  | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.67/20.45  | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 145.67/20.45  | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 145.67/20.45  | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | ALPHA: (2538) implies:
% 145.67/20.45  | | | | | | | | | | | | | | |   (2539)  op(e2, e2) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | REF_CLOSE: (5), (1818), (2539), (function-axioms) are
% 145.67/20.45  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | |   (2540)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 145.67/20.45  | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 145.67/20.45  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.45  | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.67/20.45  | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.45  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 145.67/20.45  | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 145.67/20.45  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.67/20.45  | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 145.67/20.45  | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 145.67/20.45  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.45  | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.67/20.45  | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.67/20.45  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.67/20.45  | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.67/20.45  | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 145.67/20.45  | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (2414), (2438), (2540),
% 145.67/20.45  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | | | |            #614.
% 145.67/20.45  | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | |   (2541)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 145.67/20.45  | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | REF_CLOSE: (278), (376), (1823), (2416), (2541) are
% 145.67/20.45  | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 145.67/20.45  | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | End of split
% 145.67/20.45  | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | |   (2542)  all_36_2 = e2
% 145.67/20.45  | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | COMBINE_EQS: (304), (2542) imply:
% 145.67/20.45  | | | | | | | | | | |   (2543)  all_14_2 = e2
% 145.67/20.45  | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | SIMP: (2543) implies:
% 145.67/20.45  | | | | | | | | | | |   (2544)  all_14_2 = e2
% 145.67/20.45  | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | COMBINE_EQS: (280), (2544) imply:
% 145.67/20.45  | | | | | | | | | | |   (2545)  all_44_2 = e2
% 145.67/20.45  | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | REDUCE: (336), (2544) imply:
% 145.67/20.45  | | | | | | | | | | |   (2546)   ~ (all_52_1 = e2)
% 145.67/20.45  | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | REDUCE: (51), (2544) imply:
% 145.67/20.45  | | | | | | | | | | |   (2547)  op(e3, e3) = e2
% 145.67/20.45  | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | BETA: splitting (222) gives:
% 145.67/20.45  | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | |   (2548)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 145.67/20.45  | | | | | | | | | | | |             & op(e2, e2) = e2)
% 145.67/20.45  | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | REF_CLOSE: (5), (166), (1818), (2546), (2548),
% 145.67/20.45  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | |            #613.
% 145.67/20.45  | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | |   (2549)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 145.67/20.45  | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 145.67/20.45  | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | BETA: splitting (2549) gives:
% 145.67/20.45  | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | |   (2550)  all_56_5 = e2 & op(e2, e1) = e2
% 145.67/20.45  | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | ALPHA: (2550) implies:
% 145.67/20.45  | | | | | | | | | | | | |   (2551)  op(e2, e1) = e2
% 145.67/20.45  | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | BETA: splitting (214) gives:
% 145.67/20.45  | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | |   (2552)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 145.67/20.45  | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 145.67/20.45  | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | BETA: splitting (2552) gives:
% 145.67/20.45  | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | |   (2553)  all_56_6 = e2 & op(e1, e3) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | ALPHA: (2553) implies:
% 145.67/20.45  | | | | | | | | | | | | | | |   (2554)  all_56_6 = e2
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230), (234),
% 145.67/20.45  | | | | | | | | | | | | | | |            (2547), (2554), (function-axioms) are inconsistent
% 145.67/20.45  | | | | | | | | | | | | | | |            by sub-proof #1050.
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | |   (2555)  all_56_7 = e2 & op(e1, e2) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | ALPHA: (2555) implies:
% 145.67/20.45  | | | | | | | | | | | | | | |   (2556)  all_56_7 = e2
% 145.67/20.45  | | | | | | | | | | | | | | |   (2557)  op(e1, e2) = e2
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 145.67/20.45  | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | Case 1:
% 145.67/20.45  | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | |   (2558)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 145.67/20.45  | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 145.67/20.45  | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.67/20.45  | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.67/20.45  | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.67/20.45  | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 145.67/20.45  | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 145.67/20.45  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.67/20.45  | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 145.67/20.45  | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 145.67/20.45  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.45  | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.67/20.45  | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.67/20.45  | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 145.67/20.45  | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 145.67/20.45  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 145.67/20.45  | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (1818), (2547), (2558),
% 145.67/20.45  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.45  | | | | | | | | | | | | | | | |            #662.
% 145.67/20.45  | | | | | | | | | | | | | | | | 
% 145.67/20.45  | | | | | | | | | | | | | | | Case 2:
% 145.67/20.45  | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | |   (2559)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 145.67/20.46  | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 145.67/20.46  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.46  | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.67/20.46  | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.46  | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 145.67/20.46  | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 145.67/20.46  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.67/20.46  | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 145.67/20.46  | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 145.67/20.46  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.46  | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.67/20.46  | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.67/20.46  | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.67/20.46  | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.67/20.46  | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 145.67/20.46  | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | BETA: splitting (2559) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2560)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 145.67/20.46  | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.46  | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.67/20.46  | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.46  | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 145.67/20.46  | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 145.67/20.46  | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | ALPHA: (2560) implies:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2561)  all_57_14 = e1
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2562)  op(e1, e1) = e1
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 145.67/20.46  | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (2562) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2563)  all_4_2 = e1
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 145.67/20.46  | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (161), (2557) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2564)  all_52_6 = e2
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 145.67/20.46  | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (164), (2551) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2565)  all_52_9 = e2
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | REDUCE: (348), (2563) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2566)   ~ (all_52_2 = e1)
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | REDUCE: (135), (2564) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2567)   ~ (all_52_4 = e2)
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | REDUCE: (127), (2564) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2568)   ~ (all_52_7 = e2)
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | SIMP: (2568) implies:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2569)   ~ (all_52_7 = e2)
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | REDUCE: (116), (2565) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2570)   ~ (all_52_13 = e2)
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | REDUCE: (366), (2563) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2571)   ~ (all_52_14 = e1)
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | REDUCE: (374), (2563) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2572)   ~ (e3 = e1)
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | REDUCE: (371), (2563) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | |   (2573)   ~ (e2 = e1)
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | |   (2574)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.46  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.46  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 145.67/20.46  | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | BETA: splitting (2574) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |   (2575)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | BETA: splitting (2575) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |   (2576)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2546), (2576), (function-axioms) are
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |   (2577)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (162), (2414), (2566), (2577),
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |            #723.
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |   (2578)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | BETA: splitting (2578) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |   (2579)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (2547), (2562), (2579),
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |            #712.
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |   (2580)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2580) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |   (2581)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2581) implies:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |   (2582)   ~ (all_57_14 = e2)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |   (2583)  op(e1, e2) = e1
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e1, e2,
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |              e1, simplifying with (2557), (2583) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |   (2584)  e2 = e1
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | REDUCE: (6), (2584) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |   (2585)  $false
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | CLOSE: (2585) is inconsistent.
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |   (2586)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (1818), (2557), (2586),
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |            #617.
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.46  | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | |   (2587)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.67/20.46  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 145.67/20.46  | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 145.67/20.46  | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.67/20.46  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | BETA: splitting (2587) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |   (2588)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | BETA: splitting (2588) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |   (2589)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2414), (2547), (2589), (function-axioms) are
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #710.
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |   (2590)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2590) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |   (2591)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2591) implies:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |   (2592)  op(e0, e0) = e1
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2414), (2592), (function-axioms) are
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #978.
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |   (2593)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2593) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |   (2594)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2594) implies:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |   (2595)   ~ (all_57_10 = e0)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |   (2596)  op(e3, e0) = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |   (2597)  op(e3, e3) = all_57_10
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (167), (2596) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |   (2598)  all_52_12 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (2547), (2597)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |   (2599)  all_57_10 = e2
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (2598) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |   (2600)   ~ (all_52_4 = e3)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (2598) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | |   (2601)   ~ (all_52_8 = e3)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | |   (2602)  all_54_1 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (2600), (2602) are inconsistent by
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #988.
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | |   (2603)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | |   (2604)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2604) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (2605)  all_56_6 = e3 & op(e1, e3) = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2605) implies:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (2606)  all_56_6 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2603) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2607)  all_54_1 = e2
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (2607) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2608)  all_52_4 = e2
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2567), (2608) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2609)  $false
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2609) is inconsistent.
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2610)   ~ (all_54_1 = e2)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2611)  all_54_1 = e1 | all_54_1 = e0
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2611) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2612)  all_54_1 = e1
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (2612) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2613)  all_52_4 = e1
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (2613) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2614)   ~ (all_52_7 = e1)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2614) implies:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2615)   ~ (all_52_7 = e1)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2616)  all_54_13 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (2616) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2617)  all_52_7 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2617) implies:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2618)  all_52_7 = e3
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (2618) imply:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2619)   ~ (all_52_11 = e3)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2619) implies:
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2620)   ~ (all_52_11 = e3)
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (168), (212),
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (214), (219), (2551), (2601), (2606),
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2620), (function-axioms) are inconsistent by
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #605.
% 145.67/20.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2621)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (1815), (2569), (2615), (2621) are
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #982.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2622)  all_54_1 = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (2622) imply:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2623)  all_52_4 = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1813), (2623) imply:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2624)  $false
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2624) is inconsistent.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (2625)  all_56_7 = e3 & op(e1, e2) = e3
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2625) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (2626)  all_56_7 = e3
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2556), (2626) imply:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (2627)  e3 = e2
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (2627) imply:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (2628)  $false
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2628) is inconsistent.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |   (2629)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2629) gives:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (2630)  all_56_8 = e3 & op(e1, e1) = e3
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2630) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (2631)  op(e1, e1) = e3
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2562), (2631), (function-axioms) are
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (2632)  all_56_11 = e3 & op(e1, e0) = e3
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2632) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (2633)  all_56_11 = e3
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2634)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2634) gives:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2635)  all_56_6 = e0 & op(e1, e3) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2635) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2636)  op(e1, e3) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (169), (271), (1813), (2545), (2567),
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2603), (2636), (function-axioms) are inconsistent
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #604.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2637)  all_56_7 = e0 & op(e1, e2) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (1814), (2637), (function-axioms) are
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1029.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2638)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2638) gives:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2639)  all_56_8 = e0 & op(e1, e1) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2639) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2640)  op(e1, e1) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2562), (2640), (function-axioms) are
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2641)  all_56_11 = e0 & op(e1, e0) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2641) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2642)  all_56_11 = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2633), (2642) are inconsistent by sub-proof
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #772.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |   (2643)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2643) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |   (2644)  op(e1, e1) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2562), (2644), (function-axioms) are
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |   (2645)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (2645) gives:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |   (2646)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2547), (2646), (function-axioms) are
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |   (2647)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2647) gives:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |   (2648)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2648) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |   (2649)  op(e2, e0) = e2
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2412), (2649), (function-axioms) are
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |   (2650)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2650) gives:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |   (2651)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2651) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |   (2652)  op(e1, e0) = e1
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2571), (2652), (function-axioms) are
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |   (2653)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2653) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |   (2654)  op(e0, e0) = all_57_15
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |   (2655)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2655) gives:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |   (2656)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (1818), (2414), (2562), (2654), (2656),
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |            #717.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |   (2657)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2657) gives:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |   (2658)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2658) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |   (2659)  op(e1, e1) = e2
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (2562), (2659), (function-axioms) are
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |   (2660)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (1818), (2547), (2660),
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | |            #827.
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | |   (2661)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 145.67/20.47  | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 145.67/20.47  | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.47  | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.67/20.47  | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.67/20.47  | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.67/20.47  | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.67/20.47  | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 145.67/20.47  | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | ALPHA: (2661) implies:
% 145.67/20.47  | | | | | | | | | | | | | | | | |   (2662)  op(e0, e0) = e0
% 145.67/20.47  | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2414), (2662), (function-axioms) are
% 145.67/20.47  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 145.67/20.47  | | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | |   (2663)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 145.67/20.47  | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 145.67/20.47  | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | BETA: splitting (2663) gives:
% 145.67/20.47  | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | |   (2664)  all_56_8 = e2 & op(e1, e1) = e2
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | ALPHA: (2664) implies:
% 145.67/20.47  | | | | | | | | | | | | | | |   (2665)  op(e1, e1) = e2
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (237), (1818), (2414),
% 145.67/20.47  | | | | | | | | | | | | | | |            (2547), (2665), (function-axioms) are inconsistent
% 145.67/20.47  | | | | | | | | | | | | | | |            by sub-proof #629.
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | |   (2666)  all_56_11 = e2 & op(e1, e0) = e2
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | ALPHA: (2666) implies:
% 145.67/20.47  | | | | | | | | | | | | | | |   (2667)  op(e1, e0) = e2
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | REF_CLOSE: (159), (2413), (2667), (function-axioms) are
% 145.67/20.47  | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | |   (2668)  all_56_10 = e2 & op(e2, e0) = e2
% 145.67/20.47  | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | ALPHA: (2668) implies:
% 145.67/20.47  | | | | | | | | | | | | |   (2669)  op(e2, e0) = e2
% 145.67/20.47  | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | REF_CLOSE: (163), (2412), (2669), (function-axioms) are
% 145.67/20.47  | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 145.67/20.47  | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | End of split
% 145.67/20.47  | | | | | | | | | 
% 145.67/20.47  | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | 
% 145.67/20.47  | | | | | | | | |   (2670)  all_22_2 = e1
% 145.67/20.47  | | | | | | | | |   (2671)  ( ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0 &
% 145.67/20.47  | | | | | | | | |             op(e3, e1) = all_22_1 & $i(all_22_0) &
% 145.67/20.47  | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e1) =
% 145.67/20.47  | | | | | | | | |             all_22_1 & $i(all_22_1))
% 145.67/20.47  | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | COMBINE_EQS: (320), (2670) imply:
% 145.67/20.47  | | | | | | | | |   (2672)  all_14_2 = e1
% 145.67/20.47  | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | SIMP: (2672) implies:
% 145.67/20.47  | | | | | | | | |   (2673)  all_14_2 = e1
% 145.67/20.47  | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | COMBINE_EQS: (312), (2673) imply:
% 145.67/20.47  | | | | | | | | |   (2674)  all_34_2 = e1
% 145.67/20.47  | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | REDUCE: (336), (2673) imply:
% 145.67/20.47  | | | | | | | | |   (2675)   ~ (all_52_1 = e1)
% 145.67/20.47  | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | REDUCE: (51), (2673) imply:
% 145.67/20.47  | | | | | | | | |   (2676)  op(e3, e3) = e1
% 145.67/20.47  | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | BETA: splitting (67) gives:
% 145.67/20.47  | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | |   (2677)   ~ (all_24_2 = e2)
% 145.67/20.47  | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | REDUCE: (318), (2677) imply:
% 145.67/20.47  | | | | | | | | | |   (2678)   ~ (all_10_2 = e2)
% 145.67/20.47  | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | BETA: splitting (81) gives:
% 145.67/20.47  | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | |   (2679)   ~ (all_34_2 = e1)
% 145.67/20.47  | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | REDUCE: (2674), (2679) imply:
% 145.67/20.47  | | | | | | | | | | |   (2680)  $false
% 145.67/20.47  | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | CLOSE: (2680) is inconsistent.
% 145.67/20.47  | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | |   (2681)  ( ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0
% 145.67/20.47  | | | | | | | | | | |             & op(e3, e1) = all_34_1 & $i(all_34_0) &
% 145.67/20.47  | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e3, e1)
% 145.67/20.47  | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 145.67/20.47  | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | BETA: splitting (93) gives:
% 145.67/20.47  | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | |   (2682)   ~ (all_42_2 = e3)
% 145.67/20.47  | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | REDUCE: (302), (2682) imply:
% 145.67/20.47  | | | | | | | | | | | |   (2683)   ~ (all_10_2 = e3)
% 145.67/20.47  | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | BETA: splitting (188) gives:
% 145.67/20.47  | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | |   (2684)  all_54_15 = e3
% 145.67/20.47  | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | REF_CLOSE: (245), (2683), (2684) are inconsistent by
% 145.67/20.47  | | | | | | | | | | | | |            sub-proof #1049.
% 145.67/20.47  | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | |   (2685)   ~ (all_54_15 = e3)
% 145.67/20.47  | | | | | | | | | | | | |   (2686)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 145.67/20.47  | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | BETA: splitting (2686) gives:
% 145.67/20.47  | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | |   (2687)  all_54_15 = e2
% 145.67/20.47  | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | REF_CLOSE: (245), (2678), (2687) are inconsistent by
% 145.67/20.47  | | | | | | | | | | | | | |            sub-proof #1048.
% 145.67/20.47  | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | |   (2688)   ~ (all_54_15 = e2)
% 145.67/20.47  | | | | | | | | | | | | | |   (2689)  all_54_15 = e1 | all_54_15 = e0
% 145.67/20.47  | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | BETA: splitting (2689) gives:
% 145.67/20.47  | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | Case 1:
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | |   (2690)  all_54_15 = e1
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | REF_CLOSE: (245), (375), (2690) are inconsistent by sub-proof
% 145.67/20.47  | | | | | | | | | | | | | | |            #1047.
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | Case 2:
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | |   (2691)  all_54_15 = e0
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | COMBINE_EQS: (245), (2691) imply:
% 145.67/20.47  | | | | | | | | | | | | | | |   (2692)  all_10_2 = e0
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.47  | | | | | | | | | | | | | | | SIMP: (2692) implies:
% 145.67/20.47  | | | | | | | | | | | | | | |   (2693)  all_10_2 = e0
% 145.67/20.47  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (368), (2693) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2694)   ~ (all_52_12 = e0)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (2678), (2693) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2695)   ~ (e2 = e0)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (375), (2693) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2696)   ~ (e1 = e0)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (45), (2693) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2697)  op(e0, e0) = e0
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | |   (2698)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 145.67/20.48  | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 145.67/20.48  | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (169), (1813), (2676), (2698),
% 145.67/20.48  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.48  | | | | | | | | | | | | | | | |            #937.
% 145.67/20.48  | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | |   (2699)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 145.67/20.48  | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 145.67/20.48  | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | BETA: splitting (2699) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | |   (2700)  all_56_4 = e0 & op(e3, e1) = e0
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | ALPHA: (2700) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | |   (2701)  all_56_4 = e0
% 145.67/20.48  | | | | | | | | | | | | | | | | |   (2702)  op(e3, e1) = e0
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 145.67/20.48  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (2702) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | |   (2703)  all_52_8 = e0
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | REDUCE: (361), (2703) imply:
% 145.67/20.48  | | | | | | | | | | | | | | | | |   (2704)   ~ (all_4_2 = e0)
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | SIMP: (2704) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | |   (2705)   ~ (all_4_2 = e0)
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | |   (2706)  all_54_10 = e3
% 145.67/20.48  | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (2706) are inconsistent by sub-proof
% 145.67/20.48  | | | | | | | | | | | | | | | | | |            #1173.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | |   (2707)   ~ (all_54_10 = e3)
% 145.67/20.48  | | | | | | | | | | | | | | | | | |   (2708)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 145.67/20.48  | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | BETA: splitting (2708) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | |   (2709)  all_54_10 = e2
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (2709) are inconsistent by sub-proof
% 145.67/20.48  | | | | | | | | | | | | | | | | | | |            #1168.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | |   (2710)   ~ (all_54_10 = e2)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | |   (2711)  all_54_10 = e1 | all_54_10 = e0
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | BETA: splitting (2711) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |   (2712)  all_54_10 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (2712) imply:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |   (2713)  all_4_2 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | SIMP: (2713) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |   (2714)  all_4_2 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (2714) imply:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |   (2715)   ~ (all_52_14 = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (2714) imply:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |   (2716)   ~ (e3 = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (2714) imply:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |   (2717)   ~ (e2 = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | |   (2718)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (166), (1818), (2675), (2718),
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | |            #603.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | |   (2719)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2719) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | |   (2720)  all_56_5 = e1 & op(e2, e1) = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2720) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | |   (2721)  all_56_5 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |   (2722)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2722) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |   (2723)  all_56_9 = e1 & op(e3, e0) = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2723) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |   (2724)  all_56_9 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (233), (235), (2676),
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |            (2701), (2724), (function-axioms) are inconsistent
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #914.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |   (2725)  all_56_10 = e1 & op(e2, e0) = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2725) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |   (2726)  all_56_10 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (220), (222), (223),
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |            (1818), (2721), (2726), (function-axioms) are
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #676.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |   (2727)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (159), (2697), (2715), (2727),
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |            #960.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | |   (2728)  all_56_10 = e1 & op(e2, e0) = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2728) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | |   (2729)  op(e2, e0) = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |   (2730)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (1818), (2676), (2730),
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |            #602.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |   (2731)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2731) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |   (2732)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2732) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |   (2733)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2671) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (2734)   ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0 &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_22_1 & $i(all_22_0) &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2734) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (2735)  op(e3, e1) = all_22_1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2676), (2681), (2702), (2733), (2735),
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |            #600.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (2736)   ~ (all_22_1 = e0) & op(e3, e1) = all_22_1 &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_22_1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2736) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (2737)  op(e3, e1) = all_22_1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2676), (2681), (2702), (2733), (2737),
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |            #600.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |   (2738)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2738) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |   (2739)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2739) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (2740)  all_57_11 = e2 & op(e2, e0) = e2
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2740) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (2741)  op(e2, e0) = e2
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (2729), (2741), (function-axioms) are
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #904.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (2742)   ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2742) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (2743)   ~ (all_57_12 = e0)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |   (2744)  op(e2, e2) = all_57_12
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1818), (2743), (2744), (function-axioms) are
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |   (2745)  all_54_10 = e0
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (2705), (2745) are inconsistent by
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | |   (2746)  all_56_9 = e0 & op(e3, e0) = e0
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2694), (2746), (function-axioms) are
% 145.67/20.48  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | |   (2747)  all_42_2 = e3
% 145.67/20.48  | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | COMBINE_EQS: (302), (2747) imply:
% 145.67/20.48  | | | | | | | | | | | |   (2748)  all_10_2 = e3
% 145.67/20.48  | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | SIMP: (2748) implies:
% 145.67/20.48  | | | | | | | | | | | |   (2749)  all_10_2 = e3
% 145.67/20.48  | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | REDUCE: (45), (2749) imply:
% 145.67/20.48  | | | | | | | | | | | |   (2750)  op(e0, e0) = e3
% 145.67/20.48  | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | BETA: splitting (237) gives:
% 145.67/20.48  | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | |   (2751)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 145.67/20.48  | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 145.67/20.48  | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.67/20.48  | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.67/20.48  | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.67/20.48  | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 145.67/20.48  | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 145.67/20.48  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.67/20.48  | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 145.67/20.48  | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 145.67/20.48  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.48  | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.67/20.48  | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.67/20.48  | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 145.67/20.48  | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 145.67/20.48  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 145.67/20.48  | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | REF_CLOSE: (5), (8), (1818), (2676), (2751),
% 145.67/20.48  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.48  | | | | | | | | | | | | |            #602.
% 145.67/20.48  | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | |   (2752)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 145.67/20.48  | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 145.67/20.48  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.48  | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.67/20.48  | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.48  | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 145.67/20.48  | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 145.67/20.48  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.67/20.48  | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 145.67/20.48  | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 145.67/20.48  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.48  | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.67/20.48  | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.67/20.48  | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.67/20.48  | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.67/20.48  | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 145.67/20.48  | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | BETA: splitting (2752) gives:
% 145.67/20.48  | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | |   (2753)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 145.67/20.48  | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 145.67/20.48  | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.48  | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.67/20.48  | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.48  | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 145.67/20.48  | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 145.67/20.48  | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.67/20.48  | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | ALPHA: (2753) implies:
% 145.67/20.48  | | | | | | | | | | | | | |   (2754)  all_57_14 = e1
% 145.67/20.48  | | | | | | | | | | | | | |   (2755)  op(e1, e1) = e1
% 145.67/20.48  | | | | | | | | | | | | | |   (2756)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 145.67/20.48  | | | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.48  | | | | | | | | | | | | | |             $i(all_57_10))
% 145.67/20.48  | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | BETA: splitting (2756) gives:
% 145.67/20.48  | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | |   (2757)  all_57_6 = e3 & op(e3, e1) = e3
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | ALPHA: (2757) implies:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2758)  all_57_6 = e3
% 145.67/20.48  | | | | | | | | | | | | | | |   (2759)  op(e3, e1) = e3
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 145.67/20.48  | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (2755) gives:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2760)  all_4_2 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 145.67/20.48  | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (2759) gives:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2761)  all_52_8 = e3
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (133), (2761) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2762)   ~ (all_52_4 = e3)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (359), (2760) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2763)   ~ (all_52_6 = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (122), (2761) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2764)   ~ (all_52_9 = e3)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | SIMP: (2764) implies:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2765)   ~ (all_52_9 = e3)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (120), (2761) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2766)   ~ (all_52_11 = e3)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | SIMP: (2766) implies:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2767)   ~ (all_52_11 = e3)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (119), (2761) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2768)   ~ (all_52_12 = e3)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | SIMP: (2768) implies:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2769)   ~ (all_52_12 = e3)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (362), (2760) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2770)   ~ (all_52_9 = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (364), (2760) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2771)   ~ (all_52_11 = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (366), (2760) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2772)   ~ (all_52_14 = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (374), (2760) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2773)   ~ (e3 = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | REDUCE: (371), (2760) imply:
% 145.67/20.48  | | | | | | | | | | | | | | |   (2774)   ~ (e2 = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | |   (2775)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 145.67/20.48  | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 145.67/20.48  | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | BETA: splitting (2775) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | |   (2776)  all_56_2 = e3 & op(e2, e3) = e3
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | ALPHA: (2776) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | |   (2777)  all_56_2 = e3
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | |   (2778)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 145.67/20.48  | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | BETA: splitting (2778) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | |   (2779)  all_56_4 = e3 & op(e3, e1) = e3
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | ALPHA: (2779) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | |   (2780)  all_56_4 = e3
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |   (2781)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (166), (1818), (2675), (2781),
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |            #603.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |   (2782)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (2782) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | |   (2783)  all_56_5 = e1 & op(e2, e1) = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2783) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | |   (2784)  all_56_5 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | |   (2785)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2785) gives:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |   (2786)  all_56_9 = e1 & op(e3, e0) = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2786) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |   (2787)  all_56_9 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (229), (233),
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |            (235), (1813), (2676), (2787), (function-axioms)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #913.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |   (2788)  all_56_10 = e1 & op(e2, e0) = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2788) implies:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |   (2789)  all_56_10 = e1
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (220), (222), (223),
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |            (2777), (2784), (2789), (function-axioms) are
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #678.
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | |   (2790)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 145.67/20.48  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (2750), (2772), (2790),
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | |            #732.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | |   (2791)  all_56_10 = e1 & op(e2, e0) = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | ALPHA: (2791) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | |   (2792)  all_56_10 = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | |   (2793)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2793) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | |   (2794)  all_56_2 = e2 & op(e2, e3) = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2794) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | |   (2795)  op(e2, e3) = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (166), (197), (260), (1816), (2765),
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | |            (2770), (2795), (function-axioms) are inconsistent
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #599.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | |   (2796)  all_56_3 = e2 & op(e2, e2) = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2796) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | |   (2797)  op(e2, e2) = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1818), (2797), (function-axioms) are
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | |   (2798)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2798) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | |   (2799)  all_56_5 = e2 & op(e2, e1) = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2799) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | |   (2800)  all_56_5 = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | |   (2801)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2801) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (2802)  all_56_12 = e1 & op(e0, e3) = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2802) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (2803)  all_56_12 = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (228), (232), (2676),
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | |            (2777), (2803), (function-axioms) are inconsistent
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #928.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (2804)  all_56_13 = e1 & op(e0, e2) = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2804) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | |   (2805)  all_56_13 = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2806)  all_54_6 = e3
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2765), (2806) are inconsistent by
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #650.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2807)   ~ (all_54_6 = e3)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2808)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2808) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2809)  all_54_6 = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2809) imply:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2810)  all_52_9 = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2810) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2811)  all_52_9 = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (2811) imply:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2812)   ~ (all_52_1 = e2)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (2811) imply:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2813)   ~ (all_52_11 = e2)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2813) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2814)   ~ (all_52_11 = e2)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (2811) imply:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2815)   ~ (all_52_13 = e2)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2815) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2816)   ~ (all_52_13 = e2)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2765), (2811) imply:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2817)   ~ (e3 = e2)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2818)  all_54_14 = e3
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2767), (2818) are inconsistent by
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #903.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2819)   ~ (all_54_14 = e3)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2820)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2820) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2821)  all_54_14 = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2814), (2821) are inconsistent by
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #902.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2822)   ~ (all_54_14 = e2)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2823)  all_54_14 = e1 | all_54_14 = e0
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2823) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2824)  all_54_14 = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (2771), (2824) are inconsistent by
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #753.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2825)  all_54_14 = e0
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (2825) imply:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2826)  all_52_11 = e0
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2826) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2827)  all_52_11 = e0
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (2827) imply:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2828)   ~ (all_52_3 = e0)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2814), (2827) imply:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2829)   ~ (e2 = e0)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2771), (2827) imply:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2830)   ~ (e1 = e0)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2831)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2831) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2832)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2832) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2833)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2812), (2833), (function-axioms) are
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2834)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2834) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2835)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2835) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2836)  op(e1, e3) = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (164),
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (228), (1818), (2676),
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2765), (2828), (2836), (function-axioms) are
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #598.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2837)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2837) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2838)  op(e1, e3) = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (164),
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (228), (1818), (2676),
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2765), (2828), (2838), (function-axioms) are
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #598.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2839)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2839) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2840)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2762), (2840), (function-axioms) are
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2841)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2841) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2842)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2842) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2843)  op(e3, e3) = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2676), (2843), (function-axioms) are
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2844)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2844) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2845)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2845) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2846)  op(e0, e0) = e2
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (2678), (2846), (function-axioms) are
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2847)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2847) implies:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2848)  op(e2, e2) = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (220), (2777), (2792), (2800),
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2848), (function-axioms) are inconsistent by
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #597.
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2849)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2849) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2850)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2850) gives:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.49  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2851)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2851) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2852)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2852) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2853)  op(e0, e0) = e1
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2750), (2853), (function-axioms) are
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2854)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2854) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2855)   ~ (all_57_6 = e3)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2758), (2855) imply:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2856)  $false
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2856) is inconsistent.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2857)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (2750), (2769), (2857),
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1020.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2858)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2858) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2859)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2676), (2859), (function-axioms) are
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2860)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2860) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2861)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2861) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2862)  op(e2, e0) = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2816), (2862), (function-axioms) are
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2863)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2863) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2864)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2864) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2865)  op(e1, e0) = e1
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2772), (2865), (function-axioms) are
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2866)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2866) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2867)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2868)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (1818), (2762), (2868),
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #596.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2869)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2869) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2870)  all_56_7 = e3 & op(e1, e2) = e3
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2870) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2871)  all_56_7 = e3
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2872)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2872) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2873)  all_56_1 = e2 & op(e3, e2) = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2873) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2874)  all_56_1 = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2875)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2875) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2876)  all_56_12 = e2 & op(e0, e3) = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2876) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2877)  all_56_12 = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2867) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2878)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2878) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2879)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2879) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2880)  op(e0, e3) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2828), (2880), (function-axioms) are
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2881)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2881) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2882)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2882) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2883)  op(e0, e3) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2828), (2883), (function-axioms) are
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2884)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2884) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2885)  op(e3, e3) = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (228), (230), (2777),
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2877), (2885), (function-axioms) are inconsistent
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #787.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2886)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2886) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2887)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2887) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2888)  op(e0, e2) = e0
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1815), (2888), (function-axioms) are
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2889)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2889) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2890)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_6)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2890) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2891)   ~ (all_57_6 = e3)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2758), (2891) imply:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2892)  $false
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2892) is inconsistent.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2893)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2893) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2894)  op(e2, e2) = e1
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (220), (2777), (2792), (2800),
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2894), (function-axioms) are inconsistent by
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #597.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2895)  all_56_13 = e2 & op(e0, e2) = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2895) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2896)  all_56_13 = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2805), (2896) imply:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2897)  e2 = e1
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2874), (2897) imply:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2898)  all_56_1 = e1
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2899)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2899) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2900)  all_56_0 = e2 & op(e3, e3) = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2900) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2901)  op(e3, e3) = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2676), (2901), (function-axioms) are
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2874), (2898) are inconsistent by sub-proof
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #595.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2902)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2902) gives:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2903)  all_56_4 = e2 & op(e3, e1) = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2903) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2904)  all_56_4 = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (167), (169), (235), (2676), (2762),
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2769), (2904), (function-axioms) are inconsistent
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #998.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2905)  all_56_9 = e2 & op(e3, e0) = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2905) implies:
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2906)  all_56_9 = e2
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (169), (229), (235),
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1813), (2676), (2898), (2906), (function-axioms)
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #592.
% 145.67/20.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2907)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2907) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2908)  all_56_14 = e2 & op(e0, e1) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2908) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2909)  op(e0, e1) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (2814), (2909), (function-axioms) are
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1092.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2910)  all_56_15 = e2 & op(e0, e0) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2910) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2911)  all_56_15 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2912)  op(e0, e0) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (138), (145), (158),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (161), (162), (163), (164), (166), (167),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (169), (189), (197), (205), (210), (211), (221),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (228), (238), (246), (260), (1816),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (1818), (2676), (2754), (2755), (2758), (2762),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2763), (2765), (2767), (2769), (2770), (2771),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2772), (2792), (2814), (2816), (2911), (2912),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #587.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2913)  all_56_3 = e2 & op(e2, e2) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2913) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2914)  op(e2, e2) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1818), (2914), (function-axioms) are
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2915)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2915) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2916)  all_56_7 = e2 & op(e1, e2) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2916) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2917)  all_56_7 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2871), (2917) imply:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2918)  e3 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2780), (2918) imply:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2919)  all_56_4 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (167), (169), (235), (2676), (2762),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2769), (2919), (function-axioms) are inconsistent
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #998.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2920)  all_56_13 = e2 & op(e0, e2) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2920) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2921)  all_56_13 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2805), (2921) imply:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2922)  e2 = e1
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2800), (2922) imply:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2923)  all_56_5 = e1
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (145), (163), (166),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (197), (220), (222), (223), (260), (1816), (2765),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2770), (2792), (2816), (2923), (function-axioms)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #586.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2924)  all_56_13 = e3 & op(e0, e2) = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2805), (2924) are inconsistent by sub-proof
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #585.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2925)  all_54_6 = e1 | all_54_6 = e0
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (1816), (2770), (2925) are inconsistent by
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #649.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | |   (2926)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2926) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (2927)  all_56_14 = e1 & op(e0, e1) = e1
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2927) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (2928)  op(e0, e1) = e1
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2929)  all_54_6 = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2765), (2929) are inconsistent by
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #650.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | |   (2930)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2930) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2931)  all_54_6 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2931) imply:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2932)  all_52_9 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2932) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2933)  all_52_9 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (2933) imply:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2934)   ~ (all_52_11 = e2)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2934) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2935)   ~ (all_52_11 = e2)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (189), (246), (2767), (2771), (2928),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2935), (function-axioms) are inconsistent by
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #731.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (2936)  all_54_6 = e1 | all_54_6 = e0
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (1816), (2770), (2936) are inconsistent by
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #649.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (2937)  all_56_15 = e1 & op(e0, e0) = e1
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2937) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (2938)  op(e0, e0) = e1
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2750), (2938), (function-axioms) are
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | |   (2939)  all_56_10 = e2 & op(e2, e0) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2792), (2939) are inconsistent by sub-proof
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | |            #679.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | |   (2940)  all_56_5 = e3 & op(e2, e1) = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2765), (2940), (function-axioms) are
% 145.67/20.51  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | |   (2941)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 145.67/20.51  | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (156), (2755), (2767), (2941),
% 145.67/20.51  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.51  | | | | | | | | | | | | | | | | | |            #733.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | |   (2942)  all_56_3 = e3 & op(e2, e2) = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | ALPHA: (2942) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | |   (2943)  op(e2, e2) = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1818), (2943), (function-axioms) are
% 145.67/20.51  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | |   (2944)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 145.67/20.51  | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 145.67/20.51  | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | BETA: splitting (2944) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | |   (2945)  all_56_5 = e3 & op(e2, e1) = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2765), (2945), (function-axioms) are
% 145.67/20.51  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | |   (2946)  all_56_10 = e3 & op(e2, e0) = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | ALPHA: (2946) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | |   (2947)  all_56_10 = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | |   (2948)  op(e2, e0) = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | |   (2949)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 145.67/20.51  | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | BETA: splitting (2949) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | |   (2950)  all_56_9 = e1 & op(e3, e0) = e1
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | ALPHA: (2950) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | |   (2951)  all_56_9 = e1
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (229), (233),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | |            (235), (1813), (2676), (2951), (function-axioms)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #913.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | |   (2952)  all_56_10 = e1 & op(e2, e0) = e1
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2947), (2952) are inconsistent by sub-proof
% 145.67/20.51  | | | | | | | | | | | | | | | | | | |            #584.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | |   (2953)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 145.67/20.51  | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (205), (210),
% 145.67/20.51  | | | | | | | | | | | | | | | | | |            (2678), (2750), (2947), (2948), (2953),
% 145.67/20.51  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.51  | | | | | | | | | | | | | | | | | |            #742.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | |   (2954)   ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.51  | | | | | | | | | | | | | | |           $i(all_57_10)
% 145.67/20.51  | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | ALPHA: (2954) implies:
% 145.67/20.51  | | | | | | | | | | | | | | |   (2955)   ~ (all_57_10 = e1)
% 145.67/20.51  | | | | | | | | | | | | | | |   (2956)  op(e3, e3) = all_57_10
% 145.67/20.51  | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | REF_CLOSE: (2676), (2955), (2956), (function-axioms) are
% 145.67/20.51  | | | | | | | | | | | | | | |            inconsistent by sub-proof #893.
% 145.67/20.51  | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | |   (2957)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 145.67/20.51  | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 145.67/20.51  | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.51  | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.67/20.51  | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.67/20.51  | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.67/20.51  | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.67/20.51  | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 145.67/20.51  | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | ALPHA: (2957) implies:
% 145.67/20.51  | | | | | | | | | | | | | |   (2958)  op(e0, e0) = e0
% 145.67/20.51  | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | REF_CLOSE: (7), (2750), (2958), (function-axioms) are
% 145.67/20.51  | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 145.67/20.51  | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | End of split
% 145.67/20.51  | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | |   (2959)  all_24_2 = e2
% 145.67/20.51  | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | COMBINE_EQS: (318), (2959) imply:
% 145.67/20.51  | | | | | | | | | |   (2960)  all_10_2 = e2
% 145.67/20.51  | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | REDUCE: (367), (2960) imply:
% 145.67/20.51  | | | | | | | | | |   (2961)   ~ (all_52_11 = e2)
% 145.67/20.51  | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | REDUCE: (369), (2960) imply:
% 145.67/20.51  | | | | | | | | | |   (2962)   ~ (all_52_13 = e2)
% 145.67/20.51  | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | REDUCE: (370), (2960) imply:
% 145.67/20.51  | | | | | | | | | |   (2963)   ~ (all_52_14 = e2)
% 145.67/20.51  | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | REDUCE: (45), (2960) imply:
% 145.67/20.51  | | | | | | | | | |   (2964)  op(e0, e0) = e2
% 145.67/20.51  | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | BETA: splitting (237) gives:
% 145.67/20.51  | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | |   (2965)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 145.67/20.51  | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 145.67/20.51  | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 145.67/20.51  | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 145.67/20.51  | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 145.67/20.51  | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 145.67/20.51  | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 145.67/20.51  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.67/20.51  | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 145.67/20.51  | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 145.67/20.51  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.51  | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 145.67/20.51  | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 145.67/20.51  | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 145.67/20.51  | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 145.67/20.51  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 145.67/20.51  | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | REF_CLOSE: (5), (8), (1818), (2676), (2965),
% 145.67/20.51  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.51  | | | | | | | | | | |            #602.
% 145.67/20.51  | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | |   (2966)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 145.67/20.51  | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 145.67/20.51  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.51  | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.67/20.51  | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.51  | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 145.67/20.51  | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 145.67/20.51  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 145.67/20.51  | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 145.67/20.51  | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 145.67/20.51  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.51  | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 145.67/20.51  | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 145.67/20.51  | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 145.67/20.51  | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 145.67/20.51  | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 145.67/20.51  | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | BETA: splitting (2966) gives:
% 145.67/20.51  | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | |   (2967)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 145.67/20.51  | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 145.67/20.51  | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 145.67/20.51  | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 145.67/20.51  | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 145.67/20.51  | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 145.67/20.51  | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 145.67/20.51  | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 145.67/20.51  | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | ALPHA: (2967) implies:
% 145.67/20.51  | | | | | | | | | | | |   (2968)  all_57_14 = e1
% 145.67/20.51  | | | | | | | | | | | |   (2969)  op(e1, e1) = e1
% 145.67/20.51  | | | | | | | | | | | |   (2970)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15
% 145.67/20.51  | | | | | | | | | | | |               = e1) & op(e0, e0) = all_57_15 &
% 145.67/20.51  | | | | | | | | | | | |             $i(all_57_15))
% 145.67/20.51  | | | | | | | | | | | |   (2971)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 145.67/20.51  | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 145.67/20.51  | | | | | | | | | | | |             $i(all_57_10))
% 145.67/20.51  | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | BETA: splitting (210) gives:
% 145.67/20.51  | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | |   (2972)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 145.67/20.51  | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 145.67/20.51  | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | BETA: splitting (2972) gives:
% 145.67/20.51  | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | |   (2973)  all_56_9 = e2 & op(e3, e0) = e2
% 145.67/20.51  | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | ALPHA: (2973) implies:
% 145.67/20.51  | | | | | | | | | | | | | |   (2974)  all_56_9 = e2
% 145.67/20.51  | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 145.67/20.51  | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | |   (2975)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 145.67/20.51  | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 145.67/20.51  | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | BETA: splitting (2975) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | |   (2976)  all_56_12 = e2 & op(e0, e3) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | ALPHA: (2976) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | |   (2977)  all_56_12 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | |   (2978)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 145.67/20.51  | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (169), (1813), (2676), (2978),
% 145.67/20.51  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.51  | | | | | | | | | | | | | | | | |            #937.
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | |   (2979)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 145.67/20.51  | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | BETA: splitting (2979) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | |   (2980)  all_56_4 = e0 & op(e3, e1) = e0
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | ALPHA: (2980) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | |   (2981)  all_56_4 = e0
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | |   (2982)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | BETA: splitting (2982) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | |   (2983)  all_56_4 = e2 & op(e3, e1) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | ALPHA: (2983) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | |   (2984)  all_56_4 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (169), (229), (1813), (2676), (2974),
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | |            (2984), (function-axioms) are inconsistent by
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | |            sub-proof #583.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | |   (2985)  all_56_5 = e2 & op(e2, e1) = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | ALPHA: (2985) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | |   (2986)  all_56_5 = e2
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | |   (2987)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (2981), (2986), (2987) are inconsistent
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #582.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | |   (2988)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2988) gives:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | |   (2989)  all_56_8 = e3 & op(e1, e1) = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2989) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | |   (2990)  op(e1, e1) = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2969), (2990), (function-axioms) are
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | |   (2991)  all_56_14 = e3 & op(e0, e1) = e3
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2991) implies:
% 145.67/20.51  | | | | | | | | | | | | | | | | | | | | | |   (2992)  all_56_14 = e3
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (206), (229),
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (2676), (2964), (2974), (2977),
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |            (2981), (2992), (function-axioms) are inconsistent
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #579.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | |   (2993)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 145.67/20.52  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (2993) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | |   (2994)  all_56_8 = e2 & op(e1, e1) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | ALPHA: (2994) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | |   (2995)  op(e1, e1) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | |   (2996)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2996) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |   (2997)  all_56_0 = e0 & op(e3, e3) = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2997) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |   (2998)  op(e3, e3) = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2676), (2998), (function-axioms) are
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #957.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |   (2999)  all_56_2 = e0 & op(e2, e3) = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2999) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |   (3000)  all_56_2 = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |   (3001)  all_56_15 = e0 & op(e0, e0) = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3001) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |   (3002)  op(e0, e0) = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2964), (3002), (function-axioms) are
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |   (3003)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3003) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |   (3004)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3005)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1818), (3000), (3005), (function-axioms) are
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #673.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3006)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3006) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (3007)  all_56_5 = e2 & op(e2, e1) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3007) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (3008)  all_56_5 = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (157), (219), (1815), (2977),
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |            (2981), (2995), (3004), (3008), (function-axioms)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #578.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (3009)  all_56_10 = e2 & op(e2, e0) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3009) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (3010)  op(e2, e0) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2962), (3010), (function-axioms) are
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | |   (3011)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3011) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |   (3012)  all_56_6 = e0 & op(e1, e3) = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3012) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |   (3013)  all_56_6 = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |   (3014)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3014) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3015)  all_56_0 = e3 & op(e3, e3) = e3
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3015) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3016)  op(e3, e3) = e3
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2676), (3016), (function-axioms) are
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3017)  all_56_2 = e3 & op(e2, e3) = e3
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3017) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3018)  all_56_2 = e3
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (3019)  all_56_15 = e0 & op(e0, e0) = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3019) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (3020)  op(e0, e0) = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2964), (3020), (function-axioms) are
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (3021)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3021) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (3022)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3023)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (1818), (3018), (3023),
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            #577.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3024)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3024) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3025)  all_56_5 = e2 & op(e2, e1) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3025) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3026)  all_56_5 = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (157), (219), (1815), (2977),
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2981), (2995), (3022), (3026), (function-axioms)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #578.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3027)  all_56_10 = e2 & op(e2, e0) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3027) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3028)  op(e2, e0) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (2962), (3028), (function-axioms) are
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |   (3029)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3029) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3030)  all_56_6 = e3 & op(e1, e3) = e3
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3013), (3030) are inconsistent by sub-proof
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |            #576.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3031)  all_56_12 = e3 & op(e0, e3) = e3
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2977), (3031) are inconsistent by sub-proof
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | |            #575.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |   (3032)  all_56_12 = e0 & op(e0, e3) = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2977), (3032) are inconsistent by sub-proof
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | |            #871.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | |   (3033)  all_56_14 = e2 & op(e0, e1) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | ALPHA: (3033) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | |   (3034)  op(e0, e1) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (2961), (3034), (function-axioms) are
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1092.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | |   (3035)  all_56_9 = e0 & op(e3, e0) = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2974), (3035) are inconsistent by sub-proof
% 145.67/20.52  | | | | | | | | | | | | | | | | | |            #746.
% 145.67/20.52  | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | |   (3036)  all_56_13 = e2 & op(e0, e2) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | ALPHA: (3036) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | |   (3037)  all_56_13 = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (139), (156),
% 145.67/20.52  | | | | | | | | | | | | | | | |            (157), (158), (159), (163), (166), (169), (205),
% 145.67/20.52  | | | | | | | | | | | | | | | |            (206), (209), (211), (212), (213), (214), (215),
% 145.67/20.52  | | | | | | | | | | | | | | | |            (217), (218), (219), (221), (222), (223), (224),
% 145.67/20.52  | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (231), (232), (233),
% 145.67/20.52  | | | | | | | | | | | | | | | |            (234), (235), (1813), (1815), (1818), (2675),
% 145.67/20.52  | | | | | | | | | | | | | | | |            (2676), (2961), (2962), (2963), (2964), (2969),
% 145.67/20.52  | | | | | | | | | | | | | | | |            (2970), (2974), (3037), (function-axioms) are
% 145.67/20.52  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #556.
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | End of split
% 145.67/20.52  | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | |   (3038)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 145.67/20.52  | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 145.67/20.52  | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | BETA: splitting (3038) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | |   (3039)  all_56_14 = e2 & op(e0, e1) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | ALPHA: (3039) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | |   (3040)  op(e0, e1) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | REF_CLOSE: (156), (2961), (3040), (function-axioms) are
% 145.67/20.52  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1092.
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | |   (3041)  all_56_15 = e2 & op(e0, e0) = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | ALPHA: (3041) implies:
% 145.67/20.52  | | | | | | | | | | | | | | | |   (3042)  all_56_15 = e2
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | |   (3043)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 145.67/20.52  | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (169), (1813), (2676), (3043),
% 145.67/20.52  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 145.67/20.52  | | | | | | | | | | | | | | | | |            #937.
% 145.67/20.52  | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | Case 2:
% 145.67/20.52  | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | |   (3044)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 145.67/20.52  | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | BETA: splitting (3044) gives:
% 145.67/20.52  | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | Case 1:
% 145.67/20.52  | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | |   (3045)  all_56_4 = e0 & op(e3, e1) = e0
% 145.67/20.52  | | | | | | | | | | | | | | | | | | 
% 145.67/20.52  | | | | | | | | | | | | | | | | | | ALPHA: (3045) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | |   (3046)  all_56_4 = e0
% 146.07/20.52  | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | |   (3047)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (3047) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | |   (3048)  all_56_4 = e2 & op(e3, e1) = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | ALPHA: (3048) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | |   (3049)  all_56_4 = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (169), (229), (1813), (2676), (2974),
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | |            (3049), (function-axioms) are inconsistent by
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | |            sub-proof #583.
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | |   (3050)  all_56_5 = e2 & op(e2, e1) = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | ALPHA: (3050) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | |   (3051)  all_56_5 = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | |   (3052)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (3046), (3051), (3052) are inconsistent
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #582.
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | |   (3053)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3053) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | |   (3054)  all_56_8 = e3 & op(e1, e1) = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3054) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | |   (3055)  op(e1, e1) = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2969), (3055), (function-axioms) are
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | |   (3056)  all_56_14 = e3 & op(e0, e1) = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3056) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | |   (3057)  all_56_14 = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | |   (3058)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3058) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3059)  all_56_0 = e3 & op(e3, e3) = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3059) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3060)  op(e3, e3) = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2676), (3060), (function-axioms) are
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3061)  all_56_1 = e3 & op(e3, e2) = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3061) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | |   (3062)  all_56_1 = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (3063)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3063) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3064)  all_56_12 = e1 & op(e0, e3) = e1
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3064) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3065)  all_56_12 = e1
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3066)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3066) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3067)  all_56_0 = e2 & op(e3, e3) = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3067) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3068)  op(e3, e3) = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (229), (231), (2974),
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3062), (3068), (function-axioms) are inconsistent
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #654.
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3069)  all_56_2 = e2 & op(e2, e3) = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3069) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3070)  all_56_2 = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (232), (234),
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (2676), (2974), (3046), (3062), (3065),
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3070), (function-axioms) are inconsistent by
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #572.
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3071)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3071) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3072)  all_56_6 = e2 & op(e1, e3) = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3072) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3073)  all_56_6 = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3074)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (228), (2676), (3065), (3073),
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3074), (function-axioms) are inconsistent by
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #568.
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3075)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3075) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3076)  all_56_6 = e3 & op(e1, e3) = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3076) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3077)  all_56_6 = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3073), (3077) imply:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3078)  e3 = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3078) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3079)  e3 = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3062), (3079) imply:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3080)  all_56_1 = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (2676), (2974), (3046),
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3080), (function-axioms) are inconsistent by
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #555.
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3081)  all_56_12 = e3 & op(e0, e3) = e3
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (2676), (2974), (3046),
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3062), (3065), (3081), (function-axioms) are
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #573.
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3082)  all_56_12 = e2 & op(e0, e3) = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3082) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3083)  all_56_12 = e2
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (206), (229),
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (2676), (2964), (2974), (3046),
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3057), (3083), (function-axioms) are inconsistent
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #579.
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3084)  all_56_13 = e1 & op(e0, e2) = e1
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3084) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3085)  all_56_13 = e1
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3086)  all_56_15 = e0 & op(e0, e0) = e0
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3086) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3087)  op(e0, e0) = e0
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2964), (3087), (function-axioms) are
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3088)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3088) implies:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3089)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3089) gives:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3090)  all_56_9 = e0 & op(e3, e0) = e0
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2974), (3090) are inconsistent by sub-proof
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #746.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3091)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3091) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3092)  all_56_10 = e0 & op(e2, e0) = e0
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3092) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3093)  all_56_10 = e0
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3094)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3094) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3095)  all_56_2 = e3 & op(e2, e3) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3095) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3096)  all_56_2 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (221), (222), (1818),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3093), (3096), (function-axioms) are inconsistent
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #554.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3097)  all_56_3 = e3 & op(e2, e2) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3097) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3098)  op(e2, e2) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1818), (3098), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3099)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3099) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3100)  all_56_5 = e3 & op(e2, e1) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3100) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3101)  all_56_5 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3051), (3101) imply:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3102)  e3 = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3062), (3102) imply:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3103)  all_56_1 = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (2676), (2974), (3046),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3103), (function-axioms) are inconsistent by
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #555.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3104)  all_56_10 = e3 & op(e2, e0) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3104) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3105)  all_56_10 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3093), (3105) are inconsistent by sub-proof
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1134.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3106)  all_56_11 = e0 & op(e1, e0) = e0
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3106) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3107)  all_56_11 = e0
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3108)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3108) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3109)  all_56_9 = e3 & op(e3, e0) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (2676), (2974), (3046),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3062), (3109), (function-axioms) are inconsistent
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #553.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3110)  all_56_10 = e3 & op(e2, e0) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3110) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3111)  all_56_10 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3112)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3112) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3113)  all_56_2 = e1 & op(e2, e3) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3113) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3114)  op(e2, e3) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (2675), (3114), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1177.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3115)  all_56_3 = e1 & op(e2, e2) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3115) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3116)  all_56_3 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3117)  op(e2, e2) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (224), (226), (3062),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3085), (3116), (3117), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #736.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3118)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3118) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3119)  all_56_5 = e1 & op(e2, e1) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3119) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3120)  all_56_5 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3051), (3120) imply:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3121)  e2 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (229), (233), (2676),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2974), (3062), (3121), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #581.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3122)  all_56_10 = e1 & op(e2, e0) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3122) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3123)  all_56_10 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3111), (3123) imply:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3124)  e3 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3062), (3124) imply:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3125)  all_56_1 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (2676), (2974), (3046),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3125), (function-axioms) are inconsistent by
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #593.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3126)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3126) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3127)  all_56_11 = e3 & op(e1, e0) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3127) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3128)  all_56_11 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3107), (3128) are inconsistent by sub-proof
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #772.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3129)  all_56_15 = e3 & op(e0, e0) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (2676), (2974), (3042),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3046), (3062), (3129), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #552.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (3130)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3130) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3131)  all_56_14 = e1 & op(e0, e1) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3131) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3132)  all_56_14 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3057), (3132) imply:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3133)  e3 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3062), (3133) imply:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3134)  all_56_1 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (2676), (2974), (3046),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3134), (function-axioms) are inconsistent by
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #593.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3135)  all_56_15 = e1 & op(e0, e0) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3135) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3136)  op(e0, e0) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2964), (3136), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #978.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | |   (3137)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (2974), (3046), (3137) are inconsistent
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #652.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | |   (3138)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | BETA: splitting (3138) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | |   (3139)  all_56_8 = e2 & op(e1, e1) = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (3139) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | |   (3140)  all_56_8 = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | |   (3141)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3141) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | |   (3142)  all_56_0 = e3 & op(e3, e3) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3142) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | |   (3143)  op(e3, e3) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2676), (3143), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | |   (3144)  all_56_1 = e3 & op(e3, e2) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3144) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | |   (3145)  all_56_1 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | |   (3146)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3146) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |   (3147)  all_56_1 = e2 & op(e3, e2) = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3147) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |   (3148)  all_56_1 = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (2676), (2974), (3046),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |            (3148), (function-axioms) are inconsistent by
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #555.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |   (3149)  all_56_3 = e2 & op(e2, e2) = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3149) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |   (3150)  op(e2, e2) = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1818), (3150), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | |   (3151)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3151) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |   (3152)  all_56_7 = e2 & op(e1, e2) = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3152) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |   (3153)  all_56_7 = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (3154)  all_56_15 = e0 & op(e0, e0) = e0
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3154) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (3155)  op(e0, e0) = e0
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2964), (3155), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (3156)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3156) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |   (3157)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3158)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3158) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3159)  all_56_6 = e1 & op(e1, e3) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3159) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3160)  all_56_6 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3161)  op(e1, e3) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (228), (232),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (2676), (3160), (3161), (function-axioms)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #547.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3162)  all_56_7 = e1 & op(e1, e2) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3162) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3163)  all_56_7 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3153), (3163) imply:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3164)  e2 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (229), (233), (2676),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2974), (3145), (3164), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #581.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3165)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3165) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3166)  all_56_8 = e1 & op(e1, e1) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3166) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3167)  all_56_8 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3140), (3167) imply:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3168)  e2 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (229), (233), (2676),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (2974), (3145), (3168), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #581.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3169)  all_56_11 = e1 & op(e1, e0) = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3169) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3170)  all_56_11 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3171)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3171) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3172)  all_56_9 = e3 & op(e3, e0) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (2676), (2974), (3046),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3145), (3172), (function-axioms) are inconsistent
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #553.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3173)  all_56_10 = e3 & op(e2, e0) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3173) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3174)  all_56_10 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (2974), (3157), (3170), (3174) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #744.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3175)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3175) gives:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3176)  all_56_11 = e3 & op(e1, e0) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3176) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3177)  all_56_11 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3170), (3177) imply:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3178)  e3 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3145), (3178) imply:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3179)  all_56_1 = e1
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (2676), (2974), (3046),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3179), (function-axioms) are inconsistent by
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #593.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3180)  all_56_15 = e3 & op(e0, e0) = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (235), (2676), (2974), (3042),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3046), (3145), (3180), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #552.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |   (3181)  all_56_13 = e2 & op(e0, e2) = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3181) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |   (3182)  all_56_13 = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (139), (156),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |            (157), (158), (159), (163), (166), (169), (205),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |            (206), (209), (211), (212), (213), (214), (215),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (219), (221), (222), (223), (224),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (231), (232), (233),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (1813), (1815), (1818), (2675),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |            (2676), (2961), (2962), (2963), (2964), (2969),
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |            (2970), (2974), (3182), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #556.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | |   (3183)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (2974), (3046), (3183) are inconsistent
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #652.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | |   (3184)  all_56_14 = e2 & op(e0, e1) = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | ALPHA: (3184) implies:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | |   (3185)  op(e0, e1) = e2
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (2961), (3185), (function-axioms) are
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1092.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.53  | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | |   (3186)  all_56_9 = e0 & op(e3, e0) = e0
% 146.07/20.53  | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2974), (3186) are inconsistent by sub-proof
% 146.07/20.53  | | | | | | | | | | | | | | | | | |            #746.
% 146.07/20.53  | | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | | End of split
% 146.07/20.53  | | | | | | | | | | | | | | | | 
% 146.07/20.53  | | | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | |   (3187)  all_56_10 = e2 & op(e2, e0) = e2
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | ALPHA: (3187) implies:
% 146.07/20.54  | | | | | | | | | | | | | |   (3188)  op(e2, e0) = e2
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | REF_CLOSE: (163), (2962), (3188), (function-axioms) are
% 146.07/20.54  | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | |   (3189)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 146.07/20.54  | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 146.07/20.54  | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | BETA: splitting (3189) gives:
% 146.07/20.54  | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | |   (3190)  all_56_11 = e2 & op(e1, e0) = e2
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | ALPHA: (3190) implies:
% 146.07/20.54  | | | | | | | | | | | | | |   (3191)  op(e1, e0) = e2
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | REF_CLOSE: (159), (2963), (3191), (function-axioms) are
% 146.07/20.54  | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | |   (3192)  all_56_15 = e2 & op(e0, e0) = e2
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | ALPHA: (3192) implies:
% 146.07/20.54  | | | | | | | | | | | | | |   (3193)  all_56_15 = e2
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | BETA: splitting (2971) gives:
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | |   (3194)  all_57_6 = e3 & op(e3, e1) = e3
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | ALPHA: (3194) implies:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3195)  all_57_6 = e3
% 146.07/20.54  | | | | | | | | | | | | | | |   (3196)  op(e3, e1) = e3
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 146.07/20.54  | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (2969) gives:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3197)  all_4_2 = e1
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 146.07/20.54  | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (3196) gives:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3198)  all_52_8 = e3
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REDUCE: (133), (3198) imply:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3199)   ~ (all_52_4 = e3)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REDUCE: (359), (3197) imply:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3200)   ~ (all_52_6 = e1)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REDUCE: (122), (3198) imply:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3201)   ~ (all_52_9 = e3)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | SIMP: (3201) implies:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3202)   ~ (all_52_9 = e3)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REDUCE: (120), (3198) imply:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3203)   ~ (all_52_11 = e3)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | SIMP: (3203) implies:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3204)   ~ (all_52_11 = e3)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REDUCE: (119), (3198) imply:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3205)   ~ (all_52_12 = e3)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | SIMP: (3205) implies:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3206)   ~ (all_52_12 = e3)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REDUCE: (362), (3197) imply:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3207)   ~ (all_52_9 = e1)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REDUCE: (364), (3197) imply:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3208)   ~ (all_52_11 = e1)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REDUCE: (366), (3197) imply:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3209)   ~ (all_52_14 = e1)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REDUCE: (374), (3197) imply:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3210)   ~ (e3 = e1)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REDUCE: (371), (3197) imply:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3211)   ~ (e2 = e1)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | |   (3212)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 146.07/20.54  | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (166), (1818), (2675), (3212),
% 146.07/20.54  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.54  | | | | | | | | | | | | | | | |            #603.
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | |   (3213)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 146.07/20.54  | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | BETA: splitting (3213) gives:
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | |   (3214)  all_56_5 = e1 & op(e2, e1) = e1
% 146.07/20.54  | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | ALPHA: (3214) implies:
% 146.07/20.54  | | | | | | | | | | | | | | | | |   (3215)  all_56_5 = e1
% 146.07/20.54  | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 146.07/20.54  | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | |   (3216)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 146.07/20.54  | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 146.07/20.54  | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | | BETA: splitting (3216) gives:
% 146.07/20.54  | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | | |   (3217)  all_56_9 = e1 & op(e3, e0) = e1
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | ALPHA: (3217) implies:
% 146.07/20.54  | | | | | | | | | | | | | | | | | | |   (3218)  all_56_9 = e1
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (229), (233),
% 146.07/20.54  | | | | | | | | | | | | | | | | | | |            (235), (1813), (2676), (3218), (function-axioms)
% 146.07/20.54  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #913.
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | | |   (3219)  all_56_10 = e1 & op(e2, e0) = e1
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | ALPHA: (3219) implies:
% 146.07/20.54  | | | | | | | | | | | | | | | | | | |   (3220)  all_56_10 = e1
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (145), (163), (166),
% 146.07/20.54  | | | | | | | | | | | | | | | | | | |            (197), (220), (222), (223), (260), (1816), (2962),
% 146.07/20.54  | | | | | | | | | | | | | | | | | | |            (3202), (3207), (3215), (3220), (function-axioms)
% 146.07/20.54  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #586.
% 146.07/20.54  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | |   (3221)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 146.07/20.54  | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 146.07/20.54  | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (2964), (3209), (3221),
% 146.07/20.54  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.54  | | | | | | | | | | | | | | | | | |            #615.
% 146.07/20.54  | | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | |   (3222)  all_56_10 = e1 & op(e2, e0) = e1
% 146.07/20.54  | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | ALPHA: (3222) implies:
% 146.07/20.54  | | | | | | | | | | | | | | | | |   (3223)  all_56_10 = e1
% 146.07/20.54  | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (138), (145), (158),
% 146.07/20.54  | | | | | | | | | | | | | | | | |            (159), (161), (162), (163), (164), (166), (167),
% 146.07/20.54  | | | | | | | | | | | | | | | | |            (169), (189), (197), (205), (210), (211), (221),
% 146.07/20.54  | | | | | | | | | | | | | | | | |            (222), (223), (228), (238), (246), (260), (1816),
% 146.07/20.54  | | | | | | | | | | | | | | | | |            (1818), (2676), (2961), (2962), (2964), (2968),
% 146.07/20.54  | | | | | | | | | | | | | | | | |            (2969), (3193), (3195), (3199), (3200), (3202),
% 146.07/20.54  | | | | | | | | | | | | | | | | |            (3204), (3206), (3207), (3208), (3209), (3223),
% 146.07/20.54  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.54  | | | | | | | | | | | | | | | | |            #587.
% 146.07/20.54  | | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | |   (3224)   ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.54  | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | ALPHA: (3224) implies:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3225)   ~ (all_57_10 = e1)
% 146.07/20.54  | | | | | | | | | | | | | | |   (3226)  op(e3, e3) = all_57_10
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 146.07/20.54  | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (2676), (3226)
% 146.07/20.54  | | | | | | | | | | | | | | |              gives:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3227)  all_57_10 = e1
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REDUCE: (3225), (3227) imply:
% 146.07/20.54  | | | | | | | | | | | | | | |   (3228)  $false
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | CLOSE: (3228) is inconsistent.
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | |   (3229)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 146.07/20.54  | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 146.07/20.54  | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.54  | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.07/20.54  | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.07/20.54  | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.07/20.54  | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.07/20.54  | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 146.07/20.54  | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | ALPHA: (3229) implies:
% 146.07/20.54  | | | | | | | | | | | |   (3230)  op(e0, e0) = e0
% 146.07/20.54  | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | REF_CLOSE: (5), (2964), (3230), (function-axioms) are
% 146.07/20.54  | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 146.07/20.54  | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | 
% 146.07/20.54  | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | 
% 146.07/20.54  | | | | | | | End of split
% 146.07/20.54  | | | | | | | 
% 146.07/20.54  | | | | | | End of split
% 146.07/20.54  | | | | | | 
% 146.07/20.54  | | | | | Case 2:
% 146.07/20.54  | | | | | | 
% 146.07/20.54  | | | | | |   (3231)  all_14_2 = e0
% 146.07/20.54  | | | | | | 
% 146.07/20.54  | | | | | | REDUCE: (336), (3231) imply:
% 146.07/20.54  | | | | | |   (3232)   ~ (all_52_1 = e0)
% 146.07/20.54  | | | | | | 
% 146.07/20.54  | | | | | | REDUCE: (340), (3231) imply:
% 146.07/20.54  | | | | | |   (3233)   ~ (all_52_3 = e0)
% 146.07/20.54  | | | | | | 
% 146.07/20.54  | | | | | | REDUCE: (342), (3231) imply:
% 146.07/20.54  | | | | | |   (3234)   ~ (all_52_4 = e0)
% 146.07/20.54  | | | | | | 
% 146.07/20.54  | | | | | | REDUCE: (344), (3231) imply:
% 146.07/20.54  | | | | | |   (3235)   ~ (all_52_8 = e0)
% 146.07/20.54  | | | | | | 
% 146.07/20.54  | | | | | | REDUCE: (346), (3231) imply:
% 146.07/20.54  | | | | | |   (3236)   ~ (all_52_12 = e0)
% 146.07/20.54  | | | | | | 
% 146.07/20.54  | | | | | | REDUCE: (51), (3231) imply:
% 146.07/20.54  | | | | | |   (3237)  op(e3, e3) = e0
% 146.07/20.54  | | | | | | 
% 146.07/20.54  | | | | | | BETA: splitting (55) gives:
% 146.07/20.54  | | | | | | 
% 146.07/20.54  | | | | | | Case 1:
% 146.07/20.54  | | | | | | | 
% 146.07/20.54  | | | | | | |   (3238)   ~ (all_16_2 = e0)
% 146.07/20.54  | | | | | | | 
% 146.07/20.54  | | | | | | | REDUCE: (327), (3238) imply:
% 146.07/20.54  | | | | | | |   (3239)   ~ (all_6_2 = e0)
% 146.07/20.54  | | | | | | | 
% 146.07/20.54  | | | | | | | BETA: splitting (61) gives:
% 146.07/20.54  | | | | | | | 
% 146.07/20.54  | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | 
% 146.07/20.54  | | | | | | | |   (3240)   ~ (all_20_2 = e1)
% 146.07/20.54  | | | | | | | | 
% 146.07/20.54  | | | | | | | | REDUCE: (282), (3240) imply:
% 146.07/20.54  | | | | | | | |   (3241)   ~ (all_6_2 = e1)
% 146.07/20.54  | | | | | | | | 
% 146.07/20.54  | | | | | | | | BETA: splitting (198) gives:
% 146.07/20.54  | | | | | | | | 
% 146.07/20.54  | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | 
% 146.07/20.54  | | | | | | | | |   (3242)  all_54_5 = e3
% 146.07/20.54  | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | COMBINE_EQS: (267), (3242) imply:
% 146.07/20.54  | | | | | | | | |   (3243)  all_6_2 = e3
% 146.07/20.54  | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | REDUCE: (372), (3243) imply:
% 146.07/20.54  | | | | | | | | |   (3244)  $false
% 146.07/20.54  | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | CLOSE: (3244) is inconsistent.
% 146.07/20.54  | | | | | | | | | 
% 146.07/20.54  | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | 
% 146.07/20.54  | | | | | | | | |   (3245)   ~ (all_54_5 = e3)
% 146.07/20.54  | | | | | | | | |   (3246)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 146.07/20.54  | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | BETA: splitting (3246) gives:
% 146.07/20.54  | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | |   (3247)  all_54_5 = e2
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | COMBINE_EQS: (267), (3247) imply:
% 146.07/20.54  | | | | | | | | | |   (3248)  all_6_2 = e2
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | REDUCE: (347), (3248) imply:
% 146.07/20.54  | | | | | | | | | |   (3249)   ~ (all_52_1 = e2)
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | REDUCE: (350), (3248) imply:
% 146.07/20.54  | | | | | | | | | |   (3250)   ~ (all_52_4 = e2)
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | REDUCE: (352), (3248) imply:
% 146.07/20.54  | | | | | | | | | |   (3251)   ~ (all_52_6 = e2)
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | REDUCE: (356), (3248) imply:
% 146.07/20.54  | | | | | | | | | |   (3252)   ~ (all_52_9 = e2)
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | REDUCE: (358), (3248) imply:
% 146.07/20.54  | | | | | | | | | |   (3253)   ~ (all_52_13 = e2)
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | REDUCE: (372), (3248) imply:
% 146.07/20.54  | | | | | | | | | |   (3254)   ~ (e3 = e2)
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | REDUCE: (39), (3248) imply:
% 146.07/20.54  | | | | | | | | | |   (3255)  op(e2, e2) = e2
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | BETA: splitting (67) gives:
% 146.07/20.54  | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | |   (3256)   ~ (all_24_2 = e2)
% 146.07/20.54  | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | REDUCE: (318), (3256) imply:
% 146.07/20.54  | | | | | | | | | | |   (3257)   ~ (all_10_2 = e2)
% 146.07/20.54  | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | BETA: splitting (93) gives:
% 146.07/20.54  | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | |   (3258)   ~ (all_42_2 = e3)
% 146.07/20.54  | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | REDUCE: (302), (3258) imply:
% 146.07/20.54  | | | | | | | | | | | |   (3259)   ~ (all_10_2 = e3)
% 146.07/20.54  | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | BETA: splitting (238) gives:
% 146.07/20.54  | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | |   (3260)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.54  | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.54  | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.07/20.54  | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.07/20.54  | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.07/20.54  | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.54  | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.07/20.54  | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.07/20.54  | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.54  | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.07/20.54  | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.07/20.54  | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.07/20.54  | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.07/20.54  | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.07/20.54  | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.54  | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.07/20.54  | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 146.07/20.54  | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 146.07/20.54  | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.07/20.54  | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 146.07/20.54  | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 146.07/20.54  | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.54  | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.54  | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.07/20.54  | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.07/20.54  | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 146.07/20.54  | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 146.07/20.54  | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 146.07/20.54  | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.54  | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 146.07/20.54  | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 146.07/20.54  | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 146.07/20.54  | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 146.07/20.54  | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 146.07/20.54  | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.54  | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.54  | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.54  | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.07/20.54  | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | BETA: splitting (3260) gives:
% 146.07/20.54  | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | |   (3261)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.54  | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.07/20.54  | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.07/20.54  | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.07/20.54  | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.54  | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.07/20.54  | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.07/20.54  | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.07/20.54  | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.07/20.54  | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (166), (188), (245), (375), (3249),
% 146.07/20.54  | | | | | | | | | | | | | |            (3255), (3257), (3259), (3261), (function-axioms)
% 146.07/20.54  | | | | | | | | | | | | | |            are inconsistent by sub-proof #546.
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | |   (3262)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.54  | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.54  | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.07/20.54  | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.07/20.54  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.07/20.54  | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.54  | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 146.07/20.54  | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.54  | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.07/20.54  | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 146.07/20.54  | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 146.07/20.54  | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.54  | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.07/20.54  | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.07/20.54  | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.54  | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.07/20.54  | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.07/20.54  | | | | | | | | | | | | | |             $i(all_57_10))
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | BETA: splitting (3262) gives:
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | |   (3263)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.54  | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.54  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.07/20.54  | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.07/20.54  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.07/20.54  | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.07/20.54  | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.07/20.54  | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.54  | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | BETA: splitting (3263) gives:
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | Case 1:
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | |   (3264)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.54  | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.54  | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.07/20.54  | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.07/20.54  | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | ALPHA: (3264) implies:
% 146.07/20.54  | | | | | | | | | | | | | | | |   (3265)  op(e1, e1) = e2
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (3265), (function-axioms) are
% 146.07/20.54  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | |   (3266)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.54  | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.54  | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.07/20.54  | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.07/20.54  | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | ALPHA: (3266) implies:
% 146.07/20.54  | | | | | | | | | | | | | | | |   (3267)  op(e0, e0) = e2
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (3257), (3267), (function-axioms) are
% 146.07/20.54  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 146.07/20.54  | | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | |   (3268)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.07/20.54  | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.07/20.54  | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.07/20.54  | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 146.07/20.54  | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 146.07/20.54  | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 146.07/20.54  | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.54  | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.54  | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 146.07/20.54  | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.54  | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.54  | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.54  | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (45), (3237), (3255), (3257), (3268),
% 146.07/20.54  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.54  | | | | | | | | | | | | | | |            #545.
% 146.07/20.54  | | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | | End of split
% 146.07/20.54  | | | | | | | | | | | | | 
% 146.07/20.54  | | | | | | | | | | | | Case 2:
% 146.07/20.54  | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | |   (3269)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.55  | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.55  | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.55  | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.55  | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.55  | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.55  | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.55  | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.07/20.55  | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.07/20.55  | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.55  | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.07/20.55  | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.07/20.55  | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.07/20.55  | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.07/20.55  | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.07/20.55  | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.07/20.55  | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.55  | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.55  | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.55  | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 146.07/20.55  | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 146.07/20.55  | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 146.07/20.55  | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 146.07/20.55  | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 146.07/20.55  | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.07/20.55  | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.07/20.55  | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.07/20.55  | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 146.07/20.55  | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 146.07/20.55  | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.55  | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.55  | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.55  | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.07/20.55  | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.07/20.55  | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.55  | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.07/20.55  | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.07/20.55  | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.07/20.55  | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.07/20.55  | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.07/20.55  | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.55  | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.55  | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.55  | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.55  | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.55  | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.55  | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.55  | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.55  | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.55  | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.55  | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.55  | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.55  | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.55  | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.55  | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.55  | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.55  | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.55  | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | BETA: splitting (3269) gives:
% 146.07/20.55  | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | |   (3270)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.55  | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.55  | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.55  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.55  | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.55  | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.55  | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.55  | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.07/20.55  | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.07/20.55  | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.55  | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.07/20.55  | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.07/20.55  | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.07/20.55  | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.07/20.55  | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.07/20.55  | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.55  | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.55  | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.55  | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | BETA: splitting (3270) gives:
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | |   (3271)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.55  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.55  | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.55  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.55  | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.55  | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.55  | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.55  | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | REF_CLOSE: (45), (164), (375), (3252), (3271),
% 146.07/20.55  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.55  | | | | | | | | | | | | | | |            #544.
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | Case 2:
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | |   (3272)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.55  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.07/20.55  | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 146.07/20.55  | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.55  | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 146.07/20.55  | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 146.07/20.55  | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.55  | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.55  | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 146.07/20.55  | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 146.07/20.55  | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.55  | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 146.07/20.55  | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | BETA: splitting (3272) gives:
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3273)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.55  | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.07/20.55  | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 146.07/20.55  | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.55  | | | | | | | | | | | | | | | |           $i(all_57_12)
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | ALPHA: (3273) implies:
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3274)  op(e0, e0) = e1
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (375), (3274), (function-axioms) are
% 146.07/20.55  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1116.
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | Case 2:
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3275)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.07/20.55  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.07/20.55  | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.07/20.55  | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.55  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.55  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.55  | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | REF_CLOSE: (3237), (3275), (function-axioms) are inconsistent
% 146.07/20.55  | | | | | | | | | | | | | | | |            by sub-proof #542.
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | End of split
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | End of split
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | Case 2:
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | |   (3276)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.07/20.55  | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.07/20.55  | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.07/20.55  | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.07/20.55  | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.07/20.55  | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.07/20.55  | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.07/20.55  | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 146.07/20.55  | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.55  | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.07/20.55  | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.55  | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 146.07/20.55  | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 146.07/20.55  | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 146.07/20.55  | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 146.07/20.55  | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 146.07/20.55  | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.07/20.55  | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 146.07/20.55  | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.55  | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 146.07/20.55  | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 146.07/20.55  | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.55  | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.55  | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.55  | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.55  | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.55  | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.55  | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.55  | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.55  | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.55  | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.55  | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.55  | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.55  | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.55  | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.55  | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | BETA: splitting (3276) gives:
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | |   (3277)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.07/20.55  | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.07/20.55  | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.07/20.55  | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.07/20.55  | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.07/20.55  | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.07/20.55  | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.07/20.55  | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | BETA: splitting (3277) gives:
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3278)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.07/20.55  | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.07/20.55  | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | ALPHA: (3278) implies:
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3279)  op(e2, e0) = e2
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3253), (3279), (function-axioms) are
% 146.07/20.55  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | Case 2:
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3280)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.07/20.55  | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.07/20.55  | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | ALPHA: (3280) implies:
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3281)  op(e1, e0) = e1
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (164), (166), (188), (193), (220),
% 146.07/20.55  | | | | | | | | | | | | | | | |            (245), (334), (362), (366), (369), (371), (374),
% 146.07/20.55  | | | | | | | | | | | | | | | |            (375), (3232), (3255), (3257), (3259), (3281),
% 146.07/20.55  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.55  | | | | | | | | | | | | | | | |            #539.
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | End of split
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | Case 2:
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | |   (3282)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.07/20.55  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.55  | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.55  | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.07/20.55  | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.07/20.55  | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.55  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.07/20.55  | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.07/20.55  | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.07/20.55  | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.07/20.55  | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.55  | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.55  | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.55  | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.55  | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.55  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.55  | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.55  | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.55  | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.55  | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.55  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.55  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.55  | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.55  | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.55  | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.55  | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | BETA: splitting (3282) gives:
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3283)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.07/20.55  | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.55  | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.55  | | | | | | | | | | | | | | | |           $i(all_57_13)
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | ALPHA: (3283) implies:
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3284)  op(e2, e0) = e2
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3253), (3284), (function-axioms) are
% 146.07/20.55  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | Case 2:
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3285)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.07/20.55  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 146.07/20.55  | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 146.07/20.55  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 146.07/20.55  | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 146.07/20.55  | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 146.07/20.55  | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 146.07/20.55  | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 146.07/20.55  | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 146.07/20.55  | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 146.07/20.55  | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 146.07/20.55  | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 146.07/20.55  | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 146.07/20.55  | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.07/20.55  | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 146.07/20.55  | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.07/20.55  | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 146.07/20.55  | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 146.07/20.55  | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 146.07/20.55  | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 146.07/20.55  | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 146.07/20.55  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 146.07/20.55  | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 146.07/20.55  | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 146.07/20.55  | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | BETA: splitting (3285) gives:
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | |   (3286)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 146.07/20.55  | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | | ALPHA: (3286) implies:
% 146.07/20.55  | | | | | | | | | | | | | | | | |   (3287)  op(e1, e0) = e1
% 146.07/20.55  | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (164), (166), (188), (193), (220),
% 146.07/20.55  | | | | | | | | | | | | | | | | |            (245), (334), (362), (366), (369), (371), (374),
% 146.07/20.55  | | | | | | | | | | | | | | | | |            (375), (3232), (3255), (3257), (3259), (3287),
% 146.07/20.55  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.55  | | | | | | | | | | | | | | | | |            #539.
% 146.07/20.55  | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.55  | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | |   (3288)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.07/20.55  | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 146.07/20.55  | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.55  | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 146.07/20.55  | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 146.07/20.55  | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 146.07/20.55  | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 146.07/20.55  | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 146.07/20.55  | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 146.07/20.55  | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | | ALPHA: (3288) implies:
% 146.07/20.55  | | | | | | | | | | | | | | | | |   (3289)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.55  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.07/20.55  | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.55  | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.07/20.55  | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.07/20.55  | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.07/20.55  | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.07/20.55  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.55  | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.07/20.55  | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.07/20.55  | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (158), (371), (3233), (3237),
% 146.07/20.55  | | | | | | | | | | | | | | | | |            (3255), (3289), (function-axioms) are inconsistent
% 146.07/20.55  | | | | | | | | | | | | | | | | |            by sub-proof #536.
% 146.07/20.55  | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | End of split
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | End of split
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | End of split
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | End of split
% 146.07/20.55  | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | End of split
% 146.07/20.55  | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | Case 2:
% 146.07/20.55  | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | |   (3290)  all_42_2 = e3
% 146.07/20.55  | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | COMBINE_EQS: (302), (3290) imply:
% 146.07/20.55  | | | | | | | | | | | |   (3291)  all_10_2 = e3
% 146.07/20.55  | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | SIMP: (3291) implies:
% 146.07/20.55  | | | | | | | | | | | |   (3292)  all_10_2 = e3
% 146.07/20.55  | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | REDUCE: (349), (3292) imply:
% 146.07/20.55  | | | | | | | | | | | |   (3293)   ~ (all_52_3 = e3)
% 146.07/20.55  | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | REDUCE: (368), (3292) imply:
% 146.07/20.55  | | | | | | | | | | | |   (3294)   ~ (all_52_12 = e3)
% 146.07/20.55  | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | REDUCE: (369), (3292) imply:
% 146.07/20.55  | | | | | | | | | | | |   (3295)   ~ (all_52_13 = e3)
% 146.07/20.55  | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | REDUCE: (45), (3292) imply:
% 146.07/20.55  | | | | | | | | | | | |   (3296)  op(e0, e0) = e3
% 146.07/20.55  | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | BETA: splitting (102) gives:
% 146.07/20.55  | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | |   (3297)   ~ (all_48_2 = e0)
% 146.07/20.55  | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | REDUCE: (298), (3297) imply:
% 146.07/20.55  | | | | | | | | | | | | |   (3298)   ~ (all_4_2 = e0)
% 146.07/20.55  | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | BETA: splitting (193) gives:
% 146.07/20.55  | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | |   (3299)  all_54_10 = e3
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (3299) are inconsistent by sub-proof
% 146.07/20.55  | | | | | | | | | | | | | |            #1173.
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | Case 2:
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | |   (3300)   ~ (all_54_10 = e3)
% 146.07/20.55  | | | | | | | | | | | | | |   (3301)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | BETA: splitting (3301) gives:
% 146.07/20.55  | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | |   (3302)  all_54_10 = e2
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (3302) are inconsistent by sub-proof
% 146.07/20.55  | | | | | | | | | | | | | | |            #1168.
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | Case 2:
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | |   (3303)   ~ (all_54_10 = e2)
% 146.07/20.55  | | | | | | | | | | | | | | |   (3304)  all_54_10 = e1 | all_54_10 = e0
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | BETA: splitting (3304) gives:
% 146.07/20.55  | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3305)  all_54_10 = e1
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (3305) imply:
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3306)  all_4_2 = e1
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | SIMP: (3306) implies:
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3307)  all_4_2 = e1
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | REDUCE: (348), (3307) imply:
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3308)   ~ (all_52_2 = e1)
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | REDUCE: (366), (3307) imply:
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3309)   ~ (all_52_14 = e1)
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | REDUCE: (374), (3307) imply:
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3310)   ~ (e3 = e1)
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | REDUCE: (371), (3307) imply:
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3311)   ~ (e2 = e1)
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | REDUCE: (36), (3307) imply:
% 146.07/20.55  | | | | | | | | | | | | | | | |   (3312)  op(e1, e1) = e1
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 146.07/20.55  | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | |   (3313)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.07/20.55  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.07/20.55  | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.07/20.55  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.07/20.55  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 146.07/20.55  | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 146.07/20.55  | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.55  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.07/20.55  | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 146.07/20.55  | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 146.07/20.55  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 146.07/20.55  | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 146.07/20.55  | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 146.07/20.55  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 146.07/20.55  | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.55  | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.55  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.55  | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.07/20.55  | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | | BETA: splitting (3313) gives:
% 146.07/20.55  | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | | |   (3314)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.55  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.55  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.07/20.55  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.07/20.55  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.07/20.55  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.55  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.07/20.55  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.07/20.55  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.55  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.07/20.55  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.07/20.55  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.07/20.55  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.07/20.55  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.07/20.55  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.55  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.07/20.55  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.07/20.55  | | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | | | BETA: splitting (3314) gives:
% 146.07/20.55  | | | | | | | | | | | | | | | | | | 
% 146.07/20.55  | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.55  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |   (3315)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (3249), (3315), (function-axioms) are
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |   (3316)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3308), (3316), (function-axioms) are
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1025.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | |   (3317)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.07/20.56  | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | BETA: splitting (3317) gives:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |   (3318)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (3296), (3312), (3318),
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |            #1024.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |   (3319)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (3319) gives:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |   (3320)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (3320) implies:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |   (3321)  op(e3, e3) = e2
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3237), (3321), (function-axioms) are
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |   (3322)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (3255), (3296), (3322),
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |            #1023.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | |   (3323)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.56  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.56  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.56  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.07/20.56  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.07/20.56  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 146.07/20.56  | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 146.07/20.56  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.07/20.56  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 146.07/20.56  | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 146.07/20.56  | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.56  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.07/20.56  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.07/20.56  | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.56  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.56  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.56  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.56  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.56  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.56  | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | BETA: splitting (3323) gives:
% 146.07/20.56  | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | |   (3324)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | BETA: splitting (3324) gives:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |   (3325)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (3252), (3296), (3325),
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |            #1021.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |   (3326)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (3294), (3296), (3326),
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |            #1020.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | |   (3327)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.07/20.56  | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | BETA: splitting (3327) gives:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |   (3328)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (3253), (3309), (3328),
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |            #535.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |   (3329)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (3329) gives:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |   (3330)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (3330) implies:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |   (3331)  op(e2, e0) = e2
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3253), (3331), (function-axioms) are
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |   (3332)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3332) gives:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |   (3333)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3333) implies:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |   (3334)  op(e1, e0) = e1
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3309), (3334), (function-axioms) are
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |   (3335)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | ALPHA: (3335) implies:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |   (3336)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3336) gives:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |   (3337)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (3233), (3237), (3337),
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |            #538.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |   (3338)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (36), (3237), (3255), (3312), (3338),
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | |            #534.
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | |   (3339)  all_54_10 = e0
% 146.07/20.56  | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | | REF_CLOSE: (334), (3298), (3339) are inconsistent by
% 146.07/20.56  | | | | | | | | | | | | | | | |            sub-proof #1033.
% 146.07/20.56  | | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | End of split
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | Case 2:
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | |   (3340)  all_48_2 = e0
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | COMBINE_EQS: (298), (3340) imply:
% 146.07/20.56  | | | | | | | | | | | | |   (3341)  all_4_2 = e0
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | REDUCE: (348), (3341) imply:
% 146.07/20.56  | | | | | | | | | | | | |   (3342)   ~ (all_52_2 = e0)
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | REDUCE: (359), (3341) imply:
% 146.07/20.56  | | | | | | | | | | | | |   (3343)   ~ (all_52_6 = e0)
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | REDUCE: (362), (3341) imply:
% 146.07/20.56  | | | | | | | | | | | | |   (3344)   ~ (all_52_9 = e0)
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | REDUCE: (364), (3341) imply:
% 146.07/20.56  | | | | | | | | | | | | |   (3345)   ~ (all_52_11 = e0)
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | REDUCE: (374), (3341) imply:
% 146.07/20.56  | | | | | | | | | | | | |   (3346)   ~ (e3 = e0)
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | REDUCE: (371), (3341) imply:
% 146.07/20.56  | | | | | | | | | | | | |   (3347)   ~ (e2 = e0)
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | REDUCE: (36), (3341) imply:
% 146.07/20.56  | | | | | | | | | | | | |   (3348)  op(e1, e1) = e0
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | BETA: splitting (224) gives:
% 146.07/20.56  | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | Case 1:
% 146.07/20.56  | | | | | | | | | | | | | | 
% 146.07/20.56  | | | | | | | | | | | | | |   (3349)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 146.07/20.56  | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 146.07/20.56  | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | REF_CLOSE: (5), (169), (3234), (3255), (3349),
% 146.07/20.57  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.57  | | | | | | | | | | | | | |            #1012.
% 146.07/20.57  | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | |   (3350)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 146.07/20.57  | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 146.07/20.57  | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | BETA: splitting (3350) gives:
% 146.07/20.57  | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | |   (3351)  all_56_7 = e0 & op(e1, e2) = e0
% 146.07/20.57  | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | REF_CLOSE: (161), (3343), (3351), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1029.
% 146.07/20.57  | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | |   (3352)  all_56_13 = e0 & op(e0, e2) = e0
% 146.07/20.57  | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | ALPHA: (3352) implies:
% 146.07/20.57  | | | | | | | | | | | | | | |   (3353)  op(e0, e2) = e0
% 146.07/20.57  | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | |   (3354)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 146.07/20.57  | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 146.07/20.57  | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (166), (3232), (3255), (3354),
% 146.07/20.57  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.57  | | | | | | | | | | | | | | | |            #541.
% 146.07/20.57  | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | |   (3355)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 146.07/20.57  | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 146.07/20.57  | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | BETA: splitting (3355) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | |   (3356)  all_56_5 = e0 & op(e2, e1) = e0
% 146.07/20.57  | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3344), (3356), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1144.
% 146.07/20.57  | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | |   (3357)  all_56_10 = e0 & op(e2, e0) = e0
% 146.07/20.57  | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | ALPHA: (3357) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | |   (3358)  op(e2, e0) = e0
% 146.07/20.57  | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | |   (3359)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.07/20.57  | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 146.07/20.57  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | BETA: splitting (3359) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |   (3360)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | ALPHA: (3360) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |   (3361)  op(e3, e3) = e3
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3237), (3361), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |   (3362)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | ALPHA: (3362) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |   (3363)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |               = e2) & op(e0, e0) = all_57_15 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |   (3364)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3364) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |   (3365)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3365) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |   (3366)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (3249), (3366), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |   (3367)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3367) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3368)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3368) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3369)  op(e2, e2) = e3
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3255), (3369), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3370)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3370) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3371)  op(e1, e1) = all_57_14
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3372)  op(e1, e3) = e1
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (157), (3353) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3373)  all_52_7 = e0
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14, e1, e1, simplifying with (3348), (3371)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3374)  all_57_14 = e0
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (3372) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3375)  all_52_2 = e1
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, e2, simplifying with (163), (3358) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3376)  all_52_13 = e0
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (3375) imply:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3377)   ~ (all_52_3 = e1)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3377) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3378)   ~ (all_52_3 = e1)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (3375) imply:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3379)   ~ (all_52_6 = e1)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3379) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3380)   ~ (all_52_6 = e1)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |   (3381)  all_54_12 = e3
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (3293), (3381) are inconsistent by
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1093.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |   (3382)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (3383)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3383) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3384)  all_56_4 = e2 & op(e3, e1) = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3384) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3385)  all_56_4 = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3386)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3386) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3387)  all_56_1 = e1 & op(e3, e2) = e1
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3387) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3388)  all_56_1 = e1
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (167), (235), (3237), (3294),
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3385), (3388), (function-axioms) are inconsistent
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #533.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3389)  all_56_3 = e1 & op(e2, e2) = e1
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3389) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3390)  op(e2, e2) = e1
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3255), (3390), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3391)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (161), (169), (224), (3234), (3255),
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3343), (3380), (3391), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1009.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3392)  all_56_5 = e2 & op(e2, e1) = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3392) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3393)  op(e2, e1) = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3252), (3393), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | |   (3394)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3394) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3395)  all_56_8 = e2 & op(e1, e1) = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3395) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3396)  op(e1, e1) = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3348), (3396), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3397)  all_56_14 = e2 & op(e0, e1) = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3397) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3398)  op(e0, e1) = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (138), (156), (248), (3233), (3378), (3382),
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3398), (function-axioms) are inconsistent by
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1089.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |   (3399)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3399) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |   (3400)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3400) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3401)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3401) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3402)  op(e1, e1) = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3348), (3402), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3403)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3403) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3404)  op(e0, e0) = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (139), (156), (157), (158), (163),
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (238), (3237), (3249), (3252),
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |            (3253), (3255), (3345), (3348), (3363), (3404),
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |            #527.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |   (3405)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3405) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3406)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3406) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3407)  op(e3, e3) = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3237), (3407), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |   (3408)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3408) gives:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |   (3409)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3409) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |   (3410)  op(e0, e0) = e2
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (139), (156), (157), (158), (163),
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (238), (3237), (3249), (3252),
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |            (3253), (3255), (3345), (3348), (3363), (3410),
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |            #527.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |   (3411)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3411) implies:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |   (3412)  op(e2, e2) = e1
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3255), (3412), (function-axioms) are
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.57  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |   (3413)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3413) gives:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |   (3414)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3414) gives:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |   (3415)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (3252), (3296), (3415),
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |            #1021.
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |   (3416)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (3294), (3296), (3416),
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |            #1020.
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |   (3417)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3417) gives:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |   (3418)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3253), (3348), (3418), (function-axioms)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #530.
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |   (3419)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3419) gives:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |   (3420)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3420) implies:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |   (3421)  op(e2, e0) = e2
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3253), (3421), (function-axioms) are
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |   (3422)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3422) gives:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |   (3423)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3423) implies:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |   (3424)   ~ (all_57_14 = e0)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |   (3425)  op(e1, e1) = all_57_14
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3348), (3424), (3425), (function-axioms) are
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1026.
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |   (3426)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3426) implies:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |   (3427)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3427) gives:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (3428)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3428) gives:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3429)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3429) implies:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3430)  op(e0, e3) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (157), (158), (3353), (3430),
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1123.
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3431)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3431) gives:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3432)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3432) implies:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3433)  op(e0, e3) = e0
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (157), (158), (3353), (3433),
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1123.
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3434)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3434) implies:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3435)  op(e3, e3) = e2
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3237), (3435), (function-axioms) are
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (3436)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (156), (3255), (3345), (3348), (3436),
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | |            #528.
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | |   (3437)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.07/20.58  | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.58  | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.07/20.58  | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 146.07/20.58  | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (3296), (3348), (3437),
% 146.07/20.58  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.58  | | | | | | | | | | | | | | | | | |            #1001.
% 146.07/20.58  | | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | End of split
% 146.07/20.58  | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | |   (3438)  all_24_2 = e2
% 146.07/20.58  | | | | | | | | | | |   (3439)  ( ~ (all_24_0 = e3) & op(all_24_1, e0) = all_24_0
% 146.07/20.58  | | | | | | | | | | |             & op(e0, e2) = all_24_1 & $i(all_24_0) &
% 146.07/20.58  | | | | | | | | | | |             $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0, e2)
% 146.07/20.58  | | | | | | | | | | |             = all_24_1 & $i(all_24_1))
% 146.07/20.58  | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | COMBINE_EQS: (318), (3438) imply:
% 146.07/20.58  | | | | | | | | | | |   (3440)  all_10_2 = e2
% 146.07/20.58  | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | COMBINE_EQS: (306), (3440) imply:
% 146.07/20.58  | | | | | | | | | | |   (3441)  all_40_2 = e2
% 146.07/20.58  | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | REDUCE: (367), (3440) imply:
% 146.07/20.58  | | | | | | | | | | |   (3442)   ~ (all_52_11 = e2)
% 146.07/20.58  | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | REDUCE: (370), (3440) imply:
% 146.07/20.58  | | | | | | | | | | |   (3443)   ~ (all_52_14 = e2)
% 146.07/20.58  | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | REDUCE: (45), (3440) imply:
% 146.07/20.58  | | | | | | | | | | |   (3444)  op(e0, e0) = e2
% 146.07/20.58  | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | BETA: splitting (218) gives:
% 146.07/20.58  | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | |   (3445)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 146.07/20.58  | | | | | | | | | | | |             & op(e2, e1) = e2)
% 146.07/20.58  | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | BETA: splitting (3445) gives:
% 146.07/20.58  | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | |   (3446)  all_56_4 = e2 & op(e3, e1) = e2
% 146.07/20.58  | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | ALPHA: (3446) implies:
% 146.07/20.58  | | | | | | | | | | | | |   (3447)  all_56_4 = e2
% 146.07/20.58  | | | | | | | | | | | | |   (3448)  op(e3, e1) = e2
% 146.07/20.58  | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | BETA: splitting (232) gives:
% 146.07/20.58  | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | |   (3449)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 146.07/20.58  | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 146.07/20.58  | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | REF_CLOSE: (5), (166), (3237), (3249), (3449),
% 146.07/20.58  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.58  | | | | | | | | | | | | | |            #526.
% 146.07/20.58  | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | |   (3450)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 146.07/20.58  | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 146.07/20.58  | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | BETA: splitting (3450) gives:
% 146.07/20.58  | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | |   (3451)  all_56_6 = e2 & op(e1, e3) = e2
% 146.07/20.58  | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | ALPHA: (3451) implies:
% 146.07/20.58  | | | | | | | | | | | | | | |   (3452)  all_56_6 = e2
% 146.07/20.58  | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 146.07/20.58  | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | Case 1:
% 146.07/20.58  | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | |   (3453)   ~ (all_40_2 = e2)
% 146.07/20.58  | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | REDUCE: (3441), (3453) imply:
% 146.07/20.58  | | | | | | | | | | | | | | | |   (3454)  $false
% 146.07/20.58  | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | | CLOSE: (3454) is inconsistent.
% 146.07/20.58  | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | Case 2:
% 146.07/20.58  | | | | | | | | | | | | | | | | 
% 146.07/20.58  | | | | | | | | | | | | | | | |   (3455)  ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0
% 146.07/20.59  | | | | | | | | | | | | | | | |             & op(e0, e2) = all_40_1 & $i(all_40_0) &
% 146.07/20.59  | | | | | | | | | | | | | | | |             $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e0, e2)
% 146.07/20.59  | | | | | | | | | | | | | | | |             = all_40_1 & $i(all_40_1))
% 146.07/20.59  | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | |   (3456)   ~ (all_48_2 = e0)
% 146.07/20.59  | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | REDUCE: (298), (3456) imply:
% 146.07/20.59  | | | | | | | | | | | | | | | | |   (3457)   ~ (all_4_2 = e0)
% 146.07/20.59  | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | |   (3458)  all_54_10 = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (3458) are inconsistent by sub-proof
% 146.07/20.59  | | | | | | | | | | | | | | | | | |            #1173.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | |   (3459)   ~ (all_54_10 = e3)
% 146.07/20.59  | | | | | | | | | | | | | | | | | |   (3460)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 146.07/20.59  | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | BETA: splitting (3460) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | |   (3461)  all_54_10 = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (3461) are inconsistent by sub-proof
% 146.07/20.59  | | | | | | | | | | | | | | | | | | |            #1168.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | |   (3462)   ~ (all_54_10 = e2)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | |   (3463)  all_54_10 = e1 | all_54_10 = e0
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | BETA: splitting (3463) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | |   (3464)  all_54_10 = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (3464) imply:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | |   (3465)  all_4_2 = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | SIMP: (3465) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | |   (3466)  all_4_2 = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (3466) imply:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | |   (3467)   ~ (all_52_6 = e1)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (3466) imply:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | |   (3468)   ~ (all_52_14 = e1)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (3466) imply:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | |   (3469)   ~ (e3 = e1)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (3466) imply:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | |   (3470)   ~ (e2 = e1)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3466) imply:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | |   (3471)  op(e1, e1) = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |   (3472)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3472) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |   (3473)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (3249), (3255), (3444), (3473),
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |            #1000.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |   (3474)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3474) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |   (3475)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3475) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |   (3476)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3476) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |   (3477)  op(e1, e1) = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (3471), (3477), (function-axioms) are
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |   (3478)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3478) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |   (3479)   ~ (all_57_5 = e0)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |   (3480)  op(e3, e2) = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (3481)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3481) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3482)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3482) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3483)  op(e3, e3) = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3237), (3483), (function-axioms) are
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3484)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3484) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3485)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e0, e0) = all_57_15 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3444), (3479), (3485), (function-axioms) are
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #525.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (3486)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3486) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3487)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3487) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3488)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3489)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3488) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3490)  all_57_7 = e2 & op(e2, e1) = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3490) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3491)  op(e2, e1) = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3252), (3491), (function-axioms) are
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3492)   ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3492) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3493)   ~ (all_57_12 = e1)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3494)  op(e2, e2) = all_57_12
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3489) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3495)  all_57_6 = e3 & op(e3, e1) = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3495) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3496)  op(e3, e1) = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3, e1,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (3448), (3496) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3497)  e3 = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (3497) imply:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3498)  $false
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3498) is inconsistent.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3499)   ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3499) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3500)  op(e3, e3) = all_57_10
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (3255), (3494)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3501)  all_57_12 = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (169), (3480) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3502)  all_52_4 = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (3237), (3500)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3503)  all_57_10 = e0
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (3502) imply:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3504)   ~ (all_52_6 = e3)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3504) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3505)   ~ (all_52_6 = e3)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (3502) imply:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3506)   ~ (all_52_12 = e3)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3506) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3507)   ~ (all_52_12 = e3)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3508)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3508) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3509)  all_56_6 = e3 & op(e1, e3) = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3509) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3510)  all_56_6 = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3452), (3510) are inconsistent by sub-proof
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1057.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3511)  all_56_7 = e3 & op(e1, e2) = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3505), (3511), (function-axioms) are
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3512)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3512) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3513)  all_56_8 = e3 & op(e1, e1) = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3513) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3514)  op(e1, e1) = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (159), (161), (213), (3452), (3467),
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3468), (3514), (function-axioms) are inconsistent
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #522.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3515)  all_56_11 = e3 & op(e1, e0) = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3515) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3516)  op(e1, e0) = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3517)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3517) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3518)  all_56_1 = e1 & op(e3, e2) = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3518) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3519)  all_56_1 = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (167), (235), (3237), (3447),
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3507), (3519), (function-axioms) are inconsistent
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #533.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3520)  all_56_3 = e1 & op(e2, e2) = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3520) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3521)  op(e2, e2) = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3493), (3494), (3521), (function-axioms) are
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3522)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3522) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3523)  all_56_7 = e1 & op(e1, e2) = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3523) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3524)  op(e1, e2) = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3467), (3524), (function-axioms) are
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3525)  all_56_13 = e1 & op(e0, e2) = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3525) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3526)  op(e0, e2) = e1
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3439), (3455), (3516), (3526), (function-axioms)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #520.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3527)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3527) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3528)  op(e0, e0) = e0
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3444), (3528), (function-axioms) are
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |   (3529)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3529) gives:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |   (3530)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3530) implies:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |   (3531)  op(e3, e3) = e2
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3237), (3531), (function-axioms) are
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |   (3532)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.59  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3532) gives:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (3533)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3533) implies:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (3534)  op(e1, e2) = e1
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3467), (3534), (function-axioms) are
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (3535)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3535) implies:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (3536)  op(e2, e2) = e1
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3255), (3536), (function-axioms) are
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |   (3537)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3537) gives:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |   (3538)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3538) gives:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |   (3539)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (3252), (3444), (3539),
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |            #977.
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |   (3540)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (3237), (3444), (3471), (3540),
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |            #518.
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |   (3541)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3541) gives:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |   (3542)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (3253), (3468), (3542),
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |            #535.
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |   (3543)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3543) gives:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |   (3544)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3544) implies:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |   (3545)  op(e2, e0) = e2
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3253), (3545), (function-axioms) are
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |   (3546)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3546) gives:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (3547)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3547) implies:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (3548)  op(e1, e0) = e1
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3468), (3548), (function-axioms) are
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (3549)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3549) implies:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (3550)  op(e0, e0) = all_57_15
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |   (3551)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3551) gives:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3552)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3233), (3444), (3550), (3552),
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |            #900.
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3553)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (36), (3237), (3255), (3471), (3553),
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | |            #534.
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | |   (3554)  all_54_10 = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (3457), (3554) are inconsistent by
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | End of split
% 146.07/20.60  | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.60  | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | |   (3555)  all_48_2 = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (3555) imply:
% 146.07/20.60  | | | | | | | | | | | | | | | | |   (3556)  all_4_2 = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | REDUCE: (364), (3556) imply:
% 146.07/20.60  | | | | | | | | | | | | | | | | |   (3557)   ~ (all_52_11 = e0)
% 146.07/20.60  | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | REDUCE: (374), (3556) imply:
% 146.07/20.60  | | | | | | | | | | | | | | | | |   (3558)   ~ (e3 = e0)
% 146.07/20.60  | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | REDUCE: (371), (3556) imply:
% 146.07/20.60  | | | | | | | | | | | | | | | | |   (3559)   ~ (e2 = e0)
% 146.07/20.60  | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | REDUCE: (36), (3556) imply:
% 146.07/20.60  | | | | | | | | | | | | | | | | |   (3560)  op(e1, e1) = e0
% 146.07/20.60  | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 146.07/20.60  | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | |   (3561)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.07/20.60  | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 146.07/20.60  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | BETA: splitting (3561) gives:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | |   (3562)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 146.07/20.60  | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.07/20.60  | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.07/20.60  | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 146.07/20.60  | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 146.07/20.60  | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | ALPHA: (3562) implies:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | |   (3563)  op(e3, e3) = e3
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3237), (3563), (function-axioms) are
% 146.07/20.60  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.60  | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.60  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |   (3564)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | ALPHA: (3564) implies:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |   (3565)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               = e2) & op(e0, e0) = all_57_15 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (139), (156), (157), (158), (163),
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |            (164), (166), (238), (3237), (3249), (3252),
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |            (3253), (3255), (3444), (3557), (3560), (3565),
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |            #527.
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | |   (3566)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.07/20.61  | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 146.07/20.61  | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (3444), (3560), (3566),
% 146.07/20.61  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.61  | | | | | | | | | | | | | | | | | |            #614.
% 146.07/20.61  | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | |   (3567)  all_56_12 = e2 & op(e0, e3) = e2
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | ALPHA: (3567) implies:
% 146.07/20.61  | | | | | | | | | | | | | | |   (3568)  all_56_12 = e2
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | |   (3569)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 146.07/20.61  | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | BETA: splitting (3569) gives:
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | |   (3570)  all_56_6 = e2 & op(e1, e3) = e2
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | ALPHA: (3570) implies:
% 146.07/20.61  | | | | | | | | | | | | | | | | |   (3571)  all_56_6 = e2
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230), (234),
% 146.07/20.61  | | | | | | | | | | | | | | | | |            (3237), (3568), (3571), (function-axioms) are
% 146.07/20.61  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #517.
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | |   (3572)  all_56_7 = e2 & op(e1, e2) = e2
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | ALPHA: (3572) implies:
% 146.07/20.61  | | | | | | | | | | | | | | | | |   (3573)  op(e1, e2) = e2
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3251), (3573), (function-axioms) are
% 146.07/20.61  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1171.
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | |   (3574)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 146.07/20.61  | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (159), (371), (3443), (3574),
% 146.07/20.61  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.61  | | | | | | | | | | | | | | | |            #973.
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | |   (3575)  all_56_5 = e2 & op(e2, e1) = e2
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | ALPHA: (3575) implies:
% 146.07/20.61  | | | | | | | | | | | | |   (3576)  op(e2, e1) = e2
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | REF_CLOSE: (164), (3252), (3576), (function-axioms) are
% 146.07/20.61  | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | |   (3577)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 146.07/20.61  | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | REF_CLOSE: (36), (156), (371), (3442), (3577),
% 146.07/20.61  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.61  | | | | | | | | | | | |            #972.
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | |   (3578)  all_54_5 = e1 | all_54_5 = e0
% 146.07/20.61  | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | REF_CLOSE: (267), (3239), (3241), (3578) are inconsistent by
% 146.07/20.61  | | | | | | | | | |            sub-proof #866.
% 146.07/20.61  | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | 
% 146.07/20.61  | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | 
% 146.07/20.61  | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | 
% 146.07/20.61  | | | | | | | |   (3579)  all_20_2 = e1
% 146.07/20.61  | | | | | | | |   (3580)  ( ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 &
% 146.07/20.61  | | | | | | | |             op(e2, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1))
% 146.07/20.61  | | | | | | | |           | ( ~ (all_20_1 = e3) & op(e2, e1) = all_20_1 &
% 146.07/20.61  | | | | | | | |             $i(all_20_1))
% 146.07/20.61  | | | | | | | | 
% 146.07/20.61  | | | | | | | | COMBINE_EQS: (282), (3579) imply:
% 146.07/20.61  | | | | | | | |   (3581)  all_6_2 = e1
% 146.07/20.61  | | | | | | | | 
% 146.07/20.61  | | | | | | | | COMBINE_EQS: (331), (3581) imply:
% 146.07/20.61  | | | | | | | |   (3582)  all_38_2 = e1
% 146.07/20.61  | | | | | | | | 
% 146.07/20.61  | | | | | | | | REDUCE: (347), (3581) imply:
% 146.07/20.61  | | | | | | | |   (3583)   ~ (all_52_1 = e1)
% 146.07/20.61  | | | | | | | | 
% 146.07/20.61  | | | | | | | | REDUCE: (358), (3581) imply:
% 146.07/20.61  | | | | | | | |   (3584)   ~ (all_52_13 = e1)
% 146.07/20.61  | | | | | | | | 
% 146.07/20.61  | | | | | | | | REDUCE: (39), (3581) imply:
% 146.07/20.61  | | | | | | | |   (3585)  op(e2, e2) = e1
% 146.07/20.61  | | | | | | | | 
% 146.07/20.61  | | | | | | | | BETA: splitting (67) gives:
% 146.07/20.61  | | | | | | | | 
% 146.07/20.61  | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | 
% 146.07/20.61  | | | | | | | | |   (3586)   ~ (all_24_2 = e2)
% 146.07/20.61  | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | REDUCE: (318), (3586) imply:
% 146.07/20.61  | | | | | | | | |   (3587)   ~ (all_10_2 = e2)
% 146.07/20.61  | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | BETA: splitting (87) gives:
% 146.07/20.61  | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | |   (3588)   ~ (all_38_2 = e1)
% 146.07/20.61  | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | REDUCE: (3582), (3588) imply:
% 146.07/20.61  | | | | | | | | | |   (3589)  $false
% 146.07/20.61  | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | CLOSE: (3589) is inconsistent.
% 146.07/20.61  | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | |   (3590)  ( ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0
% 146.07/20.61  | | | | | | | | | |             & op(e2, e1) = all_38_1 & $i(all_38_0) &
% 146.07/20.61  | | | | | | | | | |             $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e2, e1)
% 146.07/20.61  | | | | | | | | | |             = all_38_1 & $i(all_38_1))
% 146.07/20.61  | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | BETA: splitting (93) gives:
% 146.07/20.61  | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | |   (3591)   ~ (all_42_2 = e3)
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | REDUCE: (302), (3591) imply:
% 146.07/20.61  | | | | | | | | | | |   (3592)   ~ (all_10_2 = e3)
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | BETA: splitting (188) gives:
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | |   (3593)  all_54_15 = e3
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | REF_CLOSE: (245), (3592), (3593) are inconsistent by
% 146.07/20.61  | | | | | | | | | | | |            sub-proof #1049.
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | |   (3594)   ~ (all_54_15 = e3)
% 146.07/20.61  | | | | | | | | | | | |   (3595)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | BETA: splitting (3595) gives:
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | |   (3596)  all_54_15 = e2
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | REF_CLOSE: (245), (3587), (3596) are inconsistent by
% 146.07/20.61  | | | | | | | | | | | | |            sub-proof #1048.
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | |   (3597)   ~ (all_54_15 = e2)
% 146.07/20.61  | | | | | | | | | | | | |   (3598)  all_54_15 = e1 | all_54_15 = e0
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | BETA: splitting (3598) gives:
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | |   (3599)  all_54_15 = e1
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | REF_CLOSE: (245), (375), (3599) are inconsistent by sub-proof
% 146.07/20.61  | | | | | | | | | | | | | |            #1047.
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | |   (3600)  all_54_15 = e0
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | COMBINE_EQS: (245), (3600) imply:
% 146.07/20.61  | | | | | | | | | | | | | |   (3601)  all_10_2 = e0
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | SIMP: (3601) implies:
% 146.07/20.61  | | | | | | | | | | | | | |   (3602)  all_10_2 = e0
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | REDUCE: (369), (3602) imply:
% 146.07/20.61  | | | | | | | | | | | | | |   (3603)   ~ (all_52_13 = e0)
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | REDUCE: (3592), (3602) imply:
% 146.07/20.61  | | | | | | | | | | | | | |   (3604)   ~ (e3 = e0)
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | REDUCE: (3587), (3602) imply:
% 146.07/20.61  | | | | | | | | | | | | | |   (3605)   ~ (e2 = e0)
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | REDUCE: (375), (3602) imply:
% 146.07/20.61  | | | | | | | | | | | | | |   (3606)   ~ (e1 = e0)
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | |   (3607)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 146.07/20.61  | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | REF_CLOSE: (4), (166), (3232), (3585), (3607),
% 146.07/20.61  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.61  | | | | | | | | | | | | | | |            #516.
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | |   (3608)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 146.07/20.61  | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | BETA: splitting (3608) gives:
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | |   (3609)  all_56_5 = e0 & op(e2, e1) = e0
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | ALPHA: (3609) implies:
% 146.07/20.61  | | | | | | | | | | | | | | | |   (3610)  op(e2, e1) = e0
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 146.07/20.61  | | | | | | | | | | | | | | | |              e1, e2, simplifying with (164), (3610) gives:
% 146.07/20.61  | | | | | | | | | | | | | | | |   (3611)  all_52_9 = e0
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | REDUCE: (362), (3611) imply:
% 146.07/20.61  | | | | | | | | | | | | | | | |   (3612)   ~ (all_4_2 = e0)
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | SIMP: (3612) implies:
% 146.07/20.61  | | | | | | | | | | | | | | | |   (3613)   ~ (all_4_2 = e0)
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | |   (3614)  all_54_10 = e3
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (3614) are inconsistent by sub-proof
% 146.07/20.61  | | | | | | | | | | | | | | | | |            #1173.
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | |   (3615)   ~ (all_54_10 = e3)
% 146.07/20.61  | | | | | | | | | | | | | | | | |   (3616)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | |   (3617)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.07/20.61  | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 146.07/20.61  | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (3237), (3585), (3617),
% 146.07/20.61  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.61  | | | | | | | | | | | | | | | | | |            #515.
% 146.07/20.61  | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | |   (3618)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.07/20.61  | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.07/20.61  | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 146.07/20.61  | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | BETA: splitting (3618) gives:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |   (3619)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | ALPHA: (3619) implies:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |   (3620)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3580), (3585), (3590), (3610), (3620),
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |            #513.
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |   (3621)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | ALPHA: (3621) implies:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |   (3622)  op(e0, e0) = e0
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |   (3623)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = all_57_10 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | BETA: splitting (3623) gives:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | |   (3624)  all_57_9 = e3 & op(e3, e0) = e3
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | ALPHA: (3624) implies:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | |   (3625)  op(e3, e0) = e3
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3616) gives:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | |   (3626)  all_54_10 = e2
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (3626) are inconsistent by sub-proof
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | |            #1168.
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | |   (3627)  all_54_10 = e1 | all_54_10 = e0
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3627) gives:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | |   (3628)  all_54_10 = e1
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (3628) imply:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | |   (3629)  all_4_2 = e1
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | SIMP: (3629) implies:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | |   (3630)  all_4_2 = e1
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (3630) imply:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | |   (3631)   ~ (all_52_14 = e1)
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (3630) imply:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | |   (3632)   ~ (e3 = e1)
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (159), (163), (167), (209), (3584),
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | |            (3622), (3625), (3631), (function-axioms) are
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #510.
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | |   (3633)  all_54_10 = e0
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (3613), (3633) are inconsistent by
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | |   (3634)   ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | ALPHA: (3634) implies:
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | |   (3635)   ~ (all_57_10 = e0)
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | |   (3636)  op(e3, e3) = all_57_10
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3237), (3635), (3636), (function-axioms) are
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #543.
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | |   (3637)  all_56_10 = e0 & op(e2, e0) = e0
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3603), (3637), (function-axioms) are
% 146.07/20.61  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #540.
% 146.07/20.61  | | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | End of split
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | |   (3638)  all_42_2 = e3
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | COMBINE_EQS: (302), (3638) imply:
% 146.07/20.61  | | | | | | | | | | |   (3639)  all_10_2 = e3
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | SIMP: (3639) implies:
% 146.07/20.61  | | | | | | | | | | |   (3640)  all_10_2 = e3
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | REDUCE: (367), (3640) imply:
% 146.07/20.61  | | | | | | | | | | |   (3641)   ~ (all_52_11 = e3)
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | REDUCE: (45), (3640) imply:
% 146.07/20.61  | | | | | | | | | | |   (3642)  op(e0, e0) = e3
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | BETA: splitting (237) gives:
% 146.07/20.61  | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | Case 1:
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | |   (3643)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 146.07/20.61  | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 146.07/20.61  | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.07/20.61  | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.07/20.61  | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.07/20.61  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 146.07/20.61  | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 146.07/20.61  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.07/20.61  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 146.07/20.61  | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 146.07/20.61  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.61  | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.07/20.61  | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.07/20.61  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 146.07/20.61  | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 146.07/20.61  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | | REF_CLOSE: (6), (7), (3237), (3585), (3643),
% 146.07/20.61  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.07/20.61  | | | | | | | | | | | |            #515.
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | Case 2:
% 146.07/20.61  | | | | | | | | | | | | 
% 146.07/20.61  | | | | | | | | | | | |   (3644)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 146.07/20.61  | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 146.07/20.62  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.62  | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.07/20.62  | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.62  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 146.07/20.62  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 146.07/20.62  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.07/20.62  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 146.07/20.62  | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 146.07/20.62  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.62  | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.07/20.62  | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.07/20.62  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.07/20.62  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.07/20.62  | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 146.07/20.62  | | | | | | | | | | | | 
% 146.07/20.62  | | | | | | | | | | | | BETA: splitting (3644) gives:
% 146.07/20.62  | | | | | | | | | | | | 
% 146.07/20.62  | | | | | | | | | | | | Case 1:
% 146.07/20.62  | | | | | | | | | | | | | 
% 146.07/20.62  | | | | | | | | | | | | |   (3645)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 146.07/20.62  | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 146.07/20.62  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.07/20.62  | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.07/20.62  | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.62  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 146.07/20.62  | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 146.07/20.62  | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.07/20.62  | | | | | | | | | | | | | 
% 146.07/20.62  | | | | | | | | | | | | | ALPHA: (3645) implies:
% 146.07/20.62  | | | | | | | | | | | | |   (3646)  op(e1, e1) = e1
% 146.07/20.62  | | | | | | | | | | | | |   (3647)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 146.07/20.62  | | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 146.07/20.62  | | | | | | | | | | | | |             $i(all_57_12))
% 146.07/20.62  | | | | | | | | | | | | | 
% 146.07/20.62  | | | | | | | | | | | | | BETA: splitting (3647) gives:
% 146.07/20.62  | | | | | | | | | | | | | 
% 146.07/20.62  | | | | | | | | | | | | | Case 1:
% 146.07/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | |   (3648)  all_57_7 = e2 & op(e2, e1) = e2
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | ALPHA: (3648) implies:
% 146.50/20.62  | | | | | | | | | | | | | |   (3649)  all_57_7 = e2
% 146.50/20.62  | | | | | | | | | | | | | |   (3650)  op(e2, e1) = e2
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 146.50/20.62  | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (3646) gives:
% 146.50/20.62  | | | | | | | | | | | | | |   (3651)  all_4_2 = e1
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 146.50/20.62  | | | | | | | | | | | | | |              e1, e2, simplifying with (164), (3650) gives:
% 146.50/20.62  | | | | | | | | | | | | | |   (3652)  all_52_9 = e2
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REDUCE: (145), (3652) imply:
% 146.50/20.62  | | | | | | | | | | | | | |   (3653)   ~ (all_52_1 = e2)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REDUCE: (348), (3651) imply:
% 146.50/20.62  | | | | | | | | | | | | | |   (3654)   ~ (all_52_2 = e1)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REDUCE: (359), (3651) imply:
% 146.50/20.62  | | | | | | | | | | | | | |   (3655)   ~ (all_52_6 = e1)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REDUCE: (122), (3652) imply:
% 146.50/20.62  | | | | | | | | | | | | | |   (3656)   ~ (all_52_8 = e2)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REDUCE: (361), (3651) imply:
% 146.50/20.62  | | | | | | | | | | | | | |   (3657)   ~ (all_52_8 = e1)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REDUCE: (117), (3652) imply:
% 146.50/20.62  | | | | | | | | | | | | | |   (3658)   ~ (all_52_11 = e2)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | SIMP: (3658) implies:
% 146.50/20.62  | | | | | | | | | | | | | |   (3659)   ~ (all_52_11 = e2)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REDUCE: (116), (3652) imply:
% 146.50/20.62  | | | | | | | | | | | | | |   (3660)   ~ (all_52_13 = e2)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | SIMP: (3660) implies:
% 146.50/20.62  | | | | | | | | | | | | | |   (3661)   ~ (all_52_13 = e2)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REDUCE: (364), (3651) imply:
% 146.50/20.62  | | | | | | | | | | | | | |   (3662)   ~ (all_52_11 = e1)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REDUCE: (366), (3651) imply:
% 146.50/20.62  | | | | | | | | | | | | | |   (3663)   ~ (all_52_14 = e1)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REDUCE: (374), (3651) imply:
% 146.50/20.62  | | | | | | | | | | | | | |   (3664)   ~ (e3 = e1)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REDUCE: (371), (3651) imply:
% 146.50/20.62  | | | | | | | | | | | | | |   (3665)   ~ (e2 = e1)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | |   (3666)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 146.50/20.62  | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 146.50/20.62  | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (3585), (3653), (3666),
% 146.50/20.62  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.62  | | | | | | | | | | | | | | |            #1138.
% 146.50/20.62  | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | |   (3667)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 146.50/20.62  | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 146.50/20.62  | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | BETA: splitting (3667) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | |   (3668)  all_56_5 = e2 & op(e2, e1) = e2
% 146.50/20.62  | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | ALPHA: (3668) implies:
% 146.50/20.62  | | | | | | | | | | | | | | | |   (3669)  all_56_5 = e2
% 146.50/20.62  | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | |   (3670)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 146.50/20.62  | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 146.50/20.62  | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | BETA: splitting (3670) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | |   (3671)  all_56_9 = e1 & op(e3, e0) = e1
% 146.50/20.62  | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | ALPHA: (3671) implies:
% 146.50/20.62  | | | | | | | | | | | | | | | | | |   (3672)  all_56_9 = e1
% 146.50/20.62  | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | |   (3673)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 146.50/20.62  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (3673) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |   (3674)  all_56_12 = e1 & op(e0, e3) = e1
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (3674) implies:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |   (3675)  all_56_12 = e1
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | |   (3676)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3676) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |   (3677)  all_56_6 = e3 & op(e1, e3) = e3
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (119),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |            (120), (124), (133), (156), (157), (159), (161),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (166), (167), (168), (169), (189),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |            (201), (205), (210), (212), (213), (214), (219),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (226), (227),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |            (228), (232), (233), (238), (246), (270), (3232),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |            (3234), (3235), (3585), (3587), (3641), (3642),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |            (3646), (3647), (3649), (3650), (3653), (3654),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |            (3655), (3656), (3657), (3659), (3661), (3662),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |            (3663), (3669), (3672), (3675), (3677),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |            #501.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |   (3678)  all_56_7 = e3 & op(e1, e2) = e3
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3678) implies:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | |   (3679)  all_56_7 = e3
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | |   (3680)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3680) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |   (3681)  all_56_0 = e3 & op(e3, e3) = e3
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3681) implies:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |   (3682)  op(e3, e3) = e3
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3237), (3682), (function-axioms) are
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |   (3683)  all_56_2 = e3 & op(e2, e3) = e3
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3683) implies:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |   (3684)  all_56_2 = e3
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (3685)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (166), (3232), (3585), (3685),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | |            #516.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (3686)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3686) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3687)  all_56_5 = e0 & op(e2, e1) = e0
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3687) implies:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3688)  all_56_5 = e0
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3669), (3688) are inconsistent by sub-proof
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            #509.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3689)  all_56_10 = e0 & op(e2, e0) = e0
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3689) implies:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3690)  all_56_10 = e0
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (124), (157), (169),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (189), (221), (222), (223), (224), (246), (3234),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3585), (3641), (3650), (3659), (3662), (3679),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3684), (3690), (function-axioms) are inconsistent
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #508.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | |   (3691)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3691) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |   (3692)  all_56_6 = e3 & op(e1, e3) = e3
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (119),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            (120), (124), (133), (156), (157), (159), (161),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (166), (167), (168), (169), (189),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            (201), (205), (210), (212), (213), (214), (219),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (226), (227),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            (228), (232), (233), (238), (246), (270), (3232),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            (3234), (3235), (3585), (3587), (3641), (3642),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            (3646), (3647), (3649), (3650), (3653), (3654),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            (3655), (3656), (3657), (3659), (3661), (3662),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            (3663), (3669), (3672), (3675), (3692),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            #501.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |   (3693)  all_56_12 = e3 & op(e0, e3) = e3
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3675), (3693) are inconsistent by sub-proof
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | |            #919.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | |   (3694)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (163), (205),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | |            (209), (210), (3587), (3642), (3646), (3694),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | |            #500.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |   (3695)  all_56_13 = e1 & op(e0, e2) = e1
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (224), (226),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |            (227), (3234), (3585), (3695), (function-axioms)
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #499.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | |   (3696)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 146.50/20.62  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (3696) gives:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |   (3697)  all_56_14 = e1 & op(e0, e1) = e1
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (3697) implies:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |   (3698)  op(e0, e1) = e1
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (189), (246), (3641), (3659), (3662),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |            (3698), (function-axioms) are inconsistent by
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |            sub-proof #731.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |   (3699)  all_56_15 = e1 & op(e0, e0) = e1
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (3699) implies:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |   (3700)  op(e0, e0) = e1
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |            (3672), (3700), (function-axioms) are inconsistent
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | |            by sub-proof #496.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | |   (3701)  all_56_10 = e1 & op(e2, e0) = e1
% 146.50/20.62  | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3584), (3701), (function-axioms) are
% 146.50/20.62  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 146.50/20.62  | | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | |   (3702)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 146.50/20.62  | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 146.50/20.62  | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (3642), (3663), (3702),
% 146.50/20.62  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.62  | | | | | | | | | | | | | | | | |            #732.
% 146.50/20.62  | | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | |   (3703)  all_56_10 = e2 & op(e2, e0) = e2
% 146.50/20.62  | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | ALPHA: (3703) implies:
% 146.50/20.62  | | | | | | | | | | | | | | | |   (3704)  op(e2, e0) = e2
% 146.50/20.62  | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3661), (3704), (function-axioms) are
% 146.50/20.62  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.50/20.62  | | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | |   (3705)   ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.62  | | | | | | | | | | | | | |           $i(all_57_12)
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | ALPHA: (3705) implies:
% 146.50/20.62  | | | | | | | | | | | | | |   (3706)   ~ (all_57_12 = e1)
% 146.50/20.62  | | | | | | | | | | | | | |   (3707)  op(e2, e2) = all_57_12
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | | REF_CLOSE: (3585), (3706), (3707), (function-axioms) are
% 146.50/20.62  | | | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 146.50/20.62  | | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | |   (3708)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 146.50/20.62  | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 146.50/20.62  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.62  | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.50/20.62  | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.50/20.62  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.50/20.62  | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.50/20.62  | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 146.50/20.62  | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | ALPHA: (3708) implies:
% 146.50/20.62  | | | | | | | | | | | | |   (3709)  op(e0, e0) = e0
% 146.50/20.62  | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | | REF_CLOSE: (7), (3642), (3709), (function-axioms) are
% 146.50/20.62  | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 146.50/20.62  | | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | End of split
% 146.50/20.62  | | | | | | | | | 
% 146.50/20.62  | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | 
% 146.50/20.62  | | | | | | | | |   (3710)  all_24_2 = e2
% 146.50/20.62  | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | COMBINE_EQS: (318), (3710) imply:
% 146.50/20.62  | | | | | | | | |   (3711)  all_10_2 = e2
% 146.50/20.62  | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | SIMP: (3711) implies:
% 146.50/20.62  | | | | | | | | |   (3712)  all_10_2 = e2
% 146.50/20.62  | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | COMBINE_EQS: (306), (3712) imply:
% 146.50/20.62  | | | | | | | | |   (3713)  all_40_2 = e2
% 146.50/20.62  | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | REDUCE: (370), (3712) imply:
% 146.50/20.62  | | | | | | | | |   (3714)   ~ (all_52_14 = e2)
% 146.50/20.62  | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | REDUCE: (45), (3712) imply:
% 146.50/20.62  | | | | | | | | |   (3715)  op(e0, e0) = e2
% 146.50/20.62  | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | BETA: splitting (237) gives:
% 146.50/20.62  | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | |   (3716)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 146.50/20.62  | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 146.50/20.62  | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.50/20.62  | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.50/20.62  | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.50/20.62  | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 146.50/20.62  | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 146.50/20.62  | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.50/20.62  | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 146.50/20.62  | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 146.50/20.62  | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.62  | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.50/20.62  | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.50/20.62  | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 146.50/20.62  | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 146.50/20.62  | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 146.50/20.62  | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | REF_CLOSE: (6), (7), (3237), (3585), (3716),
% 146.50/20.62  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.62  | | | | | | | | | |            #515.
% 146.50/20.62  | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | Case 2:
% 146.50/20.62  | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | |   (3717)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 146.50/20.62  | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 146.50/20.62  | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.62  | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.50/20.62  | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.62  | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 146.50/20.62  | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 146.50/20.62  | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.50/20.62  | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 146.50/20.62  | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 146.50/20.62  | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.62  | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.50/20.62  | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.50/20.62  | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.50/20.62  | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.50/20.62  | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 146.50/20.62  | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | BETA: splitting (3717) gives:
% 146.50/20.62  | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | Case 1:
% 146.50/20.62  | | | | | | | | | | | 
% 146.50/20.62  | | | | | | | | | | |   (3718)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 146.50/20.62  | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 146.50/20.63  | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.63  | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.50/20.63  | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.63  | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 146.50/20.63  | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 146.50/20.63  | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.50/20.63  | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | ALPHA: (3718) implies:
% 146.50/20.63  | | | | | | | | | | |   (3719)  op(e1, e1) = e1
% 146.50/20.63  | | | | | | | | | | |   (3720)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 146.50/20.63  | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.63  | | | | | | | | | | |             $i(all_57_12))
% 146.50/20.63  | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | BETA: splitting (3720) gives:
% 146.50/20.63  | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | |   (3721)  all_57_7 = e2 & op(e2, e1) = e2
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | ALPHA: (3721) implies:
% 146.50/20.63  | | | | | | | | | | | |   (3722)  op(e2, e1) = e2
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 146.50/20.63  | | | | | | | | | | | |              e1, e1, simplifying with (36), (3719) gives:
% 146.50/20.63  | | | | | | | | | | | |   (3723)  all_4_2 = e1
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 146.50/20.63  | | | | | | | | | | | |              e1, e2, simplifying with (164), (3722) gives:
% 146.50/20.63  | | | | | | | | | | | |   (3724)  all_52_9 = e2
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | REDUCE: (145), (3724) imply:
% 146.50/20.63  | | | | | | | | | | | |   (3725)   ~ (all_52_1 = e2)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | REDUCE: (348), (3723) imply:
% 146.50/20.63  | | | | | | | | | | | |   (3726)   ~ (all_52_2 = e1)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | REDUCE: (359), (3723) imply:
% 146.50/20.63  | | | | | | | | | | | |   (3727)   ~ (all_52_6 = e1)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | REDUCE: (122), (3724) imply:
% 146.50/20.63  | | | | | | | | | | | |   (3728)   ~ (all_52_8 = e2)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | REDUCE: (361), (3723) imply:
% 146.50/20.63  | | | | | | | | | | | |   (3729)   ~ (all_52_8 = e1)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | REDUCE: (117), (3724) imply:
% 146.50/20.63  | | | | | | | | | | | |   (3730)   ~ (all_52_11 = e2)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | SIMP: (3730) implies:
% 146.50/20.63  | | | | | | | | | | | |   (3731)   ~ (all_52_11 = e2)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | REDUCE: (116), (3724) imply:
% 146.50/20.63  | | | | | | | | | | | |   (3732)   ~ (all_52_13 = e2)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | SIMP: (3732) implies:
% 146.50/20.63  | | | | | | | | | | | |   (3733)   ~ (all_52_13 = e2)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | REDUCE: (364), (3723) imply:
% 146.50/20.63  | | | | | | | | | | | |   (3734)   ~ (all_52_11 = e1)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | REDUCE: (366), (3723) imply:
% 146.50/20.63  | | | | | | | | | | | |   (3735)   ~ (all_52_14 = e1)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | REDUCE: (371), (3723) imply:
% 146.50/20.63  | | | | | | | | | | | |   (3736)   ~ (e2 = e1)
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | BETA: splitting (199) gives:
% 146.50/20.63  | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | |   (3737)  all_54_4 = e3
% 146.50/20.63  | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | COMBINE_EQS: (268), (3737) imply:
% 146.50/20.63  | | | | | | | | | | | | |   (3738)  all_52_1 = e3
% 146.50/20.63  | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | REDUCE: (144), (3738) imply:
% 146.50/20.63  | | | | | | | | | | | | |   (3739)   ~ (all_52_13 = e3)
% 146.50/20.63  | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | SIMP: (3739) implies:
% 146.50/20.63  | | | | | | | | | | | | |   (3740)   ~ (all_52_13 = e3)
% 146.50/20.63  | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | BETA: splitting (87) gives:
% 146.50/20.63  | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | |   (3741)   ~ (all_38_2 = e1)
% 146.50/20.63  | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | REDUCE: (3582), (3741) imply:
% 146.50/20.63  | | | | | | | | | | | | | |   (3742)  $false
% 146.50/20.63  | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | CLOSE: (3742) is inconsistent.
% 146.50/20.63  | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | |   (3743)  ( ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0
% 146.50/20.63  | | | | | | | | | | | | | |             & op(e2, e1) = all_38_1 & $i(all_38_0) &
% 146.50/20.63  | | | | | | | | | | | | | |             $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e2, e1)
% 146.50/20.63  | | | | | | | | | | | | | |             = all_38_1 & $i(all_38_1))
% 146.50/20.63  | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 146.50/20.63  | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | |   (3744)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 146.50/20.63  | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 146.50/20.63  | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (3585), (3725), (3744),
% 146.50/20.63  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.63  | | | | | | | | | | | | | | |            #1138.
% 146.50/20.63  | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | |   (3745)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 146.50/20.63  | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 146.50/20.63  | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | BETA: splitting (3745) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | |   (3746)  all_56_5 = e2 & op(e2, e1) = e2
% 146.50/20.63  | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | ALPHA: (3746) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | |   (3747)  all_56_5 = e2
% 146.50/20.63  | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | |   (3748)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 146.50/20.63  | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (166), (3232), (3585), (3748),
% 146.50/20.63  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.63  | | | | | | | | | | | | | | | | |            #516.
% 146.50/20.63  | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | |   (3749)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 146.50/20.63  | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 146.50/20.63  | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | BETA: splitting (3749) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | |   (3750)  all_56_5 = e0 & op(e2, e1) = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | ALPHA: (3750) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | |   (3751)  op(e2, e1) = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3580), (3585), (3720), (3743), (3751),
% 146.50/20.63  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.63  | | | | | | | | | | | | | | | | | |            #513.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | |   (3752)  all_56_10 = e0 & op(e2, e0) = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | ALPHA: (3752) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | |   (3753)  all_56_10 = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | |   (3754)  all_54_7 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (3740), (3754) are inconsistent by
% 146.50/20.63  | | | | | | | | | | | | | | | | | | |            sub-proof #1163.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | |   (3755)   ~ (all_54_7 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | |   (3756)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | BETA: splitting (3756) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | |   (3757)  all_54_7 = e2
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (3733), (3757) are inconsistent by
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | |            sub-proof #1162.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | |   (3758)   ~ (all_54_7 = e2)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | |   (3759)  all_54_7 = e1 | all_54_7 = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | BETA: splitting (3759) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | |   (3760)  all_54_7 = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (3584), (3760) are inconsistent by
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | |            sub-proof #495.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | |   (3761)  all_54_7 = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (3761) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | |   (3762)  all_52_13 = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | SIMP: (3762) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | |   (3763)  all_52_13 = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (3763) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | |   (3764)   ~ (all_52_14 = e0)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | SIMP: (3764) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | |   (3765)   ~ (all_52_14 = e0)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | REDUCE: (3740), (3763) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | |   (3766)   ~ (e3 = e0)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | REDUCE: (3733), (3763) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | |   (3767)   ~ (e2 = e0)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | REDUCE: (3584), (3763) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | |   (3768)   ~ (e1 = e0)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | |   (3769)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3769) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | |   (3770)  all_56_9 = e1 & op(e3, e0) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3770) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | |   (3771)  all_56_9 = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | |   (3772)  op(e3, e0) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | |   (3773)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3773) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (3774)  all_56_9 = e3 & op(e3, e0) = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3774) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (3775)  op(e3, e0) = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (3772), (3775), (function-axioms) are
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #512.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (3776)  all_56_10 = e3 & op(e2, e0) = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3776) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (3777)  all_56_10 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3753), (3777) are inconsistent by sub-proof
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | |            #1134.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | |   (3778)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3778) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (3779)  all_56_11 = e3 & op(e1, e0) = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3779) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | |   (3780)  all_56_11 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3781)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3781) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3782)  all_56_12 = e1 & op(e0, e3) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3782) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3783)  all_56_12 = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3784)  all_54_2 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3784) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3785)  all_52_8 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3785) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3786)  all_52_8 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (3786) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3787)   ~ (all_52_11 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3787) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3788)   ~ (all_52_11 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3789)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3789) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3790)  all_56_12 = e3 & op(e0, e3) = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3783), (3790) are inconsistent by sub-proof
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #919.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3791)  all_56_13 = e3 & op(e0, e2) = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (90), (3713), (3772), (3791), (function-axioms)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #979.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3792)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (3715), (3788), (3792),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #990.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3793)   ~ (all_54_2 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (3793) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3794)   ~ (all_52_8 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3795)  all_54_11 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (3795) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3796)  all_52_14 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3796) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3797)  all_52_14 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (3797) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3798)   ~ (all_52_6 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (3797) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3799)   ~ (all_52_12 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (90), (158),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (161), (162), (163), (166), (167), (168),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (205), (208), (209), (210), (211), (212), (214),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (219), (223), (226), (227), (228),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (371), (3233), (3235), (3237),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3580), (3585), (3713), (3714), (3715), (3719),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3720), (3725), (3726), (3727), (3733), (3735),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3743), (3747), (3753), (3771), (3772), (3780),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3783), (3794), (3798), (3799), (function-axioms)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #479.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3800)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (3714), (3735), (3765), (3800) are
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #478.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3801)  all_56_13 = e1 & op(e0, e2) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (224), (226),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (3234), (3585), (3801), (function-axioms)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #499.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3802)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3802) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3803)  all_56_14 = e1 & op(e0, e1) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3803) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3804)  op(e0, e1) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3805)  all_54_2 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3805) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3806)  all_52_8 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3806) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3807)  all_52_8 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (3807) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3808)   ~ (all_52_11 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3808) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3809)   ~ (all_52_11 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (189), (246), (3731), (3734), (3804),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3809), (function-axioms) are inconsistent by
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #731.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3810)   ~ (all_54_2 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (270), (3810) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3811)   ~ (all_52_8 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3812)  all_54_11 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (3812) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3813)  all_52_14 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3813) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3814)  all_52_14 = e3
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (3814) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3815)   ~ (all_52_6 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (3814) imply:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3816)   ~ (all_52_12 = e3)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3817)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3817) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3818)  all_56_0 = e1 & op(e3, e3) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3818) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3819)  op(e3, e3) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (229), (233),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (3234), (3771), (3819), (function-axioms)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #913.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3820)  all_56_2 = e1 & op(e2, e3) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3820) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3821)  op(e2, e3) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (3583), (3821), (function-axioms) are
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1177.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3822)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3822) gives:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3823)  all_56_6 = e1 & op(e1, e3) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3823) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3824)  op(e1, e3) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3726), (3824), (function-axioms) are
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3825)  all_56_12 = e1 & op(e0, e3) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3825) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3826)  all_56_12 = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (90), (158),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (161), (162), (163), (166), (167), (168),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (205), (208), (209), (210), (211), (212), (214),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (219), (223), (226), (227), (228),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (232), (233), (234), (235),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (371), (3233), (3235), (3237),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3580), (3585), (3713), (3714), (3715), (3719),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3720), (3725), (3726), (3727), (3733), (3735),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3743), (3747), (3753), (3771), (3772), (3780),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3811), (3815), (3816), (3826), (function-axioms)
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #479.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3827)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (3714), (3735), (3765), (3827) are
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #478.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3828)  all_56_15 = e1 & op(e0, e0) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3828) implies:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3829)  op(e0, e0) = e1
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (205), (210), (3771),
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3780), (3829), (function-axioms) are inconsistent
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #497.
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.63  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (3830)  all_56_15 = e3 & op(e0, e0) = e3
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3830) implies:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | | |   (3831)  op(e0, e0) = e3
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3715), (3831), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | |   (3832)  all_56_10 = e1 & op(e2, e0) = e1
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3584), (3832), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | |   (3833)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (3715), (3735), (3833),
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | |            #615.
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | |   (3834)  all_56_10 = e2 & op(e2, e0) = e2
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | ALPHA: (3834) implies:
% 146.50/20.64  | | | | | | | | | | | | | | | |   (3835)  op(e2, e0) = e2
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3733), (3835), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | |   (3836)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 146.50/20.64  | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | REF_CLOSE: (268), (3232), (3583), (3725), (3836) are
% 146.50/20.64  | | | | | | | | | | | | |            inconsistent by sub-proof #636.
% 146.50/20.64  | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | |   (3837)   ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.64  | | | | | | | | | | | |           $i(all_57_12)
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | ALPHA: (3837) implies:
% 146.50/20.64  | | | | | | | | | | | |   (3838)   ~ (all_57_12 = e1)
% 146.50/20.64  | | | | | | | | | | | |   (3839)  op(e2, e2) = all_57_12
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | REF_CLOSE: (3585), (3838), (3839), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | |   (3840)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 146.50/20.64  | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 146.50/20.64  | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.64  | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.50/20.64  | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.50/20.64  | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.50/20.64  | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.50/20.64  | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 146.50/20.64  | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | ALPHA: (3840) implies:
% 146.50/20.64  | | | | | | | | | | |   (3841)  op(e0, e0) = e0
% 146.50/20.64  | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | REF_CLOSE: (5), (3715), (3841), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 146.50/20.64  | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | 
% 146.50/20.64  | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | 
% 146.50/20.64  | | | | | | | End of split
% 146.50/20.64  | | | | | | | 
% 146.50/20.64  | | | | | | Case 2:
% 146.50/20.64  | | | | | | | 
% 146.50/20.64  | | | | | | |   (3842)  all_16_2 = e0
% 146.50/20.64  | | | | | | | 
% 146.50/20.64  | | | | | | | COMBINE_EQS: (327), (3842) imply:
% 146.50/20.64  | | | | | | |   (3843)  all_6_2 = e0
% 146.50/20.64  | | | | | | | 
% 146.50/20.64  | | | | | | | SIMP: (3843) implies:
% 146.50/20.64  | | | | | | |   (3844)  all_6_2 = e0
% 146.50/20.64  | | | | | | | 
% 146.50/20.64  | | | | | | | REDUCE: (354), (3844) imply:
% 146.50/20.64  | | | | | | |   (3845)   ~ (all_52_7 = e0)
% 146.50/20.64  | | | | | | | 
% 146.50/20.64  | | | | | | | REDUCE: (356), (3844) imply:
% 146.50/20.64  | | | | | | |   (3846)   ~ (all_52_9 = e0)
% 146.50/20.64  | | | | | | | 
% 146.50/20.64  | | | | | | | REDUCE: (358), (3844) imply:
% 146.50/20.64  | | | | | | |   (3847)   ~ (all_52_13 = e0)
% 146.50/20.64  | | | | | | | 
% 146.50/20.64  | | | | | | | REDUCE: (372), (3844) imply:
% 146.50/20.64  | | | | | | |   (3848)   ~ (e3 = e0)
% 146.50/20.64  | | | | | | | 
% 146.50/20.64  | | | | | | | REDUCE: (39), (3844) imply:
% 146.50/20.64  | | | | | | |   (3849)  op(e2, e2) = e0
% 146.50/20.64  | | | | | | | 
% 146.50/20.64  | | | | | | | BETA: splitting (67) gives:
% 146.50/20.64  | | | | | | | 
% 146.50/20.64  | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | 
% 146.50/20.64  | | | | | | | |   (3850)   ~ (all_24_2 = e2)
% 146.50/20.64  | | | | | | | | 
% 146.50/20.64  | | | | | | | | REDUCE: (318), (3850) imply:
% 146.50/20.64  | | | | | | | |   (3851)   ~ (all_10_2 = e2)
% 146.50/20.64  | | | | | | | | 
% 146.50/20.64  | | | | | | | | BETA: splitting (93) gives:
% 146.50/20.64  | | | | | | | | 
% 146.50/20.64  | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | 
% 146.50/20.64  | | | | | | | | |   (3852)   ~ (all_42_2 = e3)
% 146.50/20.64  | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | REDUCE: (302), (3852) imply:
% 146.50/20.64  | | | | | | | | |   (3853)   ~ (all_10_2 = e3)
% 146.50/20.64  | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | BETA: splitting (188) gives:
% 146.50/20.64  | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | |   (3854)  all_54_15 = e3
% 146.50/20.64  | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | REF_CLOSE: (245), (3853), (3854) are inconsistent by
% 146.50/20.64  | | | | | | | | | |            sub-proof #1049.
% 146.50/20.64  | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | |   (3855)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 146.50/20.64  | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | BETA: splitting (3855) gives:
% 146.50/20.64  | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | |   (3856)  all_54_15 = e2
% 146.50/20.64  | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | REF_CLOSE: (245), (3851), (3856) are inconsistent by
% 146.50/20.64  | | | | | | | | | | |            sub-proof #1048.
% 146.50/20.64  | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | |   (3857)  all_54_15 = e1 | all_54_15 = e0
% 146.50/20.64  | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | BETA: splitting (3857) gives:
% 146.50/20.64  | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | |   (3858)  all_54_15 = e1
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | REF_CLOSE: (245), (375), (3858) are inconsistent by sub-proof
% 146.50/20.64  | | | | | | | | | | | |            #1047.
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | |   (3859)  all_54_15 = e0
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | COMBINE_EQS: (245), (3859) imply:
% 146.50/20.64  | | | | | | | | | | | |   (3860)  all_10_2 = e0
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | SIMP: (3860) implies:
% 146.50/20.64  | | | | | | | | | | | |   (3861)  all_10_2 = e0
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | REDUCE: (367), (3861) imply:
% 146.50/20.64  | | | | | | | | | | | |   (3862)   ~ (all_52_11 = e0)
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | REDUCE: (375), (3861) imply:
% 146.50/20.64  | | | | | | | | | | | |   (3863)   ~ (e1 = e0)
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | BETA: splitting (216) gives:
% 146.50/20.64  | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | |   (3864)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 146.50/20.64  | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 146.50/20.64  | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | BETA: splitting (3864) gives:
% 146.50/20.64  | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | |   (3865)  all_56_4 = e0 & op(e3, e1) = e0
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | REF_CLOSE: (168), (3235), (3865), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | |   (3866)  all_56_5 = e0 & op(e2, e1) = e0
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | REF_CLOSE: (164), (3846), (3866), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | | | | |            inconsistent by sub-proof #1144.
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | |   (3867)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 146.50/20.64  | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 146.50/20.64  | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | BETA: splitting (3867) gives:
% 146.50/20.64  | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | |   (3868)  all_56_8 = e0 & op(e1, e1) = e0
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | ALPHA: (3868) implies:
% 146.50/20.64  | | | | | | | | | | | | | |   (3869)  op(e1, e1) = e0
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0,
% 146.50/20.64  | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (3869) gives:
% 146.50/20.64  | | | | | | | | | | | | | |   (3870)  all_4_2 = e0
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | REDUCE: (371), (3870) imply:
% 146.50/20.64  | | | | | | | | | | | | | |   (3871)   ~ (e2 = e0)
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 146.50/20.64  | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | |   (3872)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 146.50/20.64  | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 146.50/20.64  | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.50/20.64  | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.50/20.64  | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.50/20.64  | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 146.50/20.64  | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 146.50/20.64  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.50/20.64  | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 146.50/20.64  | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 146.50/20.64  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.64  | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.50/20.64  | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.50/20.64  | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 146.50/20.64  | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 146.50/20.64  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 146.50/20.64  | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (3237), (3849), (3872),
% 146.50/20.64  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.64  | | | | | | | | | | | | | | |            #477.
% 146.50/20.64  | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | |   (3873)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 146.50/20.64  | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 146.50/20.64  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.64  | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.50/20.64  | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.64  | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 146.50/20.64  | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 146.50/20.64  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.50/20.64  | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 146.50/20.64  | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 146.50/20.64  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.64  | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.50/20.64  | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.50/20.64  | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.50/20.64  | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.50/20.64  | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 146.50/20.64  | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | BETA: splitting (3873) gives:
% 146.50/20.64  | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | |   (3874)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 146.50/20.64  | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 146.50/20.64  | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.64  | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.50/20.64  | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.64  | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 146.50/20.64  | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 146.50/20.64  | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | ALPHA: (3874) implies:
% 146.50/20.64  | | | | | | | | | | | | | | | |   (3875)  op(e1, e1) = e1
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3869), (3875), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | |   (3876)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 146.50/20.64  | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 146.50/20.64  | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.64  | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.50/20.64  | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.50/20.64  | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.50/20.64  | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.50/20.64  | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | ALPHA: (3876) implies:
% 146.50/20.64  | | | | | | | | | | | | | | | |   (3877)  op(e0, e0) = e0
% 146.50/20.64  | | | | | | | | | | | | | | | |   (3878)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 146.50/20.64  | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 146.50/20.64  | | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.50/20.64  | | | | | | | | | | | | | | | |   (3879)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10
% 146.50/20.64  | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = all_57_10 &
% 146.50/20.64  | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 146.50/20.64  | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | |   (3880)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.64  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.50/20.64  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.64  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.50/20.64  | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.64  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.50/20.64  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.50/20.64  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 146.50/20.64  | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 146.50/20.64  | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 146.50/20.64  | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.50/20.64  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.64  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.50/20.64  | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 146.50/20.64  | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 146.50/20.64  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 146.50/20.64  | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 146.50/20.64  | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 146.50/20.64  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 146.50/20.64  | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.50/20.64  | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.50/20.64  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.64  | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.50/20.64  | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | BETA: splitting (3880) gives:
% 146.50/20.64  | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | |   (3881)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.50/20.64  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.50/20.64  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.50/20.64  | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | BETA: splitting (3881) gives:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |   (3882)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | BETA: splitting (3882) gives:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |   (3883)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | ALPHA: (3883) implies:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |   (3884)  op(e1, e1) = e3
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (45), (156), (164), (168), (216),
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |            (237), (367), (3235), (3237), (3846), (3849),
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |            (3884), (function-axioms) are inconsistent by
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |            sub-proof #475.
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |   (3885)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | ALPHA: (3885) implies:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |   (3886)  op(e0, e0) = e3
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3877), (3886), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |   (3887)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3849), (3877), (3887), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #474.
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | |   (3888)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 146.50/20.64  | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.50/20.64  | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.50/20.64  | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | BETA: splitting (3888) gives:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |   (3889)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3869), (3877), (3889), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #894.
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |   (3890)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | BETA: splitting (3890) gives:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |   (3891)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | ALPHA: (3891) implies:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |   (3892)  op(e3, e3) = e2
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3237), (3892), (function-axioms) are
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |   (3893)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (3849), (3877), (3893),
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | |            #664.
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | | End of split
% 146.50/20.64  | | | | | | | | | | | | | | | | | 
% 146.50/20.64  | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.64  | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | |   (3894)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.50/20.65  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.50/20.65  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.50/20.65  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.50/20.65  | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.50/20.65  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.50/20.65  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 146.50/20.65  | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 146.50/20.65  | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 146.50/20.65  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.50/20.65  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 146.50/20.65  | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 146.50/20.65  | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.50/20.65  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.50/20.65  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.50/20.65  | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.50/20.65  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.50/20.65  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.50/20.65  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.50/20.65  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.50/20.65  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.50/20.65  | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | BETA: splitting (3894) gives:
% 146.50/20.65  | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | |   (3895)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.50/20.65  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.50/20.65  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.50/20.65  | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | BETA: splitting (3895) gives:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |   (3896)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3237), (3877), (3896), (function-axioms) are
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |   (3897)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3237), (3877), (3878), (3897),
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |            #472.
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | |   (3898)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.50/20.65  | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.50/20.65  | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 146.50/20.65  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.50/20.65  | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | BETA: splitting (3898) gives:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |   (3899)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3879), (3899) are inconsistent by sub-proof #470.
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |   (3900)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | BETA: splitting (3900) gives:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |   (3901)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | | ALPHA: (3901) implies:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |   (3902)   ~ (all_57_13 = e1)
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3869), (3878), (3902), (function-axioms) are
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #959.
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |   (3903)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (156), (157), (158), (3233), (3845), (3862),
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |            (3869), (3903), (function-axioms) are inconsistent
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | |            by sub-proof #755.
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | |   (3904)  all_56_14 = e0 & op(e0, e1) = e0
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | ALPHA: (3904) implies:
% 146.50/20.65  | | | | | | | | | | | | | |   (3905)  op(e0, e1) = e0
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | REF_CLOSE: (156), (3862), (3905), (function-axioms) are
% 146.50/20.65  | | | | | | | | | | | | | |            inconsistent by sub-proof #1124.
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | End of split
% 146.50/20.65  | | | | | | | | | 
% 146.50/20.65  | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | 
% 146.50/20.65  | | | | | | | | |   (3906)  all_42_2 = e3
% 146.50/20.65  | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | COMBINE_EQS: (302), (3906) imply:
% 146.50/20.65  | | | | | | | | |   (3907)  all_10_2 = e3
% 146.50/20.65  | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | SIMP: (3907) implies:
% 146.50/20.65  | | | | | | | | |   (3908)  all_10_2 = e3
% 146.50/20.65  | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | REDUCE: (368), (3908) imply:
% 146.50/20.65  | | | | | | | | |   (3909)   ~ (all_52_12 = e3)
% 146.50/20.65  | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | REDUCE: (370), (3908) imply:
% 146.50/20.65  | | | | | | | | |   (3910)   ~ (all_52_14 = e3)
% 146.50/20.65  | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | REDUCE: (45), (3908) imply:
% 146.50/20.65  | | | | | | | | |   (3911)  op(e0, e0) = e3
% 146.50/20.65  | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | BETA: splitting (237) gives:
% 146.50/20.65  | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | |   (3912)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 146.50/20.65  | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 146.50/20.65  | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.50/20.65  | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.50/20.65  | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.50/20.65  | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 146.50/20.65  | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 146.50/20.65  | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.50/20.65  | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 146.50/20.65  | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 146.50/20.65  | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.65  | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.50/20.65  | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.50/20.65  | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 146.50/20.65  | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 146.50/20.65  | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 146.50/20.65  | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | REF_CLOSE: (5), (7), (3237), (3849), (3912),
% 146.50/20.65  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.65  | | | | | | | | | |            #477.
% 146.50/20.65  | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | |   (3913)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 146.50/20.65  | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 146.50/20.65  | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.65  | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.50/20.65  | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.65  | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 146.50/20.65  | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 146.50/20.65  | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.50/20.65  | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 146.50/20.65  | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 146.50/20.65  | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.65  | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.50/20.65  | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.50/20.65  | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.50/20.65  | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.50/20.65  | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 146.50/20.65  | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | BETA: splitting (3913) gives:
% 146.50/20.65  | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | |   (3914)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 146.50/20.65  | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 146.50/20.65  | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.65  | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.50/20.65  | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.65  | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 146.50/20.65  | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 146.50/20.65  | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.50/20.65  | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | ALPHA: (3914) implies:
% 146.50/20.65  | | | | | | | | | | |   (3915)  all_57_14 = e1
% 146.50/20.65  | | | | | | | | | | |   (3916)  op(e1, e1) = e1
% 146.50/20.65  | | | | | | | | | | |   (3917)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 146.50/20.65  | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.65  | | | | | | | | | | |             $i(all_57_12))
% 146.50/20.65  | | | | | | | | | | |   (3918)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 146.50/20.65  | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 146.50/20.65  | | | | | | | | | | |             $i(all_57_10))
% 146.50/20.65  | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | BETA: splitting (205) gives:
% 146.50/20.65  | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | |   (3919)  all_56_15 = e0 & op(e0, e0) = e0
% 146.50/20.65  | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | ALPHA: (3919) implies:
% 146.50/20.65  | | | | | | | | | | | |   (3920)  op(e0, e0) = e0
% 146.50/20.65  | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | REF_CLOSE: (7), (3911), (3920), (function-axioms) are
% 146.50/20.65  | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 146.50/20.65  | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | |   (3921)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 146.50/20.65  | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 146.50/20.65  | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 146.50/20.65  | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 146.50/20.65  | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 146.50/20.65  | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | ALPHA: (3921) implies:
% 146.50/20.65  | | | | | | | | | | | |   (3922)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 146.50/20.65  | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 146.50/20.65  | | | | | | | | | | | |               e1) = e0)
% 146.50/20.65  | | | | | | | | | | | |   (3923)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 146.50/20.65  | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 146.50/20.65  | | | | | | | | | | | |               e0) = e0)
% 146.50/20.65  | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | BETA: splitting (3922) gives:
% 146.50/20.65  | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | |   (3924)  all_56_12 = e0 & op(e0, e3) = e0
% 146.50/20.65  | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | ALPHA: (3924) implies:
% 146.50/20.65  | | | | | | | | | | | | |   (3925)  op(e0, e3) = e0
% 146.50/20.65  | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | REF_CLOSE: (158), (3233), (3925), (function-axioms) are
% 146.50/20.65  | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 146.50/20.65  | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | |   (3926)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 146.50/20.65  | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 146.50/20.65  | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | BETA: splitting (3926) gives:
% 146.50/20.65  | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | |   (3927)  all_56_13 = e0 & op(e0, e2) = e0
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | ALPHA: (3927) implies:
% 146.50/20.65  | | | | | | | | | | | | | |   (3928)  op(e0, e2) = e0
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | REF_CLOSE: (157), (3845), (3928), (function-axioms) are
% 146.50/20.65  | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | |   (3929)  all_56_14 = e0 & op(e0, e1) = e0
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | ALPHA: (3929) implies:
% 146.50/20.65  | | | | | | | | | | | | | |   (3930)  op(e0, e1) = e0
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | BETA: splitting (3923) gives:
% 146.50/20.65  | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | |   (3931)  all_56_9 = e0 & op(e3, e0) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | REF_CLOSE: (167), (3236), (3931), (function-axioms) are
% 146.50/20.65  | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 146.50/20.65  | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | |   (3932)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 146.50/20.65  | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 146.50/20.65  | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | BETA: splitting (3932) gives:
% 146.50/20.65  | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3933)  all_56_10 = e0 & op(e2, e0) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3847), (3933), (function-axioms) are
% 146.50/20.65  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #540.
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | Case 2:
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3934)  all_56_11 = e0 & op(e1, e0) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | ALPHA: (3934) implies:
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3935)  all_56_11 = e0
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3936)  op(e1, e0) = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 146.50/20.65  | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (156), (3930) gives:
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3937)  all_52_11 = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 146.50/20.65  | | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (159), (3936) gives:
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3938)  all_52_14 = e0
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 146.50/20.65  | | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (3916) gives:
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3939)  all_4_2 = e1
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | REDUCE: (140), (3938) imply:
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3940)   ~ (all_52_2 = e0)
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | REDUCE: (348), (3939) imply:
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3941)   ~ (all_52_2 = e1)
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | REDUCE: (359), (3939) imply:
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3942)   ~ (all_52_6 = e1)
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | REDUCE: (362), (3939) imply:
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3943)   ~ (all_52_9 = e1)
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | REDUCE: (366), (3938), (3939) imply:
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3944)   ~ (e1 = e0)
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | REDUCE: (374), (3939) imply:
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3945)   ~ (e3 = e1)
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | REDUCE: (371), (3939) imply:
% 146.50/20.65  | | | | | | | | | | | | | | | |   (3946)   ~ (e2 = e1)
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 146.50/20.65  | | | | | | | | | | | | | | | | 
% 146.50/20.65  | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.65  | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | |   (3947)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.66  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.50/20.66  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.66  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.50/20.66  | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.66  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.50/20.66  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 146.50/20.66  | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 146.50/20.66  | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 146.50/20.66  | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.50/20.66  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.66  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.50/20.66  | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 146.50/20.66  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 146.50/20.66  | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 146.50/20.66  | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 146.50/20.66  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 146.50/20.66  | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.50/20.66  | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.50/20.66  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.66  | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.50/20.66  | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | BETA: splitting (3947) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | |   (3948)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.50/20.66  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.50/20.66  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.50/20.66  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.50/20.66  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.50/20.66  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.50/20.66  | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | BETA: splitting (3948) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | |   (3949)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.50/20.66  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | BETA: splitting (3949) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |   (3950)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | ALPHA: (3950) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |   (3951)  op(e1, e1) = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (45), (156), (237), (367), (3237),
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |            (3849), (3930), (3951), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #476.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |   (3952)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | ALPHA: (3952) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |   (3953)   ~ (all_57_12 = e3)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |   (3954)  op(e2, e2) = all_57_12
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | |   (3955)  op(e2, e3) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | |   (3956)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3956) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3957)  all_56_6 = e1 & op(e1, e3) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3957) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3958)  op(e1, e3) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3941), (3958), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3959)  all_56_7 = e1 & op(e1, e2) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3959) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3960)  op(e1, e2) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (3942), (3960), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | |   (3961)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3961) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3962)  all_56_8 = e1 & op(e1, e1) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (3849), (3954)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3963)  all_57_12 = e0
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (166), (3955) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3964)  all_52_1 = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (3964) imply:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3965)   ~ (all_52_2 = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | SIMP: (3965) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3966)   ~ (all_52_2 = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (3964) imply:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3967)   ~ (all_52_9 = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | SIMP: (3967) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3968)   ~ (all_52_9 = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (3964) imply:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3969)   ~ (all_52_13 = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | SIMP: (3969) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | |   (3970)   ~ (all_52_13 = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | |   (3971)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3971) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | |   (3972)  all_56_9 = e2 & op(e3, e0) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3972) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | |   (3973)  all_56_9 = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (3974)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3974) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3975)  all_56_12 = e2 & op(e0, e3) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3975) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (3976)  all_56_12 = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3977)  all_54_6 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (3977) imply:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3978)  all_52_9 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3978) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3979)  all_52_9 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (3979) imply:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3980)  op(e2, e1) = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3981)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3981) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3982)  all_56_4 = e2 & op(e3, e1) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3982) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3983)  all_56_4 = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3984)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3984) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3985)  all_56_9 = e1 & op(e3, e0) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3985) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3986)  all_56_9 = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3973), (3986) are inconsistent by sub-proof
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #948.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3987)  all_56_10 = e1 & op(e2, e0) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3987) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3988)  op(e2, e0) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3989)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3989) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3990)  all_56_0 = e1 & op(e3, e3) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3990) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3991)  op(e3, e3) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (169), (229), (3234), (3973), (3983),
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3991), (function-axioms) are inconsistent by
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #583.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3992)  all_56_2 = e1 & op(e2, e3) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3992) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3993)  op(e2, e3) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3994)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (166), (3849), (3993), (3994),
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #624.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3995)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3995) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3996)  all_56_5 = e2 & op(e2, e1) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3996) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3997)  all_56_5 = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3998)  op(e2, e1) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (3999)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3999) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4000)  all_56_4 = e3 & op(e3, e1) = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4000) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4001)  all_56_4 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3983), (4001) are inconsistent by sub-proof
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1068.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4002)  all_56_5 = e3 & op(e2, e1) = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3980), (3998), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1135.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4003)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4003) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4004)  all_56_8 = e3 & op(e1, e1) = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4004) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4005)  op(e1, e1) = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (374), (4005), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4006)  all_56_14 = e3 & op(e0, e1) = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4006) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4007)  all_56_14 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (164), (216), (217),
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3846), (3983), (3997), (4007), (function-axioms)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #468.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4008)  all_56_10 = e2 & op(e2, e0) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4008) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4009)  op(e2, e0) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (3988), (4009), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #904.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4010)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4010) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4011)  all_56_6 = e1 & op(e1, e3) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4011) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4012)  op(e1, e3) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3941), (4012), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4013)  all_56_12 = e1 & op(e0, e3) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4013) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4014)  all_56_12 = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3976), (4014) are inconsistent by sub-proof
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1122.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4015)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4015) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4016)  all_56_11 = e1 & op(e1, e0) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4016) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4017)  op(e1, e0) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3936), (4017), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #467.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4018)  all_56_15 = e1 & op(e0, e0) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4018) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4019)  op(e0, e0) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3911), (4019), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4020)  all_56_5 = e2 & op(e2, e1) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4020) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4021)  op(e2, e1) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3980), (4021), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1135.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4022)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (3916), (3930), (4022),
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #466.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4023)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (166), (260), (3846), (3943), (3955),
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4023), (function-axioms) are inconsistent by
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #648.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4024)  all_56_13 = e2 & op(e0, e2) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4024) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4025)  all_56_13 = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4026)  all_54_6 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (4026) imply:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4027)  all_52_9 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4027) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4028)  all_52_9 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (4028) imply:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4029)  op(e2, e1) = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4030)  all_54_8 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (4030) imply:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4031)  all_52_2 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4031) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4032)  all_52_2 = e3
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (4032) imply:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4033)   ~ (all_52_6 = e3)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4033) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4034)   ~ (all_52_6 = e3)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4035)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4035) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4036)  all_56_4 = e2 & op(e3, e1) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4036) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4037)  all_56_4 = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4038)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4038) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4039)  all_56_0 = e1 & op(e3, e3) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4039) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4040)  op(e3, e3) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (169), (229), (3234), (3973), (4037),
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4040), (function-axioms) are inconsistent by
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #583.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4041)  all_56_1 = e1 & op(e3, e2) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4041) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4042)  all_56_1 = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (161), (227), (3849), (4025),
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4034), (4042), (function-axioms) are inconsistent
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #464.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4043)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4043) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4044)  all_56_4 = e1 & op(e3, e1) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4037), (4044) are inconsistent by sub-proof
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1066.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4045)  all_56_9 = e1 & op(e3, e0) = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4045) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4046)  all_56_9 = e1
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3973), (4046) are inconsistent by sub-proof
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #948.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4047)  all_56_5 = e2 & op(e2, e1) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4047) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4048)  op(e2, e1) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4029), (4048), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1135.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4049)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (3916), (3930), (4049),
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #466.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4050)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (3940), (3941), (3966), (4050) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #460.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4051)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (166), (260), (3846), (3943), (3955),
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4051), (function-axioms) are inconsistent by
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #648.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | |   (4052)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4052) gives:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4053)  all_56_14 = e2 & op(e0, e1) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4053) implies:
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4054)  op(e0, e1) = e2
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3930), (4054), (function-axioms) are
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1008.
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4055)  all_56_15 = e2 & op(e0, e0) = e2
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4055) implies:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4056)  op(e0, e0) = e2
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (209), (211), (3935),
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            (3973), (4056), (function-axioms) are inconsistent
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #487.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | |   (4057)  all_56_10 = e2 & op(e2, e0) = e2
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4057) implies:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | |   (4058)  op(e2, e0) = e2
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3970), (4058), (function-axioms) are
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | |   (4059)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4059) gives:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | |   (4060)  all_56_11 = e2 & op(e1, e0) = e2
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3935), (4060) are inconsistent by sub-proof
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | |            #459.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | |   (4061)  all_56_15 = e2 & op(e0, e0) = e2
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4061) implies:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | |   (4062)  op(e0, e0) = e2
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3911), (4062), (function-axioms) are
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | |   (4063)  all_56_11 = e1 & op(e1, e0) = e1
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4063) implies:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | |   (4064)  op(e1, e0) = e1
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3936), (4064), (function-axioms) are
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #467.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |   (4065)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3941), (4065), (function-axioms) are
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1025.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | |   (4066)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.50/20.67  | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | BETA: splitting (4066) gives:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |   (4067)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (36), (3911), (3916), (4067),
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |            #1024.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |   (4068)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (3237), (3911), (3917), (4068),
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |            #457.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | |   (4069)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.50/20.67  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.50/20.67  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.50/20.67  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.50/20.67  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.50/20.67  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 146.50/20.67  | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 146.50/20.67  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.50/20.67  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 146.50/20.67  | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 146.50/20.67  | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.50/20.67  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.50/20.67  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.50/20.67  | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.50/20.67  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.50/20.67  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.50/20.67  | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | BETA: splitting (4069) gives:
% 146.50/20.67  | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | |   (4070)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (3909), (3911), (3918), (4070),
% 146.50/20.67  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.67  | | | | | | | | | | | | | | | | | |            #455.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | |   (4071)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.50/20.67  | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | BETA: splitting (4071) gives:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |   (4072)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (4072) gives:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |   (4073)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | ALPHA: (4073) implies:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |   (4074)   ~ (all_57_12 = e0)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |   (4075)  op(e2, e2) = all_57_12
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3849), (4074), (4075), (function-axioms) are
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |   (4076)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | ALPHA: (4076) implies:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |   (4077)  op(e1, e0) = e1
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3936), (4077), (function-axioms) are
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #467.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |   (4078)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (4078) gives:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |   (4079)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | ALPHA: (4079) implies:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |   (4080)  op(e1, e1) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3916), (4080), (function-axioms) are
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |   (4081)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4081) gives:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |   (4082)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4082) implies:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |   (4083)   ~ (all_57_14 = e0)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |   (4084)  op(e1, e0) = e1
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3936), (4084), (function-axioms) are
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #467.
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |   (4085)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4085) implies:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |   (4086)  op(e0, e0) = all_57_15
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |   (4087)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4087) gives:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.67  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |   (4088)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4088) gives:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |   (4089)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4089) implies:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |   (4090)  op(e0, e3) = e0
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3233), (4090), (function-axioms) are
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |   (4091)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4091) gives:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4092)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4092) implies:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4093)  op(e0, e3) = e0
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3233), (4093), (function-axioms) are
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4094)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4094) implies:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |   (4095)  op(e3, e3) = e2
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (157), (3845), (3849), (3911), (4086),
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |            (4087), (4095), (function-axioms) are inconsistent
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #826.
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |   (4096)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (3916), (3917), (3918), (4096),
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | |            #454.
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | |   (4097)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 146.50/20.68  | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 146.50/20.68  | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.68  | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.50/20.68  | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.50/20.68  | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.50/20.68  | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.50/20.68  | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | ALPHA: (4097) implies:
% 146.50/20.68  | | | | | | | | | | |   (4098)  op(e0, e0) = e0
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | REF_CLOSE: (7), (3911), (4098), (function-axioms) are
% 146.50/20.68  | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | 
% 146.50/20.68  | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | 
% 146.50/20.68  | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | 
% 146.50/20.68  | | | | | | | |   (4099)  all_24_2 = e2
% 146.50/20.68  | | | | | | | | 
% 146.50/20.68  | | | | | | | | COMBINE_EQS: (318), (4099) imply:
% 146.50/20.68  | | | | | | | |   (4100)  all_10_2 = e2
% 146.50/20.68  | | | | | | | | 
% 146.50/20.68  | | | | | | | | REDUCE: (368), (4100) imply:
% 146.50/20.68  | | | | | | | |   (4101)   ~ (all_52_12 = e2)
% 146.50/20.68  | | | | | | | | 
% 146.50/20.68  | | | | | | | | REDUCE: (369), (4100) imply:
% 146.50/20.68  | | | | | | | |   (4102)   ~ (all_52_13 = e2)
% 146.50/20.68  | | | | | | | | 
% 146.50/20.68  | | | | | | | | REDUCE: (370), (4100) imply:
% 146.50/20.68  | | | | | | | |   (4103)   ~ (all_52_14 = e2)
% 146.50/20.68  | | | | | | | | 
% 146.50/20.68  | | | | | | | | REDUCE: (45), (4100) imply:
% 146.50/20.68  | | | | | | | |   (4104)  op(e0, e0) = e2
% 146.50/20.68  | | | | | | | | 
% 146.50/20.68  | | | | | | | | BETA: splitting (237) gives:
% 146.50/20.68  | | | | | | | | 
% 146.50/20.68  | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | 
% 146.50/20.68  | | | | | | | | |   (4105)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 146.50/20.68  | | | | | | | | |                 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 146.50/20.68  | | | | | | | | |                 op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.50/20.68  | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.50/20.68  | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.50/20.68  | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 146.50/20.68  | | | | | | | | |                 = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 146.50/20.68  | | | | | | | | |                 all_57_15 & $i(all_57_15)))) | (all_57_12 = e2
% 146.50/20.68  | | | | | | | | |             & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 146.50/20.68  | | | | | | | | |                 e3) | ( ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.68  | | | | | | | | |                 all_57_10 & $i(all_57_10))) & ((all_57_4 = e1
% 146.50/20.68  | | | | | | | | |                 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) &
% 146.50/20.68  | | | | | | | | |                 op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 146.50/20.68  | | | | | | | | |             ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~
% 146.50/20.68  | | | | | | | | |                 (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 146.50/20.68  | | | | | | | | |                 $i(all_57_15))))
% 146.50/20.68  | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | REF_CLOSE: (5), (7), (3237), (3849), (4105), (function-axioms)
% 146.50/20.68  | | | | | | | | |            are inconsistent by sub-proof #477.
% 146.50/20.68  | | | | | | | | | 
% 146.50/20.68  | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | 
% 146.50/20.68  | | | | | | | | |   (4106)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 146.50/20.68  | | | | | | | | |                 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 146.50/20.68  | | | | | | | | |                 op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.68  | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.50/20.68  | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.68  | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 146.50/20.68  | | | | | | | | |                 = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 146.50/20.68  | | | | | | | | |                 all_57_15 & $i(all_57_15)))) | (all_57_15 = e0
% 146.50/20.68  | | | | | | | | |             & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 146.50/20.68  | | | | | | | | |                 e3) | ( ~ (all_57_10 = e0) & op(e3, e3) =
% 146.50/20.68  | | | | | | | | |                 all_57_10 & $i(all_57_10))) & ((all_57_11 = e2
% 146.50/20.68  | | | | | | | | |                 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 146.50/20.68  | | | | | | | | |                 op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.50/20.68  | | | | | | | | |             ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 146.50/20.68  | | | | | | | | |                 (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 146.50/20.68  | | | | | | | | |                 $i(all_57_14))))
% 146.50/20.68  | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | BETA: splitting (4106) gives:
% 146.50/20.68  | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | |   (4107)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 146.50/20.68  | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 146.50/20.68  | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.50/20.68  | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 146.50/20.68  | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.68  | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 146.50/20.68  | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 146.50/20.68  | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.50/20.68  | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | ALPHA: (4107) implies:
% 146.50/20.68  | | | | | | | | | |   (4108)  op(e1, e1) = e1
% 146.50/20.68  | | | | | | | | | |   (4109)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 146.50/20.68  | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.68  | | | | | | | | | |             $i(all_57_12))
% 146.50/20.68  | | | | | | | | | |   (4110)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 146.50/20.68  | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 146.50/20.68  | | | | | | | | | |             $i(all_57_10))
% 146.50/20.68  | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | BETA: splitting (205) gives:
% 146.50/20.68  | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | |   (4111)  all_56_15 = e0 & op(e0, e0) = e0
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | ALPHA: (4111) implies:
% 146.50/20.68  | | | | | | | | | | |   (4112)  op(e0, e0) = e0
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | REF_CLOSE: (5), (4104), (4112), (function-axioms) are
% 146.50/20.68  | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | |   (4113)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 146.50/20.68  | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 146.50/20.68  | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 146.50/20.68  | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 146.50/20.68  | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | ALPHA: (4113) implies:
% 146.50/20.68  | | | | | | | | | | |   (4114)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 146.50/20.68  | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 146.50/20.68  | | | | | | | | | | |               e1) = e0)
% 146.50/20.68  | | | | | | | | | | |   (4115)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 146.50/20.68  | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 146.50/20.68  | | | | | | | | | | |               e0) = e0)
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | BETA: splitting (4114) gives:
% 146.50/20.68  | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | |   (4116)  all_56_12 = e0 & op(e0, e3) = e0
% 146.50/20.68  | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | ALPHA: (4116) implies:
% 146.50/20.68  | | | | | | | | | | | |   (4117)  op(e0, e3) = e0
% 146.50/20.68  | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | REF_CLOSE: (158), (3233), (4117), (function-axioms) are
% 146.50/20.68  | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 146.50/20.68  | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | |   (4118)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 146.50/20.68  | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 146.50/20.68  | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | BETA: splitting (4118) gives:
% 146.50/20.68  | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | |   (4119)  all_56_13 = e0 & op(e0, e2) = e0
% 146.50/20.68  | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | ALPHA: (4119) implies:
% 146.50/20.68  | | | | | | | | | | | | |   (4120)  op(e0, e2) = e0
% 146.50/20.68  | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | REF_CLOSE: (157), (3845), (4120), (function-axioms) are
% 146.50/20.68  | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 146.50/20.68  | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | |   (4121)  all_56_14 = e0 & op(e0, e1) = e0
% 146.50/20.68  | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | ALPHA: (4121) implies:
% 146.50/20.68  | | | | | | | | | | | | |   (4122)  all_56_14 = e0
% 146.50/20.68  | | | | | | | | | | | | |   (4123)  op(e0, e1) = e0
% 146.50/20.68  | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | BETA: splitting (4115) gives:
% 146.50/20.68  | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | |   (4124)  all_56_9 = e0 & op(e3, e0) = e0
% 146.50/20.68  | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | REF_CLOSE: (167), (3236), (4124), (function-axioms) are
% 146.50/20.68  | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 146.50/20.68  | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | |   (4125)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 146.50/20.68  | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 146.50/20.68  | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | BETA: splitting (4125) gives:
% 146.50/20.68  | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | |   (4126)  all_56_10 = e0 & op(e2, e0) = e0
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | REF_CLOSE: (163), (3847), (4126), (function-axioms) are
% 146.50/20.68  | | | | | | | | | | | | | | |            inconsistent by sub-proof #540.
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | |   (4127)  all_56_11 = e0 & op(e1, e0) = e0
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | ALPHA: (4127) implies:
% 146.50/20.68  | | | | | | | | | | | | | | |   (4128)  all_56_11 = e0
% 146.50/20.68  | | | | | | | | | | | | | | |   (4129)  op(e1, e0) = e0
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 146.50/20.68  | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (156), (4123) gives:
% 146.50/20.68  | | | | | | | | | | | | | | |   (4130)  all_52_11 = e0
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 146.50/20.68  | | | | | | | | | | | | | | |              e0, e0, e1, simplifying with (159), (4129) gives:
% 146.50/20.68  | | | | | | | | | | | | | | |   (4131)  all_52_14 = e0
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 146.50/20.68  | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (4108) gives:
% 146.50/20.68  | | | | | | | | | | | | | | |   (4132)  all_4_2 = e1
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | REDUCE: (348), (4132) imply:
% 146.50/20.68  | | | | | | | | | | | | | | |   (4133)   ~ (all_52_2 = e1)
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | REDUCE: (359), (4132) imply:
% 146.50/20.68  | | | | | | | | | | | | | | |   (4134)   ~ (all_52_6 = e1)
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | REDUCE: (366), (4131), (4132) imply:
% 146.50/20.68  | | | | | | | | | | | | | | |   (4135)   ~ (e1 = e0)
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | REDUCE: (4103), (4131) imply:
% 146.50/20.68  | | | | | | | | | | | | | | |   (4136)   ~ (e2 = e0)
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | REDUCE: (374), (4132) imply:
% 146.50/20.68  | | | | | | | | | | | | | | |   (4137)   ~ (e3 = e1)
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | REDUCE: (371), (4132) imply:
% 146.50/20.68  | | | | | | | | | | | | | | |   (4138)   ~ (e2 = e1)
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 146.50/20.68  | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | |   (4139)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.68  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.50/20.68  | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.68  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.50/20.68  | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.68  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.50/20.68  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.50/20.68  | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.50/20.68  | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 146.50/20.68  | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 146.50/20.68  | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 146.50/20.68  | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.50/20.68  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.50/20.68  | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.50/20.68  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 146.50/20.68  | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 146.50/20.68  | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 146.50/20.68  | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 146.50/20.68  | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 146.50/20.68  | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 146.50/20.68  | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 146.50/20.68  | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.50/20.68  | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.50/20.68  | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.68  | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.50/20.68  | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | BETA: splitting (4139) gives:
% 146.50/20.68  | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | |   (4140)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.68  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.50/20.68  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.68  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.50/20.68  | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.68  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.50/20.68  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.50/20.68  | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | BETA: splitting (4140) gives:
% 146.50/20.68  | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | |   (4141)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.50/20.68  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.50/20.68  | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | BETA: splitting (4141) gives:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |   (4142)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | ALPHA: (4142) implies:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |   (4143)  op(e1, e1) = e3
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (45), (159), (237), (370), (3237),
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |            (3849), (4129), (4143), (function-axioms) are
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #452.
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |   (4144)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | ALPHA: (4144) implies:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |   (4145)  op(e0, e0) = e3
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4104), (4145), (function-axioms) are
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | |   (4146)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.50/20.68  | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (162), (4104), (4133), (4146),
% 146.50/20.68  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.68  | | | | | | | | | | | | | | | | | |            #723.
% 146.50/20.68  | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | End of split
% 146.50/20.68  | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | |   (4147)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.50/20.68  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.50/20.68  | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.50/20.68  | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.50/20.68  | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.50/20.68  | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 146.50/20.68  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 146.50/20.68  | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.50/20.68  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.50/20.68  | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.50/20.68  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.50/20.68  | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.50/20.68  | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | BETA: splitting (4147) gives:
% 146.50/20.68  | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | |   (4148)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.50/20.68  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 146.50/20.68  | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | BETA: splitting (4148) gives:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |   (4149)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | ALPHA: (4149) implies:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |   (4150)  op(e1, e1) = e2
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (4108), (4150), (function-axioms) are
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |   (4151)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.50/20.68  | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.68  | | | | | | | | | | | | | | | | | | | ALPHA: (4151) implies:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |   (4152)   ~ (all_57_10 = e2)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |   (4153)  op(e3, e2) = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |   (4154)  op(e3, e3) = all_57_10
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (169), (4153) gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |   (4155)  all_52_4 = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (3237), (4154)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |              gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |   (4156)  all_57_10 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | REDUCE: (133), (4155) imply:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |   (4157)   ~ (all_52_8 = e3)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | SIMP: (4157) implies:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |   (4158)   ~ (all_52_8 = e3)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | REDUCE: (132), (4155) imply:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |   (4159)   ~ (all_52_12 = e3)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | SIMP: (4159) implies:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | |   (4160)   ~ (all_52_12 = e3)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | |   (4161)  all_54_3 = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (4160), (4161) are inconsistent by
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | |            sub-proof #451.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | |   (4162)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4162) gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | |   (4163)  all_54_3 = e2
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (4101), (4163) are inconsistent by
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | |            sub-proof #760.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | |   (4164)   ~ (all_54_3 = e2)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | |   (4165)  all_54_3 = e1 | all_54_3 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4165) gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | |   (4166)  all_54_3 = e1
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4166) imply:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | |   (4167)  all_52_12 = e1
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (4167) imply:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | |   (4168)   ~ (all_52_13 = e1)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | SIMP: (4168) implies:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | |   (4169)   ~ (all_52_13 = e1)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (4167) imply:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | |   (4170)  op(e3, e0) = e1
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | |   (4171)  all_54_7 = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (4171) imply:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | |   (4172)  all_52_13 = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4172) implies:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | |   (4173)  all_52_13 = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (4173) imply:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | |   (4174)   ~ (all_52_9 = e3)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | |   (4175)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4175) gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (4176)  all_56_9 = e3 & op(e3, e0) = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4176) implies:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (4177)  op(e3, e0) = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (4170), (4177), (function-axioms) are
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #512.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (4178)  all_56_10 = e3 & op(e2, e0) = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4178) implies:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (4179)  all_56_10 = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | |   (4180)  op(e2, e0) = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4181)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (168), (220),
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (3849), (4158), (4179),
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4180), (4181), (function-axioms) are inconsistent
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #674.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4182)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4182) gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4183)  all_56_8 = e3 & op(e1, e1) = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4183) implies:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4184)  op(e1, e1) = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (45), (159), (237), (370), (3237),
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (3849), (4129), (4184), (function-axioms) are
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #452.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4185)  all_56_14 = e3 & op(e0, e1) = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4185) implies:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4186)  all_56_14 = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4122), (4186) imply:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4187)  e3 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4187) implies:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4188)  e3 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4179), (4188) imply:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4189)  all_56_10 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (221), (222),
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (3849), (4174), (4189), (function-axioms)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #450.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | |   (4190)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (4104), (4128), (4190),
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | |            #488.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | |   (4191)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (3847), (4102), (4169), (4191) are
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #449.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | |   (4192)  all_54_3 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4192) imply:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | |   (4193)  all_52_12 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3236), (4193) imply:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | |   (4194)  $false
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4194) is inconsistent.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | |   (4195)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.50/20.69  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.50/20.69  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.50/20.69  | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (161), (3237), (4109), (4134), (4195),
% 146.50/20.69  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.69  | | | | | | | | | | | | | | | | | |            #448.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | |   (4196)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.50/20.69  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.69  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.50/20.69  | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.50/20.69  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.50/20.69  | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.50/20.69  | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.50/20.69  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.50/20.69  | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.50/20.69  | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.50/20.69  | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.69  | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.50/20.69  | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.50/20.69  | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.50/20.69  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.50/20.69  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.50/20.69  | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.50/20.69  | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.50/20.69  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.50/20.69  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.50/20.69  | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 146.50/20.69  | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 146.50/20.69  | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 146.50/20.69  | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 146.50/20.69  | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.50/20.69  | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.50/20.69  | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.50/20.69  | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 146.50/20.69  | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 146.50/20.69  | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.50/20.69  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.50/20.69  | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.50/20.69  | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.50/20.69  | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.50/20.69  | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.50/20.69  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.50/20.69  | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.50/20.69  | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.50/20.69  | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.50/20.69  | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.50/20.69  | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.50/20.69  | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.50/20.69  | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.50/20.69  | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.50/20.69  | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.50/20.69  | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.50/20.69  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.50/20.69  | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.50/20.69  | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.50/20.69  | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.50/20.69  | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.50/20.69  | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.50/20.69  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.50/20.69  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.50/20.69  | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.50/20.69  | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.50/20.69  | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.50/20.69  | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.50/20.69  | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.50/20.69  | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | BETA: splitting (4196) gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.69  | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | |   (4197)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.50/20.69  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.69  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.50/20.69  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.50/20.69  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.50/20.69  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.50/20.69  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.50/20.69  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.50/20.69  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.50/20.69  | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.50/20.69  | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.50/20.69  | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.50/20.69  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.50/20.69  | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.50/20.69  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.50/20.69  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.50/20.69  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.50/20.69  | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.50/20.69  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.50/20.69  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.50/20.69  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.50/20.69  | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | BETA: splitting (4197) gives:
% 146.50/20.69  | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | Case 1:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | |   (4198)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.50/20.69  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.50/20.69  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 146.50/20.69  | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4104), (4110), (4198), (function-axioms) are
% 146.50/20.69  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #447.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | |   (4199)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.50/20.69  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 146.50/20.69  | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 146.50/20.69  | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (3237), (4104), (4108), (4199),
% 146.50/20.69  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.50/20.69  | | | | | | | | | | | | | | | | | |            #518.
% 146.50/20.69  | | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | | End of split
% 146.50/20.69  | | | | | | | | | | | | | | | | | 
% 146.50/20.69  | | | | | | | | | | | | | | | | Case 2:
% 146.50/20.69  | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | |   (4200)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.81/20.69  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.81/20.69  | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.81/20.69  | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.81/20.69  | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.81/20.69  | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.81/20.69  | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.81/20.69  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 146.81/20.69  | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.69  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.81/20.69  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.69  | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 146.81/20.69  | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 146.81/20.69  | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 146.81/20.69  | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 146.81/20.69  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 146.81/20.69  | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.81/20.69  | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 146.81/20.69  | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.81/20.69  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.81/20.69  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.81/20.69  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.81/20.69  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.81/20.69  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.81/20.69  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.81/20.69  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.69  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.81/20.69  | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | BETA: splitting (4200) gives:
% 146.81/20.69  | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | |   (4201)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.81/20.69  | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.81/20.69  | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.81/20.69  | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | BETA: splitting (4201) gives:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |   (4202)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | ALPHA: (4202) implies:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |   (4203)  op(e2, e0) = e2
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4102), (4203), (function-axioms) are
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |   (4204)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | ALPHA: (4204) implies:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |   (4205)  op(e1, e0) = e1
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4129), (4205), (function-axioms) are
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #467.
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.69  | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | |   (4206)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.81/20.69  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.81/20.69  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.81/20.69  | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | BETA: splitting (4206) gives:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |   (4207)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | ALPHA: (4207) implies:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |   (4208)  op(e2, e0) = e2
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4102), (4208), (function-axioms) are
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |   (4209)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 146.81/20.69  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | BETA: splitting (4209) gives:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | |   (4210)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | | ALPHA: (4210) implies:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | |   (4211)  op(e1, e0) = e1
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4129), (4211), (function-axioms) are
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #467.
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.69  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |   (4212)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | ALPHA: (4212) implies:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |   (4213)  op(e0, e0) = all_57_15
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |   (4214)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4214) gives:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |   (4215)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3233), (4104), (4213), (4215),
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |            #900.
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |   (4216)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (4108), (4109), (4110), (4216),
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | |            #454.
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | Case 2:
% 146.81/20.70  | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | |   (4217)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 146.81/20.70  | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 146.81/20.70  | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.81/20.70  | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 146.81/20.70  | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 146.81/20.70  | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 146.81/20.70  | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 146.81/20.70  | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 146.81/20.70  | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | ALPHA: (4217) implies:
% 146.81/20.70  | | | | | | | | | |   (4218)  op(e0, e0) = e0
% 146.81/20.70  | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | REF_CLOSE: (5), (4104), (4218), (function-axioms) are
% 146.81/20.70  | | | | | | | | | |            inconsistent by sub-proof #1043.
% 146.81/20.70  | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | 
% 146.81/20.70  | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | 
% 146.81/20.70  | | | | | | | End of split
% 146.81/20.70  | | | | | | | 
% 146.81/20.70  | | | | | | End of split
% 146.81/20.70  | | | | | | 
% 146.81/20.70  | | | | | End of split
% 146.81/20.70  | | | | | 
% 146.81/20.70  | | | | Case 2:
% 146.81/20.70  | | | | | 
% 146.81/20.70  | | | | |   (4219)  all_10_2 = e1
% 146.81/20.70  | | | | |   (4220)  ( ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 & op(e0,
% 146.81/20.70  | | | | |               e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 146.81/20.70  | | | | |             (all_10_1 = e2) & op(e0, e1) = all_10_1 & $i(all_10_1))
% 146.81/20.70  | | | | | 
% 146.81/20.70  | | | | | COMBINE_EQS: (308), (4219) imply:
% 146.81/20.70  | | | | |   (4221)  all_30_2 = e1
% 146.81/20.70  | | | | | 
% 146.81/20.70  | | | | | REDUCE: (349), (4219) imply:
% 146.81/20.70  | | | | |   (4222)   ~ (all_52_3 = e1)
% 146.81/20.70  | | | | | 
% 146.81/20.70  | | | | | REDUCE: (360), (4219) imply:
% 146.81/20.70  | | | | |   (4223)   ~ (all_52_7 = e1)
% 146.81/20.70  | | | | | 
% 146.81/20.70  | | | | | REDUCE: (367), (4219) imply:
% 146.81/20.70  | | | | |   (4224)   ~ (all_52_11 = e1)
% 146.81/20.70  | | | | | 
% 146.81/20.70  | | | | | REDUCE: (369), (4219) imply:
% 146.81/20.70  | | | | |   (4225)   ~ (all_52_13 = e1)
% 146.81/20.70  | | | | | 
% 146.81/20.70  | | | | | REDUCE: (370), (4219) imply:
% 146.81/20.70  | | | | |   (4226)   ~ (all_52_14 = e1)
% 146.81/20.70  | | | | | 
% 146.81/20.70  | | | | | REDUCE: (45), (4219) imply:
% 146.81/20.70  | | | | |   (4227)  op(e0, e0) = e1
% 146.81/20.70  | | | | | 
% 146.81/20.70  | | | | | BETA: splitting (209) gives:
% 146.81/20.70  | | | | | 
% 146.81/20.70  | | | | | Case 1:
% 146.81/20.70  | | | | | | 
% 146.81/20.70  | | | | | |   (4228)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 &
% 146.81/20.70  | | | | | |             op(e2, e0) = e1)
% 146.81/20.70  | | | | | | 
% 146.81/20.70  | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 146.81/20.70  | | | | | |            (4227), (4228), (function-axioms) are inconsistent by
% 146.81/20.70  | | | | | |            sub-proof #444.
% 146.81/20.70  | | | | | | 
% 146.81/20.70  | | | | | Case 2:
% 146.81/20.70  | | | | | | 
% 146.81/20.70  | | | | | |   (4229)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 &
% 146.81/20.70  | | | | | |             op(e0, e0) = e1)
% 146.81/20.70  | | | | | | 
% 146.81/20.70  | | | | | | BETA: splitting (4229) gives:
% 146.81/20.70  | | | | | | 
% 146.81/20.70  | | | | | | Case 1:
% 146.81/20.70  | | | | | | | 
% 146.81/20.70  | | | | | | |   (4230)  all_56_11 = e1 & op(e1, e0) = e1
% 146.81/20.70  | | | | | | | 
% 146.81/20.70  | | | | | | | ALPHA: (4230) implies:
% 146.81/20.70  | | | | | | |   (4231)  op(e1, e0) = e1
% 146.81/20.70  | | | | | | | 
% 146.81/20.70  | | | | | | | REF_CLOSE: (159), (4226), (4231), (function-axioms) are
% 146.81/20.70  | | | | | | |            inconsistent by sub-proof #961.
% 146.81/20.70  | | | | | | | 
% 146.81/20.70  | | | | | | Case 2:
% 146.81/20.70  | | | | | | | 
% 146.81/20.70  | | | | | | |   (4232)  all_56_15 = e1 & op(e0, e0) = e1
% 146.81/20.70  | | | | | | | 
% 146.81/20.70  | | | | | | | ALPHA: (4232) implies:
% 146.81/20.70  | | | | | | |   (4233)  all_56_15 = e1
% 146.81/20.70  | | | | | | | 
% 146.81/20.70  | | | | | | | BETA: splitting (52) gives:
% 146.81/20.70  | | | | | | | 
% 146.81/20.70  | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | 
% 146.81/20.70  | | | | | | | |   (4234)   ~ (all_14_2 = e0)
% 146.81/20.70  | | | | | | | | 
% 146.81/20.70  | | | | | | | | BETA: splitting (55) gives:
% 146.81/20.70  | | | | | | | | 
% 146.81/20.70  | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | 
% 146.81/20.70  | | | | | | | | |   (4235)   ~ (all_16_2 = e0)
% 146.81/20.70  | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | REDUCE: (327), (4235) imply:
% 146.81/20.70  | | | | | | | | |   (4236)   ~ (all_6_2 = e0)
% 146.81/20.70  | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | BETA: splitting (61) gives:
% 146.81/20.70  | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | |   (4237)   ~ (all_20_2 = e1)
% 146.81/20.70  | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | REDUCE: (282), (4237) imply:
% 146.81/20.70  | | | | | | | | | |   (4238)   ~ (all_6_2 = e1)
% 146.81/20.70  | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | BETA: splitting (198) gives:
% 146.81/20.70  | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | |   (4239)  all_54_5 = e3
% 146.81/20.70  | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | REF_CLOSE: (267), (372), (4239) are inconsistent by sub-proof
% 146.81/20.70  | | | | | | | | | | |            #443.
% 146.81/20.70  | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | Case 2:
% 146.81/20.70  | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | |   (4240)   ~ (all_54_5 = e3)
% 146.81/20.70  | | | | | | | | | | |   (4241)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 146.81/20.70  | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | BETA: splitting (4241) gives:
% 146.81/20.70  | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | |   (4242)  all_54_5 = e2
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | COMBINE_EQS: (267), (4242) imply:
% 146.81/20.70  | | | | | | | | | | | |   (4243)  all_6_2 = e2
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | SIMP: (4243) implies:
% 146.81/20.70  | | | | | | | | | | | |   (4244)  all_6_2 = e2
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | REDUCE: (347), (4244) imply:
% 146.81/20.70  | | | | | | | | | | | |   (4245)   ~ (all_52_1 = e2)
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | REDUCE: (350), (4244) imply:
% 146.81/20.70  | | | | | | | | | | | |   (4246)   ~ (all_52_4 = e2)
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | REDUCE: (356), (4244) imply:
% 146.81/20.70  | | | | | | | | | | | |   (4247)   ~ (all_52_9 = e2)
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | REDUCE: (358), (4244) imply:
% 146.81/20.70  | | | | | | | | | | | |   (4248)   ~ (all_52_13 = e2)
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | REDUCE: (372), (4244) imply:
% 146.81/20.70  | | | | | | | | | | | |   (4249)   ~ (e3 = e2)
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | REDUCE: (39), (4244) imply:
% 146.81/20.70  | | | | | | | | | | | |   (4250)  op(e2, e2) = e2
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | BETA: splitting (64) gives:
% 146.81/20.70  | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | |   (4251)   ~ (all_22_2 = e1)
% 146.81/20.70  | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | REDUCE: (320), (4251) imply:
% 146.81/20.70  | | | | | | | | | | | | |   (4252)   ~ (all_14_2 = e1)
% 146.81/20.70  | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | BETA: splitting (76) gives:
% 146.81/20.70  | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | |   (4253)   ~ (all_30_2 = e1)
% 146.81/20.70  | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | REDUCE: (4221), (4253) imply:
% 146.81/20.70  | | | | | | | | | | | | | |   (4254)  $false
% 146.81/20.70  | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | CLOSE: (4254) is inconsistent.
% 146.81/20.70  | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | Case 2:
% 146.81/20.70  | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | |   (4255)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0
% 146.81/20.70  | | | | | | | | | | | | | |             & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 146.81/20.70  | | | | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1)
% 146.81/20.70  | | | | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 146.81/20.70  | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 146.81/20.70  | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | |   (4256)   ~ (all_36_2 = e2)
% 146.81/20.70  | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | REDUCE: (304), (4256) imply:
% 146.81/20.70  | | | | | | | | | | | | | | |   (4257)   ~ (all_14_2 = e2)
% 146.81/20.70  | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 146.81/20.70  | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | |   (4258)  all_54_0 = e3
% 146.81/20.70  | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (4258) imply:
% 146.81/20.70  | | | | | | | | | | | | | | | |   (4259)  all_14_2 = e3
% 146.81/20.70  | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | SIMP: (4259) implies:
% 146.81/20.70  | | | | | | | | | | | | | | | |   (4260)  all_14_2 = e3
% 146.81/20.70  | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | REDUCE: (342), (4260) imply:
% 146.81/20.70  | | | | | | | | | | | | | | | |   (4261)   ~ (all_52_4 = e3)
% 146.81/20.70  | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | REDUCE: (344), (4260) imply:
% 146.81/20.70  | | | | | | | | | | | | | | | |   (4262)   ~ (all_52_8 = e3)
% 146.81/20.70  | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | REDUCE: (346), (4260) imply:
% 146.81/20.70  | | | | | | | | | | | | | | | |   (4263)   ~ (all_52_12 = e3)
% 146.81/20.70  | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | REDUCE: (51), (4260) imply:
% 146.81/20.70  | | | | | | | | | | | | | | | |   (4264)  op(e3, e3) = e3
% 146.81/20.70  | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 146.81/20.70  | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | |   (4265)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.81/20.70  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.81/20.70  | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.81/20.70  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 146.81/20.70  | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 146.81/20.70  | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 146.81/20.70  | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 146.81/20.70  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 146.81/20.70  | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 146.81/20.70  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 146.81/20.70  | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.81/20.70  | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | BETA: splitting (4265) gives:
% 146.81/20.70  | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | |   (4266)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.81/20.70  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.81/20.70  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (166), (4227), (4245), (4250), (4266),
% 146.81/20.70  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.70  | | | | | | | | | | | | | | | | | |            #442.
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | |   (4267)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 146.81/20.70  | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.81/20.70  | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | BETA: splitting (4267) gives:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |   (4268)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (371), (4261), (4268),
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |            #1086.
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |   (4269)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | BETA: splitting (4269) gives:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |   (4270)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | ALPHA: (4270) implies:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |   (4271)  op(e3, e3) = e2
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4264), (4271), (function-axioms) are
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |   (4272)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4227), (4250), (4272), (function-axioms) are
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #441.
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | End of split
% 146.81/20.70  | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.70  | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | |   (4273)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.81/20.70  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.81/20.70  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.81/20.70  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.81/20.70  | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.81/20.70  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 146.81/20.70  | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 146.81/20.70  | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 146.81/20.70  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 146.81/20.70  | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 146.81/20.70  | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 146.81/20.70  | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.81/20.70  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.81/20.70  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.81/20.70  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.81/20.70  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.81/20.70  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.70  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.81/20.70  | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | BETA: splitting (4273) gives:
% 146.81/20.70  | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | |   (4274)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.81/20.70  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.81/20.70  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.81/20.70  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.70  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (167), (168), (4247), (4262), (4263),
% 146.81/20.70  | | | | | | | | | | | | | | | | | |            (4274), (function-axioms) are inconsistent by
% 146.81/20.70  | | | | | | | | | | | | | | | | | |            sub-proof #440.
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.70  | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.70  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | |   (4275)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.81/20.71  | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.81/20.71  | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 146.81/20.71  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 146.81/20.71  | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.81/20.71  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.81/20.71  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | BETA: splitting (4275) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4276)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4264), (4276), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4277)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (4277) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |   (4278)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | ALPHA: (4278) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |   (4279)  op(e2, e0) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4248), (4279), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |   (4280)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4280) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |   (4281)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4281) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |   (4282)  op(e1, e0) = e1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4226), (4282), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |   (4283)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4283) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |   (4284)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (371), (374), (4250), (4264),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |            (4284), (function-axioms) are inconsistent by
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1075.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | |   (4285)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | REF_CLOSE: (278), (4234), (4252), (4257), (4285) are
% 146.81/20.71  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | |   (4286)  all_36_2 = e2
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | COMBINE_EQS: (304), (4286) imply:
% 146.81/20.71  | | | | | | | | | | | | | | |   (4287)  all_14_2 = e2
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | SIMP: (4287) implies:
% 146.81/20.71  | | | | | | | | | | | | | | |   (4288)  all_14_2 = e2
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | REDUCE: (51), (4288) imply:
% 146.81/20.71  | | | | | | | | | | | | | | |   (4289)  op(e3, e3) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | |   (4290)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 146.81/20.71  | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | BETA: splitting (4290) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | |   (4291)  all_56_9 = e2 & op(e3, e0) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | ALPHA: (4291) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | |   (4292)  all_56_9 = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | |   (4293)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | BETA: splitting (4293) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4294)  all_56_0 = e1 & op(e3, e3) = e1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | ALPHA: (4294) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4295)  op(e3, e3) = e1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4289), (4295), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4296)  all_56_1 = e1 & op(e3, e2) = e1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | ALPHA: (4296) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4297)  all_56_1 = e1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |   (4298)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (4289), (4297), (4298),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            #1071.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |   (4299)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4299) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |   (4300)  all_56_4 = e0 & op(e3, e1) = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4300) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |   (4301)  all_56_4 = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (235),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |            (4289), (4292), (4301), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #651.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |   (4302)  all_56_9 = e0 & op(e3, e0) = e0
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4292), (4302) are inconsistent by sub-proof
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |            #746.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | |   (4303)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | BETA: splitting (4303) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4304)  all_56_4 = e1 & op(e3, e1) = e1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | ALPHA: (4304) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4305)  op(e3, e1) = e1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |   (4306)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (4289), (4292), (4306), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #653.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |   (4307)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4307) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |   (4308)  all_56_4 = e3 & op(e3, e1) = e3
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4308) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |   (4309)  op(e3, e1) = e3
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (4305), (4309), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #439.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |   (4310)  all_56_9 = e3 & op(e3, e0) = e3
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4310) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |   (4311)  all_56_9 = e3
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4292), (4311) are inconsistent by sub-proof
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | |            #964.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4312)  all_56_9 = e1 & op(e3, e0) = e1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4292), (4312) are inconsistent by sub-proof
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |            #656.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | |   (4313)  all_56_10 = e2 & op(e2, e0) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | ALPHA: (4313) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | |   (4314)  op(e2, e0) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4248), (4314), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | |   (4315)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 146.81/20.71  | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | BETA: splitting (4315) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | |   (4316)  all_56_11 = e2 & op(e1, e0) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | ALPHA: (4316) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | |   (4317)  op(e1, e0) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | |   (4318)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (229), (231),
% 146.81/20.71  | | | | | | | | | | | | | | | | | |            (235), (4247), (4289), (4318), (function-axioms)
% 146.81/20.71  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #1061.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | |   (4319)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 146.81/20.71  | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | BETA: splitting (4319) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4320)  all_56_8 = e2 & op(e1, e1) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | ALPHA: (4320) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4321)  op(e1, e1) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (4321), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4322)  all_56_14 = e2 & op(e0, e1) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | ALPHA: (4322) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4323)  all_56_14 = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4324)  op(e0, e1) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |              e2, e1, e0, simplifying with (156), (4324) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4325)  all_52_11 = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (159), (4317) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4326)  all_52_14 = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | REDUCE: (366), (4326) imply:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | |   (4327)   ~ (all_4_2 = e2)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (4220) gives:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |   (4328)   ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_10_1 & $i(all_10_0) &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | ALPHA: (4328) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |   (4329)  op(e0, e1) = all_10_1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (124), (132),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (133), (134), (139), (156), (158), (163), (164),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (190), (207), (212),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (213), (214), (219), (224), (225), (227), (228),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (230), (234), (237), (238), (247), (371), (4223),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (4227), (4245), (4246), (4247), (4248), (4255),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (4289), (4317), (4323), (4324), (4329),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            #421.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |   (4330)   ~ (all_10_1 = e2) & op(e0, e1) = all_10_1 &
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | ALPHA: (4330) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |   (4331)  op(e0, e1) = all_10_1
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (124), (132),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (133), (134), (139), (156), (158), (163), (164),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (190), (207), (212),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (213), (214), (219), (224), (225), (227), (228),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (230), (234), (237), (238), (247), (371), (4223),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (4227), (4245), (4246), (4247), (4248), (4255),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (4289), (4317), (4323), (4324), (4331),
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | |            #421.
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | |   (4332)  all_56_15 = e2 & op(e0, e0) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | ALPHA: (4332) implies:
% 146.81/20.71  | | | | | | | | | | | | | | | | |   (4333)  op(e0, e0) = e2
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4227), (4333), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #978.
% 146.81/20.71  | | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | |   (4334)  all_22_2 = e1
% 146.81/20.71  | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | COMBINE_EQS: (320), (4334) imply:
% 146.81/20.71  | | | | | | | | | | | | |   (4335)  all_14_2 = e1
% 146.81/20.71  | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | REDUCE: (336), (4335) imply:
% 146.81/20.71  | | | | | | | | | | | | |   (4336)   ~ (all_52_1 = e1)
% 146.81/20.71  | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | REDUCE: (342), (4335) imply:
% 146.81/20.71  | | | | | | | | | | | | |   (4337)   ~ (all_52_4 = e1)
% 146.81/20.71  | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | REDUCE: (346), (4335) imply:
% 146.81/20.71  | | | | | | | | | | | | |   (4338)   ~ (all_52_12 = e1)
% 146.81/20.71  | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | REDUCE: (51), (4335) imply:
% 146.81/20.71  | | | | | | | | | | | | |   (4339)  op(e3, e3) = e1
% 146.81/20.71  | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | BETA: splitting (225) gives:
% 146.81/20.71  | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | |   (4340)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 146.81/20.71  | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 146.81/20.71  | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | BETA: splitting (4340) gives:
% 146.81/20.71  | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | Case 1:
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | |   (4341)  all_56_1 = e1 & op(e3, e2) = e1
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | REF_CLOSE: (169), (4337), (4341), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | |            inconsistent by sub-proof #420.
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | |   (4342)  all_56_3 = e1 & op(e2, e2) = e1
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | ALPHA: (4342) implies:
% 146.81/20.71  | | | | | | | | | | | | | | |   (4343)  op(e2, e2) = e1
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | | REF_CLOSE: (6), (4250), (4343), (function-axioms) are
% 146.81/20.71  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 146.81/20.71  | | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | | End of split
% 146.81/20.71  | | | | | | | | | | | | | | 
% 146.81/20.71  | | | | | | | | | | | | | Case 2:
% 146.81/20.71  | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | |   (4344)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 146.81/20.72  | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 146.81/20.72  | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | BETA: splitting (4344) gives:
% 146.81/20.72  | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | Case 1:
% 146.81/20.72  | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | |   (4345)  all_56_7 = e1 & op(e1, e2) = e1
% 146.81/20.72  | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | ALPHA: (4345) implies:
% 146.81/20.72  | | | | | | | | | | | | | | |   (4346)  op(e1, e2) = e1
% 146.81/20.72  | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | Case 1:
% 146.81/20.72  | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | |   (4347)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 146.81/20.72  | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 146.81/20.72  | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | BETA: splitting (4347) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | |   (4348)  all_56_2 = e1 & op(e2, e3) = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | ALPHA: (4348) implies:
% 146.81/20.72  | | | | | | | | | | | | | | | | |   (4349)  op(e2, e3) = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (4336), (4349), (function-axioms) are
% 146.81/20.72  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1177.
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | |   (4350)  all_56_3 = e1 & op(e2, e2) = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | ALPHA: (4350) implies:
% 146.81/20.72  | | | | | | | | | | | | | | | | |   (4351)  op(e2, e2) = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4250), (4351), (function-axioms) are
% 146.81/20.72  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | End of split
% 146.81/20.72  | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | Case 2:
% 146.81/20.72  | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | |   (4352)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 146.81/20.72  | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 146.81/20.72  | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | BETA: splitting (4352) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | |   (4353)  all_56_5 = e1 & op(e2, e1) = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | ALPHA: (4353) implies:
% 146.81/20.72  | | | | | | | | | | | | | | | | |   (4354)  all_56_5 = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | |   (4355)  op(e2, e1) = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | |   (4356)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.81/20.72  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.81/20.72  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 146.81/20.72  | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | BETA: splitting (4356) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |   (4357)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (142), (161), (162), (166), (4227), (4245),
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |            (4346), (4357), (function-axioms) are inconsistent
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |            by sub-proof #419.
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |   (4358)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (4358) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |   (4359)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (4227), (4359),
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |            #438.
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |   (4360)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4227), (4250), (4339), (4360),
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |            #418.
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.72  | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | |   (4361)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.81/20.72  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 146.81/20.72  | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 146.81/20.72  | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.81/20.72  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | BETA: splitting (4361) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |   (4362)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (4362) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |   (4363)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4247), (4339), (4363), (function-axioms)
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #417.
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |   (4364)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4364) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |   (4365)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4365) implies:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |   (4366)  op(e2, e1) = e2
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4247), (4366), (function-axioms) are
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |   (4367)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4367) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |   (4368)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4368) implies:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |   (4369)  op(e2, e2) = e0
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4250), (4369), (function-axioms) are
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |   (4370)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) &
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4370) implies:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |   (4371)  op(e1, e0) = all_57_13
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |   (4372)  op(e1, e1) = e0
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |   (4373)  op(e3, e0) = e3
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |              all_57_13, e0, e1, simplifying with (159), (4371)
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |   (4374)  all_57_13 = all_52_14
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e0,
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (4372) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |   (4375)  all_4_2 = e0
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (161), (4346) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |   (4376)  all_52_6 = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (164), (4355) gives:
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | |   (4377)  all_52_9 = e1
% 146.81/20.72  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (167), (4373) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | |   (4378)  all_52_12 = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (4376) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | |   (4379)   ~ (all_52_2 = e1)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (4378) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | |   (4380)   ~ (all_52_4 = e3)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (4376) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | |   (4381)   ~ (all_52_14 = e1)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (4378) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | |   (4382)   ~ (all_52_8 = e3)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (4377) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | |   (4383)   ~ (all_52_13 = e1)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4247), (4377) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | |   (4384)   ~ (e2 = e1)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (374), (4375) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | |   (4385)   ~ (e3 = e0)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (4375) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | |   (4386)   ~ (e2 = e0)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | |   (4387)  all_54_1 = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (4380), (4387) are inconsistent by
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #988.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | |   (4388)   ~ (all_54_1 = e3)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | |   (4389)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | |   (4390)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4390) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (4391)  all_56_4 = e3 & op(e3, e1) = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4391) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (4392)  op(e3, e1) = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4382), (4392), (function-axioms) are
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (4393)  all_56_5 = e3 & op(e2, e1) = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4393) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (4394)  all_56_5 = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4354), (4394) are inconsistent by sub-proof
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | |            #416.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | |   (4395)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4395) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (4396)  all_56_8 = e3 & op(e1, e1) = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4396) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (4397)  op(e1, e1) = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4372), (4397), (function-axioms) are
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (4398)  all_56_14 = e3 & op(e0, e1) = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4398) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (4399)  all_56_14 = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4389) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4400)  all_54_1 = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (4246), (4400) are inconsistent by
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #768.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4401)   ~ (all_54_1 = e2)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4402)  all_54_1 = e1 | all_54_1 = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4403)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (4250), (4380), (4403),
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1165.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4404)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4404) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4405)  all_56_7 = e3 & op(e1, e2) = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4405) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4406)  all_56_7 = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4407)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4407) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4408)  all_56_6 = e1 & op(e1, e3) = e1
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4408) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4409)  op(e1, e3) = e1
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4379), (4409), (function-axioms) are
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4345) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4410)  all_56_7 = e1
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4406), (4410) are inconsistent by sub-proof
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1106.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4411)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4411) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4412)  all_56_8 = e1 & op(e1, e1) = e1
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4412) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4413)  op(e1, e1) = e1
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4372), (4413), (function-axioms) are
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4414)  all_56_11 = e1 & op(e1, e0) = e1
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4414) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4415)  op(e1, e0) = e1
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4226), (4415), (function-axioms) are
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4416)  all_56_13 = e3 & op(e0, e2) = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4416) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4417)  all_56_13 = e3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4418)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4418) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4419)  all_56_12 = e2 & op(e0, e3) = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4419) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4420)  all_56_12 = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4421)  all_56_15 = e0 & op(e0, e0) = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4421) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4422)  op(e0, e0) = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (159), (163), (167), (209), (4225),
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4226), (4373), (4422), (function-axioms) are
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #510.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4423)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4423) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4424)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4402) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4425)  all_54_1 = e1
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (4425) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4426)  all_52_4 = e1
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4337), (4426) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4427)  $false
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4427) is inconsistent.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4428)  all_54_1 = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (4428) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4429)  all_52_4 = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (4429) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4430)   ~ (all_52_7 = e0)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4430) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4431)   ~ (all_52_7 = e0)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (157), (4399), (4420), (4424), (4431),
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #621.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4432)  all_56_13 = e2 & op(e0, e2) = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4432) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4433)  all_56_13 = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4250), (4433), (function-axioms) are inconsistent
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1104.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4434)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4434) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4435)  all_56_14 = e2 & op(e0, e1) = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4435) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4436)  all_56_14 = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4399), (4436) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4437)  e3 = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4437) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4438)  e3 = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4417), (4438) imply:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4439)  all_56_13 = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4250), (4439), (function-axioms) are inconsistent
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1104.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4440)  all_56_15 = e2 & op(e0, e0) = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4440) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4441)  op(e0, e0) = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4227), (4441), (function-axioms) are
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #978.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |   (4442)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | BETA: splitting (4442) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |   (4443)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4339), (4443), (function-axioms) are
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |   (4444)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4444) gives:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | |   (4445)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4445) implies:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | |   (4446)  op(e2, e0) = e2
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4248), (4446), (function-axioms) are
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.75  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |   (4447)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4447) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |   (4448)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4448) implies:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |   (4449)  op(e1, e0) = e1
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4226), (4449), (function-axioms) are
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |   (4450)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4450) implies:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |   (4451)  op(e0, e0) = all_57_15
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |   (4452)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4452) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |   (4453)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4453) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |   (4454)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4454) implies:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |   (4455)  op(e2, e2) = e3
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4250), (4455), (function-axioms) are
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |   (4456)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4456) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (4457)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4457) implies:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (4458)  op(e1, e1) = e3
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (374), (4458), (function-axioms) are
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (4459)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4459) implies:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |   (4460)  op(e3, e3) = e2
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4339), (4460), (function-axioms) are
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |   (4461)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4461) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |   (4462)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4462) implies:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |   (4463)  op(e1, e1) = e2
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (4463), (function-axioms) are
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |   (4464)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4227), (4250), (4451), (4464),
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | |            #415.
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | |   (4465)  all_56_10 = e1 & op(e2, e0) = e1
% 146.81/20.76  | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | ALPHA: (4465) implies:
% 146.81/20.76  | | | | | | | | | | | | | | | | |   (4466)  all_56_10 = e1
% 146.81/20.76  | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 146.81/20.76  | | | | | | | | | | | | | | | | |            (4227), (4466), (function-axioms) are inconsistent
% 146.81/20.76  | | | | | | | | | | | | | | | | |            by sub-proof #445.
% 146.81/20.76  | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | |   (4467)  all_56_13 = e1 & op(e0, e2) = e1
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | REF_CLOSE: (157), (4223), (4467), (function-axioms) are
% 146.81/20.76  | | | | | | | | | | | | | | |            inconsistent by sub-proof #414.
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | |   (4468)  all_54_5 = e1 | all_54_5 = e0
% 146.81/20.76  | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | REF_CLOSE: (267), (4236), (4238), (4468) are inconsistent by
% 146.81/20.76  | | | | | | | | | | | |            sub-proof #866.
% 146.81/20.76  | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | |   (4469)  all_20_2 = e1
% 146.81/20.76  | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | COMBINE_EQS: (282), (4469) imply:
% 146.81/20.76  | | | | | | | | | |   (4470)  all_6_2 = e1
% 146.81/20.76  | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | REDUCE: (347), (4470) imply:
% 146.81/20.76  | | | | | | | | | |   (4471)   ~ (all_52_1 = e1)
% 146.81/20.76  | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | REDUCE: (350), (4470) imply:
% 146.81/20.76  | | | | | | | | | |   (4472)   ~ (all_52_4 = e1)
% 146.81/20.76  | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | REDUCE: (372), (4470) imply:
% 146.81/20.76  | | | | | | | | | |   (4473)   ~ (e3 = e1)
% 146.81/20.76  | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | REDUCE: (39), (4470) imply:
% 146.81/20.76  | | | | | | | | | |   (4474)  op(e2, e2) = e1
% 146.81/20.76  | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | BETA: splitting (64) gives:
% 146.81/20.76  | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | |   (4475)   ~ (all_22_2 = e1)
% 146.81/20.76  | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | REDUCE: (320), (4475) imply:
% 146.81/20.76  | | | | | | | | | | |   (4476)   ~ (all_14_2 = e1)
% 146.81/20.76  | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | BETA: splitting (230) gives:
% 146.81/20.76  | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | |   (4477)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 146.81/20.76  | | | | | | | | | | | |             & op(e2, e3) = e1)
% 146.81/20.76  | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | BETA: splitting (4477) gives:
% 146.81/20.76  | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | |   (4478)  all_56_0 = e1 & op(e3, e3) = e1
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | ALPHA: (4478) implies:
% 146.81/20.76  | | | | | | | | | | | | |   (4479)  op(e3, e3) = e1
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | REF_CLOSE: (51), (4476), (4479), (function-axioms) are
% 146.81/20.76  | | | | | | | | | | | | |            inconsistent by sub-proof #413.
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | |   (4480)  all_56_2 = e1 & op(e2, e3) = e1
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | ALPHA: (4480) implies:
% 146.81/20.76  | | | | | | | | | | | | |   (4481)  op(e2, e3) = e1
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | REF_CLOSE: (166), (4471), (4481), (function-axioms) are
% 146.81/20.76  | | | | | | | | | | | | |            inconsistent by sub-proof #1177.
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | |   (4482)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 146.81/20.76  | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 146.81/20.76  | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | BETA: splitting (4482) gives:
% 146.81/20.76  | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | |   (4483)  all_56_6 = e1 & op(e1, e3) = e1
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | ALPHA: (4483) implies:
% 146.81/20.76  | | | | | | | | | | | | |   (4484)  all_56_6 = e1
% 146.81/20.76  | | | | | | | | | | | | |   (4485)  op(e1, e3) = e1
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | BETA: splitting (231) gives:
% 146.81/20.76  | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | |   (4486)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 146.81/20.76  | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 146.81/20.76  | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | BETA: splitting (4486) gives:
% 146.81/20.76  | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | |   (4487)  all_56_0 = e1 & op(e3, e3) = e1
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | ALPHA: (4487) implies:
% 146.81/20.76  | | | | | | | | | | | | | | |   (4488)  op(e3, e3) = e1
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (228), (232),
% 146.81/20.76  | | | | | | | | | | | | | | |            (234), (4484), (4485), (4488), (function-axioms)
% 146.81/20.76  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #547.
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | |   (4489)  all_56_1 = e1 & op(e3, e2) = e1
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | REF_CLOSE: (169), (4472), (4489), (function-axioms) are
% 146.81/20.76  | | | | | | | | | | | | | | |            inconsistent by sub-proof #420.
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | End of split
% 146.81/20.76  | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | |   (4490)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 146.81/20.76  | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 146.81/20.76  | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | BETA: splitting (4490) gives:
% 146.81/20.76  | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | |   (4491)  all_56_4 = e1 & op(e3, e1) = e1
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | ALPHA: (4491) implies:
% 146.81/20.76  | | | | | | | | | | | | | | |   (4492)  all_56_4 = e1
% 146.81/20.76  | | | | | | | | | | | | | | |   (4493)  op(e3, e1) = e1
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 146.81/20.76  | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (4485) gives:
% 146.81/20.76  | | | | | | | | | | | | | | |   (4494)  all_52_2 = e1
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 146.81/20.76  | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (4493) gives:
% 146.81/20.76  | | | | | | | | | | | | | | |   (4495)  all_52_8 = e1
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | REDUCE: (140), (4494) imply:
% 146.81/20.76  | | | | | | | | | | | | | | |   (4496)   ~ (all_52_14 = e1)
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | REDUCE: (122), (4495) imply:
% 146.81/20.76  | | | | | | | | | | | | | | |   (4497)   ~ (all_52_9 = e1)
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | SIMP: (4497) implies:
% 146.81/20.76  | | | | | | | | | | | | | | |   (4498)   ~ (all_52_9 = e1)
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | REDUCE: (344), (4495) imply:
% 146.81/20.76  | | | | | | | | | | | | | | |   (4499)   ~ (all_14_2 = e1)
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | REDUCE: (361), (4495) imply:
% 146.81/20.76  | | | | | | | | | | | | | | |   (4500)   ~ (all_4_2 = e1)
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | SIMP: (4500) implies:
% 146.81/20.76  | | | | | | | | | | | | | | |   (4501)   ~ (all_4_2 = e1)
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | |   (4502)  all_54_10 = e3
% 146.81/20.76  | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | REF_CLOSE: (334), (374), (4502) are inconsistent by sub-proof
% 146.81/20.76  | | | | | | | | | | | | | | | |            #1173.
% 146.81/20.76  | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | |   (4503)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 146.81/20.76  | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | BETA: splitting (4503) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | |   (4504)  all_54_10 = e2
% 146.81/20.76  | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (4504) are inconsistent by sub-proof
% 146.81/20.76  | | | | | | | | | | | | | | | | |            #1168.
% 146.81/20.76  | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | |   (4505)   ~ (all_54_10 = e2)
% 146.81/20.76  | | | | | | | | | | | | | | | | |   (4506)  all_54_10 = e1 | all_54_10 = e0
% 146.81/20.76  | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | |   (4507)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 146.81/20.76  | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 146.81/20.76  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | BETA: splitting (4507) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |   (4508)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | ALPHA: (4508) implies:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |   (4509)  op(e3, e3) = e3
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |   (4510)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |               = e3) & op(e0, e0) = all_57_15 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |   (4511)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = all_57_14 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |   (4512)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = all_57_12 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | BETA: splitting (4506) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4513)  all_54_10 = e1
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (4501), (4513) are inconsistent by
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |            sub-proof #1167.
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4514)  all_54_10 = e0
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (4514) imply:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4515)  all_4_2 = e0
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | SIMP: (4515) implies:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4516)  all_4_2 = e0
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (4516) imply:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4517)   ~ (all_52_9 = e0)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (364), (4516) imply:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4518)   ~ (all_52_11 = e0)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (4516) imply:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4519)   ~ (e2 = e0)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (4501), (4516) imply:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4520)   ~ (e1 = e0)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (4516) imply:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4521)  op(e1, e1) = e0
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e3,
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (51), (4509) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4522)  all_14_2 = e3
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (336), (4522) imply:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4523)   ~ (all_52_1 = e3)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (342), (4522) imply:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4524)   ~ (all_52_4 = e3)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | REDUCE: (346), (4522) imply:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | |   (4525)   ~ (all_52_12 = e3)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |   (4526)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4526) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |   (4527)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4527) gives:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |   (4528)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4510), (4511), (4528), (function-axioms) are
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #814.
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.76  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |   (4529)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4510), (4512), (4529), (function-axioms) are
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |   (4530)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4530) gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |   (4531)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (169), (4521), (4524), (4531),
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |            #412.
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |   (4532)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (168), (4227), (4493), (4509),
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |            (4532), (function-axioms) are inconsistent by
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #411.
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |   (4533)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4533) gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |   (4534)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4534) gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |   (4535)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4535) gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4536)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4536) implies:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4537)  op(e3, e1) = e3
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (4493), (4537), (function-axioms) are
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #439.
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4538)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4538) implies:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4539)  op(e3, e3) = e1
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4509), (4539), (function-axioms) are
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |   (4540)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4540) gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4541)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4541) implies:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4542)   ~ (all_57_12 = e1)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4543)  op(e2, e2) = all_57_12
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4474), (4542), (4543), (function-axioms) are
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4544)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4525), (4544), (function-axioms) are
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1081.
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |   (4545)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4545) gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |   (4546)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4509), (4546), (function-axioms) are
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |   (4547)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4547) gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4548)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4548) implies:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4549)   ~ (all_57_12 = e0)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4550)  op(e2, e0) = e2
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | |   (4551)  op(e2, e2) = all_57_12
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (4552)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4552) gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4553)  all_56_0 = e3 & op(e3, e3) = e3
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (163), (4550) gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4554)  all_52_13 = e2
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (4474), (4551)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4555)  all_57_12 = e1
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (4554) imply:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4556)   ~ (all_52_1 = e2)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (4554) imply:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4557)   ~ (all_52_9 = e2)
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4558)  all_54_6 = e3
% 146.81/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (4558) imply:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4559)  all_52_9 = e3
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (4559) imply:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4560)  op(e2, e1) = e3
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4561)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4561) gives:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4562)  all_56_4 = e2 & op(e3, e1) = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4562) implies:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4563)  all_56_4 = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4492), (4563) are inconsistent by sub-proof
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #980.
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4564)  all_56_5 = e2 & op(e2, e1) = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4564) implies:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4565)  op(e2, e1) = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4560), (4565), (function-axioms) are
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1135.
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4566)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4566) gives:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4567)  all_56_8 = e2 & op(e1, e1) = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4567) implies:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4568)  op(e1, e1) = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4521), (4568), (function-axioms) are
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4569)  all_56_14 = e2 & op(e0, e1) = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4569) implies:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4570)  all_56_14 = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4571)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (4509), (4556), (4571),
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #410.
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4572)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4572) gives:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4573)  all_56_6 = e2 & op(e1, e3) = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4573) implies:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4574)  all_56_6 = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4484), (4574) are inconsistent by sub-proof
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1172.
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4575)  all_56_12 = e2 & op(e0, e3) = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4575) implies:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4576)  all_56_12 = e2
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4577)  all_56_15 = e0 & op(e0, e0) = e0
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4233), (4577) are inconsistent by sub-proof
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #409.
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4578)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4578) implies:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4579)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4579) gives:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4580)  all_56_12 = e0 & op(e0, e3) = e0
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4576), (4580) are inconsistent by sub-proof
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #871.
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4581)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4581) gives:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4582)  all_56_13 = e0 & op(e0, e2) = e0
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4582) implies:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4583)  all_56_13 = e0
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4584)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4584) gives:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4585)  all_56_12 = e3 & op(e0, e3) = e3
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4576), (4585) are inconsistent by sub-proof
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #575.
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4586)  all_56_13 = e3 & op(e0, e2) = e3
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4583), (4586) are inconsistent by sub-proof
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #408.
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4587)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4587) gives:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4588)  all_56_14 = e3 & op(e0, e1) = e3
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4570), (4588) are inconsistent by sub-proof
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #424.
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4589)  all_56_15 = e3 & op(e0, e0) = e3
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4589) implies:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4590)  all_56_15 = e3
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4233), (4590) imply:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4591)  e3 = e1
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4591) imply:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4592)  $false
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4592) is inconsistent.
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4593)  all_56_14 = e0 & op(e0, e1) = e0
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4570), (4593) are inconsistent by sub-proof
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1101.
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4594)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4594) gives:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4595)  all_54_6 = e2
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (4595) imply:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4596)  all_52_9 = e2
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4557), (4596) imply:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4597)  $false
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4597) is inconsistent.
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4598)  all_54_6 = e1 | all_54_6 = e0
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (4498), (4517), (4598) are inconsistent by
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #649.
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4599)  all_56_2 = e3 & op(e2, e3) = e3
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (4523), (4599), (function-axioms) are
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #917.
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (4600)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4600) gives:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4601)  all_56_6 = e3 & op(e1, e3) = e3
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4601) implies:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4602)  all_56_6 = e3
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4484), (4602) imply:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4603)  e3 = e1
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (4603) imply:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4604)  $false
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4604) is inconsistent.
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4605)  all_56_12 = e3 & op(e0, e3) = e3
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4605) implies:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4606)  all_56_12 = e3
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (166), (228),
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (4471), (4509), (4606),
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            #407.
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.26/20.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |   (4607)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4607) gives:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (4608)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4608) implies:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (4609)  op(e1, e0) = e1
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4226), (4609), (function-axioms) are
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (4610)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4610) implies:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (4611)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4611) gives:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4612)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4509), (4511), (4512), (4612),
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            #406.
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4613)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (156), (4518), (4521), (4613),
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            #756.
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |   (4614)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | ALPHA: (4614) implies:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |   (4615)  op(e2, e2) = e2
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4474), (4615), (function-axioms) are
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | |   (4616)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.29/20.78  | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.29/20.78  | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.29/20.78  | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | BETA: splitting (4616) gives:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |   (4617)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | ALPHA: (4617) implies:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |   (4618)  op(e1, e1) = e1
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (334), (4501), (4506), (4618),
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |            #897.
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |   (4619)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | ALPHA: (4619) implies:
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |   (4620)  op(e0, e0) = e0
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4227), (4620), (function-axioms) are
% 147.29/20.78  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 147.29/20.78  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | Case 2:
% 147.29/20.78  | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | |   (4621)  all_56_9 = e1 & op(e3, e0) = e1
% 147.29/20.78  | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | ALPHA: (4621) implies:
% 147.29/20.78  | | | | | | | | | | | | | | |   (4622)  all_56_9 = e1
% 147.29/20.78  | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 147.29/20.78  | | | | | | | | | | | | | | |            (4227), (4622), (function-axioms) are inconsistent
% 147.29/20.78  | | | | | | | | | | | | | | |            by sub-proof #496.
% 147.29/20.78  | | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | Case 2:
% 147.29/20.78  | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | |   (4623)  all_56_12 = e1 & op(e0, e3) = e1
% 147.29/20.78  | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | ALPHA: (4623) implies:
% 147.29/20.78  | | | | | | | | | | | | |   (4624)  op(e0, e3) = e1
% 147.29/20.78  | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | REF_CLOSE: (158), (4222), (4624), (function-axioms) are
% 147.29/20.78  | | | | | | | | | | | | |            inconsistent by sub-proof #405.
% 147.29/20.78  | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | End of split
% 147.29/20.78  | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | Case 2:
% 147.29/20.78  | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | |   (4625)  all_22_2 = e1
% 147.29/20.78  | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | COMBINE_EQS: (320), (4625) imply:
% 147.29/20.78  | | | | | | | | | | |   (4626)  all_14_2 = e1
% 147.29/20.78  | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | SIMP: (4626) implies:
% 147.29/20.78  | | | | | | | | | | |   (4627)  all_14_2 = e1
% 147.29/20.78  | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | REDUCE: (338), (4627) imply:
% 147.29/20.78  | | | | | | | | | | |   (4628)   ~ (all_52_2 = e1)
% 147.29/20.78  | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | REDUCE: (51), (4627) imply:
% 147.29/20.78  | | | | | | | | | | |   (4629)  op(e3, e3) = e1
% 147.29/20.78  | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | BETA: splitting (237) gives:
% 147.29/20.78  | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | Case 1:
% 147.29/20.78  | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | |   (4630)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 147.29/20.78  | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 147.29/20.78  | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.29/20.78  | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.29/20.78  | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.29/20.78  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 147.29/20.78  | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 147.29/20.78  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.29/20.78  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 147.29/20.78  | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 147.29/20.78  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.29/20.78  | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.29/20.78  | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.29/20.78  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 147.29/20.78  | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 147.29/20.78  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 147.29/20.78  | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | REF_CLOSE: (6), (8), (4474), (4629), (4630),
% 147.29/20.78  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.78  | | | | | | | | | | | |            #898.
% 147.29/20.78  | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | Case 2:
% 147.29/20.78  | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | |   (4631)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.29/20.78  | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.29/20.78  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.29/20.78  | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.29/20.78  | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.29/20.78  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.29/20.78  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.29/20.78  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.29/20.78  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.29/20.78  | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.29/20.78  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.29/20.78  | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.29/20.78  | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.29/20.78  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.29/20.78  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.29/20.78  | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.29/20.78  | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | BETA: splitting (4631) gives:
% 147.29/20.78  | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | Case 1:
% 147.29/20.78  | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | |   (4632)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 147.29/20.78  | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 147.29/20.78  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.29/20.78  | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.29/20.78  | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.29/20.78  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 147.29/20.78  | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 147.29/20.78  | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.29/20.78  | | | | | | | | | | | | | 
% 147.29/20.78  | | | | | | | | | | | | | ALPHA: (4632) implies:
% 147.29/20.78  | | | | | | | | | | | | |   (4633)  op(e1, e1) = e1
% 147.29/20.78  | | | | | | | | | | | | |   (4634)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 147.29/20.78  | | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 147.29/20.78  | | | | | | | | | | | | |             $i(all_57_12))
% 147.29/20.78  | | | | | | | | | | | | |   (4635)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 147.29/20.78  | | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 147.29/20.78  | | | | | | | | | | | | |             $i(all_57_10))
% 147.29/20.78  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (36), (45), (116), (140), (156),
% 147.29/20.79  | | | | | | | | | | | | |            (159), (162), (163), (164), (193), (237), (238),
% 147.29/20.79  | | | | | | | | | | | | |            (334), (366), (367), (371), (374), (4227), (4474),
% 147.29/20.79  | | | | | | | | | | | | |            (4628), (4629), (4633), (4634), (4635),
% 147.29/20.79  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.79  | | | | | | | | | | | | |            #398.
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | |   (4636)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 147.29/20.79  | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 147.29/20.79  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.29/20.79  | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.29/20.79  | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.29/20.79  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.29/20.79  | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.29/20.79  | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | ALPHA: (4636) implies:
% 147.29/20.79  | | | | | | | | | | | | |   (4637)  op(e0, e0) = e0
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | REF_CLOSE: (4), (4227), (4637), (function-axioms) are
% 147.29/20.79  | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | End of split
% 147.29/20.79  | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | End of split
% 147.29/20.79  | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | End of split
% 147.29/20.79  | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | End of split
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | |   (4638)  all_16_2 = e0
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | COMBINE_EQS: (327), (4638) imply:
% 147.29/20.79  | | | | | | | | |   (4639)  all_6_2 = e0
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | SIMP: (4639) implies:
% 147.29/20.79  | | | | | | | | |   (4640)  all_6_2 = e0
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | REDUCE: (347), (4640) imply:
% 147.29/20.79  | | | | | | | | |   (4641)   ~ (all_52_1 = e0)
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | REDUCE: (350), (4640) imply:
% 147.29/20.79  | | | | | | | | |   (4642)   ~ (all_52_4 = e0)
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | REDUCE: (352), (4640) imply:
% 147.29/20.79  | | | | | | | | |   (4643)   ~ (all_52_6 = e0)
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | REDUCE: (354), (4640) imply:
% 147.29/20.79  | | | | | | | | |   (4644)   ~ (all_52_7 = e0)
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | REDUCE: (356), (4640) imply:
% 147.29/20.79  | | | | | | | | |   (4645)   ~ (all_52_9 = e0)
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | REDUCE: (358), (4640) imply:
% 147.29/20.79  | | | | | | | | |   (4646)   ~ (all_52_13 = e0)
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | REDUCE: (372), (4640) imply:
% 147.29/20.79  | | | | | | | | |   (4647)   ~ (e3 = e0)
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | REDUCE: (39), (4640) imply:
% 147.29/20.79  | | | | | | | | |   (4648)  op(e2, e2) = e0
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | BETA: splitting (64) gives:
% 147.29/20.79  | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | |   (4649)   ~ (all_22_2 = e1)
% 147.29/20.79  | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | REDUCE: (320), (4649) imply:
% 147.29/20.79  | | | | | | | | | |   (4650)   ~ (all_14_2 = e1)
% 147.29/20.79  | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | BETA: splitting (76) gives:
% 147.29/20.79  | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | |   (4651)   ~ (all_30_2 = e1)
% 147.29/20.79  | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | REDUCE: (4221), (4651) imply:
% 147.29/20.79  | | | | | | | | | | |   (4652)  $false
% 147.29/20.79  | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | CLOSE: (4652) is inconsistent.
% 147.29/20.79  | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | |   (4653)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0
% 147.29/20.79  | | | | | | | | | | |             & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 147.29/20.79  | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1)
% 147.29/20.79  | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 147.29/20.79  | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | BETA: splitting (84) gives:
% 147.29/20.79  | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | |   (4654)   ~ (all_36_2 = e2)
% 147.29/20.79  | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | REDUCE: (304), (4654) imply:
% 147.29/20.79  | | | | | | | | | | | |   (4655)   ~ (all_14_2 = e2)
% 147.29/20.79  | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | BETA: splitting (203) gives:
% 147.29/20.79  | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | |   (4656)  all_54_0 = e3
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | COMBINE_EQS: (278), (4656) imply:
% 147.29/20.79  | | | | | | | | | | | | |   (4657)  all_14_2 = e3
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | SIMP: (4657) implies:
% 147.29/20.79  | | | | | | | | | | | | |   (4658)  all_14_2 = e3
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | REDUCE: (338), (4658) imply:
% 147.29/20.79  | | | | | | | | | | | | |   (4659)   ~ (all_52_2 = e3)
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | REDUCE: (342), (4658) imply:
% 147.29/20.79  | | | | | | | | | | | | |   (4660)   ~ (all_52_4 = e3)
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | REDUCE: (344), (4658) imply:
% 147.29/20.79  | | | | | | | | | | | | |   (4661)   ~ (all_52_8 = e3)
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | REDUCE: (346), (4658) imply:
% 147.29/20.79  | | | | | | | | | | | | |   (4662)   ~ (all_52_12 = e3)
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | REDUCE: (51), (4658) imply:
% 147.29/20.79  | | | | | | | | | | | | |   (4663)  op(e3, e3) = e3
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | BETA: splitting (238) gives:
% 147.29/20.79  | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | |   (4664)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.29/20.79  | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.29/20.79  | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.29/20.79  | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.29/20.79  | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.29/20.79  | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.29/20.79  | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.29/20.79  | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.29/20.79  | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 147.29/20.79  | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 147.29/20.79  | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 147.29/20.79  | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.29/20.79  | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.29/20.79  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 147.29/20.79  | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 147.29/20.79  | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 147.29/20.79  | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 147.29/20.79  | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 147.29/20.79  | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 147.29/20.79  | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 147.29/20.79  | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.29/20.79  | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.29/20.79  | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | BETA: splitting (4664) gives:
% 147.29/20.79  | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | |   (4665)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.29/20.79  | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.29/20.79  | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.29/20.79  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.29/20.79  | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.29/20.79  | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.29/20.79  | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.29/20.79  | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.29/20.79  | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.29/20.79  | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.29/20.79  | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | BETA: splitting (4665) gives:
% 147.29/20.79  | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | |   (4666)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.29/20.79  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.29/20.79  | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.29/20.79  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | BETA: splitting (4666) gives:
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4667)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.29/20.79  | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.29/20.79  | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | ALPHA: (4667) implies:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4668)  op(e1, e1) = e3
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (374), (4668), (function-axioms) are
% 147.29/20.79  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4669)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.29/20.79  | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.29/20.79  | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | ALPHA: (4669) implies:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4670)  op(e0, e0) = e3
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4227), (4670), (function-axioms) are
% 147.29/20.79  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | End of split
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | |   (4671)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.29/20.79  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.29/20.79  | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.29/20.79  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.29/20.79  | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (4227), (4648), (4671),
% 147.29/20.79  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.79  | | | | | | | | | | | | | | | |            #397.
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | End of split
% 147.29/20.79  | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | |   (4672)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.29/20.79  | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.29/20.79  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.29/20.79  | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.29/20.79  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.29/20.79  | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 147.29/20.79  | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.29/20.79  | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.29/20.79  | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.29/20.79  | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 147.29/20.79  | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.29/20.79  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.29/20.79  | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.29/20.79  | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.29/20.79  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.29/20.79  | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.29/20.79  | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | BETA: splitting (4672) gives:
% 147.29/20.79  | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | |   (4673)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.29/20.79  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.29/20.79  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.29/20.79  | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.29/20.79  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.29/20.79  | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (371), (4660), (4673),
% 147.29/20.79  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.79  | | | | | | | | | | | | | | | |            #1086.
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | |   (4674)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.29/20.79  | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.29/20.79  | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 147.29/20.79  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 147.29/20.79  | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.29/20.79  | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.29/20.79  | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (4227), (4648), (4663), (4674),
% 147.29/20.79  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.79  | | | | | | | | | | | | | | | |            #395.
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | End of split
% 147.29/20.79  | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | End of split
% 147.29/20.79  | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | |   (4675)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.29/20.79  | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.29/20.79  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.29/20.79  | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.29/20.79  | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.29/20.79  | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.29/20.79  | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.29/20.79  | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.29/20.79  | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.29/20.79  | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.29/20.79  | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.29/20.79  | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 147.29/20.79  | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 147.29/20.79  | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 147.29/20.79  | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.29/20.79  | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 147.29/20.79  | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.29/20.79  | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 147.29/20.79  | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 147.29/20.79  | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.29/20.79  | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.29/20.79  | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.29/20.79  | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.29/20.79  | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.29/20.79  | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.29/20.79  | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.29/20.79  | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.29/20.79  | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.29/20.79  | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.29/20.79  | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.29/20.79  | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.29/20.79  | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.29/20.79  | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.29/20.79  | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.29/20.79  | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.29/20.79  | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.29/20.79  | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.29/20.79  | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.29/20.79  | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.29/20.79  | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.29/20.79  | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.29/20.79  | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.29/20.79  | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.29/20.79  | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.29/20.79  | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.29/20.79  | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.29/20.79  | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | BETA: splitting (4675) gives:
% 147.29/20.79  | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | |   (4676)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.29/20.79  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.29/20.79  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.29/20.79  | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.29/20.79  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.29/20.79  | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.29/20.79  | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.29/20.79  | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.29/20.79  | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.29/20.79  | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.29/20.79  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.29/20.79  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.29/20.79  | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.29/20.79  | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.29/20.79  | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.29/20.79  | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.29/20.79  | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | BETA: splitting (4676) gives:
% 147.29/20.79  | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | |   (4677)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.29/20.79  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.29/20.79  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.29/20.79  | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.29/20.79  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.29/20.79  | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.29/20.79  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (4661), (4663), (4677),
% 147.29/20.79  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.79  | | | | | | | | | | | | | | | |            #860.
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | |   (4678)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.29/20.79  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.29/20.79  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.29/20.79  | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.29/20.79  | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 147.29/20.79  | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 147.29/20.79  | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 147.29/20.79  | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 147.29/20.79  | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 147.29/20.79  | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | BETA: splitting (4678) gives:
% 147.29/20.79  | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4679)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.29/20.79  | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.29/20.79  | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.29/20.79  | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.29/20.79  | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | ALPHA: (4679) implies:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4680)   ~ (all_57_12 = e1)
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4681)   ~ (all_57_8 = e0)
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4682)  op(e0, e1) = all_57_8
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4683)  op(e2, e1) = e2
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4684)  op(e2, e2) = all_57_12
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 147.29/20.79  | | | | | | | | | | | | | | | | |              all_57_8, e1, e0, simplifying with (156), (4682)
% 147.29/20.79  | | | | | | | | | | | | | | | | |              gives:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4685)  all_57_8 = all_52_11
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 147.29/20.79  | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (164), (4683) gives:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4686)  all_52_9 = e2
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 147.29/20.79  | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (4648), (4684)
% 147.29/20.79  | | | | | | | | | | | | | | | | |              gives:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4687)  all_57_12 = e0
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | REDUCE: (4681), (4685) imply:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4688)   ~ (all_52_11 = e0)
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | REDUCE: (4680), (4687) imply:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4689)   ~ (e1 = e0)
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | REDUCE: (145), (4686) imply:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4690)   ~ (all_52_1 = e2)
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | REDUCE: (117), (4686) imply:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4691)   ~ (all_52_11 = e2)
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | SIMP: (4691) implies:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4692)   ~ (all_52_11 = e2)
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | REDUCE: (116), (4686) imply:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4693)   ~ (all_52_13 = e2)
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | SIMP: (4693) implies:
% 147.29/20.79  | | | | | | | | | | | | | | | | |   (4694)   ~ (all_52_13 = e2)
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 147.29/20.79  | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | |   (4695)  all_54_7 = e3
% 147.29/20.79  | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (4695) imply:
% 147.29/20.79  | | | | | | | | | | | | | | | | | |   (4696)  all_52_13 = e3
% 147.29/20.79  | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | SIMP: (4696) implies:
% 147.29/20.79  | | | | | | | | | | | | | | | | | |   (4697)  all_52_13 = e3
% 147.29/20.79  | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | REDUCE: (144), (4697) imply:
% 147.29/20.79  | | | | | | | | | | | | | | | | | |   (4698)   ~ (all_52_1 = e3)
% 147.29/20.79  | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | REDUCE: (109), (4697) imply:
% 147.29/20.79  | | | | | | | | | | | | | | | | | |   (4699)   ~ (all_52_14 = e3)
% 147.29/20.79  | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | SIMP: (4699) implies:
% 147.29/20.79  | | | | | | | | | | | | | | | | | |   (4700)   ~ (all_52_14 = e3)
% 147.29/20.79  | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | |   (4701)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 147.29/20.79  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (166), (4648), (4698), (4701),
% 147.29/20.79  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.79  | | | | | | | | | | | | | | | | | | |            #690.
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | |   (4702)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 147.29/20.79  | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | BETA: splitting (4702) gives:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | |   (4703)  all_56_5 = e3 & op(e2, e1) = e3
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | ALPHA: (4703) implies:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | |   (4704)  op(e2, e1) = e3
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4683), (4704), (function-axioms) are
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1135.
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | |   (4705)  all_56_10 = e3 & op(e2, e0) = e3
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | ALPHA: (4705) implies:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | |   (4706)  all_56_10 = e3
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | |   (4707)  op(e2, e0) = e3
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | |   (4708)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (166), (4648), (4690), (4708),
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | |            #613.
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | |   (4709)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 147.29/20.79  | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4709) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | |   (4710)  all_56_5 = e2 & op(e2, e1) = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4710) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | |   (4711)  all_56_5 = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | |   (4712)  all_56_15 = e0 & op(e0, e0) = e0
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4712) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | |   (4713)  op(e0, e0) = e0
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4227), (4713), (function-axioms) are
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | |   (4714)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4714) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | |   (4715)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | |   (4716)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4716) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (4717)  all_56_2 = e1 & op(e2, e3) = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4717) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (4718)  all_56_2 = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (4719)  op(e2, e3) = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4720)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (168), (220),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (4648), (4661), (4706),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            (4707), (4720), (function-axioms) are inconsistent
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #674.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (4721)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4721) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4722)  all_56_8 = e3 & op(e1, e1) = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4722) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4723)  op(e1, e1) = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (374), (4723), (function-axioms) are
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4724)  all_56_14 = e3 & op(e0, e1) = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4724) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4725)  all_56_14 = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4726)  op(e0, e1) = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4727)  all_54_4 = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (4698), (4727) are inconsistent by
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #843.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4728)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4728) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4729)  all_54_4 = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (4690), (4729) are inconsistent by
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1175.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4730)  all_54_4 = e1 | all_54_4 = e0
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4731)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4731) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4732)  all_56_12 = e2 & op(e0, e3) = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4732) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4733)  all_56_12 = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (157), (4644), (4715), (4725), (4733),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #621.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4734)  all_56_13 = e2 & op(e0, e2) = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4734) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4735)  all_56_13 = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4736)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (4648), (4660), (4736),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #596.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4737)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4737) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4738)  all_56_7 = e3 & op(e1, e2) = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4738) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4739)  all_56_7 = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4740)  all_54_14 = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4740) imply:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4741)  all_52_11 = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4741) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4742)  all_52_11 = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (4742) imply:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4743)   ~ (all_52_3 = e3)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (4742) imply:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4744)   ~ (all_52_7 = e3)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4745)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4745) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4746)  all_56_1 = e1 & op(e3, e2) = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4746) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4747)  all_56_1 = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4748)  all_54_13 = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (4744), (4748) are inconsistent by
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #845.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4749)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4220) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4750)   ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 &
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_10_1 & $i(all_10_0) &
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4750) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4751)  op(e0, e1) = all_10_1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (139), (140), (143),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (148), (164), (166), (191), (192), (195),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (222), (233), (247), (248), (249),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (268), (4223), (4226), (4641), (4644),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4645), (4648), (4653), (4659), (4663), (4700),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4707), (4711), (4719), (4725), (4726), (4730),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4743), (4747), (4749), (4751), (function-axioms)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #390.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4752)   ~ (all_10_1 = e2) & op(e0, e1) = all_10_1 &
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4752) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4753)  op(e0, e1) = all_10_1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (139), (140), (143),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (148), (164), (166), (191), (192), (195),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (222), (233), (247), (248), (249),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (258), (268), (4223), (4226), (4641), (4644),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4645), (4648), (4653), (4659), (4663), (4700),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4707), (4711), (4719), (4725), (4726), (4730),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4743), (4747), (4749), (4753), (function-axioms)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #390.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4754)  all_56_3 = e1 & op(e2, e2) = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4754) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4755)  all_56_3 = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4756)  op(e2, e2) = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (166), (220), (222),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4706), (4718), (4719), (4755), (4756),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #387.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4757)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4757) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4758)  all_56_7 = e1 & op(e1, e2) = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4758) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4759)  all_56_7 = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4739), (4759) imply:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4760)  e3 = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4760) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4761)  e3 = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4706), (4761) imply:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4762)  all_56_10 = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4227), (4762), (function-axioms) are inconsistent
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #445.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4763)  all_56_13 = e1 & op(e0, e2) = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4763) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4764)  all_56_13 = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (207), (4227), (4715),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (4725), (4764), (function-axioms) are inconsistent
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #386.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4765)   ~ (all_54_14 = e3)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (246), (4765) imply:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4766)   ~ (all_52_11 = e3)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (4726), (4766), (function-axioms) are
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1147.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4767)  all_56_13 = e3 & op(e0, e2) = e3
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4735), (4767) are inconsistent by sub-proof
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #563.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4768)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4768) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4769)  all_56_14 = e2 & op(e0, e1) = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4769) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4770)  op(e0, e1) = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (4692), (4770), (function-axioms) are
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1092.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4771)  all_56_15 = e2 & op(e0, e0) = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4771) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (4772)  op(e0, e0) = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4227), (4772), (function-axioms) are
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #978.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (4773)  all_56_3 = e1 & op(e2, e2) = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4773) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (4774)  op(e2, e2) = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4680), (4684), (4774), (function-axioms) are
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1014.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | |   (4775)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4775) gives:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (4776)  all_56_5 = e1 & op(e2, e1) = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4711), (4776) are inconsistent by sub-proof
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            #482.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (4777)  all_56_10 = e1 & op(e2, e0) = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4777) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (4778)  all_56_10 = e1
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            (4227), (4778), (function-axioms) are inconsistent
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #445.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | |   (4779)  all_56_10 = e2 & op(e2, e0) = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4779) implies:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | |   (4780)  op(e2, e0) = e2
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4707), (4780), (function-axioms) are
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #854.
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | | End of split
% 147.29/20.80  | | | | | | | | | | | | | | | | | | 
% 147.29/20.80  | | | | | | | | | | | | | | | | | Case 2:
% 147.29/20.80  | | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | | |   (4781)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 147.39/20.80  | | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (4225), (4646), (4694), (4781) are
% 147.39/20.80  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #449.
% 147.39/20.80  | | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | | End of split
% 147.39/20.80  | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | Case 2:
% 147.39/20.80  | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | |   (4782)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.39/20.80  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.39/20.80  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.39/20.80  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.39/20.80  | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.39/20.80  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.39/20.80  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.39/20.80  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.39/20.80  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.39/20.80  | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (4662), (4782), (function-axioms) are
% 147.39/20.80  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1081.
% 147.39/20.80  | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | End of split
% 147.39/20.80  | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | End of split
% 147.39/20.80  | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | Case 2:
% 147.39/20.80  | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | |   (4783)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.39/20.80  | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.39/20.80  | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.39/20.80  | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.39/20.80  | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.39/20.80  | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.39/20.80  | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.39/20.80  | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.39/20.80  | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 147.39/20.80  | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 147.39/20.80  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.39/20.80  | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.39/20.80  | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 147.39/20.80  | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 147.39/20.80  | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 147.39/20.80  | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 147.39/20.80  | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 147.39/20.80  | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.39/20.80  | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 147.39/20.80  | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.39/20.80  | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 147.39/20.80  | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 147.39/20.80  | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.39/20.80  | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.39/20.80  | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.39/20.80  | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.39/20.80  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.39/20.80  | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.39/20.80  | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.39/20.80  | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.39/20.80  | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.39/20.80  | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.39/20.80  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.39/20.80  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.39/20.80  | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.39/20.80  | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.39/20.80  | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.39/20.80  | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.39/20.80  | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.39/20.80  | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | BETA: splitting (4783) gives:
% 147.39/20.80  | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | Case 1:
% 147.39/20.80  | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | |   (4784)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.39/20.80  | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.39/20.80  | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.39/20.80  | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.39/20.80  | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.39/20.80  | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.39/20.80  | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.39/20.80  | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.39/20.80  | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.39/20.80  | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4663), (4784), (function-axioms) are
% 147.39/20.80  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 147.39/20.80  | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | Case 2:
% 147.39/20.80  | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | |   (4785)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.39/20.80  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.39/20.80  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.39/20.80  | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.39/20.80  | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.39/20.80  | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.39/20.80  | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.39/20.80  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.39/20.80  | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.39/20.80  | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.39/20.80  | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.39/20.80  | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.39/20.80  | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.39/20.80  | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.39/20.80  | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.39/20.80  | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.39/20.80  | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.39/20.80  | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.39/20.80  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.39/20.80  | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.39/20.80  | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.39/20.80  | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.39/20.80  | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.39/20.80  | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.39/20.80  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.39/20.80  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.39/20.80  | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.39/20.80  | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.39/20.80  | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.39/20.80  | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.39/20.80  | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.39/20.80  | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | BETA: splitting (4785) gives:
% 147.39/20.80  | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | Case 1:
% 147.39/20.80  | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | |   (4786)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.39/20.80  | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.39/20.80  | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.39/20.80  | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.39/20.80  | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.39/20.80  | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | | ALPHA: (4786) implies:
% 147.39/20.80  | | | | | | | | | | | | | | | | |   (4787)   ~ (all_57_12 = e0)
% 147.39/20.80  | | | | | | | | | | | | | | | | |   (4788)  op(e2, e2) = all_57_12
% 147.39/20.80  | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (4648), (4787), (4788), (function-axioms) are
% 147.39/20.80  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 147.39/20.80  | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | Case 2:
% 147.39/20.80  | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | |   (4789)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.39/20.80  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.39/20.80  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.39/20.80  | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.39/20.80  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.39/20.80  | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.39/20.80  | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.39/20.80  | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.39/20.80  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.39/20.80  | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.39/20.80  | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.39/20.80  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.39/20.80  | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.39/20.80  | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.39/20.80  | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | | BETA: splitting (4789) gives:
% 147.39/20.80  | | | | | | | | | | | | | | | | | 
% 147.39/20.80  | | | | | | | | | | | | | | | | | Case 1:
% 147.39/20.80  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | |   (4790)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | ALPHA: (4790) implies:
% 147.39/20.81  | | | | | | | | | | | | | | | | | |   (4791)  op(e1, e0) = e1
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4226), (4791), (function-axioms) are
% 147.39/20.81  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | |   (4792)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.39/20.81  | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.39/20.81  | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | ALPHA: (4792) implies:
% 147.39/20.81  | | | | | | | | | | | | | | | | | |   (4793)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.39/20.81  | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.39/20.81  | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | BETA: splitting (4793) gives:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |   (4794)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | BETA: splitting (4794) gives:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |   (4795)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | ALPHA: (4795) implies:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |   (4796)  op(e2, e2) = e3
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4648), (4796), (function-axioms) are
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |   (4797)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (374), (4663), (4797),
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |            #1077.
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |   (4798)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | BETA: splitting (4798) gives:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |   (4799)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | ALPHA: (4799) implies:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |   (4800)  op(e1, e1) = e2
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (4800), (function-axioms) are
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |   (4801)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (4648), (4663), (4801),
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | |            #824.
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | |   (4802)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 147.39/20.81  | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | REF_CLOSE: (278), (4234), (4650), (4655), (4802) are
% 147.39/20.81  | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 147.39/20.81  | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | |   (4803)  all_36_2 = e2
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | COMBINE_EQS: (304), (4803) imply:
% 147.39/20.81  | | | | | | | | | | | |   (4804)  all_14_2 = e2
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | SIMP: (4804) implies:
% 147.39/20.81  | | | | | | | | | | | |   (4805)  all_14_2 = e2
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | COMBINE_EQS: (280), (4805) imply:
% 147.39/20.81  | | | | | | | | | | | |   (4806)  all_44_2 = e2
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | REDUCE: (342), (4805) imply:
% 147.39/20.81  | | | | | | | | | | | |   (4807)   ~ (all_52_4 = e2)
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | REDUCE: (344), (4805) imply:
% 147.39/20.81  | | | | | | | | | | | |   (4808)   ~ (all_52_8 = e2)
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | REDUCE: (51), (4805) imply:
% 147.39/20.81  | | | | | | | | | | | |   (4809)  op(e3, e3) = e2
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | BETA: splitting (237) gives:
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | |   (4810)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 147.39/20.81  | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 147.39/20.81  | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.39/20.81  | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.39/20.81  | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.39/20.81  | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 147.39/20.81  | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 147.39/20.81  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.39/20.81  | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 147.39/20.81  | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 147.39/20.81  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.39/20.81  | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.39/20.81  | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.39/20.81  | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 147.39/20.81  | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 147.39/20.81  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 147.39/20.81  | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (157), (161), (169), (224), (4643),
% 147.39/20.81  | | | | | | | | | | | | |            (4644), (4809), (4810), (function-axioms) are
% 147.39/20.81  | | | | | | | | | | | | |            inconsistent by sub-proof #385.
% 147.39/20.81  | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | |   (4811)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.39/20.81  | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.39/20.81  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.39/20.81  | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.39/20.81  | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.39/20.81  | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.39/20.81  | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.39/20.81  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.39/20.81  | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.39/20.81  | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.39/20.81  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.39/20.81  | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.39/20.81  | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.39/20.81  | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.39/20.81  | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.39/20.81  | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.39/20.81  | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | BETA: splitting (4811) gives:
% 147.39/20.81  | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | |   (4812)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 147.39/20.81  | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 147.39/20.81  | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.39/20.81  | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.39/20.81  | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.39/20.81  | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 147.39/20.81  | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 147.39/20.81  | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.39/20.81  | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | ALPHA: (4812) implies:
% 147.39/20.81  | | | | | | | | | | | | | |   (4813)  op(e1, e1) = e1
% 147.39/20.81  | | | | | | | | | | | | | |   (4814)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15
% 147.39/20.81  | | | | | | | | | | | | | |               = e1) & op(e0, e0) = all_57_15 &
% 147.39/20.81  | | | | | | | | | | | | | |             $i(all_57_15))
% 147.39/20.81  | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | BETA: splitting (4814) gives:
% 147.39/20.81  | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | |   (4815)  all_57_8 = e0 & op(e0, e1) = e0
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | ALPHA: (4815) implies:
% 147.39/20.81  | | | | | | | | | | | | | | |   (4816)  op(e0, e1) = e0
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 147.39/20.81  | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (156), (4816) gives:
% 147.39/20.81  | | | | | | | | | | | | | | |   (4817)  all_52_11 = e0
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 147.39/20.81  | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (4813) gives:
% 147.39/20.81  | | | | | | | | | | | | | | |   (4818)  all_4_2 = e1
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | REDUCE: (138), (4817) imply:
% 147.39/20.81  | | | | | | | | | | | | | | |   (4819)   ~ (all_52_3 = e0)
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | REDUCE: (120), (4817) imply:
% 147.39/20.81  | | | | | | | | | | | | | | |   (4820)   ~ (all_52_8 = e0)
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | REDUCE: (361), (4818) imply:
% 147.39/20.81  | | | | | | | | | | | | | | |   (4821)   ~ (all_52_8 = e1)
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | REDUCE: (4224), (4817) imply:
% 147.39/20.81  | | | | | | | | | | | | | | |   (4822)   ~ (e1 = e0)
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | REDUCE: (371), (4818) imply:
% 147.39/20.81  | | | | | | | | | | | | | | |   (4823)   ~ (e2 = e1)
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | |   (4824)  all_54_2 = e3
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (4824) imply:
% 147.39/20.81  | | | | | | | | | | | | | | | |   (4825)  all_52_8 = e3
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | REDUCE: (133), (4825) imply:
% 147.39/20.81  | | | | | | | | | | | | | | | |   (4826)   ~ (all_52_4 = e3)
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | REDUCE: (122), (4825) imply:
% 147.39/20.81  | | | | | | | | | | | | | | | |   (4827)   ~ (all_52_9 = e3)
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | SIMP: (4827) implies:
% 147.39/20.81  | | | | | | | | | | | | | | | |   (4828)   ~ (all_52_9 = e3)
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | |   (4829)  all_54_1 = e3
% 147.39/20.81  | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (4829) imply:
% 147.39/20.81  | | | | | | | | | | | | | | | | |   (4830)  all_52_4 = e3
% 147.39/20.81  | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | REDUCE: (4826), (4830) imply:
% 147.39/20.81  | | | | | | | | | | | | | | | | |   (4831)  $false
% 147.39/20.81  | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | CLOSE: (4831) is inconsistent.
% 147.39/20.81  | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | |   (4832)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 147.39/20.81  | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 147.39/20.81  | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | |   (4833)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | BETA: splitting (4833) gives:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |   (4834)  all_56_0 = e0 & op(e3, e3) = e0
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | ALPHA: (4834) implies:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |   (4835)  op(e3, e3) = e0
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4809), (4835), (function-axioms) are
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |   (4836)  all_56_2 = e0 & op(e2, e3) = e0
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | ALPHA: (4836) implies:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |   (4837)  all_56_2 = e0
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (221), (222),
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |            (223), (4648), (4828), (4837), (function-axioms)
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #646.
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | |   (4838)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 147.39/20.81  | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | BETA: splitting (4838) gives:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |   (4839)  all_56_6 = e0 & op(e1, e3) = e0
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | ALPHA: (4839) implies:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |   (4840)  op(e1, e3) = e0
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (96), (169), (271), (4642), (4806), (4807),
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |            (4832), (4840), (function-axioms) are inconsistent
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |            by sub-proof #604.
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |   (4841)  all_56_12 = e0 & op(e0, e3) = e0
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | ALPHA: (4841) implies:
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |   (4842)  op(e0, e3) = e0
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4819), (4842), (function-axioms) are
% 147.39/20.81  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 147.39/20.81  | | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | |   (4843)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | | REF_CLOSE: (270), (4808), (4820), (4821), (4843) are
% 147.39/20.81  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #382.
% 147.39/20.81  | | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | |   (4844)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 147.39/20.81  | | | | | | | | | | | | | | |           $i(all_57_15)
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | ALPHA: (4844) implies:
% 147.39/20.81  | | | | | | | | | | | | | | |   (4845)   ~ (all_57_15 = e1)
% 147.39/20.81  | | | | | | | | | | | | | | |   (4846)  op(e0, e0) = all_57_15
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | | REF_CLOSE: (4227), (4845), (4846), (function-axioms) are
% 147.39/20.81  | | | | | | | | | | | | | | |            inconsistent by sub-proof #940.
% 147.39/20.81  | | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | |   (4847)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 147.39/20.81  | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 147.39/20.81  | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.39/20.81  | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.39/20.81  | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.39/20.81  | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.39/20.81  | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.39/20.81  | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 147.39/20.81  | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | ALPHA: (4847) implies:
% 147.39/20.81  | | | | | | | | | | | | | |   (4848)  op(e0, e0) = e0
% 147.39/20.81  | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | | REF_CLOSE: (4), (4227), (4848), (function-axioms) are
% 147.39/20.81  | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 147.39/20.81  | | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | |   (4849)  all_22_2 = e1
% 147.39/20.81  | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | COMBINE_EQS: (320), (4849) imply:
% 147.39/20.81  | | | | | | | | | |   (4850)  all_14_2 = e1
% 147.39/20.81  | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | REDUCE: (336), (4850) imply:
% 147.39/20.81  | | | | | | | | | |   (4851)   ~ (all_52_1 = e1)
% 147.39/20.81  | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | REDUCE: (338), (4850) imply:
% 147.39/20.81  | | | | | | | | | |   (4852)   ~ (all_52_2 = e1)
% 147.39/20.81  | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | REDUCE: (51), (4850) imply:
% 147.39/20.81  | | | | | | | | | |   (4853)  op(e3, e3) = e1
% 147.39/20.81  | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | BETA: splitting (237) gives:
% 147.39/20.81  | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | |   (4854)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 147.39/20.81  | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 147.39/20.81  | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.39/20.81  | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.39/20.81  | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.39/20.81  | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 147.39/20.81  | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 147.39/20.81  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.39/20.81  | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 147.39/20.81  | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 147.39/20.81  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.39/20.81  | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.39/20.81  | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.39/20.81  | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 147.39/20.81  | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 147.39/20.81  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 147.39/20.81  | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | REF_CLOSE: (5), (8), (4648), (4853), (4854),
% 147.39/20.81  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.39/20.81  | | | | | | | | | | |            #602.
% 147.39/20.81  | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | |   (4855)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.39/20.81  | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.39/20.81  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.39/20.81  | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.39/20.81  | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.39/20.81  | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.39/20.81  | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.39/20.81  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.39/20.81  | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.39/20.81  | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.39/20.81  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.39/20.81  | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.39/20.81  | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.39/20.81  | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.39/20.81  | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.39/20.81  | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.39/20.81  | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | BETA: splitting (4855) gives:
% 147.39/20.81  | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | Case 1:
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | |   (4856)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 147.39/20.81  | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 147.39/20.81  | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.39/20.81  | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.39/20.81  | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.39/20.81  | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 147.39/20.81  | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 147.39/20.81  | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | ALPHA: (4856) implies:
% 147.39/20.81  | | | | | | | | | | | |   (4857)  op(e1, e1) = e1
% 147.39/20.81  | | | | | | | | | | | |   (4858)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 147.39/20.81  | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 147.39/20.81  | | | | | | | | | | | |             $i(all_57_12))
% 147.39/20.81  | | | | | | | | | | | |   (4859)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 147.39/20.81  | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 147.39/20.81  | | | | | | | | | | | |             $i(all_57_10))
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (116),
% 147.39/20.81  | | | | | | | | | | | |            (140), (156), (159), (162), (163), (164), (166),
% 147.39/20.81  | | | | | | | | | | | |            (193), (205), (210), (211), (221), (237), (238),
% 147.39/20.81  | | | | | | | | | | | |            (334), (362), (366), (367), (371), (374), (4227),
% 147.39/20.81  | | | | | | | | | | | |            (4851), (4852), (4853), (4857), (4858), (4859),
% 147.39/20.81  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.39/20.81  | | | | | | | | | | | |            #381.
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | |   (4860)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 147.39/20.81  | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 147.39/20.81  | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.39/20.81  | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.39/20.81  | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.39/20.81  | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.39/20.81  | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.39/20.81  | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | ALPHA: (4860) implies:
% 147.39/20.81  | | | | | | | | | | | |   (4861)  op(e0, e0) = e0
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | | REF_CLOSE: (4), (4227), (4861), (function-axioms) are
% 147.39/20.81  | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 147.39/20.81  | | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | | 
% 147.39/20.81  | | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | | 
% 147.39/20.81  | | | | | | | | End of split
% 147.39/20.81  | | | | | | | | 
% 147.39/20.81  | | | | | | | Case 2:
% 147.39/20.81  | | | | | | | | 
% 147.39/20.82  | | | | | | | |   (4862)  all_14_2 = e0
% 147.39/20.82  | | | | | | | | 
% 147.39/20.82  | | | | | | | | REDUCE: (336), (4862) imply:
% 147.39/20.82  | | | | | | | |   (4863)   ~ (all_52_1 = e0)
% 147.39/20.82  | | | | | | | | 
% 147.39/20.82  | | | | | | | | REDUCE: (338), (4862) imply:
% 147.39/20.82  | | | | | | | |   (4864)   ~ (all_52_2 = e0)
% 147.39/20.82  | | | | | | | | 
% 147.39/20.82  | | | | | | | | REDUCE: (340), (4862) imply:
% 147.39/20.82  | | | | | | | |   (4865)   ~ (all_52_3 = e0)
% 147.39/20.82  | | | | | | | | 
% 147.39/20.82  | | | | | | | | REDUCE: (346), (4862) imply:
% 147.39/20.82  | | | | | | | |   (4866)   ~ (all_52_12 = e0)
% 147.39/20.82  | | | | | | | | 
% 147.39/20.82  | | | | | | | | REDUCE: (51), (4862) imply:
% 147.39/20.82  | | | | | | | |   (4867)  op(e3, e3) = e0
% 147.39/20.82  | | | | | | | | 
% 147.39/20.82  | | | | | | | | BETA: splitting (55) gives:
% 147.39/20.82  | | | | | | | | 
% 147.39/20.82  | | | | | | | | Case 1:
% 147.39/20.82  | | | | | | | | | 
% 147.39/20.82  | | | | | | | | |   (4868)   ~ (all_16_2 = e0)
% 147.39/20.82  | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | REDUCE: (327), (4868) imply:
% 147.39/20.82  | | | | | | | | |   (4869)   ~ (all_6_2 = e0)
% 147.39/20.82  | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | BETA: splitting (61) gives:
% 147.39/20.82  | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | Case 1:
% 147.39/20.82  | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | |   (4870)   ~ (all_20_2 = e1)
% 147.39/20.82  | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | REDUCE: (282), (4870) imply:
% 147.39/20.82  | | | | | | | | | |   (4871)   ~ (all_6_2 = e1)
% 147.39/20.82  | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | BETA: splitting (198) gives:
% 147.39/20.82  | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | Case 1:
% 147.39/20.82  | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | |   (4872)  all_54_5 = e3
% 147.39/20.82  | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | REF_CLOSE: (267), (372), (4872) are inconsistent by sub-proof
% 147.39/20.82  | | | | | | | | | | |            #443.
% 147.39/20.82  | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | Case 2:
% 147.39/20.82  | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | |   (4873)   ~ (all_54_5 = e3)
% 147.39/20.82  | | | | | | | | | | |   (4874)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 147.39/20.82  | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | BETA: splitting (4874) gives:
% 147.39/20.82  | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | Case 1:
% 147.39/20.82  | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | |   (4875)  all_54_5 = e2
% 147.39/20.82  | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | COMBINE_EQS: (267), (4875) imply:
% 147.39/20.82  | | | | | | | | | | | |   (4876)  all_6_2 = e2
% 147.39/20.82  | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | SIMP: (4876) implies:
% 147.39/20.82  | | | | | | | | | | | |   (4877)  all_6_2 = e2
% 147.39/20.82  | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | REDUCE: (347), (4877) imply:
% 147.39/20.82  | | | | | | | | | | | |   (4878)   ~ (all_52_1 = e2)
% 147.39/20.82  | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | REDUCE: (356), (4877) imply:
% 147.39/20.82  | | | | | | | | | | | |   (4879)   ~ (all_52_9 = e2)
% 147.39/20.82  | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | REDUCE: (358), (4877) imply:
% 147.39/20.82  | | | | | | | | | | | |   (4880)   ~ (all_52_13 = e2)
% 147.39/20.82  | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | REDUCE: (372), (4877) imply:
% 147.39/20.82  | | | | | | | | | | | |   (4881)   ~ (e3 = e2)
% 147.39/20.82  | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | REDUCE: (39), (4877) imply:
% 147.39/20.82  | | | | | | | | | | | |   (4882)  op(e2, e2) = e2
% 147.39/20.82  | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | BETA: splitting (238) gives:
% 147.39/20.82  | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | Case 1:
% 147.39/20.82  | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | |   (4883)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.39/20.82  | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.39/20.82  | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.39/20.82  | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.39/20.82  | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.39/20.82  | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.39/20.82  | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.39/20.82  | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.39/20.82  | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.39/20.82  | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.39/20.82  | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 147.39/20.82  | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 147.39/20.82  | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 147.39/20.82  | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 147.39/20.82  | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.39/20.82  | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.39/20.82  | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.39/20.82  | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 147.39/20.82  | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 147.39/20.82  | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 147.39/20.82  | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 147.39/20.82  | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 147.39/20.82  | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 147.39/20.82  | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 147.39/20.82  | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 147.39/20.82  | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 147.39/20.82  | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.39/20.82  | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.39/20.82  | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.39/20.82  | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | BETA: splitting (4883) gives:
% 147.39/20.82  | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | Case 1:
% 147.39/20.82  | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | |   (4884)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.39/20.82  | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.39/20.82  | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.39/20.82  | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.39/20.82  | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.39/20.82  | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.39/20.82  | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.39/20.82  | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.39/20.82  | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.39/20.82  | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.39/20.82  | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (166), (4227), (4878), (4882), (4884),
% 147.39/20.82  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.39/20.82  | | | | | | | | | | | | | |            #442.
% 147.39/20.82  | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | Case 2:
% 147.39/20.82  | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | |   (4885)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.39/20.82  | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.39/20.82  | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.39/20.82  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.39/20.82  | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.39/20.82  | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 147.39/20.82  | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.39/20.82  | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.39/20.82  | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.39/20.82  | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 147.39/20.82  | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.39/20.82  | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.39/20.82  | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.39/20.82  | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.39/20.82  | | | | | | | | | | | | | |             $i(all_57_10))
% 147.39/20.82  | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | BETA: splitting (4885) gives:
% 147.39/20.82  | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | Case 1:
% 147.39/20.82  | | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | |   (4886)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.39/20.82  | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.39/20.82  | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.39/20.82  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.39/20.82  | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.39/20.82  | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.39/20.82  | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.39/20.82  | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 147.39/20.82  | | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (371), (4227), (4886),
% 147.39/20.82  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.39/20.82  | | | | | | | | | | | | | | |            #438.
% 147.39/20.82  | | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | Case 2:
% 147.39/20.82  | | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | |   (4887)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.39/20.82  | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.39/20.82  | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.39/20.82  | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 147.39/20.82  | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 147.39/20.82  | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 147.39/20.82  | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.39/20.82  | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.39/20.82  | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 147.39/20.82  | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.39/20.82  | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.39/20.82  | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.39/20.82  | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.39/20.82  | | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (4227), (4867), (4882), (4887),
% 147.39/20.82  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.39/20.82  | | | | | | | | | | | | | | |            #380.
% 147.39/20.82  | | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | End of split
% 147.39/20.82  | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | End of split
% 147.39/20.82  | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | Case 2:
% 147.39/20.82  | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | |   (4888)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.39/20.82  | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.39/20.82  | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.39/20.82  | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.39/20.82  | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.39/20.82  | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.39/20.82  | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.39/20.82  | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.39/20.82  | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.39/20.82  | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.39/20.82  | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.39/20.82  | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.39/20.82  | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.39/20.82  | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.39/20.82  | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.39/20.82  | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.39/20.82  | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 147.39/20.82  | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 147.39/20.82  | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 147.39/20.82  | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.39/20.82  | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 147.39/20.82  | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.39/20.82  | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 147.39/20.82  | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 147.39/20.82  | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.39/20.82  | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.39/20.82  | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.39/20.82  | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.39/20.82  | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.39/20.82  | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.39/20.82  | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.39/20.82  | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.39/20.82  | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.39/20.82  | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.39/20.82  | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.39/20.82  | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.39/20.82  | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.39/20.82  | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.39/20.82  | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.39/20.82  | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.39/20.82  | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.39/20.82  | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.39/20.82  | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.39/20.82  | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.39/20.82  | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.39/20.82  | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.39/20.82  | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.39/20.82  | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.39/20.82  | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.39/20.82  | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.39/20.82  | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.39/20.82  | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | BETA: splitting (4888) gives:
% 147.39/20.82  | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | Case 1:
% 147.39/20.82  | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | |   (4889)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.39/20.82  | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.39/20.82  | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.39/20.82  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.39/20.82  | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.39/20.82  | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.39/20.82  | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.39/20.82  | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.39/20.82  | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.39/20.82  | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.39/20.82  | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.39/20.82  | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.39/20.82  | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.39/20.82  | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.39/20.82  | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.39/20.82  | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.39/20.82  | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | BETA: splitting (4889) gives:
% 147.39/20.82  | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | Case 1:
% 147.39/20.82  | | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | |   (4890)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.39/20.82  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.39/20.82  | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.39/20.82  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.39/20.82  | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.39/20.82  | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.39/20.82  | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.39/20.82  | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 147.39/20.82  | | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | | BETA: splitting (4890) gives:
% 147.39/20.82  | | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | | Case 1:
% 147.39/20.82  | | | | | | | | | | | | | | | | 
% 147.39/20.82  | | | | | | | | | | | | | | | |   (4891)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.39/20.82  | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.39/20.82  | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.39/20.82  | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.39/20.82  | | | | | | | | | | | | | | | |           $i(all_57_10)
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | ALPHA: (4891) implies:
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4892)   ~ (all_57_8 = e0)
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4893)  op(e0, e1) = all_57_8
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4894)  op(e3, e1) = e3
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 147.47/20.82  | | | | | | | | | | | | | | | |              all_57_8, e1, e0, simplifying with (156), (4893)
% 147.47/20.82  | | | | | | | | | | | | | | | |              gives:
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4895)  all_57_8 = all_52_11
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 147.47/20.82  | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (4894) gives:
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4896)  all_52_8 = e3
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | REDUCE: (4892), (4895) imply:
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4897)   ~ (all_52_11 = e0)
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | REDUCE: (122), (4896) imply:
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4898)   ~ (all_52_9 = e3)
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | SIMP: (4898) implies:
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4899)   ~ (all_52_9 = e3)
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | REDUCE: (120), (4896) imply:
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4900)   ~ (all_52_11 = e3)
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | SIMP: (4900) implies:
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4901)   ~ (all_52_11 = e3)
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.82  | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | |   (4902)  all_54_14 = e3
% 147.47/20.82  | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (4901), (4902) are inconsistent by
% 147.47/20.82  | | | | | | | | | | | | | | | | |            sub-proof #903.
% 147.47/20.82  | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.82  | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | |   (4903)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 147.47/20.82  | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | BETA: splitting (4903) gives:
% 147.47/20.82  | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | |   (4904)  all_54_14 = e2
% 147.47/20.82  | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4904) imply:
% 147.47/20.82  | | | | | | | | | | | | | | | | | |   (4905)  all_52_11 = e2
% 147.47/20.82  | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | SIMP: (4905) implies:
% 147.47/20.82  | | | | | | | | | | | | | | | | | |   (4906)  all_52_11 = e2
% 147.47/20.82  | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | REDUCE: (138), (4906) imply:
% 147.47/20.82  | | | | | | | | | | | | | | | | | |   (4907)   ~ (all_52_3 = e2)
% 147.47/20.82  | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | REDUCE: (156), (4906) imply:
% 147.47/20.82  | | | | | | | | | | | | | | | | | |   (4908)  op(e0, e1) = e2
% 147.47/20.82  | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | |   (4909)   ~ (all_30_2 = e1)
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | REDUCE: (4221), (4909) imply:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | |   (4910)  $false
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | CLOSE: (4910) is inconsistent.
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | |   (4911)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0
% 147.47/20.82  | | | | | | | | | | | | | | | | | | |             & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 147.47/20.82  | | | | | | | | | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1)
% 147.47/20.82  | | | | | | | | | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | |   (4912)  all_54_12 = e3
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (4912) imply:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | |   (4913)  all_52_3 = e3
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | SIMP: (4913) implies:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | |   (4914)  all_52_3 = e3
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (4914) imply:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | |   (4915)   ~ (all_52_1 = e3)
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (4914) imply:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | |   (4916)   ~ (all_52_2 = e3)
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | BETA: splitting (4911) gives:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |   (4917)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 &
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_30_1 & $i(all_30_0) &
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4917) implies:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |   (4918)  op(e0, e1) = all_30_1
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (144), (145), (148), (163), (166), (195),
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |            (196), (197), (199), (258), (259), (260), (268),
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |            (4220), (4863), (4864), (4878), (4879), (4880),
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |            (4899), (4908), (4915), (4916), (4918),
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |            #376.
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |   (4919)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 &
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | ALPHA: (4919) implies:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |   (4920)  op(e0, e1) = all_30_1
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (144), (145), (148), (163), (166), (195),
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |            (196), (197), (199), (258), (259), (260), (268),
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |            (4220), (4863), (4864), (4878), (4879), (4880),
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |            (4899), (4908), (4915), (4916), (4920),
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | |            #376.
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | |   (4921)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (4222), (4865), (4907), (4921) are
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #881.
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.82  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.82  | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.82  | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | |   (4922)  all_54_14 = e1 | all_54_14 = e0
% 147.47/20.82  | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (4224), (4897), (4922) are inconsistent by
% 147.47/20.82  | | | | | | | | | | | | | | | | | |            sub-proof #375.
% 147.47/20.82  | | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | | End of split
% 147.47/20.82  | | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | End of split
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | Case 2:
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4923)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 147.47/20.82  | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 147.47/20.82  | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 147.47/20.82  | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | ALPHA: (4923) implies:
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4924)  op(e2, e1) = e2
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4879), (4924), (function-axioms) are
% 147.47/20.82  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | End of split
% 147.47/20.82  | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | Case 2:
% 147.47/20.82  | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | |   (4925)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.82  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.47/20.82  | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.47/20.82  | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.82  | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 147.47/20.82  | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 147.47/20.82  | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.82  | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.82  | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 147.47/20.82  | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 147.47/20.82  | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.82  | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 147.47/20.82  | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 147.47/20.82  | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | BETA: splitting (4925) gives:
% 147.47/20.82  | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | Case 1:
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4926)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.82  | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.47/20.82  | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.47/20.82  | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.82  | | | | | | | | | | | | | | | |           $i(all_57_12)
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | ALPHA: (4926) implies:
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4927)  op(e2, e1) = e2
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4879), (4927), (function-axioms) are
% 147.47/20.82  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | Case 2:
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | |   (4928)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.82  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.82  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.82  | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.82  | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.82  | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.82  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.82  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.82  | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | | REF_CLOSE: (4867), (4928), (function-axioms) are inconsistent
% 147.47/20.82  | | | | | | | | | | | | | | | |            by sub-proof #542.
% 147.47/20.82  | | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | | End of split
% 147.47/20.82  | | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | | End of split
% 147.47/20.82  | | | | | | | | | | | | | | 
% 147.47/20.82  | | | | | | | | | | | | | Case 2:
% 147.47/20.82  | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | |   (4929)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.83  | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.83  | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.47/20.83  | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.47/20.83  | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.47/20.83  | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.47/20.83  | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.47/20.83  | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 147.47/20.83  | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.83  | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.47/20.83  | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.83  | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 147.47/20.83  | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 147.47/20.83  | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 147.47/20.83  | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 147.47/20.83  | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 147.47/20.83  | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.47/20.83  | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 147.47/20.83  | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.83  | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 147.47/20.83  | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 147.47/20.83  | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.83  | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.83  | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.83  | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.83  | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.83  | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.83  | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.83  | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.83  | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.83  | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.83  | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.83  | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.83  | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.83  | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.83  | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.83  | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.83  | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.83  | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | BETA: splitting (4929) gives:
% 147.47/20.83  | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | |   (4930)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.83  | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.83  | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.47/20.83  | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.47/20.83  | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.47/20.83  | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.47/20.83  | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.47/20.83  | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (4226), (4880), (4930),
% 147.47/20.83  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.83  | | | | | | | | | | | | | | |            #535.
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | |   (4931)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.47/20.83  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.83  | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.83  | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.47/20.83  | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.47/20.83  | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.83  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.47/20.83  | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.47/20.83  | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.47/20.83  | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.47/20.83  | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.83  | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.83  | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.83  | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.83  | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.83  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.83  | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.83  | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.83  | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.83  | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.83  | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.83  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.83  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.83  | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.83  | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.83  | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.83  | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.83  | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | BETA: splitting (4931) gives:
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | |   (4932)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.47/20.83  | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.83  | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.83  | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.47/20.83  | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | ALPHA: (4932) implies:
% 147.47/20.83  | | | | | | | | | | | | | | | |   (4933)  op(e2, e0) = e2
% 147.47/20.83  | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4880), (4933), (function-axioms) are
% 147.47/20.83  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 147.47/20.83  | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | |   (4934)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.47/20.83  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.47/20.83  | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.47/20.83  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.47/20.83  | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.47/20.83  | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.47/20.83  | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.47/20.83  | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.47/20.83  | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.47/20.83  | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.47/20.83  | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.47/20.83  | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.47/20.83  | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.47/20.83  | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.47/20.83  | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.83  | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.47/20.83  | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.47/20.83  | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.47/20.83  | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.47/20.83  | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.47/20.83  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.47/20.83  | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.47/20.83  | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.47/20.83  | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.47/20.83  | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | BETA: splitting (4934) gives:
% 147.47/20.83  | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | |   (4935)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.47/20.83  | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.47/20.83  | | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | | ALPHA: (4935) implies:
% 147.47/20.83  | | | | | | | | | | | | | | | | |   (4936)  op(e1, e0) = e1
% 147.47/20.83  | | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4226), (4936), (function-axioms) are
% 147.47/20.83  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 147.47/20.83  | | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | |   (4937)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.47/20.83  | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.83  | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.83  | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.83  | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.47/20.83  | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.47/20.83  | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.83  | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.47/20.83  | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.47/20.83  | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.47/20.83  | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.47/20.83  | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.47/20.83  | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.47/20.83  | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.47/20.83  | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.47/20.83  | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.47/20.83  | | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | | ALPHA: (4937) implies:
% 147.47/20.83  | | | | | | | | | | | | | | | | |   (4938)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.83  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.83  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.47/20.83  | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.47/20.83  | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.47/20.83  | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.83  | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.83  | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.47/20.83  | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.83  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.83  | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.47/20.83  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.47/20.83  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.47/20.83  | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.47/20.83  | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.83  | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.47/20.83  | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.47/20.83  | | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (158), (371), (4865), (4867),
% 147.47/20.83  | | | | | | | | | | | | | | | | |            (4882), (4938), (function-axioms) are inconsistent
% 147.47/20.83  | | | | | | | | | | | | | | | | |            by sub-proof #536.
% 147.47/20.83  | | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | End of split
% 147.47/20.83  | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | End of split
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | End of split
% 147.47/20.83  | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | End of split
% 147.47/20.83  | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | End of split
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | |   (4939)  all_54_5 = e1 | all_54_5 = e0
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | REF_CLOSE: (267), (4869), (4871), (4939) are inconsistent by
% 147.47/20.83  | | | | | | | | | | | |            sub-proof #866.
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | End of split
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | End of split
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | |   (4940)  all_20_2 = e1
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | COMBINE_EQS: (282), (4940) imply:
% 147.47/20.83  | | | | | | | | | |   (4941)  all_6_2 = e1
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | SIMP: (4941) implies:
% 147.47/20.83  | | | | | | | | | |   (4942)  all_6_2 = e1
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | REDUCE: (372), (4942) imply:
% 147.47/20.83  | | | | | | | | | |   (4943)   ~ (e3 = e1)
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | REDUCE: (39), (4942) imply:
% 147.47/20.83  | | | | | | | | | |   (4944)  op(e2, e2) = e1
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | BETA: splitting (237) gives:
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | |   (4945)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 147.47/20.83  | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 147.47/20.83  | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.47/20.83  | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.47/20.83  | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.47/20.83  | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.47/20.83  | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 147.47/20.83  | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 147.47/20.83  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.83  | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.47/20.83  | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.47/20.83  | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | REF_CLOSE: (6), (7), (4867), (4944), (4945),
% 147.47/20.83  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.83  | | | | | | | | | | |            #515.
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | |   (4946)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.47/20.83  | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.47/20.83  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.83  | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.47/20.83  | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.83  | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.47/20.83  | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.47/20.83  | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.47/20.83  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.83  | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.47/20.83  | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.47/20.83  | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.47/20.83  | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.47/20.83  | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | BETA: splitting (4946) gives:
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | |   (4947)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 147.47/20.83  | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 147.47/20.83  | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.83  | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.47/20.83  | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.83  | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 147.47/20.83  | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 147.47/20.83  | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | ALPHA: (4947) implies:
% 147.47/20.83  | | | | | | | | | | | |   (4948)  op(e1, e1) = e1
% 147.47/20.83  | | | | | | | | | | | |   (4949)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15
% 147.47/20.83  | | | | | | | | | | | |               = e1) & op(e0, e0) = all_57_15 &
% 147.47/20.83  | | | | | | | | | | | |             $i(all_57_15))
% 147.47/20.83  | | | | | | | | | | | |   (4950)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 147.47/20.83  | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.83  | | | | | | | | | | | |             $i(all_57_12))
% 147.47/20.83  | | | | | | | | | | | |   (4951)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 147.47/20.83  | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.83  | | | | | | | | | | | |             $i(all_57_10))
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (36), (116), (158), (159),
% 147.47/20.83  | | | | | | | | | | | |            (163), (164), (238), (4226), (4227), (4865),
% 147.47/20.83  | | | | | | | | | | | |            (4867), (4944), (4948), (4949), (4950), (4951),
% 147.47/20.83  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.83  | | | | | | | | | | | |            #370.
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | |   (4952)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 147.47/20.83  | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 147.47/20.83  | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.83  | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.47/20.83  | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.47/20.83  | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.47/20.83  | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.47/20.83  | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | ALPHA: (4952) implies:
% 147.47/20.83  | | | | | | | | | | | |   (4953)  op(e0, e0) = e0
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | REF_CLOSE: (4), (4227), (4953), (function-axioms) are
% 147.47/20.83  | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | End of split
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | End of split
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | End of split
% 147.47/20.83  | | | | | | | | | 
% 147.47/20.83  | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | 
% 147.47/20.83  | | | | | | | | |   (4954)  all_16_2 = e0
% 147.47/20.83  | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | COMBINE_EQS: (327), (4954) imply:
% 147.47/20.83  | | | | | | | | |   (4955)  all_6_2 = e0
% 147.47/20.83  | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | SIMP: (4955) implies:
% 147.47/20.83  | | | | | | | | |   (4956)  all_6_2 = e0
% 147.47/20.83  | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | REDUCE: (358), (4956) imply:
% 147.47/20.83  | | | | | | | | |   (4957)   ~ (all_52_13 = e0)
% 147.47/20.83  | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | REDUCE: (372), (4956) imply:
% 147.47/20.83  | | | | | | | | |   (4958)   ~ (e3 = e0)
% 147.47/20.83  | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | REDUCE: (39), (4956) imply:
% 147.47/20.83  | | | | | | | | |   (4959)  op(e2, e2) = e0
% 147.47/20.83  | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | BETA: splitting (205) gives:
% 147.47/20.83  | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | |   (4960)  all_56_15 = e0 & op(e0, e0) = e0
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | ALPHA: (4960) implies:
% 147.47/20.83  | | | | | | | | | |   (4961)  op(e0, e0) = e0
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | REF_CLOSE: (4), (4227), (4961), (function-axioms) are
% 147.47/20.83  | | | | | | | | | |            inconsistent by sub-proof #1040.
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | |   (4962)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 147.47/20.83  | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 147.47/20.83  | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 147.47/20.83  | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 147.47/20.83  | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | ALPHA: (4962) implies:
% 147.47/20.83  | | | | | | | | | |   (4963)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 147.47/20.83  | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 147.47/20.83  | | | | | | | | | |               e0) = e0)
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | BETA: splitting (237) gives:
% 147.47/20.83  | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | |   (4964)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 147.47/20.83  | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 147.47/20.83  | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.47/20.83  | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.47/20.83  | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.47/20.83  | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.47/20.83  | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 147.47/20.83  | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 147.47/20.83  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.83  | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.47/20.83  | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.47/20.83  | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | REF_CLOSE: (5), (7), (4867), (4959), (4964),
% 147.47/20.83  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.83  | | | | | | | | | | |            #477.
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | |   (4965)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.47/20.83  | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.47/20.83  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.83  | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.47/20.83  | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.83  | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.47/20.83  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.47/20.83  | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.47/20.83  | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.47/20.83  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.83  | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.47/20.83  | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.47/20.83  | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.47/20.83  | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.47/20.83  | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | BETA: splitting (4965) gives:
% 147.47/20.83  | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | |   (4966)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 147.47/20.83  | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 147.47/20.83  | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.83  | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.47/20.83  | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.83  | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 147.47/20.83  | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 147.47/20.83  | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | ALPHA: (4966) implies:
% 147.47/20.83  | | | | | | | | | | | |   (4967)  op(e1, e1) = e1
% 147.47/20.83  | | | | | | | | | | | |   (4968)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15
% 147.47/20.83  | | | | | | | | | | | |               = e1) & op(e0, e0) = all_57_15 &
% 147.47/20.83  | | | | | | | | | | | |             $i(all_57_15))
% 147.47/20.83  | | | | | | | | | | | |   (4969)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 147.47/20.83  | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.83  | | | | | | | | | | | |             $i(all_57_12))
% 147.47/20.83  | | | | | | | | | | | |   (4970)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 147.47/20.83  | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.83  | | | | | | | | | | | |             $i(all_57_10))
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | BETA: splitting (4968) gives:
% 147.47/20.83  | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | |   (4971)  all_57_8 = e0 & op(e0, e1) = e0
% 147.47/20.83  | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | ALPHA: (4971) implies:
% 147.47/20.83  | | | | | | | | | | | | |   (4972)  all_57_8 = e0
% 147.47/20.83  | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | BETA: splitting (4963) gives:
% 147.47/20.83  | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | |   (4973)  all_56_9 = e0 & op(e3, e0) = e0
% 147.47/20.83  | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | REF_CLOSE: (167), (4866), (4973), (function-axioms) are
% 147.47/20.83  | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 147.47/20.83  | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | |   (4974)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 147.47/20.83  | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 147.47/20.83  | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | BETA: splitting (4974) gives:
% 147.47/20.83  | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | |   (4975)  all_56_10 = e0 & op(e2, e0) = e0
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | REF_CLOSE: (163), (4957), (4975), (function-axioms) are
% 147.47/20.83  | | | | | | | | | | | | | | |            inconsistent by sub-proof #540.
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | Case 2:
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | |   (4976)  all_56_11 = e0 & op(e1, e0) = e0
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | ALPHA: (4976) implies:
% 147.47/20.83  | | | | | | | | | | | | | | |   (4977)  op(e1, e0) = e0
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 147.47/20.83  | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | |   (4978)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.83  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.83  | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.83  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.83  | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.83  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.83  | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.83  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.83  | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.83  | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 147.47/20.83  | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 147.47/20.83  | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 147.47/20.83  | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.83  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.83  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.47/20.83  | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.47/20.83  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 147.47/20.83  | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 147.47/20.83  | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 147.47/20.83  | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 147.47/20.83  | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 147.47/20.83  | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 147.47/20.83  | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 147.47/20.83  | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.83  | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.83  | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.83  | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.47/20.83  | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | BETA: splitting (4978) gives:
% 147.47/20.83  | | | | | | | | | | | | | | | | 
% 147.47/20.83  | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.83  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | |   (4979)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.84  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.84  | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.84  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | BETA: splitting (4979) gives:
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | |   (4980)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.84  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | BETA: splitting (4980) gives:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (4981)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | ALPHA: (4981) implies:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (4982)  op(e1, e1) = e3
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (45), (159), (237), (370), (4867),
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |            (4959), (4977), (4982), (function-axioms) are
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #452.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (4983)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | ALPHA: (4983) implies:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (4984)  op(e0, e0) = e3
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4227), (4984), (function-axioms) are
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | |   (4985)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (4227), (4959), (4985),
% 147.47/20.84  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.84  | | | | | | | | | | | | | | | | | |            #397.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | |   (4986)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.47/20.84  | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.84  | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 147.47/20.84  | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.47/20.84  | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (4227), (4867), (4967), (4969),
% 147.47/20.84  | | | | | | | | | | | | | | | | |            (4986), (function-axioms) are inconsistent by
% 147.47/20.84  | | | | | | | | | | | | | | | | |            sub-proof #374.
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | |   (4987)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.84  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.84  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.84  | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.84  | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.84  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.84  | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.47/20.84  | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.47/20.84  | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.84  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.84  | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.84  | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.84  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.84  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.84  | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 147.47/20.84  | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 147.47/20.84  | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.47/20.84  | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 147.47/20.84  | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.47/20.84  | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.47/20.84  | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 147.47/20.84  | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 147.47/20.84  | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.84  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.84  | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.47/20.84  | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.47/20.84  | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.84  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.47/20.84  | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.47/20.84  | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.47/20.84  | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.84  | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.84  | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.84  | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.84  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.84  | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.84  | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.84  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.84  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.84  | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.84  | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.84  | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | BETA: splitting (4987) gives:
% 147.47/20.84  | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | |   (4988)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.84  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.47/20.84  | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | BETA: splitting (4988) gives:
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | |   (4989)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.84  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4970), (4972), (4989), (function-axioms) are
% 147.47/20.84  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #373.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | |   (4990)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | BETA: splitting (4990) gives:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (4991)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | ALPHA: (4991) implies:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (4992)   ~ (all_57_8 = e0)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | REDUCE: (4972), (4992) imply:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (4993)  $false
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | CLOSE: (4993) is inconsistent.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (4994)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4867), (4967), (4994), (function-axioms) are
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #519.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | |   (4995)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.47/20.84  | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.47/20.84  | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.47/20.84  | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 147.47/20.84  | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 147.47/20.84  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 147.47/20.84  | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.47/20.84  | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 147.47/20.84  | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.84  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.84  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.84  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.84  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.84  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | BETA: splitting (4995) gives:
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | |   (4996)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.47/20.84  | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.47/20.84  | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | BETA: splitting (4996) gives:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (4997)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | ALPHA: (4997) implies:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (4998)   ~ (all_57_12 = e0)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (4999)  op(e2, e2) = all_57_12
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4959), (4998), (4999), (function-axioms) are
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (5000)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | ALPHA: (5000) implies:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (5001)  op(e1, e0) = e1
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4226), (5001), (function-axioms) are
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | |   (5002)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.84  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.84  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | BETA: splitting (5002) gives:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (5003)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | ALPHA: (5003) implies:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (5004)  op(e1, e1) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4967), (5004), (function-axioms) are
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |   (5005)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.47/20.84  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | BETA: splitting (5005) gives:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |   (5006)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | ALPHA: (5006) implies:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |   (5007)  op(e1, e0) = e1
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4226), (5007), (function-axioms) are
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |   (5008)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | ALPHA: (5008) implies:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |   (5009)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5009) gives:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |   (5010)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (4865), (4867), (5010),
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |            #538.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |   (5011)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (4967), (4969), (4970), (5011),
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | |            #454.
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | |   (5012)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 147.47/20.84  | | | | | | | | | | | | |           $i(all_57_15)
% 147.47/20.84  | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | ALPHA: (5012) implies:
% 147.47/20.84  | | | | | | | | | | | | |   (5013)   ~ (all_57_15 = e1)
% 147.47/20.84  | | | | | | | | | | | | |   (5014)  op(e0, e0) = all_57_15
% 147.47/20.84  | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | | REF_CLOSE: (4227), (5013), (5014), (function-axioms) are
% 147.47/20.84  | | | | | | | | | | | | |            inconsistent by sub-proof #940.
% 147.47/20.84  | | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | | End of split
% 147.47/20.84  | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | Case 2:
% 147.47/20.84  | | | | | | | | | | | | 
% 147.47/20.84  | | | | | | | | | | | |   (5015)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 147.47/20.85  | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 147.47/20.85  | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.85  | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.47/20.85  | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.47/20.85  | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.47/20.85  | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.47/20.85  | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 147.47/20.85  | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | ALPHA: (5015) implies:
% 147.47/20.85  | | | | | | | | | | | |   (5016)  op(e0, e0) = e0
% 147.47/20.85  | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | REF_CLOSE: (4), (4227), (5016), (function-axioms) are
% 147.47/20.85  | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 147.47/20.85  | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | End of split
% 147.47/20.85  | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | End of split
% 147.47/20.85  | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | End of split
% 147.47/20.85  | | | | | | | | | 
% 147.47/20.85  | | | | | | | | End of split
% 147.47/20.85  | | | | | | | | 
% 147.47/20.85  | | | | | | | End of split
% 147.47/20.85  | | | | | | | 
% 147.47/20.85  | | | | | | End of split
% 147.47/20.85  | | | | | | 
% 147.47/20.85  | | | | | End of split
% 147.47/20.85  | | | | | 
% 147.47/20.85  | | | | End of split
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | Case 2:
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | |   (5017)  all_8_2 = e3
% 147.47/20.85  | | | |   (5018)  ( ~ (all_8_0 = e2) & op(all_8_1, e1) = all_8_0 & op(e1, e3) =
% 147.47/20.85  | | | |             all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) &
% 147.47/20.85  | | | |             op(e1, e3) = all_8_1 & $i(all_8_1))
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | | COMBINE_EQS: (329), (5017) imply:
% 147.47/20.85  | | | |   (5019)  all_4_2 = e3
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | | SIMP: (5019) implies:
% 147.47/20.85  | | | |   (5020)  all_4_2 = e3
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | | COMBINE_EQS: (316), (5020) imply:
% 147.47/20.85  | | | |   (5021)  all_12_2 = e3
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | | REDUCE: (348), (5020) imply:
% 147.47/20.85  | | | |   (5022)   ~ (all_52_2 = e3)
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | | REDUCE: (359), (5020) imply:
% 147.47/20.85  | | | |   (5023)   ~ (all_52_6 = e3)
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | | REDUCE: (361), (5020) imply:
% 147.47/20.85  | | | |   (5024)   ~ (all_52_8 = e3)
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | | REDUCE: (362), (5020) imply:
% 147.47/20.85  | | | |   (5025)   ~ (all_52_9 = e3)
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | | REDUCE: (364), (5020) imply:
% 147.47/20.85  | | | |   (5026)   ~ (all_52_11 = e3)
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | | REDUCE: (366), (5020) imply:
% 147.47/20.85  | | | |   (5027)   ~ (all_52_14 = e3)
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | | BETA: splitting (219) gives:
% 147.47/20.85  | | | | 
% 147.47/20.85  | | | | Case 1:
% 147.47/20.85  | | | | | 
% 147.47/20.85  | | | | |   (5028)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2,
% 147.47/20.85  | | | | |               e1) = e3)
% 147.47/20.85  | | | | | 
% 147.47/20.85  | | | | | REF_CLOSE: (164), (168), (5024), (5025), (5028), (function-axioms) are
% 147.47/20.85  | | | | |            inconsistent by sub-proof #369.
% 147.47/20.85  | | | | | 
% 147.47/20.85  | | | | Case 2:
% 147.47/20.85  | | | | | 
% 147.47/20.85  | | | | |   (5029)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0,
% 147.47/20.85  | | | | |               e1) = e3)
% 147.47/20.85  | | | | | 
% 147.47/20.85  | | | | | BETA: splitting (5029) gives:
% 147.47/20.85  | | | | | 
% 147.47/20.85  | | | | | Case 1:
% 147.47/20.85  | | | | | | 
% 147.47/20.85  | | | | | |   (5030)  all_56_8 = e3 & op(e1, e1) = e3
% 147.47/20.85  | | | | | | 
% 147.47/20.85  | | | | | | ALPHA: (5030) implies:
% 147.47/20.85  | | | | | |   (5031)  all_56_8 = e3
% 147.47/20.85  | | | | | |   (5032)  op(e1, e1) = e3
% 147.47/20.85  | | | | | | 
% 147.47/20.85  | | | | | | BETA: splitting (46) gives:
% 147.47/20.85  | | | | | | 
% 147.47/20.85  | | | | | | Case 1:
% 147.47/20.85  | | | | | | | 
% 147.47/20.85  | | | | | | |   (5033)   ~ (all_10_2 = e1)
% 147.47/20.85  | | | | | | | 
% 147.47/20.85  | | | | | | | BETA: splitting (49) gives:
% 147.47/20.85  | | | | | | | 
% 147.47/20.85  | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | 
% 147.47/20.85  | | | | | | | |   (5034)   ~ (all_12_2 = e3)
% 147.47/20.85  | | | | | | | | 
% 147.47/20.85  | | | | | | | | REDUCE: (5021), (5034) imply:
% 147.47/20.85  | | | | | | | |   (5035)  $false
% 147.47/20.85  | | | | | | | | 
% 147.47/20.85  | | | | | | | | CLOSE: (5035) is inconsistent.
% 147.47/20.85  | | | | | | | | 
% 147.47/20.85  | | | | | | | Case 2:
% 147.47/20.85  | | | | | | | | 
% 147.47/20.85  | | | | | | | |   (5036)  ( ~ (all_12_0 = e0) & op(all_12_1, e1) = all_12_0 &
% 147.47/20.85  | | | | | | | |             op(e1, e3) = all_12_1 & $i(all_12_0) & $i(all_12_1))
% 147.47/20.85  | | | | | | | |           | ( ~ (all_12_1 = e2) & op(e1, e3) = all_12_1 &
% 147.47/20.85  | | | | | | | |             $i(all_12_1))
% 147.47/20.85  | | | | | | | | 
% 147.47/20.85  | | | | | | | | BETA: splitting (52) gives:
% 147.47/20.85  | | | | | | | | 
% 147.47/20.85  | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | 
% 147.47/20.85  | | | | | | | | |   (5037)   ~ (all_14_2 = e0)
% 147.47/20.85  | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | BETA: splitting (55) gives:
% 147.47/20.85  | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | |   (5038)   ~ (all_16_2 = e0)
% 147.47/20.85  | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | REDUCE: (327), (5038) imply:
% 147.47/20.85  | | | | | | | | | |   (5039)   ~ (all_6_2 = e0)
% 147.47/20.85  | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | BETA: splitting (61) gives:
% 147.47/20.85  | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | |   (5040)   ~ (all_20_2 = e1)
% 147.47/20.85  | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | REDUCE: (282), (5040) imply:
% 147.47/20.85  | | | | | | | | | | |   (5041)   ~ (all_6_2 = e1)
% 147.47/20.85  | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | BETA: splitting (198) gives:
% 147.47/20.85  | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | |   (5042)  all_54_5 = e3
% 147.47/20.85  | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | REF_CLOSE: (267), (372), (5042) are inconsistent by sub-proof
% 147.47/20.85  | | | | | | | | | | | |            #443.
% 147.47/20.85  | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | Case 2:
% 147.47/20.85  | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | |   (5043)   ~ (all_54_5 = e3)
% 147.47/20.85  | | | | | | | | | | | |   (5044)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 147.47/20.85  | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | BETA: splitting (5044) gives:
% 147.47/20.85  | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | |   (5045)  all_54_5 = e2
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | COMBINE_EQS: (267), (5045) imply:
% 147.47/20.85  | | | | | | | | | | | | |   (5046)  all_6_2 = e2
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | SIMP: (5046) implies:
% 147.47/20.85  | | | | | | | | | | | | |   (5047)  all_6_2 = e2
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | REDUCE: (347), (5047) imply:
% 147.47/20.85  | | | | | | | | | | | | |   (5048)   ~ (all_52_1 = e2)
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | REDUCE: (350), (5047) imply:
% 147.47/20.85  | | | | | | | | | | | | |   (5049)   ~ (all_52_4 = e2)
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | REDUCE: (352), (5047) imply:
% 147.47/20.85  | | | | | | | | | | | | |   (5050)   ~ (all_52_6 = e2)
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | REDUCE: (356), (5047) imply:
% 147.47/20.85  | | | | | | | | | | | | |   (5051)   ~ (all_52_9 = e2)
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | REDUCE: (358), (5047) imply:
% 147.47/20.85  | | | | | | | | | | | | |   (5052)   ~ (all_52_13 = e2)
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | REDUCE: (372), (5047) imply:
% 147.47/20.85  | | | | | | | | | | | | |   (5053)   ~ (e3 = e2)
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | REDUCE: (39), (5047) imply:
% 147.47/20.85  | | | | | | | | | | | | |   (5054)  op(e2, e2) = e2
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 147.47/20.85  | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | |   (5055)   ~ (all_22_2 = e1)
% 147.47/20.85  | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | REDUCE: (320), (5055) imply:
% 147.47/20.85  | | | | | | | | | | | | | |   (5056)   ~ (all_14_2 = e1)
% 147.47/20.85  | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 147.47/20.85  | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | |   (5057)   ~ (all_24_2 = e2)
% 147.47/20.85  | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | REDUCE: (318), (5057) imply:
% 147.47/20.85  | | | | | | | | | | | | | | |   (5058)   ~ (all_10_2 = e2)
% 147.47/20.85  | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 147.47/20.85  | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | |   (5059)   ~ (all_36_2 = e2)
% 147.47/20.85  | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | REDUCE: (304), (5059) imply:
% 147.47/20.85  | | | | | | | | | | | | | | | |   (5060)   ~ (all_14_2 = e2)
% 147.47/20.85  | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 147.47/20.85  | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | |   (5061)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.85  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.85  | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.85  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 147.47/20.85  | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 147.47/20.85  | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 147.47/20.85  | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 147.47/20.85  | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 147.47/20.85  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 147.47/20.85  | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 147.47/20.85  | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 147.47/20.85  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 147.47/20.85  | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.85  | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.47/20.85  | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | BETA: splitting (5061) gives:
% 147.47/20.85  | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | |   (5062)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.85  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.85  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | BETA: splitting (5062) gives:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |   (5063)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (5048), (5063), (function-axioms) are
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |   (5064)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5032), (5064), (function-axioms) are inconsistent
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |            by sub-proof #368.
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | |   (5065)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 147.47/20.85  | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.47/20.85  | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | BETA: splitting (5065) gives:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |   (5066)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (5032), (5058), (5066),
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |            #367.
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |   (5067)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | BETA: splitting (5067) gives:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |   (5068)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | | ALPHA: (5068) implies:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |   (5069)  op(e3, e3) = e2
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (5037), (5056), (5060),
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |            (5069), (function-axioms) are inconsistent by
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |            sub-proof #366.
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |   (5070)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (45), (5054), (5058), (5070),
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | |            #1084.
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | End of split
% 147.47/20.85  | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.85  | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | |   (5071)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.85  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.85  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.47/20.85  | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.47/20.85  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.47/20.85  | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 147.47/20.85  | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 147.47/20.85  | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.47/20.85  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 147.47/20.85  | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 147.47/20.85  | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 147.47/20.85  | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.85  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.85  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.85  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.85  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.85  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.85  | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | BETA: splitting (5071) gives:
% 147.47/20.85  | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | |   (5072)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.47/20.85  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | BETA: splitting (5072) gives:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |   (5073)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (164), (5033), (5051), (5073),
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |            #544.
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |   (5074)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (164), (5032), (5051), (5054), (5074),
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |            #433.
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | |   (5075)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.47/20.85  | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 147.47/20.85  | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.85  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.85  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | BETA: splitting (5075) gives:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |   (5076)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.47/20.85  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | BETA: splitting (5076) gives:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.85  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |   (5077)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | ALPHA: (5077) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |   (5078)  op(e3, e3) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (5037), (5056), (5060),
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |            (5078), (function-axioms) are inconsistent by
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |            sub-proof #1139.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |   (5079)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | ALPHA: (5079) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |   (5080)  op(e3, e3) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (5037), (5056), (5060),
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |            (5080), (function-axioms) are inconsistent by
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |            sub-proof #1139.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |   (5081)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | BETA: splitting (5081) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |   (5082)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | ALPHA: (5082) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |   (5083)  op(e2, e0) = e2
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5052), (5083), (function-axioms) are
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |   (5084)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5084) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |   (5085)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5085) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |   (5086)  op(e2, e2) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5054), (5086), (function-axioms) are
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |   (5087)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | ALPHA: (5087) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |   (5088)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5088) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |   (5089)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5089) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |   (5090)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5090) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |   (5091)  op(e2, e2) = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5054), (5091), (function-axioms) are
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |   (5092)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5092) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |   (5093)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5093) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |   (5094)  op(e0, e3) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (5095)  all_54_0 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (5095) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (5096)  all_14_2 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (336), (5096) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (5097)   ~ (all_52_1 = e3)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (5096) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (5098)  op(e3, e3) = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5099)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (5054), (5097), (5099),
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            #365.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5100)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5100) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5101)  all_56_5 = e3 & op(e2, e1) = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5025), (5101), (function-axioms) are
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5102)  all_56_10 = e3 & op(e2, e0) = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5102) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5103)  all_56_10 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5104)  op(e2, e0) = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5105)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5105) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (158), (5094) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5106)  all_52_3 = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (163), (5104) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5107)  all_52_13 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (5106) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5108)   ~ (all_10_2 = e0)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5108) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5109)   ~ (all_10_2 = e0)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (5107) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5110)   ~ (all_10_2 = e3)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5110) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5111)   ~ (all_10_2 = e3)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5112)  all_54_15 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5112) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5113)  all_10_2 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5111), (5113) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5114)  $false
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5114) is inconsistent.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5115)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5115) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5116)  all_54_15 = e2
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5116) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5117)  all_10_2 = e2
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5058), (5117) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5118)  $false
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5118) is inconsistent.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5119)  all_54_15 = e1 | all_54_15 = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5119) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5120)  all_54_15 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5120) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5121)  all_10_2 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5033), (5121) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5122)  $false
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5122) is inconsistent.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5123)  all_54_15 = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5123) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5124)  all_10_2 = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5109), (5124) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5125)  $false
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5125) is inconsistent.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5126)  all_56_2 = e3 & op(e2, e3) = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5126) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5127)  all_56_2 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (220), (221), (5054),
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5103), (5127), (function-axioms) are inconsistent
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #363.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5128)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5128) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5129)  all_56_6 = e3 & op(e1, e3) = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5129) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5130)  all_56_6 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213), (214),
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5031), (5032), (5130), (function-axioms) are
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #607.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5131)  all_56_12 = e3 & op(e0, e3) = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5131) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5132)  all_56_12 = e3
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5133)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (5048), (5098), (5133),
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #410.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5134)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5134) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5135)  all_56_6 = e2 & op(e1, e3) = e2
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5135) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5136)  all_56_6 = e2
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5137)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5137) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5138)  all_56_0 = e0 & op(e3, e3) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5138) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5139)  op(e3, e3) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5098), (5139), (function-axioms) are
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5140)  all_56_2 = e0 & op(e2, e3) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5140) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5141)  all_56_2 = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5142)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5142) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5143)  all_56_2 = e1 & op(e2, e3) = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5143) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5144)  all_56_2 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5141), (5144) are inconsistent by sub-proof
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1060.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5145)  all_56_3 = e1 & op(e2, e2) = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5145) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5146)  op(e2, e2) = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5054), (5146), (function-axioms) are
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5147)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5147) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5148)  all_56_5 = e1 & op(e2, e1) = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5148) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5149)  all_56_5 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5150)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5150) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5151)  all_56_0 = e1 & op(e3, e3) = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5151) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5152)  op(e3, e3) = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5098), (5152), (function-axioms) are
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5153)  all_56_2 = e1 & op(e2, e3) = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5153) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5154)  all_56_2 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5141), (5154) are inconsistent by sub-proof
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1060.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5155)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5155) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5156)  all_56_6 = e1 & op(e1, e3) = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5156) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5157)  all_56_6 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5136), (5157) are inconsistent by sub-proof
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1172.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5158)  all_56_12 = e1 & op(e0, e3) = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5158) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5159)  all_56_12 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5132), (5159) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5160)  e3 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5160) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5161)  e3 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5103), (5161) imply:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5162)  all_56_10 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (220), (223), (5054),
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5149), (5162), (function-axioms) are inconsistent
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #681.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5163)  all_56_10 = e1 & op(e2, e0) = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5163) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5164)  all_56_10 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5103), (5164) are inconsistent by sub-proof
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #677.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5165)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5165) gives:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5166)  all_56_6 = e0 & op(e1, e3) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5166) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5167)  all_56_6 = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5136), (5167) are inconsistent by sub-proof
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #724.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5168)  all_56_12 = e0 & op(e0, e3) = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5168) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5169)  all_56_12 = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5132), (5169) are inconsistent by sub-proof
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1052.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5170)  all_56_12 = e2 & op(e0, e3) = e2
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5132), (5170) are inconsistent by sub-proof
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #993.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (5171)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (5037), (5056), (5060), (5171) are
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |   (5172)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5172) implies:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |   (5173)  op(e3, e3) = e2
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (5037), (5056), (5060),
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |            (5173), (function-axioms) are inconsistent by
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #366.
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |   (5174)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.47/20.86  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5174) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |   (5175)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5175) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |   (5176)  op(e1, e1) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (5176), (function-axioms) are
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |   (5177)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5177) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |   (5178)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_6)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5178) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |   (5179)  op(e3, e3) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (5037), (5056), (5060),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |            (5179), (function-axioms) are inconsistent by
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #728.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |   (5180)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5180) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |   (5181)  op(e2, e2) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5054), (5181), (function-axioms) are
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | |   (5182)  all_36_2 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | |   (5183)  ( ~ (all_36_0 = e1) & op(all_36_1, e3) = all_36_0
% 147.47/20.87  | | | | | | | | | | | | | | | |             & op(e3, e2) = all_36_1 & $i(all_36_0) &
% 147.47/20.87  | | | | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e3, e2)
% 147.47/20.87  | | | | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 147.47/20.87  | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (5182) imply:
% 147.47/20.87  | | | | | | | | | | | | | | | |   (5184)  all_14_2 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | SIMP: (5184) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | |   (5185)  all_14_2 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | REDUCE: (51), (5185) imply:
% 147.47/20.87  | | | | | | | | | | | | | | | |   (5186)  op(e3, e3) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | |   (5187)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 147.47/20.87  | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 147.47/20.87  | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | BETA: splitting (5187) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | |   (5188)  all_56_9 = e2 & op(e3, e0) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | ALPHA: (5188) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | |   (5189)  all_56_9 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | |   (5190)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | BETA: splitting (5190) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |   (5191)  all_56_12 = e2 & op(e0, e3) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | ALPHA: (5191) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |   (5192)  all_56_12 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |   (5193)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |            (5186), (5192), (5193), (function-axioms) are
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |   (5194)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5194) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | |   (5195)  all_56_6 = e3 & op(e1, e3) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5195) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | |   (5196)  all_56_6 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |   (5197)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |            (5186), (5189), (5197), (function-axioms) are
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #653.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |   (5198)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5198) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |   (5199)  all_56_4 = e3 & op(e3, e1) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5199) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |   (5200)  all_56_4 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (5201)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5201) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5202)  all_56_1 = e3 & op(e3, e2) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5202) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5203)  all_56_1 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (229), (231), (5186),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5189), (5203), (function-axioms) are inconsistent
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #654.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5204)  all_56_3 = e3 & op(e2, e2) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5204) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5205)  op(e2, e2) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5054), (5205), (function-axioms) are
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | |   (5206)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5206) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5207)  all_56_7 = e3 & op(e1, e2) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5207) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5208)  all_56_7 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5209)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5209) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5210)  all_56_6 = e1 & op(e1, e3) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5196), (5210) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #792.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5211)  all_56_7 = e1 & op(e1, e2) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5208), (5211) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1126.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5212)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5212) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5213)  all_56_8 = e1 & op(e1, e1) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5213) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5214)  op(e1, e1) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (5214), (function-axioms) are
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5215)  all_56_11 = e1 & op(e1, e0) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5215) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5216)  all_56_11 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5217)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5217) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5218)  all_56_6 = e0 & op(e1, e3) = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5196), (5218) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #778.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5219)  all_56_7 = e0 & op(e1, e2) = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5208), (5219) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1151.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5220)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (5032), (5216), (5220),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #362.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5221)  all_56_13 = e3 & op(e0, e2) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5221) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5222)  all_56_13 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5223)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5223) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5224)  all_56_9 = e1 & op(e3, e0) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5189), (5224) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #656.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5225)  all_56_10 = e1 & op(e2, e0) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5225) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5226)  all_56_10 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5227)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5227) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5228)  all_56_2 = e3 & op(e2, e3) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5228) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5229)  all_56_2 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (228), (230), (5186),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5192), (5229), (function-axioms) are inconsistent
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #787.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5230)  all_56_3 = e3 & op(e2, e2) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5230) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5231)  op(e2, e2) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5054), (5231), (function-axioms) are
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5232)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5232) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5233)  all_56_5 = e3 & op(e2, e1) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5233) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5234)  all_56_5 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5235)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5235) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5236)  all_56_4 = e1 & op(e3, e1) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5236) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5237)  all_56_4 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5200), (5237) imply:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5238)  e3 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5234), (5238) imply:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5239)  all_56_5 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (220), (223), (5054),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5226), (5239), (function-axioms) are inconsistent
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #681.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5240)  all_56_5 = e1 & op(e2, e1) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5240) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5241)  all_56_5 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (220), (223), (5054),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5226), (5241), (function-axioms) are inconsistent
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #681.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5242)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5242) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5243)  all_56_8 = e1 & op(e1, e1) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5243) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5244)  all_56_8 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5031), (5244) imply:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5245)  e3 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5234), (5245) imply:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5246)  all_56_5 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (220), (223), (5054),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5226), (5246), (function-axioms) are inconsistent
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #681.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5247)  all_56_14 = e1 & op(e0, e1) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5247) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5248)  all_56_14 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5249)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5249) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5250)  all_56_4 = e0 & op(e3, e1) = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5200), (5250) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #361.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5251)  all_56_5 = e0 & op(e2, e1) = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5234), (5251) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #885.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5252)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5252) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5253)  all_56_8 = e0 & op(e1, e1) = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5031), (5253) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #360.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5254)  all_56_14 = e0 & op(e0, e1) = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5248), (5254) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1118.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5255)  all_56_10 = e3 & op(e2, e0) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5255) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5256)  all_56_10 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5226), (5256) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #677.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5257)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5257) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5258)  all_56_11 = e1 & op(e1, e0) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5258) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5259)  all_56_11 = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5260)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5260) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5261)  all_56_6 = e0 & op(e1, e3) = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5261) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5262)  all_56_6 = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5196), (5262) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #784.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5263)  all_56_7 = e0 & op(e1, e2) = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5263) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5264)  all_56_7 = e0
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5265)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5265) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5266)  all_56_6 = e2 & op(e1, e3) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5266) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5267)  all_56_6 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5196), (5267) imply:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5268)  e3 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5268) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5269)  e3 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5222), (5269) imply:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5270)  all_56_13 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5054), (5270), (function-axioms) are inconsistent
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1104.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5271)  all_56_7 = e2 & op(e1, e2) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5271) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5272)  all_56_7 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5264), (5272) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #483.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5273)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5273) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5274)  all_56_8 = e2 & op(e1, e1) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5274) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5275)  op(e1, e1) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (5275), (function-axioms) are
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5276)  all_56_11 = e2 & op(e1, e0) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5276) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5277)  all_56_11 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (213), (5031), (5196), (5264),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5277) are inconsistent by sub-proof #609.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5278)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (5032), (5259), (5278),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #610.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5279)  all_56_15 = e1 & op(e0, e0) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5279) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5280)  op(e0, e0) = e1
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (205), (218),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (5032), (5051), (5054),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5192), (5200), (5222), (5280), (function-axioms)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #359.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |   (5281)  all_56_9 = e3 & op(e3, e0) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5281) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |   (5282)  all_56_9 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5189), (5282) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | |            #964.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | |   (5283)  all_56_12 = e3 & op(e0, e3) = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5283) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | |   (5284)  all_56_12 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5192), (5284) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | |            #869.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |   (5285)  all_56_13 = e2 & op(e0, e2) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | ALPHA: (5285) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |   (5286)  all_56_13 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |            (5054), (5286), (function-axioms) are inconsistent
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |            by sub-proof #1104.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | |   (5287)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 147.47/20.87  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | BETA: splitting (5287) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |   (5288)  all_56_14 = e2 & op(e0, e1) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | ALPHA: (5288) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |   (5289)  all_56_14 = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |   (5290)  op(e0, e1) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |   (5291)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |            (5186), (5189), (5291), (function-axioms) are
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #653.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |   (5292)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (217),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |            (5031), (5032), (5189), (5289), (5290), (5292),
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | |            #353.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |   (5293)  all_56_15 = e2 & op(e0, e0) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | ALPHA: (5293) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |   (5294)  op(e0, e0) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5058), (5294), (function-axioms) are
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | |   (5295)  all_56_10 = e2 & op(e2, e0) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | ALPHA: (5295) implies:
% 147.47/20.87  | | | | | | | | | | | | | | | | | |   (5296)  op(e2, e0) = e2
% 147.47/20.87  | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5052), (5296), (function-axioms) are
% 147.47/20.87  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 147.47/20.87  | | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | End of split
% 147.47/20.87  | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.87  | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | |   (5297)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 147.47/20.87  | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 147.47/20.87  | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | BETA: splitting (5297) gives:
% 147.47/20.87  | | | | | | | | | | | | | | | | | 
% 147.47/20.87  | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.87  | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | |   (5298)  all_56_11 = e2 & op(e1, e0) = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | ALPHA: (5298) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | |   (5299)  all_56_11 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | |   (5300)  op(e1, e0) = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | |   (5301)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | BETA: splitting (5301) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |   (5302)  all_56_12 = e2 & op(e0, e3) = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | ALPHA: (5302) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |   (5303)  all_56_12 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | |   (5304)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230),
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | |            (5186), (5303), (5304), (function-axioms) are
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #786.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | |   (5305)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5305) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | |   (5306)  all_56_6 = e3 & op(e1, e3) = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5306) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | |   (5307)  all_56_6 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | |            (5299), (5307) are inconsistent by sub-proof #608.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | |   (5308)  all_56_12 = e3 & op(e0, e3) = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5308) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | |   (5309)  all_56_12 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5303), (5309) are inconsistent by sub-proof
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | |            #869.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |   (5310)  all_56_13 = e2 & op(e0, e2) = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | ALPHA: (5310) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |   (5311)  all_56_13 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |            (5054), (5311), (function-axioms) are inconsistent
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |            by sub-proof #1104.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | |   (5312)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | BETA: splitting (5312) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |   (5313)  all_56_14 = e2 & op(e0, e1) = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | ALPHA: (5313) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |   (5314)  all_56_14 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |   (5315)  op(e0, e1) = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |              e2, e1, e0, simplifying with (156), (5315) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |   (5316)  all_52_11 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |              e2, e0, e1, simplifying with (159), (5300) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |   (5317)  all_52_14 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (5317) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |   (5318)   ~ (all_52_2 = e2)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (5317) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | |   (5319)   ~ (all_10_2 = e2)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | |   (5320)   ~ (all_42_2 = e3)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | REDUCE: (302), (5320) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | |   (5321)   ~ (all_10_2 = e3)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | |   (5322)  all_54_15 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5322) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | |   (5323)  all_10_2 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5321), (5323) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | |   (5324)  $false
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5324) is inconsistent.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | |   (5325)   ~ (all_54_15 = e3)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | |   (5326)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5326) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | |   (5327)  all_54_15 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5327) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | |   (5328)  all_10_2 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5058), (5328) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | |   (5329)  $false
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5329) is inconsistent.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | |   (5330)   ~ (all_54_15 = e2)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | |   (5331)  all_54_15 = e1 | all_54_15 = e0
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5331) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | |   (5332)  all_54_15 = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5332) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | |   (5333)  all_10_2 = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5033), (5333) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | |   (5334)  $false
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5334) is inconsistent.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | |   (5335)  all_54_15 = e0
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5335) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | |   (5336)  all_10_2 = e0
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (5336) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | |   (5337)   ~ (all_52_3 = e0)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (5336) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | |   (5338)   ~ (all_52_7 = e0)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5321), (5336) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | |   (5339)   ~ (e3 = e0)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5058), (5336) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | |   (5340)   ~ (e2 = e0)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5033), (5336) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | |   (5341)   ~ (e1 = e0)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (5336) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | |   (5342)  op(e0, e0) = e0
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |   (5343)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5343) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5344)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5344) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5345)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5345) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5346)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5346) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5347)  op(e2, e3) = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (166), (5347) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5348)  all_52_1 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5048), (5348) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5349)  $false
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5349) is inconsistent.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5350)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5350) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5351)  op(e0, e0) = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5342), (5351), (function-axioms) are
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5352)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (5342), (5352), (function-axioms) are
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #352.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5353)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5353) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5354)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (5032), (5058), (5354),
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #367.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5355)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5355) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5356)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5356) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5357)  all_57_10 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5358)   ~ (all_57_14 = e2)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5359)   ~ (all_57_3 = e3)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5360)  op(e1, e2) = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5361)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5361) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5362)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5362) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5363)  op(e3, e3) = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5186), (5363), (function-axioms) are
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5364)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5364) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5365)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e3, e3) = all_57_10 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5357), (5359), (5365) are inconsistent by
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1018.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5366)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5366) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5367)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5367) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5368)  op(e1, e1) = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (5368), (function-axioms) are
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5369)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5369) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5370)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5371)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5371) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5372)  all_57_11 = e2 & op(e2, e0) = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5372) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5373)  op(e2, e0) = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5052), (5373), (function-axioms) are
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5374)   ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5374) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5375)   ~ (all_57_12 = e0)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5376)  op(e2, e2) = all_57_12
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5370) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5377)  all_57_13 = e1 & op(e1, e0) = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5377) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5378)  op(e1, e0) = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5300), (5378), (function-axioms) are
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1125.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5379)   ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5379) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5380)   ~ (all_57_14 = e0)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5381)  op(e1, e1) = all_57_14
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14, e1, e1, simplifying with (5032), (5381)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5382)  all_57_14 = e3
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (161), (5360) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5383)  all_52_6 = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (5054), (5376)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5384)  all_57_12 = e2
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (5383) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5385)   ~ (all_52_2 = e1)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5023), (5383) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5386)   ~ (e3 = e1)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5050), (5383) imply:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5387)   ~ (e2 = e1)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5388)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5388) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5389)  all_56_1 = e0 & op(e3, e2) = e0
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5389) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5390)  all_56_1 = e0
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5391)  op(e3, e2) = e0
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5392)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5392) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5393)  all_56_12 = e1 & op(e0, e3) = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5393) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5394)  op(e0, e3) = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5183), (5391), (5394), (function-axioms) are
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #767.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5395)  all_56_13 = e1 & op(e0, e2) = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5395) implies:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5396)  all_56_13 = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213), (227),
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5031), (5054), (5299), (5390), (5396),
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #351.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5397)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5397) gives:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5398)  all_56_14 = e1 & op(e0, e1) = e1
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5314), (5398) are inconsistent by sub-proof
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #357.
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.88  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5399)  all_56_15 = e1 & op(e0, e0) = e1
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5399) implies:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5400)  op(e0, e0) = e1
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5342), (5400), (function-axioms) are
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5401)  all_56_3 = e0 & op(e2, e2) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5401) implies:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5402)  op(e2, e2) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5054), (5402), (function-axioms) are
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5403)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5403) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5404)  all_56_7 = e0 & op(e1, e2) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5404) implies:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5405)  all_56_7 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5406)  all_54_8 = e3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (5022), (5406) are inconsistent by
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #394.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5407)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5407) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5408)  all_54_8 = e2
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (5318), (5408) are inconsistent by
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #463.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5409)  all_54_8 = e1 | all_54_8 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5409) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5410)  all_54_8 = e1
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (5385), (5410) are inconsistent by
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #462.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5411)  all_54_8 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (5411) imply:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5412)  all_52_2 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5412) implies:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5413)  all_52_2 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (5413) imply:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5414)  op(e1, e3) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (162), (213), (5032), (5300),
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5405), (5414), (function-axioms) are inconsistent
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #349.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5415)  all_56_13 = e0 & op(e0, e2) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5415) implies:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5416)  op(e0, e2) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (5338), (5416), (function-axioms) are
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5417)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (45), (5054), (5058), (5417),
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1084.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |   (5418)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5418) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5419)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5419) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5420)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (5051), (5342), (5420),
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1039.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5421)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5421) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5422)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5422) implies:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5423)  op(e0, e0) = e1
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5342), (5423), (function-axioms) are
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5424)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (5032), (5054), (5424),
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #434.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5425)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5425) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5426)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5186), (5426), (function-axioms) are
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5427)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5427) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5428)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5428) implies:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5429)  op(e1, e1) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (5429), (function-axioms) are
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5430)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5430) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5431)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5431) implies:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5432)  op(e1, e0) = e1
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5300), (5432), (function-axioms) are
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1125.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5433)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5433) implies:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5434)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (157), (158), (5032), (5054),
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5315), (5337), (5338), (5434), (function-axioms)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #348.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | |   (5435)  all_42_2 = e3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (5435) imply:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | |   (5436)  all_10_2 = e3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (5436) imply:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | |   (5437)  op(e0, e0) = e3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |   (5438)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5438) gives:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |   (5439)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5439) implies:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |   (5440)  op(e3, e3) = e3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5186), (5440), (function-axioms) are
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |   (5441)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5441) implies:
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |   (5442)  all_57_12 = e2
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |   (5443)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e0, e0) = all_57_15 &
% 147.47/20.89  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | |   (5444)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e1, e1) = all_57_14 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | |   (5445)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e3, e3) = all_57_10 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5445) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | |   (5446)  all_57_3 = e3 & op(e3, e2) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5446) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | |   (5447)  all_57_3 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | |   (5448)  op(e3, e2) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (5449)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5449) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5450)  all_56_1 = e3 & op(e3, e2) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5450) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5451)  all_56_1 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (158), (162),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (167), (168), (205), (206), (211),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (216), (217), (220), (221), (223),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (229), (230), (231), (234),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (5031), (5032), (5051), (5054), (5058),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5186), (5299), (5300), (5314), (5315), (5437),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5442), (5444), (5447), (5451), (function-axioms)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #316.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5452)  all_56_3 = e3 & op(e2, e2) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5452) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5453)  op(e2, e2) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5054), (5453), (function-axioms) are
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (5454)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5454) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5455)  all_56_7 = e3 & op(e1, e2) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5455) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5456)  all_56_7 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5299), (5456) are inconsistent by sub-proof #643.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5457)  all_56_13 = e3 & op(e0, e2) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5457) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5458)  all_56_13 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (139), (157),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (162), (164), (166), (167), (168), (169),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (205), (206), (209), (211), (212), (213), (216),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (220), (221), (223), (224), (225), (227),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (234), (235), (238), (5031),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5032), (5051), (5054), (5058), (5186), (5299),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5300), (5314), (5315), (5437), (5442), (5443),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5444), (5447), (5448), (5458), (function-axioms)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #300.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | |   (5459)   ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5459) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | |   (5460)   ~ (all_57_10 = e2)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (5461)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5461) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5462)  all_56_1 = e3 & op(e3, e2) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5462) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5463)  all_56_1 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5464)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5464) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5465)  all_56_0 = e3 & op(e3, e3) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5465) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5466)  op(e3, e3) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5186), (5466), (function-axioms) are
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5467)  all_56_2 = e3 & op(e2, e3) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5467) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5468)  all_56_2 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5469)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (220), (221), (229),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (5054), (5186), (5463), (5468), (5469),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #344.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5470)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5470) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5471)  all_56_11 = e3 & op(e1, e0) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213), (224),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (5031), (5054), (5299), (5463),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5471), (function-axioms) are inconsistent by
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #317.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5472)  all_56_15 = e3 & op(e0, e0) = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5472) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5473)  all_56_15 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5474)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5474) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5475)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5475) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5476)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5476) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5477)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5477) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5478)  op(e2, e3) = e2
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (212), (213),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (223), (224), (225), (227), (5031),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5054), (5299), (5463), (5468), (5478),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #340.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5479)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5479) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5480)  op(e2, e3) = e2
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (212), (213),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (223), (224), (225), (227), (5031),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5054), (5299), (5463), (5468), (5480),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #340.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5481)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5032), (5481), (function-axioms) are inconsistent
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #368.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5482)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5482) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5483)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5483) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5484)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5484) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5485)  all_57_3 = e3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (158), (162),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (167), (168), (205), (206), (211),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (216), (217), (220), (221), (223),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (227), (229), (230), (231), (234),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (5031), (5032), (5051), (5054), (5058),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5186), (5299), (5300), (5314), (5315), (5437),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5442), (5444), (5463), (5485), (function-axioms)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #316.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5486)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5486) implies:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5487)  op(e0, e0) = e2
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5058), (5487), (function-axioms) are
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5488)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (45), (5054), (5058), (5460), (5488),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #299.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5489)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5489) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5490)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (211), (212),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (220), (221), (224), (225), (227), (229),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (5031), (5032), (5051), (5054), (5186),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5299), (5437), (5463), (5467), (5473), (5490),
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #337.
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5491)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5491) gives:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5492)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5186), (5492), (function-axioms) are
% 147.47/20.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5493)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5493) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5494)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5494) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5495)  op(e1, e1) = e0
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (5495), (function-axioms) are
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5496)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5496) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5497)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5497) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5498)  op(e1, e0) = e1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5300), (5498), (function-axioms) are
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1125.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5499)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5499) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5500)  op(e0, e0) = all_57_15
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5501)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (139), (157), (158), (5054), (5315),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5437), (5444), (5460), (5500), (5501),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #297.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5502)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5502) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5503)  all_56_6 = e3 & op(e1, e3) = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5503) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5504)  all_56_6 = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5299), (5504) are inconsistent by sub-proof #608.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5505)  all_56_12 = e3 & op(e0, e3) = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5505) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5506)  all_56_12 = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5507)  op(e0, e3) = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5508)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5508) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5509)  all_56_12 = e1 & op(e0, e3) = e1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5509) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5510)  all_56_12 = e1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5506), (5510) are inconsistent by sub-proof
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1056.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5511)  all_56_13 = e1 & op(e0, e2) = e1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5511) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5512)  all_56_13 = e1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (205), (5315), (5437), (5506),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5512), (function-axioms) are inconsistent by
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #335.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5513)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5513) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5514)  all_56_14 = e1 & op(e0, e1) = e1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5314), (5514) are inconsistent by sub-proof
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #357.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5515)  all_56_15 = e1 & op(e0, e0) = e1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5515) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5516)  all_56_15 = e1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5517)  op(e0, e0) = e1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5518)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5518) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5519)  all_56_9 = e3 & op(e3, e0) = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5519) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5520)  all_56_9 = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (229), (231), (5186),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5463), (5520), (function-axioms) are inconsistent
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #345.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5521)  all_56_10 = e3 & op(e2, e0) = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5521) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5522)  all_56_10 = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5523)  all_56_15 = e0 & op(e0, e0) = e0
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5523) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5524)  op(e0, e0) = e0
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5437), (5524), (function-axioms) are
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5525)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5525) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5526)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5527)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5528)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5528) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5529)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5529) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5530)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5530) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5531)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5531) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5532)  op(e2, e3) = e2
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (216), (221),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (5031), (5054), (5186), (5299), (5315),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5463), (5522), (5527), (5532), (function-axioms)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #332.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5533)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5533) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5534)  op(e2, e3) = e2
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (166), (216), (221),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (5031), (5054), (5186), (5299), (5315),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5463), (5522), (5527), (5534), (function-axioms)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #332.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5535)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (212), (225),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5032), (5054), (5299), (5315), (5437), (5463),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5506), (5517), (5526), (5535), (function-axioms)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #327.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5536)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5536) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5537)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5537) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5538)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5538) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5539)  all_57_3 = e3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (45), (158), (162),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (167), (168), (205), (212), (216),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (220), (221), (225), (230), (231), (238),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5031), (5032), (5051), (5054), (5058), (5186),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5299), (5300), (5314), (5315), (5437), (5442),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5444), (5463), (5506), (5507), (5516), (5517),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5522), (5539), (function-axioms) are inconsistent
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #318.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5540)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5540) implies:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5541)  op(e0, e0) = e2
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5058), (5541), (function-axioms) are
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5542)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (45), (5054), (5058), (5460), (5542),
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #299.
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5543)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5543) gives:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.91  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5544)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5544) gives:
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5545)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (162), (164), (168),
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (217), (220), (225), (230), (5032), (5051),
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5054), (5186), (5299), (5314), (5315), (5437),
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5463), (5506), (5522), (5526), (5545),
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #324.
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.47/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5546)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5546) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5547)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5547) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5548)  op(e2, e1) = e2
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5051), (5548), (function-axioms) are
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5549)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5549) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5550)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5550) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5551)  op(e3, e0) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (167), (5299), (5437), (5517),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5522), (5527), (5551), (function-axioms) are
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #321.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5552)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5552) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5553)  op(e3, e0) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (167), (5299), (5437), (5517),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5522), (5527), (5553), (function-axioms) are
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #321.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5554)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5554) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5555)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5186), (5555), (function-axioms) are
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5556)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5556) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5557)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5557) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5558)  op(e1, e1) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5032), (5437), (5517), (5558),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #331.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5559)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5559) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5560)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5560) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5561)  op(e1, e0) = e1
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5300), (5561), (function-axioms) are
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1125.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5562)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5562) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5563)  op(e0, e0) = all_57_15
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5564)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (139), (157), (158), (5054), (5315),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5437), (5444), (5460), (5563), (5564),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #297.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5565)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5565) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5566)  all_56_11 = e3 & op(e1, e0) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213), (224),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (5031), (5054), (5299), (5463),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5566), (function-axioms) are inconsistent by
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #342.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5567)  all_56_15 = e3 & op(e0, e0) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5516), (5567) are inconsistent by sub-proof
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #338.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5568)  all_56_3 = e3 & op(e2, e2) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5568) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5569)  op(e2, e2) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5054), (5569), (function-axioms) are
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | |   (5570)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5570) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5571)  all_56_7 = e3 & op(e1, e2) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5571) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5572)  all_56_7 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5299), (5572) are inconsistent by sub-proof #643.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5573)  all_56_13 = e3 & op(e0, e2) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5573) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5574)  all_56_13 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5443) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5575)  all_57_5 = e0 & op(e0, e2) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (139), (157), (158), (205), (5315),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5437), (5574), (5575), (function-axioms) are
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #313.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5576)   ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_15)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5576) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5577)   ~ (all_57_15 = e2)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5578)  op(e0, e0) = all_57_15
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5579)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5579) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5580)  all_56_0 = e3 & op(e3, e3) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5580) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5581)  op(e3, e3) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5186), (5581), (function-axioms) are
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5582)  all_56_2 = e3 & op(e2, e3) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5582) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5583)  all_56_2 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5584)  op(e2, e3) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5585)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5585) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5586)  all_56_0 = e3 & op(e3, e3) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5586) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5587)  op(e3, e3) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5186), (5587), (function-axioms) are
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5588)  all_56_1 = e3 & op(e3, e2) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5588) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5589)  all_56_1 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (224), (225), (5054),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5574), (5589), (function-axioms) are inconsistent
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #877.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5590)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5590) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5591)  all_56_4 = e3 & op(e3, e1) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5591) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5592)  all_56_4 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (217), (220),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (221), (223), (5031), (5054), (5314), (5583),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5592), (function-axioms) are inconsistent by
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #312.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5593)  all_56_9 = e3 & op(e3, e0) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5593) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5594)  all_56_9 = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5595)  op(e3, e0) = e3
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5596)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5596) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5597)  all_56_9 = e1 & op(e3, e0) = e1
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5594), (5597) are inconsistent by sub-proof
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #493.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5598)  all_56_10 = e1 & op(e2, e0) = e1
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (167), (205),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (206), (212), (217), (220), (223), (225), (229),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (5032), (5054), (5186), (5299), (5314),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5437), (5574), (5583), (5595), (5598),
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #306.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5599)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5599) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5600)  all_56_11 = e1 & op(e1, e0) = e1
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5600) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5601)  op(e1, e0) = e1
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5300), (5601), (function-axioms) are
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1125.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5602)  all_56_15 = e1 & op(e0, e0) = e1
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5602) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5603)  op(e0, e0) = e1
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5604)  all_56_15 = e0 & op(e0, e0) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5604) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5605)  op(e0, e0) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5437), (5605), (function-axioms) are
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5606)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5606) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5607)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5607) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5608)  all_56_12 = e0 & op(e0, e3) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5608) implies:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5609)  op(e0, e3) = e0
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.92  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5610)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5610) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5611)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5611) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5612)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5612) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5613)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5613) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5614)  op(e2, e3) = e2
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (5437), (5584), (5603), (5614),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #296.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5615)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5615) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5616)  all_57_15 = e3
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5617)  op(e2, e3) = e2
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (5437), (5584), (5603), (5617),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #296.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5618)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5032), (5618), (function-axioms) are inconsistent
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #368.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5619)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5619) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5620)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5620) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5621)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5621) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5622)  all_57_3 = e3
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5623)  op(e3, e2) = e3
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (139), (157),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (162), (164), (166), (167), (168), (169),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (205), (206), (209), (211), (212), (213), (216),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (220), (221), (223), (224), (225), (227),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (231), (234), (235), (238), (5031),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5032), (5051), (5054), (5058), (5186), (5299),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5300), (5314), (5315), (5437), (5442), (5443),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5444), (5574), (5622), (5623), (function-axioms)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #300.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5624)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5624) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5625)  op(e0, e0) = e2
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5058), (5625), (function-axioms) are
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5626)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (45), (5054), (5058), (5460), (5626),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #299.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5627)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5627) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5628)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5628) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5629)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5629) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5630)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5630) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5631)  all_57_15 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5632)  op(e3, e1) = e3
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5577), (5631) imply:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5633)   ~ (e2 = e1)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5634)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (5186), (5583), (5634),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #310.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5635)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5635) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5636)  all_56_6 = e1 & op(e1, e3) = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5636) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5637)  op(e1, e3) = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5638)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (5054), (5583), (5638),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #364.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5639)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5639) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5640)  all_56_5 = e1 & op(e2, e1) = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5640) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5641)  all_56_5 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5642)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5642) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5643)  all_56_1 = e1 & op(e3, e2) = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5643) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5644)  all_56_1 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5645)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (168), (217), (5032), (5186),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5314), (5632), (5641), (5644), (5645),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #304.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5646)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5646) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5647)  all_56_4 = e0 & op(e3, e1) = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5647) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5648)  op(e3, e1) = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e0,
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0, simplifying with (5437), (5603) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5649)  e3 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (5648) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5650)  all_52_8 = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (5632) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5651)  all_52_8 = e3
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5650), (5651) imply:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5652)  e3 = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (168), (217), (5032), (5314),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5632), (5641), (5649), (5652), (function-axioms)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #303.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5653)  all_56_9 = e0 & op(e3, e0) = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (5437), (5595), (5603), (5653),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #323.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5654)  all_56_3 = e1 & op(e2, e2) = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5654) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5655)  op(e2, e2) = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5054), (5655), (function-axioms) are
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5656)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5656) gives:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5657)  all_56_7 = e1 & op(e1, e2) = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (162), (212), (5032), (5299), (5437),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5603), (5637), (5657), (function-axioms) are
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #329.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5658)  all_56_13 = e1 & op(e0, e2) = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5658) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5659)  all_56_13 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5574), (5659) are inconsistent by sub-proof
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1121.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5660)  all_56_10 = e1 & op(e2, e0) = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5660) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5661)  all_56_10 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (167), (212),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (220), (223), (225), (229), (230), (5032),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5054), (5186), (5299), (5314), (5437), (5574),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5583), (5595), (5603), (5607), (5661),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #307.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5662)  all_56_12 = e1 & op(e0, e3) = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5662) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5663)  all_56_12 = e1
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (5314), (5574), (5607), (5663) are
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1100.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5664)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5664) implies:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5665)  op(e2, e1) = e2
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5051), (5665), (function-axioms) are
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5666)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (164), (5032), (5051), (5054), (5437),
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5603), (5666), (function-axioms) are inconsistent
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #302.
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.93  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5667)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5667) gives:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5668)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5186), (5668), (function-axioms) are
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5669)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5669) gives:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5670)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5670) implies:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5671)  op(e1, e1) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5032), (5437), (5603), (5671),
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #331.
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5672)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5672) gives:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5673)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5673) implies:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5674)  op(e1, e0) = e1
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5300), (5674), (function-axioms) are
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1125.
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5675)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5675) implies:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5676)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (139), (157), (158), (5054), (5315),
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5437), (5444), (5578), (5609), (5676),
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #298.
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5677)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5677) gives:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5678)  all_56_13 = e0 & op(e0, e2) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5678) implies:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5679)  op(e0, e2) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (139), (157), (158), (5315), (5574),
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5607), (5679), (function-axioms) are inconsistent
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #314.
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5680)  all_56_14 = e0 & op(e0, e1) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5680) implies:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5681)  op(e0, e1) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5315), (5681), (function-axioms) are
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1008.
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5682)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (158), (205), (206),
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (212), (213), (5031), (5299), (5314), (5315),
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5437), (5574), (5578), (5682), (function-axioms)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #301.
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |   (5683)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (5032), (5437), (5683),
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |            #295.
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | |   (5684)  all_56_15 = e2 & op(e0, e0) = e2
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (5684) implies:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | |   (5685)  op(e0, e0) = e2
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5058), (5685), (function-axioms) are
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | |   (5686)  all_56_15 = e2 & op(e0, e0) = e2
% 147.80/20.94  | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | ALPHA: (5686) implies:
% 147.80/20.94  | | | | | | | | | | | | | | | | | |   (5687)  op(e0, e0) = e2
% 147.80/20.94  | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5058), (5687), (function-axioms) are
% 147.80/20.94  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 147.80/20.94  | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | |   (5688)  all_24_2 = e2
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | COMBINE_EQS: (318), (5688) imply:
% 147.80/20.94  | | | | | | | | | | | | | | |   (5689)  all_10_2 = e2
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | SIMP: (5689) implies:
% 147.80/20.94  | | | | | | | | | | | | | | |   (5690)  all_10_2 = e2
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | REDUCE: (367), (5690) imply:
% 147.80/20.94  | | | | | | | | | | | | | | |   (5691)   ~ (all_52_11 = e2)
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | REDUCE: (370), (5690) imply:
% 147.80/20.94  | | | | | | | | | | | | | | |   (5692)   ~ (all_52_14 = e2)
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | REDUCE: (45), (5690) imply:
% 147.80/20.94  | | | | | | | | | | | | | | |   (5693)  op(e0, e0) = e2
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (45), (51), (122), (139), (142),
% 147.80/20.94  | | | | | | | | | | | | | | |            (148), (156), (157), (158), (159), (161), (162),
% 147.80/20.94  | | | | | | | | | | | | | | |            (163), (164), (166), (168), (169), (203), (214),
% 147.80/20.94  | | | | | | | | | | | | | | |            (218), (237), (238), (278), (342), (344), (5032),
% 147.80/20.94  | | | | | | | | | | | | | | |            (5033), (5037), (5050), (5051), (5052), (5054),
% 147.80/20.94  | | | | | | | | | | | | | | |            (5056), (5691), (5692), (5693), (function-axioms)
% 147.80/20.94  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #288.
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | End of split
% 147.80/20.94  | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | |   (5694)  all_22_2 = e1
% 147.80/20.94  | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | COMBINE_EQS: (320), (5694) imply:
% 147.80/20.94  | | | | | | | | | | | | | |   (5695)  all_14_2 = e1
% 147.80/20.94  | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | SIMP: (5695) implies:
% 147.80/20.94  | | | | | | | | | | | | | |   (5696)  all_14_2 = e1
% 147.80/20.94  | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | REDUCE: (342), (5696) imply:
% 147.80/20.94  | | | | | | | | | | | | | |   (5697)   ~ (all_52_4 = e1)
% 147.80/20.94  | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | REDUCE: (344), (5696) imply:
% 147.80/20.94  | | | | | | | | | | | | | |   (5698)   ~ (all_52_8 = e1)
% 147.80/20.94  | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | REDUCE: (51), (5696) imply:
% 147.80/20.94  | | | | | | | | | | | | | |   (5699)  op(e3, e3) = e1
% 147.80/20.94  | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 147.80/20.94  | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | |   (5700)   ~ (all_24_2 = e2)
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | REDUCE: (318), (5700) imply:
% 147.80/20.94  | | | | | | | | | | | | | | |   (5701)   ~ (all_10_2 = e2)
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (45), (93), (124), (138),
% 147.80/20.94  | | | | | | | | | | | | | | |            (139), (156), (157), (158), (161), (162), (163),
% 147.80/20.94  | | | | | | | | | | | | | | |            (164), (166), (169), (188), (205), (206), (207),
% 147.80/20.94  | | | | | | | | | | | | | | |            (209), (210), (212), (213), (214), (216), (217),
% 147.80/20.94  | | | | | | | | | | | | | | |            (218), (220), (221), (223), (224), (225), (227),
% 147.80/20.94  | | | | | | | | | | | | | | |            (228), (229), (231), (232), (233), (234), (235),
% 147.80/20.94  | | | | | | | | | | | | | | |            (238), (245), (302), (349), (367), (5023), (5025),
% 147.80/20.94  | | | | | | | | | | | | | | |            (5031), (5032), (5033), (5048), (5049), (5050),
% 147.80/20.94  | | | | | | | | | | | | | | |            (5051), (5052), (5054), (5697), (5699), (5701),
% 147.80/20.94  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.94  | | | | | | | | | | | | | | |            #277.
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | |   (5702)  all_24_2 = e2
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | COMBINE_EQS: (318), (5702) imply:
% 147.80/20.94  | | | | | | | | | | | | | | |   (5703)  all_10_2 = e2
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | SIMP: (5703) implies:
% 147.80/20.94  | | | | | | | | | | | | | | |   (5704)  all_10_2 = e2
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | REDUCE: (367), (5704) imply:
% 147.80/20.94  | | | | | | | | | | | | | | |   (5705)   ~ (all_52_11 = e2)
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | REDUCE: (45), (5704) imply:
% 147.80/20.94  | | | | | | | | | | | | | | |   (5706)  op(e0, e0) = e2
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 147.80/20.94  | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | |   (5707)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 147.80/20.94  | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 147.80/20.94  | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | BETA: splitting (5707) gives:
% 147.80/20.94  | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | |   (5708)  all_56_4 = e2 & op(e3, e1) = e2
% 147.80/20.94  | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | ALPHA: (5708) implies:
% 147.80/20.94  | | | | | | | | | | | | | | | | |   (5709)  op(e3, e1) = e2
% 147.80/20.94  | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 147.80/20.94  | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | |   (5710)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.80/20.94  | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 147.80/20.94  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | BETA: splitting (5710) gives:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |   (5711)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | ALPHA: (5711) implies:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |   (5712)  op(e3, e3) = e3
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5699), (5712), (function-axioms) are
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |   (5713)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | ALPHA: (5713) implies:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |   (5714)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |               = e2) & op(e0, e0) = all_57_15 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | BETA: splitting (5714) gives:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | |   (5715)  all_57_5 = e0 & op(e0, e2) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | ALPHA: (5715) implies:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | |   (5716)  all_57_5 = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | |   (5717)  op(e0, e2) = e0
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |   (5718)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5718) gives:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |   (5719)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.94  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5719) gives:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |   (5720)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (5048), (5720), (function-axioms) are
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |   (5721)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5032), (5721), (function-axioms) are inconsistent
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #368.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |   (5722)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5722) gives:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |   (5723)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (5716), (5723), (function-axioms) are
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #276.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |   (5724)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5724) gives:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |   (5725)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5725) implies:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |   (5726)  op(e3, e3) = e2
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5699), (5726), (function-axioms) are
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |   (5727)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5054), (5716), (5727), (function-axioms) are
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #532.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |   (5728)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5728) gives:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |   (5729)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5729) gives:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |   (5730)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (164), (5033), (5051), (5730),
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |            #544.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |   (5731)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (45), (5032), (5033), (5054), (5731),
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |            #293.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |   (5732)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5732) gives:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |   (5733)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5699), (5733), (function-axioms) are
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |   (5734)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5734) gives:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |   (5735)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5735) implies:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |   (5736)  op(e2, e0) = e2
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5052), (5736), (function-axioms) are
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |   (5737)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5737) gives:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (5738)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5738) implies:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (5739)  op(e2, e2) = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5054), (5739), (function-axioms) are
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (5740)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5740) implies:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (5741)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (157), (5717) gives:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (5742)  all_52_7 = e0
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (5709) gives:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (5743)  all_52_8 = e2
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (5742) imply:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (5744)   ~ (all_52_3 = e0)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (5742) imply:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (5745)   ~ (all_52_11 = e0)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5745) implies:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |   (5746)   ~ (all_52_11 = e0)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (156), (158), (5032), (5054), (5699),
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |            (5741), (5744), (5746), (function-axioms) are
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #287.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | |   (5747)   ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | |           $i(all_57_15)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | ALPHA: (5747) implies:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | |   (5748)   ~ (all_57_15 = e2)
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | |   (5749)  op(e0, e0) = all_57_15
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5706), (5748), (5749), (function-axioms) are
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #901.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | |   (5750)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.80/20.95  | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.95  | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.80/20.95  | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.80/20.95  | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5032), (5706), (5750),
% 147.80/20.95  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.95  | | | | | | | | | | | | | | | | | |            #291.
% 147.80/20.95  | | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | |   (5751)  all_56_5 = e2 & op(e2, e1) = e2
% 147.80/20.95  | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | ALPHA: (5751) implies:
% 147.80/20.95  | | | | | | | | | | | | | | | | |   (5752)  op(e2, e1) = e2
% 147.80/20.95  | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5051), (5752), (function-axioms) are
% 147.80/20.95  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 147.80/20.95  | | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | |   (5753)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 147.80/20.95  | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 147.80/20.95  | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (5032), (5705), (5753),
% 147.80/20.95  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.95  | | | | | | | | | | | | | | | |            #275.
% 147.80/20.95  | | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | |   (5754)  all_54_5 = e1 | all_54_5 = e0
% 147.80/20.95  | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | | REF_CLOSE: (267), (5039), (5041), (5754) are inconsistent by
% 147.80/20.95  | | | | | | | | | | | | |            sub-proof #866.
% 147.80/20.95  | | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | End of split
% 147.80/20.95  | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | Case 2:
% 147.80/20.95  | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | |   (5755)  all_20_2 = e1
% 147.80/20.95  | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | COMBINE_EQS: (282), (5755) imply:
% 147.80/20.95  | | | | | | | | | | |   (5756)  all_6_2 = e1
% 147.80/20.95  | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | SIMP: (5756) implies:
% 147.80/20.95  | | | | | | | | | | |   (5757)  all_6_2 = e1
% 147.80/20.95  | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | COMBINE_EQS: (331), (5757) imply:
% 147.80/20.95  | | | | | | | | | | |   (5758)  all_38_2 = e1
% 147.80/20.95  | | | | | | | | | | | 
% 147.80/20.95  | | | | | | | | | | | REDUCE: (347), (5757) imply:
% 147.80/20.96  | | | | | | | | | | |   (5759)   ~ (all_52_1 = e1)
% 147.80/20.96  | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | REDUCE: (352), (5757) imply:
% 147.80/20.96  | | | | | | | | | | |   (5760)   ~ (all_52_6 = e1)
% 147.80/20.96  | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | REDUCE: (358), (5757) imply:
% 147.80/20.96  | | | | | | | | | | |   (5761)   ~ (all_52_13 = e1)
% 147.80/20.96  | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | REDUCE: (372), (5757) imply:
% 147.80/20.96  | | | | | | | | | | |   (5762)   ~ (e3 = e1)
% 147.80/20.96  | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | REDUCE: (39), (5757) imply:
% 147.80/20.96  | | | | | | | | | | |   (5763)  op(e2, e2) = e1
% 147.80/20.96  | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | BETA: splitting (225) gives:
% 147.80/20.96  | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | |   (5764)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 147.80/20.96  | | | | | | | | | | | |             & op(e2, e2) = e1)
% 147.80/20.96  | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | BETA: splitting (5764) gives:
% 147.80/20.96  | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | |   (5765)  all_56_1 = e1 & op(e3, e2) = e1
% 147.80/20.96  | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | ALPHA: (5765) implies:
% 147.80/20.96  | | | | | | | | | | | | |   (5766)  all_56_1 = e1
% 147.80/20.96  | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 147.80/20.96  | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (226), (227),
% 147.80/20.96  | | | | | | | | | | | | |            (5023), (5025), (5763), (5766), (function-axioms)
% 147.80/20.96  | | | | | | | | | | | | |            are inconsistent by sub-proof #262.
% 147.80/20.96  | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | |   (5767)  all_56_3 = e1 & op(e2, e2) = e1
% 147.80/20.96  | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | ALPHA: (5767) implies:
% 147.80/20.96  | | | | | | | | | | | | |   (5768)  all_56_3 = e1
% 147.80/20.96  | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 147.80/20.96  | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | |   (5769)   ~ (all_22_2 = e1)
% 147.80/20.96  | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | REDUCE: (320), (5769) imply:
% 147.80/20.96  | | | | | | | | | | | | | |   (5770)   ~ (all_14_2 = e1)
% 147.80/20.96  | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 147.80/20.96  | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | |   (5771)   ~ (all_24_2 = e2)
% 147.80/20.96  | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | REDUCE: (318), (5771) imply:
% 147.80/20.96  | | | | | | | | | | | | | | |   (5772)   ~ (all_10_2 = e2)
% 147.80/20.96  | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | |   (5773)   ~ (all_38_2 = e1)
% 147.80/20.96  | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | REDUCE: (5758), (5773) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | |   (5774)  $false
% 147.80/20.96  | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | CLOSE: (5774) is inconsistent.
% 147.80/20.96  | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | |   (5775)  ( ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0
% 147.80/20.96  | | | | | | | | | | | | | | | |             & op(e2, e1) = all_38_1 & $i(all_38_0) &
% 147.80/20.96  | | | | | | | | | | | | | | | |             $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e2, e1)
% 147.80/20.96  | | | | | | | | | | | | | | | |             = all_38_1 & $i(all_38_1))
% 147.80/20.96  | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | |   (5776)   ~ (all_36_2 = e2)
% 147.80/20.96  | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | REDUCE: (304), (5776) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | |   (5777)   ~ (all_14_2 = e2)
% 147.80/20.96  | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | |   (5778)  all_54_0 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (5778) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | |   (5779)  all_14_2 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | SIMP: (5779) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | |   (5780)  all_14_2 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | REDUCE: (336), (5780) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | |   (5781)   ~ (all_52_1 = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | REDUCE: (342), (5780) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | |   (5782)   ~ (all_52_4 = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | REDUCE: (51), (5780) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | |   (5783)  op(e3, e3) = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | |   (5784)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (5768), (5782), (5784),
% 147.80/20.96  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.96  | | | | | | | | | | | | | | | | | | |            #261.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | |   (5785)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | BETA: splitting (5785) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | |   (5786)  all_56_7 = e3 & op(e1, e2) = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5023), (5786), (function-axioms) are
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | |   (5787)  all_56_13 = e3 & op(e0, e2) = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | ALPHA: (5787) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | |   (5788)  all_56_13 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | |   (5789)  op(e0, e2) = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | |   (5790)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5790) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5791)  all_56_2 = e3 & op(e2, e3) = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (5781), (5791), (function-axioms) are
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #917.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5792)  all_56_3 = e3 & op(e2, e2) = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5792) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5793)  all_56_3 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5768), (5793) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5794)  e3 = e1
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (224), (226),
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |            (227), (5023), (5763), (5768), (5788), (5794),
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |            #259.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | |   (5795)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5795) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5796)  all_56_5 = e3 & op(e2, e1) = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5025), (5796), (function-axioms) are
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5797)  all_56_10 = e3 & op(e2, e0) = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5797) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5798)  all_56_10 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5799)  op(e2, e0) = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (157), (5789) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5800)  all_52_7 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (163), (5799) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5801)  all_52_13 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5801) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5802)   ~ (all_52_12 = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (5801) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5803)   ~ (all_10_2 = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | SIMP: (5803) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | |   (5804)   ~ (all_10_2 = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | |   (5805)  all_54_15 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (5804), (5805) are inconsistent by
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1049.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | |   (5806)   ~ (all_54_15 = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | |   (5807)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5807) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | |   (5808)  all_54_15 = e2
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (5772), (5808) are inconsistent by
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1048.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | |   (5809)   ~ (all_54_15 = e2)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | |   (5810)  all_54_15 = e1 | all_54_15 = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5810) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5811)  all_54_15 = e1
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (5033), (5811) are inconsistent by
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1047.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5812)  all_54_15 = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (5812) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5813)  all_10_2 = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5813) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5814)  all_10_2 = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (5814) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5815)   ~ (all_52_3 = e0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (5814) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5816)   ~ (all_52_11 = e0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5804), (5814) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5817)   ~ (e3 = e0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5772), (5814) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5818)   ~ (e2 = e0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5033), (5814) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5819)   ~ (e1 = e0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (5814) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | |   (5820)  op(e0, e0) = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5821)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5821) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5822)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5822) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5823)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5823) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5824)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5824) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5825)   ~ (all_57_1 = e1)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5826)  op(e2, e3) = e2
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5827)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5827) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5828)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5828) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5829)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = all_57_14 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5032), (5825), (5829), (function-axioms) are
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #815.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5830)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5830) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5831)  op(e2, e2) = e2
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5763), (5831), (function-axioms) are
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5832)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5832) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5833)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5833) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5834)  op(e1, e1) = e1
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (5834), (function-axioms) are
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5835)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5835) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5836)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5837)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = all_57_10 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5836) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5838)  all_57_11 = e2 & op(e2, e0) = e2
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5838) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5839)  op(e2, e0) = e2
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5799), (5839), (function-axioms) are
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #854.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5840)   ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5840) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5841)   ~ (all_57_12 = e0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5842)  op(e2, e2) = all_57_12
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5837) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5843)  all_57_9 = e3 & op(e3, e0) = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5843) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5844)  op(e3, e0) = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (167), (5844) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5845)  all_52_12 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5802), (5845) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5846)  $false
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5846) is inconsistent.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5847)   ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5847) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5848)   ~ (all_57_10 = e0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5849)  op(e3, e3) = all_57_10
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (5763), (5842)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5850)  all_57_12 = e1
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (166), (5826) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5851)  all_52_1 = e2
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (5783), (5849)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5852)  all_57_10 = e3
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (5851) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5853)   ~ (all_52_9 = e2)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5853) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5854)   ~ (all_52_9 = e2)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5781), (5851) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5855)   ~ (e3 = e2)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5856)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5856) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5857)  all_56_2 = e2 & op(e2, e3) = e2
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5857) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5858)  all_56_2 = e2
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5859)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5859) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5860)  all_56_2 = e0 & op(e2, e3) = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5858), (5860) are inconsistent by sub-proof
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #726.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5861)  all_56_3 = e0 & op(e2, e2) = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5861) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5862)  op(e2, e2) = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5763), (5862), (function-axioms) are
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5863)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5863) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5864)  all_56_5 = e0 & op(e2, e1) = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5864) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5865)  op(e2, e1) = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5775) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5866)   ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0 &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_38_1 & $i(all_38_0) &
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_38_1)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5866) implies:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5867)   ~ (all_38_0 = e3)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5868)  op(e2, e1) = all_38_1
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5869)  op(all_38_1, e2) = all_38_0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_1,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (5865), (5868) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5870)  all_38_1 = e0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_38_0,
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (5789) gives:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5871)  all_38_0 = e3 |  ~ (op(e0, e2) = all_38_0)
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5869), (5870) imply:
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5872)  op(e0, e2) = all_38_0
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.96  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5871) gives:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5873)   ~ (op(e0, e2) = all_38_0)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | PRED_UNIFY: (5872), (5873) imply:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5874)  $false
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5874) is inconsistent.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5875)  all_38_0 = e3
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5867), (5875) imply:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5876)  $false
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5876) is inconsistent.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5877)   ~ (all_38_1 = e0) & op(e2, e1) = all_38_1 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_38_1)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5877) implies:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5878)   ~ (all_38_1 = e0)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5879)  op(e2, e1) = all_38_1
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5865), (5878), (5879), (function-axioms) are
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #801.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5880)  all_56_10 = e0 & op(e2, e0) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5880) implies:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5881)  all_56_10 = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5798), (5881) are inconsistent by sub-proof
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1134.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5882)  all_56_3 = e2 & op(e2, e2) = e2
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5882) implies:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5883)  op(e2, e2) = e2
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5763), (5883), (function-axioms) are
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5884)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (5798), (5854), (5884),
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #258.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5885)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5885) implies:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5886)  op(e0, e0) = e3
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5820), (5886), (function-axioms) are
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5887)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (5820), (5887), (function-axioms) are
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #352.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5888)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5888) gives:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5889)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (5032), (5782), (5889),
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #294.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5890)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (168), (5024), (5772), (5783), (5890),
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #861.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |   (5891)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5891) gives:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5892)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5892) gives:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5893)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (5024), (5783), (5893),
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #860.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5894)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5894) gives:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5895)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5895) implies:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5896)  op(e0, e0) = e1
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5820), (5896), (function-axioms) are
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5897)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5897) gives:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5898)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5898) implies:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5899)  op(e2, e2) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5763), (5899), (function-axioms) are
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5900)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5900) implies:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5901)  op(e3, e0) = e3
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (5802), (5901), (function-axioms) are
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1082.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5902)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5902) gives:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5903)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5783), (5903), (function-axioms) are
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5904)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5904) gives:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5905)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5905) implies:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5906)  op(e1, e1) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (5906), (function-axioms) are
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5907)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5907) gives:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5908)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5908) implies:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5909)  op(e2, e2) = e0
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5763), (5909), (function-axioms) are
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5910)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5910) implies:
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (5911)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.80/20.97  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (158), (5032), (5783), (5815), (5816),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5911), (function-axioms) are inconsistent by
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #695.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | |   (5912)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (5037), (5770), (5777), (5912) are
% 147.80/20.98  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | |   (5913)  all_36_2 = e2
% 147.80/20.98  | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (5913) imply:
% 147.80/20.98  | | | | | | | | | | | | | | | | |   (5914)  all_14_2 = e2
% 147.80/20.98  | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | SIMP: (5914) implies:
% 147.80/20.98  | | | | | | | | | | | | | | | | |   (5915)  all_14_2 = e2
% 147.80/20.98  | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | REDUCE: (336), (5915) imply:
% 147.80/20.98  | | | | | | | | | | | | | | | | |   (5916)   ~ (all_52_1 = e2)
% 147.80/20.98  | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | REDUCE: (51), (5915) imply:
% 147.80/20.98  | | | | | | | | | | | | | | | | |   (5917)  op(e3, e3) = e2
% 147.80/20.98  | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | |   (5918)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (5763), (5917), (5918),
% 147.80/20.98  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.98  | | | | | | | | | | | | | | | | | |            #761.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | |   (5919)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.80/20.98  | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | BETA: splitting (5919) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |   (5920)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | ALPHA: (5920) implies:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |   (5921)  op(e1, e1) = e1
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (5921), (function-axioms) are
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |   (5922)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | ALPHA: (5922) implies:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |   (5923)  all_57_15 = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |   (5924)  op(e0, e0) = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |   (5925)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |   (5926)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5926) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |   (5927)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5927) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |   (5928)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (5916), (5928), (function-axioms) are
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |   (5929)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (5924), (5929), (function-axioms) are
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #352.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |   (5930)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5930) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |   (5931)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (5032), (5772), (5931),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |            #367.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |   (5932)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5932) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |   (5933)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5933) implies:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |   (5934)  op(e1, e2) = e1
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (161), (5934) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |   (5935)  all_52_6 = e1
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5760), (5935) imply:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |   (5936)  $false
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5936) is inconsistent.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |   (5937)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (168), (5024), (5772), (5937),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            #862.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |   (5938)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | BETA: splitting (5938) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |   (5939)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5939) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |   (5940)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5940) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |   (5941)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5941) implies:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |   (5942)  op(e3, e1) = e3
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5024), (5942), (function-axioms) are
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |   (5943)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5943) implies:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |   (5944)  op(e3, e3) = e1
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (124), (127),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            (138), (139), (144), (145), (147), (156), (158),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            (159), (161), (163), (164), (166), (168), (190),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            (191), (206), (209), (212), (213), (214), (216),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (220), (222), (223), (224), (226),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (232), (233), (234), (235),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            (238), (247), (248), (349), (360), (5023), (5024),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            (5025), (5031), (5032), (5033), (5759), (5763),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            (5768), (5923), (5924), (5925), (5944),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | |            #241.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |   (5945)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (5032), (5924), (5925), (5945),
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |            #243.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |   (5946)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5946) gives:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |   (5947)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5917), (5947), (function-axioms) are
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.98  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |   (5948)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5948) gives:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |   (5949)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5949) implies:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |   (5950)  op(e1, e1) = e0
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (5950), (function-axioms) are
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |   (5951)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5951) gives:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5952)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5952) implies:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5953)  all_57_12 = e0
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5954)   ~ (all_57_11 = e2)
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5925), (5953), (5954) are inconsistent by
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #890.
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5955)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5955) implies:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5956)  op(e0, e0) = all_57_15
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5957)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (45), (5924) gives:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5958)  all_10_2 = e0
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (5958) imply:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5959)   ~ (all_52_3 = e0)
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (5958) imply:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5960)   ~ (all_52_7 = e0)
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (5958) imply:
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |   (5961)   ~ (all_52_11 = e0)
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (157), (158), (5032), (5957), (5959),
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |            (5960), (5961), (function-axioms) are inconsistent
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #240.
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | Case 2:
% 147.80/20.99  | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | |   (5962)  all_24_2 = e2
% 147.80/20.99  | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | COMBINE_EQS: (318), (5962) imply:
% 147.80/20.99  | | | | | | | | | | | | | | |   (5963)  all_10_2 = e2
% 147.80/20.99  | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | REDUCE: (349), (5963) imply:
% 147.80/20.99  | | | | | | | | | | | | | | |   (5964)   ~ (all_52_3 = e2)
% 147.80/20.99  | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | REDUCE: (369), (5963) imply:
% 147.80/20.99  | | | | | | | | | | | | | | |   (5965)   ~ (all_52_13 = e2)
% 147.80/20.99  | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | REDUCE: (370), (5963) imply:
% 147.80/20.99  | | | | | | | | | | | | | | |   (5966)   ~ (all_52_14 = e2)
% 147.80/20.99  | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | REDUCE: (45), (5963) imply:
% 147.80/20.99  | | | | | | | | | | | | | | |   (5967)  op(e0, e0) = e2
% 147.80/20.99  | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (45), (51), (138), (139),
% 147.80/20.99  | | | | | | | | | | | | | | |            (142), (143), (156), (157), (158), (159), (161),
% 147.80/20.99  | | | | | | | | | | | | | | |            (162), (163), (164), (166), (167), (168), (169),
% 147.80/20.99  | | | | | | | | | | | | | | |            (191), (205), (206), (209), (212), (213), (214),
% 147.80/20.99  | | | | | | | | | | | | | | |            (216), (218), (220), (222), (223), (224), (226),
% 147.80/20.99  | | | | | | | | | | | | | | |            (227), (228), (229), (230), (232), (233), (234),
% 147.80/20.99  | | | | | | | | | | | | | | |            (235), (237), (238), (248), (336), (340), (342),
% 147.80/20.99  | | | | | | | | | | | | | | |            (344), (346), (5023), (5025), (5031), (5032),
% 147.80/20.99  | | | | | | | | | | | | | | |            (5033), (5037), (5763), (5768), (5770), (5964),
% 147.80/20.99  | | | | | | | | | | | | | | |            (5965), (5966), (5967), (function-axioms) are
% 147.80/20.99  | | | | | | | | | | | | | | |            inconsistent by sub-proof #229.
% 147.80/20.99  | | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | Case 2:
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | |   (5968)  all_22_2 = e1
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | COMBINE_EQS: (320), (5968) imply:
% 147.80/20.99  | | | | | | | | | | | | | |   (5969)  all_14_2 = e1
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | REDUCE: (51), (5969) imply:
% 147.80/20.99  | | | | | | | | | | | | | |   (5970)  op(e3, e3) = e1
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (124), (127),
% 147.80/20.99  | | | | | | | | | | | | | |            (138), (139), (144), (145), (147), (156), (158),
% 147.80/20.99  | | | | | | | | | | | | | |            (159), (161), (163), (164), (166), (168), (190),
% 147.80/20.99  | | | | | | | | | | | | | |            (191), (206), (209), (212), (213), (214), (216),
% 147.80/20.99  | | | | | | | | | | | | | |            (217), (218), (220), (222), (223), (224), (226),
% 147.80/20.99  | | | | | | | | | | | | | |            (227), (228), (229), (232), (233), (234), (235),
% 147.80/20.99  | | | | | | | | | | | | | |            (237), (238), (247), (248), (349), (360), (5023),
% 147.80/20.99  | | | | | | | | | | | | | |            (5024), (5025), (5031), (5032), (5033), (5759),
% 147.80/20.99  | | | | | | | | | | | | | |            (5763), (5768), (5970), (function-axioms) are
% 147.80/20.99  | | | | | | | | | | | | | |            inconsistent by sub-proof #228.
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | Case 2:
% 147.80/20.99  | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | |   (5971)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 147.80/20.99  | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 147.80/20.99  | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | BETA: splitting (5971) gives:
% 147.80/20.99  | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | Case 1:
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | |   (5972)  all_56_7 = e1 & op(e1, e2) = e1
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | ALPHA: (5972) implies:
% 147.80/20.99  | | | | | | | | | | | | |   (5973)  op(e1, e2) = e1
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | REF_CLOSE: (161), (5760), (5973), (function-axioms) are
% 147.80/20.99  | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | Case 2:
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | |   (5974)  all_56_13 = e1 & op(e0, e2) = e1
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | ALPHA: (5974) implies:
% 147.80/20.99  | | | | | | | | | | | | |   (5975)  all_56_13 = e1
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 147.80/20.99  | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (226), (227),
% 147.80/20.99  | | | | | | | | | | | | |            (5023), (5025), (5763), (5975), (function-axioms)
% 147.80/20.99  | | | | | | | | | | | | |            are inconsistent by sub-proof #226.
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | End of split
% 147.80/20.99  | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | Case 2:
% 147.80/20.99  | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | |   (5976)  all_16_2 = e0
% 147.80/20.99  | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | COMBINE_EQS: (327), (5976) imply:
% 147.80/20.99  | | | | | | | | | |   (5977)  all_6_2 = e0
% 147.80/20.99  | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | SIMP: (5977) implies:
% 147.80/20.99  | | | | | | | | | |   (5978)  all_6_2 = e0
% 147.80/20.99  | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | REDUCE: (347), (5978) imply:
% 147.80/20.99  | | | | | | | | | |   (5979)   ~ (all_52_1 = e0)
% 147.80/20.99  | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | REDUCE: (358), (5978) imply:
% 147.80/20.99  | | | | | | | | | |   (5980)   ~ (all_52_13 = e0)
% 147.80/20.99  | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | REDUCE: (372), (5978) imply:
% 147.80/20.99  | | | | | | | | | |   (5981)   ~ (e3 = e0)
% 147.80/20.99  | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | REDUCE: (39), (5978) imply:
% 147.80/20.99  | | | | | | | | | |   (5982)  op(e2, e2) = e0
% 147.80/20.99  | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | BETA: splitting (64) gives:
% 147.80/20.99  | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | Case 1:
% 147.80/20.99  | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | |   (5983)   ~ (all_22_2 = e1)
% 147.80/20.99  | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | REDUCE: (320), (5983) imply:
% 147.80/20.99  | | | | | | | | | | |   (5984)   ~ (all_14_2 = e1)
% 147.80/20.99  | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | BETA: splitting (67) gives:
% 147.80/20.99  | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | Case 1:
% 147.80/20.99  | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | |   (5985)   ~ (all_24_2 = e2)
% 147.80/20.99  | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | REDUCE: (318), (5985) imply:
% 147.80/20.99  | | | | | | | | | | | |   (5986)   ~ (all_10_2 = e2)
% 147.80/20.99  | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | BETA: splitting (84) gives:
% 147.80/20.99  | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | Case 1:
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | |   (5987)   ~ (all_36_2 = e2)
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | REDUCE: (304), (5987) imply:
% 147.80/20.99  | | | | | | | | | | | | |   (5988)   ~ (all_14_2 = e2)
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | REF_CLOSE: (5), (6), (51), (158), (162), (163), (164), (166),
% 147.80/20.99  | | | | | | | | | | | | |            (188), (203), (221), (222), (223), (228), (237),
% 147.80/20.99  | | | | | | | | | | | | |            (245), (278), (336), (349), (369), (5025), (5032),
% 147.80/20.99  | | | | | | | | | | | | |            (5033), (5037), (5982), (5984), (5986), (5988),
% 147.80/20.99  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.99  | | | | | | | | | | | | |            #225.
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | Case 2:
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | |   (5989)  all_36_2 = e2
% 147.80/20.99  | | | | | | | | | | | | |   (5990)  ( ~ (all_36_0 = e1) & op(all_36_1, e3) = all_36_0
% 147.80/20.99  | | | | | | | | | | | | |             & op(e3, e2) = all_36_1 & $i(all_36_0) &
% 147.80/20.99  | | | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e3, e2)
% 147.80/20.99  | | | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | COMBINE_EQS: (304), (5989) imply:
% 147.80/20.99  | | | | | | | | | | | | |   (5991)  all_14_2 = e2
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | SIMP: (5991) implies:
% 147.80/20.99  | | | | | | | | | | | | |   (5992)  all_14_2 = e2
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | REDUCE: (51), (5992) imply:
% 147.80/20.99  | | | | | | | | | | | | |   (5993)  op(e3, e3) = e2
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | BETA: splitting (237) gives:
% 147.80/20.99  | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | Case 1:
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | |   (5994)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 147.80/20.99  | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 147.80/20.99  | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 147.80/20.99  | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 147.80/20.99  | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 147.80/20.99  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 147.80/20.99  | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 147.80/20.99  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.80/20.99  | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 147.80/20.99  | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 147.80/20.99  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.99  | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 147.80/20.99  | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 147.80/20.99  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 147.80/20.99  | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 147.80/20.99  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (5982), (5993), (5994),
% 147.80/20.99  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 147.80/20.99  | | | | | | | | | | | | | |            #662.
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | Case 2:
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | |   (5995)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 147.80/20.99  | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 147.80/20.99  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.99  | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 147.80/20.99  | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 147.80/20.99  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 147.80/20.99  | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 147.80/20.99  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 147.80/20.99  | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 147.80/20.99  | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 147.80/20.99  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 147.80/20.99  | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 147.80/20.99  | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 147.80/20.99  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 147.80/20.99  | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 147.80/20.99  | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | BETA: splitting (5995) gives:
% 147.80/20.99  | | | | | | | | | | | | | | 
% 147.80/20.99  | | | | | | | | | | | | | | Case 1:
% 147.80/20.99  | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | |   (5996)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 148.09/20.99  | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 148.09/20.99  | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.09/20.99  | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.09/20.99  | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.09/20.99  | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 148.09/20.99  | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 148.09/20.99  | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.09/20.99  | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | ALPHA: (5996) implies:
% 148.09/20.99  | | | | | | | | | | | | | | |   (5997)  op(e1, e1) = e1
% 148.09/20.99  | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (5997), (function-axioms) are
% 148.09/20.99  | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 148.09/20.99  | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | Case 2:
% 148.09/20.99  | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | |   (5998)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 148.09/20.99  | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 148.09/20.99  | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.09/20.99  | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.09/20.99  | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.09/20.99  | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.09/20.99  | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.09/20.99  | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 148.09/20.99  | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | ALPHA: (5998) implies:
% 148.09/20.99  | | | | | | | | | | | | | | |   (5999)  op(e0, e0) = e0
% 148.09/20.99  | | | | | | | | | | | | | | |   (6000)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.09/20.99  | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.09/20.99  | | | | | | | | | | | | | | |             $i(all_57_12))
% 148.09/20.99  | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | BETA: splitting (6000) gives:
% 148.09/20.99  | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | Case 1:
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6001)  all_57_11 = e2 & op(e2, e0) = e2
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | ALPHA: (6001) implies:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6002)  op(e2, e0) = e2
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 148.09/20.99  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (45), (5999) gives:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6003)  all_10_2 = e0
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 148.09/20.99  | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (163), (6002) gives:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6004)  all_52_13 = e2
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | REDUCE: (144), (6004) imply:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6005)   ~ (all_52_1 = e2)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | REDUCE: (349), (6003) imply:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6006)   ~ (all_52_3 = e0)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | REDUCE: (360), (6003) imply:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6007)   ~ (all_52_7 = e0)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | REDUCE: (116), (6004) imply:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6008)   ~ (all_52_9 = e2)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | REDUCE: (367), (6003) imply:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6009)   ~ (all_52_11 = e0)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | REDUCE: (112), (6004) imply:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6010)   ~ (all_52_12 = e2)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | REDUCE: (368), (6003) imply:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6011)   ~ (all_52_12 = e0)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | REDUCE: (109), (6004) imply:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6012)   ~ (all_52_14 = e2)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | SIMP: (6012) implies:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6013)   ~ (all_52_14 = e2)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | REDUCE: (370), (6003) imply:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6014)   ~ (all_52_14 = e0)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | REDUCE: (5986), (6003) imply:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6015)   ~ (e2 = e0)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | REDUCE: (5033), (6003) imply:
% 148.09/20.99  | | | | | | | | | | | | | | | |   (6016)   ~ (e1 = e0)
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 148.09/20.99  | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | Case 1:
% 148.09/20.99  | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | |   (6017)  all_54_11 = e3
% 148.09/20.99  | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5027), (6017) are inconsistent by
% 148.09/20.99  | | | | | | | | | | | | | | | | |            sub-proof #661.
% 148.09/20.99  | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | Case 2:
% 148.09/20.99  | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | |   (6018)   ~ (all_54_11 = e3)
% 148.09/20.99  | | | | | | | | | | | | | | | | |   (6019)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 148.09/20.99  | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 148.09/20.99  | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | Case 1:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | |   (6020)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 148.09/20.99  | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 148.09/20.99  | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | BETA: splitting (6020) gives:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | |   (6021)  all_56_4 = e2 & op(e3, e1) = e2
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | ALPHA: (6021) implies:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | |   (6022)  all_56_4 = e2
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | |   (6023)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6023) gives:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | |   (6024)  all_56_4 = e0 & op(e3, e1) = e0
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6022), (6024) are inconsistent by sub-proof
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | |            #1070.
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | |   (6025)  all_56_5 = e0 & op(e2, e1) = e0
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6025) implies:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | |   (6026)  all_56_5 = e0
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | |   (6027)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | |            (168), (207), (212), (213), (214), (216), (220),
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (227), (228), (229), (230), (231),
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (5023), (5024), (5025), (5031),
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | |            (5032), (5982), (5993), (5999), (6005), (6022),
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | |            (6027), (function-axioms) are inconsistent by
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #220.
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | |   (6028)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6028) gives:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | |   (6029)  all_56_8 = e1 & op(e1, e1) = e1
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6029) implies:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | |   (6030)  op(e1, e1) = e1
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (6030), (function-axioms) are
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/20.99  | | | | | | | | | | | | | | | | | | | | | | |   (6031)  all_56_14 = e1 & op(e0, e1) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6031) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | |   (6032)  all_56_14 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | |   (6033)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (166), (5982), (6005), (6033),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | |            #613.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | |   (6034)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6034) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (6035)  all_56_5 = e2 & op(e2, e1) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6035) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (6036)  all_56_5 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6026), (6036) are inconsistent by sub-proof
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |            #509.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (6037)  all_56_10 = e2 & op(e2, e0) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6037) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (6038)  all_56_10 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6039)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6039) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6040)  all_56_0 = e3 & op(e3, e3) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6040) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6041)  op(e3, e3) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5993), (6041), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6042)  all_56_1 = e3 & op(e3, e2) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6042) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6043)  all_56_1 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6044)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6044) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6045)  all_56_9 = e1 & op(e3, e0) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6045) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6046)  all_56_9 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (168), (229), (235),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5024), (5993), (6022), (6046), (function-axioms)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #484.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6047)  all_56_10 = e1 & op(e2, e0) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6047) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6048)  all_56_10 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6038), (6048) imply:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6049)  e2 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6022), (6049) imply:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6050)  all_56_4 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (218), (5032),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6032), (6050), (function-axioms) are inconsistent
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #254.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6051)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6051) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6052)  all_56_11 = e1 & op(e1, e0) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6052) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6053)  all_56_11 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6054)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6054) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6055)  all_56_12 = e2 & op(e0, e3) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213), (214),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (230), (234), (5031), (5032), (5993),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6055), (function-axioms) are inconsistent by
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #426.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6056)  all_56_13 = e2 & op(e0, e2) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6056) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6057)  all_56_13 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6058)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6058) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6059)  all_56_9 = e3 & op(e3, e0) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6059) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6060)  all_56_9 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (227), (229),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (5023), (5982), (5993), (6057), (6060),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #218.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6061)  all_56_10 = e3 & op(e2, e0) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6061) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6062)  op(e2, e0) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6002), (6062), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #854.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6063)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6063) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6064)  all_56_11 = e3 & op(e1, e0) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6064) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6065)  all_56_11 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6053), (6065) imply:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6066)  e3 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6043), (6066) imply:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6067)  all_56_1 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (161), (227), (5023), (5982),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6057), (6067), (function-axioms) are inconsistent
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #464.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6068)  all_56_15 = e3 & op(e0, e0) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6068) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6069)  op(e0, e0) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5999), (6069), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6070)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (216), (217), (5032),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5999), (6022), (6070), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #216.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6071)  all_56_15 = e1 & op(e0, e0) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6071) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6072)  op(e0, e0) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5999), (6072), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6073)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6073) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6074)  all_56_4 = e3 & op(e3, e1) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6074) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6075)  op(e3, e1) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5024), (6075), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6076)  all_56_9 = e3 & op(e3, e0) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6076) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6077)  all_56_9 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6078)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6078) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6079)  all_56_12 = e2 & op(e0, e3) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213), (214),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (230), (234), (5031), (5032), (5993),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6079), (function-axioms) are inconsistent by
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #426.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6080)  all_56_13 = e2 & op(e0, e2) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6080) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6081)  all_56_13 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (227), (229),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (5023), (5982), (5993), (6077), (6081),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #218.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6082)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (216), (217), (5032),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5999), (6022), (6082), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #216.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | |   (6083)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6083) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | |   (6084)  all_56_8 = e0 & op(e1, e1) = e0
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6084) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | |   (6085)  op(e1, e1) = e0
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (6085), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | |   (6086)  all_56_14 = e0 & op(e0, e1) = e0
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6086) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | |   (6087)  op(e0, e1) = e0
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |   (6088)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |            (168), (207), (212), (213), (214), (216), (220),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (227), (228), (229), (230), (231),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (5023), (5024), (5025), (5031),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |            (5032), (5982), (5993), (5999), (6005), (6022),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |            (6088), (function-axioms) are inconsistent by
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #220.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |   (6089)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6089) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | |   (6090)  all_56_8 = e1 & op(e1, e1) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6090) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | |   (6091)  op(e1, e1) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (6091), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | |   (6092)  all_56_14 = e1 & op(e0, e1) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6092) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | |   (6093)  op(e0, e1) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6087), (6093), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #899.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | |   (6094)  all_56_5 = e2 & op(e2, e1) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | ALPHA: (6094) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | |   (6095)  op(e2, e1) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6008), (6095), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | |   (6096)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | BETA: splitting (6096) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | |   (6097)  all_56_8 = e2 & op(e1, e1) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | ALPHA: (6097) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | |   (6098)  op(e1, e1) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (6098), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | |   (6099)  all_56_14 = e2 & op(e0, e1) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | ALPHA: (6099) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | |   (6100)  all_56_14 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | |   (6101)  op(e0, e1) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | |   (6102)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6102) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | |   (6103)  all_56_6 = e2 & op(e1, e3) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6103) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | |   (6104)  all_56_6 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |   (6105)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6105) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | |   (6106)  all_56_2 = e3 & op(e2, e3) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6106) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | |   (6107)  all_56_2 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | |   (6108)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6108) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (6109)  all_56_9 = e2 & op(e3, e0) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6109) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (6110)  all_56_9 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (217), (229),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (235), (5031), (5032), (5993), (6100),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |            (6101), (6110), (function-axioms) are inconsistent
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #215.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (6111)  all_56_10 = e2 & op(e2, e0) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6111) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | |   (6112)  all_56_10 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6019) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6113)  all_54_11 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6013), (6113) are inconsistent by
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #393.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6114)   ~ (all_54_11 = e2)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6115)  all_54_11 = e1 | all_54_11 = e0
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6115) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6116)  all_54_11 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6116) imply:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6117)  all_52_14 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6117) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6118)  all_52_14 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (6118) imply:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6119)   ~ (all_52_6 = e1)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (6118) imply:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6120)   ~ (all_52_12 = e1)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5027), (6118) imply:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6121)   ~ (e3 = e1)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6013), (6118) imply:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6122)   ~ (e2 = e1)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6123)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6123) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6124)  all_56_1 = e2 & op(e3, e2) = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6124) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6125)  all_56_1 = e2
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6126)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6126) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6127)  all_56_0 = e3 & op(e3, e3) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6127) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6128)  op(e3, e3) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5993), (6128), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6129)  all_56_1 = e3 & op(e3, e2) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6129) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6130)  all_56_1 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6125), (6130) are inconsistent by sub-proof
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #950.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6131)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6131) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6132)  all_56_4 = e3 & op(e3, e1) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6132) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6133)  op(e3, e1) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5024), (6133), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6134)  all_56_9 = e3 & op(e3, e0) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6134) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6135)  all_56_9 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6136)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6136) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6137)  all_56_0 = e1 & op(e3, e3) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6137) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6138)  op(e3, e3) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5993), (6138), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6139)  all_56_1 = e1 & op(e3, e2) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6125), (6139) are inconsistent by sub-proof
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #923.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6140)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6140) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6141)  all_56_4 = e1 & op(e3, e1) = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6141) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6142)  all_56_4 = e1
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6143)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6143) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6144)  all_56_1 = e3 & op(e3, e2) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6144) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6145)  all_56_1 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (229), (5993), (6135), (6142),
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6145), (function-axioms) are inconsistent by
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #346.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6146)  all_56_3 = e3 & op(e2, e2) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6146) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6147)  op(e2, e2) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5982), (6147), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6148)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6148) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6149)  all_56_7 = e3 & op(e1, e2) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5023), (6149), (function-axioms) are
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6150)  all_56_13 = e3 & op(e0, e2) = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6150) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6151)  all_56_13 = e3
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6152)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6152) gives:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6153)  all_56_4 = e0 & op(e3, e1) = e0
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6142), (6153) are inconsistent by sub-proof
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #347.
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6154)  all_56_5 = e0 & op(e2, e1) = e0
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6154) implies:
% 148.09/21.00  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6155)  all_56_5 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6156)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6156) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6157)  all_56_2 = e2 & op(e2, e3) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6157) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6158)  op(e2, e3) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (6005), (6158), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1181.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6159)  all_56_3 = e2 & op(e2, e2) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6159) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6160)  op(e2, e2) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (224), (225),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (5023), (6125), (6160), (function-axioms)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #921.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6161)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6161) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6162)  all_56_5 = e2 & op(e2, e1) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6155), (6162) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #389.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6163)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6163) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6164)  all_56_0 = e0 & op(e3, e3) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6164) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6165)  op(e3, e3) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5993), (6165), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6166)  all_56_1 = e0 & op(e3, e2) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6166) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6167)  all_56_1 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6125), (6167) imply:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6168)  e2 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6168) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6169)  e2 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6112), (6169) imply:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6170)  all_56_10 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (221), (222),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (5025), (5982), (6170), (function-axioms)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #450.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6171)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6171) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6172)  all_56_4 = e0 & op(e3, e1) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6172) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6173)  all_56_4 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6142), (6173) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #657.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6174)  all_56_9 = e0 & op(e3, e0) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6174) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6175)  all_56_9 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6135), (6175) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1067.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6176)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6176) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6177)  all_56_8 = e0 & op(e1, e1) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6177) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6178)  op(e1, e1) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (6178), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6179)  all_56_14 = e0 & op(e0, e1) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6179) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6180)  op(e0, e1) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6181)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6181) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6182)  all_56_4 = e2 & op(e3, e1) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6182) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6183)  all_56_4 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6184)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6184) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6185)  all_56_0 = e0 & op(e3, e3) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6185) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6186)  all_56_0 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6187)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6187) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6188)  all_56_0 = e1 & op(e3, e3) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6186), (6188) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #214.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6189)  all_56_1 = e1 & op(e3, e2) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6125), (6189) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #923.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6140) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6141), (6183) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1066.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6190)  all_56_9 = e1 & op(e3, e0) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6135), (6190) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #493.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6191)  all_56_1 = e0 & op(e3, e2) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6125), (6191) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #924.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6192)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6192) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6193)  all_56_4 = e0 & op(e3, e1) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6183), (6193) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1070.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6194)  all_56_9 = e0 & op(e3, e0) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6135), (6194) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #446.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6195)  all_56_5 = e2 & op(e2, e1) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6195) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6196)  all_56_5 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6197)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6197) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6198)  all_56_12 = e2 & op(e0, e3) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6198) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6199)  all_56_12 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6200)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (6151), (6199), (6200) are inconsistent
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1120.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6201)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6201) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6202)  all_56_14 = e1 & op(e0, e1) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6202) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6203)  all_56_14 = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (216), (5032), (6142), (6196),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6203), (function-axioms) are inconsistent by
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #256.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6204)  all_56_15 = e1 & op(e0, e0) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6204) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6205)  op(e0, e0) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5999), (6205), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6206)  all_56_13 = e2 & op(e0, e2) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6206) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6207)  all_56_13 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6151), (6207) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1105.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6208)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6208) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6101), (6180), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1008.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6209)  all_56_15 = e2 & op(e0, e0) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6209) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6210)  op(e0, e0) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5999), (6210), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6096) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6211)  all_56_8 = e2 & op(e1, e1) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6211) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6212)  op(e1, e1) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (6212), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6101), (6180), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1008.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6213)  all_56_9 = e1 & op(e3, e0) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6213) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6214)  all_56_9 = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6135), (6214) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1064.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6215)  all_56_3 = e2 & op(e2, e2) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6215) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6216)  op(e2, e2) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5982), (6216), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6217)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6217) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6218)  all_56_7 = e2 & op(e1, e2) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6218) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6219)  all_56_7 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6220)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (6104), (6119), (6220),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #524.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6221)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6221) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6222)  all_56_8 = e1 & op(e1, e1) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6222) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6223)  op(e1, e1) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (6223), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6224)  all_56_11 = e1 & op(e1, e0) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6224) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6225)  all_56_11 = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6226)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6226) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6227)  all_56_6 = e0 & op(e1, e3) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6227) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6228)  all_56_6 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6104), (6228) imply:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6229)  e2 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (221), (222), (5982),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6107), (6112), (6229), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #213.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6230)  all_56_7 = e0 & op(e1, e2) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6230) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6231)  all_56_7 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6219), (6231) imply:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6232)  e2 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6112), (6232) imply:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6233)  all_56_10 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (221), (222), (5982),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6107), (6233), (function-axioms) are inconsistent
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #554.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6234)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (5032), (6225), (6234),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #610.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6235)  all_56_13 = e2 & op(e0, e2) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6235) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6236)  all_56_13 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6237)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6237) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6238)  all_56_1 = e1 & op(e3, e2) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6238) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6239)  all_56_1 = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (161), (227), (5023), (5982),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6236), (6239), (function-axioms) are inconsistent
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #464.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6240)  all_56_3 = e1 & op(e2, e2) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6240) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6241)  op(e2, e2) = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5982), (6241), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6242)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (132), (161), (169), (200), (227),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (5023), (5982), (6010), (6011), (6119),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6120), (6242), (function-axioms) are inconsistent
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #212.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6243)  all_54_11 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6014), (6243) are inconsistent by
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #211.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | |   (6244)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6244) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (6245)  all_56_11 = e2 & op(e1, e0) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6245) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (6246)  all_56_11 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | |            (6104), (6246) are inconsistent by sub-proof #281.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (6247)  all_56_15 = e2 & op(e0, e0) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6247) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (6248)  op(e0, e0) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5999), (6248), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | |   (6249)  all_56_3 = e3 & op(e2, e2) = e3
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6249) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | |   (6250)  op(e2, e2) = e3
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5982), (6250), (function-axioms) are
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | |   (6251)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (5025), (6002), (6251),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | |            #224.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | |   (6252)  all_56_7 = e2 & op(e1, e2) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6252) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | |   (6253)  all_56_7 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | |   (6254)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6254) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | |   (6255)  all_56_4 = e0 & op(e3, e1) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6255) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | |   (6256)  all_56_4 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | |   (6257)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6257) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (6258)  all_56_2 = e3 & op(e2, e3) = e3
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6258) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | |   (6259)  all_56_2 = e3
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6260)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6260) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6261)  all_56_9 = e2 & op(e3, e0) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6261) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6262)  all_56_9 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (217), (229),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (235), (5031), (5032), (5993), (6100),
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6101), (6262), (function-axioms) are inconsistent
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #215.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6263)  all_56_10 = e2 & op(e2, e0) = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6263) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6264)  all_56_10 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6265)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6265) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6266)  all_56_9 = e3 & op(e3, e0) = e3
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6266) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6267)  all_56_9 = e3
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6019) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6268)  all_54_11 = e2
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6013), (6268) are inconsistent by
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #393.
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6269)   ~ (all_54_11 = e2)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6270)  all_54_11 = e1 | all_54_11 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6270) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6271)  all_54_11 = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6271) imply:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6272)  all_52_14 = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6272) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6273)  all_52_14 = e1
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (6273) imply:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6274)   ~ (all_52_6 = e1)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (6273) imply:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6275)   ~ (all_52_12 = e1)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6013), (6273) imply:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6276)   ~ (e2 = e1)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6277)  all_54_3 = e3
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (6277) imply:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6278)  all_52_12 = e3
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (6278) imply:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6279)   ~ (all_52_4 = e3)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6280)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6280) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6281)  all_56_6 = e0 & op(e1, e3) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6281) implies:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6282)  op(e1, e3) = e0
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.01  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6283)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (229), (231), (5982),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5993), (6267), (6283), (function-axioms) are
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #219.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6284)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6284) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6285)  all_56_7 = e3 & op(e1, e2) = e3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5023), (6285), (function-axioms) are
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6286)  all_56_13 = e3 & op(e0, e2) = e3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6286) implies:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6287)  all_56_13 = e3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6288)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (161), (169), (227), (5023),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5982), (5993), (6259), (6279), (6287), (6288),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #209.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6289)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6289) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6290)  all_56_6 = e1 & op(e1, e3) = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6290) implies:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6291)  op(e1, e3) = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (6282), (6291), (function-axioms) are
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6292)  all_56_12 = e1 & op(e0, e3) = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6292) implies:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6293)  all_56_12 = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6294)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6294) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6295)  all_56_1 = e1 & op(e3, e2) = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6295) implies:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6296)  all_56_1 = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6297)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6297) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6298)  all_56_4 = e1 & op(e3, e1) = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6256), (6298) are inconsistent by sub-proof
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #309.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6299)  all_56_5 = e1 & op(e2, e1) = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6299) implies:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6300)  all_56_5 = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6301)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (169), (220),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (227), (5023), (5982), (6259),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6267), (6279), (6287), (6300), (6301),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #208.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6302)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6302) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6303)  all_56_11 = e1 & op(e1, e0) = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6303) implies:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6304)  all_56_11 = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6305)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6305) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6306)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6306) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6307)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (6005), (6307), (function-axioms) are
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6308)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6308) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6309)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6309) implies:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6310)  op(e1, e3) = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (162), (212), (5032), (6253),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6304), (6310), (function-axioms) are inconsistent
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #237.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6311)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6311) implies:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6312)  op(e0, e0) = e3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (205), (6100), (6287), (6293),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6312), (function-axioms) are inconsistent by
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #311.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6313)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6313) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6314)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (5032), (6279), (6314),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #294.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6315)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6315) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6316)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6316) implies:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6317)  op(e1, e2) = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (6274), (6317), (function-axioms) are
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6318)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (224), (226), (5999),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6287), (6296), (6318), (function-axioms) are
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #207.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6319)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6319) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6320)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6320) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6321)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (5024), (6008), (6321),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1083.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6322)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (5032), (5999), (6000), (6322),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #243.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6323)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6323) gives:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6324)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5993), (6324), (function-axioms) are
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6325)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (156), (157), (158), (5032), (6000),
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6006), (6007), (6009), (6325), (function-axioms)
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #206.
% 148.09/21.02  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6326)  all_56_15 = e1 & op(e0, e0) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6326) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6327)  op(e0, e0) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5999), (6327), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6328)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (5032), (6100), (6328),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #326.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6329)  all_56_3 = e1 & op(e2, e2) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6329) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6330)  op(e2, e2) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5982), (6330), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6331)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (227), (5023), (5982),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6274), (6279), (6331), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #205.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6332)  all_56_7 = e0 & op(e1, e2) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6332) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6333)  all_56_7 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6253), (6333) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6334)  e2 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (221), (222), (5982),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6259), (6264), (6334), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #213.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6335)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6335) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6336)  all_56_8 = e0 & op(e1, e1) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6336) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6337)  op(e1, e1) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (6337), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6338)  all_56_11 = e0 & op(e1, e0) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6338) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6339)  all_56_11 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6340)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (229), (231), (5982),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5993), (6267), (6340), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #219.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6341)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6341) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6342)  all_56_7 = e3 & op(e1, e2) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5023), (6342), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6343)  all_56_13 = e3 & op(e0, e2) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6343) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6344)  all_56_13 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6345)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6345) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6346)  all_56_4 = e1 & op(e3, e1) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6256), (6346) are inconsistent by sub-proof
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #309.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6347)  all_56_5 = e1 & op(e2, e1) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6347) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6348)  all_56_5 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6349)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (169), (220),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (227), (5023), (5982), (6259),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6267), (6279), (6344), (6348), (6349),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #208.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6350)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6350) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6351)  all_56_11 = e1 & op(e1, e0) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6351) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6352)  all_56_11 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6339), (6352) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6353)  e1 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6348), (6353) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6354)  all_56_5 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (111), (119), (132), (142), (161), (162),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (168), (169), (200), (209), (212), (216),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (220), (221), (222), (223), (224), (225),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (229), (230), (231), (235), (249),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (5023), (5025), (5031), (5032), (5982),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5990), (5993), (5999), (6010), (6011), (6013),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6014), (6019), (6100), (6101), (6253), (6259),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6267), (6354), (function-axioms) are inconsistent
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #202.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6355)  all_56_15 = e1 & op(e0, e0) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6355) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6356)  op(e0, e0) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5999), (6356), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6357)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (5032), (6100), (6357),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #326.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6358)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (6010), (6011), (6275), (6358) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #758.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6359)  all_54_11 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6014), (6359) are inconsistent by
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #211.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6360)  all_56_10 = e3 & op(e2, e0) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6360) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6361)  op(e2, e0) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6002), (6361), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #854.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6362)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6362) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6363)  all_56_11 = e3 & op(e1, e0) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6363) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6364)  all_56_11 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6019) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6365)  all_54_11 = e2
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6013), (6365) are inconsistent by
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #393.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6366)   ~ (all_54_11 = e2)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6367)  all_54_11 = e1 | all_54_11 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6367) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6368)  all_54_11 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6368) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6369)  all_52_14 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6369) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6370)  all_52_14 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (6370) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6371)   ~ (all_52_6 = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (6370) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6372)   ~ (all_52_12 = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6013), (6370) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6373)   ~ (e2 = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6374)  all_54_3 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (6374) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6375)  all_52_12 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (6375) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6376)   ~ (all_52_4 = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6377)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6377) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6378)  all_56_6 = e0 & op(e1, e3) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6378) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6379)  op(e1, e3) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6380)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (5982), (6376), (6380),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #596.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6381)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6381) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6382)  all_56_7 = e3 & op(e1, e2) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5023), (6382), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6383)  all_56_13 = e3 & op(e0, e2) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6383) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6384)  all_56_13 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6385)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (161), (162), (6371), (6379), (6385),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #665.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6386)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6386) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6387)  all_56_8 = e1 & op(e1, e1) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6387) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6388)  op(e1, e1) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (6388), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6389)  all_56_11 = e1 & op(e1, e0) = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6389) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6390)  all_56_11 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6364), (6390) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6391)  e3 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6391) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6392)  e3 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6384), (6392) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6393)  all_56_13 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (227), (5023), (5982),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6376), (6393), (function-axioms) are inconsistent
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #210.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6394)  all_56_7 = e0 & op(e1, e2) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6394) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6395)  all_56_7 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6253), (6395) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6396)  e2 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (221), (222), (5982),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6259), (6264), (6396), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #213.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6397)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6397) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6398)  all_56_8 = e0 & op(e1, e1) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6398) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6399)  op(e1, e1) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (6399), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6400)  all_56_11 = e0 & op(e1, e0) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6400) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6401)  all_56_11 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6364), (6401) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6402)  e3 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6402) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6403)  e3 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6259), (6403) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6404)  all_56_2 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (221), (222),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (5025), (5982), (6404), (function-axioms)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #646.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6405)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (6010), (6011), (6372), (6405) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #758.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6406)  all_54_11 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6014), (6406) are inconsistent by
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #211.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6407)  all_56_15 = e3 & op(e0, e0) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6407) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6408)  op(e0, e0) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5999), (6408), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6409)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6409) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6410)  all_56_11 = e2 & op(e1, e0) = e2
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6410) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6411)  all_56_11 = e2
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6253), (6411) are inconsistent by sub-proof #200.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6412)  all_56_15 = e2 & op(e0, e0) = e2
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6412) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6413)  op(e0, e0) = e2
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5999), (6413), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (6414)  all_56_3 = e3 & op(e2, e2) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6414) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (6415)  op(e2, e2) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5982), (6415), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | |   (6416)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (5025), (6002), (6416),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | |            #224.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | |   (6417)  all_56_5 = e0 & op(e2, e1) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6417) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | |   (6418)  all_56_5 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | |   (6419)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6419) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (6420)  all_56_2 = e3 & op(e2, e3) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6420) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | |   (6421)  all_56_2 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6422)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6422) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6423)  all_56_9 = e3 & op(e3, e0) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6423) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6424)  all_56_9 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (111), (119), (132), (142), (161), (162),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (168), (169), (200), (209), (212), (216),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (220), (221), (222), (223), (224), (225),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (226), (227), (229), (230), (231), (235), (249),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (5023), (5025), (5031), (5032), (5982),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5990), (5993), (5999), (6010), (6011), (6013),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6014), (6019), (6100), (6101), (6253), (6418),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6421), (6424), (function-axioms) are inconsistent
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #202.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6425)  all_56_10 = e3 & op(e2, e0) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6425) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6426)  op(e2, e0) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6002), (6426), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #854.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6427)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6427) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6428)  all_56_11 = e3 & op(e1, e0) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6428) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6429)  all_56_11 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6019) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6430)  all_54_11 = e2
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6013), (6430) are inconsistent by
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #393.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6431)   ~ (all_54_11 = e2)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6432)  all_54_11 = e1 | all_54_11 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6432) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6433)  all_54_11 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6433) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6434)  all_52_14 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6434) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6435)  all_52_14 = e1
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (6435) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6436)   ~ (all_52_12 = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6013), (6435) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6437)   ~ (e2 = e1)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6438)  all_54_3 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (6438) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6439)  all_52_12 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (6439) imply:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6440)   ~ (all_52_4 = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6441)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (5982), (6440), (6441),
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #596.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6442)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6442) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6443)  all_56_7 = e3 & op(e1, e2) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5023), (6443), (function-axioms) are
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6444)  all_56_13 = e3 & op(e0, e2) = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6444) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6445)  all_56_13 = e3
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6446)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6446) gives:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6447)  all_56_0 = e0 & op(e3, e3) = e0
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6447) implies:
% 148.09/21.03  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6448)  op(e3, e3) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5993), (6448), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6449)  all_56_1 = e0 & op(e3, e2) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6449) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6450)  op(e3, e2) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6451)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (161), (169), (227), (5023),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5982), (5993), (6421), (6440), (6445), (6451),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #209.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6452)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6452) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6453)  all_56_6 = e1 & op(e1, e3) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6453) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6454)  all_56_6 = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6455)  op(e1, e3) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6456)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6456) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6457)  all_56_6 = e0 & op(e1, e3) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6457) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6458)  op(e1, e3) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (6455), (6458), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6459)  all_56_7 = e0 & op(e1, e2) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6459) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6460)  all_56_7 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (159), (214), (5032), (6013),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6454), (6460), (function-axioms) are inconsistent
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #238.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6461)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6461) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6462)  all_56_8 = e0 & op(e1, e1) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6462) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6463)  op(e1, e1) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (6463), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6464)  all_56_11 = e0 & op(e1, e0) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6429), (6464) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #199.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6465)  all_56_12 = e1 & op(e0, e3) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6465) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6466)  op(e0, e3) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5990), (6450), (6466), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #767.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6467)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (169), (216),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (221), (222), (223), (235), (5025), (5031),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5032), (5982), (5993), (6100), (6101), (6418),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6421), (6440), (6467), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #203.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6468)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (6010), (6011), (6436), (6468) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #758.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6469)  all_54_11 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (6014), (6469) are inconsistent by
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #211.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6470)  all_56_15 = e3 & op(e0, e0) = e3
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6470) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6471)  op(e0, e0) = e3
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5999), (6471), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (6472)  all_56_3 = e3 & op(e2, e2) = e3
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6472) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (6473)  op(e2, e2) = e3
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5982), (6473), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | |   (6474)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (5025), (6002), (6474),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | |            #224.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | |   (6475)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (156), (5032), (6009), (6475),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | |            #198.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |   (6476)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (159), (5032), (6013), (6476),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |            #289.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | |   (6477)   ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.09/21.04  | | | | | | | | | | | | | | | |           $i(all_57_12)
% 148.09/21.04  | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | ALPHA: (6477) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | |   (6478)   ~ (all_57_12 = e0)
% 148.09/21.04  | | | | | | | | | | | | | | | |   (6479)  op(e2, e2) = all_57_12
% 148.09/21.04  | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | REF_CLOSE: (5982), (6478), (6479), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 148.09/21.04  | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | |   (6480)  all_24_2 = e2
% 148.09/21.04  | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | COMBINE_EQS: (318), (6480) imply:
% 148.09/21.04  | | | | | | | | | | | |   (6481)  all_10_2 = e2
% 148.09/21.04  | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | SIMP: (6481) implies:
% 148.09/21.04  | | | | | | | | | | | |   (6482)  all_10_2 = e2
% 148.09/21.04  | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | REDUCE: (349), (6482) imply:
% 148.09/21.04  | | | | | | | | | | | |   (6483)   ~ (all_52_3 = e2)
% 148.09/21.04  | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | REDUCE: (367), (6482) imply:
% 148.09/21.04  | | | | | | | | | | | |   (6484)   ~ (all_52_11 = e2)
% 148.09/21.04  | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | REDUCE: (369), (6482) imply:
% 148.09/21.04  | | | | | | | | | | | |   (6485)   ~ (all_52_13 = e2)
% 148.09/21.04  | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | REDUCE: (370), (6482) imply:
% 148.09/21.04  | | | | | | | | | | | |   (6486)   ~ (all_52_14 = e2)
% 148.09/21.04  | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | REDUCE: (45), (6482) imply:
% 148.09/21.04  | | | | | | | | | | | |   (6487)  op(e0, e0) = e2
% 148.09/21.04  | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | BETA: splitting (210) gives:
% 148.09/21.04  | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | |   (6488)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 148.09/21.04  | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 148.09/21.04  | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | BETA: splitting (6488) gives:
% 148.09/21.04  | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | |   (6489)  all_56_9 = e2 & op(e3, e0) = e2
% 148.09/21.04  | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | ALPHA: (6489) implies:
% 148.09/21.04  | | | | | | | | | | | | | |   (6490)  all_56_9 = e2
% 148.09/21.04  | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 148.09/21.04  | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | |   (6491)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 148.09/21.04  | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 148.09/21.04  | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.09/21.04  | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.09/21.04  | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.09/21.04  | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 148.09/21.04  | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 148.09/21.04  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.09/21.04  | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 148.09/21.04  | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 148.09/21.04  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.09/21.04  | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.09/21.04  | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.09/21.04  | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 148.09/21.04  | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 148.09/21.04  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 148.09/21.04  | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | BETA: splitting (6491) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | |   (6492)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 148.09/21.04  | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 148.09/21.04  | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.09/21.04  | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.09/21.04  | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.09/21.04  | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 148.09/21.04  | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 148.09/21.04  | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.09/21.04  | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | ALPHA: (6492) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | |   (6493)  op(e3, e3) = e3
% 148.09/21.04  | | | | | | | | | | | | | | | |   (6494)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 148.09/21.04  | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = all_57_14 &
% 148.09/21.04  | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.09/21.04  | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | |   (6495)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 148.09/21.04  | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | BETA: splitting (6495) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | |   (6496)  all_56_0 = e0 & op(e3, e3) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | ALPHA: (6496) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | |   (6497)  op(e3, e3) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6493), (6497), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | |   (6498)  all_56_1 = e0 & op(e3, e2) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | ALPHA: (6498) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | |   (6499)  all_56_1 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |   (6500)  all_56_15 = e0 & op(e0, e0) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | ALPHA: (6500) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |   (6501)  op(e0, e0) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6487), (6501), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |   (6502)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | ALPHA: (6502) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |   (6503)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |   (6504)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |   (6505)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (6493), (6499), (6505),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |            #197.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |   (6506)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6506) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | |   (6507)  all_56_4 = e1 & op(e3, e1) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6507) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | |   (6508)  all_56_4 = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6494) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | |   (6509)  all_57_1 = e1 & op(e1, e3) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6509) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | |   (6510)  op(e1, e3) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6504) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | |   (6511)  all_56_9 = e0 & op(e3, e0) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6490), (6511) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | |            #746.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | |   (6512)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6512) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | |   (6513)  all_56_10 = e0 & op(e2, e0) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6513) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | |   (6514)  all_56_10 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (221), (222),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | |            (223), (5025), (5982), (6514), (function-axioms)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #450.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | |   (6515)  all_56_11 = e0 & op(e1, e0) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6515) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | |   (6516)  all_56_11 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (6517)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6517) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6518)  all_56_4 = e2 & op(e3, e1) = e2
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6518) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6519)  all_56_4 = e2
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6520)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (6493), (6499), (6520),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #197.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6506) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6507), (6519) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1066.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6521)  all_56_9 = e1 & op(e3, e0) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6490), (6521) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #656.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6522)  all_56_5 = e2 & op(e2, e1) = e2
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6522) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6523)  all_56_5 = e2
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6524)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5982), (6499), (6524), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #196.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6525)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6525) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6526)  all_56_7 = e3 & op(e1, e2) = e3
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5023), (6526), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6527)  all_56_13 = e3 & op(e0, e2) = e3
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6527) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6528)  all_56_13 = e3
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6529)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6529) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6530)  all_56_1 = e1 & op(e3, e2) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6530) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6531)  all_56_1 = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6499), (6531) imply:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6532)  e1 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6532) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6533)  e1 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6508), (6533) imply:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6534)  all_56_4 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (139), (157),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (158), (161), (162), (164), (209), (216), (217),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (221), (222), (223), (227), (228),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (5023), (5025), (5032),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5033), (5982), (6490), (6493), (6503), (6510),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6516), (6523), (6534), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #195.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6535)  all_56_3 = e1 & op(e2, e2) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6535) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6536)  all_56_3 = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6537)  op(e2, e2) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (45), (51), (138), (139),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (143), (156), (157), (158), (159), (161),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (163), (164), (166), (167), (168), (169),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (205), (206), (209), (212), (213), (214),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (216), (218), (220), (222), (223), (224), (226),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (232), (233), (234),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (237), (238), (248), (336), (340), (342),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (344), (346), (5023), (5025), (5031), (5032),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5033), (5037), (5984), (6483), (6485), (6486),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6487), (6536), (6537), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #229.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6538)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6538) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6539)  all_56_7 = e1 & op(e1, e2) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6539) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6540)  op(e1, e2) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (161), (162), (6510), (6540),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #911.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6541)  all_56_13 = e1 & op(e0, e2) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6541) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6542)  all_56_13 = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6528), (6542) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1121.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | |   (6543)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (5032), (6484), (6543),
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | |            #275.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | |   (6544)   ~ (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6544) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | |   (6545)   ~ (all_57_14 = e3)
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | |   (6546)  op(e1, e1) = all_57_14
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5032), (6545), (6546), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | |   (6547)  all_56_9 = e1 & op(e3, e0) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6490), (6547) are inconsistent by sub-proof
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | |            #656.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | End of split
% 148.09/21.04  | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | |   (6548)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 148.09/21.04  | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | BETA: splitting (6548) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | |   (6549)  all_56_4 = e0 & op(e3, e1) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | ALPHA: (6549) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | |   (6550)  all_56_4 = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | BETA: splitting (6494) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |   (6551)  all_57_1 = e1 & op(e1, e3) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | ALPHA: (6551) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | |   (6552)  op(e1, e3) = e1
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |   (6553)  all_56_15 = e0 & op(e0, e0) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | ALPHA: (6553) implies:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |   (6554)  op(e0, e0) = e0
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6487), (6554), (function-axioms) are
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |   (6555)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.04  | | | | | | | | | | | | | | | | | | | | ALPHA: (6555) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | |   (6556)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | |   (6557)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | |               e0) = e0)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6557) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | |   (6558)  all_56_9 = e0 & op(e3, e0) = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6490), (6558) are inconsistent by sub-proof
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | |            #746.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | |   (6559)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6559) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |   (6560)  all_56_10 = e0 & op(e2, e0) = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6560) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |   (6561)  all_56_10 = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (221), (222),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |            (223), (5025), (5982), (6561), (function-axioms)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #450.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |   (6562)  all_56_11 = e0 & op(e1, e0) = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6562) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |   (6563)  all_56_11 = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |   (6564)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6564) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |   (6565)  all_56_4 = e2 & op(e3, e1) = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6565) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |   (6566)  all_56_4 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6550), (6566) are inconsistent by sub-proof
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |            #936.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |   (6567)  all_56_5 = e2 & op(e2, e1) = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6567) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |   (6568)  all_56_5 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (139), (157),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |            (158), (161), (162), (164), (209), (216), (217),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (221), (222), (223), (227), (228),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |            (230), (231), (232), (5023), (5025), (5032),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |            (5033), (5982), (6490), (6493), (6550), (6552),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |            (6556), (6563), (6568), (function-axioms) are
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #195.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |   (6569)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (5032), (6484), (6569),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |            #275.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | |   (6570)   ~ (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.09/21.05  | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | ALPHA: (6570) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | |   (6571)   ~ (all_57_14 = e3)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | |   (6572)  op(e1, e1) = all_57_14
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5032), (6571), (6572), (function-axioms) are
% 148.09/21.05  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | |   (6573)  all_56_9 = e0 & op(e3, e0) = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6490), (6573) are inconsistent by sub-proof
% 148.09/21.05  | | | | | | | | | | | | | | | | | |            #746.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | |   (6574)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 148.09/21.05  | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 148.09/21.05  | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.09/21.05  | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.09/21.05  | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.09/21.05  | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 148.09/21.05  | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 148.09/21.05  | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.09/21.05  | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | ALPHA: (6574) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | |   (6575)  op(e2, e2) = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5982), (6575), (function-axioms) are
% 148.09/21.05  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 148.09/21.05  | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | |   (6576)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 148.09/21.05  | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 148.09/21.05  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.09/21.05  | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.09/21.05  | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.09/21.05  | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 148.09/21.05  | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 148.09/21.05  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.09/21.05  | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 148.09/21.05  | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 148.09/21.05  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.09/21.05  | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.09/21.05  | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.09/21.05  | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.09/21.05  | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.09/21.05  | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 148.09/21.05  | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5032), (6487), (6576),
% 148.09/21.05  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.05  | | | | | | | | | | | | | | |            #291.
% 148.09/21.05  | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | |   (6577)  all_56_10 = e2 & op(e2, e0) = e2
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | ALPHA: (6577) implies:
% 148.09/21.05  | | | | | | | | | | | | | |   (6578)  op(e2, e0) = e2
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | REF_CLOSE: (163), (6485), (6578), (function-axioms) are
% 148.09/21.05  | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | |   (6579)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 148.09/21.05  | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 148.09/21.05  | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | BETA: splitting (6579) gives:
% 148.09/21.05  | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | |   (6580)  all_56_11 = e2 & op(e1, e0) = e2
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | ALPHA: (6580) implies:
% 148.09/21.05  | | | | | | | | | | | | | |   (6581)  op(e1, e0) = e2
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | REF_CLOSE: (159), (6486), (6581), (function-axioms) are
% 148.09/21.05  | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | |   (6582)  all_56_15 = e2 & op(e0, e0) = e2
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | ALPHA: (6582) implies:
% 148.09/21.05  | | | | | | | | | | | | | |   (6583)  all_56_15 = e2
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 148.09/21.05  | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | |   (6584)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 148.09/21.05  | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 148.09/21.05  | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.09/21.05  | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.09/21.05  | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.09/21.05  | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 148.09/21.05  | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 148.09/21.05  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.09/21.05  | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 148.09/21.05  | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 148.09/21.05  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.09/21.05  | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.09/21.05  | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.09/21.05  | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 148.09/21.05  | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 148.09/21.05  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 148.09/21.05  | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | BETA: splitting (6584) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | |   (6585)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 148.09/21.05  | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.09/21.05  | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.09/21.05  | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.09/21.05  | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 148.09/21.05  | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 148.09/21.05  | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.09/21.05  | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | ALPHA: (6585) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | |   (6586)  op(e3, e3) = e3
% 148.09/21.05  | | | | | | | | | | | | | | | |   (6587)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 148.09/21.05  | | | | | | | | | | | | | | | |               = e3) & op(e0, e0) = all_57_15 &
% 148.09/21.05  | | | | | | | | | | | | | | | |             $i(all_57_15))
% 148.09/21.05  | | | | | | | | | | | | | | | |   (6588)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 148.09/21.05  | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = all_57_14 &
% 148.09/21.05  | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.09/21.05  | | | | | | | | | | | | | | | |   (6589)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 148.09/21.05  | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = all_57_12 &
% 148.09/21.05  | | | | | | | | | | | | | | | |             $i(all_57_12))
% 148.09/21.05  | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | BETA: splitting (6588) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | |   (6590)  all_57_1 = e1 & op(e1, e3) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | ALPHA: (6590) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | |   (6591)  op(e1, e3) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 148.09/21.05  | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (6591) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | |   (6592)  all_52_2 = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e3,
% 148.09/21.05  | | | | | | | | | | | | | | | | |              e3, e3, simplifying with (51), (6586) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | |   (6593)  all_14_2 = e3
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | REDUCE: (148), (6592) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | |   (6594)   ~ (all_52_1 = e1)
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | REDUCE: (336), (6593) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | |   (6595)   ~ (all_52_1 = e3)
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | REDUCE: (143), (6592) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | |   (6596)   ~ (all_52_3 = e1)
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | SIMP: (6596) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | |   (6597)   ~ (all_52_3 = e1)
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | REDUCE: (340), (6593) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | |   (6598)   ~ (all_52_3 = e3)
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | REDUCE: (342), (6593) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | |   (6599)   ~ (all_52_4 = e3)
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | REDUCE: (346), (6593) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | |   (6600)   ~ (all_52_12 = e3)
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | |   (6601)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 148.09/21.05  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (166), (5982), (6595), (6601),
% 148.09/21.05  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.05  | | | | | | | | | | | | | | | | | |            #690.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | |   (6602)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 148.09/21.05  | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | BETA: splitting (6602) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | |   (6603)  all_56_5 = e3 & op(e2, e1) = e3
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5025), (6603), (function-axioms) are
% 148.09/21.05  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | |   (6604)  all_56_10 = e3 & op(e2, e0) = e3
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | ALPHA: (6604) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | |   (6605)  all_56_10 = e3
% 148.09/21.05  | | | | | | | | | | | | | | | | | | |   (6606)  op(e2, e0) = e3
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | |   (6607)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6607) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | |   (6608)  all_56_12 = e3 & op(e0, e3) = e3
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6608) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | |   (6609)  all_56_12 = e3
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |   (6610)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (222),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |            (5982), (6586), (6605), (6606), (6610),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |            #194.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |   (6611)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6611) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |   (6612)  all_56_6 = e0 & op(e1, e3) = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6612) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |   (6613)  op(e1, e3) = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (6591), (6613), (function-axioms) are
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |   (6614)  all_56_12 = e0 & op(e0, e3) = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6614) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |   (6615)  all_56_12 = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6609), (6615) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |   (6616)  e3 = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6605), (6616) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |   (6617)  all_56_10 = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (221), (222),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |            (223), (5025), (5982), (6617), (function-axioms)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #450.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | |   (6618)  all_56_13 = e3 & op(e0, e2) = e3
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6618) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | |   (6619)  all_56_13 = e3
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |   (6620)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6620) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |   (6621)  all_56_6 = e2 & op(e1, e3) = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6621) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |   (6622)  all_56_6 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | |   (6623)  op(e1, e3) = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |   (6624)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (222),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |            (5982), (6586), (6605), (6606), (6624),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |            #194.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |   (6625)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6625) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (6626)  all_56_6 = e0 & op(e1, e3) = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6626) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (6627)  op(e1, e3) = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (6591), (6627), (function-axioms) are
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (6628)  all_56_12 = e0 & op(e0, e3) = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6628) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | |   (6629)  all_56_12 = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6630)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (161), (169), (227), (5023),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5982), (6599), (6629), (6630), (function-axioms)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #193.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6631)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6631) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6632)  all_56_14 = e1 & op(e0, e1) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6632) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6633)  all_56_14 = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6634)  all_54_4 = e3
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (6595), (6634) are inconsistent by
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #843.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6635)   ~ (all_54_4 = e3)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6636)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6636) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6637)  all_54_4 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (6637) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6638)  all_52_1 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6638) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6639)  all_52_1 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (6639) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6640)   ~ (all_52_3 = e2)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (6639) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6641)   ~ (all_52_9 = e2)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6641) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6642)   ~ (all_52_9 = e2)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (6639) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6643)   ~ (all_52_13 = e2)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6595), (6639) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6644)   ~ (e3 = e2)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6645)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6645) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6646)  all_56_6 = e1 & op(e1, e3) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6646) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6647)  all_56_6 = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6622), (6647) are inconsistent by sub-proof
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1172.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6648)  all_56_7 = e1 & op(e1, e2) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6648) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6649)  op(e1, e2) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (161), (162), (6591), (6649),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #911.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6650)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6650) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6651)  all_56_8 = e1 & op(e1, e1) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6651) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6652)  op(e1, e1) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (6652), (function-axioms) are
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6653)  all_56_11 = e1 & op(e1, e0) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6653) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6654)  all_56_11 = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6655)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6655) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6656)  all_56_4 = e2 & op(e3, e1) = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6656) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6657)  all_56_4 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6658)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6658) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6659)  all_56_1 = e2 & op(e3, e2) = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6659) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6660)  all_56_1 = e2
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6661)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6661) gives:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6662)  all_56_1 = e1 & op(e3, e2) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6662) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6663)  all_56_1 = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6660), (6663) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6664)  e2 = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6657), (6664) imply:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6665)  all_56_4 = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (218), (5032),
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6633), (6665), (function-axioms) are inconsistent
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #254.
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6666)  all_56_3 = e1 & op(e2, e2) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6666) implies:
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6667)  all_56_3 = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6668)  op(e2, e2) = e1
% 148.09/21.05  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (138), (142),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (156), (159), (161), (162), (163), (164), (166),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (167), (168), (169), (191), (212), (213), (214),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (222), (223), (224), (226), (227), (228),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (238), (248), (5023), (5024),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5025), (5031), (5032), (5033), (6483), (6485),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6486), (6487), (6586), (6587), (6588), (6589),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6591), (6595), (6597), (6598), (6599), (6600),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6619), (6654), (6667), (6668), (function-axioms)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #230.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6669)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (142), (161), (162), (169), (227),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5023), (5982), (6591), (6599), (6669),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #204.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6670)  all_56_3 = e2 & op(e2, e2) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6670) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6671)  op(e2, e2) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (45), (51), (122), (139), (142),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (156), (157), (158), (161), (162), (163),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (168), (169), (203), (218), (237),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (278), (342), (344), (5032), (5033),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5037), (5984), (6484), (6485), (6487), (6623),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6642), (6671), (function-axioms) are inconsistent
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #290.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6672)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6672) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6673)  all_56_7 = e2 & op(e1, e2) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6673) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6674)  all_56_7 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (162), (212), (5032), (6591),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6654), (6674), (function-axioms) are inconsistent
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #237.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6675)  all_56_13 = e2 & op(e0, e2) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6675) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6676)  all_56_13 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6619), (6676) are inconsistent by sub-proof
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1105.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6677)  all_56_5 = e2 & op(e2, e1) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6677) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6678)  op(e2, e1) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6642), (6678), (function-axioms) are
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6679)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (206),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5032), (6583), (6619), (6679), (function-axioms)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #192.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6680)  all_54_4 = e1 | all_54_4 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (5979), (6594), (6680) are inconsistent by
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #795.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6681)  all_56_15 = e1 & op(e0, e0) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6681) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6682)  op(e0, e0) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5033), (6682), (function-axioms) are
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1116.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | |   (6683)  all_56_7 = e2 & op(e1, e2) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6683) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | |   (6684)  all_56_7 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |   (6685)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (222),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |            (5982), (6586), (6605), (6606), (6685),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |            #194.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |   (6686)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6686) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (6687)  all_56_6 = e0 & op(e1, e3) = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6687) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (6688)  op(e1, e3) = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (6591), (6688), (function-axioms) are
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (6689)  all_56_12 = e0 & op(e0, e3) = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6689) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (6690)  all_56_12 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6691)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (161), (169), (227), (5023),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5982), (6599), (6690), (6691), (function-axioms)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #193.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6692)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6692) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6693)  all_56_14 = e1 & op(e0, e1) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6693) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6694)  all_56_14 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6695)  op(e0, e1) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6696)  all_54_4 = e3
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (6595), (6696) are inconsistent by
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #843.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6697)   ~ (all_54_4 = e3)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6698)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6698) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6699)  all_54_4 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (6699) imply:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6700)  all_52_1 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6700) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6701)  all_52_1 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (6701) imply:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6702)   ~ (all_52_3 = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (6701) imply:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6703)   ~ (all_52_9 = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6703) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6704)   ~ (all_52_9 = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (6701) imply:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6705)   ~ (all_52_13 = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6595), (6701) imply:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6706)   ~ (e3 = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6707)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6707) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6708)  all_56_6 = e1 & op(e1, e3) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6708) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6709)  all_56_6 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6710)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6710) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6711)  all_56_4 = e2 & op(e3, e1) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6711) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6712)  all_56_4 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6713)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6713) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6714)  all_56_2 = e2 & op(e2, e3) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6714) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6715)  all_56_2 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6716)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6716) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6717)  all_56_1 = e1 & op(e3, e2) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6717) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6718)  all_56_1 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6719)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6719) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6720)  all_56_4 = e0 & op(e3, e1) = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6720) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6721)  all_56_4 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6712), (6721) imply:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6722)  e2 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6715), (6722) imply:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6723)  all_56_2 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (221), (222), (5982),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6605), (6606), (6723), (function-axioms) are
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #670.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6724)  all_56_5 = e0 & op(e2, e1) = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6724) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6725)  all_56_5 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6726)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6726) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6727)  all_56_2 = e1 & op(e2, e3) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6727) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6728)  op(e2, e3) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (166), (222), (5982), (6606),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6725), (6728), (function-axioms) are inconsistent
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #191.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6729)  all_56_3 = e1 & op(e2, e2) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6729) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6730)  all_56_3 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (224), (6619), (6684), (6718),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6730) are inconsistent by sub-proof #271.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6731)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6731) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6732)  all_56_5 = e1 & op(e2, e1) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6732) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6733)  all_56_5 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (216), (218), (5032),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6694), (6733), (function-axioms) are inconsistent
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #247.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6734)  all_56_10 = e1 & op(e2, e0) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6734) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6735)  all_56_10 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6605), (6735) imply:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6736)  e3 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6736) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6737)  e3 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6619), (6737) imply:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6738)  all_56_13 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (227), (5023), (5982),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6599), (6738), (function-axioms) are inconsistent
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #210.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6739)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (5032), (6695), (6739),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #236.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6740)  all_56_3 = e1 & op(e2, e2) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6740) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6741)  all_56_3 = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6742)  op(e2, e2) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (138), (139),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (157), (158), (159), (161), (162),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (166), (167), (168), (169), (191),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (205), (206), (209), (212), (214), (216), (218),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (222), (223), (224), (226), (227), (228),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (229), (230), (232), (233), (235), (238), (248),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5023), (5024), (5025), (5032), (5033), (6483),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6485), (6486), (6487), (6586), (6587), (6588),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6589), (6591), (6595), (6597), (6598), (6599),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6600), (6709), (6741), (6742), (function-axioms)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #231.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6743)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (142), (161), (162), (169), (227),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5023), (5982), (6591), (6599), (6743),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #204.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6744)  all_56_3 = e2 & op(e2, e2) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6744) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6745)  op(e2, e2) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5982), (6745), (function-axioms) are
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6746)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (6606), (6704), (6746),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #190.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6747)  all_56_5 = e2 & op(e2, e1) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6747) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6748)  op(e2, e1) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6704), (6748), (function-axioms) are
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6749)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (206),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5032), (6583), (6619), (6749), (function-axioms)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #192.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6750)  all_56_7 = e1 & op(e1, e2) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6750) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6751)  op(e1, e2) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (161), (162), (6591), (6751),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #911.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6752)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (162), (212), (5032), (6591),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6684), (6752), (function-axioms) are inconsistent
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #189.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6753)  all_54_4 = e1 | all_54_4 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (5979), (6594), (6753) are inconsistent by
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #795.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6754)  all_56_15 = e1 & op(e0, e0) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6754) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6755)  op(e0, e0) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5033), (6755), (function-axioms) are
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1116.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | |   (6756)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (159), (5032), (6486), (6756),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | |            #289.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | |   (6757)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6757) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | |   (6758)  all_56_14 = e3 & op(e0, e1) = e3
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6758) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | |   (6759)  all_56_14 = e3
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | |   (6760)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (221), (222),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | |            (5982), (6586), (6605), (6606), (6760),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | |            #194.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | |   (6761)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6761) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | |   (6762)  all_56_6 = e0 & op(e1, e3) = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6762) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | |   (6763)  op(e1, e3) = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (6591), (6763), (function-axioms) are
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | |   (6764)  all_56_12 = e0 & op(e0, e3) = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6764) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | |   (6765)  all_56_12 = e0
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |   (6766)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (161), (169), (227), (5023),
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |            (5982), (6599), (6765), (6766), (function-axioms)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #193.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |   (6767)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6767) gives:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (6768)  all_56_14 = e1 & op(e0, e1) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6759), (6768) are inconsistent by sub-proof
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | |            #188.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (6769)  all_56_15 = e1 & op(e0, e0) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6769) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | |   (6770)  op(e0, e0) = e1
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (5033), (6770), (function-axioms) are
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1116.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | |   (6771)  all_56_15 = e3 & op(e0, e0) = e3
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6771) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | |   (6772)  all_56_15 = e3
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6583), (6772) imply:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | |   (6773)  e3 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | SIMP: (6773) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | |   (6774)  e3 = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (6774) imply:
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | |   (6775)  $false
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | CLOSE: (6775) is inconsistent.
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | |   (6776)   ~ (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.09/21.06  | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 148.09/21.06  | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | ALPHA: (6776) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | | |   (6777)   ~ (all_57_14 = e3)
% 148.09/21.06  | | | | | | | | | | | | | | | | |   (6778)  op(e1, e1) = all_57_14
% 148.09/21.06  | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | | REF_CLOSE: (5032), (6777), (6778), (function-axioms) are
% 148.09/21.06  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 148.09/21.06  | | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | |   (6779)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 148.09/21.06  | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 148.09/21.06  | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.09/21.06  | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.09/21.06  | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.09/21.06  | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 148.09/21.06  | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 148.09/21.06  | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.09/21.06  | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | ALPHA: (6779) implies:
% 148.09/21.06  | | | | | | | | | | | | | | | |   (6780)  op(e2, e2) = e2
% 148.09/21.06  | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5982), (6780), (function-axioms) are
% 148.09/21.06  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 148.09/21.06  | | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | | End of split
% 148.09/21.06  | | | | | | | | | | | | | | | 
% 148.09/21.06  | | | | | | | | | | | | | | Case 2:
% 148.09/21.06  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | |   (6781)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 148.09/21.07  | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 148.09/21.07  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.09/21.07  | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.09/21.07  | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.09/21.07  | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 148.09/21.07  | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 148.09/21.07  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.09/21.07  | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 148.09/21.07  | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 148.09/21.07  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.09/21.07  | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.09/21.07  | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.09/21.07  | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.09/21.07  | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.09/21.07  | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5032), (6487), (6781),
% 148.09/21.07  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.07  | | | | | | | | | | | | | | |            #291.
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | End of split
% 148.09/21.07  | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | End of split
% 148.09/21.07  | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | End of split
% 148.09/21.07  | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | End of split
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | Case 2:
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | |   (6782)  all_22_2 = e1
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | COMBINE_EQS: (320), (6782) imply:
% 148.09/21.07  | | | | | | | | | | |   (6783)  all_14_2 = e1
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | SIMP: (6783) implies:
% 148.09/21.07  | | | | | | | | | | |   (6784)  all_14_2 = e1
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | REDUCE: (336), (6784) imply:
% 148.09/21.07  | | | | | | | | | | |   (6785)   ~ (all_52_1 = e1)
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | REDUCE: (51), (6784) imply:
% 148.09/21.07  | | | | | | | | | | |   (6786)  op(e3, e3) = e1
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (45), (109), (111), (112),
% 148.09/21.07  | | | | | | | | | | |            (116), (124), (125), (127), (132), (138), (139),
% 148.09/21.07  | | | | | | | | | | |            (144), (145), (147), (156), (157), (158), (159),
% 148.09/21.07  | | | | | | | | | | |            (161), (163), (164), (166), (168), (169), (190),
% 148.09/21.07  | | | | | | | | | | |            (191), (192), (200), (206), (209), (212), (213),
% 148.09/21.07  | | | | | | | | | | |            (214), (216), (217), (218), (220), (222), (223),
% 148.09/21.07  | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (232),
% 148.09/21.07  | | | | | | | | | | |            (233), (234), (235), (237), (238), (247), (248),
% 148.09/21.07  | | | | | | | | | | |            (249), (269), (349), (360), (367), (368), (370),
% 148.09/21.07  | | | | | | | | | | |            (5023), (5024), (5025), (5027), (5031), (5032),
% 148.09/21.07  | | | | | | | | | | |            (5033), (5980), (5982), (6785), (6786),
% 148.09/21.07  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.07  | | | | | | | | | | |            #187.
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | End of split
% 148.09/21.07  | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | End of split
% 148.09/21.07  | | | | | | | | | 
% 148.09/21.07  | | | | | | | | Case 2:
% 148.09/21.07  | | | | | | | | | 
% 148.09/21.07  | | | | | | | | |   (6787)  all_14_2 = e0
% 148.09/21.07  | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | REDUCE: (340), (6787) imply:
% 148.09/21.07  | | | | | | | | |   (6788)   ~ (all_52_3 = e0)
% 148.09/21.07  | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | REDUCE: (344), (6787) imply:
% 148.09/21.07  | | | | | | | | |   (6789)   ~ (all_52_8 = e0)
% 148.09/21.07  | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | REDUCE: (346), (6787) imply:
% 148.09/21.07  | | | | | | | | |   (6790)   ~ (all_52_12 = e0)
% 148.09/21.07  | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | REDUCE: (51), (6787) imply:
% 148.09/21.07  | | | | | | | | |   (6791)  op(e3, e3) = e0
% 148.09/21.07  | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | BETA: splitting (229) gives:
% 148.09/21.07  | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | |   (6792)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 148.09/21.07  | | | | | | | | | |             & op(e3, e2) = e0)
% 148.09/21.07  | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | BETA: splitting (6792) gives:
% 148.09/21.07  | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | |   (6793)  all_56_0 = e0 & op(e3, e3) = e0
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | ALPHA: (6793) implies:
% 148.09/21.07  | | | | | | | | | | |   (6794)  all_56_0 = e0
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | BETA: splitting (55) gives:
% 148.09/21.07  | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | |   (6795)   ~ (all_16_2 = e0)
% 148.09/21.07  | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | REDUCE: (327), (6795) imply:
% 148.09/21.07  | | | | | | | | | | | |   (6796)   ~ (all_6_2 = e0)
% 148.09/21.07  | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | BETA: splitting (61) gives:
% 148.09/21.07  | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | |   (6797)   ~ (all_20_2 = e1)
% 148.09/21.07  | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | REDUCE: (282), (6797) imply:
% 148.09/21.07  | | | | | | | | | | | | |   (6798)   ~ (all_6_2 = e1)
% 148.09/21.07  | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | BETA: splitting (198) gives:
% 148.09/21.07  | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | |   (6799)  all_54_5 = e3
% 148.09/21.07  | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | REF_CLOSE: (267), (372), (6799) are inconsistent by sub-proof
% 148.09/21.07  | | | | | | | | | | | | | |            #443.
% 148.09/21.07  | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | Case 2:
% 148.09/21.07  | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | |   (6800)   ~ (all_54_5 = e3)
% 148.09/21.07  | | | | | | | | | | | | | |   (6801)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 148.09/21.07  | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | BETA: splitting (6801) gives:
% 148.09/21.07  | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | |   (6802)  all_54_5 = e2
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | COMBINE_EQS: (267), (6802) imply:
% 148.09/21.07  | | | | | | | | | | | | | | |   (6803)  all_6_2 = e2
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | SIMP: (6803) implies:
% 148.09/21.07  | | | | | | | | | | | | | | |   (6804)  all_6_2 = e2
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | REDUCE: (347), (6804) imply:
% 148.09/21.07  | | | | | | | | | | | | | | |   (6805)   ~ (all_52_1 = e2)
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | REDUCE: (352), (6804) imply:
% 148.09/21.07  | | | | | | | | | | | | | | |   (6806)   ~ (all_52_6 = e2)
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | REDUCE: (356), (6804) imply:
% 148.09/21.07  | | | | | | | | | | | | | | |   (6807)   ~ (all_52_9 = e2)
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | REDUCE: (358), (6804) imply:
% 148.09/21.07  | | | | | | | | | | | | | | |   (6808)   ~ (all_52_13 = e2)
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | REDUCE: (372), (6804) imply:
% 148.09/21.07  | | | | | | | | | | | | | | |   (6809)   ~ (e3 = e2)
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | REDUCE: (39), (6804) imply:
% 148.09/21.07  | | | | | | | | | | | | | | |   (6810)  op(e2, e2) = e2
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 148.09/21.07  | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | |   (6811)   ~ (all_24_2 = e2)
% 148.09/21.07  | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | REDUCE: (318), (6811) imply:
% 148.09/21.07  | | | | | | | | | | | | | | | |   (6812)   ~ (all_10_2 = e2)
% 148.09/21.07  | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.09/21.07  | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | |   (6813)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.09/21.07  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.09/21.07  | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.09/21.07  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.09/21.07  | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.09/21.07  | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.09/21.07  | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.09/21.07  | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.09/21.07  | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.09/21.07  | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.09/21.07  | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.09/21.07  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.09/21.07  | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.09/21.07  | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.09/21.07  | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | BETA: splitting (6813) gives:
% 148.09/21.07  | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | |   (6814)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.09/21.07  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.09/21.07  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | BETA: splitting (6814) gives:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |   (6815)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (6805), (6815), (function-axioms) are
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |   (6816)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5032), (6816), (function-axioms) are inconsistent
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |            by sub-proof #368.
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | |   (6817)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 148.09/21.07  | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.09/21.07  | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | BETA: splitting (6817) gives:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |   (6818)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (5032), (6812), (6818),
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |            #367.
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |   (6819)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (45), (6791), (6810), (6812), (6819),
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |            #545.
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | End of split
% 148.09/21.07  | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.07  | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | |   (6820)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.09/21.07  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.09/21.07  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.09/21.07  | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.09/21.07  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.09/21.07  | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.09/21.07  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.09/21.07  | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.09/21.07  | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.09/21.07  | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.09/21.07  | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.09/21.07  | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.09/21.07  | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.09/21.07  | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.09/21.07  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.09/21.07  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.09/21.07  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.09/21.07  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.09/21.07  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.09/21.07  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.09/21.07  | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | BETA: splitting (6820) gives:
% 148.09/21.07  | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | |   (6821)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.09/21.07  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.09/21.07  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.09/21.07  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | BETA: splitting (6821) gives:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | Case 1:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |   (6822)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (5024), (6807), (6822),
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |            #1083.
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |   (6823)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (45), (5032), (5033), (6810), (6823),
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.09/21.07  | | | | | | | | | | | | | | | | | | |            #293.
% 148.09/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | | End of split
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.09/21.07  | | | | | | | | | | | | | | | | | Case 2:
% 148.09/21.07  | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | |   (6824)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.40/21.07  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.40/21.07  | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.40/21.07  | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.40/21.07  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.40/21.07  | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.40/21.07  | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.40/21.07  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.40/21.07  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.40/21.07  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.40/21.07  | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | BETA: splitting (6824) gives:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | |   (6825)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.40/21.07  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.40/21.07  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.40/21.07  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.40/21.07  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.40/21.07  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.40/21.07  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.40/21.07  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.40/21.07  | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | BETA: splitting (6825) gives:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6826)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | ALPHA: (6826) implies:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6827)  op(e2, e0) = e2
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6808), (6827), (function-axioms) are
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6828)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | ALPHA: (6828) implies:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6829)   ~ (all_57_14 = e0)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6830)   ~ (all_57_9 = e3)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6831)  op(e1, e0) = e1
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6832)  op(e1, e1) = all_57_14
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6833)  op(e3, e0) = all_57_9
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (159), (6831) gives:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6834)  all_52_14 = e1
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |              all_57_14, e1, e1, simplifying with (5032), (6832)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |              gives:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6835)  all_57_14 = e3
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |              all_57_9, e0, e3, simplifying with (167), (6833)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |              gives:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6836)  all_57_9 = all_52_12
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | REDUCE: (6830), (6836) imply:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6837)   ~ (all_52_12 = e3)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (6834) imply:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6838)   ~ (all_52_6 = e1)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (6834) imply:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6839)   ~ (all_52_12 = e1)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (6834) imply:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6840)   ~ (all_10_2 = e1)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | REDUCE: (5027), (6834) imply:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | |   (6841)   ~ (e3 = e1)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | |   (6842)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6842) gives:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | |   (6843)  all_56_9 = e2 & op(e3, e0) = e2
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6843) implies:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | |   (6844)  all_56_9 = e2
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5018) gives:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | |   (6845)   ~ (all_8_0 = e2) & op(all_8_1, e1) = all_8_0 &
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.07  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6845) implies:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |   (6846)  op(e1, e3) = all_8_1
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (93), (112),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (117), (119), (122), (124), (127), (132), (133),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (138), (139), (156), (157), (158), (161), (162),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (166), (167), (168), (169), (188),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (194), (197), (200), (201), (205), (206), (207),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (212), (213), (214), (216),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (220), (221), (223), (224), (225),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (238), (245), (257), (260), (269),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (270), (302), (349), (367), (368), (5023), (5024),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (5025), (5031), (5032), (5033), (5036), (6788),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (6789), (6790), (6791), (6794), (6805), (6806),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (6807), (6810), (6812), (6831), (6837), (6838),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (6839), (6844), (6846), (function-axioms) are
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #175.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |   (6847)   ~ (all_8_1 = e0) & op(e1, e3) = all_8_1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_8_1)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6847) implies:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |   (6848)  op(e1, e3) = all_8_1
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (93), (112),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (117), (119), (122), (124), (127), (132), (133),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (138), (139), (156), (157), (158), (161), (162),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (166), (167), (168), (169), (188),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (194), (197), (200), (201), (205), (206), (207),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (208), (209), (210), (212), (213), (214), (216),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (220), (221), (223), (224), (225),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (230), (231), (232), (233),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (234), (235), (238), (245), (257), (260), (269),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (270), (302), (349), (367), (368), (5023), (5024),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (5025), (5031), (5032), (5033), (5036), (6788),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (6789), (6790), (6791), (6794), (6805), (6806),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (6807), (6810), (6812), (6831), (6837), (6838),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            (6839), (6844), (6848), (function-axioms) are
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #175.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |   (6849)  all_56_10 = e2 & op(e2, e0) = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6849) implies:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |   (6850)  op(e2, e0) = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6808), (6850), (function-axioms) are
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |   (6851)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (45), (6812), (6831), (6851),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |            #743.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |   (6852)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | BETA: splitting (6852) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |   (6853)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | ALPHA: (6853) implies:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |   (6854)  op(e2, e0) = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6808), (6854), (function-axioms) are
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |   (6855)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6855) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |   (6856)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6856) implies:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |   (6857)  op(e2, e2) = e0
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6810), (6857), (function-axioms) are
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |   (6858)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6858) implies:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |   (6859)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6859) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |   (6860)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (6788), (6791), (6860),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |            #538.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |   (6861)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (5032), (6791), (6810), (6861),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |            #174.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | |   (6862)  all_24_2 = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | COMBINE_EQS: (318), (6862) imply:
% 148.40/21.08  | | | | | | | | | | | | | | | |   (6863)  all_10_2 = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | SIMP: (6863) implies:
% 148.40/21.08  | | | | | | | | | | | | | | | |   (6864)  all_10_2 = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | REDUCE: (367), (6864) imply:
% 148.40/21.08  | | | | | | | | | | | | | | | |   (6865)   ~ (all_52_11 = e2)
% 148.40/21.08  | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | REDUCE: (45), (6864) imply:
% 148.40/21.08  | | | | | | | | | | | | | | | |   (6866)  op(e0, e0) = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | |   (6867)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 148.40/21.08  | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | BETA: splitting (6867) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | |   (6868)  all_56_4 = e2 & op(e3, e1) = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | ALPHA: (6868) implies:
% 148.40/21.08  | | | | | | | | | | | | | | | | | |   (6869)  op(e3, e1) = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |   (6870)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | BETA: splitting (6870) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |   (6871)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | ALPHA: (6871) implies:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |   (6872)  op(e3, e3) = e3
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6791), (6872), (function-axioms) are
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |   (6873)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | ALPHA: (6873) implies:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |   (6874)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |               = e2) & op(e0, e0) = all_57_15 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | BETA: splitting (6874) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |   (6875)  all_57_5 = e0 & op(e0, e2) = e0
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6875) implies:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |   (6876)  all_57_5 = e0
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | |   (6877)  op(e0, e2) = e0
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |   (6878)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6878) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |   (6879)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6879) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |   (6880)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (6805), (6880), (function-axioms) are
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |   (6881)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5032), (6881), (function-axioms) are inconsistent
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #368.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |   (6882)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6882) gives:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |   (6883)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (6876), (6883), (function-axioms) are
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #276.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |   (6884)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (6791), (6810), (6876), (6884),
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | |            #531.
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.08  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |   (6885)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6885) gives:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |   (6886)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6886) gives:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |   (6887)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (5024), (6807), (6887),
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |            #1083.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |   (6888)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (45), (5032), (5033), (6810), (6888),
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |            #293.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |   (6889)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6889) gives:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |   (6890)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6890) gives:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6891)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6891) implies:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6892)  op(e2, e0) = e2
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6808), (6892), (function-axioms) are
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6893)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6893) implies:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6894)   ~ (all_57_9 = e3)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6895)  op(e1, e0) = e1
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6896)  op(e3, e0) = all_57_9
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (159), (6895) gives:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6897)  all_52_14 = e1
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_9, e0, e3, simplifying with (167), (6896)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6898)  all_57_9 = all_52_12
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (6869) gives:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6899)  all_52_8 = e2
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6894), (6898) imply:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6900)   ~ (all_52_12 = e3)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (6899) imply:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6901)   ~ (all_52_12 = e2)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6901) implies:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6902)   ~ (all_52_12 = e2)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (6897) imply:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6903)   ~ (all_52_12 = e1)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6904)  all_54_3 = e3
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (6900), (6904) are inconsistent by
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #451.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6905)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (6790), (6902), (6903), (6905) are
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #758.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |   (6906)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6906) gives:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6907)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6907) implies:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6908)  op(e2, e0) = e2
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (6808), (6908), (function-axioms) are
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (6909)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6909) gives:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6910)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6910) implies:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6911)  op(e2, e2) = e0
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6810), (6911), (function-axioms) are
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6912)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6912) implies:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6913)  op(e0, e0) = all_57_15
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6914)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6914) gives:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6915)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (157), (158), (6866), (6877), (6913),
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (6915), (function-axioms) are inconsistent by
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #529.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (6916)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (5032), (6791), (6810), (6916),
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #174.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | |   (6917)   ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_15)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | ALPHA: (6917) implies:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | |   (6918)   ~ (all_57_15 = e2)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | |   (6919)  op(e0, e0) = all_57_15
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6866), (6918), (6919), (function-axioms) are
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #901.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |   (6920)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (5032), (6866), (6920),
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.40/21.09  | | | | | | | | | | | | | | | | | | |            #291.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | |   (6921)  all_56_5 = e2 & op(e2, e1) = e2
% 148.40/21.09  | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | ALPHA: (6921) implies:
% 148.40/21.09  | | | | | | | | | | | | | | | | | |   (6922)  op(e2, e1) = e2
% 148.40/21.09  | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6807), (6922), (function-axioms) are
% 148.40/21.09  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 148.40/21.09  | | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | |   (6923)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 148.40/21.09  | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 148.40/21.09  | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (5032), (6865), (6923),
% 148.40/21.09  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.40/21.09  | | | | | | | | | | | | | | | | |            #275.
% 148.40/21.09  | | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | |   (6924)  all_54_5 = e1 | all_54_5 = e0
% 148.40/21.09  | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | | REF_CLOSE: (267), (6796), (6798), (6924) are inconsistent by
% 148.40/21.09  | | | | | | | | | | | | | | |            sub-proof #866.
% 148.40/21.09  | | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | End of split
% 148.40/21.09  | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | Case 2:
% 148.40/21.09  | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | |   (6925)  all_20_2 = e1
% 148.40/21.09  | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | COMBINE_EQS: (282), (6925) imply:
% 148.40/21.09  | | | | | | | | | | | | |   (6926)  all_6_2 = e1
% 148.40/21.09  | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | REDUCE: (347), (6926) imply:
% 148.40/21.09  | | | | | | | | | | | | |   (6927)   ~ (all_52_1 = e1)
% 148.40/21.09  | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | REDUCE: (352), (6926) imply:
% 148.40/21.09  | | | | | | | | | | | | |   (6928)   ~ (all_52_6 = e1)
% 148.40/21.09  | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | REDUCE: (358), (6926) imply:
% 148.40/21.09  | | | | | | | | | | | | |   (6929)   ~ (all_52_13 = e1)
% 148.40/21.09  | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | REDUCE: (372), (6926) imply:
% 148.40/21.09  | | | | | | | | | | | | |   (6930)   ~ (e3 = e1)
% 148.40/21.09  | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | REDUCE: (39), (6926) imply:
% 148.40/21.09  | | | | | | | | | | | | |   (6931)  op(e2, e2) = e1
% 148.40/21.09  | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | BETA: splitting (221) gives:
% 148.40/21.09  | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | Case 1:
% 148.40/21.09  | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | |   (6932)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 148.40/21.09  | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.40/21.09  | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | BETA: splitting (6932) gives:
% 148.40/21.09  | | | | | | | | | | | | | | 
% 148.40/21.09  | | | | | | | | | | | | | | Case 1:
% 148.40/21.09  | | | | | | | | | | | | | | | 
% 148.40/21.10  | | | | | | | | | | | | | | |   (6933)  all_56_2 = e1 & op(e2, e3) = e1
% 148.40/21.10  | | | | | | | | | | | | | | | 
% 148.40/21.10  | | | | | | | | | | | | | | | ALPHA: (6933) implies:
% 148.40/21.10  | | | | | | | | | | | | | | |   (6934)  all_56_2 = e1
% 148.40/21.10  | | | | | | | | | | | | | | |   (6935)  op(e2, e3) = e1
% 148.40/21.10  | | | | | | | | | | | | | | | 
% 148.40/21.10  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 148.40/21.10  | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 148.40/21.10  | | | | | | | | | | | | | | |            (227), (5023), (5025), (6928), (6931), (6934),
% 148.40/21.10  | | | | | | | | | | | | | | |            (6935), (function-axioms) are inconsistent by
% 148.40/21.10  | | | | | | | | | | | | | | |            sub-proof #172.
% 148.40/21.10  | | | | | | | | | | | | | | | 
% 148.40/21.10  | | | | | | | | | | | | | | Case 2:
% 148.40/21.10  | | | | | | | | | | | | | | | 
% 148.40/21.10  | | | | | | | | | | | | | | |   (6936)  all_56_3 = e1 & op(e2, e2) = e1
% 148.40/21.10  | | | | | | | | | | | | | | | 
% 148.40/21.10  | | | | | | | | | | | | | | | ALPHA: (6936) implies:
% 148.40/21.10  | | | | | | | | | | | | | | |   (6937)  all_56_3 = e1
% 148.40/21.10  | | | | | | | | | | | | | | | 
% 148.40/21.10  | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 148.40/21.10  | | | | | | | | | | | | | | | 
% 148.40/21.10  | | | | | | | | | | | | | | | Case 1:
% 148.40/21.10  | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | |   (6938)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 148.49/21.10  | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 148.49/21.10  | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.49/21.10  | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.49/21.10  | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.49/21.10  | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 148.49/21.10  | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 148.49/21.10  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.49/21.10  | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 148.49/21.10  | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 148.49/21.10  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.49/21.10  | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.49/21.10  | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.49/21.10  | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 148.49/21.10  | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 148.49/21.10  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 148.49/21.10  | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (6791), (6931), (6938),
% 148.49/21.10  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.10  | | | | | | | | | | | | | | | |            #515.
% 148.49/21.10  | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | |   (6939)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 148.49/21.10  | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 148.49/21.10  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.49/21.10  | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.49/21.10  | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.49/21.10  | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 148.49/21.10  | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 148.49/21.10  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.49/21.10  | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 148.49/21.10  | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 148.49/21.10  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.49/21.10  | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.49/21.10  | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.49/21.10  | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.49/21.10  | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.49/21.10  | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 148.49/21.10  | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | BETA: splitting (6939) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | |   (6940)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 148.49/21.10  | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.49/21.10  | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.49/21.10  | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.49/21.10  | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 148.49/21.10  | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 148.49/21.10  | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.49/21.10  | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | ALPHA: (6940) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | |   (6941)  op(e1, e1) = e1
% 148.49/21.10  | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (6941), (function-axioms) are
% 148.49/21.10  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 148.49/21.10  | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | |   (6942)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 148.49/21.10  | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.49/21.10  | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.49/21.10  | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.49/21.10  | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.49/21.10  | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.49/21.10  | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 148.49/21.10  | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | ALPHA: (6942) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | |   (6943)  all_57_15 = e0
% 148.49/21.10  | | | | | | | | | | | | | | | | |   (6944)  op(e0, e0) = e0
% 148.49/21.10  | | | | | | | | | | | | | | | | |   (6945)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.49/21.10  | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.49/21.10  | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 148.49/21.10  | | | | | | | | | | | | | | | | |   (6946)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10
% 148.49/21.10  | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = all_57_10 &
% 148.49/21.10  | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.49/21.10  | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | BETA: splitting (6946) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | |   (6947)  all_57_9 = e3 & op(e3, e0) = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | ALPHA: (6947) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | | |   (6948)  op(e3, e0) = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 148.49/21.10  | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (45), (6944) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | |   (6949)  all_10_2 = e0
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 148.49/21.10  | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (167), (6948) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | |   (6950)  all_52_12 = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | REDUCE: (132), (6950) imply:
% 148.49/21.10  | | | | | | | | | | | | | | | | | |   (6951)   ~ (all_52_4 = e3)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | REDUCE: (360), (6949) imply:
% 148.49/21.10  | | | | | | | | | | | | | | | | | |   (6952)   ~ (all_52_7 = e0)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | REDUCE: (367), (6949) imply:
% 148.49/21.10  | | | | | | | | | | | | | | | | | |   (6953)   ~ (all_52_11 = e0)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | REDUCE: (112), (6950) imply:
% 148.49/21.10  | | | | | | | | | | | | | | | | | |   (6954)   ~ (all_52_13 = e3)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | SIMP: (6954) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | | |   (6955)   ~ (all_52_13 = e3)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | REDUCE: (369), (6949) imply:
% 148.49/21.10  | | | | | | | | | | | | | | | | | |   (6956)   ~ (all_52_13 = e0)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | REDUCE: (5033), (6949) imply:
% 148.49/21.10  | | | | | | | | | | | | | | | | | |   (6957)   ~ (e1 = e0)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | |   (6958)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (6937), (6951), (6958),
% 148.49/21.10  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.10  | | | | | | | | | | | | | | | | | | |            #261.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | |   (6959)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | BETA: splitting (6959) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | |   (6960)  all_56_7 = e3 & op(e1, e2) = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5023), (6960), (function-axioms) are
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | |   (6961)  all_56_13 = e3 & op(e0, e2) = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | ALPHA: (6961) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | |   (6962)  all_56_13 = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | |   (6963)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6963) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | |   (6964)  all_56_9 = e1 & op(e3, e0) = e1
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6964) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | |   (6965)  all_56_9 = e1
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |   (6966)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (6791), (6951), (6966),
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |            #171.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |   (6967)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6967) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |   (6968)  all_56_4 = e3 & op(e3, e1) = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6968) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |   (6969)  op(e3, e1) = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5024), (6969), (function-axioms) are
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |   (6970)  all_56_9 = e3 & op(e3, e0) = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6970) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |   (6971)  all_56_9 = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6965), (6971) imply:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |   (6972)  e3 = e1
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6962), (6972) imply:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |   (6973)  all_56_13 = e1
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (224), (226),
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |            (227), (5023), (6931), (6937), (6973),
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |            #260.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | |   (6974)  all_56_10 = e1 & op(e2, e0) = e1
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6974) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | |   (6975)  all_56_10 = e1
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (220), (222),
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | |            (223), (5025), (6931), (6937), (6975),
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | |            #264.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | |   (6976)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6976) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | |   (6977)  all_56_11 = e1 & op(e1, e0) = e1
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6977) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | |   (6978)  op(e1, e0) = e1
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |   (6979)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6979) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |   (6980)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6980) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (6981)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6981) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6982)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6982) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6983)  op(e2, e3) = e2
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (166), (196), (259), (6929), (6955),
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6956), (6983), (function-axioms) are inconsistent
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #168.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6984)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6984) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6985)  op(e2, e3) = e2
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (166), (196), (259), (6929), (6955),
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6956), (6985), (function-axioms) are inconsistent
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #168.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (6986)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (6944), (6986), (function-axioms) are
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #352.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |   (6987)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6987) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (6988)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (5032), (6951), (6988),
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |            #294.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |   (6989)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6989) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6990)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6990) implies:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6991)  op(e3, e3) = e2
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6791), (6991), (function-axioms) are
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6992)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (168), (5024), (6944), (6992),
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | |            #244.
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |   (6993)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6993) gives:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |   (6994)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.49/21.10  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6994) gives:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (6995)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6995) gives:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6996)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6996) implies:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6997)  op(e3, e1) = e3
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5024), (6997), (function-axioms) are
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6998)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6998) implies:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (6999)  op(e3, e3) = e1
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (124), (127),
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (138), (139), (144), (145), (147), (156), (158),
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (161), (163), (164), (166), (168), (190),
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (206), (212), (213), (214), (216), (217),
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (218), (222), (224), (226), (227), (228), (232),
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (238), (247), (248), (349), (360), (5023),
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5024), (5031), (5032), (5033), (6927), (6931),
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (6937), (6943), (6944), (6945), (6978), (6999),
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            #242.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (7000)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7000) gives:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7001)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7001) implies:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7002)  op(e0, e0) = e1
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6944), (7002), (function-axioms) are
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7003)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (6791), (7003), (function-axioms) are
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #167.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |   (7004)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7004) gives:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (7005)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6946), (7005) are inconsistent by sub-proof #470.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |   (7006)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (156), (157), (158), (5032), (6788),
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |            (6945), (6952), (6953), (7006), (function-axioms)
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #206.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | |   (7007)  all_56_15 = e1 & op(e0, e0) = e1
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7007) implies:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | |   (7008)  op(e0, e0) = e1
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6944), (7008), (function-axioms) are
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | |   (7009)   ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 148.49/21.11  | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | ALPHA: (7009) implies:
% 148.49/21.11  | | | | | | | | | | | | | | | | | |   (7010)   ~ (all_57_10 = e0)
% 148.49/21.11  | | | | | | | | | | | | | | | | | |   (7011)  op(e3, e3) = all_57_10
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 148.49/21.11  | | | | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (6791), (7011)
% 148.49/21.11  | | | | | | | | | | | | | | | | | |              gives:
% 148.49/21.11  | | | | | | | | | | | | | | | | | |   (7012)  all_57_10 = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | REDUCE: (7010), (7012) imply:
% 148.49/21.11  | | | | | | | | | | | | | | | | | |   (7013)  $false
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | CLOSE: (7013) is inconsistent.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | |   (7014)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 148.49/21.11  | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | BETA: splitting (7014) gives:
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | |   (7015)  all_56_5 = e1 & op(e2, e1) = e1
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | ALPHA: (7015) implies:
% 148.49/21.11  | | | | | | | | | | | | | | |   (7016)  all_56_5 = e1
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | |   (7017)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 148.49/21.11  | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 148.49/21.11  | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.49/21.11  | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.49/21.11  | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.49/21.11  | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 148.49/21.11  | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 148.49/21.11  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.49/21.11  | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 148.49/21.11  | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 148.49/21.11  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.49/21.11  | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.49/21.11  | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.49/21.11  | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 148.49/21.11  | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 148.49/21.11  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 148.49/21.11  | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (6791), (6931), (7017),
% 148.49/21.11  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.11  | | | | | | | | | | | | | | | |            #515.
% 148.49/21.11  | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | |   (7018)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 148.49/21.11  | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 148.49/21.11  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.49/21.11  | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.49/21.11  | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.49/21.11  | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 148.49/21.11  | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 148.49/21.11  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.49/21.11  | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 148.49/21.11  | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 148.49/21.11  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.49/21.11  | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.49/21.11  | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.49/21.11  | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.49/21.11  | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.49/21.11  | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 148.49/21.11  | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | BETA: splitting (7018) gives:
% 148.49/21.11  | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | |   (7019)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 148.49/21.11  | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 148.49/21.11  | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.49/21.11  | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.49/21.11  | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.49/21.11  | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 148.49/21.11  | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 148.49/21.11  | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.49/21.11  | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | ALPHA: (7019) implies:
% 148.49/21.11  | | | | | | | | | | | | | | | | |   (7020)  op(e1, e1) = e1
% 148.49/21.11  | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (7020), (function-axioms) are
% 148.49/21.11  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 148.49/21.11  | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | |   (7021)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 148.49/21.11  | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 148.49/21.11  | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.49/21.11  | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.49/21.11  | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.49/21.11  | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.49/21.11  | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.49/21.11  | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 148.49/21.11  | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | ALPHA: (7021) implies:
% 148.49/21.11  | | | | | | | | | | | | | | | | |   (7022)  op(e0, e0) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 148.49/21.11  | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | |   (7023)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | BETA: splitting (7023) gives:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | |   (7024)  all_56_4 = e0 & op(e3, e1) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (6789), (7024), (function-axioms) are
% 148.49/21.11  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | |   (7025)  all_56_5 = e0 & op(e2, e1) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7016), (7025) are inconsistent by sub-proof
% 148.49/21.11  | | | | | | | | | | | | | | | | | | |            #223.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | |   (7026)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 148.49/21.11  | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | BETA: splitting (7026) gives:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | |   (7027)  all_56_8 = e0 & op(e1, e1) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | ALPHA: (7027) implies:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | |   (7028)  op(e1, e1) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (7028), (function-axioms) are
% 148.49/21.11  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | |   (7029)  all_56_14 = e0 & op(e0, e1) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | ALPHA: (7029) implies:
% 148.49/21.11  | | | | | | | | | | | | | | | | | | |   (7030)  op(e0, e1) = e0
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (156), (367), (7022), (7030),
% 148.49/21.11  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.11  | | | | | | | | | | | | | | | | | | |            #1034.
% 148.49/21.11  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | |   (7031)  all_56_10 = e1 & op(e2, e0) = e1
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 148.49/21.11  | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 148.49/21.11  | | | | | | | | | | | | | | |            (227), (5023), (5025), (6928), (6931), (7031),
% 148.49/21.11  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.11  | | | | | | | | | | | | | | |            #166.
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | |   (7032)  all_16_2 = e0
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | COMBINE_EQS: (327), (7032) imply:
% 148.49/21.11  | | | | | | | | | | | |   (7033)  all_6_2 = e0
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | REDUCE: (356), (7033) imply:
% 148.49/21.11  | | | | | | | | | | | |   (7034)   ~ (all_52_9 = e0)
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | REDUCE: (372), (7033) imply:
% 148.49/21.11  | | | | | | | | | | | |   (7035)   ~ (e3 = e0)
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | REDUCE: (39), (7033) imply:
% 148.49/21.11  | | | | | | | | | | | |   (7036)  op(e2, e2) = e0
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (45), (156), (164), (168), (216),
% 148.49/21.11  | | | | | | | | | | | |            (237), (367), (5032), (6789), (6791), (7034),
% 148.49/21.11  | | | | | | | | | | | |            (7036), (function-axioms) are inconsistent by
% 148.49/21.11  | | | | | | | | | | | |            sub-proof #475.
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | |   (7037)  all_56_1 = e0 & op(e3, e2) = e0
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | ALPHA: (7037) implies:
% 148.49/21.11  | | | | | | | | | | |   (7038)  all_56_1 = e0
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (231), (233),
% 148.49/21.11  | | | | | | | | | | |            (235), (5024), (6791), (7038), (function-axioms)
% 148.49/21.11  | | | | | | | | | | |            are inconsistent by sub-proof #492.
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | |   (7039)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 148.49/21.11  | | | | | | | | | |             & op(e3, e0) = e0)
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | BETA: splitting (7039) gives:
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | |   (7040)  all_56_4 = e0 & op(e3, e1) = e0
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | REF_CLOSE: (168), (6789), (7040), (function-axioms) are
% 148.49/21.11  | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | |   (7041)  all_56_9 = e0 & op(e3, e0) = e0
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | ALPHA: (7041) implies:
% 148.49/21.11  | | | | | | | | | | |   (7042)  all_56_9 = e0
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (231), (233),
% 148.49/21.11  | | | | | | | | | | |            (235), (5024), (6791), (7042), (function-axioms)
% 148.49/21.11  | | | | | | | | | | |            are inconsistent by sub-proof #687.
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | 
% 148.49/21.11  | | | | | | | End of split
% 148.49/21.11  | | | | | | | 
% 148.49/21.11  | | | | | | Case 2:
% 148.49/21.11  | | | | | | | 
% 148.49/21.11  | | | | | | |   (7043)  all_10_2 = e1
% 148.49/21.11  | | | | | | | 
% 148.49/21.11  | | | | | | | REDUCE: (360), (7043) imply:
% 148.49/21.11  | | | | | | |   (7044)   ~ (all_52_7 = e1)
% 148.49/21.11  | | | | | | | 
% 148.49/21.11  | | | | | | | REDUCE: (370), (7043) imply:
% 148.49/21.11  | | | | | | |   (7045)   ~ (all_52_14 = e1)
% 148.49/21.11  | | | | | | | 
% 148.49/21.11  | | | | | | | REDUCE: (45), (7043) imply:
% 148.49/21.11  | | | | | | |   (7046)  op(e0, e0) = e1
% 148.49/21.11  | | | | | | | 
% 148.49/21.11  | | | | | | | BETA: splitting (209) gives:
% 148.49/21.11  | | | | | | | 
% 148.49/21.11  | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | 
% 148.49/21.11  | | | | | | | |   (7047)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 &
% 148.49/21.11  | | | | | | | |             op(e2, e0) = e1)
% 148.49/21.11  | | | | | | | | 
% 148.49/21.11  | | | | | | | | BETA: splitting (7047) gives:
% 148.49/21.11  | | | | | | | | 
% 148.49/21.11  | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | |   (7048)  all_56_9 = e1 & op(e3, e0) = e1
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | ALPHA: (7048) implies:
% 148.49/21.11  | | | | | | | | |   (7049)  all_56_9 = e1
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 148.49/21.11  | | | | | | | | |            (7046), (7049), (function-axioms) are inconsistent
% 148.49/21.11  | | | | | | | | |            by sub-proof #496.
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | |   (7050)  all_56_10 = e1 & op(e2, e0) = e1
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | ALPHA: (7050) implies:
% 148.49/21.11  | | | | | | | | |   (7051)  all_56_10 = e1
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 148.49/21.11  | | | | | | | | |            (7046), (7051), (function-axioms) are inconsistent
% 148.49/21.11  | | | | | | | | |            by sub-proof #445.
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | End of split
% 148.49/21.11  | | | | | | | | 
% 148.49/21.11  | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | 
% 148.49/21.11  | | | | | | | |   (7052)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 &
% 148.49/21.11  | | | | | | | |             op(e0, e0) = e1)
% 148.49/21.11  | | | | | | | | 
% 148.49/21.11  | | | | | | | | BETA: splitting (7052) gives:
% 148.49/21.11  | | | | | | | | 
% 148.49/21.11  | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | |   (7053)  all_56_11 = e1 & op(e1, e0) = e1
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | ALPHA: (7053) implies:
% 148.49/21.11  | | | | | | | | |   (7054)  op(e1, e0) = e1
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | REF_CLOSE: (159), (7045), (7054), (function-axioms) are
% 148.49/21.11  | | | | | | | | |            inconsistent by sub-proof #961.
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | |   (7055)  all_56_15 = e1 & op(e0, e0) = e1
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | ALPHA: (7055) implies:
% 148.49/21.11  | | | | | | | | |   (7056)  all_56_15 = e1
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | BETA: splitting (49) gives:
% 148.49/21.11  | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | |   (7057)   ~ (all_12_2 = e3)
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | REDUCE: (5021), (7057) imply:
% 148.49/21.11  | | | | | | | | | |   (7058)  $false
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | CLOSE: (7058) is inconsistent.
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | |   (7059)  ( ~ (all_12_0 = e0) & op(all_12_1, e1) = all_12_0
% 148.49/21.11  | | | | | | | | | |             & op(e1, e3) = all_12_1 & $i(all_12_0) &
% 148.49/21.11  | | | | | | | | | |             $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e1, e3)
% 148.49/21.11  | | | | | | | | | |             = all_12_1 & $i(all_12_1))
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | BETA: splitting (52) gives:
% 148.49/21.11  | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | |   (7060)   ~ (all_14_2 = e0)
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | BETA: splitting (55) gives:
% 148.49/21.11  | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | |   (7061)   ~ (all_16_2 = e0)
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | REDUCE: (327), (7061) imply:
% 148.49/21.11  | | | | | | | | | | | |   (7062)   ~ (all_6_2 = e0)
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | BETA: splitting (61) gives:
% 148.49/21.11  | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | |   (7063)   ~ (all_20_2 = e1)
% 148.49/21.11  | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | REDUCE: (282), (7063) imply:
% 148.49/21.11  | | | | | | | | | | | | |   (7064)   ~ (all_6_2 = e1)
% 148.49/21.11  | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | BETA: splitting (198) gives:
% 148.49/21.11  | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | |   (7065)  all_54_5 = e3
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | COMBINE_EQS: (267), (7065) imply:
% 148.49/21.11  | | | | | | | | | | | | | |   (7066)  all_6_2 = e3
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | REDUCE: (372), (7066) imply:
% 148.49/21.11  | | | | | | | | | | | | | |   (7067)  $false
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | CLOSE: (7067) is inconsistent.
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | Case 2:
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | |   (7068)   ~ (all_54_5 = e3)
% 148.49/21.11  | | | | | | | | | | | | | |   (7069)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | BETA: splitting (7069) gives:
% 148.49/21.11  | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | Case 1:
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | |   (7070)  all_54_5 = e2
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | COMBINE_EQS: (267), (7070) imply:
% 148.49/21.11  | | | | | | | | | | | | | | |   (7071)  all_6_2 = e2
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | REDUCE: (347), (7071) imply:
% 148.49/21.11  | | | | | | | | | | | | | | |   (7072)   ~ (all_52_1 = e2)
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | REDUCE: (352), (7071) imply:
% 148.49/21.11  | | | | | | | | | | | | | | |   (7073)   ~ (all_52_6 = e2)
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | REDUCE: (354), (7071) imply:
% 148.49/21.11  | | | | | | | | | | | | | | |   (7074)   ~ (all_52_7 = e2)
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | REDUCE: (356), (7071) imply:
% 148.49/21.11  | | | | | | | | | | | | | | |   (7075)   ~ (all_52_9 = e2)
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | REDUCE: (358), (7071) imply:
% 148.49/21.11  | | | | | | | | | | | | | | |   (7076)   ~ (all_52_13 = e2)
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | REDUCE: (372), (7071) imply:
% 148.49/21.11  | | | | | | | | | | | | | | |   (7077)   ~ (e3 = e2)
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.11  | | | | | | | | | | | | | | | REDUCE: (39), (7071) imply:
% 148.49/21.11  | | | | | | | | | | | | | | |   (7078)  op(e2, e2) = e2
% 148.49/21.11  | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 148.49/21.12  | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | Case 1:
% 148.49/21.12  | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | |   (7079)   ~ (all_22_2 = e1)
% 148.49/21.12  | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | REDUCE: (320), (7079) imply:
% 148.49/21.12  | | | | | | | | | | | | | | | |   (7080)   ~ (all_14_2 = e1)
% 148.49/21.12  | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 148.49/21.12  | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.12  | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | |   (7081)   ~ (all_36_2 = e2)
% 148.49/21.12  | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | REDUCE: (304), (7081) imply:
% 148.49/21.12  | | | | | | | | | | | | | | | | |   (7082)   ~ (all_14_2 = e2)
% 148.49/21.12  | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.49/21.12  | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | |   (7083)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.49/21.12  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.49/21.12  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.49/21.12  | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.49/21.12  | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | BETA: splitting (7083) gives:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |   (7084)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (166), (5032), (7046), (7072), (7084),
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |            #436.
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |   (7085)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (7085) gives:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |   (7086)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (5032), (7046), (7086),
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |            #435.
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |   (7087)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7087) gives:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |   (7088)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7088) implies:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |   (7089)  op(e3, e3) = e2
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (7060), (7080), (7082),
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |            (7089), (function-axioms) are inconsistent by
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |            sub-proof #366.
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |   (7090)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7046), (7078), (7090), (function-axioms) are
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #441.
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | End of split
% 148.49/21.12  | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | Case 2:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | |   (7091)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.49/21.12  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.49/21.12  | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.49/21.12  | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.49/21.12  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.49/21.12  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.49/21.12  | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | BETA: splitting (7091) gives:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | 
% 148.49/21.12  | | | | | | | | | | | | | | | | | | Case 1:
% 148.49/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |   (7092)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (7092) gives:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |   (7093)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (5024), (7075), (7093),
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |            #1083.
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |   (7094)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (164), (5032), (7075), (7078), (7094),
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |            #433.
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |   (7095)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | BETA: splitting (7095) gives:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |   (7096)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (7060), (7080), (7082),
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |            (7096), (function-axioms) are inconsistent by
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |            sub-proof #1079.
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |   (7097)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7097) gives:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |   (7098)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7098) implies:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |   (7099)  op(e2, e0) = e2
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7076), (7099), (function-axioms) are
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |   (7100)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7100) gives:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |   (7101)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7101) implies:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |   (7102)  op(e1, e0) = e1
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7045), (7102), (function-axioms) are
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |   (7103)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7103) implies:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |   (7104)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7104) gives:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | |   (7105)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7105) gives:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |   (7106)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7106) implies:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |   (7107)  op(e2, e2) = e3
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7078), (7107), (function-axioms) are
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |   (7108)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7108) gives:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (7109)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7109) implies:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (7110)  op(e0, e3) = e0
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | |   (7111)  op(e1, e3) = all_57_1
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.12  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7112)  all_54_0 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (7112) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7113)  all_14_2 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7113) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7114)  all_14_2 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (336), (7114) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7115)   ~ (all_52_1 = e3)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7116)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (7078), (7115), (7116),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #365.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7117)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7117) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7118)  all_56_5 = e3 & op(e2, e1) = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5025), (7118), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7119)  all_56_10 = e3 & op(e2, e0) = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7119) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7120)  op(e2, e0) = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (158), (7110) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7121)  all_52_3 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1, e3, e1, simplifying with (162), (7111)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7122)  all_57_1 = all_52_2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e0, e2, simplifying with (163), (7120) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7123)  all_52_13 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (7121) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7124)   ~ (all_52_1 = e0)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (7121) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7125)   ~ (all_52_2 = e0)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7126)  all_54_4 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7115), (7126) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #843.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7127)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7127) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7128)  all_54_4 = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7072), (7128) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1175.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7129)  all_54_4 = e1 | all_54_4 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7129) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7130)  all_54_4 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7130) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7131)  all_52_1 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7131) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7132)  all_52_1 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (7132) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7133)   ~ (all_52_2 = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7133) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7134)   ~ (all_52_2 = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7132) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7135)   ~ (all_52_9 = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7135) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7136)   ~ (all_52_9 = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7137)  all_54_8 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (5022), (7137) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #394.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7138)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7138) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7139)  all_54_8 = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (7139) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7140)  all_52_2 = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7140) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7141)  all_52_2 = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (7141) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7142)  op(e1, e3) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7143)  all_54_6 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (5025), (7143) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #650.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7144)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7144) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7145)  all_54_6 = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (7075), (7145) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #379.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7146)  all_54_6 = e1 | all_54_6 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7146) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7147)  all_54_6 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (7136), (7147) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #378.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7148)  all_54_6 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (7148) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7149)  all_52_9 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7149) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7150)  all_52_9 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (7150) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7151)  op(e2, e1) = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5018), (7059), (7142), (7151), (function-axioms)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #164.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7152)  all_54_8 = e1 | all_54_8 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (7125), (7134), (7152) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #461.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7153)  all_54_4 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7124), (7153) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #796.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7154)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (7060), (7080), (7082), (7154) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7155)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7155) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7156)  op(e3, e3) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (7060), (7080), (7082),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |            (7156), (function-axioms) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #366.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |   (7157)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7157) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |   (7158)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7158) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |   (7159)  op(e1, e1) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7159), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |   (7160)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7160) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7161)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_6)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7161) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7162)  op(e3, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (7060), (7080), (7082),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |            (7162), (function-axioms) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #728.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7163)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7163) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7164)  op(e2, e2) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7078), (7164), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | |   (7165)  all_36_2 = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | COMBINE_EQS: (304), (7165) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | |   (7166)  all_14_2 = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | REDUCE: (51), (7166) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | |   (7167)  op(e3, e3) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | |   (7168)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | BETA: splitting (7168) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | |   (7169)  all_56_4 = e2 & op(e3, e1) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | ALPHA: (7169) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | |   (7170)  all_56_4 = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | |   (7171)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7171) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | |   (7172)  all_56_6 = e2 & op(e1, e3) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7172) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | |   (7173)  all_56_6 = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | |   (7174)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7174) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |   (7175)  all_56_6 = e1 & op(e1, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7175) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |   (7176)  all_56_6 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7173), (7176) are inconsistent by sub-proof
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |            #1172.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |   (7177)  all_56_7 = e1 & op(e1, e2) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7177) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |   (7178)  all_56_7 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | |   (7179)  op(e1, e2) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |   (7180)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7180) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7181)  all_56_0 = e1 & op(e3, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7181) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7182)  op(e3, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7167), (7182), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7183)  all_56_2 = e1 & op(e2, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7183) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7184)  all_56_2 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7185)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7185) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7186)  all_56_0 = e1 & op(e3, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7186) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7187)  op(e3, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7167), (7187), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7188)  all_56_1 = e1 & op(e3, e2) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7188) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7189)  all_56_1 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7190)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7190) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7191)  all_56_0 = e0 & op(e3, e3) = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7191) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7192)  op(e3, e3) = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7167), (7192), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7193)  all_56_2 = e0 & op(e2, e3) = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7184), (7193) are inconsistent by sub-proof
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #996.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7194)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7194) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7195)  all_56_6 = e0 & op(e1, e3) = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7173), (7195) are inconsistent by sub-proof
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1054.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7196)  all_56_12 = e0 & op(e0, e3) = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7196) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7197)  all_56_12 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7198)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7078), (7184), (7198),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #163.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7199)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7199) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7200)  all_56_5 = e3 & op(e2, e1) = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5025), (7200), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7201)  all_56_10 = e3 & op(e2, e0) = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7201) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7202)  all_56_10 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7203)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7203) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7204)  all_56_12 = e3 & op(e0, e3) = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7204) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7205)  all_56_12 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7197), (7205) imply:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7206)  e3 = e0
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (223), (228),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (5025), (7078), (7173), (7202), (7205),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7206), (function-axioms) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #161.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7207)  all_56_13 = e3 & op(e0, e2) = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7207) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7208)  all_56_13 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (224), (7078), (7178), (7189),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7208), (function-axioms) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #160.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7209)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (216), (217), (5032),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7046), (7170), (7209), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #159.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7210)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (229), (235),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5024), (7167), (7170), (7210), (function-axioms)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #158.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |   (7211)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7211) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7212)  all_56_6 = e1 & op(e1, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7212) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7213)  op(e1, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (161), (162), (7179), (7213),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |            #911.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7214)  all_56_12 = e1 & op(e0, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7214) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | |   (7215)  all_56_12 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7216)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7216) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7217)  all_56_0 = e1 & op(e3, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7217) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7218)  op(e3, e3) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7167), (7218), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7219)  all_56_1 = e1 & op(e3, e2) = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7219) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7220)  all_56_1 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7221)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7221) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7222)  all_56_12 = e3 & op(e0, e3) = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7222) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7223)  all_56_12 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7215), (7223) are inconsistent by sub-proof
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1056.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7224)  all_56_13 = e3 & op(e0, e2) = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7224) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7225)  all_56_13 = e3
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (224), (7078), (7178), (7220),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7225), (function-axioms) are inconsistent by
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #160.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7226)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (216), (217), (5032),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7046), (7170), (7226), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #159.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7227)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (229), (235),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            (5024), (7167), (7170), (7227), (function-axioms)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #158.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | |   (7228)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (5032), (7045), (7228),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | |            #523.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | |   (7229)  all_56_7 = e2 & op(e1, e2) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7229) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | |   (7230)  op(e1, e2) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (7073), (7230), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1171.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | |   (7231)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7231) gives:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | |   (7232)  all_56_8 = e2 & op(e1, e1) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7232) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | |   (7233)  op(e1, e1) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7233), (function-axioms) are
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | |   (7234)  all_56_11 = e2 & op(e1, e0) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7234) implies:
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | |   (7235)  op(e1, e0) = e2
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (124), (134), (139),
% 148.58/21.13  | | | | | | | | | | | | | | | | | | | | |            (156), (158), (163), (164), (166), (168), (169),
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            (190), (207), (212), (213), (214), (224), (225),
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            (227), (228), (230), (234), (237), (238), (247),
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            (5024), (5031), (5032), (7044), (7046), (7072),
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            (7075), (7076), (7167), (7235), (function-axioms)
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #425.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |   (7236)  all_56_5 = e2 & op(e2, e1) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | ALPHA: (7236) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |   (7237)  op(e2, e1) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7075), (7237), (function-axioms) are
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | |   (7238)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 148.58/21.14  | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 148.58/21.14  | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | BETA: splitting (7238) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |   (7239)  all_56_8 = e2 & op(e1, e1) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | ALPHA: (7239) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |   (7240)  op(e1, e1) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7240), (function-axioms) are
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |   (7241)  all_56_14 = e2 & op(e0, e1) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | ALPHA: (7241) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |   (7242)  all_56_14 = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |   (7243)  op(e0, e1) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |   (7244)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7244) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |   (7245)  all_56_6 = e2 & op(e1, e3) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7245) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |   (7246)  all_56_6 = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | |   (7247)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7247) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7248)  all_56_9 = e2 & op(e3, e0) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7248) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7249)  all_56_9 = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (217), (229),
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |            (231), (235), (5031), (5032), (7167), (7242),
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |            (7243), (7249), (function-axioms) are inconsistent
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #215.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7250)  all_56_10 = e2 & op(e2, e0) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7250) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7251)  op(e2, e0) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7076), (7251), (function-axioms) are
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | |   (7252)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7252) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7253)  all_56_11 = e2 & op(e1, e0) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7253) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7254)  all_56_11 = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |            (7246), (7254) are inconsistent by sub-proof #281.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7255)  all_56_15 = e2 & op(e0, e0) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7255) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7256)  op(e0, e0) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7046), (7256), (function-axioms) are
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #978.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |   (7257)  all_56_7 = e2 & op(e1, e2) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7257) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |   (7258)  op(e1, e2) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (7073), (7258), (function-axioms) are
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1171.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |   (7259)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7259) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |   (7260)  all_56_8 = e2 & op(e1, e1) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7260) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |   (7261)  op(e1, e1) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7261), (function-axioms) are
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |   (7262)  all_56_11 = e2 & op(e1, e0) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7262) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |   (7263)  op(e1, e0) = e2
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (124), (134), (139),
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            (156), (158), (163), (164), (166), (168), (169),
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            (190), (237), (238), (247), (5024), (5032),
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            (7044), (7046), (7072), (7075), (7076), (7167),
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            (7243), (7263), (function-axioms) are inconsistent
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #428.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | |   (7264)  all_22_2 = e1
% 148.58/21.14  | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | COMBINE_EQS: (320), (7264) imply:
% 148.58/21.14  | | | | | | | | | | | | | | | |   (7265)  all_14_2 = e1
% 148.58/21.14  | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | SIMP: (7265) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | |   (7266)  all_14_2 = e1
% 148.58/21.14  | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | REDUCE: (340), (7266) imply:
% 148.58/21.14  | | | | | | | | | | | | | | | |   (7267)   ~ (all_52_3 = e1)
% 148.58/21.14  | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | REDUCE: (51), (7266) imply:
% 148.58/21.14  | | | | | | | | | | | | | | | |   (7268)  op(e3, e3) = e1
% 148.58/21.14  | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | |   (7269)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 148.58/21.14  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.58/21.14  | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | BETA: splitting (7269) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | |   (7270)  all_56_1 = e1 & op(e3, e2) = e1
% 148.58/21.14  | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | ALPHA: (7270) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | |   (7271)  all_56_1 = e1
% 148.58/21.14  | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |   (7272)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (7272) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |   (7273)  all_56_1 = e3 & op(e3, e2) = e3
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | ALPHA: (7273) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |   (7274)  all_56_1 = e3
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7271), (7274) are inconsistent by sub-proof
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |            #1069.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |   (7275)  all_56_3 = e3 & op(e2, e2) = e3
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | ALPHA: (7275) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |   (7276)  op(e2, e2) = e3
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7078), (7276), (function-axioms) are
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | End of split
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |   (7277)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 148.58/21.14  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (7277) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |   (7278)  all_56_7 = e3 & op(e1, e2) = e3
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5023), (7278), (function-axioms) are
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |   (7279)  all_56_13 = e3 & op(e0, e2) = e3
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | ALPHA: (7279) implies:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | |   (7280)  all_56_13 = e3
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |   (7281)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7281) gives:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.58/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |   (7282)  all_56_6 = e1 & op(e1, e3) = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7282) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |   (7283)  all_56_6 = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |   (7284)  op(e1, e3) = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7285)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (7073), (7283), (7285),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |            #1170.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7286)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7286) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | |   (7287)  all_56_8 = e2 & op(e1, e1) = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7287) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | |   (7288)  op(e1, e1) = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7288), (function-axioms) are
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | |   (7289)  all_56_11 = e2 & op(e1, e0) = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7289) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | |   (7290)  all_56_11 = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (7291)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (7072), (7268), (7291),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | |            #938.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | |   (7292)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7292) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7293)  all_56_6 = e2 & op(e1, e3) = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7293) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7294)  all_56_6 = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | |            (7290), (7294) are inconsistent by sub-proof #281.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7295)  all_56_12 = e2 & op(e0, e3) = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7295) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7296)  all_56_12 = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7297)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (162), (228), (7268), (7284),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7296), (7297), (function-axioms) are inconsistent
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #157.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7298)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7298) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7299)  all_56_6 = e3 & op(e1, e3) = e3
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7299) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7300)  all_56_6 = e3
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7290), (7300) are inconsistent by sub-proof #608.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7301)  all_56_12 = e3 & op(e0, e3) = e3
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7301) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7302)  all_56_12 = e3
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7296), (7302) imply:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7303)  e3 = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7280), (7303) imply:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7304)  all_56_13 = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7078), (7304), (function-axioms) are inconsistent
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1104.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |   (7305)  all_56_7 = e1 & op(e1, e2) = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7305) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |   (7306)  all_56_7 = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (224), (7078), (7271), (7280),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |            (7306), (function-axioms) are inconsistent by
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #160.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |   (7307)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (5032), (7045), (7307),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |            #523.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | |   (7308)  all_56_3 = e1 & op(e2, e2) = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | ALPHA: (7308) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | |   (7309)  op(e2, e2) = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7078), (7309), (function-axioms) are
% 148.66/21.14  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | |   (7310)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 148.66/21.14  | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.66/21.14  | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | BETA: splitting (7310) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | |   (7311)  all_56_7 = e1 & op(e1, e2) = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | ALPHA: (7311) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | |   (7312)  all_56_7 = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | |   (7313)  op(e1, e2) = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | |   (7314)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | BETA: splitting (7314) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |   (7315)  all_56_4 = e1 & op(e3, e1) = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | ALPHA: (7315) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |   (7316)  all_56_4 = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (205),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |            (207), (208), (210), (211), (212), (213), (214),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (220), (221), (223), (224),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (233), (234), (235),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |            (5023), (5025), (5031), (5032), (7046), (7056),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |            (7073), (7075), (7078), (7268), (7316),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |            #151.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |   (7317)  all_56_5 = e1 & op(e2, e1) = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | ALPHA: (7317) implies:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |   (7318)  all_56_5 = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | |   (7319)  op(e2, e1) = e1
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |   (7320)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7320) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |   (7321)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (142), (161), (162), (166), (7046), (7072),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |            (7313), (7321), (function-axioms) are inconsistent
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #419.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |   (7322)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7322) gives:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7323)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (5032), (7046), (7323),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |            #435.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |   (7324)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7046), (7078), (7268), (7324),
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | |            #418.
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.14  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |   (7325)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7325) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |   (7326)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7326) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |   (7327)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (5024), (7075), (7327),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |            #1083.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |   (7328)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (164), (5032), (7075), (7078), (7328),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |            #433.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |   (7329)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7329) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |   (7330)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7268), (7330), (function-axioms) are
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |   (7331)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7331) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |   (7332)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7332) implies:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |   (7333)  op(e2, e0) = e2
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7076), (7333), (function-axioms) are
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |   (7334)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7334) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (7335)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7335) implies:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (7336)  op(e1, e0) = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7045), (7336), (function-axioms) are
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (7337)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7337) implies:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (7338)  op(e0, e0) = all_57_15
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (7339)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (45), (117), (124),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (127), (134), (138), (139), (156), (157), (158),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (161), (164), (166), (168), (169), (189),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (205), (208), (212), (213), (214), (216),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (220), (221), (222), (223), (224),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (230), (232), (233), (235),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (246), (247), (370), (5023), (5024),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (5025), (5026), (5031), (5032), (7046), (7072),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (7074), (7075), (7267), (7268), (7312), (7313),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (7318), (7319), (7338), (7339), (function-axioms)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #142.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | |   (7340)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | BETA: splitting (7340) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |   (7341)  all_56_8 = e1 & op(e1, e1) = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | ALPHA: (7341) implies:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |   (7342)  op(e1, e1) = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (7342), (function-axioms) are
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |   (7343)  all_56_14 = e1 & op(e0, e1) = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | ALPHA: (7343) implies:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |   (7344)  all_56_14 = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (205),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |            (207), (208), (210), (211), (212), (213), (214),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (220), (221), (223), (224),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (234), (235), (5025), (5031),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |            (5032), (7046), (7056), (7073), (7075), (7078),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |            (7268), (7344), (function-axioms) are inconsistent
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |            by sub-proof #141.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.15  | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | |   (7345)  all_56_13 = e1 & op(e0, e2) = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | ALPHA: (7345) implies:
% 148.66/21.15  | | | | | | | | | | | | | | | | | |   (7346)  all_56_13 = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | |   (7347)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 148.66/21.15  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | BETA: splitting (7347) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |   (7348)  all_56_1 = e3 & op(e3, e2) = e3
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | ALPHA: (7348) implies:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | |   (7349)  all_56_1 = e3
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |   (7350)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7350) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |   (7351)  all_56_4 = e1 & op(e3, e1) = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7351) implies:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |   (7352)  all_56_4 = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (205),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (210), (211), (212), (213), (214),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (220), (221), (223), (224),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (229), (233), (234), (235),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |            (5023), (5025), (5031), (5032), (7046), (7056),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |            (7073), (7075), (7078), (7268), (7352),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |            #151.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |   (7353)  all_56_5 = e1 & op(e2, e1) = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7353) implies:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |   (7354)  all_56_5 = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | |   (7355)  op(e2, e1) = e1
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |   (7356)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7356) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |   (7357)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (166), (5032), (7046), (7072), (7357),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |            #436.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |   (7358)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7358) gives:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (7359)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (5032), (7046), (7359),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            #435.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |   (7360)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7046), (7078), (7268), (7360),
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | |            #418.
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.15  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |   (7361)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7361) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |   (7362)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7362) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (7363)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (5024), (7075), (7363),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            #1083.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (7364)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (164), (5032), (7075), (7078), (7364),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            #433.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |   (7365)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7365) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (7366)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7268), (7366), (function-axioms) are
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |   (7367)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7367) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7368)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7368) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7369)  op(e2, e0) = e2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7076), (7369), (function-axioms) are
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7370)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7370) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7371)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7371) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7372)  op(e1, e0) = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7045), (7372), (function-axioms) are
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7373)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7373) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7374)  op(e0, e0) = all_57_15
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7375)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7376)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7376) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7377)  all_56_6 = e1 & op(e1, e3) = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7377) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7378)  all_56_6 = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7379)  op(e1, e3) = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7380)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (161), (7073), (7378), (7380),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1170.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7381)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7381) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7382)  all_56_8 = e2 & op(e1, e1) = e2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7382) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7383)  op(e1, e1) = e2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7383), (function-axioms) are
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7384)  all_56_11 = e2 & op(e1, e0) = e2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7384) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7385)  all_56_11 = e2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7386)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (7072), (7268), (7386),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #938.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7387)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7387) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7388)  all_56_6 = e2 & op(e1, e3) = e2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7388) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7389)  all_56_6 = e2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7385), (7389) are inconsistent by sub-proof #281.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7390)  all_56_12 = e2 & op(e0, e3) = e2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7390) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7391)  all_56_12 = e2
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7392)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7392) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7393)  all_56_6 = e0 & op(e1, e3) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7393) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7394)  op(e1, e3) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (7379), (7394), (function-axioms) are
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7395)  all_56_7 = e0 & op(e1, e2) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7395) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7396)  all_56_7 = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7397)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (162), (228), (7268), (7379),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7391), (7397), (function-axioms) are inconsistent
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #157.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7398)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7398) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7399)  all_56_6 = e3 & op(e1, e3) = e3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7399) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7400)  all_56_6 = e3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (213), (5031), (7385), (7396),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7400) are inconsistent by sub-proof #609.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7401)  all_56_12 = e3 & op(e0, e3) = e3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (224), (225),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (5023), (7078), (7349), (7391), (7401),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #178.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7402)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7402) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7403)  all_56_8 = e0 & op(e1, e1) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7403) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7404)  op(e1, e1) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (7404), (function-axioms) are
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7405)  all_56_11 = e0 & op(e1, e0) = e0
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7385), (7405) are inconsistent by sub-proof
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #322.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7406)  all_56_7 = e1 & op(e1, e2) = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7406) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7407)  all_56_7 = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7408)  op(e1, e2) = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (45), (117), (124),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (127), (134), (138), (139), (156), (157), (158),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (161), (164), (166), (168), (169), (189),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (205), (208), (212), (213), (214), (216),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (220), (221), (222), (223), (224),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (230), (232), (233), (235),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (246), (247), (370), (5023), (5024),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5025), (5026), (5031), (5032), (7046), (7072),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7074), (7075), (7267), (7268), (7354), (7355),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7374), (7375), (7407), (7408), (function-axioms)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #142.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7409)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (5032), (7045), (7409),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #523.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | |   (7410)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7410) gives:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | |   (7411)  all_56_8 = e1 & op(e1, e1) = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7411) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | |   (7412)  op(e1, e1) = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (7412), (function-axioms) are
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | |   (7413)  all_56_14 = e1 & op(e0, e1) = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7413) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | |   (7414)  all_56_14 = e1
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (205),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | |            (207), (208), (210), (211), (212), (213), (214),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | |            (216), (217), (218), (220), (221), (223), (224),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | |            (225), (227), (228), (234), (235), (5025), (5031),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | |            (5032), (7046), (7056), (7073), (7075), (7078),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | |            (7268), (7414), (function-axioms) are inconsistent
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #141.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | |   (7415)  all_56_3 = e3 & op(e2, e2) = e3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | ALPHA: (7415) implies:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | |   (7416)  op(e2, e2) = e3
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7078), (7416), (function-axioms) are
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | |   (7417)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 148.66/21.16  | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (161), (5023), (7346), (7417),
% 148.66/21.16  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.16  | | | | | | | | | | | | | | | | | | |            #257.
% 148.66/21.16  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | | 
% 148.66/21.16  | | | | | | | | | | | | | | | End of split
% 148.66/21.16  | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | Case 2:
% 148.66/21.17  | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | |   (7418)  all_54_5 = e1 | all_54_5 = e0
% 148.66/21.17  | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | REF_CLOSE: (267), (7062), (7064), (7418) are inconsistent by
% 148.66/21.17  | | | | | | | | | | | | | | |            sub-proof #866.
% 148.66/21.17  | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | End of split
% 148.66/21.17  | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | End of split
% 148.66/21.17  | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | Case 2:
% 148.66/21.17  | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | |   (7419)  all_20_2 = e1
% 148.66/21.17  | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | COMBINE_EQS: (282), (7419) imply:
% 148.66/21.17  | | | | | | | | | | | | |   (7420)  all_6_2 = e1
% 148.66/21.17  | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | REDUCE: (352), (7420) imply:
% 148.66/21.17  | | | | | | | | | | | | |   (7421)   ~ (all_52_6 = e1)
% 148.66/21.17  | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | REDUCE: (356), (7420) imply:
% 148.66/21.17  | | | | | | | | | | | | |   (7422)   ~ (all_52_9 = e1)
% 148.66/21.17  | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | REDUCE: (372), (7420) imply:
% 148.66/21.17  | | | | | | | | | | | | |   (7423)   ~ (e3 = e1)
% 148.66/21.17  | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | REDUCE: (39), (7420) imply:
% 148.66/21.17  | | | | | | | | | | | | |   (7424)  op(e2, e2) = e1
% 148.66/21.17  | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | BETA: splitting (213) gives:
% 148.66/21.17  | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | |   (7425)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 148.66/21.17  | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 148.66/21.17  | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | BETA: splitting (7425) gives:
% 148.66/21.17  | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | |   (7426)  all_56_6 = e1 & op(e1, e3) = e1
% 148.66/21.17  | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | ALPHA: (7426) implies:
% 148.66/21.17  | | | | | | | | | | | | | | |   (7427)  all_56_6 = e1
% 148.66/21.17  | | | | | | | | | | | | | | |   (7428)  op(e1, e3) = e1
% 148.66/21.17  | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | |   (7429)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 148.66/21.17  | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 148.66/21.17  | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.66/21.17  | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.66/21.17  | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.66/21.17  | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 148.66/21.17  | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 148.66/21.17  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.66/21.17  | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 148.66/21.17  | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 148.66/21.17  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.66/21.17  | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.66/21.17  | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.66/21.17  | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 148.66/21.17  | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 148.66/21.17  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 148.66/21.17  | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | BETA: splitting (7429) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | |   (7430)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 148.66/21.17  | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 148.66/21.17  | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.66/21.17  | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.66/21.17  | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.66/21.17  | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 148.66/21.17  | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 148.66/21.17  | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.66/21.17  | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | ALPHA: (7430) implies:
% 148.66/21.17  | | | | | | | | | | | | | | | | |   (7431)  op(e3, e3) = e3
% 148.66/21.17  | | | | | | | | | | | | | | | | |   (7432)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 148.66/21.17  | | | | | | | | | | | | | | | | |               = e3) & op(e0, e0) = all_57_15 &
% 148.66/21.17  | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 148.66/21.17  | | | | | | | | | | | | | | | | |   (7433)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 148.66/21.17  | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = all_57_14 &
% 148.66/21.17  | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.66/21.17  | | | | | | | | | | | | | | | | |   (7434)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 148.66/21.17  | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = all_57_12 &
% 148.66/21.17  | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 148.66/21.17  | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | |   (7435)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | BETA: splitting (7435) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | |   (7436)  all_56_2 = e1 & op(e2, e3) = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | ALPHA: (7436) implies:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | |   (7437)  all_56_2 = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | |   (7438)  op(e2, e3) = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | |            (227), (5023), (5025), (7421), (7424), (7437),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | |            (7438), (function-axioms) are inconsistent by
% 148.66/21.17  | | | | | | | | | | | | | | | | | | |            sub-proof #172.
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | |   (7439)  all_56_3 = e1 & op(e2, e2) = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | ALPHA: (7439) implies:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | |   (7440)  all_56_3 = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |   (7441)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (168), (5024), (5032), (7046), (7431),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |            (7432), (7433), (7434), (7441), (function-axioms)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #140.
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |   (7442)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7442) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |   (7443)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (162), (164),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |            (168), (206), (209), (212), (214), (216), (217),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |            (218), (220), (222), (223), (227), (228), (229),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (237), (5023), (5024),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |            (5025), (5031), (5032), (7424), (7427), (7428),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |            (7440), (7443), (function-axioms) are inconsistent
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |            by sub-proof #138.
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |   (7444)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7444) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |   (7445)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7431), (7445), (function-axioms) are
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |   (7446)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7446) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |   (7447)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7447) implies:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |   (7448)  op(e1, e1) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (7448), (function-axioms) are
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |   (7449)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7449) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |   (7450)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7450) implies:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |   (7451)  op(e1, e0) = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7045), (7451), (function-axioms) are
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |   (7452)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7452) implies:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |   (7453)  op(e0, e0) = all_57_15
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |   (7454)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7454) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (7455)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7431), (7433), (7434), (7455),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |            #406.
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (7456)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7456) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7457)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7457) implies:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7458)  op(e1, e1) = e2
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7458), (function-axioms) are
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7459)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7459) gives:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7460)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_6)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7460) implies:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7461)  op(e3, e3) = e1
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (162), (164),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (206), (209), (212), (214), (216), (217), (218),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (222), (223), (227), (228), (229), (232),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (237), (5023), (5025), (5031),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5032), (7424), (7427), (7428), (7440), (7461),
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #139.
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7462)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7462) implies:
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7463)   ~ (all_57_15 = e1)
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7046), (7453), (7463), (function-axioms) are
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #940.
% 148.66/21.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | |   (7464)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | BETA: splitting (7464) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | |   (7465)  all_56_5 = e1 & op(e2, e1) = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | ALPHA: (7465) implies:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | |   (7466)  op(e2, e1) = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | |   (7467)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7467) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | |   (7468)  all_56_1 = e1 & op(e3, e2) = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7468) implies:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | |   (7469)  all_56_1 = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (226), (227),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | |            (5023), (5025), (7424), (7469), (function-axioms)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #262.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | |   (7470)  all_56_3 = e1 & op(e2, e2) = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7470) implies:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | |   (7471)  all_56_3 = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |   (7472)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (168), (5024), (5032), (7046), (7431),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |            (7432), (7433), (7434), (7472), (function-axioms)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #140.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |   (7473)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7473) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |   (7474)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (162), (164),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |            (168), (206), (209), (212), (214), (216), (217),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |            (218), (220), (222), (223), (227), (228), (229),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (237), (5023), (5024),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |            (5025), (5031), (5032), (7424), (7427), (7428),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |            (7471), (7474), (function-axioms) are inconsistent
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #138.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |   (7475)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7475) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |   (7476)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7431), (7476), (function-axioms) are
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |   (7477)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7477) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (7478)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7478) implies:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (7479)  op(e1, e1) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (7479), (function-axioms) are
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |   (7480)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7480) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7481)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7481) implies:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7482)  op(e1, e0) = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7045), (7482), (function-axioms) are
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7483)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7483) implies:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7484)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7484) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7485)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7431), (7433), (7434), (7485),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #406.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7486)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7486) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7487)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7487) implies:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7488)  op(e1, e1) = e2
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7488), (function-axioms) are
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7489)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7489) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7490)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_6)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7490) implies:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7491)  op(e3, e3) = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (162), (164),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (206), (209), (212), (214), (216), (217), (218),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (222), (223), (227), (228), (229), (232),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (235), (237), (5023), (5025), (5031),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (5032), (7424), (7427), (7428), (7471), (7491),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #139.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7492)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_7)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7492) implies:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7493)  op(e2, e1) = all_57_7
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_7, e1, e2, simplifying with (164), (7493)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7494)  all_57_7 = all_52_9
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_57_7,
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (7466), (7493) gives:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7495)  all_57_7 = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7494), (7495) imply:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7496)  all_52_9 = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7422), (7496) imply:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7497)  $false
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7497) is inconsistent.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | |   (7498)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (226), (227),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | |            (5023), (5025), (7421), (7424), (7498),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | |            #173.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | |   (7499)  all_56_10 = e1 & op(e2, e0) = e1
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (225), (226),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | |            (227), (5023), (5025), (7421), (7424), (7499),
% 148.66/21.18  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.18  | | | | | | | | | | | | | | | | | | |            #166.
% 148.66/21.18  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | | End of split
% 148.66/21.18  | | | | | | | | | | | | | | | | | 
% 148.66/21.18  | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.18  | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | |   (7500)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 148.66/21.19  | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 148.66/21.19  | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.66/21.19  | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.66/21.19  | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.66/21.19  | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 148.66/21.19  | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.66/21.19  | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | ALPHA: (7500) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | |   (7501)  op(e2, e2) = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7424), (7501), (function-axioms) are
% 148.66/21.19  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 148.66/21.19  | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | |   (7502)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 148.66/21.19  | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.66/21.19  | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.66/21.19  | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.19  | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 148.66/21.19  | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 148.66/21.19  | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.66/21.19  | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 148.66/21.19  | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 148.66/21.19  | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.66/21.19  | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.66/21.19  | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.66/21.19  | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.66/21.19  | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.66/21.19  | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 148.66/21.19  | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5032), (7046), (7502),
% 148.66/21.19  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.19  | | | | | | | | | | | | | | | |            #429.
% 148.66/21.19  | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | |   (7503)  all_56_7 = e1 & op(e1, e2) = e1
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | ALPHA: (7503) implies:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7504)  op(e1, e2) = e1
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | REF_CLOSE: (161), (7421), (7504), (function-axioms) are
% 148.66/21.19  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | |   (7505)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 148.66/21.19  | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 148.66/21.19  | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (5032), (7045), (7505),
% 148.66/21.19  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.19  | | | | | | | | | | | | | |            #523.
% 148.66/21.19  | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | |   (7506)  all_16_2 = e0
% 148.66/21.19  | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | COMBINE_EQS: (327), (7506) imply:
% 148.66/21.19  | | | | | | | | | | | |   (7507)  all_6_2 = e0
% 148.66/21.19  | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | REDUCE: (347), (7507) imply:
% 148.66/21.19  | | | | | | | | | | | |   (7508)   ~ (all_52_1 = e0)
% 148.66/21.19  | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | REDUCE: (352), (7507) imply:
% 148.66/21.19  | | | | | | | | | | | |   (7509)   ~ (all_52_6 = e0)
% 148.66/21.19  | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | REDUCE: (39), (7507) imply:
% 148.66/21.19  | | | | | | | | | | | |   (7510)  op(e2, e2) = e0
% 148.66/21.19  | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | BETA: splitting (237) gives:
% 148.66/21.19  | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | |   (7511)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 148.66/21.19  | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 148.66/21.19  | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.66/21.19  | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.66/21.19  | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.66/21.19  | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 148.66/21.19  | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 148.66/21.19  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.66/21.19  | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 148.66/21.19  | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 148.66/21.19  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.66/21.19  | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.66/21.19  | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.66/21.19  | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 148.66/21.19  | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 148.66/21.19  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 148.66/21.19  | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | BETA: splitting (7511) gives:
% 148.66/21.19  | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | |   (7512)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 148.66/21.19  | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 148.66/21.19  | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.66/21.19  | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.66/21.19  | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.66/21.19  | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 148.66/21.19  | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 148.66/21.19  | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.66/21.19  | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | ALPHA: (7512) implies:
% 148.66/21.19  | | | | | | | | | | | | | |   (7513)  op(e3, e3) = e3
% 148.66/21.19  | | | | | | | | | | | | | |   (7514)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 148.66/21.19  | | | | | | | | | | | | | |               = e3) & op(e0, e0) = all_57_15 &
% 148.66/21.19  | | | | | | | | | | | | | |             $i(all_57_15))
% 148.66/21.19  | | | | | | | | | | | | | |   (7515)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 148.66/21.19  | | | | | | | | | | | | | |               = e3) & op(e1, e1) = all_57_14 &
% 148.66/21.19  | | | | | | | | | | | | | |             $i(all_57_14))
% 148.66/21.19  | | | | | | | | | | | | | |   (7516)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 148.66/21.19  | | | | | | | | | | | | | |               = e3) & op(e2, e2) = all_57_12 &
% 148.66/21.19  | | | | | | | | | | | | | |             $i(all_57_12))
% 148.66/21.19  | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | BETA: splitting (7515) gives:
% 148.66/21.19  | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | |   (7517)  all_57_1 = e1 & op(e1, e3) = e1
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | ALPHA: (7517) implies:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7518)  op(e1, e3) = e1
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 148.66/21.19  | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (7518) gives:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7519)  all_52_2 = e1
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e3,
% 148.66/21.19  | | | | | | | | | | | | | | |              e3, e3, simplifying with (51), (7513) gives:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7520)  all_14_2 = e3
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | REDUCE: (148), (7519) imply:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7521)   ~ (all_52_1 = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | REDUCE: (336), (7520) imply:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7522)   ~ (all_52_1 = e3)
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | REDUCE: (143), (7519) imply:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7523)   ~ (all_52_3 = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | SIMP: (7523) implies:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7524)   ~ (all_52_3 = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | REDUCE: (142), (7519) imply:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7525)   ~ (all_52_6 = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | SIMP: (7525) implies:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7526)   ~ (all_52_6 = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | REDUCE: (140), (7519) imply:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7527)   ~ (all_52_14 = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | REDUCE: (5022), (7519) imply:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7528)   ~ (e3 = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | REDUCE: (340), (7520) imply:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7529)   ~ (all_52_3 = e3)
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | REDUCE: (342), (7520) imply:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7530)   ~ (all_52_4 = e3)
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | REDUCE: (346), (7520) imply:
% 148.66/21.19  | | | | | | | | | | | | | | |   (7531)   ~ (all_52_12 = e3)
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | |   (7532)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 148.66/21.19  | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.66/21.19  | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (166), (7510), (7522), (7532),
% 148.66/21.19  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.19  | | | | | | | | | | | | | | | |            #690.
% 148.66/21.19  | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | |   (7533)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 148.66/21.19  | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 148.66/21.19  | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | BETA: splitting (7533) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | |   (7534)  all_56_5 = e3 & op(e2, e1) = e3
% 148.66/21.19  | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5025), (7534), (function-axioms) are
% 148.66/21.19  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 148.66/21.19  | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | |   (7535)  all_56_10 = e3 & op(e2, e0) = e3
% 148.66/21.19  | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | ALPHA: (7535) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | |   (7536)  op(e2, e0) = e3
% 148.66/21.19  | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | |   (7537)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | BETA: splitting (7537) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | |   (7538)  all_56_1 = e1 & op(e3, e2) = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | ALPHA: (7538) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | |   (7539)  all_56_1 = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | |   (7540)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (7510), (7530), (7540),
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | |            #596.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | |   (7541)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7541) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | |   (7542)  all_56_7 = e3 & op(e1, e2) = e3
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (5023), (7542), (function-axioms) are
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | |   (7543)  all_56_13 = e3 & op(e0, e2) = e3
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7543) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | |   (7544)  all_56_13 = e3
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | |   (7545)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e0)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7545) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | |   (7546)  all_56_6 = e0 & op(e1, e3) = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7546) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | |   (7547)  op(e1, e3) = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (7518), (7547), (function-axioms) are
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | |   (7548)  all_56_7 = e0 & op(e1, e2) = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7548) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | |   (7549)  all_56_7 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | |   (7550)  all_54_9 = e3
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (5023), (7550) are inconsistent by
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #186.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | |   (7551)   ~ (all_54_9 = e3)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | |   (7552)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7552) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (7553)  all_54_9 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (7553) imply:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (7554)  all_52_6 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7554) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (7555)  all_52_6 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (7555) imply:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (7556)   ~ (all_52_14 = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7556) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (7557)   ~ (all_52_14 = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5023), (7555) imply:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (7558)   ~ (e3 = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7559)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7559) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7560)  all_56_6 = e1 & op(e1, e3) = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7560) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7561)  all_56_6 = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (159), (214), (5032), (7549),
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7557), (7561), (function-axioms) are inconsistent
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #238.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7562)  all_56_7 = e1 & op(e1, e2) = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7562) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7563)  op(e1, e2) = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (7526), (7563), (function-axioms) are
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7564)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (5032), (7045), (7564),
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            #523.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (7565)  all_54_9 = e1 | all_54_9 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (7509), (7526), (7565) are inconsistent by
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #137.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | |   (7566)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7566) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | |   (7567)  all_56_8 = e0 & op(e1, e1) = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7567) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | |   (7568)  op(e1, e1) = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (7568), (function-axioms) are
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | |   (7569)  all_56_11 = e0 & op(e1, e0) = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7569) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | |   (7570)  all_56_11 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | |   (7571)  op(e1, e0) = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | |   (7572)  all_54_4 = e3
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7522), (7572) are inconsistent by
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #843.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | |   (7573)   ~ (all_54_4 = e3)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | |   (7574)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | |   (7575)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7575) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7576)  all_56_6 = e2 & op(e1, e3) = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7576) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7577)  all_56_6 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (159), (161), (213), (5032), (7045),
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            (7526), (7577), (function-axioms) are inconsistent
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #522.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7578)  all_56_7 = e2 & op(e1, e2) = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7578) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7579)  all_56_7 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7580)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7580) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7581)  all_56_6 = e1 & op(e1, e3) = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7581) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7582)  all_56_6 = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7574) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7583)  all_54_4 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (7583) imply:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7584)  all_52_1 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (7584) imply:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7585)   ~ (all_52_3 = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7585) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7586)   ~ (all_52_3 = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7584) imply:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7587)   ~ (all_52_9 = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7587) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7588)   ~ (all_52_9 = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7522), (7584) imply:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7589)   ~ (e3 = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7590)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7590) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7591)  all_56_9 = e2 & op(e3, e0) = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7591) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7592)  all_56_9 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7593)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7593) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7594)  all_56_0 = e0 & op(e3, e3) = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7594) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7595)  op(e3, e3) = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (45), (159), (237), (370), (5032),
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7510), (7571), (7595), (function-axioms) are
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #452.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7596)  all_56_1 = e0 & op(e3, e2) = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7596) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7597)  all_56_1 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (225), (226), (7510),
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7544), (7597), (function-axioms) are inconsistent
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #136.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7598)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7598) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7599)  all_56_4 = e0 & op(e3, e1) = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7599) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7600)  all_56_4 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7601)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7601) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7602)  all_56_4 = e2 & op(e3, e1) = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7602) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7603)  all_56_4 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7600), (7603) imply:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7604)  e2 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7604) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7605)  e2 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7579), (7605) imply:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7606)  all_56_7 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (214), (5032), (7570), (7582),
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7606), (function-axioms) are inconsistent by
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #146.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7607)  all_56_5 = e2 & op(e2, e1) = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7607) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7608)  op(e2, e1) = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7588), (7608), (function-axioms) are
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7609)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7609) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7610)  all_56_8 = e2 & op(e1, e1) = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7610) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7611)  op(e1, e1) = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7611), (function-axioms) are
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7612)  all_56_14 = e2 & op(e0, e1) = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7612) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7613)  all_56_14 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7614)  op(e0, e1) = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7615)  all_54_12 = e3
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (7529), (7615) are inconsistent by
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1093.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7616)   ~ (all_54_12 = e3)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7617)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7617) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7618)  all_54_12 = e2
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (7586), (7618) are inconsistent by
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #882.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7619)   ~ (all_54_12 = e2)
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7620)  all_54_12 = e1 | all_54_12 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7620) gives:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7621)  all_54_12 = e1
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (7524), (7621) are inconsistent by
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1091.
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7622)  all_54_12 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (7622) imply:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7623)  all_52_3 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7623) implies:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7624)  all_52_3 = e0
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (7624) imply:
% 148.66/21.19  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7625)   ~ (all_52_11 = e0)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7625) implies:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7626)   ~ (all_52_11 = e0)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7529), (7624) imply:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7627)   ~ (e3 = e0)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7586), (7624) imply:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7628)   ~ (e2 = e0)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7524), (7624) imply:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7629)   ~ (e1 = e0)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7630)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7630) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7631)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7631) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7632)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7514), (7515), (7632), (function-axioms) are
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #814.
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7633)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7514), (7516), (7633), (function-axioms) are
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7634)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7634) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7635)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (5032), (7530), (7635),
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #294.
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7636)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7636) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7637)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7637) implies:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7638)  op(e3, e3) = e2
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (217), (229),
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (235), (5031), (5032), (7592), (7613),
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7614), (7638), (function-axioms) are inconsistent
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #215.
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7639)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7046), (7510), (7639),
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #396.
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7640)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7640) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7641)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (167), (168), (5024), (7531), (7588),
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7641), (function-axioms) are inconsistent by
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #440.
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7642)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7642) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7643)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7643) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7644)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7644) implies:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7645)  op(e3, e3) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (45), (159), (237), (370), (5032),
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7510), (7571), (7645), (function-axioms) are
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #452.
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7646)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7646) implies:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7647)  op(e3, e3) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (45), (159), (237), (370), (5032),
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7510), (7571), (7647), (function-axioms) are
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #452.
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7648)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7648) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7649)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7649) implies:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7650)  op(e2, e0) = e2
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7536), (7650), (function-axioms) are
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #854.
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7651)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7651) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7652)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7652) implies:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7653)  op(e1, e0) = e1
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7045), (7653), (function-axioms) are
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7654)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7654) implies:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7655)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7655) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7656)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7656) gives:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7657)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7657) implies:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7658)  all_57_12 = e3
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7659)   ~ (all_57_0 = e2)
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7516), (7658), (7659) are inconsistent by
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #832.
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7660)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.66/21.20  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7660) gives:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7661)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7661) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7662)   ~ (all_57_1 = e1)
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5032), (7515), (7662), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #815.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7663)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7663) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7664)  op(e3, e3) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (216), (217), (229),
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (235), (5031), (5032), (7592), (7613),
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7614), (7664), (function-axioms) are inconsistent
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #215.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7665)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7665) gives:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7666)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7666) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7667)  op(e1, e1) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7667), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7668)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (7510), (7626), (7668),
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #804.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7669)  all_56_9 = e0 & op(e3, e0) = e0
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7669) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7670)  all_56_9 = e0
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7592), (7670) imply:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7671)  e2 = e0
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7579), (7671) imply:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7672)  all_56_7 = e0
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (214), (5032), (7570), (7582),
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7672), (function-axioms) are inconsistent by
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #146.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7673)  all_56_10 = e2 & op(e2, e0) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7673) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7674)  op(e2, e0) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7536), (7674), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #854.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7675)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7675) gives:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7676)  all_56_11 = e2 & op(e1, e0) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7676) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7677)  all_56_11 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (212), (5031), (7579), (7582),
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7677) are inconsistent by sub-proof #201.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7678)  all_56_15 = e2 & op(e0, e0) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7678) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7679)  op(e0, e0) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7046), (7679), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #978.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7680)  all_54_4 = e1 | all_54_4 = e0
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7508), (7521), (7680) are inconsistent by
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #795.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7681)  all_56_7 = e1 & op(e1, e2) = e1
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7681) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7682)  op(e1, e2) = e1
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (7526), (7682), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7683)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (162), (212), (5032), (7518),
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7579), (7683), (function-axioms) are inconsistent
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #189.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | |   (7684)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7684) gives:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7685)  all_56_8 = e2 & op(e1, e1) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7685) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7686)  op(e1, e1) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7686), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7687)  all_56_11 = e2 & op(e1, e0) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7687) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7688)  all_56_11 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7689)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7689) gives:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7690)  all_56_1 = e2 & op(e3, e2) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7690) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7691)  all_56_1 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7539), (7691) are inconsistent by sub-proof
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #595.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7692)  all_56_3 = e2 & op(e2, e2) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7692) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7693)  op(e2, e2) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7510), (7693), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7694)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7694) gives:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7695)  all_56_7 = e2 & op(e1, e2) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7695) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7696)  all_56_7 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7688), (7696) are inconsistent by sub-proof #200.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7697)  all_56_13 = e2 & op(e0, e2) = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7697) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7698)  all_56_13 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7544), (7698) are inconsistent by sub-proof
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1105.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | |   (7699)  all_56_3 = e1 & op(e2, e2) = e1
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | ALPHA: (7699) implies:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | |   (7700)  op(e2, e2) = e1
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7510), (7700), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | |   (7701)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 148.66/21.21  | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (227), (5023), (7510),
% 148.66/21.21  | | | | | | | | | | | | | | | | | |            (7526), (7530), (7701), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #205.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | |   (7702)   ~ (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.66/21.21  | | | | | | | | | | | | | | |           $i(all_57_14)
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | ALPHA: (7702) implies:
% 148.66/21.21  | | | | | | | | | | | | | | |   (7703)   ~ (all_57_14 = e3)
% 148.66/21.21  | | | | | | | | | | | | | | |   (7704)  op(e1, e1) = all_57_14
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | REF_CLOSE: (5032), (7703), (7704), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | |   (7705)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 148.66/21.21  | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 148.66/21.21  | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.66/21.21  | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.66/21.21  | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.66/21.21  | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 148.66/21.21  | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 148.66/21.21  | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.66/21.21  | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | ALPHA: (7705) implies:
% 148.66/21.21  | | | | | | | | | | | | | |   (7706)  op(e2, e2) = e2
% 148.66/21.21  | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | REF_CLOSE: (5), (7510), (7706), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 148.66/21.21  | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | |   (7707)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 148.66/21.21  | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 148.66/21.21  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.66/21.21  | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.66/21.21  | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.21  | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 148.66/21.21  | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 148.66/21.21  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.66/21.21  | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 148.66/21.21  | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 148.66/21.21  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.66/21.21  | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.66/21.21  | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.66/21.21  | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.66/21.21  | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.66/21.21  | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5032), (7046), (7707),
% 148.66/21.21  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.21  | | | | | | | | | | | | |            #429.
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | |   (7708)  all_14_2 = e0
% 148.66/21.21  | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | REDUCE: (340), (7708) imply:
% 148.66/21.21  | | | | | | | | | | |   (7709)   ~ (all_52_3 = e0)
% 148.66/21.21  | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | REDUCE: (344), (7708) imply:
% 148.66/21.21  | | | | | | | | | | |   (7710)   ~ (all_52_8 = e0)
% 148.66/21.21  | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | REDUCE: (51), (7708) imply:
% 148.66/21.21  | | | | | | | | | | |   (7711)  op(e3, e3) = e0
% 148.66/21.21  | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | BETA: splitting (237) gives:
% 148.66/21.21  | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | |   (7712)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 148.66/21.21  | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 148.66/21.21  | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.66/21.21  | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.66/21.21  | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.66/21.21  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 148.66/21.21  | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 148.66/21.21  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.66/21.21  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 148.66/21.21  | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 148.66/21.21  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.66/21.21  | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.66/21.21  | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.66/21.21  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 148.66/21.21  | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 148.66/21.21  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 148.66/21.21  | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | BETA: splitting (7712) gives:
% 148.66/21.21  | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | |   (7713)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 148.66/21.21  | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 148.66/21.21  | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.66/21.21  | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.66/21.21  | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.66/21.21  | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 148.66/21.21  | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 148.66/21.21  | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | ALPHA: (7713) implies:
% 148.66/21.21  | | | | | | | | | | | | |   (7714)  op(e3, e3) = e3
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | REF_CLOSE: (7), (7711), (7714), (function-axioms) are
% 148.66/21.21  | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | |   (7715)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 148.66/21.21  | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 148.66/21.21  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.66/21.21  | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.66/21.21  | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.66/21.21  | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 148.66/21.21  | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 148.66/21.21  | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | ALPHA: (7715) implies:
% 148.66/21.21  | | | | | | | | | | | | |   (7716)  op(e2, e2) = e2
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | BETA: splitting (228) gives:
% 148.66/21.21  | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | |   (7717)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 148.66/21.21  | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 148.66/21.21  | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | BETA: splitting (7717) gives:
% 148.66/21.21  | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | |   (7718)  all_56_0 = e0 & op(e3, e3) = e0
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e2,
% 148.66/21.21  | | | | | | | | | | | | | | |              e2, e2, simplifying with (39), (7716) gives:
% 148.66/21.21  | | | | | | | | | | | | | | |   (7719)  all_6_2 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | REDUCE: (347), (7719) imply:
% 148.66/21.21  | | | | | | | | | | | | | | |   (7720)   ~ (all_52_1 = e2)
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | REDUCE: (356), (7719) imply:
% 148.66/21.21  | | | | | | | | | | | | | | |   (7721)   ~ (all_52_9 = e2)
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | REDUCE: (358), (7719) imply:
% 148.66/21.21  | | | | | | | | | | | | | | |   (7722)   ~ (all_52_13 = e2)
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | REDUCE: (372), (7719) imply:
% 148.66/21.21  | | | | | | | | | | | | | | |   (7723)   ~ (e3 = e2)
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.66/21.21  | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | |   (7724)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.21  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.66/21.21  | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.66/21.21  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.66/21.21  | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.21  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.66/21.21  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.66/21.21  | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.66/21.21  | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.66/21.21  | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.66/21.21  | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.66/21.21  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.66/21.21  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.66/21.21  | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.66/21.21  | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.66/21.21  | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.66/21.21  | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.66/21.21  | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.21  | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.66/21.21  | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | BETA: splitting (7724) gives:
% 148.66/21.21  | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | |   (7725)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.66/21.21  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.66/21.21  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.66/21.21  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.66/21.21  | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.66/21.21  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.66/21.21  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.66/21.21  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.66/21.21  | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (166), (5032), (7046), (7720), (7725),
% 148.66/21.21  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.21  | | | | | | | | | | | | | | | | |            #436.
% 148.66/21.21  | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | |   (7726)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.21  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.21  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.66/21.21  | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.66/21.21  | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.66/21.21  | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.66/21.21  | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 148.66/21.21  | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.66/21.21  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.66/21.21  | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.66/21.21  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.21  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.66/21.21  | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.66/21.21  | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | BETA: splitting (7726) gives:
% 148.66/21.21  | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | |   (7727)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 148.66/21.21  | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (5032), (7046), (7727),
% 148.66/21.21  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.21  | | | | | | | | | | | | | | | | | |            #435.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | |   (7728)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.66/21.21  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.66/21.21  | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.21  | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.66/21.21  | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7046), (7711), (7716), (7728),
% 148.66/21.21  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.21  | | | | | | | | | | | | | | | | | |            #380.
% 148.66/21.21  | | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | End of split
% 148.66/21.21  | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | Case 2:
% 148.66/21.21  | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | |   (7729)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.21  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.21  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.21  | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.21  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.21  | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.21  | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.21  | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.21  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.21  | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.21  | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.66/21.21  | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.66/21.21  | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.66/21.21  | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.66/21.21  | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.66/21.21  | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.66/21.21  | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.66/21.21  | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.66/21.21  | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.66/21.21  | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.66/21.21  | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.66/21.21  | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.66/21.21  | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.66/21.21  | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.66/21.21  | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.66/21.21  | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.66/21.21  | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.66/21.21  | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.66/21.21  | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.66/21.21  | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.66/21.21  | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.66/21.21  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.66/21.21  | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.66/21.21  | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.66/21.21  | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.66/21.21  | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.66/21.21  | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.66/21.21  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.66/21.21  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.66/21.21  | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.66/21.21  | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.66/21.21  | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.66/21.21  | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.66/21.21  | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.66/21.21  | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | BETA: splitting (7729) gives:
% 148.66/21.21  | | | | | | | | | | | | | | | | 
% 148.66/21.21  | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.21  | | | | | | | | | | | | | | | | | 
% 148.66/21.22  | | | | | | | | | | | | | | | | |   (7730)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.22  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.22  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.22  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.22  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.22  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.22  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.22  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.22  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.66/21.22  | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.66/21.22  | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.66/21.22  | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.66/21.22  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.66/21.22  | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.66/21.22  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.66/21.22  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.66/21.22  | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.66/21.22  | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.66/21.22  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.66/21.22  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.22  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.66/21.22  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.66/21.22  | | | | | | | | | | | | | | | | | 
% 148.66/21.22  | | | | | | | | | | | | | | | | | BETA: splitting (7730) gives:
% 148.66/21.22  | | | | | | | | | | | | | | | | | 
% 148.66/21.22  | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.22  | | | | | | | | | | | | | | | | | | 
% 148.66/21.22  | | | | | | | | | | | | | | | | | |   (7731)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.22  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.66/21.22  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 148.66/21.22  | | | | | | | | | | | | | | | | | | 
% 148.66/21.22  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (5024), (7721), (7731),
% 148.66/21.22  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.66/21.22  | | | | | | | | | | | | | | | | | |            #1083.
% 148.66/21.22  | | | | | | | | | | | | | | | | | | 
% 148.66/21.22  | | | | | | | | | | | | | | | | | Case 2:
% 148.66/21.22  | | | | | | | | | | | | | | | | | | 
% 148.66/21.22  | | | | | | | | | | | | | | | | | |   (7732)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.66/21.22  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 148.66/21.22  | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 148.66/21.22  | | | | | | | | | | | | | | | | | | 
% 148.66/21.22  | | | | | | | | | | | | | | | | | | BETA: splitting (7732) gives:
% 148.66/21.22  | | | | | | | | | | | | | | | | | | 
% 148.66/21.22  | | | | | | | | | | | | | | | | | | Case 1:
% 148.66/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7733)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | ALPHA: (7733) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7734)  op(e2, e1) = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7721), (7734), (function-axioms) are
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7735)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (7711), (7735), (function-axioms) are
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #167.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | |   (7736)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.96/21.22  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.96/21.22  | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.96/21.22  | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.96/21.22  | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.96/21.22  | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.96/21.22  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.96/21.22  | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.96/21.22  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.96/21.22  | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.96/21.22  | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.96/21.22  | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.96/21.22  | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.96/21.22  | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.96/21.22  | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.96/21.22  | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.96/21.22  | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.96/21.22  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.96/21.22  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.96/21.22  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.96/21.22  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.96/21.22  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.96/21.22  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.96/21.22  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.22  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | BETA: splitting (7736) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | |   (7737)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.96/21.22  | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.96/21.22  | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | BETA: splitting (7737) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7738)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | ALPHA: (7738) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7739)  op(e2, e0) = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7722), (7739), (function-axioms) are
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7740)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | ALPHA: (7740) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7741)  op(e1, e0) = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (159), (7741) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7742)  all_52_14 = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | REDUCE: (7045), (7742) imply:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7743)  $false
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | CLOSE: (7743) is inconsistent.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | |   (7744)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.96/21.22  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.96/21.22  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | BETA: splitting (7744) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7745)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | ALPHA: (7745) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7746)  op(e2, e0) = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7722), (7746), (function-axioms) are
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7747)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | BETA: splitting (7747) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |   (7748)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | ALPHA: (7748) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |   (7749)  op(e2, e2) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7716), (7749), (function-axioms) are
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |   (7750)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | ALPHA: (7750) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |   (7751)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7751) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |   (7752)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (7709), (7711), (7752),
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |            #538.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |   (7753)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (5032), (7711), (7716), (7753),
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |            #174.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | |   (7754)  all_56_2 = e0 & op(e2, e3) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | ALPHA: (7754) implies:
% 148.96/21.22  | | | | | | | | | | | | | | |   (7755)  all_56_2 = e0
% 148.96/21.22  | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213), (214),
% 148.96/21.22  | | | | | | | | | | | | | | |            (230), (232), (234), (5031), (5032), (7711),
% 148.96/21.22  | | | | | | | | | | | | | | |            (7755), (function-axioms) are inconsistent by
% 148.96/21.22  | | | | | | | | | | | | | | |            sub-proof #135.
% 148.96/21.22  | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | |   (7756)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 148.96/21.22  | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 148.96/21.22  | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | BETA: splitting (7756) gives:
% 148.96/21.22  | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | |   (7757)  all_56_6 = e0 & op(e1, e3) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | ALPHA: (7757) implies:
% 148.96/21.22  | | | | | | | | | | | | | | |   (7758)  all_56_6 = e0
% 148.96/21.22  | | | | | | | | | | | | | | |   (7759)  op(e1, e3) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | |   (7760)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 148.96/21.22  | | | | | | | | | | | | | | | |             & op(e1, e2) = e1)
% 148.96/21.22  | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | BETA: splitting (7760) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | |   (7761)  all_56_6 = e1 & op(e1, e3) = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | ALPHA: (7761) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | |   (7762)  op(e1, e3) = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (7759), (7762), (function-axioms) are
% 148.96/21.22  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | |   (7763)  all_56_7 = e1 & op(e1, e2) = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | ALPHA: (7763) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | |   (7764)  all_56_7 = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | |   (7765)  op(e1, e2) = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | |   (7766)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | BETA: splitting (7766) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7767)  all_56_6 = e2 & op(e1, e3) = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7758), (7767) are inconsistent by sub-proof
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |            #1129.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7768)  all_56_7 = e2 & op(e1, e2) = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | ALPHA: (7768) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7769)  all_56_7 = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7764), (7769) imply:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7770)  e2 = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | SIMP: (7770) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7771)  e2 = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | REDUCE: (6), (7771) imply:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7772)  $false
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | CLOSE: (7772) is inconsistent.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | |   (7773)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | BETA: splitting (7773) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7774)  all_56_8 = e2 & op(e1, e1) = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | ALPHA: (7774) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7775)  op(e1, e1) = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7775), (function-axioms) are
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7776)  all_56_11 = e2 & op(e1, e0) = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | ALPHA: (7776) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7777)  all_56_11 = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | |   (7778)  op(e1, e0) = e2
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |   (7779)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7779) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |   (7780)  all_56_0 = e1 & op(e3, e3) = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7780) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |   (7781)  op(e3, e3) = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7711), (7781), (function-axioms) are
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #957.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |   (7782)  all_56_2 = e1 & op(e2, e3) = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7782) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |   (7783)  all_56_2 = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (168), (205),
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |            (223), (231), (233), (235), (5024), (5025),
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |            (7046), (7711), (7716), (7777), (7783),
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |            #134.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |   (7784)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | BETA: splitting (7784) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |   (7785)  all_56_6 = e1 & op(e1, e3) = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7785) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |   (7786)  op(e1, e3) = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (161), (162), (7765), (7786),
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |            #911.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |   (7787)  all_56_12 = e1 & op(e0, e3) = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | ALPHA: (7787) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | |   (7788)  all_56_12 = e1
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | |   (7789)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7789) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | |   (7790)  all_56_12 = e3 & op(e0, e3) = e3
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7788), (7790) are inconsistent by sub-proof
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | |            #919.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | |   (7791)  all_56_13 = e3 & op(e0, e2) = e3
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7791) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | |   (7792)  all_56_13 = e3
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | |   (7793)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7793) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (7794)  all_56_0 = e3 & op(e3, e3) = e3
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7794) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (7795)  op(e3, e3) = e3
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7711), (7795), (function-axioms) are
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (7796)  all_56_2 = e3 & op(e2, e3) = e3
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7796) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | |   (7797)  all_56_2 = e3
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7798)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7798) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7799)  all_56_1 = e0 & op(e3, e2) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7799) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7800)  all_56_1 = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (231), (233),
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (5024), (7711), (7800), (function-axioms)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #492.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7801)  all_56_3 = e0 & op(e2, e2) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7801) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7802)  op(e2, e2) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7716), (7802), (function-axioms) are
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7803)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7803) gives:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7804)  all_56_7 = e0 & op(e1, e2) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7804) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7805)  all_56_7 = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (162), (213), (5032), (7759),
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7778), (7805), (function-axioms) are inconsistent
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #349.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7806)  all_56_13 = e0 & op(e0, e2) = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7806) implies:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7807)  all_56_13 = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7792), (7807) imply:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7808)  e3 = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7797), (7808) imply:
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7809)  all_56_2 = e0
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213), (214),
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (5031), (5032), (7711),
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7809), (function-axioms) are inconsistent by
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #135.
% 148.96/21.22  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7810)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |            (7777), (7788), (7810) are inconsistent by
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #133.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | |   (7811)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7811) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | |   (7812)  all_56_14 = e3 & op(e0, e1) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7812) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | |   (7813)  all_56_14 = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7814)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7814) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (7815)  all_56_0 = e3 & op(e3, e3) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7815) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (7816)  op(e3, e3) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7711), (7816), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (7817)  all_56_2 = e3 & op(e2, e3) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7817) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (7818)  all_56_2 = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7819)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7819) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7820)  all_56_4 = e0 & op(e3, e1) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (7710), (7820), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7821)  all_56_5 = e0 & op(e2, e1) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7821) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7822)  all_56_5 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7823)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7823) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7824)  all_56_2 = e1 & op(e2, e3) = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7824) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7825)  all_56_2 = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (168), (205),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (231), (233), (235), (5024), (5025),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7046), (7711), (7716), (7777), (7825),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #134.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7826)  all_56_3 = e1 & op(e2, e2) = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7826) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7827)  op(e2, e2) = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7716), (7827), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7828)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7828) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7829)  all_56_5 = e1 & op(e2, e1) = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7829) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7830)  all_56_5 = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7822), (7830) imply:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7831)  e1 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7831) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7832)  e1 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7764), (7832) imply:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7833)  all_56_7 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (162), (213), (5032), (7759),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7778), (7833), (function-axioms) are inconsistent
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #349.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7834)  all_56_10 = e1 & op(e2, e0) = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7834) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7835)  all_56_10 = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7046), (7835), (function-axioms) are inconsistent
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #445.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7836)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7836) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7837)  all_56_8 = e0 & op(e1, e1) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7837) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7838)  op(e1, e1) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5032), (7838), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7839)  all_56_14 = e0 & op(e0, e1) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7839) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7840)  all_56_14 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7813), (7840) imply:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7841)  e3 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7818), (7841) imply:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7842)  all_56_2 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213), (214),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (230), (232), (234), (5031), (5032), (7711),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7842), (function-axioms) are inconsistent by
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #135.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7843)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |            (7777), (7788), (7843) are inconsistent by
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #133.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | |   (7844)  all_56_15 = e3 & op(e0, e0) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7844) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | |   (7845)  op(e0, e0) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7046), (7845), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | |   (7846)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 148.96/21.23  | | | | | | | | | | | | | | | |             e1 & op(e1, e0) = e1)
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | BETA: splitting (7846) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | |   (7847)  all_56_8 = e1 & op(e1, e1) = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | ALPHA: (7847) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | |   (7848)  op(e1, e1) = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5032), (7848), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 148.96/21.23  | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | |   (7849)  all_56_11 = e1 & op(e1, e0) = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | ALPHA: (7849) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | |   (7850)  all_56_11 = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | |   (7851)  op(e1, e0) = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | |   (7852)  all_56_15 = e0 & op(e0, e0) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | ALPHA: (7852) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | |   (7853)  op(e0, e0) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7046), (7853), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | |   (7854)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 148.96/21.23  | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 148.96/21.23  | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 148.96/21.23  | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 148.96/21.23  | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | ALPHA: (7854) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | |   (7855)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 148.96/21.23  | | | | | | | | | | | | | | | | | |               e0) = e0)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | BETA: splitting (7855) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | |   (7856)  all_56_9 = e0 & op(e3, e0) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | ALPHA: (7856) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | |   (7857)  all_56_9 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (231), (233),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | |            (235), (5024), (7711), (7857), (function-axioms)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #687.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | |   (7858)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | |             e0 & op(e1, e0) = e0)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | BETA: splitting (7858) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | |   (7859)  all_56_10 = e0 & op(e2, e0) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | ALPHA: (7859) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | |   (7860)  all_56_10 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | |   (7861)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7861) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | |   (7862)  all_56_6 = e2 & op(e1, e3) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7758), (7862) are inconsistent by sub-proof
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | |            #1129.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | |   (7863)  all_56_7 = e2 & op(e1, e2) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7863) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | |   (7864)  all_56_7 = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | |   (7865)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7865) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7866)  all_56_9 = e3 & op(e3, e0) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7866) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7867)  all_56_9 = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (7868)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7868) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7869)  all_56_9 = e2 & op(e3, e0) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7869) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7870)  all_56_9 = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7867), (7870) are inconsistent by sub-proof
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            #964.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7871)  all_56_10 = e2 & op(e2, e0) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7871) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7872)  all_56_10 = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7860), (7872) imply:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7873)  e2 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7864), (7873) imply:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7874)  all_56_7 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7861) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7875)  all_56_6 = e2 & op(e1, e3) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7875) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7876)  all_56_6 = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7758), (7876) are inconsistent by sub-proof
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #724.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7864), (7874) are inconsistent by sub-proof
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #483.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7877)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7877) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7878)  all_56_8 = e2 & op(e1, e1) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7878) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7879)  op(e1, e1) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5032), (7879), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7880)  all_56_11 = e2 & op(e1, e0) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7880) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7881)  op(e1, e0) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (162), (213), (5032), (7759),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7874), (7881), (function-axioms) are inconsistent
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #349.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | |   (7882)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7882) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7883)  all_56_11 = e2 & op(e1, e0) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7883) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7884)  all_56_11 = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (212), (213), (5031),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            (7864), (7884) are inconsistent by sub-proof #200.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7885)  all_56_15 = e2 & op(e0, e0) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7885) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7886)  op(e0, e0) = e2
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7046), (7886), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #978.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7887)  all_56_10 = e3 & op(e2, e0) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7860), (7887) are inconsistent by sub-proof
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |            #813.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | |   (7888)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7888) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7889)  all_56_11 = e3 & op(e1, e0) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7889) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7890)  all_56_11 = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7850), (7890) imply:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7891)  e3 = e1
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (7891) imply:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7892)  $false
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7892) is inconsistent.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7893)  all_56_15 = e3 & op(e0, e0) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7893) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |   (7894)  op(e0, e0) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7046), (7894), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | |   (7895)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (5032), (7851), (7895),
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | |            #280.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | |   (7896)  all_56_11 = e0 & op(e1, e0) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | ALPHA: (7896) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | |   (7897)  all_56_11 = e0
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7850), (7897) are inconsistent by sub-proof
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | |            #745.
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | |   (7898)  all_56_12 = e0 & op(e0, e3) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | ALPHA: (7898) implies:
% 148.96/21.23  | | | | | | | | | | | | | | |   (7899)  op(e0, e3) = e0
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | REF_CLOSE: (158), (7709), (7899), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | |   (7900)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 148.96/21.23  | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 148.96/21.23  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.23  | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.96/21.23  | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.23  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 148.96/21.23  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 148.96/21.23  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.96/21.23  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 148.96/21.23  | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 148.96/21.23  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.23  | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.96/21.23  | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.96/21.23  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.96/21.23  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.96/21.23  | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 148.96/21.23  | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | REF_CLOSE: (4), (8), (5032), (7046), (7900),
% 148.96/21.23  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.23  | | | | | | | | | | | |            #429.
% 148.96/21.23  | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | 
% 148.96/21.23  | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | 
% 148.96/21.23  | | | | | | | End of split
% 148.96/21.23  | | | | | | | 
% 148.96/21.23  | | | | | | End of split
% 148.96/21.23  | | | | | | 
% 148.96/21.23  | | | | | Case 2:
% 148.96/21.23  | | | | | | 
% 148.96/21.23  | | | | | |   (7901)  all_56_14 = e3 & op(e0, e1) = e3
% 148.96/21.23  | | | | | | 
% 148.96/21.23  | | | | | | ALPHA: (7901) implies:
% 148.96/21.23  | | | | | |   (7902)  op(e0, e1) = e3
% 148.96/21.23  | | | | | | 
% 148.96/21.23  | | | | | | REF_CLOSE: (156), (5026), (7902), (function-axioms) are inconsistent
% 148.96/21.23  | | | | | |            by sub-proof #1147.
% 148.96/21.23  | | | | | | 
% 148.96/21.23  | | | | | End of split
% 148.96/21.23  | | | | | 
% 148.96/21.23  | | | | End of split
% 148.96/21.23  | | | | 
% 148.96/21.23  | | | End of split
% 148.96/21.23  | | | 
% 148.96/21.23  | | Case 2:
% 148.96/21.23  | | | 
% 148.96/21.23  | | |   (7903)  all_6_2 = e3
% 148.96/21.23  | | |   (7904)  ( ~ (all_6_0 = e1) & op(all_6_1, e2) = all_6_0 & op(e2, e3) =
% 148.96/21.23  | | |             all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) &
% 148.96/21.23  | | |             op(e2, e3) = all_6_1 & $i(all_6_1))
% 148.96/21.23  | | | 
% 148.96/21.23  | | | COMBINE_EQS: (330), (7903) imply:
% 148.96/21.23  | | |   (7905)  all_26_2 = e3
% 148.96/21.23  | | | 
% 148.96/21.23  | | | REDUCE: (347), (7903) imply:
% 148.96/21.23  | | |   (7906)   ~ (all_52_1 = e3)
% 148.96/21.23  | | | 
% 148.96/21.23  | | | REDUCE: (350), (7903) imply:
% 148.96/21.23  | | |   (7907)   ~ (all_52_4 = e3)
% 148.96/21.23  | | | 
% 148.96/21.23  | | | REDUCE: (352), (7903) imply:
% 148.96/21.23  | | |   (7908)   ~ (all_52_6 = e3)
% 148.96/21.23  | | | 
% 148.96/21.23  | | | REDUCE: (354), (7903) imply:
% 148.96/21.23  | | |   (7909)   ~ (all_52_7 = e3)
% 148.96/21.23  | | | 
% 148.96/21.23  | | | REDUCE: (356), (7903) imply:
% 148.96/21.23  | | |   (7910)   ~ (all_52_9 = e3)
% 148.96/21.23  | | | 
% 148.96/21.23  | | | REDUCE: (358), (7903) imply:
% 148.96/21.23  | | |   (7911)   ~ (all_52_13 = e3)
% 148.96/21.23  | | | 
% 148.96/21.23  | | | BETA: splitting (223) gives:
% 148.96/21.23  | | | 
% 148.96/21.23  | | | Case 1:
% 148.96/21.23  | | | | 
% 148.96/21.23  | | | |   (7912)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2,
% 148.96/21.23  | | | |               e2) = e3)
% 148.96/21.23  | | | | 
% 148.96/21.23  | | | | BETA: splitting (7912) gives:
% 148.96/21.23  | | | | 
% 148.96/21.23  | | | | Case 1:
% 148.96/21.23  | | | | | 
% 148.96/21.23  | | | | |   (7913)  all_56_2 = e3 & op(e2, e3) = e3
% 148.96/21.23  | | | | | 
% 148.96/21.23  | | | | | REF_CLOSE: (166), (7906), (7913), (function-axioms) are inconsistent
% 148.96/21.23  | | | | |            by sub-proof #917.
% 148.96/21.23  | | | | | 
% 148.96/21.23  | | | | Case 2:
% 148.96/21.23  | | | | | 
% 148.96/21.23  | | | | |   (7914)  all_56_3 = e3 & op(e2, e2) = e3
% 148.96/21.23  | | | | | 
% 148.96/21.23  | | | | | ALPHA: (7914) implies:
% 148.96/21.23  | | | | |   (7915)  all_56_3 = e3
% 148.96/21.23  | | | | |   (7916)  op(e2, e2) = e3
% 148.96/21.23  | | | | | 
% 148.96/21.23  | | | | | BETA: splitting (43) gives:
% 148.96/21.23  | | | | | 
% 148.96/21.23  | | | | | Case 1:
% 148.96/21.23  | | | | | | 
% 148.96/21.23  | | | | | |   (7917)   ~ (all_8_2 = e3)
% 148.96/21.23  | | | | | | 
% 148.96/21.23  | | | | | | REDUCE: (329), (7917) imply:
% 148.96/21.23  | | | | | |   (7918)   ~ (all_4_2 = e3)
% 148.96/21.23  | | | | | | 
% 148.96/21.23  | | | | | | BETA: splitting (46) gives:
% 148.96/21.23  | | | | | | 
% 148.96/21.23  | | | | | | Case 1:
% 148.96/21.23  | | | | | | | 
% 148.96/21.23  | | | | | | |   (7919)   ~ (all_10_2 = e1)
% 148.96/21.23  | | | | | | | 
% 148.96/21.23  | | | | | | | BETA: splitting (52) gives:
% 148.96/21.23  | | | | | | | 
% 148.96/21.23  | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | 
% 148.96/21.23  | | | | | | | |   (7920)   ~ (all_14_2 = e0)
% 148.96/21.23  | | | | | | | | 
% 148.96/21.23  | | | | | | | | BETA: splitting (64) gives:
% 148.96/21.23  | | | | | | | | 
% 148.96/21.23  | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | 
% 148.96/21.23  | | | | | | | | |   (7921)   ~ (all_22_2 = e1)
% 148.96/21.23  | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | REDUCE: (320), (7921) imply:
% 148.96/21.23  | | | | | | | | |   (7922)   ~ (all_14_2 = e1)
% 148.96/21.23  | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | BETA: splitting (67) gives:
% 148.96/21.23  | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | |   (7923)   ~ (all_24_2 = e2)
% 148.96/21.23  | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | REDUCE: (318), (7923) imply:
% 148.96/21.23  | | | | | | | | | |   (7924)   ~ (all_10_2 = e2)
% 148.96/21.23  | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | BETA: splitting (84) gives:
% 148.96/21.23  | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | |   (7925)   ~ (all_36_2 = e2)
% 148.96/21.23  | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | REDUCE: (304), (7925) imply:
% 148.96/21.23  | | | | | | | | | | |   (7926)   ~ (all_14_2 = e2)
% 148.96/21.23  | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | BETA: splitting (203) gives:
% 148.96/21.23  | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | |   (7927)  all_54_0 = e3
% 148.96/21.23  | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | COMBINE_EQS: (278), (7927) imply:
% 148.96/21.23  | | | | | | | | | | | |   (7928)  all_14_2 = e3
% 148.96/21.23  | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | REDUCE: (338), (7928) imply:
% 148.96/21.23  | | | | | | | | | | | |   (7929)   ~ (all_52_2 = e3)
% 148.96/21.23  | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | REDUCE: (344), (7928) imply:
% 148.96/21.23  | | | | | | | | | | | |   (7930)   ~ (all_52_8 = e3)
% 148.96/21.23  | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | REDUCE: (51), (7928) imply:
% 148.96/21.23  | | | | | | | | | | | |   (7931)  op(e3, e3) = e3
% 148.96/21.23  | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | BETA: splitting (219) gives:
% 148.96/21.23  | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | |   (7932)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 148.96/21.23  | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 148.96/21.23  | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | REF_CLOSE: (164), (168), (7910), (7930), (7932),
% 148.96/21.23  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.23  | | | | | | | | | | | | |            #369.
% 148.96/21.23  | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | |   (7933)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 148.96/21.23  | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 148.96/21.23  | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | BETA: splitting (7933) gives:
% 148.96/21.23  | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | |   (7934)  all_56_8 = e3 & op(e1, e1) = e3
% 148.96/21.23  | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | ALPHA: (7934) implies:
% 148.96/21.23  | | | | | | | | | | | | | |   (7935)  op(e1, e1) = e3
% 148.96/21.23  | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | REF_CLOSE: (36), (7918), (7935), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 148.96/21.23  | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | |   (7936)  all_56_14 = e3 & op(e0, e1) = e3
% 148.96/21.23  | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | ALPHA: (7936) implies:
% 148.96/21.23  | | | | | | | | | | | | | |   (7937)  all_56_14 = e3
% 148.96/21.23  | | | | | | | | | | | | | |   (7938)  op(e0, e1) = e3
% 148.96/21.23  | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 148.96/21.23  | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | |   (7939)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 148.96/21.23  | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | BETA: splitting (7939) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | |   (7940)  all_56_6 = e3 & op(e1, e3) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7929), (7940), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #132.
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | |   (7941)  all_56_7 = e3 & op(e1, e2) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | REF_CLOSE: (161), (7908), (7941), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | End of split
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | |   (7942)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 148.96/21.23  | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | BETA: splitting (7942) gives:
% 148.96/21.23  | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | Case 1:
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | |   (7943)  all_56_8 = e3 & op(e1, e1) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | ALPHA: (7943) implies:
% 148.96/21.23  | | | | | | | | | | | | | | | |   (7944)  op(e1, e1) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7918), (7944), (function-axioms) are
% 148.96/21.23  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | Case 2:
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.23  | | | | | | | | | | | | | | | |   (7945)  all_56_11 = e3 & op(e1, e0) = e3
% 148.96/21.23  | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | ALPHA: (7945) implies:
% 148.96/21.24  | | | | | | | | | | | | | | | |   (7946)  op(e1, e0) = e3
% 148.96/21.24  | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 148.96/21.24  | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (156), (7938) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | |   (7947)  all_52_11 = e3
% 148.96/21.24  | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 148.96/21.24  | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (159), (7946) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | |   (7948)  all_52_14 = e3
% 148.96/21.24  | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | REDUCE: (111), (7948) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | |   (7949)   ~ (all_52_12 = e3)
% 148.96/21.24  | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | REDUCE: (370), (7948) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | |   (7950)   ~ (all_10_2 = e3)
% 148.96/21.24  | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | SIMP: (7950) implies:
% 148.96/21.24  | | | | | | | | | | | | | | | |   (7951)   ~ (all_10_2 = e3)
% 148.96/21.24  | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | REDUCE: (366), (7948) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | |   (7952)   ~ (all_4_2 = e3)
% 148.96/21.24  | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | |   (7953)  all_54_15 = e3
% 148.96/21.24  | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (7951), (7953) are inconsistent by
% 148.96/21.24  | | | | | | | | | | | | | | | | |            sub-proof #1049.
% 148.96/21.24  | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | |   (7954)   ~ (all_54_15 = e3)
% 148.96/21.24  | | | | | | | | | | | | | | | | |   (7955)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | BETA: splitting (7955) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | |   (7956)  all_54_15 = e2
% 148.96/21.24  | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (7924), (7956) are inconsistent by
% 148.96/21.24  | | | | | | | | | | | | | | | | | |            sub-proof #1048.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | |   (7957)   ~ (all_54_15 = e2)
% 148.96/21.24  | | | | | | | | | | | | | | | | | |   (7958)  all_54_15 = e1 | all_54_15 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | BETA: splitting (7958) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |   (7959)  all_54_15 = e1
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (7919), (7959) are inconsistent by
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |            sub-proof #1047.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |   (7960)  all_54_15 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (7960) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |   (7961)  all_10_2 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | SIMP: (7961) implies:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |   (7962)  all_10_2 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | REDUCE: (349), (7962) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |   (7963)   ~ (all_52_3 = e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | REDUCE: (368), (7962) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |   (7964)   ~ (all_52_12 = e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | REDUCE: (369), (7962) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |   (7965)   ~ (all_52_13 = e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | REDUCE: (7951), (7962) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |   (7966)   ~ (e3 = e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | REDUCE: (7924), (7962) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |   (7967)   ~ (e2 = e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | REDUCE: (7919), (7962) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |   (7968)   ~ (e1 = e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | REDUCE: (45), (7962) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | |   (7969)  op(e0, e0) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | |   (7970)   ~ (all_48_2 = e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | REDUCE: (298), (7970) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | |   (7971)   ~ (all_4_2 = e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | |   (7972)  all_54_10 = e3
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (7918), (7972) are inconsistent by
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1173.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | |   (7973)   ~ (all_54_10 = e3)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | |   (7974)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7974) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | |   (7975)  all_54_10 = e2
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (7975) are inconsistent by sub-proof
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | |            #1168.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | |   (7976)   ~ (all_54_10 = e2)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | |   (7977)  all_54_10 = e1 | all_54_10 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7977) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | |   (7978)  all_54_10 = e1
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (7978) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | |   (7979)  all_4_2 = e1
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7979) implies:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | |   (7980)  all_4_2 = e1
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (7980) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | |   (7981)   ~ (all_52_2 = e1)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7918), (7980) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | |   (7982)   ~ (e3 = e1)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (7980) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | |   (7983)   ~ (e2 = e1)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (7980) imply:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | |   (7984)  op(e1, e1) = e1
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |   (7985)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7985) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (7986)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (162), (7969), (7981), (7984), (7986),
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |            #131.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (7987)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7987) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7988)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (169), (7907), (7984), (7988),
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            #721.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7989)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7989) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7990)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7990) implies:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7991)  op(e3, e3) = e2
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7931), (7991), (function-axioms) are
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (7992)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (7916), (7969), (7992),
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #130.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |   (7993)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7993) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (7994)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7994) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7995)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (7930), (7931), (7995),
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            #860.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7996)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (7949), (7969), (7996),
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            #859.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |   (7997)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7997) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7998)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7931), (7998), (function-axioms) are
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |   (7999)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7999) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8000)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8000) implies:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8001)  op(e1, e1) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7984), (8001), (function-axioms) are
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8002)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8002) gives:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8003)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8003) implies:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8004)  op(e2, e2) = e0
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7916), (8004), (function-axioms) are
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.24  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8005)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8005) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8006)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8006) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8007)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (158), (7931), (7963), (8007),
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #852.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8008)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8008) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8009)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8009) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8010)  op(e1, e1) = e2
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (7984), (8010), (function-axioms) are
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8011)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (45), (156), (367), (7916), (7969), (8011),
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #129.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |   (8012)  all_54_10 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (7971), (8012) are inconsistent by
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8013)  all_48_2 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (8013) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8014)  all_4_2 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (8014) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8015)  all_50_2 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (8014) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8016)   ~ (all_52_8 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (8014) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8017)   ~ (all_52_9 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (8014) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8018)  op(e1, e1) = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | |   (8019)   ~ (all_50_2 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | REDUCE: (8015), (8019) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | |   (8020)  $false
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | CLOSE: (8020) is inconsistent.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | |   (8021)  ( ~ (all_50_0 = e3) & op(all_50_1, e1) = all_50_0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_50_1 & $i(all_50_0) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | |             $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e1, e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |   (8022)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8022) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |   (8023)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8023) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |   (8024)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = all_57_12 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | |   (8025)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8025) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8026)  all_56_0 = e0 & op(e3, e3) = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8026) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8027)  op(e3, e3) = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7931), (8027), (function-axioms) are
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8028)  all_56_1 = e0 & op(e3, e2) = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8028) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8029)  all_56_1 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (163), (164),
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (220), (225), (226), (227), (7908), (7916),
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            (7965), (8017), (8024), (8029), (function-axioms)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #125.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | |   (8030)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8030) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8031)  all_56_4 = e0 & op(e3, e1) = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8016), (8031), (function-axioms) are
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8032)  all_56_9 = e0 & op(e3, e0) = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7964), (8032), (function-axioms) are
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |   (8033)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8033) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |   (8034)  op(e2, e2) = e2
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7916), (8034), (function-axioms) are
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |   (8035)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8035) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |   (8036)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8036) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |   (8037)  op(e1, e1) = e1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (164), (168), (216), (7937), (8016),
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |            (8017), (8037), (function-axioms) are inconsistent
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #124.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |   (8038)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8038) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |   (8039)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8039) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | |   (8040)  all_57_13 = e1 & op(e1, e0) = e1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8040) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | |   (8041)  op(e1, e0) = e1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8021) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8042)   ~ (all_50_0 = e3) & op(all_50_1, e1) = all_50_0 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_50_1 & $i(all_50_0) &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8042) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8043)  op(e1, e0) = all_50_1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7946), (8041), (8043), (function-axioms) are
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #123.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8044)   ~ (all_50_1 = e2) & op(e1, e0) = all_50_1 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8044) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (8045)  op(e1, e0) = all_50_1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7946), (8041), (8045), (function-axioms) are
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #123.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | |   (8046)   ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8046) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | |   (8047)   ~ (all_57_14 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | |   (8048)  op(e1, e1) = all_57_14
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8018), (8047), (8048), (function-axioms) are
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1026.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | |   (8049)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 148.96/21.25  | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | REF_CLOSE: (278), (7920), (7922), (7926), (8049) are
% 148.96/21.25  | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 148.96/21.25  | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | End of split
% 148.96/21.25  | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | |   (8050)  all_36_2 = e2
% 148.96/21.25  | | | | | | | | | | |   (8051)  ( ~ (all_36_0 = e1) & op(all_36_1, e3) = all_36_0
% 148.96/21.25  | | | | | | | | | | |             & op(e3, e2) = all_36_1 & $i(all_36_0) &
% 148.96/21.25  | | | | | | | | | | |             $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e3, e2)
% 148.96/21.25  | | | | | | | | | | |             = all_36_1 & $i(all_36_1))
% 148.96/21.25  | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | COMBINE_EQS: (304), (8050) imply:
% 148.96/21.25  | | | | | | | | | | |   (8052)  all_14_2 = e2
% 148.96/21.25  | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | SIMP: (8052) implies:
% 148.96/21.25  | | | | | | | | | | |   (8053)  all_14_2 = e2
% 148.96/21.25  | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | COMBINE_EQS: (280), (8053) imply:
% 148.96/21.25  | | | | | | | | | | |   (8054)  all_44_2 = e2
% 148.96/21.25  | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | REDUCE: (336), (8053) imply:
% 148.96/21.25  | | | | | | | | | | |   (8055)   ~ (all_52_1 = e2)
% 148.96/21.25  | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | REDUCE: (344), (8053) imply:
% 148.96/21.25  | | | | | | | | | | |   (8056)   ~ (all_52_8 = e2)
% 148.96/21.25  | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | REDUCE: (51), (8053) imply:
% 148.96/21.25  | | | | | | | | | | |   (8057)  op(e3, e3) = e2
% 148.96/21.25  | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | BETA: splitting (96) gives:
% 148.96/21.25  | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | |   (8058)   ~ (all_44_2 = e2)
% 148.96/21.25  | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | REDUCE: (8054), (8058) imply:
% 148.96/21.25  | | | | | | | | | | | |   (8059)  $false
% 148.96/21.25  | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | CLOSE: (8059) is inconsistent.
% 148.96/21.25  | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | |   (8060)  ( ~ (all_44_0 = e0) & op(all_44_1, e3) = all_44_0
% 148.96/21.25  | | | | | | | | | | | |             & op(e3, e2) = all_44_1 & $i(all_44_0) &
% 148.96/21.25  | | | | | | | | | | | |             $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e3, e2)
% 148.96/21.25  | | | | | | | | | | | |             = all_44_1 & $i(all_44_1))
% 148.96/21.25  | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | BETA: splitting (93) gives:
% 148.96/21.25  | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | |   (8061)   ~ (all_42_2 = e3)
% 148.96/21.25  | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | REDUCE: (302), (8061) imply:
% 148.96/21.25  | | | | | | | | | | | | |   (8062)   ~ (all_10_2 = e3)
% 148.96/21.25  | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | BETA: splitting (188) gives:
% 148.96/21.25  | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | |   (8063)  all_54_15 = e3
% 148.96/21.25  | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | REF_CLOSE: (245), (8062), (8063) are inconsistent by
% 148.96/21.25  | | | | | | | | | | | | | |            sub-proof #1049.
% 148.96/21.25  | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | |   (8064)   ~ (all_54_15 = e3)
% 148.96/21.25  | | | | | | | | | | | | | |   (8065)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 148.96/21.25  | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | BETA: splitting (8065) gives:
% 148.96/21.25  | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | |   (8066)  all_54_15 = e2
% 148.96/21.25  | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | REF_CLOSE: (245), (7924), (8066) are inconsistent by
% 148.96/21.25  | | | | | | | | | | | | | | |            sub-proof #1048.
% 148.96/21.25  | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | |   (8067)   ~ (all_54_15 = e2)
% 148.96/21.25  | | | | | | | | | | | | | | |   (8068)  all_54_15 = e1 | all_54_15 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | BETA: splitting (8068) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8069)  all_54_15 = e1
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | REF_CLOSE: (245), (7919), (8069) are inconsistent by
% 148.96/21.25  | | | | | | | | | | | | | | | |            sub-proof #1047.
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8070)  all_54_15 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8070) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8071)  all_10_2 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | SIMP: (8071) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8072)  all_10_2 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | REDUCE: (349), (8072) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8073)   ~ (all_52_3 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | REDUCE: (360), (8072) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8074)   ~ (all_52_7 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | REDUCE: (367), (8072) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8075)   ~ (all_52_11 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | REDUCE: (368), (8072) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8076)   ~ (all_52_12 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | REDUCE: (369), (8072) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8077)   ~ (all_52_13 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | REDUCE: (8062), (8072) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8078)   ~ (e3 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | REDUCE: (7924), (8072) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8079)   ~ (e2 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | REDUCE: (7919), (8072) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8080)   ~ (e1 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | REDUCE: (45), (8072) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | |   (8081)  op(e0, e0) = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | |   (8082)   ~ (all_48_2 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | REDUCE: (298), (8082) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | |   (8083)   ~ (all_4_2 = e0)
% 148.96/21.25  | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | |   (8084)  all_54_10 = e3
% 148.96/21.25  | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (7918), (8084) are inconsistent by
% 148.96/21.25  | | | | | | | | | | | | | | | | | |            sub-proof #1173.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | |   (8085)   ~ (all_54_10 = e3)
% 148.96/21.25  | | | | | | | | | | | | | | | | | |   (8086)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | BETA: splitting (8086) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | |   (8087)  all_54_10 = e2
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (8087) are inconsistent by sub-proof
% 148.96/21.25  | | | | | | | | | | | | | | | | | | |            #1168.
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | |   (8088)   ~ (all_54_10 = e2)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | |   (8089)  all_54_10 = e1 | all_54_10 = e0
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (8089) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8090)  all_54_10 = e1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (8090) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8091)  all_4_2 = e1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | SIMP: (8091) implies:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8092)  all_4_2 = e1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (8092) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8093)   ~ (all_52_2 = e1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (8092) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8094)   ~ (all_52_6 = e1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (8092) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8095)   ~ (all_52_14 = e1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | REDUCE: (7918), (8092) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8096)   ~ (e3 = e1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (8092) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8097)   ~ (e2 = e1)
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (8092) imply:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | |   (8098)  op(e1, e1) = e1
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.25  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |   (8099)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8099) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |   (8100)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8100) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8101)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (8055), (8101), (function-axioms) are
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8102)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (162), (8081), (8093), (8102),
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            #1045.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |   (8103)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8103) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8104)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (169), (7907), (8098), (8104),
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            #721.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8105)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8105) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |   (8106)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8106) implies:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |   (8107)  op(e1, e2) = e1
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (8094), (8107), (function-axioms) are
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |   (8108)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (7916), (8081), (8108),
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |            #130.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |   (8109)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8109) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |   (8110)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8110) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8111)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8057), (8081), (8111),
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            #766.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8112)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8112) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |   (8113)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8113) implies:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |   (8114)  op(e0, e0) = e1
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8081), (8114), (function-axioms) are
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |   (8115)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (7916), (8098), (8115),
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | |            #122.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |   (8116)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8116) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8117)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8057), (8117), (function-axioms) are
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8118)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (36), (156), (157), (158), (159),
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            (8073), (8074), (8075), (8095), (8098), (8118),
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            #763.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | |   (8119)  all_54_10 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8083), (8119) are inconsistent by
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | |   (8120)  all_48_2 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (8120) imply:
% 148.96/21.26  | | | | | | | | | | | | | | | | |   (8121)  all_4_2 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (294), (8121) imply:
% 148.96/21.26  | | | | | | | | | | | | | | | | |   (8122)  all_50_2 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | REDUCE: (361), (8121) imply:
% 148.96/21.26  | | | | | | | | | | | | | | | | |   (8123)   ~ (all_52_8 = e0)
% 148.96/21.26  | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | REDUCE: (362), (8121) imply:
% 148.96/21.26  | | | | | | | | | | | | | | | | |   (8124)   ~ (all_52_9 = e0)
% 148.96/21.26  | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | REDUCE: (366), (8121) imply:
% 148.96/21.26  | | | | | | | | | | | | | | | | |   (8125)   ~ (all_52_14 = e0)
% 148.96/21.26  | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | REDUCE: (36), (8121) imply:
% 148.96/21.26  | | | | | | | | | | | | | | | | |   (8126)  op(e1, e1) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | |   (8127)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | BETA: splitting (8127) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | |   (8128)  all_56_0 = e0 & op(e3, e3) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | ALPHA: (8128) implies:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | |   (8129)  op(e3, e3) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8057), (8129), (function-axioms) are
% 148.96/21.26  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | |   (8130)  all_56_1 = e0 & op(e3, e2) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | ALPHA: (8130) implies:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | |   (8131)  all_56_1 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | |   (8132)  op(e3, e2) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | |   (8133)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8133) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |   (8134)  all_56_0 = e0 & op(e3, e3) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8134) implies:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |   (8135)  op(e3, e3) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8057), (8135), (function-axioms) are
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |   (8136)  all_56_2 = e0 & op(e2, e3) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8136) implies:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |   (8137)  all_56_2 = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | |   (8138)  op(e2, e3) = e0
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |   (8139)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8139) gives:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8140)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8140) implies:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8141)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = all_57_12 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (163), (164),
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            (166), (220), (225), (226), (227), (7908), (7916),
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            (8077), (8124), (8131), (8141), (function-axioms)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #125.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8142)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8142) implies:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |   (8143)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |               = e2) & op(e3, e3) = all_57_10 &
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (8057), (8132), (8143),
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | |            #1030.
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.26  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |   (8144)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8144) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8145)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8145) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8146)  op(e1, e1) = e1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8126), (8146), (function-axioms) are
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8147)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8147) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8148)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8148) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8149)  all_57_13 = e1 & op(e1, e0) = e1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8149) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8150)  op(e1, e0) = e1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (159), (8150) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8151)  all_52_14 = e1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (166), (8138) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8152)  all_52_1 = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (169), (8132) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8153)  all_52_4 = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (8152) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8154)   ~ (all_52_13 = e0)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (8151) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8155)   ~ (all_52_2 = e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (132), (8153) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8156)   ~ (all_52_12 = e0)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (8151) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8157)   ~ (all_52_12 = e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (8151) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8158)   ~ (all_52_13 = e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (8159)   ~ (all_50_2 = e0)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8122), (8159) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (8160)  $false
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8160) is inconsistent.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (8161)  ( ~ (all_50_0 = e3) & op(all_50_1, e1) = all_50_0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = all_50_1 & $i(all_50_0) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_50_1)) | ( ~ (all_50_1 = e2) & op(e1, e0)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_50_1 & $i(all_50_1))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8161) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8162)   ~ (all_50_0 = e3) & op(all_50_1, e1) = all_50_0 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_50_1 & $i(all_50_0) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8162) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8163)  op(e1, e0) = all_50_1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (112), (119), (162), (163), (168), (196),
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (200), (211), (229), (230), (231), (235), (259),
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (7911), (8051), (8057), (8076), (8077),
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (8081), (8131), (8137), (8150), (8155), (8157),
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (8158), (8163), (function-axioms) are inconsistent
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #121.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8164)   ~ (all_50_1 = e2) & op(e1, e0) = all_50_1 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_50_1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8164) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8165)  op(e1, e0) = all_50_1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (112), (119), (162), (163), (168), (196),
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (200), (211), (229), (230), (231), (235), (259),
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (7911), (8051), (8057), (8076), (8077),
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (8081), (8131), (8137), (8150), (8155), (8157),
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            (8158), (8165), (function-axioms) are inconsistent
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #121.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8166)   ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8166) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8167)   ~ (all_57_14 = e0)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8168)  op(e1, e1) = all_57_14
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8126), (8167), (8168), (function-axioms) are
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1026.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |   (8169)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8169) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |   (8170)  all_56_6 = e0 & op(e1, e3) = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8170) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |   (8171)  op(e1, e3) = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |   (8172)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8172) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8173)  all_56_2 = e0 & op(e2, e3) = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8173) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8174)  all_56_2 = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8175)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8057), (8174), (8175),
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |            #1059.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |   (8176)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8176) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (8177)  all_56_6 = e1 & op(e1, e3) = e1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8177) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (8178)  op(e1, e3) = e1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (8171), (8178), (function-axioms) are
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1127.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (8179)  all_56_12 = e1 & op(e0, e3) = e1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8179) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |   (8180)  op(e0, e3) = e1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8051), (8132), (8180), (function-axioms) are
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #767.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8181)  all_56_3 = e0 & op(e2, e2) = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (225), (226),
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |            (227), (7908), (8131), (8181), (function-axioms)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #127.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |   (8182)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8182) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8183)  all_56_5 = e0 & op(e2, e1) = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8124), (8183), (function-axioms) are
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1144.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8184)  all_56_10 = e0 & op(e2, e0) = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (8077), (8184), (function-axioms) are
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #540.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |   (8185)  all_56_12 = e0 & op(e0, e3) = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8185) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |   (8186)  op(e0, e3) = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8073), (8186), (function-axioms) are
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | |   (8187)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | BETA: splitting (8187) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8188)  all_56_4 = e0 & op(e3, e1) = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8123), (8188), (function-axioms) are
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8189)  all_56_9 = e0 & op(e3, e0) = e0
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8076), (8189), (function-axioms) are
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | End of split
% 148.96/21.27  | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | |   (8190)  all_42_2 = e3
% 148.96/21.27  | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | COMBINE_EQS: (302), (8190) imply:
% 148.96/21.27  | | | | | | | | | | | | |   (8191)  all_10_2 = e3
% 148.96/21.27  | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | SIMP: (8191) implies:
% 148.96/21.27  | | | | | | | | | | | | |   (8192)  all_10_2 = e3
% 148.96/21.27  | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | REDUCE: (367), (8192) imply:
% 148.96/21.27  | | | | | | | | | | | | |   (8193)   ~ (all_52_11 = e3)
% 148.96/21.27  | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | REDUCE: (45), (8192) imply:
% 148.96/21.27  | | | | | | | | | | | | |   (8194)  op(e0, e0) = e3
% 148.96/21.27  | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | BETA: splitting (237) gives:
% 148.96/21.27  | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | |   (8195)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 148.96/21.27  | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 148.96/21.27  | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 148.96/21.27  | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 148.96/21.27  | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 148.96/21.27  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 148.96/21.27  | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 148.96/21.27  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.96/21.27  | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 148.96/21.27  | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 148.96/21.27  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.27  | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 148.96/21.27  | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 148.96/21.27  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 148.96/21.27  | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 148.96/21.27  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 148.96/21.27  | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | REF_CLOSE: (9), (7916), (8057), (8195), (function-axioms) are
% 148.96/21.27  | | | | | | | | | | | | | |            inconsistent by sub-proof #120.
% 148.96/21.27  | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | |   (8196)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 148.96/21.27  | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 148.96/21.27  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.27  | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.96/21.27  | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.27  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 148.96/21.27  | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 148.96/21.27  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 148.96/21.27  | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 148.96/21.27  | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 148.96/21.27  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.27  | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 148.96/21.27  | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 148.96/21.27  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 148.96/21.27  | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 148.96/21.27  | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 148.96/21.27  | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | BETA: splitting (8196) gives:
% 148.96/21.27  | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | |   (8197)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 148.96/21.27  | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 148.96/21.27  | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 148.96/21.27  | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 148.96/21.27  | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.27  | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 148.96/21.27  | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 148.96/21.27  | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 148.96/21.27  | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | ALPHA: (8197) implies:
% 148.96/21.27  | | | | | | | | | | | | | | |   (8198)  op(e1, e1) = e1
% 148.96/21.27  | | | | | | | | | | | | | | |   (8199)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15
% 148.96/21.27  | | | | | | | | | | | | | | |               = e1) & op(e0, e0) = all_57_15 &
% 148.96/21.27  | | | | | | | | | | | | | | |             $i(all_57_15))
% 148.96/21.27  | | | | | | | | | | | | | | |   (8200)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 148.96/21.27  | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 148.96/21.27  | | | | | | | | | | | | | | |             $i(all_57_12))
% 148.96/21.27  | | | | | | | | | | | | | | |   (8201)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 148.96/21.27  | | | | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 148.96/21.27  | | | | | | | | | | | | | | |             $i(all_57_10))
% 148.96/21.27  | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | |   (8202)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 148.96/21.27  | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 148.96/21.27  | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | BETA: splitting (8202) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | |   (8203)  all_56_6 = e3 & op(e1, e3) = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | ALPHA: (8203) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | |   (8204)  all_56_6 = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | |   (8205)  op(e1, e3) = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | |   (8206)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | BETA: splitting (8206) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8207)  all_56_4 = e3 & op(e3, e1) = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | ALPHA: (8207) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8208)  op(e3, e1) = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (8198) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8209)  all_4_2 = e1
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (8205) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8210)  all_52_2 = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (8208) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8211)  all_52_8 = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | REDUCE: (142), (8210) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8212)   ~ (all_52_6 = e3)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | REDUCE: (359), (8209) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8213)   ~ (all_52_6 = e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | REDUCE: (122), (8211) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8214)   ~ (all_52_9 = e3)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | REDUCE: (120), (8211) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8215)   ~ (all_52_11 = e3)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | REDUCE: (119), (8211) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8216)   ~ (all_52_12 = e3)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | SIMP: (8216) implies:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8217)   ~ (all_52_12 = e3)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | REDUCE: (364), (8209) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8218)   ~ (all_52_11 = e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | REDUCE: (366), (8209) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8219)   ~ (all_52_14 = e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | REDUCE: (7918), (8209) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8220)   ~ (e3 = e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | REDUCE: (371), (8209) imply:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | |   (8221)   ~ (e2 = e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |   (8222)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8222) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |   (8223)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8223) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |   (8224)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (8055), (8224), (function-axioms) are
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |   (8225)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8225) gives:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 148.96/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8226)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8226) implies:
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8227)  op(e1, e3) = e1
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8205), (8227), (function-axioms) are
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #119.
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8228)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8228) implies:
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |   (8229)  op(e1, e3) = e1
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8205), (8229), (function-axioms) are
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #119.
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |   (8230)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.15/21.27  | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8230) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |   (8231)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (169), (7907), (8198), (8231),
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |            #721.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |   (8232)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8232) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |   (8233)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8233) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |   (8234)  op(e1, e2) = e1
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (8213), (8234), (function-axioms) are
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |   (8235)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8194), (8200), (8235), (function-axioms) are
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #458.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |   (8236)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8236) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |   (8237)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (8194), (8201), (8217), (8237),
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |            #455.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |   (8238)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8238) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |   (8239)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8057), (8239), (function-axioms) are
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |   (8240)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8240) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |   (8241)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8241) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |   (8242)  op(e1, e1) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8198), (8242), (function-axioms) are
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |   (8243)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8243) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |   (8244)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8244) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |   (8245)  op(e1, e0) = e1
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8219), (8245), (function-axioms) are
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |   (8246)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8246) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |   (8247)  op(e0, e0) = all_57_15
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |   (8248)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (8194), (8247)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | |   (8249)  all_57_15 = e3
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8248) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | |   (8250)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8250) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8251)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8251) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8252)   ~ (all_57_15 = e3)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8194), (8247), (8252), (function-axioms) are
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1019.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8253)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8253) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8254)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_1)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8254) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8255)   ~ (all_57_15 = e3)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8194), (8247), (8255), (function-axioms) are
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1019.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8256)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_3)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8256) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8257)   ~ (all_57_15 = e2)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8258)   ~ (all_57_3 = e3)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8259)  op(e0, e2) = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8260)  op(e3, e2) = all_57_3
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (157), (8259) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8261)  all_52_7 = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_3, e2, e3, simplifying with (169), (8260)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8262)  all_57_3 = all_52_4
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (8261) imply:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8263)   ~ (all_52_3 = e0)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (8261) imply:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8264)   ~ (all_52_4 = e0)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (8261) imply:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8265)   ~ (all_52_6 = e0)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (8261) imply:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8266)   ~ (all_52_11 = e0)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8266) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8267)   ~ (all_52_11 = e0)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7909), (8261) imply:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8268)   ~ (e3 = e0)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8269)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8269) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8270)  all_56_1 = e1 & op(e3, e2) = e1
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8270) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8271)  op(e3, e2) = e1
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8272)  all_54_14 = e3
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (8193), (8272) are inconsistent by
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #903.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8273)   ~ (all_54_14 = e3)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8274)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8274) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8275)  all_54_14 = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (8275) imply:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8276)  all_52_11 = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8276) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8277)  all_52_11 = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (8277) imply:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8278)   ~ (all_52_9 = e2)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8193), (8277) imply:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8279)   ~ (e3 = e2)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (8277) imply:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8280)  op(e0, e1) = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8281)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (7916), (8055), (8281),
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #118.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8282)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8282) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8283)  all_56_5 = e2 & op(e2, e1) = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8283) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8284)  op(e2, e1) = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8278), (8284), (function-axioms) are
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8285)  all_56_10 = e2 & op(e2, e0) = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8285) implies:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8286)  op(e2, e0) = e2
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.28  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8287)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8287) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8288)  all_56_6 = e2 & op(e1, e3) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8288) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8289)  all_56_6 = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230), (234),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8057), (8289), (function-axioms) are inconsistent
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1050.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8290)  all_56_7 = e2 & op(e1, e2) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8290) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8291)  all_56_7 = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8292)  op(e1, e2) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8293)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8293) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8294)  all_56_0 = e0 & op(e3, e3) = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8294) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8295)  op(e3, e3) = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (161), (163),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (169), (209), (220), (221), (222),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (229), (230),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (7907), (7908), (7910),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8055), (8194), (8204), (8205), (8208), (8213),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8219), (8264), (8286), (8291), (8292), (8295),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #116.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8296)  all_56_1 = e0 & op(e3, e2) = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8264), (8296), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1013.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8297)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8297) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8298)  all_56_4 = e0 & op(e3, e1) = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8298) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8299)  op(e3, e1) = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8208), (8299), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #663.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8300)  all_56_9 = e0 & op(e3, e0) = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8300) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8301)  all_56_9 = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8302)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8302) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8303)  all_56_9 = e1 & op(e3, e0) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8301), (8303) are inconsistent by sub-proof
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #616.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8304)  all_56_10 = e1 & op(e2, e0) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8304) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8305)  op(e2, e0) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (8286), (8305), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #904.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8306)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8306) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8307)  all_56_11 = e1 & op(e1, e0) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8307) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8308)  op(e1, e0) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8219), (8308), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8309)  all_56_15 = e1 & op(e0, e0) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8309) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8310)  op(e0, e0) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8199), (8280), (8310), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #422.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8311)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8311) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8312)  all_56_8 = e2 & op(e1, e1) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8312) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8313)  op(e1, e1) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (8198), (8313), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8314)  all_56_11 = e2 & op(e1, e0) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8314) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8315)  all_56_11 = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (161), (212), (8060), (8198), (8265),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8271), (8315), (function-axioms) are inconsistent
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1015.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8316)  all_54_14 = e1 | all_54_14 = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (157), (246), (8218), (8259), (8316),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #752.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8317)  all_56_3 = e1 & op(e2, e2) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8317) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8318)  op(e2, e2) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7916), (8318), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8319)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8319) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8320)  all_56_7 = e1 & op(e1, e2) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8320) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8321)  op(e1, e2) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (8213), (8321), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8322)  all_56_13 = e1 & op(e0, e2) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8322) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8323)  all_56_13 = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8324)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8324) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8325)  all_56_12 = e2 & op(e0, e3) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8325) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8326)  all_56_12 = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230), (234),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8057), (8326), (function-axioms) are inconsistent
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #781.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8327)  all_56_13 = e2 & op(e0, e2) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8323), (8327) are inconsistent by sub-proof
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #739.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8328)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8328) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8329)  all_56_14 = e2 & op(e0, e1) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8329) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8330)  op(e0, e1) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8331)  all_56_15 = e0 & op(e0, e0) = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8331) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8332)  op(e0, e0) = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8194), (8332), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8333)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8333) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8334)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8334) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8335)  all_56_12 = e0 & op(e0, e3) = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8335) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8336)  op(e0, e3) = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8263), (8336), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8337)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8323), (8330), (8337),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #634.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8338)  all_56_15 = e2 & op(e0, e0) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8338) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8339)  op(e0, e0) = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (158), (8198), (8200), (8201), (8247),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8248), (8263), (8339), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #115.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |   (8340)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (8198), (8200), (8201), (8340),
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | |            #454.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | |   (8341)  all_56_5 = e3 & op(e2, e1) = e3
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7910), (8341), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | |   (8342)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 149.15/21.29  | | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (212), (213),
% 149.15/21.29  | | | | | | | | | | | | | | | | | |            (214), (8193), (8204), (8342), (function-axioms)
% 149.15/21.29  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #606.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | |   (8343)  all_56_7 = e3 & op(e1, e2) = e3
% 149.15/21.29  | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (7908), (8343), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 149.15/21.29  | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | |   (8344)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 149.15/21.29  | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (163), (205),
% 149.15/21.29  | | | | | | | | | | | | | | | |            (209), (210), (7924), (8194), (8198), (8344),
% 149.15/21.29  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.29  | | | | | | | | | | | | | | | |            #500.
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | |   (8345)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.15/21.29  | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.15/21.29  | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.29  | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.15/21.29  | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.15/21.29  | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.15/21.29  | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.15/21.29  | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.15/21.29  | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | ALPHA: (8345) implies:
% 149.15/21.29  | | | | | | | | | | | | | | |   (8346)  op(e0, e0) = e0
% 149.15/21.29  | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | REF_CLOSE: (7), (8194), (8346), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 149.15/21.29  | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | End of split
% 149.15/21.29  | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | |   (8347)  all_24_2 = e2
% 149.15/21.29  | | | | | | | | | |   (8348)  ( ~ (all_24_0 = e3) & op(all_24_1, e0) = all_24_0
% 149.15/21.29  | | | | | | | | | |             & op(e0, e2) = all_24_1 & $i(all_24_0) &
% 149.15/21.29  | | | | | | | | | |             $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0, e2)
% 149.15/21.29  | | | | | | | | | |             = all_24_1 & $i(all_24_1))
% 149.15/21.29  | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | COMBINE_EQS: (318), (8347) imply:
% 149.15/21.29  | | | | | | | | | |   (8349)  all_10_2 = e2
% 149.15/21.29  | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | COMBINE_EQS: (306), (8349) imply:
% 149.15/21.29  | | | | | | | | | |   (8350)  all_40_2 = e2
% 149.15/21.29  | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | REDUCE: (349), (8349) imply:
% 149.15/21.29  | | | | | | | | | |   (8351)   ~ (all_52_3 = e2)
% 149.15/21.29  | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | REDUCE: (367), (8349) imply:
% 149.15/21.29  | | | | | | | | | |   (8352)   ~ (all_52_11 = e2)
% 149.15/21.29  | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | REDUCE: (369), (8349) imply:
% 149.15/21.29  | | | | | | | | | |   (8353)   ~ (all_52_13 = e2)
% 149.15/21.29  | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | REDUCE: (370), (8349) imply:
% 149.15/21.29  | | | | | | | | | |   (8354)   ~ (all_52_14 = e2)
% 149.15/21.29  | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | REDUCE: (45), (8349) imply:
% 149.15/21.29  | | | | | | | | | |   (8355)  op(e0, e0) = e2
% 149.15/21.29  | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | BETA: splitting (84) gives:
% 149.15/21.29  | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | |   (8356)   ~ (all_36_2 = e2)
% 149.15/21.29  | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | REDUCE: (304), (8356) imply:
% 149.15/21.29  | | | | | | | | | | |   (8357)   ~ (all_14_2 = e2)
% 149.15/21.29  | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | BETA: splitting (203) gives:
% 149.15/21.29  | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | |   (8358)  all_54_0 = e3
% 149.15/21.29  | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | COMBINE_EQS: (278), (8358) imply:
% 149.15/21.29  | | | | | | | | | | | |   (8359)  all_14_2 = e3
% 149.15/21.29  | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | SIMP: (8359) implies:
% 149.15/21.29  | | | | | | | | | | | |   (8360)  all_14_2 = e3
% 149.15/21.29  | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | REDUCE: (344), (8360) imply:
% 149.15/21.29  | | | | | | | | | | | |   (8361)   ~ (all_52_8 = e3)
% 149.15/21.29  | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | REDUCE: (346), (8360) imply:
% 149.15/21.29  | | | | | | | | | | | |   (8362)   ~ (all_52_12 = e3)
% 149.15/21.29  | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | REDUCE: (51), (8360) imply:
% 149.15/21.29  | | | | | | | | | | | |   (8363)  op(e3, e3) = e3
% 149.15/21.29  | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | BETA: splitting (219) gives:
% 149.15/21.29  | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | |   (8364)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 149.15/21.29  | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 149.15/21.29  | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | REF_CLOSE: (164), (168), (7910), (8361), (8364),
% 149.15/21.29  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.29  | | | | | | | | | | | | |            #369.
% 149.15/21.29  | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | |   (8365)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 149.15/21.29  | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 149.15/21.29  | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | BETA: splitting (8365) gives:
% 149.15/21.29  | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | |   (8366)  all_56_8 = e3 & op(e1, e1) = e3
% 149.15/21.29  | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | ALPHA: (8366) implies:
% 149.15/21.29  | | | | | | | | | | | | | |   (8367)  op(e1, e1) = e3
% 149.15/21.29  | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | REF_CLOSE: (36), (7918), (8367), (function-axioms) are
% 149.15/21.29  | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 149.15/21.29  | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | |   (8368)  all_56_14 = e3 & op(e0, e1) = e3
% 149.15/21.29  | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | ALPHA: (8368) implies:
% 149.15/21.29  | | | | | | | | | | | | | |   (8369)  all_56_14 = e3
% 149.15/21.29  | | | | | | | | | | | | | |   (8370)  op(e0, e1) = e3
% 149.15/21.29  | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 149.15/21.29  | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | |   (8371)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 149.15/21.29  | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 149.15/21.29  | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (7911), (8362), (8371),
% 149.15/21.29  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.29  | | | | | | | | | | | | | | |            #113.
% 149.15/21.29  | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | |   (8372)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 149.15/21.29  | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 149.15/21.29  | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | BETA: splitting (8372) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | |   (8373)  all_56_11 = e3 & op(e1, e0) = e3
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | ALPHA: (8373) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | |   (8374)  op(e1, e0) = e3
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 149.15/21.29  | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (156), (8370) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | |   (8375)  all_52_11 = e3
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 149.15/21.29  | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (159), (8374) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | |   (8376)  all_52_14 = e3
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | REDUCE: (140), (8376) imply:
% 149.15/21.29  | | | | | | | | | | | | | | | |   (8377)   ~ (all_52_2 = e3)
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | REDUCE: (138), (8375) imply:
% 149.15/21.29  | | | | | | | | | | | | | | | |   (8378)   ~ (all_52_3 = e3)
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | REDUCE: (366), (8376) imply:
% 149.15/21.29  | | | | | | | | | | | | | | | |   (8379)   ~ (all_4_2 = e3)
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | |   (8380)   ~ (all_40_2 = e2)
% 149.15/21.29  | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | REDUCE: (8350), (8380) imply:
% 149.15/21.29  | | | | | | | | | | | | | | | | |   (8381)  $false
% 149.15/21.29  | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | CLOSE: (8381) is inconsistent.
% 149.15/21.29  | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | |   (8382)  ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0
% 149.15/21.29  | | | | | | | | | | | | | | | | |             & op(e0, e2) = all_40_1 & $i(all_40_0) &
% 149.15/21.29  | | | | | | | | | | | | | | | | |             $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e0, e2)
% 149.15/21.29  | | | | | | | | | | | | | | | | |             = all_40_1 & $i(all_40_1))
% 149.15/21.29  | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | |   (8383)   ~ (all_48_2 = e0)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | REDUCE: (298), (8383) imply:
% 149.15/21.29  | | | | | | | | | | | | | | | | | |   (8384)   ~ (all_4_2 = e0)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | |   (8385)  all_54_10 = e3
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (7918), (8385) are inconsistent by
% 149.15/21.29  | | | | | | | | | | | | | | | | | | |            sub-proof #1173.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | |   (8386)   ~ (all_54_10 = e3)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | |   (8387)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | BETA: splitting (8387) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | |   (8388)  all_54_10 = e2
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (8388) are inconsistent by sub-proof
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | |            #1168.
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | |   (8389)   ~ (all_54_10 = e2)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | |   (8390)  all_54_10 = e1 | all_54_10 = e0
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8390) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | |   (8391)  all_54_10 = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (8391) imply:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | |   (8392)  all_4_2 = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | SIMP: (8392) implies:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | |   (8393)  all_4_2 = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (8393) imply:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | |   (8394)   ~ (all_52_2 = e1)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (8393) imply:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | |   (8395)   ~ (all_52_6 = e1)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | REDUCE: (7918), (8393) imply:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | |   (8396)   ~ (e3 = e1)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (8393) imply:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | |   (8397)   ~ (e2 = e1)
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (8393) imply:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | |   (8398)  op(e1, e1) = e1
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.29  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |   (8399)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8399) gives:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |   (8400)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (162), (8355), (8394), (8398), (8400),
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |            #722.
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |   (8401)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8401) gives:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |   (8402)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (169), (7907), (8398), (8402),
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |            #721.
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |   (8403)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8403) gives:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (8404)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8404) implies:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (8405)  op(e3, e3) = e2
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8363), (8405), (function-axioms) are
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (8406)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8406) gives:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8407)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8407) implies:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8408)  op(e1, e2) = e1
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (8395), (8408), (function-axioms) are
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8409)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8409) implies:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8410)  op(e2, e2) = e1
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7916), (8410), (function-axioms) are
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |   (8411)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8411) gives:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |   (8412)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8412) gives:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |   (8413)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (8361), (8363), (8413),
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |            #860.
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |   (8414)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (8355), (8362), (8414),
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |            #976.
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |   (8415)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8415) gives:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |   (8416)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8363), (8416), (function-axioms) are
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |   (8417)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8417) gives:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (8418)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8418) implies:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (8419)  op(e2, e0) = e2
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (8353), (8419), (function-axioms) are
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |   (8420)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8420) gives:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8421)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8421) implies:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8422)  op(e2, e2) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (36), (159), (161), (162), (163), (167),
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (168), (169), (238), (334), (348), (359), (366),
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (371), (7907), (7918), (8353), (8355), (8361),
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (8362), (8363), (8384), (8390), (8422),
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |            #631.
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8423)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8423) implies:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8424)  op(e0, e0) = all_57_15
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8425)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8425) gives:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8426)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8426) gives:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8427)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8427) implies:
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8428)  all_57_12 = e3
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8429)   ~ (all_57_15 = e3)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8430)   ~ (all_57_0 = e2)
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8431)  op(e0, e3) = e0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8432)  op(e2, e3) = all_57_0
% 149.15/21.30  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (90),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (116), (117), (120), (138), (139), (144), (145),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (156), (157), (158), (159), (161), (162),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (166), (167), (168), (169), (189),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (205), (206), (207), (209), (211), (212),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (218), (219), (228), (229), (230),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (234), (235), (237), (238), (246),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (268), (348), (364), (366), (370), (371), (7906),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7907), (7908), (7910), (7911), (7916), (7918),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8348), (8350), (8351), (8352), (8354), (8355),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8361), (8363), (8369), (8370), (8374), (8378),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8382), (8425), (8428), (8429), (8430), (8431),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8432), (function-axioms) are inconsistent by
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #105.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8433)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8355), (8398), (8424), (8433),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #718.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8434)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8434) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8435)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8435) implies:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8436)  op(e1, e1) = e2
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (8398), (8436), (function-axioms) are
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8437)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (7916), (8370), (8437),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #103.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | |   (8438)  all_54_10 = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8384), (8438) are inconsistent by
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | |   (8439)  all_48_2 = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (8439) imply:
% 149.15/21.31  | | | | | | | | | | | | | | | | | |   (8440)  all_4_2 = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | REDUCE: (348), (8440) imply:
% 149.15/21.31  | | | | | | | | | | | | | | | | | |   (8441)   ~ (all_52_2 = e0)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | REDUCE: (361), (8440) imply:
% 149.15/21.31  | | | | | | | | | | | | | | | | | |   (8442)   ~ (all_52_8 = e0)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | REDUCE: (362), (8440) imply:
% 149.15/21.31  | | | | | | | | | | | | | | | | | |   (8443)   ~ (all_52_9 = e0)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | REDUCE: (7918), (8440) imply:
% 149.15/21.31  | | | | | | | | | | | | | | | | | |   (8444)   ~ (e3 = e0)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | REDUCE: (371), (8440) imply:
% 149.15/21.31  | | | | | | | | | | | | | | | | | |   (8445)   ~ (e2 = e0)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | REDUCE: (36), (8440) imply:
% 149.15/21.31  | | | | | | | | | | | | | | | | | |   (8446)  op(e1, e1) = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |   (8447)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | BETA: splitting (8447) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |   (8448)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | ALPHA: (8448) implies:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |   (8449)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |               = e3) & op(e0, e0) = all_57_15 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |   (8450)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = all_57_14 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |   (8451)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = all_57_12 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8451) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | |   (8452)  all_57_0 = e2 & op(e2, e3) = e2
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8452) implies:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | |   (8453)  op(e2, e3) = e2
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |   (8454)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8454) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |   (8455)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8455) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |   (8456)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8449), (8450), (8456), (function-axioms) are
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #814.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |   (8457)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8449), (8451), (8457), (function-axioms) are
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |   (8458)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8458) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |   (8459)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (169), (7907), (8446), (8459),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            #412.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |   (8460)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8460) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (8461)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8461) implies:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (8462)  op(e3, e3) = e2
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8363), (8462), (function-axioms) are
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |   (8463)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8463) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8464)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8464) implies:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8465)  op(e1, e2) = e1
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (161), (8465) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8466)  all_52_6 = e1
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (166), (8453) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8467)  all_52_1 = e2
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (8467) imply:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8468)   ~ (all_52_2 = e2)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8468) implies:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8469)   ~ (all_52_2 = e2)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (8466) imply:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8470)   ~ (all_52_2 = e1)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (195), (258), (8377), (8441), (8469), (8470) are
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #102.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8471)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8471) implies:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8472)  op(e2, e2) = e1
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7916), (8472), (function-axioms) are
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |   (8473)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8473) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |   (8474)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8474) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |   (8475)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (8361), (8363), (8475),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            #860.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |   (8476)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (8355), (8362), (8476),
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            #976.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |   (8477)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8477) gives:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |   (8478)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8363), (8478), (function-axioms) are
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.31  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |   (8479)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8479) gives:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (8480)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8480) implies:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (8481)  op(e2, e0) = e2
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (8353), (8481), (function-axioms) are
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |   (8482)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8482) gives:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8483)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8483) implies:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8484)   ~ (all_57_14 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8485)  op(e1, e1) = all_57_14
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8446), (8484), (8485), (function-axioms) are
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1026.
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8486)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8486) implies:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8487)  op(e0, e0) = all_57_15
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8488)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8488) gives:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8489)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8489) gives:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8490)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8490) implies:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8491)  all_57_12 = e3
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8492)   ~ (all_57_15 = e3)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8493)   ~ (all_57_0 = e2)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8494)  op(e0, e3) = e0
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8495)  op(e2, e3) = all_57_0
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (90),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (116), (117), (120), (138), (139), (144), (145),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (147), (156), (157), (158), (159), (161), (162),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (163), (164), (166), (167), (168), (169), (189),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (199), (205), (206), (207), (209), (211), (212),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (215), (218), (219), (228), (229), (230),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (232), (234), (235), (237), (238), (246),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (268), (348), (364), (366), (370), (371), (7906),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7907), (7908), (7910), (7911), (7916), (7918),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8348), (8350), (8351), (8352), (8354), (8355),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8361), (8363), (8369), (8370), (8374), (8378),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8382), (8488), (8491), (8492), (8493), (8494),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8495), (function-axioms) are inconsistent by
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #105.
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8496)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8355), (8450), (8487), (8496), (function-axioms)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #628.
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8497)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8497) gives:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8498)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_4)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8498) implies:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8499)  op(e1, e1) = e2
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8446), (8499), (function-axioms) are
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8500)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_7))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (7916), (8370), (8500),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #103.
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | |   (8501)   ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8501) implies:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | |   (8502)   ~ (all_57_12 = e3)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | |   (8503)  op(e2, e2) = all_57_12
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7916), (8502), (8503), (function-axioms) are
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #126.
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |   (8504)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | ALPHA: (8504) implies:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |   (8505)  op(e2, e2) = e2
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7916), (8505), (function-axioms) are
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |   (8506)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | BETA: splitting (8506) gives:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |   (8507)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | ALPHA: (8507) implies:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |   (8508)  op(e1, e1) = e1
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (164), (168), (216), (8369), (8442),
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |            (8443), (8508), (function-axioms) are inconsistent
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |            by sub-proof #124.
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |   (8509)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | ALPHA: (8509) implies:
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |   (8510)  op(e0, e0) = e0
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8355), (8510), (function-axioms) are
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | |   (8511)  all_56_15 = e3 & op(e0, e0) = e3
% 149.15/21.32  | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | ALPHA: (8511) implies:
% 149.15/21.32  | | | | | | | | | | | | | | | |   (8512)  op(e0, e0) = e3
% 149.15/21.32  | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8355), (8512), (function-axioms) are
% 149.15/21.32  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 149.15/21.32  | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | |   (8513)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | REF_CLOSE: (278), (7920), (7922), (8357), (8513) are
% 149.15/21.32  | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | |   (8514)  all_36_2 = e2
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | COMBINE_EQS: (304), (8514) imply:
% 149.15/21.32  | | | | | | | | | | |   (8515)  all_14_2 = e2
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | SIMP: (8515) implies:
% 149.15/21.32  | | | | | | | | | | |   (8516)  all_14_2 = e2
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | REDUCE: (336), (8516) imply:
% 149.15/21.32  | | | | | | | | | | |   (8517)   ~ (all_52_1 = e2)
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | REDUCE: (51), (8516) imply:
% 149.15/21.32  | | | | | | | | | | |   (8518)  op(e3, e3) = e2
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | BETA: splitting (237) gives:
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | |   (8519)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.15/21.32  | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.15/21.32  | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.15/21.32  | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.15/21.32  | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.15/21.32  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.15/21.32  | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.15/21.32  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.15/21.32  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.15/21.32  | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.15/21.32  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.32  | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.15/21.32  | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.15/21.32  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.15/21.32  | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.15/21.32  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | REF_CLOSE: (9), (7916), (8518), (8519), (function-axioms) are
% 149.15/21.32  | | | | | | | | | | | |            inconsistent by sub-proof #120.
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | |   (8520)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.15/21.32  | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.15/21.32  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.32  | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.15/21.32  | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.32  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.15/21.32  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.15/21.32  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.15/21.32  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.15/21.32  | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.15/21.32  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.32  | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.15/21.32  | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.15/21.32  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.15/21.32  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.15/21.32  | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | BETA: splitting (8520) gives:
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | |   (8521)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.15/21.32  | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.15/21.32  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.32  | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.15/21.32  | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.32  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.15/21.32  | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.15/21.32  | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | ALPHA: (8521) implies:
% 149.15/21.32  | | | | | | | | | | | | |   (8522)  op(e1, e1) = e1
% 149.15/21.32  | | | | | | | | | | | | |   (8523)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 149.15/21.32  | | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.32  | | | | | | | | | | | | |             $i(all_57_10))
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (90),
% 149.15/21.32  | | | | | | | | | | | | |            (116), (117), (120), (138), (139), (144), (145),
% 149.15/21.32  | | | | | | | | | | | | |            (147), (156), (157), (158), (159), (161), (162),
% 149.15/21.32  | | | | | | | | | | | | |            (163), (164), (166), (167), (168), (169), (189),
% 149.15/21.32  | | | | | | | | | | | | |            (199), (205), (206), (207), (209), (211), (212),
% 149.15/21.32  | | | | | | | | | | | | |            (214), (215), (218), (219), (228), (229), (230),
% 149.15/21.32  | | | | | | | | | | | | |            (231), (232), (234), (235), (237), (238), (246),
% 149.15/21.32  | | | | | | | | | | | | |            (268), (348), (364), (366), (370), (371), (7906),
% 149.15/21.32  | | | | | | | | | | | | |            (7907), (7908), (7910), (7911), (7916), (7918),
% 149.15/21.32  | | | | | | | | | | | | |            (8348), (8350), (8351), (8352), (8354), (8355),
% 149.15/21.32  | | | | | | | | | | | | |            (8517), (8518), (8522), (8523), (function-axioms)
% 149.15/21.32  | | | | | | | | | | | | |            are inconsistent by sub-proof #109.
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | |   (8524)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.15/21.32  | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.15/21.32  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.32  | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.15/21.32  | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.15/21.32  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.15/21.32  | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.15/21.32  | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | ALPHA: (8524) implies:
% 149.15/21.32  | | | | | | | | | | | | |   (8525)  op(e0, e0) = e0
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | REF_CLOSE: (5), (8355), (8525), (function-axioms) are
% 149.15/21.32  | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | End of split
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | |   (8526)  all_22_2 = e1
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | COMBINE_EQS: (320), (8526) imply:
% 149.15/21.32  | | | | | | | | |   (8527)  all_14_2 = e1
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | SIMP: (8527) implies:
% 149.15/21.32  | | | | | | | | |   (8528)  all_14_2 = e1
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | REDUCE: (336), (8528) imply:
% 149.15/21.32  | | | | | | | | |   (8529)   ~ (all_52_1 = e1)
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | REDUCE: (338), (8528) imply:
% 149.15/21.32  | | | | | | | | |   (8530)   ~ (all_52_2 = e1)
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | REDUCE: (340), (8528) imply:
% 149.15/21.32  | | | | | | | | |   (8531)   ~ (all_52_3 = e1)
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | REDUCE: (342), (8528) imply:
% 149.15/21.32  | | | | | | | | |   (8532)   ~ (all_52_4 = e1)
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | REDUCE: (344), (8528) imply:
% 149.15/21.32  | | | | | | | | |   (8533)   ~ (all_52_8 = e1)
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | REDUCE: (346), (8528) imply:
% 149.15/21.32  | | | | | | | | |   (8534)   ~ (all_52_12 = e1)
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | REDUCE: (51), (8528) imply:
% 149.15/21.32  | | | | | | | | |   (8535)  op(e3, e3) = e1
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | BETA: splitting (70) gives:
% 149.15/21.32  | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | |   (8536)   ~ (all_26_2 = e3)
% 149.15/21.32  | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | REDUCE: (7905), (8536) imply:
% 149.15/21.32  | | | | | | | | | |   (8537)  $false
% 149.15/21.32  | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | CLOSE: (8537) is inconsistent.
% 149.15/21.32  | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | |   (8538)  ( ~ (all_26_0 = e0) & op(all_26_1, e2) = all_26_0
% 149.15/21.32  | | | | | | | | | |             & op(e2, e3) = all_26_1 & $i(all_26_0) &
% 149.15/21.32  | | | | | | | | | |             $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e2, e3)
% 149.15/21.32  | | | | | | | | | |             = all_26_1 & $i(all_26_1))
% 149.15/21.32  | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | BETA: splitting (67) gives:
% 149.15/21.32  | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | |   (8539)   ~ (all_24_2 = e2)
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | REDUCE: (318), (8539) imply:
% 149.15/21.32  | | | | | | | | | | |   (8540)   ~ (all_10_2 = e2)
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | BETA: splitting (93) gives:
% 149.15/21.32  | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | |   (8541)   ~ (all_42_2 = e3)
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | REDUCE: (302), (8541) imply:
% 149.15/21.32  | | | | | | | | | | | |   (8542)   ~ (all_10_2 = e3)
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | BETA: splitting (188) gives:
% 149.15/21.32  | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | |   (8543)  all_54_15 = e3
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | REF_CLOSE: (245), (8542), (8543) are inconsistent by
% 149.15/21.32  | | | | | | | | | | | | |            sub-proof #1049.
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | |   (8544)   ~ (all_54_15 = e3)
% 149.15/21.32  | | | | | | | | | | | | |   (8545)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | BETA: splitting (8545) gives:
% 149.15/21.32  | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | |   (8546)  all_54_15 = e2
% 149.15/21.32  | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | REF_CLOSE: (245), (8540), (8546) are inconsistent by
% 149.15/21.32  | | | | | | | | | | | | | |            sub-proof #1048.
% 149.15/21.32  | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | |   (8547)   ~ (all_54_15 = e2)
% 149.15/21.32  | | | | | | | | | | | | | |   (8548)  all_54_15 = e1 | all_54_15 = e0
% 149.15/21.32  | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | BETA: splitting (8548) gives:
% 149.15/21.32  | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | |   (8549)  all_54_15 = e1
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | REF_CLOSE: (245), (7919), (8549) are inconsistent by
% 149.15/21.32  | | | | | | | | | | | | | | |            sub-proof #1047.
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | Case 2:
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | |   (8550)  all_54_15 = e0
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | COMBINE_EQS: (245), (8550) imply:
% 149.15/21.32  | | | | | | | | | | | | | | |   (8551)  all_10_2 = e0
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | SIMP: (8551) implies:
% 149.15/21.32  | | | | | | | | | | | | | | |   (8552)  all_10_2 = e0
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | REDUCE: (349), (8552) imply:
% 149.15/21.32  | | | | | | | | | | | | | | |   (8553)   ~ (all_52_3 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | REDUCE: (360), (8552) imply:
% 149.15/21.32  | | | | | | | | | | | | | | |   (8554)   ~ (all_52_7 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | REDUCE: (367), (8552) imply:
% 149.15/21.32  | | | | | | | | | | | | | | |   (8555)   ~ (all_52_11 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | REDUCE: (368), (8552) imply:
% 149.15/21.32  | | | | | | | | | | | | | | |   (8556)   ~ (all_52_12 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | REDUCE: (369), (8552) imply:
% 149.15/21.32  | | | | | | | | | | | | | | |   (8557)   ~ (all_52_13 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | REDUCE: (8542), (8552) imply:
% 149.15/21.32  | | | | | | | | | | | | | | |   (8558)   ~ (e3 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | REDUCE: (8540), (8552) imply:
% 149.15/21.32  | | | | | | | | | | | | | | |   (8559)   ~ (e2 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | REDUCE: (7919), (8552) imply:
% 149.15/21.32  | | | | | | | | | | | | | | |   (8560)   ~ (e1 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | REDUCE: (45), (8552) imply:
% 149.15/21.32  | | | | | | | | | | | | | | |   (8561)  op(e0, e0) = e0
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | BETA: splitting (102) gives:
% 149.15/21.32  | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | |   (8562)   ~ (all_48_2 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | REDUCE: (298), (8562) imply:
% 149.15/21.32  | | | | | | | | | | | | | | | |   (8563)   ~ (all_4_2 = e0)
% 149.15/21.32  | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 149.15/21.32  | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.32  | | | | | | | | | | | | | | | | | 
% 149.15/21.32  | | | | | | | | | | | | | | | | |   (8564)  all_54_10 = e3
% 149.15/21.33  | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (7918), (8564) are inconsistent by
% 149.15/21.33  | | | | | | | | | | | | | | | | |            sub-proof #1173.
% 149.15/21.33  | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | |   (8565)   ~ (all_54_10 = e3)
% 149.15/21.33  | | | | | | | | | | | | | | | | |   (8566)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | |   (8567)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.15/21.33  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.15/21.33  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.15/21.33  | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | BETA: splitting (8567) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |   (8568)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | BETA: splitting (8568) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |   (8569)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (7918), (8561), (8569),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |            #865.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |   (8570)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (162), (8530), (8561), (8570),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |            #1045.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |   (8571)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | BETA: splitting (8571) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |   (8572)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (169), (371), (7907), (8572),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |            #1086.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |   (8573)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (7916), (8535), (8561), (8573),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |            #101.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | |   (8574)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.15/21.33  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.15/21.33  | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.15/21.33  | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.33  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | BETA: splitting (8574) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |   (8575)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | BETA: splitting (8575) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |   (8576)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8576) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |   (8577)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8577) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |   (8578)  op(e0, e0) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (116),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |            (140), (156), (159), (162), (163), (164), (166),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |            (193), (205), (210), (211), (221), (237), (238),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |            (334), (362), (366), (367), (371), (7916), (7918),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |            (8529), (8530), (8535), (8578), (function-axioms)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #99.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |   (8579)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8579) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |   (8580)  op(e2, e1) = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |   (8581)  op(e2, e2) = all_57_12
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8566) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | |   (8582)  all_54_10 = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (8582) are inconsistent by sub-proof
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | |            #1168.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | |   (8583)   ~ (all_54_10 = e2)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | |   (8584)  all_54_10 = e1 | all_54_10 = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8584) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | |   (8585)  all_54_10 = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (8585) imply:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | |   (8586)  all_4_2 = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8586) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | |   (8587)  all_4_2 = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (359), (8587) imply:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | |   (8588)   ~ (all_52_6 = e1)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (8587) imply:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | |   (8589)   ~ (all_52_9 = e1)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (8587) imply:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | |   (8590)   ~ (all_52_14 = e1)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7918), (8587) imply:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | |   (8591)   ~ (e3 = e1)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (8587) imply:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | |   (8592)   ~ (e2 = e1)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | |   (8593)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8593) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (8594)  all_56_9 = e1 & op(e3, e0) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8534), (8594), (function-axioms) are
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #970.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (8595)  all_56_10 = e1 & op(e2, e0) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8595) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (8596)  all_56_10 = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (8597)  op(e2, e0) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8598)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (169), (220),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (7910), (8532), (8596), (8598),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | |            #98.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8599)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8599) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8600)  all_56_7 = e1 & op(e1, e2) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8600) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8601)  op(e1, e2) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (8588), (8601), (function-axioms) are
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8602)  all_56_13 = e1 & op(e0, e2) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8602) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8603)  all_56_13 = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8604)  op(e0, e2) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e1,
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (157), (8604) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8605)  all_52_7 = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e2, simplifying with (163), (8597) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8606)  all_52_13 = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (164), (8580) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8607)  all_52_9 = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (7916), (8581)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8608)  all_57_12 = e3
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (8607) imply:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8609)   ~ (all_52_1 = e2)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7910), (8607) imply:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8610)   ~ (e3 = e2)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8611)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (166), (7916), (8609), (8611),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #118.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8612)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8612) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8613)  all_56_5 = e2 & op(e2, e1) = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8613) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8614)  all_56_5 = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8615)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8615) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8616)  all_56_2 = e0 & op(e2, e3) = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7904), (8538), (8604), (8616), (function-axioms)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #95.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8617)  all_56_3 = e0 & op(e2, e2) = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8617) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8618)  op(e2, e2) = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (161), (169), (227), (7907), (7908),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8603), (8618), (function-axioms) are inconsistent
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #210.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8619)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8619) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8620)  all_56_5 = e0 & op(e2, e1) = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8620) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8621)  all_56_5 = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8614), (8621) are inconsistent by sub-proof
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #509.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8622)  all_56_10 = e0 & op(e2, e0) = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (8557), (8622), (function-axioms) are
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #540.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8623)  all_56_10 = e2 & op(e2, e0) = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8623) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (8624)  op(e2, e0) = e2
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (8597), (8624), (function-axioms) are
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #904.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | |   (8625)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8625) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (8626)  all_56_11 = e1 & op(e1, e0) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8626) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (8627)  op(e1, e0) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8590), (8627), (function-axioms) are
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (8628)  all_56_15 = e1 & op(e0, e0) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8628) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |   (8629)  op(e0, e0) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (116),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (156), (159), (162), (163), (164), (166),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (205), (210), (211), (221), (237), (238),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (334), (362), (366), (367), (371), (7916), (7918),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |            (8529), (8530), (8535), (8629), (function-axioms)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #99.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | |   (8630)  all_54_10 = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8563), (8630) are inconsistent by
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |   (8631)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8631) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |   (8632)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8632) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |   (8633)  op(e0, e0) = e1
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (116),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |            (140), (156), (159), (162), (163), (164), (166),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |            (193), (205), (210), (211), (221), (237), (238),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |            (334), (362), (366), (367), (371), (7916), (7918),
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |            (8529), (8530), (8535), (8633), (function-axioms)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #99.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |   (8634)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8634) gives:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | |   (8635)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8635) implies:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | |   (8636)  op(e2, e2) = e0
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7916), (8636), (function-axioms) are
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.33  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |   (8637)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8637) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |   (8638)   ~ (all_57_13 = e1)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |   (8639)  op(e1, e1) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |   (8640)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7916), (8535), (8640),
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |            #100.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |   (8641)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8638), (8639), (8641), (function-axioms) are
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #958.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |   (8642)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | BETA: splitting (8642) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |   (8643)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8535), (8643), (function-axioms) are
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |   (8644)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8644) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |   (8645)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8645) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |   (8646)   ~ (all_57_13 = e1)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |   (8647)  op(e1, e1) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (237), (7916), (8535), (8646),
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |            (8647), (function-axioms) are inconsistent by
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |            sub-proof #94.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |   (8648)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8648) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |   (8649)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8649) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |   (8650)  op(e2, e2) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7916), (8650), (function-axioms) are
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |   (8651)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8651) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |   (8652)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8566) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |   (8653)  all_54_10 = e2
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (8653) are inconsistent by sub-proof
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |            #1168.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |   (8654)   ~ (all_54_10 = e2)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |   (8655)  all_54_10 = e1 | all_54_10 = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8655) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (8656)  all_54_10 = e1
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (8656) imply:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (8657)  all_4_2 = e1
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8657) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (8658)  all_4_2 = e1
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (8658) imply:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (8659)   ~ (e2 = e1)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (8658) imply:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (8660)  op(e1, e1) = e1
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (156), (157), (158), (8553), (8554),
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |            (8555), (8652), (8660), (function-axioms) are
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #764.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (8661)  all_54_10 = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8563), (8661) are inconsistent by
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | |   (8662)  all_48_2 = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | COMBINE_EQS: (298), (8662) imply:
% 149.15/21.34  | | | | | | | | | | | | | | | |   (8663)  all_4_2 = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | REDUCE: (361), (8663) imply:
% 149.15/21.34  | | | | | | | | | | | | | | | |   (8664)   ~ (all_52_8 = e0)
% 149.15/21.34  | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | REDUCE: (36), (8663) imply:
% 149.15/21.34  | | | | | | | | | | | | | | | |   (8665)  op(e1, e1) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | |   (8666)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.15/21.34  | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.15/21.34  | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.34  | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.15/21.34  | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7916), (8535), (8666),
% 149.15/21.34  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.34  | | | | | | | | | | | | | | | | |            #100.
% 149.15/21.34  | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | |   (8667)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.34  | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.15/21.34  | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.15/21.34  | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.34  | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.15/21.34  | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.15/21.34  | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.15/21.34  | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.15/21.34  | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | BETA: splitting (8667) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | |   (8668)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.15/21.34  | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.15/21.34  | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | ALPHA: (8668) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | |   (8669)  op(e1, e1) = e1
% 149.15/21.34  | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8665), (8669), (function-axioms) are
% 149.15/21.34  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | |   (8670)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.15/21.34  | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.15/21.34  | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.15/21.34  | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | ALPHA: (8670) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | |   (8671)  all_57_15 = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | |   (8672)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.15/21.34  | | | | | | | | | | | | | | | | | |   (8673)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |   (8674)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e0)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | BETA: splitting (8674) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |   (8675)  all_56_0 = e0 & op(e3, e3) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | ALPHA: (8675) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |   (8676)  op(e3, e3) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8535), (8676), (function-axioms) are
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #957.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |   (8677)  all_56_1 = e0 & op(e3, e2) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | ALPHA: (8677) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | |   (8678)  op(e3, e2) = e0
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8672) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |   (8679)  all_57_13 = e1 & op(e1, e0) = e1
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8679) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | |   (8680)  all_57_13 = e1
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |   (8681)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8681) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |   (8682)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (162), (8530), (8561), (8665), (8682),
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |            #895.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |   (8683)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8683) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (8684)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8684) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (8685)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8685) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (8686)  op(e1, e1) = e2
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8665), (8686), (function-axioms) are
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (8687)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8687) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (8688)  op(e3, e2) = e3
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (8678), (8688), (function-axioms) are
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1032.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |   (8689)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8689) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (8690)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8690) implies:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (8691)  op(e3, e3) = e2
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8535), (8691), (function-axioms) are
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |   (8692)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8692) gives:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.34  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8693)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8693) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8694)  op(e0, e0) = e2
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8561), (8694), (function-axioms) are
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8695)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8695) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8696)  op(e2, e2) = e1
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (45), (156), (162),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            (238), (367), (8530), (8535), (8561), (8665),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            (8671), (8673), (8680), (8696), (function-axioms)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #888.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |   (8697)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8697) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |   (8698)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8698) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (8699)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8699) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8700)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8700) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8701)  op(e0, e0) = e1
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (116),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (156), (159), (162), (163), (164), (166),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (205), (210), (211), (221), (237), (238),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (334), (362), (366), (367), (371), (7916), (7918),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (8529), (8530), (8535), (8701), (function-axioms)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #99.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8702)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8702) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8703)   ~ (all_57_6 = e3)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8704)  op(e2, e1) = e2
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8705)  op(e3, e1) = all_57_6
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (164), (8704) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8706)  all_52_9 = e2
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_6, e1, e3, simplifying with (168), (8705)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8707)  all_57_6 = all_52_8
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (169), (8678) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8708)  all_52_4 = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8703), (8707) imply:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8709)   ~ (all_52_8 = e3)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (8708) imply:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8710)   ~ (all_52_8 = e0)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (8706) imply:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8711)   ~ (all_52_8 = e2)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8712)  all_54_2 = e3
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (8709), (8712) are inconsistent by
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #184.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8713)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (8533), (8664), (8711), (8713) are
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #382.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (8714)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8714) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8715)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8715) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8716)  op(e0, e0) = e1
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (116),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (140), (156), (159), (162), (163), (164), (166),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (193), (205), (210), (211), (221), (237), (238),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (334), (362), (366), (367), (371), (7916), (7918),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (8529), (8530), (8535), (8716), (function-axioms)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #99.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8717)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8717) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8718)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8718) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8719)  all_57_12 = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8720)   ~ (all_57_11 = e2)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8673), (8719), (8720) are inconsistent by
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #890.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8721)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8721) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8722)   ~ (all_57_13 = e1)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (237), (7916), (8535), (8665),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            (8722), (function-axioms) are inconsistent by
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #94.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |   (8723)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8723) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (8724)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8535), (8724), (function-axioms) are
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |   (8725)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8725) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8726)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8726) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8727)   ~ (all_57_13 = e1)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (237), (7916), (8535), (8665),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (8727), (function-axioms) are inconsistent by
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #94.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |   (8728)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (156), (157), (158), (8553), (8554), (8555),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            (8665), (8728), (function-axioms) are inconsistent
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #755.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | |   (8729)   ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | ALPHA: (8729) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | |   (8730)   ~ (all_57_14 = e0)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | |   (8731)  op(e1, e1) = all_57_14
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8665), (8730), (8731), (function-axioms) are
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1026.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | |   (8732)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e0)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | BETA: splitting (8732) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | |   (8733)  all_56_4 = e0 & op(e3, e1) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8664), (8733), (function-axioms) are
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | |   (8734)  all_56_9 = e0 & op(e3, e0) = e0
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8556), (8734), (function-axioms) are
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | |   (8735)  all_42_2 = e3
% 149.15/21.35  | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | COMBINE_EQS: (302), (8735) imply:
% 149.15/21.35  | | | | | | | | | | | |   (8736)  all_10_2 = e3
% 149.15/21.35  | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | SIMP: (8736) implies:
% 149.15/21.35  | | | | | | | | | | | |   (8737)  all_10_2 = e3
% 149.15/21.35  | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | REDUCE: (367), (8737) imply:
% 149.15/21.35  | | | | | | | | | | | |   (8738)   ~ (all_52_11 = e3)
% 149.15/21.35  | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | REDUCE: (368), (8737) imply:
% 149.15/21.35  | | | | | | | | | | | |   (8739)   ~ (all_52_12 = e3)
% 149.15/21.35  | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | REDUCE: (45), (8737) imply:
% 149.15/21.35  | | | | | | | | | | | |   (8740)  op(e0, e0) = e3
% 149.15/21.35  | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | BETA: splitting (219) gives:
% 149.15/21.35  | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | |   (8741)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 149.15/21.35  | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 149.15/21.35  | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | BETA: splitting (8741) gives:
% 149.15/21.35  | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | |   (8742)  all_56_4 = e3 & op(e3, e1) = e3
% 149.15/21.35  | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | ALPHA: (8742) implies:
% 149.15/21.35  | | | | | | | | | | | | | |   (8743)  all_56_4 = e3
% 149.15/21.35  | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 149.15/21.35  | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | |   (8744)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 149.15/21.35  | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 149.15/21.35  | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | REF_CLOSE: (8), (166), (7906), (8535), (8744),
% 149.15/21.35  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.15/21.35  | | | | | | | | | | | | | | |            #916.
% 149.15/21.35  | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | |   (8745)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 149.15/21.35  | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 149.15/21.35  | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | BETA: splitting (8745) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | |   (8746)  all_56_6 = e3 & op(e1, e3) = e3
% 149.15/21.35  | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | ALPHA: (8746) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | |   (8747)  all_56_6 = e3
% 149.15/21.35  | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | |   (8748)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.15/21.35  | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.15/21.35  | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.15/21.35  | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.15/21.35  | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.15/21.35  | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.15/21.35  | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.15/21.35  | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.15/21.35  | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.15/21.35  | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.15/21.35  | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.15/21.35  | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.15/21.35  | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.15/21.35  | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.15/21.35  | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.15/21.35  | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.15/21.35  | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | BETA: splitting (8748) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | |   (8749)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 149.15/21.35  | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.15/21.35  | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.15/21.35  | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.15/21.35  | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 149.15/21.35  | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 149.15/21.35  | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.15/21.35  | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | ALPHA: (8749) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | | | |   (8750)  op(e3, e3) = e3
% 149.15/21.35  | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | |   (8751)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 149.15/21.35  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | BETA: splitting (8751) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | |   (8752)  all_56_0 = e1 & op(e3, e3) = e1
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8535), (8750), (function-axioms) are
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | |   (8753)  all_56_2 = e1 & op(e2, e3) = e1
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | ALPHA: (8753) implies:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | |   (8754)  all_56_2 = e1
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (228), (230),
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | |            (232), (8747), (8750), (8754), (function-axioms)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #93.
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | End of split
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | Case 2:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | |   (8755)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 149.15/21.35  | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | BETA: splitting (8755) gives:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | 
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.15/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.35  | | | | | | | | | | | | | | | | | | | |   (8756)  all_56_6 = e1 & op(e1, e3) = e1
% 149.38/21.35  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8747), (8756) are inconsistent by sub-proof
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |            #792.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |   (8757)  all_56_12 = e1 & op(e0, e3) = e1
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | ALPHA: (8757) implies:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |   (8758)  op(e0, e3) = e1
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8531), (8758), (function-axioms) are
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #405.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.36  | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | |   (8759)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | ALPHA: (8759) implies:
% 149.38/21.36  | | | | | | | | | | | | | | | | | |   (8760)  op(e2, e2) = e2
% 149.38/21.36  | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7916), (8760), (function-axioms) are
% 149.38/21.36  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | End of split
% 149.38/21.36  | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | |   (8761)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.38/21.36  | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.38/21.36  | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.38/21.36  | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.38/21.36  | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.38/21.36  | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.38/21.36  | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.38/21.36  | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.38/21.36  | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.38/21.36  | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.38/21.36  | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.38/21.36  | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.38/21.36  | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.38/21.36  | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.38/21.36  | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.38/21.36  | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.38/21.36  | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | BETA: splitting (8761) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | |   (8762)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | ALPHA: (8762) implies:
% 149.38/21.36  | | | | | | | | | | | | | | | | | |   (8763)  op(e1, e1) = e1
% 149.38/21.36  | | | | | | | | | | | | | | | | | |   (8764)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 149.38/21.36  | | | | | | | | | | | | | | | | | |   (8765)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 149.38/21.36  | | | | | | | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |   (8766)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (8766) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |   (8767)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8767) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |   (8768)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7916), (8763), (8768), (function-axioms) are
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #92.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |   (8769)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (8530), (8769), (function-axioms) are
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1025.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |   (8770)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8770) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |   (8771)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (169), (7907), (8763), (8771),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |            #721.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |   (8772)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8772) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8773)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8773) implies:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8774)  op(e3, e3) = e2
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8535), (8774), (function-axioms) are
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8775)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8740), (8764), (8775), (function-axioms) are
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #458.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |   (8776)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (8776) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |   (8777)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8777) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |   (8778)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8778) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8779)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8779) implies:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8780)  op(e0, e0) = e1
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (116),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            (140), (156), (159), (162), (163), (164), (166),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            (193), (205), (210), (211), (221), (237), (238),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            (334), (362), (366), (367), (371), (7918), (8529),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            (8530), (8535), (8763), (8764), (8765), (8780),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            #381.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8781)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8781) implies:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8782)   ~ (all_57_6 = e3)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8535), (8765), (8782), (function-axioms) are
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #456.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |   (8783)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8783) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8784)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8784) implies:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8785)  op(e0, e0) = e1
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (116),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            (140), (156), (159), (162), (163), (164), (166),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            (193), (205), (210), (211), (221), (237), (238),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            (334), (362), (366), (367), (371), (7918), (8529),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            (8530), (8535), (8763), (8764), (8765), (8785),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            #381.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8786)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8739), (8786), (function-axioms) are
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1081.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |   (8787)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8787) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |   (8788)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8535), (8788), (function-axioms) are
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |   (8789)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8789) gives:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8790)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8790) implies:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8791)   ~ (all_57_13 = e1)
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |   (8792)  op(e1, e1) = e0
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (237), (7916), (8535), (8791),
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            (8792), (function-axioms) are inconsistent by
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #94.
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.36  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |   (8793)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8793) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |   (8794)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8794) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |   (8795)  op(e2, e2) = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7916), (8795), (function-axioms) are
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |   (8796)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8796) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |   (8797)  op(e0, e0) = all_57_15
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |   (8798)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8798) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |   (8799)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8535), (8740), (8797), (8799),
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |            #952.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |   (8800)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (8535), (8763), (8764), (8765),
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |            (8798), (8800), (function-axioms) are inconsistent
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #91.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | |   (8801)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.38/21.37  | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.38/21.37  | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | ALPHA: (8801) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | |   (8802)  op(e0, e0) = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8740), (8802), (function-axioms) are
% 149.38/21.37  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | |   (8803)  all_56_12 = e3 & op(e0, e3) = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | ALPHA: (8803) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | |   (8804)  all_56_12 = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | |   (8805)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 149.38/21.37  | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | BETA: splitting (8805) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | |   (8806)  all_56_6 = e3 & op(e1, e3) = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | ALPHA: (8806) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | |   (8807)  all_56_6 = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |   (8808)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e0)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (8808) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8809)  all_56_0 = e0 & op(e3, e3) = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | ALPHA: (8809) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8810)  op(e3, e3) = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8535), (8810), (function-axioms) are
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #957.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8811)  all_56_2 = e0 & op(e2, e3) = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | ALPHA: (8811) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8812)  all_56_2 = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |   (8813)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8535), (8812), (8813),
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |            #549.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |   (8814)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8814) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |   (8815)  all_56_6 = e2 & op(e1, e3) = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8815) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |   (8816)  all_56_6 = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8807), (8816) imply:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |   (8817)  e3 = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8743), (8817) imply:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |   (8818)  all_56_4 = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (167), (169), (235), (7907), (8535),
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |            (8739), (8818), (function-axioms) are inconsistent
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #998.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |   (8819)  all_56_12 = e2 & op(e0, e3) = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8819) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |   (8820)  all_56_12 = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8804), (8820) imply:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |   (8821)  e3 = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8743), (8821) imply:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |   (8822)  all_56_4 = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (167), (169), (235), (7907), (8535),
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |            (8739), (8822), (function-axioms) are inconsistent
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #998.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |   (8823)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e3) = e0)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (8823) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8824)  all_56_6 = e0 & op(e1, e3) = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | ALPHA: (8824) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8825)  all_56_6 = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8807), (8825) imply:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8826)  e3 = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8743), (8826) imply:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8827)  all_56_4 = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (167), (169), (235), (7907), (8535),
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |            (8739), (8827), (function-axioms) are inconsistent
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |            by sub-proof #90.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8828)  all_56_12 = e0 & op(e0, e3) = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | ALPHA: (8828) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8829)  all_56_12 = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8804), (8829) imply:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8830)  e3 = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8743), (8830) imply:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8831)  all_56_4 = e0
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (167), (169), (235), (7907), (8535),
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |            (8739), (8831), (function-axioms) are inconsistent
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |            by sub-proof #90.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | |   (8832)  all_56_7 = e3 & op(e1, e2) = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (7908), (8832), (function-axioms) are
% 149.38/21.37  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | |   (8833)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 149.38/21.37  | | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 149.38/21.37  | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (163),
% 149.38/21.37  | | | | | | | | | | | | | | | | |            (205), (209), (210), (7918), (8540), (8740),
% 149.38/21.37  | | | | | | | | | | | | | | | | |            (8833), (function-axioms) are inconsistent by
% 149.38/21.37  | | | | | | | | | | | | | | | | |            sub-proof #770.
% 149.38/21.37  | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | |   (8834)  all_56_5 = e3 & op(e2, e1) = e3
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | REF_CLOSE: (164), (7910), (8834), (function-axioms) are
% 149.38/21.37  | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | |   (8835)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 149.38/21.37  | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 149.38/21.37  | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | REF_CLOSE: (36), (156), (7918), (8738), (8835),
% 149.38/21.37  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.38/21.37  | | | | | | | | | | | | |            #883.
% 149.38/21.37  | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | End of split
% 149.38/21.37  | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | |   (8836)  all_24_2 = e2
% 149.38/21.37  | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | COMBINE_EQS: (318), (8836) imply:
% 149.38/21.37  | | | | | | | | | | |   (8837)  all_10_2 = e2
% 149.38/21.37  | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | REDUCE: (367), (8837) imply:
% 149.38/21.37  | | | | | | | | | | |   (8838)   ~ (all_52_11 = e2)
% 149.38/21.37  | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | REDUCE: (45), (8837) imply:
% 149.38/21.37  | | | | | | | | | | |   (8839)  op(e0, e0) = e2
% 149.38/21.37  | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | BETA: splitting (237) gives:
% 149.38/21.37  | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | |   (8840)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.38/21.37  | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.38/21.37  | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.38/21.37  | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.38/21.37  | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.38/21.37  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.38/21.37  | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.38/21.37  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.38/21.37  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.38/21.37  | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.38/21.37  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.38/21.37  | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.38/21.37  | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.38/21.37  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.38/21.37  | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.38/21.37  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.38/21.37  | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | REF_CLOSE: (8), (9), (7916), (8535), (8840),
% 149.38/21.37  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.38/21.37  | | | | | | | | | | | |            #100.
% 149.38/21.37  | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | |   (8841)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.38/21.37  | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.38/21.37  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.38/21.37  | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.38/21.37  | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.38/21.37  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.38/21.37  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.38/21.37  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.38/21.37  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.38/21.37  | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.38/21.37  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.38/21.37  | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.38/21.37  | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.38/21.37  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.38/21.37  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.38/21.37  | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.38/21.37  | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | BETA: splitting (8841) gives:
% 149.38/21.37  | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | |   (8842)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.38/21.37  | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.38/21.37  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.38/21.37  | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.38/21.37  | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.38/21.37  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.38/21.37  | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.38/21.37  | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.38/21.37  | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | ALPHA: (8842) implies:
% 149.38/21.37  | | | | | | | | | | | | |   (8843)  op(e1, e1) = e1
% 149.38/21.37  | | | | | | | | | | | | |   (8844)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 149.38/21.37  | | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 149.38/21.37  | | | | | | | | | | | | |             $i(all_57_12))
% 149.38/21.37  | | | | | | | | | | | | |   (8845)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 149.38/21.37  | | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 149.38/21.37  | | | | | | | | | | | | |             $i(all_57_10))
% 149.38/21.37  | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | BETA: splitting (8845) gives:
% 149.38/21.37  | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | |   (8846)  all_57_6 = e3 & op(e3, e1) = e3
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | ALPHA: (8846) implies:
% 149.38/21.37  | | | | | | | | | | | | | |   (8847)  op(e3, e1) = e3
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 149.38/21.37  | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (8843) gives:
% 149.38/21.37  | | | | | | | | | | | | | |   (8848)  all_4_2 = e1
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 149.38/21.37  | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (8847) gives:
% 149.38/21.37  | | | | | | | | | | | | | |   (8849)  all_52_8 = e3
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | REDUCE: (359), (8848) imply:
% 149.38/21.37  | | | | | | | | | | | | | |   (8850)   ~ (all_52_6 = e1)
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | REDUCE: (122), (8849) imply:
% 149.38/21.37  | | | | | | | | | | | | | |   (8851)   ~ (all_52_9 = e3)
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | REDUCE: (120), (8849) imply:
% 149.38/21.37  | | | | | | | | | | | | | |   (8852)   ~ (all_52_11 = e3)
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | SIMP: (8852) implies:
% 149.38/21.37  | | | | | | | | | | | | | |   (8853)   ~ (all_52_11 = e3)
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | REDUCE: (119), (8849) imply:
% 149.38/21.37  | | | | | | | | | | | | | |   (8854)   ~ (all_52_12 = e3)
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | SIMP: (8854) implies:
% 149.38/21.37  | | | | | | | | | | | | | |   (8855)   ~ (all_52_12 = e3)
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | REDUCE: (364), (8848) imply:
% 149.38/21.37  | | | | | | | | | | | | | |   (8856)   ~ (all_52_11 = e1)
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | REDUCE: (366), (8848) imply:
% 149.38/21.37  | | | | | | | | | | | | | |   (8857)   ~ (all_52_14 = e1)
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | REDUCE: (7918), (8848) imply:
% 149.38/21.37  | | | | | | | | | | | | | |   (8858)   ~ (e3 = e1)
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | REDUCE: (371), (8848) imply:
% 149.38/21.37  | | | | | | | | | | | | | |   (8859)   ~ (e2 = e1)
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 149.38/21.37  | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | |   (8860)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 149.38/21.37  | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 149.38/21.37  | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | BETA: splitting (8860) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | |   (8861)  all_56_9 = e1 & op(e3, e0) = e1
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8534), (8861), (function-axioms) are
% 149.38/21.37  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #970.
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | |   (8862)  all_56_10 = e1 & op(e2, e0) = e1
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | ALPHA: (8862) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | |   (8863)  all_56_10 = e1
% 149.38/21.37  | | | | | | | | | | | | | | | |   (8864)  op(e2, e0) = e1
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | |   (8865)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 149.38/21.37  | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 149.38/21.37  | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | BETA: splitting (8865) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | |   (8866)  all_56_12 = e1 & op(e0, e3) = e1
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | ALPHA: (8866) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | |   (8867)  op(e0, e3) = e1
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (8531), (8867), (function-axioms) are
% 149.38/21.37  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #405.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | |   (8868)  all_56_13 = e1 & op(e0, e2) = e1
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | ALPHA: (8868) implies:
% 149.38/21.37  | | | | | | | | | | | | | | | | | |   (8869)  all_56_13 = e1
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |   (8870)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | BETA: splitting (8870) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8871)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (162), (8530), (8839), (8843), (8871),
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |            #722.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |   (8872)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8872) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |   (8873)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (169), (7907), (8843), (8873),
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |            #721.
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |   (8874)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8874) gives:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |   (8875)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.38/21.37  | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8875) implies:
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8876)  op(e3, e3) = e2
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8535), (8876), (function-axioms) are
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8877)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8877) gives:
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (8878)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8878) implies:
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (8879)  op(e1, e2) = e1
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (8850), (8879), (function-axioms) are
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (8880)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8880) implies:
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (8881)  op(e2, e2) = e1
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (226), (227),
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |            (7908), (7910), (7914), (7915), (7916), (8869),
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |            (8881), (function-axioms) are inconsistent by
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #227.
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | End of split
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | Case 2:
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |   (8882)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.38/21.38  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (8882) gives:
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | 
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.38/21.38  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |   (8883)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8883) gives:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |   (8884)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8884) gives:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8885)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8885) implies:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8886)  op(e0, e0) = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |            (8863), (8886), (function-axioms) are inconsistent
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #445.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8887)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8887) implies:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8888)   ~ (all_57_6 = e3)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8535), (8845), (8888), (function-axioms) are
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #456.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |   (8889)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8889) gives:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8890)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8890) implies:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8891)  op(e0, e0) = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |            (8863), (8891), (function-axioms) are inconsistent
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #445.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8892)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (8855), (8892), (function-axioms) are
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1081.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |   (8893)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8893) gives:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |   (8894)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8535), (8894), (function-axioms) are
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |   (8895)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8895) gives:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8896)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8896) implies:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8897)  op(e2, e0) = e2
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (8864), (8897), (function-axioms) are
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #904.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |   (8898)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8898) gives:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (8899)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8899) implies:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (8900)  op(e1, e0) = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8857), (8900), (function-axioms) are
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (8901)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8901) implies:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (8902)  op(e0, e0) = all_57_15
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |   (8903)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8903) gives:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (8904)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8904) gives:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (8905)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_0)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8905) implies:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (8906)  op(e0, e3) = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8907)  all_54_14 = e3
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (8853), (8907) are inconsistent by
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #903.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | |   (8908)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (138), (158), (246), (8838), (8856), (8906),
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            (8908), (function-axioms) are inconsistent by
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #110.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |   (8909)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e0 & $i(all_57_3))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8839), (8843), (8902), (8909),
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | |            #718.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |   (8910)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (8535), (8843), (8844), (8845),
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |            (8903), (8910), (function-axioms) are inconsistent
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #91.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | |   (8911)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 149.44/21.38  | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 149.44/21.38  | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | BETA: splitting (8911) gives:
% 149.44/21.38  | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | |   (8912)  all_56_14 = e1 & op(e0, e1) = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | ALPHA: (8912) implies:
% 149.44/21.38  | | | | | | | | | | | | | | | | | |   (8913)  op(e0, e1) = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (189), (246), (8838), (8853), (8856),
% 149.44/21.38  | | | | | | | | | | | | | | | | | |            (8913), (function-axioms) are inconsistent by
% 149.44/21.38  | | | | | | | | | | | | | | | | | |            sub-proof #731.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | |   (8914)  all_56_15 = e1 & op(e0, e0) = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | ALPHA: (8914) implies:
% 149.44/21.38  | | | | | | | | | | | | | | | | | |   (8915)  op(e0, e0) = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 149.44/21.38  | | | | | | | | | | | | | | | | | |            (8863), (8915), (function-axioms) are inconsistent
% 149.44/21.38  | | | | | | | | | | | | | | | | | |            by sub-proof #445.
% 149.44/21.38  | | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | End of split
% 149.44/21.38  | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | |   (8916)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 149.44/21.38  | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 149.44/21.38  | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | BETA: splitting (8916) gives:
% 149.44/21.38  | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | Case 1:
% 149.44/21.38  | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | |   (8917)  all_56_11 = e1 & op(e1, e0) = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | ALPHA: (8917) implies:
% 149.44/21.38  | | | | | | | | | | | | | | | |   (8918)  op(e1, e0) = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8857), (8918), (function-axioms) are
% 149.44/21.38  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 149.44/21.38  | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | Case 2:
% 149.44/21.38  | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | |   (8919)  all_56_15 = e1 & op(e0, e0) = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | 
% 149.44/21.38  | | | | | | | | | | | | | | | | ALPHA: (8919) implies:
% 149.44/21.38  | | | | | | | | | | | | | | | |   (8920)  op(e0, e0) = e1
% 149.44/21.38  | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (116),
% 149.44/21.39  | | | | | | | | | | | | | | | |            (140), (156), (159), (162), (163), (164), (166),
% 149.44/21.39  | | | | | | | | | | | | | | | |            (193), (205), (210), (211), (221), (237), (238),
% 149.44/21.39  | | | | | | | | | | | | | | | |            (334), (362), (366), (367), (371), (7918), (8529),
% 149.44/21.39  | | | | | | | | | | | | | | | |            (8530), (8535), (8843), (8844), (8845), (8920),
% 149.44/21.39  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.39  | | | | | | | | | | | | | | | |            #381.
% 149.44/21.39  | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | |   (8921)   ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.44/21.39  | | | | | | | | | | | | | |           $i(all_57_10)
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | ALPHA: (8921) implies:
% 149.44/21.39  | | | | | | | | | | | | | |   (8922)   ~ (all_57_10 = e1)
% 149.44/21.39  | | | | | | | | | | | | | |   (8923)  op(e3, e3) = all_57_10
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | REF_CLOSE: (8535), (8922), (8923), (function-axioms) are
% 149.44/21.39  | | | | | | | | | | | | | |            inconsistent by sub-proof #893.
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | |   (8924)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.44/21.39  | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.44/21.39  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.39  | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.44/21.39  | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.44/21.39  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.44/21.39  | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.44/21.39  | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.44/21.39  | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | ALPHA: (8924) implies:
% 149.44/21.39  | | | | | | | | | | | | |   (8925)  op(e0, e0) = e0
% 149.44/21.39  | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | REF_CLOSE: (5), (8839), (8925), (function-axioms) are
% 149.44/21.39  | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 149.44/21.39  | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | 
% 149.44/21.39  | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | 
% 149.44/21.39  | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | 
% 149.44/21.39  | | | | | | | |   (8926)  all_14_2 = e0
% 149.44/21.39  | | | | | | | |   (8927)  ( ~ (all_14_0 = e2) & op(all_14_1, e3) = all_14_0 &
% 149.44/21.39  | | | | | | | |             op(e3, e0) = all_14_1 & $i(all_14_0) & $i(all_14_1))
% 149.44/21.39  | | | | | | | |           | ( ~ (all_14_1 = e1) & op(e3, e0) = all_14_1 &
% 149.44/21.39  | | | | | | | |             $i(all_14_1))
% 149.44/21.39  | | | | | | | | 
% 149.44/21.39  | | | | | | | | COMBINE_EQS: (314), (8926) imply:
% 149.44/21.39  | | | | | | | |   (8928)  all_28_2 = e0
% 149.44/21.39  | | | | | | | | 
% 149.44/21.39  | | | | | | | | REDUCE: (336), (8926) imply:
% 149.44/21.39  | | | | | | | |   (8929)   ~ (all_52_1 = e0)
% 149.44/21.39  | | | | | | | | 
% 149.44/21.39  | | | | | | | | REDUCE: (340), (8926) imply:
% 149.44/21.39  | | | | | | | |   (8930)   ~ (all_52_3 = e0)
% 149.44/21.39  | | | | | | | | 
% 149.44/21.39  | | | | | | | | REDUCE: (342), (8926) imply:
% 149.44/21.39  | | | | | | | |   (8931)   ~ (all_52_4 = e0)
% 149.44/21.39  | | | | | | | | 
% 149.44/21.39  | | | | | | | | REDUCE: (344), (8926) imply:
% 149.44/21.39  | | | | | | | |   (8932)   ~ (all_52_8 = e0)
% 149.44/21.39  | | | | | | | | 
% 149.44/21.39  | | | | | | | | REDUCE: (51), (8926) imply:
% 149.44/21.39  | | | | | | | |   (8933)  op(e3, e3) = e0
% 149.44/21.39  | | | | | | | | 
% 149.44/21.39  | | | | | | | | BETA: splitting (67) gives:
% 149.44/21.39  | | | | | | | | 
% 149.44/21.39  | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | 
% 149.44/21.39  | | | | | | | | |   (8934)   ~ (all_24_2 = e2)
% 149.44/21.39  | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | REDUCE: (318), (8934) imply:
% 149.44/21.39  | | | | | | | | |   (8935)   ~ (all_10_2 = e2)
% 149.44/21.39  | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | BETA: splitting (73) gives:
% 149.44/21.39  | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | |   (8936)   ~ (all_28_2 = e0)
% 149.44/21.39  | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | REDUCE: (8928), (8936) imply:
% 149.44/21.39  | | | | | | | | | |   (8937)  $false
% 149.44/21.39  | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | CLOSE: (8937) is inconsistent.
% 149.44/21.39  | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | |   (8938)  ( ~ (all_28_0 = e1) & op(all_28_1, e3) = all_28_0
% 149.44/21.39  | | | | | | | | | |             & op(e3, e0) = all_28_1 & $i(all_28_0) &
% 149.44/21.39  | | | | | | | | | |             $i(all_28_1)) | ( ~ (all_28_1 = e2) & op(e3, e0)
% 149.44/21.39  | | | | | | | | | |             = all_28_1 & $i(all_28_1))
% 149.44/21.39  | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | BETA: splitting (93) gives:
% 149.44/21.39  | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | |   (8939)   ~ (all_42_2 = e3)
% 149.44/21.39  | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | REDUCE: (302), (8939) imply:
% 149.44/21.39  | | | | | | | | | | |   (8940)   ~ (all_10_2 = e3)
% 149.44/21.39  | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | BETA: splitting (188) gives:
% 149.44/21.39  | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | |   (8941)  all_54_15 = e3
% 149.44/21.39  | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | REF_CLOSE: (245), (8940), (8941) are inconsistent by
% 149.44/21.39  | | | | | | | | | | | |            sub-proof #1049.
% 149.44/21.39  | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | |   (8942)   ~ (all_54_15 = e3)
% 149.44/21.39  | | | | | | | | | | | |   (8943)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 149.44/21.39  | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | BETA: splitting (8943) gives:
% 149.44/21.39  | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | |   (8944)  all_54_15 = e2
% 149.44/21.39  | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | REF_CLOSE: (245), (8935), (8944) are inconsistent by
% 149.44/21.39  | | | | | | | | | | | | |            sub-proof #1048.
% 149.44/21.39  | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | |   (8945)   ~ (all_54_15 = e2)
% 149.44/21.39  | | | | | | | | | | | | |   (8946)  all_54_15 = e1 | all_54_15 = e0
% 149.44/21.39  | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | BETA: splitting (8946) gives:
% 149.44/21.39  | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | |   (8947)  all_54_15 = e1
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | REF_CLOSE: (245), (7919), (8947) are inconsistent by
% 149.44/21.39  | | | | | | | | | | | | | |            sub-proof #1047.
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | |   (8948)  all_54_15 = e0
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | COMBINE_EQS: (245), (8948) imply:
% 149.44/21.39  | | | | | | | | | | | | | |   (8949)  all_10_2 = e0
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | SIMP: (8949) implies:
% 149.44/21.39  | | | | | | | | | | | | | |   (8950)  all_10_2 = e0
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | REDUCE: (360), (8950) imply:
% 149.44/21.39  | | | | | | | | | | | | | |   (8951)   ~ (all_52_7 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | REDUCE: (369), (8950) imply:
% 149.44/21.39  | | | | | | | | | | | | | |   (8952)   ~ (all_52_13 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | REDUCE: (8940), (8950) imply:
% 149.44/21.39  | | | | | | | | | | | | | |   (8953)   ~ (e3 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | REDUCE: (8935), (8950) imply:
% 149.44/21.39  | | | | | | | | | | | | | |   (8954)   ~ (e2 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | REDUCE: (45), (8950) imply:
% 149.44/21.39  | | | | | | | | | | | | | |   (8955)  op(e0, e0) = e0
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 149.44/21.39  | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | |   (8956)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 149.44/21.39  | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (7916), (8931), (8956),
% 149.44/21.39  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.39  | | | | | | | | | | | | | | |            #89.
% 149.44/21.39  | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | |   (8957)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 149.44/21.39  | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | BETA: splitting (8957) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | |   (8958)  all_56_7 = e0 & op(e1, e2) = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | ALPHA: (8958) implies:
% 149.44/21.39  | | | | | | | | | | | | | | | |   (8959)  op(e1, e2) = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | |   (8960)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | BETA: splitting (8960) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8961)  all_56_2 = e0 & op(e2, e3) = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (8929), (8961), (function-axioms) are
% 149.44/21.39  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #840.
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8962)  all_56_3 = e0 & op(e2, e2) = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | ALPHA: (8962) implies:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8963)  op(e2, e2) = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7916), (8963), (function-axioms) are
% 149.44/21.39  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | |   (8964)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 149.44/21.39  | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | BETA: splitting (8964) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8965)  all_56_5 = e0 & op(e2, e1) = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | ALPHA: (8965) implies:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8966)  op(e2, e1) = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0,
% 149.44/21.39  | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (161), (8959) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8967)  all_52_6 = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 149.44/21.39  | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (164), (8966) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8968)  all_52_9 = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | REDUCE: (142), (8967) imply:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8969)   ~ (all_52_2 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | REDUCE: (127), (8967) imply:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8970)   ~ (all_52_7 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | REDUCE: (125), (8967) imply:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8971)   ~ (all_52_14 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | SIMP: (8971) implies:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8972)   ~ (all_52_14 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | REDUCE: (117), (8968) imply:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8973)   ~ (all_52_11 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | SIMP: (8973) implies:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8974)   ~ (all_52_11 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | REDUCE: (362), (8968) imply:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8975)   ~ (all_4_2 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | SIMP: (8975) implies:
% 149.44/21.39  | | | | | | | | | | | | | | | | | |   (8976)   ~ (all_4_2 = e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | |   (8977)  all_54_10 = e3
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (7918), (8977) are inconsistent by
% 149.44/21.39  | | | | | | | | | | | | | | | | | | |            sub-proof #1173.
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | |   (8978)   ~ (all_54_10 = e3)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | |   (8979)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | BETA: splitting (8979) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | |   (8980)  all_54_10 = e2
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (371), (8980) are inconsistent by sub-proof
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | |            #1168.
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | |   (8981)   ~ (all_54_10 = e2)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | |   (8982)  all_54_10 = e1 | all_54_10 = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | BETA: splitting (8982) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | |   (8983)  all_54_10 = e1
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (334), (8983) imply:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | |   (8984)  all_4_2 = e1
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | SIMP: (8984) implies:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | |   (8985)  all_4_2 = e1
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | REDUCE: (348), (8985) imply:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | |   (8986)   ~ (all_52_2 = e1)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | REDUCE: (366), (8985) imply:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | |   (8987)   ~ (all_52_14 = e1)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | REDUCE: (7918), (8985) imply:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | |   (8988)   ~ (e3 = e1)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | REDUCE: (371), (8985) imply:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | |   (8989)   ~ (e2 = e1)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (8985) imply:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | |   (8990)  op(e1, e1) = e1
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |   (8991)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8991) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |   (8992)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (162), (8955), (8986), (8990), (8992),
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |            #131.
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |   (8993)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8993) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |   (8994)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (169), (7907), (8990), (8994),
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |            #721.
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |   (8995)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (7916), (8933), (8955), (8995),
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |            #88.
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |   (8996)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8996) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |   (8997)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8997) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |   (8998)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8933), (8955), (8998), (function-axioms) are
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #473.
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |   (8999)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8999) gives:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (9000)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9000) implies:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (9001)  op(e0, e0) = e1
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8955), (9001), (function-axioms) are
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |   (9002)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8933), (8990), (9002), (function-axioms) are
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #519.
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.39  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |   (9003)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9003) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |   (9004)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9004) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (9005)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9005) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (9006)  all_57_10 = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (9007)   ~ (all_57_9 = e3)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (9008)  op(e2, e0) = e2
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9009)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (7916), (8933), (9009),
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |            #87.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9010)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9010) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9011)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9011) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9012)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e1) & op(e0, e0) = all_57_15 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9012) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9013)  all_57_8 = e0 & op(e0, e1) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9013) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9014)  op(e0, e1) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (8974), (9014), (function-axioms) are
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1124.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9015)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_15)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9015) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9016)   ~ (all_57_15 = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9017)  op(e0, e0) = all_57_15
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (163), (9008) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9018)  all_52_13 = e2
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (9018) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9019)   ~ (all_52_1 = e2)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (9018) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9020)   ~ (all_52_14 = e2)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9020) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9021)   ~ (all_52_14 = e2)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9022)  all_54_11 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (9022) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9023)  all_52_14 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9023) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9024)  all_52_14 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (9024) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9025)   ~ (all_52_2 = e3)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9026)  all_54_8 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (9025), (9026) are inconsistent by
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #394.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9027)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9028)  all_54_4 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (9028) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9029)  all_52_1 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7906), (9029) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9030)  $false
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9030) is inconsistent.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9031)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9032)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9032) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9033)  all_56_9 = e1 & op(e3, e0) = e1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9033) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9034)  op(e3, e0) = e1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9031) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9035)  all_54_4 = e2
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (9019), (9035) are inconsistent by
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1175.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9036)  all_54_4 = e1 | all_54_4 = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9036) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9037)  all_54_4 = e1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (9037) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9038)  all_52_1 = e1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9038) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9039)  all_52_1 = e1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (9039) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9040)   ~ (all_52_2 = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (9039) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9041)   ~ (all_52_3 = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9041) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9042)   ~ (all_52_3 = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8927) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9043)   ~ (all_14_0 = e2) & op(all_14_1, e3) = all_14_0 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_14_1 & $i(all_14_0) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9043) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9044)   ~ (all_14_0 = e2)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9045)  op(e3, e0) = all_14_1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9046)  op(all_14_1, e3) = all_14_0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8938) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9047)   ~ (all_28_0 = e1) & op(all_28_1, e3) = all_28_0 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_28_1 & $i(all_28_0) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9047) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9048)  op(e3, e0) = all_28_1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (162), (191), (248), (258), (8930), (8969),
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8986), (9027), (9034), (9042), (9044), (9045),
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9046), (9048), (function-axioms) are inconsistent
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #86.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9049)   ~ (all_28_1 = e2) & op(e3, e0) = all_28_1 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9049) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9050)  op(e3, e0) = all_28_1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (162), (191), (248), (258), (8930), (8969),
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (8986), (9027), (9034), (9042), (9044), (9045),
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9046), (9050), (function-axioms) are inconsistent
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #86.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9051)   ~ (all_14_1 = e1) & op(e3, e0) = all_14_1 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_14_1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9051) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9052)   ~ (all_14_1 = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9053)  op(e3, e0) = all_14_1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8938) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9054)   ~ (all_28_0 = e1) & op(all_28_1, e3) = all_28_0 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_28_1 & $i(all_28_0) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9054) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9055)  op(e3, e0) = all_28_1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9034), (9052), (9053), (9055), (function-axioms)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #85.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9056)   ~ (all_28_1 = e2) & op(e3, e0) = all_28_1 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_28_1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9056) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9057)  op(e3, e0) = all_28_1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9034), (9052), (9053), (9057), (function-axioms)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #85.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9058)  all_54_4 = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (8929), (9058) are inconsistent by
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #796.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9059)  all_56_10 = e1 & op(e2, e0) = e1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9059) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9060)  op(e2, e0) = e1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (9008), (9060), (function-axioms) are
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #904.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9061)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8987), (9016), (9017), (9061),
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #939.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9062)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (8972), (8987), (9021), (9062) are
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #478.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9063)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9063) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9064)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) & op(e3, e3) = all_57_10 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9006), (9007), (9064) are inconsistent by
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #471.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (9065)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9065) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |   (9066)  op(e1, e0) = e1
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8987), (9066), (function-axioms) are
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |   (9067)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (36), (156), (157), (158), (159),
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |            (8930), (8951), (8974), (8987), (8990), (9067),
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | |            #763.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | |   (9068)  all_54_10 = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (334), (8976), (9068) are inconsistent by
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1033.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | |   (9069)  all_56_10 = e0 & op(e2, e0) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (8952), (9069), (function-axioms) are
% 149.44/21.40  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #540.
% 149.44/21.40  | | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | |   (9070)  all_56_13 = e0 & op(e0, e2) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | ALPHA: (9070) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | |   (9071)  op(e0, e2) = e0
% 149.44/21.40  | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | REF_CLOSE: (157), (8951), (9071), (function-axioms) are
% 149.44/21.40  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 149.44/21.40  | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | End of split
% 149.44/21.40  | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | |   (9072)  all_42_2 = e3
% 149.44/21.40  | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | COMBINE_EQS: (302), (9072) imply:
% 149.44/21.40  | | | | | | | | | | |   (9073)  all_10_2 = e3
% 149.44/21.40  | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | SIMP: (9073) implies:
% 149.44/21.40  | | | | | | | | | | |   (9074)  all_10_2 = e3
% 149.44/21.40  | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | REDUCE: (368), (9074) imply:
% 149.44/21.40  | | | | | | | | | | |   (9075)   ~ (all_52_12 = e3)
% 149.44/21.40  | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | REDUCE: (45), (9074) imply:
% 149.44/21.40  | | | | | | | | | | |   (9076)  op(e0, e0) = e3
% 149.44/21.40  | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | BETA: splitting (237) gives:
% 149.44/21.40  | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | |   (9077)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.44/21.40  | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.44/21.40  | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.44/21.40  | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.44/21.40  | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.44/21.40  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.44/21.40  | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.44/21.40  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.44/21.40  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.44/21.40  | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.44/21.40  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.40  | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.44/21.40  | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.44/21.40  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.44/21.40  | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.44/21.40  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.44/21.40  | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | REF_CLOSE: (7), (9), (7916), (8933), (9077),
% 149.44/21.40  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.40  | | | | | | | | | | | |            #87.
% 149.44/21.40  | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | |   (9078)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.44/21.40  | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.44/21.40  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.40  | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.44/21.40  | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.40  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.44/21.40  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.44/21.40  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.44/21.40  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.44/21.40  | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.44/21.40  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.40  | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.44/21.40  | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.44/21.40  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.44/21.40  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.44/21.40  | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.44/21.40  | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | BETA: splitting (9078) gives:
% 149.44/21.40  | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | |   (9079)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.44/21.40  | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.44/21.40  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.40  | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.44/21.40  | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.40  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.44/21.40  | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.44/21.40  | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.44/21.40  | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | ALPHA: (9079) implies:
% 149.44/21.40  | | | | | | | | | | | | |   (9080)  all_57_14 = e1
% 149.44/21.40  | | | | | | | | | | | | |   (9081)  op(e1, e1) = e1
% 149.44/21.40  | | | | | | | | | | | | |   (9082)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 149.44/21.40  | | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.40  | | | | | | | | | | | | |             $i(all_57_12))
% 149.44/21.40  | | | | | | | | | | | | |   (9083)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 149.44/21.40  | | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 149.44/21.40  | | | | | | | | | | | | |             $i(all_57_10))
% 149.44/21.40  | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | BETA: splitting (235) gives:
% 149.44/21.40  | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | |   (9084)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 149.44/21.40  | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 149.44/21.40  | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (7907), (8933), (9084),
% 149.44/21.40  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.40  | | | | | | | | | | | | | |            #171.
% 149.44/21.40  | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | Case 2:
% 149.44/21.40  | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | |   (9085)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 149.44/21.40  | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 149.44/21.40  | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | BETA: splitting (9085) gives:
% 149.44/21.40  | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | |   (9086)  all_56_4 = e3 & op(e3, e1) = e3
% 149.44/21.40  | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | ALPHA: (9086) implies:
% 149.44/21.40  | | | | | | | | | | | | | | |   (9087)  op(e3, e1) = e3
% 149.44/21.40  | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | |   (9088)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | |             & op(e1, e2) = e3)
% 149.44/21.40  | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | BETA: splitting (9088) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9089)  all_56_6 = e3 & op(e1, e3) = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | ALPHA: (9089) implies:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9090)  all_56_6 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9091)  op(e1, e3) = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 149.44/21.40  | | | | | | | | | | | | | | | | |              e1, e1, simplifying with (36), (9081) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9092)  all_4_2 = e1
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e3,
% 149.44/21.40  | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (9091) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9093)  all_52_2 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 149.44/21.40  | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (9087) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9094)  all_52_8 = e3
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | REDUCE: (142), (9093) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9095)   ~ (all_52_6 = e3)
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | REDUCE: (359), (9092) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9096)   ~ (all_52_6 = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | REDUCE: (122), (9094) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9097)   ~ (all_52_9 = e3)
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | REDUCE: (119), (9094) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9098)   ~ (all_52_12 = e3)
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | REDUCE: (362), (9092) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9099)   ~ (all_52_9 = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | REDUCE: (366), (9092) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9100)   ~ (all_52_14 = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | REDUCE: (7918), (9092) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9101)   ~ (e3 = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | REDUCE: (371), (9092) imply:
% 149.44/21.40  | | | | | | | | | | | | | | | | |   (9102)   ~ (e2 = e1)
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.44/21.40  | | | | | | | | | | | | | | | | | 
% 149.44/21.40  | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.40  | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | |   (9103)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.44/21.41  | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.44/21.41  | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | BETA: splitting (9103) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |   (9104)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | BETA: splitting (9104) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |   (9105)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7916), (9081), (9105), (function-axioms) are
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #92.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |   (9106)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9106) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |   (9107)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9107) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |   (9108)   ~ (all_57_14 = e3)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |   (9109)  op(e1, e3) = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9091), (9109), (function-axioms) are
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #119.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |   (9110)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9110) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |   (9111)  op(e1, e3) = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9091), (9111), (function-axioms) are
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #119.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |   (9112)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | BETA: splitting (9112) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |   (9113)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (169), (7907), (9081), (9113),
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |            #721.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |   (9114)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (8933), (9076), (9082), (9114),
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |            #457.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | |   (9115)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.44/21.41  | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | BETA: splitting (9115) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |   (9116)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (9075), (9076), (9083), (9116),
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |            #455.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |   (9117)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | BETA: splitting (9117) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |   (9118)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9118) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |   (9119)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9119) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |   (9120)   ~ (all_57_12 = e0)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |   (9121)  op(e2, e0) = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |   (9122)  op(e2, e2) = all_57_12
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | |   (9123)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e1)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9123) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9124)  all_56_4 = e1 & op(e3, e1) = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9124) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9125)  op(e3, e1) = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (9087), (9125), (function-axioms) are
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #439.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9126)  all_56_5 = e1 & op(e2, e1) = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9126) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9127)  op(e2, e1) = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9099), (9127), (function-axioms) are
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #704.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | |   (9128)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e1) = e1)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9128) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9129)  all_56_8 = e1 & op(e1, e1) = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (163), (9121) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9130)  all_52_13 = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (7916), (9122)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9131)  all_57_12 = e3
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (9130) imply:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9132)   ~ (all_52_1 = e2)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (9130) imply:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9133)   ~ (all_52_14 = e2)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9133) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9134)   ~ (all_52_14 = e2)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7911), (9130) imply:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9135)   ~ (e3 = e2)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | |   (9136)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9136) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9137)  all_56_6 = e2 & op(e1, e3) = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9137) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9138)  all_56_6 = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9090), (9138) are inconsistent by sub-proof
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |            #1057.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9139)  all_56_7 = e2 & op(e1, e2) = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9139) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9140)  all_56_7 = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9141)  op(e1, e2) = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (161), (163),
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (169), (209), (220), (221), (222),
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (223), (224), (225), (226), (227), (229), (230),
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (232), (233), (235), (7907), (7908), (7910),
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (8931), (8933), (9076), (9087), (9090), (9091),
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (9096), (9100), (9121), (9132), (9140), (9141),
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |            #116.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | |   (9142)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (159), (9081), (9134), (9142),
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | |            #715.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9143)  all_56_14 = e1 & op(e0, e1) = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9143) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9144)  all_56_14 = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | |   (9145)  op(e0, e1) = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | |   (9146)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9146) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9147)  all_56_4 = e0 & op(e3, e1) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8932), (9147), (function-axioms) are
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9148)  all_56_5 = e0 & op(e2, e1) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9148) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9149)  all_56_5 = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9150)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9150) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9151)  all_56_4 = e2 & op(e3, e1) = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9151) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9152)  op(e3, e1) = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9087), (9152), (function-axioms) are
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #504.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9153)  all_56_5 = e2 & op(e2, e1) = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9149), (9153) are inconsistent by sub-proof
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #389.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9154)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9154) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9155)  all_56_8 = e2 & op(e1, e1) = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9155) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9156)  op(e1, e1) = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (9081), (9156), (function-axioms) are
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9157)  all_56_14 = e2 & op(e0, e1) = e2
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9144), (9157) are inconsistent by sub-proof
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #248.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | |   (9158)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9158) gives:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9159)  all_56_8 = e0 & op(e1, e1) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9159) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9160)  op(e1, e1) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9081), (9160), (function-axioms) are
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1038.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9161)  all_56_14 = e0 & op(e0, e1) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9161) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |   (9162)  op(e0, e1) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9145), (9162), (function-axioms) are
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #899.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |   (9163)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9163) implies:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |   (9164)  op(e1, e0) = e1
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (9100), (9164), (function-axioms) are
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |   (9165)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.44/21.41  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (36), (158), (159), (8930), (8933),
% 149.44/21.42  | | | | | | | | | | | | | | | | | | | |            (9081), (9082), (9083), (9100), (9165),
% 149.44/21.42  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.42  | | | | | | | | | | | | | | | | | | | |            #371.
% 149.44/21.42  | | | | | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.42  | | | | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | | | | End of split
% 149.44/21.42  | | | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | | | End of split
% 149.44/21.42  | | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | | Case 2:
% 149.44/21.42  | | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | | |   (9166)  all_56_7 = e3 & op(e1, e2) = e3
% 149.44/21.42  | | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (7908), (9166), (function-axioms) are
% 149.44/21.42  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 149.44/21.42  | | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | | End of split
% 149.44/21.42  | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | Case 2:
% 149.44/21.42  | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | |   (9167)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 149.44/21.42  | | | | | | | | | | | | | | | |             e3 & op(e1, e0) = e3)
% 149.44/21.42  | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (163), (205),
% 149.44/21.42  | | | | | | | | | | | | | | | |            (209), (210), (8935), (9076), (9081), (9167),
% 149.44/21.42  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.42  | | | | | | | | | | | | | | | |            #500.
% 149.44/21.42  | | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | End of split
% 149.44/21.42  | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | Case 2:
% 149.44/21.42  | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | |   (9168)  all_56_9 = e3 & op(e3, e0) = e3
% 149.44/21.42  | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | ALPHA: (9168) implies:
% 149.44/21.42  | | | | | | | | | | | | | | |   (9169)  op(e3, e0) = e3
% 149.44/21.42  | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | | REF_CLOSE: (167), (9075), (9169), (function-axioms) are
% 149.44/21.42  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1082.
% 149.44/21.42  | | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | | End of split
% 149.44/21.42  | | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | End of split
% 149.44/21.42  | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | Case 2:
% 149.44/21.42  | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | |   (9170)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.44/21.42  | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.44/21.42  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.42  | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.44/21.42  | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.44/21.42  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.44/21.42  | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.44/21.42  | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.44/21.42  | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | ALPHA: (9170) implies:
% 149.44/21.42  | | | | | | | | | | | | |   (9171)  op(e0, e0) = e0
% 149.44/21.42  | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | REF_CLOSE: (7), (9076), (9171), (function-axioms) are
% 149.44/21.42  | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 149.44/21.42  | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | End of split
% 149.44/21.42  | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | End of split
% 149.44/21.42  | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | End of split
% 149.44/21.42  | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | End of split
% 149.44/21.42  | | | | | | | | | 
% 149.44/21.42  | | | | | | | | Case 2:
% 149.44/21.42  | | | | | | | | | 
% 149.44/21.42  | | | | | | | | |   (9172)  all_24_2 = e2
% 149.44/21.42  | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | COMBINE_EQS: (318), (9172) imply:
% 149.44/21.42  | | | | | | | | |   (9173)  all_10_2 = e2
% 149.44/21.42  | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | SIMP: (9173) implies:
% 149.44/21.42  | | | | | | | | |   (9174)  all_10_2 = e2
% 149.44/21.42  | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | REDUCE: (369), (9174) imply:
% 149.44/21.42  | | | | | | | | |   (9175)   ~ (all_52_13 = e2)
% 149.44/21.42  | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | REDUCE: (45), (9174) imply:
% 149.44/21.42  | | | | | | | | |   (9176)  op(e0, e0) = e2
% 149.44/21.42  | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | BETA: splitting (237) gives:
% 149.44/21.42  | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | Case 1:
% 149.44/21.42  | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | |   (9177)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.44/21.42  | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.44/21.42  | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.44/21.42  | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.44/21.42  | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.44/21.42  | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.44/21.42  | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.44/21.42  | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.44/21.42  | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.44/21.42  | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.44/21.42  | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.42  | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.44/21.42  | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.44/21.42  | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.44/21.42  | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.44/21.42  | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.44/21.42  | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | REF_CLOSE: (7), (9), (7916), (8933), (9177),
% 149.44/21.42  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.42  | | | | | | | | | |            #87.
% 149.44/21.42  | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | Case 2:
% 149.44/21.42  | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | |   (9178)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.44/21.42  | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.44/21.42  | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.42  | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.44/21.42  | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.42  | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.44/21.42  | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.44/21.42  | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.44/21.42  | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.44/21.42  | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.44/21.42  | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.42  | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.44/21.42  | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.44/21.42  | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.44/21.42  | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.44/21.42  | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.44/21.42  | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | BETA: splitting (9178) gives:
% 149.44/21.42  | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | Case 1:
% 149.44/21.42  | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | |   (9179)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.44/21.42  | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.44/21.42  | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.44/21.42  | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.44/21.42  | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.42  | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.44/21.42  | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.44/21.42  | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.44/21.42  | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | ALPHA: (9179) implies:
% 149.44/21.42  | | | | | | | | | | |   (9180)  op(e1, e1) = e1
% 149.44/21.42  | | | | | | | | | | |   (9181)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 149.44/21.42  | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 149.44/21.42  | | | | | | | | | | |             $i(all_57_12))
% 149.44/21.42  | | | | | | | | | | |   (9182)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 149.44/21.42  | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 149.44/21.42  | | | | | | | | | | |             $i(all_57_10))
% 149.44/21.42  | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 149.44/21.42  | | | | | | | | | | |              e1, e1, simplifying with (36), (9180) gives:
% 149.44/21.42  | | | | | | | | | | |   (9183)  all_4_2 = e1
% 149.44/21.42  | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | REDUCE: (348), (9183) imply:
% 149.44/21.42  | | | | | | | | | | |   (9184)   ~ (all_52_2 = e1)
% 149.44/21.42  | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | REDUCE: (359), (9183) imply:
% 149.44/21.42  | | | | | | | | | | |   (9185)   ~ (all_52_6 = e1)
% 149.44/21.42  | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | REDUCE: (366), (9183) imply:
% 149.44/21.42  | | | | | | | | | | |   (9186)   ~ (all_52_14 = e1)
% 149.44/21.42  | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | REDUCE: (7918), (9183) imply:
% 149.44/21.42  | | | | | | | | | | |   (9187)   ~ (e3 = e1)
% 149.44/21.42  | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | REDUCE: (371), (9183) imply:
% 149.44/21.42  | | | | | | | | | | |   (9188)   ~ (e2 = e1)
% 149.44/21.42  | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | BETA: splitting (238) gives:
% 149.44/21.42  | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | Case 1:
% 149.44/21.42  | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | |   (9189)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.44/21.42  | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.42  | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.44/21.42  | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.44/21.42  | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.44/21.42  | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.42  | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.44/21.42  | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.44/21.42  | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.42  | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.44/21.42  | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.44/21.42  | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.44/21.42  | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.44/21.42  | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.44/21.42  | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.42  | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.44/21.42  | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.44/21.42  | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.44/21.42  | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.44/21.42  | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.44/21.42  | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.44/21.42  | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.44/21.42  | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.44/21.42  | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.44/21.42  | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.44/21.42  | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.44/21.42  | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.44/21.42  | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.44/21.42  | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.42  | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.44/21.42  | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.44/21.42  | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.44/21.42  | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.44/21.42  | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.44/21.42  | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.44/21.42  | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.44/21.42  | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.44/21.42  | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.44/21.42  | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | BETA: splitting (9189) gives:
% 149.44/21.42  | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | Case 1:
% 149.44/21.42  | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | |   (9190)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.44/21.42  | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.42  | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.44/21.42  | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.44/21.42  | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.44/21.42  | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.44/21.42  | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.44/21.42  | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.44/21.42  | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.44/21.42  | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.44/21.42  | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.44/21.42  | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.44/21.42  | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.44/21.42  | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.44/21.42  | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.44/21.42  | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.44/21.42  | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.44/21.42  | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (162), (9176), (9180), (9184), (9190),
% 149.44/21.42  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.44/21.42  | | | | | | | | | | | | |            #722.
% 149.44/21.42  | | | | | | | | | | | | | 
% 149.44/21.42  | | | | | | | | | | | | Case 2:
% 149.44/21.42  | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | |   (9191)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.56/21.42  | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.56/21.42  | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.56/21.42  | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.56/21.42  | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.56/21.42  | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.56/21.42  | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.56/21.42  | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.56/21.42  | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.56/21.42  | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.56/21.42  | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.56/21.42  | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.56/21.42  | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.56/21.42  | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.56/21.42  | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.56/21.42  | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.56/21.42  | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.56/21.42  | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.56/21.42  | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.56/21.42  | | | | | | | | | | | | |             $i(all_57_10))
% 149.56/21.42  | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | BETA: splitting (9191) gives:
% 149.56/21.42  | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | Case 1:
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | |   (9192)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.56/21.42  | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.56/21.42  | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.56/21.42  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.56/21.42  | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.56/21.42  | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (169), (7907), (9180), (9192),
% 149.56/21.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.56/21.42  | | | | | | | | | | | | | |            #721.
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | Case 2:
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | |   (9193)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.56/21.42  | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.56/21.42  | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.56/21.42  | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.56/21.42  | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.56/21.42  | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.56/21.42  | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.56/21.42  | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.56/21.42  | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | REF_CLOSE: (5), (161), (8933), (9181), (9185), (9193),
% 149.56/21.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.56/21.42  | | | | | | | | | | | | | |            #448.
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | End of split
% 149.56/21.42  | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | End of split
% 149.56/21.42  | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | Case 2:
% 149.56/21.42  | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | |   (9194)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.56/21.42  | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.56/21.42  | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.56/21.42  | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.56/21.42  | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.56/21.42  | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.56/21.42  | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.56/21.42  | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.56/21.42  | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.56/21.42  | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.56/21.42  | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.56/21.42  | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.56/21.42  | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.56/21.42  | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.56/21.42  | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.56/21.42  | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.56/21.42  | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.56/21.42  | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.56/21.42  | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.56/21.42  | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.56/21.42  | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.56/21.42  | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.56/21.42  | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.56/21.42  | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.56/21.42  | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.56/21.42  | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.56/21.42  | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.56/21.42  | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.56/21.42  | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.56/21.42  | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.56/21.42  | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.56/21.42  | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.56/21.42  | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.56/21.42  | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.56/21.42  | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.56/21.42  | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.56/21.42  | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.56/21.42  | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.56/21.42  | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.56/21.42  | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.56/21.42  | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.56/21.42  | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.56/21.42  | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.56/21.42  | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.56/21.42  | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.56/21.42  | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.56/21.42  | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.56/21.42  | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.56/21.42  | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.56/21.42  | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.56/21.42  | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.56/21.42  | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.56/21.42  | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.56/21.42  | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.56/21.42  | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.56/21.42  | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.56/21.42  | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.56/21.42  | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | BETA: splitting (9194) gives:
% 149.56/21.42  | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | Case 1:
% 149.56/21.42  | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | |   (9195)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.56/21.42  | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.56/21.42  | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.56/21.42  | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.56/21.42  | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.56/21.42  | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.56/21.42  | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.56/21.42  | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.56/21.42  | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.56/21.42  | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.56/21.42  | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.56/21.42  | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.56/21.42  | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.56/21.42  | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.56/21.42  | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.56/21.42  | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.56/21.42  | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.56/21.42  | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.56/21.42  | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.56/21.42  | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.56/21.42  | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | BETA: splitting (9195) gives:
% 149.56/21.42  | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | Case 1:
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | |   (9196)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.56/21.42  | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.56/21.42  | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.56/21.42  | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.56/21.42  | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.56/21.42  | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.56/21.42  | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | REF_CLOSE: (6), (9176), (9182), (9196), (function-axioms) are
% 149.56/21.42  | | | | | | | | | | | | | |            inconsistent by sub-proof #447.
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | Case 2:
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | |   (9197)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.56/21.42  | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.56/21.42  | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.56/21.42  | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.56/21.42  | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.56/21.42  | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.56/21.42  | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.56/21.42  | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.56/21.42  | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.56/21.42  | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8933), (9176), (9180), (9197),
% 149.56/21.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.56/21.42  | | | | | | | | | | | | | |            #518.
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | End of split
% 149.56/21.42  | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | Case 2:
% 149.56/21.42  | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | |   (9198)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.56/21.42  | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.56/21.42  | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.56/21.42  | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.56/21.42  | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.56/21.42  | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.56/21.42  | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.56/21.42  | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.56/21.42  | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.56/21.42  | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.56/21.42  | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.56/21.42  | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.56/21.42  | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.56/21.42  | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.56/21.42  | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.56/21.42  | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.56/21.42  | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.56/21.42  | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.56/21.42  | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.56/21.42  | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.56/21.42  | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.56/21.42  | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.56/21.42  | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.56/21.42  | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.56/21.42  | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.56/21.42  | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.56/21.42  | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.56/21.42  | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.56/21.42  | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.56/21.42  | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.56/21.42  | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.56/21.42  | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.56/21.42  | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.56/21.42  | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.56/21.42  | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.56/21.42  | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.56/21.42  | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.56/21.42  | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | BETA: splitting (9198) gives:
% 149.56/21.42  | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | Case 1:
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | |   (9199)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.56/21.42  | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.56/21.42  | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.56/21.42  | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.56/21.42  | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.56/21.42  | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.56/21.42  | | | | | | | | | | | | | |             $i(all_57_14))
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (9175), (9186), (9199),
% 149.56/21.42  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.56/21.42  | | | | | | | | | | | | | |            #535.
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | Case 2:
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | |   (9200)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.56/21.42  | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.56/21.42  | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.56/21.42  | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.56/21.42  | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.56/21.42  | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.56/21.42  | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.56/21.42  | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.56/21.42  | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.56/21.42  | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.56/21.42  | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.56/21.42  | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.56/21.42  | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.56/21.42  | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.56/21.42  | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.56/21.42  | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.56/21.42  | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.56/21.42  | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.56/21.42  | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.56/21.42  | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.56/21.42  | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.56/21.42  | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.56/21.42  | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.56/21.42  | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.56/21.42  | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.56/21.42  | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.56/21.42  | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.56/21.42  | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | BETA: splitting (9200) gives:
% 149.56/21.42  | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | Case 1:
% 149.56/21.42  | | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | |   (9201)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.56/21.42  | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.56/21.42  | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.56/21.42  | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.56/21.42  | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.56/21.42  | | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | | ALPHA: (9201) implies:
% 149.56/21.42  | | | | | | | | | | | | | | |   (9202)  op(e2, e0) = e2
% 149.56/21.42  | | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | | REF_CLOSE: (163), (9175), (9202), (function-axioms) are
% 149.56/21.42  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 149.56/21.42  | | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | Case 2:
% 149.56/21.42  | | | | | | | | | | | | | | | 
% 149.56/21.42  | | | | | | | | | | | | | | |   (9203)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.56/21.42  | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.56/21.42  | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.56/21.42  | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.56/21.42  | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.56/21.42  | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.56/21.42  | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.56/21.42  | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.56/21.42  | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.56/21.42  | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.56/21.42  | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.56/21.42  | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.56/21.42  | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.56/21.42  | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.56/21.43  | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.56/21.43  | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.56/21.43  | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.56/21.43  | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.56/21.43  | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.56/21.43  | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.56/21.43  | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.56/21.43  | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.56/21.43  | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.56/21.43  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.56/21.43  | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.56/21.43  | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.56/21.43  | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.56/21.43  | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | BETA: splitting (9203) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | |   (9204)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.56/21.43  | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.56/21.43  | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.56/21.43  | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | ALPHA: (9204) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | |   (9205)  op(e1, e0) = e1
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | REF_CLOSE: (159), (9186), (9205), (function-axioms) are
% 149.56/21.43  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | |   (9206)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.56/21.43  | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.56/21.43  | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.56/21.43  | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.56/21.43  | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.56/21.43  | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.56/21.43  | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.56/21.43  | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.56/21.43  | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.56/21.43  | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.56/21.43  | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 149.56/21.43  | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.56/21.43  | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.56/21.43  | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.56/21.43  | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.56/21.43  | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.56/21.43  | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 149.56/21.43  | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.56/21.43  | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.56/21.43  | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.56/21.43  | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | ALPHA: (9206) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | |   (9207)  op(e0, e0) = all_57_15
% 149.56/21.43  | | | | | | | | | | | | | | | |   (9208)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.56/21.43  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.56/21.43  | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.56/21.43  | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.56/21.43  | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.56/21.43  | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.56/21.43  | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.56/21.43  | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.56/21.43  | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.56/21.43  | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.56/21.43  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.56/21.43  | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.56/21.43  | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.56/21.43  | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.56/21.43  | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.56/21.43  | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.56/21.43  | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.56/21.43  | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.56/21.43  | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (158), (8930), (9176), (9180), (9181),
% 149.56/21.43  | | | | | | | | | | | | | | | |            (9182), (9207), (9208), (function-axioms) are
% 149.56/21.43  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #115.
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | End of split
% 149.56/21.43  | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | End of split
% 149.56/21.43  | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | End of split
% 149.56/21.43  | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | End of split
% 149.56/21.43  | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | End of split
% 149.56/21.43  | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | |   (9209)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.56/21.43  | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.56/21.43  | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.56/21.43  | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.56/21.43  | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.56/21.43  | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.56/21.43  | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.56/21.43  | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.56/21.43  | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | ALPHA: (9209) implies:
% 149.56/21.43  | | | | | | | | | | |   (9210)  op(e0, e0) = e0
% 149.56/21.43  | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | REF_CLOSE: (5), (9176), (9210), (function-axioms) are
% 149.56/21.43  | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 149.56/21.43  | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | End of split
% 149.56/21.43  | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | End of split
% 149.56/21.43  | | | | | | | | | 
% 149.56/21.43  | | | | | | | | End of split
% 149.56/21.43  | | | | | | | | 
% 149.56/21.43  | | | | | | | End of split
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | Case 2:
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | |   (9211)  all_10_2 = e1
% 149.56/21.43  | | | | | | |   (9212)  ( ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 &
% 149.56/21.43  | | | | | | |             op(e0, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) |
% 149.56/21.43  | | | | | | |           ( ~ (all_10_1 = e2) & op(e0, e1) = all_10_1 &
% 149.56/21.43  | | | | | | |             $i(all_10_1))
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | | COMBINE_EQS: (308), (9211) imply:
% 149.56/21.43  | | | | | | |   (9213)  all_30_2 = e1
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | | REDUCE: (349), (9211) imply:
% 149.56/21.43  | | | | | | |   (9214)   ~ (all_52_3 = e1)
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | | REDUCE: (360), (9211) imply:
% 149.56/21.43  | | | | | | |   (9215)   ~ (all_52_7 = e1)
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | | REDUCE: (367), (9211) imply:
% 149.56/21.43  | | | | | | |   (9216)   ~ (all_52_11 = e1)
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | | REDUCE: (368), (9211) imply:
% 149.56/21.43  | | | | | | |   (9217)   ~ (all_52_12 = e1)
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | | REDUCE: (369), (9211) imply:
% 149.56/21.43  | | | | | | |   (9218)   ~ (all_52_13 = e1)
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | | REDUCE: (370), (9211) imply:
% 149.56/21.43  | | | | | | |   (9219)   ~ (all_52_14 = e1)
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | | REDUCE: (45), (9211) imply:
% 149.56/21.43  | | | | | | |   (9220)  op(e0, e0) = e1
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | | BETA: splitting (209) gives:
% 149.56/21.43  | | | | | | | 
% 149.56/21.43  | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | 
% 149.56/21.43  | | | | | | | |   (9221)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 &
% 149.56/21.43  | | | | | | | |             op(e2, e0) = e1)
% 149.56/21.43  | | | | | | | | 
% 149.56/21.43  | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 149.56/21.43  | | | | | | | |            (9220), (9221), (function-axioms) are inconsistent by
% 149.56/21.43  | | | | | | | |            sub-proof #444.
% 149.56/21.43  | | | | | | | | 
% 149.56/21.43  | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | 
% 149.56/21.43  | | | | | | | |   (9222)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 &
% 149.56/21.43  | | | | | | | |             op(e0, e0) = e1)
% 149.56/21.43  | | | | | | | | 
% 149.56/21.43  | | | | | | | | BETA: splitting (9222) gives:
% 149.56/21.43  | | | | | | | | 
% 149.56/21.43  | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | 
% 149.56/21.43  | | | | | | | | |   (9223)  all_56_11 = e1 & op(e1, e0) = e1
% 149.56/21.43  | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | ALPHA: (9223) implies:
% 149.56/21.43  | | | | | | | | |   (9224)  op(e1, e0) = e1
% 149.56/21.43  | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | REF_CLOSE: (159), (9219), (9224), (function-axioms) are
% 149.56/21.43  | | | | | | | | |            inconsistent by sub-proof #961.
% 149.56/21.43  | | | | | | | | | 
% 149.56/21.43  | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | 
% 149.56/21.43  | | | | | | | | |   (9225)  all_56_15 = e1 & op(e0, e0) = e1
% 149.56/21.43  | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | ALPHA: (9225) implies:
% 149.56/21.43  | | | | | | | | |   (9226)  all_56_15 = e1
% 149.56/21.43  | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | BETA: splitting (52) gives:
% 149.56/21.43  | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | |   (9227)   ~ (all_14_2 = e0)
% 149.56/21.43  | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | BETA: splitting (64) gives:
% 149.56/21.43  | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | |   (9228)   ~ (all_22_2 = e1)
% 149.56/21.43  | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | REDUCE: (320), (9228) imply:
% 149.56/21.43  | | | | | | | | | | |   (9229)   ~ (all_14_2 = e1)
% 149.56/21.43  | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | BETA: splitting (76) gives:
% 149.56/21.43  | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | |   (9230)   ~ (all_30_2 = e1)
% 149.56/21.43  | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | REDUCE: (9213), (9230) imply:
% 149.56/21.43  | | | | | | | | | | | |   (9231)  $false
% 149.56/21.43  | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | CLOSE: (9231) is inconsistent.
% 149.56/21.43  | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | |   (9232)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0
% 149.56/21.43  | | | | | | | | | | | |             & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 149.56/21.43  | | | | | | | | | | | |             $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1)
% 149.56/21.43  | | | | | | | | | | | |             = all_30_1 & $i(all_30_1))
% 149.56/21.43  | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | BETA: splitting (84) gives:
% 149.56/21.43  | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | |   (9233)   ~ (all_36_2 = e2)
% 149.56/21.43  | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | REDUCE: (304), (9233) imply:
% 149.56/21.43  | | | | | | | | | | | | |   (9234)   ~ (all_14_2 = e2)
% 149.56/21.43  | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | BETA: splitting (203) gives:
% 149.56/21.43  | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | |   (9235)  all_54_0 = e3
% 149.56/21.43  | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | COMBINE_EQS: (278), (9235) imply:
% 149.56/21.43  | | | | | | | | | | | | | |   (9236)  all_14_2 = e3
% 149.56/21.43  | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | SIMP: (9236) implies:
% 149.56/21.43  | | | | | | | | | | | | | |   (9237)  all_14_2 = e3
% 149.56/21.43  | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | REDUCE: (344), (9237) imply:
% 149.56/21.43  | | | | | | | | | | | | | |   (9238)   ~ (all_52_8 = e3)
% 149.56/21.43  | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | REDUCE: (346), (9237) imply:
% 149.56/21.43  | | | | | | | | | | | | | |   (9239)   ~ (all_52_12 = e3)
% 149.56/21.43  | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 149.56/21.43  | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | |   (9240)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 149.56/21.43  | | | | | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 149.56/21.43  | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | REF_CLOSE: (163), (167), (7911), (9239), (9240),
% 149.56/21.43  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.56/21.43  | | | | | | | | | | | | | | |            #113.
% 149.56/21.43  | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | |   (9241)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 149.56/21.43  | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 149.56/21.43  | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | BETA: splitting (9241) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | |   (9242)  all_56_11 = e3 & op(e1, e0) = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | ALPHA: (9242) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | |   (9243)  all_56_11 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | |   (9244)  op(e1, e0) = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | |   (9245)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | |             & op(e2, e1) = e3)
% 149.56/21.43  | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (7910), (9238), (9245),
% 149.56/21.43  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.56/21.43  | | | | | | | | | | | | | | | | |            #369.
% 149.56/21.43  | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | |   (9246)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 149.56/21.43  | | | | | | | | | | | | | | | | |             e3 & op(e0, e1) = e3)
% 149.56/21.43  | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | BETA: splitting (9246) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | |   (9247)  all_56_8 = e3 & op(e1, e1) = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | ALPHA: (9247) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | |   (9248)  op(e1, e1) = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (7918), (9248), (function-axioms) are
% 149.56/21.43  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1078.
% 149.56/21.43  | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | |   (9249)  all_56_14 = e3 & op(e0, e1) = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | ALPHA: (9249) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | |   (9250)  all_56_14 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | |   (9251)  op(e0, e1) = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 149.56/21.43  | | | | | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (156), (9251) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | |   (9252)  all_52_11 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 149.56/21.43  | | | | | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (159), (9244) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | |   (9253)  all_52_14 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | REDUCE: (138), (9252) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | |   (9254)   ~ (all_52_3 = e3)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |   (9255)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.56/21.43  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | BETA: splitting (9255) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |   (9256)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | ALPHA: (9256) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |   (9257)  op(e3, e3) = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |   (9258)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = all_57_12 &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9258) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | |   (9259)  all_57_0 = e2 & op(e2, e3) = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9259) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | |   (9260)  op(e2, e3) = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9212) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | |   (9261)   ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_10_1 & $i(all_10_0) &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9261) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | |   (9262)  op(e0, e1) = all_10_1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | |   (9263)  op(all_10_1, e0) = all_10_0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9232) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9264)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_30_1 & $i(all_30_0) &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9264) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9265)   ~ (all_30_0 = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9266)  op(e0, e1) = all_30_1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9267)  op(all_30_1, e0) = all_30_0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (144), (166), (167), (196), (200), (259),
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |            (269), (7911), (9217), (9218), (9239), (9251),
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |            (9260), (9262), (9263), (9265), (9266), (9267),
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |            #84.
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9268)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9268) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9269)   ~ (all_30_1 = e3)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9270)  op(e0, e1) = all_30_1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9251), (9262), (9269), (9270), (function-axioms)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #391.
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | |   (9271)   ~ (all_10_1 = e2) & op(e0, e1) = all_10_1 &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | |           $i(all_10_1)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9271) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | |   (9272)   ~ (all_10_1 = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | |   (9273)  op(e0, e1) = all_10_1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9232) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9274)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e1) = all_30_1 & $i(all_30_0) &
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9274) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9275)  op(e0, e1) = all_30_1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, simplifying with (9251), (9275) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9276)  all_30_1 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |              all_30_1, e1, e0, simplifying with (9273), (9275)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9277)  all_30_1 = all_10_1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |              e3, e2, simplifying with (166), (9260) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9278)  all_52_1 = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9276), (9277) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9279)  all_10_1 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (147), (9278) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9280)   ~ (all_52_3 = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9280) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9281)   ~ (all_52_3 = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (9278) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9282)   ~ (all_52_9 = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9282) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9283)   ~ (all_52_9 = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (9278) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9284)   ~ (all_52_13 = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9284) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | |   (9285)   ~ (all_52_13 = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | |   (9286)  all_54_12 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (9254), (9286) are inconsistent by
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1093.
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | |   (9287)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9287) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | |   (9288)  all_54_12 = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (9281), (9288) are inconsistent by
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #882.
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | |   (9289)  all_54_12 = e1 | all_54_12 = e0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9289) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9290)  all_54_12 = e1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (9214), (9290) are inconsistent by
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1091.
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9291)  all_54_12 = e0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (9291) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9292)  all_52_3 = e0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9292) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9293)  all_52_3 = e0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (9293) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9294)   ~ (all_52_7 = e0)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9294) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9295)   ~ (all_52_7 = e0)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9296)  all_54_7 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9296) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9297)  all_52_13 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7911), (9297) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9298)  $false
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9298) is inconsistent.
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9299)   ~ (all_54_7 = e3)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9300)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9300) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9301)  all_54_7 = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9301) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9302)  all_52_13 = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9285), (9302) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9303)  $false
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9303) is inconsistent.
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9304)   ~ (all_54_7 = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9305)  all_54_7 = e1 | all_54_7 = e0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9305) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9306)  all_54_7 = e1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9306) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9307)  all_52_13 = e1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9218), (9307) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9308)  $false
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9308) is inconsistent.
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9309)  all_54_7 = e0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9309) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9310)  all_52_13 = e0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (9310) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9311)   ~ (all_52_9 = e0)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7911), (9310) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9312)   ~ (e3 = e0)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9285), (9310) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9313)   ~ (e2 = e0)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9218), (9310) imply:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9314)   ~ (e1 = e0)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9315)  all_54_13 = e3
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (7909), (9315) are inconsistent by
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #845.
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9316)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9317)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e2, e0) = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9317) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9318)  all_56_9 = e2 & op(e3, e0) = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9318) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9319)  all_56_9 = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9320)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9320) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9321)  all_56_4 = e2 & op(e3, e1) = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9321) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9322)  all_56_4 = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9323)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9323) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9324)  all_56_6 = e2 & op(e1, e3) = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9324) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9325)  all_56_6 = e2
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9326)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e1)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (166), (9257), (9260), (9326),
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #841.
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9327)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e3) = e1)
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9327) gives:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9328)  all_56_6 = e1 & op(e1, e3) = e1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9328) implies:
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9329)  all_56_6 = e1
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.43  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9325), (9329) imply:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9330)  e2 = e1
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9330) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9331)  e2 = e1
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9319), (9331) imply:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9332)  all_56_9 = e1
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (205), (210), (9220),
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9243), (9332), (function-axioms) are inconsistent
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #497.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9333)  all_56_12 = e1 & op(e0, e3) = e1
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9333) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9334)  op(e0, e3) = e1
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9214), (9334), (function-axioms) are
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #405.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9335)  all_56_7 = e2 & op(e1, e2) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9335) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9336)  op(e1, e2) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (161), (247), (9215), (9295), (9316),
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9336), (function-axioms) are inconsistent by
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #836.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9337)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9337) gives:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9338)  all_56_8 = e2 & op(e1, e1) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9338) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9339)  all_56_8 = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9340)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e1) = e0)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9340) gives:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9341)  all_56_4 = e0 & op(e3, e1) = e0
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9322), (9341) are inconsistent by sub-proof
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1070.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9342)  all_56_5 = e0 & op(e2, e1) = e0
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9311), (9342), (function-axioms) are
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1144.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9343)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e1) = e0)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9343) gives:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9344)  all_56_8 = e0 & op(e1, e1) = e0
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9344) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9345)  all_56_8 = e0
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9339), (9345) imply:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9346)  e2 = e0
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (9346) imply:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9347)  $false
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9347) is inconsistent.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9348)  all_56_14 = e0 & op(e0, e1) = e0
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9250), (9348) are inconsistent by sub-proof
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #469.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9349)  all_56_11 = e2 & op(e1, e0) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (205), (211), (9226),
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9319), (9349) are inconsistent by sub-proof #83.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9350)  all_56_5 = e2 & op(e2, e1) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9350) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9351)  op(e2, e1) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9283), (9351), (function-axioms) are
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9352)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e1) = e2)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9352) gives:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9353)  all_56_8 = e2 & op(e1, e1) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9353) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9354)  op(e1, e1) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (371), (9354), (function-axioms) are
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1169.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9355)  all_56_14 = e2 & op(e0, e1) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9355) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9356)  op(e0, e1) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9272), (9273), (9275), (9356), (function-axioms)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #377.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9357)  all_56_10 = e2 & op(e2, e0) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9357) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9358)  op(e2, e0) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9285), (9358), (function-axioms) are
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9359)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e0) = e2)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9359) gives:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9360)  all_56_11 = e2 & op(e1, e0) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9243), (9360) are inconsistent by sub-proof
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #775.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9361)  all_56_15 = e2 & op(e0, e0) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9361) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9362)  op(e0, e0) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9220), (9362), (function-axioms) are
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #978.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | |   (9363)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 &
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | |           $i(all_30_1)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9363) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | |   (9364)   ~ (all_30_1 = e3)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | |   (9365)  op(e0, e1) = all_30_1
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9251), (9273), (9364), (9365), (function-axioms)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #391.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | |   (9366)   ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9366) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | |   (9367)   ~ (all_57_12 = e3)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | |   (9368)  op(e2, e2) = all_57_12
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7916), (9367), (9368), (function-axioms) are
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #126.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | |   (9369)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | ALPHA: (9369) implies:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | |   (9370)  op(e2, e2) = e2
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7916), (9370), (function-axioms) are
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | End of split
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | 
% 149.56/21.44  | | | | | | | | | | | | | | | | | | Case 2:
% 149.56/21.44  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |   (9371)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | BETA: splitting (9371) gives:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |   (9372)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | ALPHA: (9372) implies:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |   (9373)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |               = e1) & op(e0, e0) = all_57_15 &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |             $i(all_57_15))
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9373) gives:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | |   (9374)  all_57_8 = e0 & op(e0, e1) = e0
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9374) implies:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | |   (9375)  op(e0, e1) = e0
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9212), (9232), (9251), (9375),
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | |            #80.
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | |   (9376)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | |           $i(all_57_15)
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | ALPHA: (9376) implies:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | |   (9377)   ~ (all_57_15 = e1)
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | |   (9378)  op(e0, e0) = all_57_15
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9220), (9377), (9378), (function-axioms) are
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #940.
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |   (9379)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | ALPHA: (9379) implies:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |   (9380)  op(e0, e0) = e0
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9220), (9380), (function-axioms) are
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | Case 2:
% 149.64/21.44  | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | |   (9381)  all_56_15 = e3 & op(e0, e0) = e3
% 149.64/21.44  | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | ALPHA: (9381) implies:
% 149.64/21.44  | | | | | | | | | | | | | | | |   (9382)  op(e0, e0) = e3
% 149.64/21.44  | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9220), (9382), (function-axioms) are
% 149.64/21.44  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 149.64/21.44  | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | Case 2:
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | |   (9383)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | REF_CLOSE: (278), (9227), (9229), (9234), (9383) are
% 149.64/21.44  | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | Case 2:
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | |   (9384)  all_36_2 = e2
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | COMBINE_EQS: (304), (9384) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9385)  all_14_2 = e2
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | SIMP: (9385) implies:
% 149.64/21.44  | | | | | | | | | | | | |   (9386)  all_14_2 = e2
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (338), (9386) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9387)   ~ (all_52_2 = e2)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (51), (9386) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9388)  op(e3, e3) = e2
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | |   (9389)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.64/21.44  | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.64/21.44  | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.64/21.44  | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.64/21.44  | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.64/21.44  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.64/21.44  | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.64/21.44  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.44  | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.64/21.44  | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.64/21.44  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.44  | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.64/21.44  | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.64/21.44  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.64/21.44  | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.64/21.44  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | REF_CLOSE: (9), (7916), (9388), (9389), (function-axioms) are
% 149.64/21.44  | | | | | | | | | | | | | |            inconsistent by sub-proof #120.
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | Case 2:
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | |   (9390)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.64/21.44  | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.64/21.44  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.44  | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.64/21.44  | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.44  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.64/21.44  | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.64/21.44  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.44  | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.64/21.44  | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.64/21.44  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.44  | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.44  | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.44  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.64/21.44  | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.64/21.44  | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (124), (127), (138), (139), (142),
% 149.64/21.44  | | | | | | | | | | | | | |            (143), (156), (190), (191), (194), (195), (247),
% 149.64/21.44  | | | | | | | | | | | | | |            (248), (257), (258), (348), (359), (7908), (7909),
% 149.64/21.44  | | | | | | | | | | | | | |            (9214), (9215), (9220), (9387), (9390),
% 149.64/21.44  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.44  | | | | | | | | | | | | | |            #77.
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | Case 2:
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | |   (9391)  all_22_2 = e1
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | COMBINE_EQS: (320), (9391) imply:
% 149.64/21.44  | | | | | | | | | | |   (9392)  all_14_2 = e1
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | SIMP: (9392) implies:
% 149.64/21.44  | | | | | | | | | | |   (9393)  all_14_2 = e1
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | REDUCE: (336), (9393) imply:
% 149.64/21.44  | | | | | | | | | | |   (9394)   ~ (all_52_1 = e1)
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | REDUCE: (338), (9393) imply:
% 149.64/21.44  | | | | | | | | | | |   (9395)   ~ (all_52_2 = e1)
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | REDUCE: (51), (9393) imply:
% 149.64/21.44  | | | | | | | | | | |   (9396)  op(e3, e3) = e1
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (116),
% 149.64/21.44  | | | | | | | | | | |            (140), (156), (159), (162), (163), (164), (166),
% 149.64/21.44  | | | | | | | | | | |            (193), (205), (210), (211), (221), (237), (238),
% 149.64/21.44  | | | | | | | | | | |            (334), (362), (366), (367), (371), (7916), (7918),
% 149.64/21.44  | | | | | | | | | | |            (9220), (9394), (9395), (9396), (function-axioms)
% 149.64/21.44  | | | | | | | | | | |            are inconsistent by sub-proof #99.
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | End of split
% 149.64/21.44  | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | Case 2:
% 149.64/21.44  | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | |   (9397)  all_14_2 = e0
% 149.64/21.44  | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | REDUCE: (342), (9397) imply:
% 149.64/21.44  | | | | | | | | | |   (9398)   ~ (all_52_4 = e0)
% 149.64/21.44  | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | REDUCE: (51), (9397) imply:
% 149.64/21.44  | | | | | | | | | |   (9399)  op(e3, e3) = e0
% 149.64/21.44  | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | BETA: splitting (237) gives:
% 149.64/21.44  | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | |   (9400)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.64/21.44  | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.64/21.44  | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.64/21.44  | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.64/21.44  | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.64/21.44  | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.64/21.44  | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.64/21.44  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.44  | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.64/21.44  | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.64/21.44  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.44  | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.64/21.44  | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.64/21.44  | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.64/21.44  | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.64/21.44  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | REF_CLOSE: (7), (9), (7916), (9399), (9400),
% 149.64/21.44  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.44  | | | | | | | | | | |            #87.
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | Case 2:
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | |   (9401)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.64/21.44  | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.64/21.44  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.44  | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.64/21.44  | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.44  | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.64/21.44  | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.64/21.44  | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.44  | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.64/21.44  | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.64/21.44  | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.44  | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.44  | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.44  | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.64/21.44  | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.64/21.44  | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | BETA: splitting (9401) gives:
% 149.64/21.44  | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | |   (9402)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.64/21.44  | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.64/21.44  | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.44  | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.64/21.44  | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.44  | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.64/21.44  | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.64/21.44  | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.64/21.44  | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | ALPHA: (9402) implies:
% 149.64/21.44  | | | | | | | | | | | |   (9403)  op(e1, e1) = e1
% 149.64/21.44  | | | | | | | | | | | |   (9404)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15
% 149.64/21.44  | | | | | | | | | | | |               = e1) & op(e0, e0) = all_57_15 &
% 149.64/21.44  | | | | | | | | | | | |             $i(all_57_15))
% 149.64/21.44  | | | | | | | | | | | |   (9405)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 149.64/21.44  | | | | | | | | | | | |               = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.44  | | | | | | | | | | | |             $i(all_57_12))
% 149.64/21.44  | | | | | | | | | | | |   (9406)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10
% 149.64/21.44  | | | | | | | | | | | |               = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.44  | | | | | | | | | | | |             $i(all_57_10))
% 149.64/21.44  | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | BETA: splitting (9404) gives:
% 149.64/21.44  | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | |   (9407)  all_57_8 = e0 & op(e0, e1) = e0
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | ALPHA: (9407) implies:
% 149.64/21.44  | | | | | | | | | | | | |   (9408)  all_57_8 = e0
% 149.64/21.44  | | | | | | | | | | | | |   (9409)  op(e0, e1) = e0
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 149.64/21.44  | | | | | | | | | | | | |              e0, e1, e0, simplifying with (156), (9409) gives:
% 149.64/21.44  | | | | | | | | | | | | |   (9410)  all_52_11 = e0
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 149.64/21.44  | | | | | | | | | | | | |              e1, e1, simplifying with (36), (9403) gives:
% 149.64/21.44  | | | | | | | | | | | | |   (9411)  all_4_2 = e1
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (348), (9411) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9412)   ~ (all_52_2 = e1)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (138), (9410) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9413)   ~ (all_52_3 = e0)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (359), (9411) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9414)   ~ (all_52_6 = e1)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (124), (9410) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9415)   ~ (all_52_7 = e0)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (120), (9410) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9416)   ~ (all_52_8 = e0)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (361), (9411) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9417)   ~ (all_52_8 = e1)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (117), (9410) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9418)   ~ (all_52_9 = e0)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (362), (9411) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9419)   ~ (all_52_9 = e1)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (9216), (9410) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9420)   ~ (e1 = e0)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (7918), (9411) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9421)   ~ (e3 = e1)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | REDUCE: (371), (9411) imply:
% 149.64/21.44  | | | | | | | | | | | | |   (9422)   ~ (e2 = e1)
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | BETA: splitting (190) gives:
% 149.64/21.44  | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | |   (9423)  all_54_13 = e3
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | REF_CLOSE: (247), (7909), (9423) are inconsistent by
% 149.64/21.44  | | | | | | | | | | | | | |            sub-proof #845.
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | Case 2:
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | |   (9424)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 149.64/21.44  | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | |   (9425)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 149.64/21.44  | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 149.64/21.44  | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | BETA: splitting (9425) gives:
% 149.64/21.44  | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | |   (9426)  all_56_12 = e3 & op(e0, e3) = e3
% 149.64/21.44  | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | ALPHA: (9426) implies:
% 149.64/21.44  | | | | | | | | | | | | | | | |   (9427)  all_56_12 = e3
% 149.64/21.44  | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 149.64/21.44  | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | |   (9428)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 149.64/21.44  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 149.64/21.44  | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | BETA: splitting (9428) gives:
% 149.64/21.44  | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | |   (9429)  all_56_1 = e1 & op(e3, e2) = e1
% 149.64/21.44  | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | ALPHA: (9429) implies:
% 149.64/21.44  | | | | | | | | | | | | | | | | | |   (9430)  all_56_1 = e1
% 149.64/21.44  | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |   (9431)  all_54_6 = e3
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (7910), (9431) are inconsistent by
% 149.64/21.44  | | | | | | | | | | | | | | | | | | |            sub-proof #650.
% 149.64/21.44  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | |   (9432)   ~ (all_54_6 = e3)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | |   (9433)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | BETA: splitting (9433) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | |   (9434)  all_54_6 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (9434) imply:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | |   (9435)  all_52_9 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | SIMP: (9435) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | |   (9436)  all_52_9 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (9436) imply:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | |   (9437)   ~ (all_52_8 = e2)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (9436) imply:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | |   (9438)   ~ (all_52_13 = e2)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | SIMP: (9438) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | |   (9439)   ~ (all_52_13 = e2)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | REDUCE: (7910), (9436) imply:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | |   (9440)   ~ (e3 = e2)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | |   (9441)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (7916), (9398), (9441),
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | |            #89.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | |   (9442)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9442) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | |   (9443)  all_56_7 = e0 & op(e1, e2) = e0
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9443) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | |   (9444)  all_56_7 = e0
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | |   (9445)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9445) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | |   (9446)  all_56_2 = e1 & op(e2, e3) = e1
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9446) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | |   (9447)  op(e2, e3) = e1
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (9448)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (7916), (9430), (9448),
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | |            #76.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | |   (9449)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9449) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9450)  all_56_7 = e2 & op(e1, e2) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9450) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9451)  op(e1, e2) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (161), (247), (9215), (9415), (9424),
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            (9451), (function-axioms) are inconsistent by
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #836.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9452)  all_56_13 = e2 & op(e0, e2) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9452) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9453)  all_56_13 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9454)  all_54_2 = e3
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (9454) imply:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9455)  all_52_8 = e3
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9455) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9456)  all_52_8 = e3
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (119), (9456) imply:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9457)   ~ (all_52_12 = e3)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9457) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9458)   ~ (all_52_12 = e3)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9459)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e2)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9459) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9460)  all_56_0 = e2 & op(e3, e3) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9460) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9461)  op(e3, e3) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9399), (9461), (function-axioms) are
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9462)  all_56_1 = e2 & op(e3, e2) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9462) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9463)  all_56_1 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9430), (9463) are inconsistent by sub-proof
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #595.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9464)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e2)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9464) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9465)  all_56_4 = e2 & op(e3, e1) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9465) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9466)  all_56_4 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (167), (235), (9399), (9430),
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9458), (9466), (function-axioms) are inconsistent
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #533.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9467)  all_56_9 = e2 & op(e3, e0) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9467) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9468)  all_56_9 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9469)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e2) = e2)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9469) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9470)  all_56_6 = e2 & op(e1, e3) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9470) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9471)  all_56_6 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9472)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9472) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9473)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9473) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9474)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9474) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9475)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9475) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9476)  op(e2, e3) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (9447), (9476), (function-axioms) are
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #842.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9477)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9477) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9478)  op(e2, e3) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (9447), (9478), (function-axioms) are
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #842.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9479)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (162), (9220), (9412), (9479),
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #403.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9480)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9480) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9481)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (169), (7907), (9403), (9481),
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #721.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9482)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9482) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9483)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9483) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9484)  op(e3, e3) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230), (234),
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9471), (9484), (function-axioms) are inconsistent
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #1050.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9485)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9485) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9486)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9486) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9487)  op(e0, e0) = e2
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9488)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9488) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9489)  all_56_12 = e1 & op(e0, e3) = e1
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9489) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9490)  all_56_12 = e1
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9427), (9490) are inconsistent by sub-proof
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1056.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9491)  all_56_13 = e1 & op(e0, e2) = e1
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9491) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9492)  all_56_13 = e1
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9453), (9492) are inconsistent by sub-proof
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1110.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9493)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e0) = e1)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9409), (9487), (9493),
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #75.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9494)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9494) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9495)   ~ (all_57_7 = e2)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9496)  op(e2, e2) = e1
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9405), (9495), (9496), (function-axioms) are
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #713.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9497)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9497) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9498)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9498) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9499)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9406), (9408), (9499), (function-axioms) are
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #373.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9500)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9500) gives:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9501)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9501) implies:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9502)   ~ (all_57_8 = e0)
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9408), (9502) imply:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9503)  $false
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9503) is inconsistent.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9504)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (9458), (9504), (function-axioms) are
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1081.
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.45  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9505)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9505) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9506)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (163), (9219), (9439), (9506),
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #535.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9507)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9507) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9508)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9508) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9509)  op(e2, e0) = e2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9439), (9509), (function-axioms) are
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9510)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (158), (159), (9219), (9399),
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9403), (9405), (9406), (9413), (9510),
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #372.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9511)  all_56_7 = e2 & op(e1, e2) = e2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9511) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9512)  op(e1, e2) = e2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (161), (247), (9215), (9415), (9424),
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9512), (function-axioms) are inconsistent by
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #836.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9513)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e1, e0) = e2)
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9513) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9514)  all_56_8 = e2 & op(e1, e1) = e2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9514) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9515)  op(e1, e1) = e2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (9403), (9515), (function-axioms) are
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9516)  all_56_11 = e2 & op(e1, e0) = e2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (205), (211), (9226),
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9468), (9516) are inconsistent by sub-proof #83.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9517)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (9416), (9417), (9437), (9517) are
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #382.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | |   (9518)  all_56_3 = e1 & op(e2, e2) = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9518) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | |   (9519)  op(e2, e2) = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (9520)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e3)
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9520) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9521)  all_56_1 = e3 & op(e3, e2) = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9521) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9522)  all_56_1 = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9430), (9522) are inconsistent by sub-proof
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            #1069.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7916), (9519), (function-axioms) are
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |   (9523)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9523) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9524)  all_56_7 = e3 & op(e1, e2) = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9524) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9525)  all_56_7 = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9444), (9525) imply:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9526)  e3 = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (9526) imply:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9527)  $false
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9527) is inconsistent.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9528)  all_56_13 = e3 & op(e0, e2) = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9528) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9529)  all_56_13 = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (226), (9430), (9444), (9519),
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            (9529), (function-axioms) are inconsistent by
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #506.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | |   (9530)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9530) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | |   (9531)  all_56_5 = e1 & op(e2, e1) = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9531) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | |   (9532)  op(e2, e1) = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9419), (9532), (function-axioms) are
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #704.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | |   (9533)  all_56_10 = e1 & op(e2, e0) = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9533) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | |   (9534)  all_56_10 = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | |            (9220), (9534), (function-axioms) are inconsistent
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #445.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | |   (9535)  all_56_13 = e0 & op(e0, e2) = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9535) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | |   (9536)  op(e0, e2) = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9415), (9536), (function-axioms) are
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | |   (9537)  all_54_6 = e1 | all_54_6 = e0
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (9418), (9419), (9537) are inconsistent by
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | |            sub-proof #649.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | |   (9538)  all_56_3 = e1 & op(e2, e2) = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | ALPHA: (9538) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | |   (9539)  op(e2, e2) = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (36), (116), (158), (159),
% 149.64/21.46  | | | | | | | | | | | | | | | | | |            (163), (164), (238), (9219), (9220), (9399),
% 149.64/21.46  | | | | | | | | | | | | | | | | | |            (9403), (9404), (9405), (9406), (9413), (9539),
% 149.64/21.46  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.46  | | | | | | | | | | | | | | | | | |            #370.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | |   (9540)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 149.64/21.46  | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (161), (9215), (9414), (9540),
% 149.64/21.46  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.46  | | | | | | | | | | | | | | | | |            #74.
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | |   (9541)  all_56_13 = e3 & op(e0, e2) = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | ALPHA: (9541) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | |   (9542)  all_56_13 = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | |   (9543)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | BETA: splitting (9543) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | |   (9544)  all_56_1 = e1 & op(e3, e2) = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | ALPHA: (9544) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | |   (9545)  all_56_1 = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | |   (9546)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e2)
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (7916), (9545), (9546),
% 149.64/21.46  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.46  | | | | | | | | | | | | | | | | | | |            #76.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | |   (9547)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e2) = e2)
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | BETA: splitting (9547) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | |   (9548)  all_56_7 = e2 & op(e1, e2) = e2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | ALPHA: (9548) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | |   (9549)  op(e1, e2) = e2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (161), (247), (9215), (9415), (9424),
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | |            (9549), (function-axioms) are inconsistent by
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | |            sub-proof #836.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | |   (9550)  all_56_13 = e2 & op(e0, e2) = e2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | ALPHA: (9550) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | |   (9551)  all_56_13 = e2
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9542), (9551) are inconsistent by sub-proof
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | |            #1105.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | |   (9552)  all_56_3 = e1 & op(e2, e2) = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | ALPHA: (9552) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | |   (9553)  op(e2, e2) = e1
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (36), (116), (158), (159),
% 149.64/21.46  | | | | | | | | | | | | | | | | | |            (163), (164), (238), (9219), (9220), (9399),
% 149.64/21.46  | | | | | | | | | | | | | | | | | |            (9403), (9404), (9405), (9406), (9413), (9553),
% 149.64/21.46  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.46  | | | | | | | | | | | | | | | | | |            #370.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | |   (9554)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 149.64/21.46  | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (161), (9215), (9414), (9554),
% 149.64/21.46  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.46  | | | | | | | | | | | | | | | | |            #74.
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | |   (9555)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 149.64/21.46  | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 149.64/21.46  | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | BETA: splitting (9555) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | |   (9556)  all_56_14 = e3 & op(e0, e1) = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | ALPHA: (9556) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | |   (9557)  all_56_14 = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (164), (168), (216), (9403), (9416),
% 149.64/21.46  | | | | | | | | | | | | | | | |            (9418), (9557), (function-axioms) are inconsistent
% 149.64/21.46  | | | | | | | | | | | | | | | |            by sub-proof #124.
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | |   (9558)  all_56_15 = e3 & op(e0, e0) = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | ALPHA: (9558) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | |   (9559)  op(e0, e0) = e3
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9220), (9559), (function-axioms) are
% 149.64/21.46  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | |   (9560)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 149.64/21.46  | | | | | | | | | | | | |           $i(all_57_15)
% 149.64/21.46  | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | ALPHA: (9560) implies:
% 149.64/21.46  | | | | | | | | | | | | |   (9561)   ~ (all_57_15 = e1)
% 149.64/21.46  | | | | | | | | | | | | |   (9562)  op(e0, e0) = all_57_15
% 149.64/21.46  | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | REF_CLOSE: (9220), (9561), (9562), (function-axioms) are
% 149.64/21.46  | | | | | | | | | | | | |            inconsistent by sub-proof #940.
% 149.64/21.46  | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | |   (9563)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.64/21.46  | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.64/21.46  | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.46  | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.46  | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.46  | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.64/21.46  | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.64/21.46  | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.64/21.46  | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | ALPHA: (9563) implies:
% 149.64/21.46  | | | | | | | | | | | |   (9564)  op(e0, e0) = e0
% 149.64/21.46  | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | REF_CLOSE: (4), (9220), (9564), (function-axioms) are
% 149.64/21.46  | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 149.64/21.46  | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | | 
% 149.64/21.46  | | | | | | | | End of split
% 149.64/21.46  | | | | | | | | 
% 149.64/21.46  | | | | | | | End of split
% 149.64/21.46  | | | | | | | 
% 149.64/21.46  | | | | | | End of split
% 149.64/21.46  | | | | | | 
% 149.64/21.46  | | | | | Case 2:
% 149.64/21.46  | | | | | | 
% 149.64/21.46  | | | | | |   (9565)  all_8_2 = e3
% 149.64/21.46  | | | | | |   (9566)  ( ~ (all_8_0 = e2) & op(all_8_1, e1) = all_8_0 & op(e1,
% 149.64/21.46  | | | | | |               e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~
% 149.64/21.46  | | | | | |             (all_8_1 = e0) & op(e1, e3) = all_8_1 & $i(all_8_1))
% 149.64/21.46  | | | | | | 
% 149.64/21.46  | | | | | | COMBINE_EQS: (329), (9565) imply:
% 149.64/21.46  | | | | | |   (9567)  all_4_2 = e3
% 149.64/21.46  | | | | | | 
% 149.64/21.46  | | | | | | SIMP: (9567) implies:
% 149.64/21.46  | | | | | |   (9568)  all_4_2 = e3
% 149.64/21.46  | | | | | | 
% 149.64/21.46  | | | | | | COMBINE_EQS: (316), (9568) imply:
% 149.64/21.46  | | | | | |   (9569)  all_12_2 = e3
% 149.64/21.46  | | | | | | 
% 149.64/21.46  | | | | | | REDUCE: (361), (9568) imply:
% 149.64/21.46  | | | | | |   (9570)   ~ (all_52_8 = e3)
% 149.64/21.46  | | | | | | 
% 149.64/21.46  | | | | | | REDUCE: (364), (9568) imply:
% 149.64/21.46  | | | | | |   (9571)   ~ (all_52_11 = e3)
% 149.64/21.46  | | | | | | 
% 149.64/21.46  | | | | | | REDUCE: (366), (9568) imply:
% 149.64/21.46  | | | | | |   (9572)   ~ (all_52_14 = e3)
% 149.64/21.46  | | | | | | 
% 149.64/21.46  | | | | | | BETA: splitting (219) gives:
% 149.64/21.46  | | | | | | 
% 149.64/21.46  | | | | | | Case 1:
% 149.64/21.46  | | | | | | | 
% 149.64/21.46  | | | | | | |   (9573)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 &
% 149.64/21.46  | | | | | | |             op(e2, e1) = e3)
% 149.64/21.46  | | | | | | | 
% 149.64/21.46  | | | | | | | REF_CLOSE: (164), (168), (7910), (9570), (9573), (function-axioms)
% 149.64/21.46  | | | | | | |            are inconsistent by sub-proof #369.
% 149.64/21.46  | | | | | | | 
% 149.64/21.46  | | | | | | Case 2:
% 149.64/21.46  | | | | | | | 
% 149.64/21.46  | | | | | | |   (9574)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 &
% 149.64/21.46  | | | | | | |             op(e0, e1) = e3)
% 149.64/21.46  | | | | | | | 
% 149.64/21.46  | | | | | | | BETA: splitting (9574) gives:
% 149.64/21.46  | | | | | | | 
% 149.64/21.46  | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | 
% 149.64/21.46  | | | | | | | |   (9575)  all_56_8 = e3 & op(e1, e1) = e3
% 149.64/21.46  | | | | | | | | 
% 149.64/21.46  | | | | | | | | ALPHA: (9575) implies:
% 149.64/21.46  | | | | | | | |   (9576)  all_56_8 = e3
% 149.64/21.46  | | | | | | | |   (9577)  op(e1, e1) = e3
% 149.64/21.46  | | | | | | | | 
% 149.64/21.46  | | | | | | | | BETA: splitting (49) gives:
% 149.64/21.46  | | | | | | | | 
% 149.64/21.46  | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | 
% 149.64/21.46  | | | | | | | | |   (9578)   ~ (all_12_2 = e3)
% 149.64/21.46  | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | REDUCE: (9569), (9578) imply:
% 149.64/21.46  | | | | | | | | |   (9579)  $false
% 149.64/21.46  | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | CLOSE: (9579) is inconsistent.
% 149.64/21.46  | | | | | | | | | 
% 149.64/21.46  | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | 
% 149.64/21.46  | | | | | | | | |   (9580)  ( ~ (all_12_0 = e0) & op(all_12_1, e1) = all_12_0 &
% 149.64/21.46  | | | | | | | | |             op(e1, e3) = all_12_1 & $i(all_12_0) &
% 149.64/21.46  | | | | | | | | |             $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e1, e3) =
% 149.64/21.46  | | | | | | | | |             all_12_1 & $i(all_12_1))
% 149.64/21.46  | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | BETA: splitting (46) gives:
% 149.64/21.46  | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | |   (9581)   ~ (all_10_2 = e1)
% 149.64/21.46  | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | BETA: splitting (52) gives:
% 149.64/21.46  | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | |   (9582)   ~ (all_14_2 = e0)
% 149.64/21.46  | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | BETA: splitting (64) gives:
% 149.64/21.46  | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | |   (9583)   ~ (all_22_2 = e1)
% 149.64/21.46  | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | REDUCE: (320), (9583) imply:
% 149.64/21.46  | | | | | | | | | | | |   (9584)   ~ (all_14_2 = e1)
% 149.64/21.46  | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | BETA: splitting (67) gives:
% 149.64/21.46  | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | |   (9585)   ~ (all_24_2 = e2)
% 149.64/21.46  | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | REDUCE: (318), (9585) imply:
% 149.64/21.46  | | | | | | | | | | | | |   (9586)   ~ (all_10_2 = e2)
% 149.64/21.46  | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | BETA: splitting (84) gives:
% 149.64/21.46  | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | |   (9587)   ~ (all_36_2 = e2)
% 149.64/21.46  | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | REDUCE: (304), (9587) imply:
% 149.64/21.46  | | | | | | | | | | | | | |   (9588)   ~ (all_14_2 = e2)
% 149.64/21.46  | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.64/21.46  | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | |   (9589)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.46  | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.46  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.46  | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.46  | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.46  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.46  | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.46  | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.46  | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.46  | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.46  | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.46  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.46  | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.46  | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.46  | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.46  | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.46  | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.64/21.46  | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.64/21.46  | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.64/21.46  | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.64/21.46  | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.64/21.46  | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.46  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.46  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.64/21.46  | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.64/21.46  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.64/21.46  | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.64/21.46  | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.64/21.46  | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.46  | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.64/21.46  | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.64/21.46  | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.64/21.46  | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.64/21.46  | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.64/21.46  | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.64/21.46  | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.46  | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.46  | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.64/21.46  | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | BETA: splitting (9589) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | |   (9590)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.46  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.46  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.46  | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.46  | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.46  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.46  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.46  | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.46  | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.46  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.46  | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.46  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.46  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.46  | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.46  | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.46  | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.46  | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | BETA: splitting (9590) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | |   (9591)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.46  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.46  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.46  | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.46  | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.46  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.46  | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.46  | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | BETA: splitting (9591) gives:
% 149.64/21.46  | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | |   (9592)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | ALPHA: (9592) implies:
% 149.64/21.46  | | | | | | | | | | | | | | | | | |   (9593)   ~ (all_57_12 = e3)
% 149.64/21.46  | | | | | | | | | | | | | | | | | |   (9594)  op(e2, e2) = all_57_12
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7916), (9593), (9594), (function-axioms) are
% 149.64/21.46  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #126.
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.46  | | | | | | | | | | | | | | | | | | 
% 149.64/21.46  | | | | | | | | | | | | | | | | | |   (9595)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.46  | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.46  | | | | | | | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | ALPHA: (9595) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | |   (9596)   ~ (all_57_12 = e3)
% 149.64/21.47  | | | | | | | | | | | | | | | | | |   (9597)  op(e2, e2) = all_57_12
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7916), (9596), (9597), (function-axioms) are
% 149.64/21.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #126.
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | End of split
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | |   (9598)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.47  | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (9577), (9598), (function-axioms) are inconsistent
% 149.64/21.47  | | | | | | | | | | | | | | | | |            by sub-proof #368.
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | End of split
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | |   (9599)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.64/21.47  | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.64/21.47  | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.64/21.47  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.64/21.47  | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.64/21.47  | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.64/21.47  | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.47  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.64/21.47  | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.64/21.47  | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.64/21.47  | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | BETA: splitting (9599) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | |   (9600)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.64/21.47  | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (7907), (9577), (9600),
% 149.64/21.47  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.47  | | | | | | | | | | | | | | | | |            #294.
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | |   (9601)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.64/21.47  | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.64/21.47  | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | BETA: splitting (9601) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | |   (9602)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | ALPHA: (9602) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | |   (9603)  op(e3, e3) = e2
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (9582), (9584), (9588),
% 149.64/21.47  | | | | | | | | | | | | | | | | | |            (9603), (function-axioms) are inconsistent by
% 149.64/21.47  | | | | | | | | | | | | | | | | | |            sub-proof #366.
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | |   (9604)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.64/21.47  | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | BETA: splitting (9604) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9605)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | ALPHA: (9605) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9606)  op(e0, e0) = e2
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (9586), (9606), (function-axioms) are
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1097.
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9607)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | ALPHA: (9607) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9608)  op(e2, e2) = e1
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7916), (9608), (function-axioms) are
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | End of split
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | End of split
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | End of split
% 149.64/21.47  | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | |   (9609)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.47  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.47  | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.64/21.47  | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.64/21.47  | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.64/21.47  | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.47  | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.64/21.47  | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.64/21.47  | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.64/21.47  | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.64/21.47  | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.64/21.47  | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.47  | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.47  | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.47  | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.64/21.47  | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.64/21.47  | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.64/21.47  | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.64/21.47  | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.64/21.47  | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.64/21.47  | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.64/21.47  | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.64/21.47  | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.64/21.47  | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.64/21.47  | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.64/21.47  | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.64/21.47  | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.64/21.47  | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.64/21.47  | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.64/21.47  | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.64/21.47  | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.64/21.47  | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.64/21.47  | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.64/21.47  | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.64/21.47  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.64/21.47  | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.64/21.47  | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.64/21.47  | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.64/21.47  | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.64/21.47  | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.64/21.47  | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.64/21.47  | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.64/21.47  | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.64/21.47  | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | BETA: splitting (9609) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | |   (9610)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.47  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.47  | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.64/21.47  | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.64/21.47  | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.64/21.47  | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.64/21.47  | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.64/21.47  | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.64/21.47  | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.64/21.47  | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | BETA: splitting (9610) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | |   (9611)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.64/21.47  | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.64/21.47  | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (168), (203), (278), (9570), (9582), (9584),
% 149.64/21.47  | | | | | | | | | | | | | | | | |            (9588), (9611), (function-axioms) are inconsistent
% 149.64/21.47  | | | | | | | | | | | | | | | | |            by sub-proof #727.
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | |   (9612)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.64/21.47  | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.64/21.47  | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | BETA: splitting (9612) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | |   (9613)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |           $i(all_57_12)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | ALPHA: (9613) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | |   (9614)  op(e0, e0) = e1
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (9581), (9614), (function-axioms) are
% 149.64/21.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1116.
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | |   (9615)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | BETA: splitting (9615) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9616)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           $i(all_57_11)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | ALPHA: (9616) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9617)  op(e2, e2) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (51), (158), (162), (163), (164), (166),
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            (188), (203), (221), (222), (223), (228), (237),
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            (245), (278), (336), (349), (369), (7910), (9577),
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            (9581), (9582), (9584), (9586), (9588), (9617),
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            #225.
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9618)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | ALPHA: (9618) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9619)  op(e1, e1) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9577), (9619), (function-axioms) are
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | End of split
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | End of split
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | |   (9620)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.64/21.47  | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.64/21.47  | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.64/21.47  | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.64/21.47  | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.64/21.47  | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.64/21.47  | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.47  | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.64/21.47  | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.64/21.47  | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.64/21.47  | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.64/21.47  | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.64/21.47  | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.64/21.47  | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.64/21.47  | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.64/21.47  | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.64/21.47  | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.64/21.47  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.64/21.47  | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.64/21.47  | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.64/21.47  | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.64/21.47  | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.64/21.47  | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.64/21.47  | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | BETA: splitting (9620) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | |   (9621)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.64/21.47  | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.64/21.47  | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.64/21.47  | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (9582), (9584), (9588),
% 149.64/21.47  | | | | | | | | | | | | | | | | |            (9621), (function-axioms) are inconsistent by
% 149.64/21.47  | | | | | | | | | | | | | | | | |            sub-proof #1079.
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | |   (9622)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.64/21.47  | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.64/21.47  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.64/21.47  | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.64/21.47  | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.64/21.47  | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | BETA: splitting (9622) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | |   (9623)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | ALPHA: (9623) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | |   (9624)  op(e1, e1) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9577), (9624), (function-axioms) are
% 149.64/21.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #896.
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | |   (9625)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.64/21.47  | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.64/21.47  | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | BETA: splitting (9625) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9626)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | ALPHA: (9626) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9627)  op(e2, e2) = e0
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (51), (158), (162), (163), (164), (166),
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            (188), (203), (221), (222), (223), (228), (237),
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            (245), (278), (336), (349), (369), (7910), (9577),
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            (9581), (9582), (9584), (9586), (9588), (9627),
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |            #225.
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9628)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | ALPHA: (9628) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9629)  op(e0, e0) = all_57_15
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |   (9630)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | |   (9631)  all_54_0 = e3
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (9631) imply:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | |   (9632)  all_14_2 = e3
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | SIMP: (9632) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | |   (9633)  all_14_2 = e3
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | REDUCE: (340), (9633) imply:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | |   (9634)   ~ (all_52_3 = e3)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | |   (9635)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e2) = e3)
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9635) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | |   (9636)  all_56_12 = e3 & op(e0, e3) = e3
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9634), (9636), (function-axioms) are
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #73.
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | |   (9637)  all_56_13 = e3 & op(e0, e2) = e3
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9637) implies:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | |   (9638)  op(e0, e2) = e3
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (157), (9638) gives:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | |   (9639)  all_52_7 = e3
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7909), (9639) imply:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | |   (9640)  $false
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9640) is inconsistent.
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.47  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |   (9641)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9641) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |   (9642)  all_56_14 = e3 & op(e0, e1) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9642) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |   (9643)  op(e0, e1) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (9571), (9643), (function-axioms) are
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1147.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |   (9644)  all_56_15 = e3 & op(e0, e0) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9644) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |   (9645)  op(e0, e0) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (45), (9629)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |   (9646)  all_57_15 = all_10_2
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (9629), (9645)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |   (9647)  all_57_15 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9646), (9647) imply:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |   (9648)  all_10_2 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | SIMP: (9648) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |   (9649)  all_10_2 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |   (9650)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9650) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |   (9651)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9651) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |   (9652)  op(e3, e3) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |   (9653)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |   (9654)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               = e3) & op(e2, e2) = all_57_12 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7916), (9577), (9630), (9652), (9653),
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |            (9654), (function-axioms) are inconsistent by
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #72.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |   (9655)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9655) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |   (9656)  op(e2, e2) = e2
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7916), (9656), (function-axioms) are
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |   (9657)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9577), (9645), (9657),
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |            #295.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9658)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (278), (9582), (9584), (9588), (9658) are
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | |   (9659)  all_36_2 = e2
% 149.64/21.48  | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | COMBINE_EQS: (304), (9659) imply:
% 149.64/21.48  | | | | | | | | | | | | | |   (9660)  all_14_2 = e2
% 149.64/21.48  | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | SIMP: (9660) implies:
% 149.64/21.48  | | | | | | | | | | | | | |   (9661)  all_14_2 = e2
% 149.64/21.48  | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | REDUCE: (336), (9661) imply:
% 149.64/21.48  | | | | | | | | | | | | | |   (9662)   ~ (all_52_1 = e2)
% 149.64/21.48  | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | REDUCE: (338), (9661) imply:
% 149.64/21.48  | | | | | | | | | | | | | |   (9663)   ~ (all_52_2 = e2)
% 149.64/21.48  | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | REDUCE: (346), (9661) imply:
% 149.64/21.48  | | | | | | | | | | | | | |   (9664)   ~ (all_52_12 = e2)
% 149.64/21.48  | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | REDUCE: (51), (9661) imply:
% 149.64/21.48  | | | | | | | | | | | | | |   (9665)  op(e3, e3) = e2
% 149.64/21.48  | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.64/21.48  | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | |   (9666)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.64/21.48  | | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.64/21.48  | | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.64/21.48  | | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.48  | | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.64/21.48  | | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.64/21.48  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.48  | | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.64/21.48  | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | REF_CLOSE: (9), (7916), (9665), (9666), (function-axioms) are
% 149.64/21.48  | | | | | | | | | | | | | | |            inconsistent by sub-proof #120.
% 149.64/21.48  | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | |   (9667)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.64/21.48  | | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.64/21.48  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.48  | | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.48  | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.64/21.48  | | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.48  | | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.64/21.48  | | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.64/21.48  | | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.48  | | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.48  | | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.64/21.48  | | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.64/21.48  | | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.64/21.48  | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | BETA: splitting (9667) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | |   (9668)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.64/21.48  | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.48  | | | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.48  | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.64/21.48  | | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.64/21.48  | | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.64/21.48  | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | ALPHA: (9668) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | |   (9669)  op(e1, e1) = e1
% 149.64/21.48  | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9577), (9669), (function-axioms) are
% 149.64/21.48  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 149.64/21.48  | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | |   (9670)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.64/21.48  | | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.48  | | | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.48  | | | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.64/21.48  | | | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.64/21.48  | | | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.64/21.48  | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | ALPHA: (9670) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | |   (9671)  all_57_15 = e0
% 149.64/21.48  | | | | | | | | | | | | | | | |   (9672)  op(e0, e0) = e0
% 149.64/21.48  | | | | | | | | | | | | | | | |   (9673)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.64/21.48  | | | | | | | | | | | | | | | |   (9674)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.48  | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.48  | | | | | | | | | | | | | | | |             $i(all_57_12))
% 149.64/21.48  | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | |   (9675)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 149.64/21.48  | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | BETA: splitting (9675) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | |   (9676)  all_56_0 = e3 & op(e3, e3) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | ALPHA: (9676) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | |   (9677)  op(e3, e3) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9665), (9677), (function-axioms) are
% 149.64/21.48  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | |   (9678)  all_56_2 = e3 & op(e2, e3) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (7906), (9678), (function-axioms) are
% 149.64/21.48  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #917.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | |   (9679)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 149.64/21.48  | | | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 149.64/21.48  | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | BETA: splitting (9679) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | |   (9680)  all_56_6 = e3 & op(e1, e3) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | ALPHA: (9680) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | |   (9681)  all_56_6 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213), (214),
% 149.64/21.48  | | | | | | | | | | | | | | | | | |            (9576), (9577), (9681), (function-axioms) are
% 149.64/21.48  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #607.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | |   (9682)  all_56_12 = e3 & op(e0, e3) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | ALPHA: (9682) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | |   (9683)  all_56_12 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | |   (9684)  op(e0, e3) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | |   (9685)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (7907), (9665), (9685),
% 149.64/21.48  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.48  | | | | | | | | | | | | | | | | | | |            #660.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | |   (9686)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | BETA: splitting (9686) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9687)  all_56_4 = e3 & op(e3, e1) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | ALPHA: (9687) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9688)  op(e3, e1) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9570), (9688), (function-axioms) are
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9689)  all_56_9 = e3 & op(e3, e0) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | ALPHA: (9689) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9690)  op(e3, e0) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (45), (9672) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9691)  all_10_2 = e0
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (158), (9684) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9692)  all_52_3 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (167), (9690) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9693)  all_52_12 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (9692) imply:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9694)   ~ (all_52_2 = e3)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (9691) imply:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9695)   ~ (all_52_7 = e0)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (9691) imply:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9696)   ~ (all_52_11 = e0)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (9586), (9691) imply:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9697)   ~ (e2 = e0)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | REDUCE: (9581), (9691) imply:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | |   (9698)   ~ (e1 = e0)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |   (9699)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9699) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |   (9700)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9700) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |   (9701)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (9662), (9701), (function-axioms) are
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |   (9702)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9702) gives:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |   (9703)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_14)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9703) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |   (9704)   ~ (all_57_14 = e3)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |   (9705)  op(e1, e1) = all_57_14
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9577), (9704), (9705), (function-axioms) are
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #816.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |   (9706)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9706) implies:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |   (9707)  op(e0, e0) = e3
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (157), (205),
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |            (206), (207), (9586), (9683), (9695), (9707),
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | |            #632.
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.48  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |   (9708)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9708) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |   (9709)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (7907), (9577), (9709),
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |            #294.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |   (9710)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9710) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9711)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9711) implies:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9712)   ~ (all_57_14 = e2)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9713)  op(e1, e1) = all_57_14
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9714)  op(e1, e2) = e1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14, e1, e1, simplifying with (9577), (9713)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9715)  all_57_14 = e3
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (161), (9714) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9716)  all_52_6 = e1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (9716) imply:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9717)   ~ (all_52_2 = e1)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (9716) imply:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9718)   ~ (all_52_14 = e1)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9718) implies:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9719)   ~ (all_52_14 = e1)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (9720)  all_54_8 = e3
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (9694), (9720) are inconsistent by
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #394.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | |   (9721)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9721) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9722)  all_54_8 = e2
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (9722) imply:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9723)  all_52_2 = e2
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9663), (9723) imply:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9724)  $false
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9724) is inconsistent.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9725)  all_54_8 = e1 | all_54_8 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9725) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9726)  all_54_8 = e1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (9726) imply:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9727)  all_52_2 = e1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9717), (9727) imply:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9728)  $false
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9728) is inconsistent.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9729)  all_54_8 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (9729) imply:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9730)  all_52_2 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (9730) imply:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9731)   ~ (all_52_1 = e0)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9732)  all_54_4 = e3
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (7906), (9732) are inconsistent by
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #843.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9733)   ~ (all_54_4 = e3)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9734)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9734) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9735)  all_54_4 = e2
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (9662), (9735) are inconsistent by
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1175.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9736)  all_54_4 = e1 | all_54_4 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9736) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9737)  all_54_4 = e1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (9737) imply:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9738)  all_52_1 = e1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9738) implies:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9739)  all_52_1 = e1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (9739) imply:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9740)   ~ (all_52_13 = e1)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9740) implies:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9741)   ~ (all_52_13 = e1)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7906), (9739) imply:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9742)   ~ (e3 = e1)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (51), (159), (163), (167), (209),
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (346), (7916), (9577), (9690), (9719),
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9741), (function-axioms) are inconsistent by
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #70.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9743)  all_54_4 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (9731), (9743) are inconsistent by
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #796.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9744)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (7916), (9672), (9744),
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |            #130.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |   (9745)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9745) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |   (9746)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9746) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |   (9747)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9747) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9748)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9748) implies:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9749)  op(e3, e1) = e3
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9570), (9749), (function-axioms) are
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9750)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9750) implies:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9751)  op(e3, e3) = e1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9665), (9751), (function-axioms) are
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |   (9752)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9672), (9673), (9674), (9752),
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |            #69.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |   (9753)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9753) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |   (9754)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9665), (9754), (function-axioms) are
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |   (9755)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9755) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9756)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9756) implies:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9757)   ~ (all_57_13 = e1)
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9758)  op(e1, e1) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9673), (9757), (9758), (function-axioms) are
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #959.
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |   (9759)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9759) gives:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.50  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (9760)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9760) implies:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (9761)  all_57_12 = e0
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (9762)   ~ (all_57_11 = e2)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9674), (9761), (9762) are inconsistent by
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #890.
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (9763)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9763) implies:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |   (9764)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (156), (157), (7916), (9577),
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |            (9671), (9684), (9695), (9696), (9764),
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | |            #67.
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | |   (9765)  all_24_2 = e2
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | COMBINE_EQS: (318), (9765) imply:
% 149.64/21.51  | | | | | | | | | | | | |   (9766)  all_10_2 = e2
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | REDUCE: (45), (9766) imply:
% 149.64/21.51  | | | | | | | | | | | | |   (9767)  op(e0, e0) = e2
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | |   (9768)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.64/21.51  | | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.64/21.51  | | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.64/21.51  | | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.64/21.51  | | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.64/21.51  | | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.64/21.51  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.51  | | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.64/21.51  | | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.64/21.51  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.51  | | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.64/21.51  | | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.64/21.51  | | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.64/21.51  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | BETA: splitting (9768) gives:
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | |   (9769)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 149.64/21.51  | | | | | | | | | | | | | | |               & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 149.64/21.51  | | | | | | | | | | | | | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.64/21.51  | | | | | | | | | | | | | | |           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.64/21.51  | | | | | | | | | | | | | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 149.64/21.51  | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 149.64/21.51  | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | ALPHA: (9769) implies:
% 149.64/21.51  | | | | | | | | | | | | | | |   (9770)  op(e3, e3) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | REF_CLOSE: (9), (51), (159), (163), (167), (211), (346),
% 149.64/21.51  | | | | | | | | | | | | | | |            (7911), (9572), (9767), (9770), (function-axioms)
% 149.64/21.51  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #65.
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | |   (9771)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 149.64/21.51  | | | | | | | | | | | | | | |               & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 149.64/21.51  | | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.51  | | | | | | | | | | | | | | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.64/21.51  | | | | | | | | | | | | | | |               (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 149.64/21.51  | | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 149.64/21.51  | | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | ALPHA: (9771) implies:
% 149.64/21.51  | | | | | | | | | | | | | | |   (9772)  op(e2, e2) = e2
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | REF_CLOSE: (9), (7916), (9772), (function-axioms) are
% 149.64/21.51  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | |   (9773)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.64/21.51  | | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.64/21.51  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.51  | | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.64/21.51  | | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.51  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.64/21.51  | | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.64/21.51  | | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.51  | | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.64/21.51  | | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.64/21.51  | | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.51  | | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.51  | | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.51  | | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.64/21.51  | | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.64/21.51  | | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (9577), (9767), (9773),
% 149.64/21.51  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.51  | | | | | | | | | | | | | |            #291.
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | |   (9774)  all_22_2 = e1
% 149.64/21.51  | | | | | | | | | | | |   (9775)  ( ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0
% 149.64/21.51  | | | | | | | | | | | |             & op(e3, e1) = all_22_1 & $i(all_22_0) &
% 149.64/21.51  | | | | | | | | | | | |             $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e1)
% 149.64/21.51  | | | | | | | | | | | |             = all_22_1 & $i(all_22_1))
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | COMBINE_EQS: (320), (9774) imply:
% 149.64/21.51  | | | | | | | | | | | |   (9776)  all_14_2 = e1
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | COMBINE_EQS: (312), (9776) imply:
% 149.64/21.51  | | | | | | | | | | | |   (9777)  all_34_2 = e1
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | REDUCE: (336), (9776) imply:
% 149.64/21.51  | | | | | | | | | | | |   (9778)   ~ (all_52_1 = e1)
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | REDUCE: (338), (9776) imply:
% 149.64/21.51  | | | | | | | | | | | |   (9779)   ~ (all_52_2 = e1)
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | REDUCE: (342), (9776) imply:
% 149.64/21.51  | | | | | | | | | | | |   (9780)   ~ (all_52_4 = e1)
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | REDUCE: (344), (9776) imply:
% 149.64/21.51  | | | | | | | | | | | |   (9781)   ~ (all_52_8 = e1)
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | REDUCE: (346), (9776) imply:
% 149.64/21.51  | | | | | | | | | | | |   (9782)   ~ (all_52_12 = e1)
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | REDUCE: (51), (9776) imply:
% 149.64/21.51  | | | | | | | | | | | |   (9783)  op(e3, e3) = e1
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.64/21.51  | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | |   (9784)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.64/21.51  | | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.64/21.51  | | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.64/21.51  | | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.64/21.51  | | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.64/21.51  | | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.64/21.51  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.51  | | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.64/21.51  | | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.64/21.51  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.51  | | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.64/21.51  | | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.64/21.51  | | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.64/21.51  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7916), (9783), (9784),
% 149.64/21.51  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.51  | | | | | | | | | | | | |            #100.
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | |   (9785)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.64/21.51  | | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.64/21.51  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.51  | | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.64/21.51  | | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.51  | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.64/21.51  | | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.64/21.51  | | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.64/21.51  | | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.64/21.51  | | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.64/21.51  | | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.51  | | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.51  | | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.51  | | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.64/21.51  | | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.64/21.51  | | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | BETA: splitting (9785) gives:
% 149.64/21.51  | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | |   (9786)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.64/21.51  | | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.64/21.51  | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.51  | | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.64/21.51  | | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.51  | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.64/21.51  | | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.64/21.51  | | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | ALPHA: (9786) implies:
% 149.64/21.51  | | | | | | | | | | | | | |   (9787)  op(e1, e1) = e1
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | REF_CLOSE: (8), (9577), (9787), (function-axioms) are
% 149.64/21.51  | | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | |   (9788)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.64/21.51  | | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.64/21.51  | | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.64/21.51  | | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.51  | | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.51  | | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.64/21.51  | | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.64/21.51  | | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | ALPHA: (9788) implies:
% 149.64/21.51  | | | | | | | | | | | | | |   (9789)  all_57_15 = e0
% 149.64/21.51  | | | | | | | | | | | | | |   (9790)  op(e0, e0) = e0
% 149.64/21.51  | | | | | | | | | | | | | |   (9791)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 149.64/21.51  | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | | |             $i(all_57_14))
% 149.64/21.51  | | | | | | | | | | | | | |   (9792)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.64/21.51  | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.64/21.51  | | | | | | | | | | | | | |             $i(all_57_12))
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 149.64/21.51  | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | |   (9793)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 149.64/21.51  | | | | | | | | | | | | | | |             & op(e2, e3) = e3)
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | REF_CLOSE: (8), (166), (7906), (9783), (9793),
% 149.64/21.51  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.51  | | | | | | | | | | | | | | |            #916.
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | |   (9794)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 149.64/21.51  | | | | | | | | | | | | | | |             e3 & op(e0, e3) = e3)
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | BETA: splitting (9794) gives:
% 149.64/21.51  | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | |   (9795)  all_56_6 = e3 & op(e1, e3) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | ALPHA: (9795) implies:
% 149.64/21.51  | | | | | | | | | | | | | | | |   (9796)  all_56_6 = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (212), (213), (214),
% 149.64/21.51  | | | | | | | | | | | | | | | |            (9576), (9577), (9796), (function-axioms) are
% 149.64/21.51  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #607.
% 149.64/21.51  | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | |   (9797)  all_56_12 = e3 & op(e0, e3) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | ALPHA: (9797) implies:
% 149.64/21.51  | | | | | | | | | | | | | | | |   (9798)  all_56_12 = e3
% 149.64/21.51  | | | | | | | | | | | | | | | |   (9799)  op(e0, e3) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 149.64/21.51  | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | |   (9800)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | |             & op(e3, e2) = e3)
% 149.64/21.51  | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | BETA: splitting (9800) gives:
% 149.64/21.51  | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9801)  all_56_0 = e3 & op(e3, e3) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | ALPHA: (9801) implies:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9802)  op(e3, e3) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (166), (228),
% 149.64/21.51  | | | | | | | | | | | | | | | | | |            (230), (232), (9778), (9798), (9802),
% 149.64/21.51  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.51  | | | | | | | | | | | | | | | | | |            #407.
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9803)  all_56_1 = e3 & op(e3, e2) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | ALPHA: (9803) implies:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9804)  op(e3, e2) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7907), (9804), (function-axioms) are
% 149.64/21.51  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1166.
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | |   (9805)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | |             & op(e3, e0) = e3)
% 149.64/21.51  | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | BETA: splitting (9805) gives:
% 149.64/21.51  | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9806)  all_56_4 = e3 & op(e3, e1) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | ALPHA: (9806) implies:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9807)  op(e3, e1) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9570), (9807), (function-axioms) are
% 149.64/21.51  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9808)  all_56_9 = e3 & op(e3, e0) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | ALPHA: (9808) implies:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9809)  op(e3, e0) = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 149.64/21.51  | | | | | | | | | | | | | | | | | |              e0, e0, simplifying with (45), (9790) gives:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9810)  all_10_2 = e0
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 149.64/21.51  | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (158), (9799) gives:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9811)  all_52_3 = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 149.64/21.51  | | | | | | | | | | | | | | | | | |              e3, e0, e3, simplifying with (167), (9809) gives:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9812)  all_52_12 = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | REDUCE: (360), (9810) imply:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9813)   ~ (all_52_7 = e0)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | REDUCE: (367), (9810) imply:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9814)   ~ (all_52_11 = e0)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | REDUCE: (112), (9812) imply:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9815)   ~ (all_52_13 = e3)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | REDUCE: (111), (9812) imply:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9816)   ~ (all_52_14 = e3)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | REDUCE: (369), (9810) imply:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9817)   ~ (all_52_13 = e0)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | REDUCE: (9581), (9810) imply:
% 149.64/21.51  | | | | | | | | | | | | | | | | | |   (9818)   ~ (e1 = e0)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |   (9819)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |               e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |           (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |               e2) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | BETA: splitting (9819) gives:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |   (9820)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |           | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9820) gives:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |   (9821)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |           | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7916), (9790), (9821), (function-axioms) are
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #64.
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |   (9822)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_2) & $i(all_57_14))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (162), (9779), (9790), (9822),
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |            #1045.
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |   (9823)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |           (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |           | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9823) gives:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |   (9824)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_10))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (169), (7907), (9577), (9824),
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |            #294.
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |   (9825)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |               e1) = all_57_14 & $i(all_57_3) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |             all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (7916), (9783), (9790), (9825),
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | |            #101.
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | End of split
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | Case 2:
% 149.64/21.51  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |   (9826)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.64/21.51  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |           (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |           | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |               = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | BETA: splitting (9826) gives:
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | 
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |   (9827)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |           (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_13))
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9827) gives:
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | | 
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.64/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | |   (9828)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | |             all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | |               e2) = all_57_12 & op(e2, e1) = e2 &
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_6) & $i(all_57_12))
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9828) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9829)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_10)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9829) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9830)  op(e3, e1) = e3
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9570), (9830), (function-axioms) are
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9831)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |             e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9831) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9832)   ~ (all_57_12 = e1)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9833)   ~ (all_57_6 = e3)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9834)  op(e2, e1) = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9835)  op(e2, e2) = all_57_12
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9836)  op(e3, e1) = all_57_6
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |              e1, e2, simplifying with (164), (9834) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9837)  all_52_9 = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (7916), (9835)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9838)  all_57_12 = e3
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |              all_57_6, e1, e3, simplifying with (168), (9836)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9839)  all_57_6 = all_52_8
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (9837) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9840)   ~ (all_52_1 = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (9837) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9841)   ~ (all_52_8 = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (9837) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9842)   ~ (all_52_11 = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | SIMP: (9842) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9843)   ~ (all_52_11 = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (9837) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9844)   ~ (all_52_13 = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | SIMP: (9844) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9845)   ~ (all_52_13 = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7910), (9837) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | |   (9846)   ~ (e3 = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | |   (9847)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9847) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |   (9848)  all_56_2 = e0 & op(e2, e3) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9848) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |   (9849)  all_56_2 = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |   (9850)  op(e2, e3) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (9851)  all_54_7 = e3
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9851) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (9852)  all_52_13 = e3
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7911), (9852) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (9853)  $false
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9853) is inconsistent.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (9854)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9855)  all_54_2 = e3
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (9570), (9855) are inconsistent by
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #184.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9856)   ~ (all_54_2 = e3)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9857)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9857) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9858)  all_54_2 = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (9841), (9858) are inconsistent by
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #183.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9859)   ~ (all_54_2 = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9860)  all_54_2 = e1 | all_54_2 = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9860) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9861)  all_54_2 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (9781), (9861) are inconsistent by
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #384.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9862)  all_54_2 = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (9862) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9863)  all_52_8 = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9863) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9864)  all_52_8 = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (9864) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9865)   ~ (all_52_4 = e0)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (9864) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9866)   ~ (all_52_11 = e0)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9570), (9864) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9867)   ~ (e3 = e0)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9841), (9864) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9868)   ~ (e2 = e0)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9869)   ~ (all_34_2 = e1)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9777), (9869) imply:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9870)  $false
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9870) is inconsistent.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9871)  ( ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e3, e1) = all_34_1 & $i(all_34_0) &
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e3, e1)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             = all_34_1 & $i(all_34_1))
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9872)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e0)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9872) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9873)  all_56_1 = e0 & op(e3, e2) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9865), (9873), (function-axioms) are
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1013.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9874)  all_56_3 = e0 & op(e2, e2) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9874) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9875)  op(e2, e2) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (45), (109), (111), (112),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (116), (124), (125), (127), (132), (138), (139),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (144), (145), (147), (156), (157), (158), (159),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (166), (168), (169), (190),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (192), (200), (206), (209), (212), (213),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (214), (216), (217), (218), (220), (222), (223),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (232),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (237), (238), (247), (248),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (249), (269), (349), (360), (367), (368), (370),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7908), (7910), (9570), (9572), (9576), (9577),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9581), (9778), (9783), (9817), (9875),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #187.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9876)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e0, e2) = e0)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9876) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9877)  all_56_7 = e0 & op(e1, e2) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9877) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9878)  all_56_7 = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9879)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9879) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9880)  all_56_2 = e1 & op(e2, e3) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9880) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9881)  op(e2, e3) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (166), (259), (9817), (9845), (9854),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9881), (function-axioms) are inconsistent by
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1160.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9882)  all_56_3 = e1 & op(e2, e2) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9882) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9883)  all_56_3 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9884)  op(e2, e2) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (124), (127),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (138), (139), (144), (145), (147), (156), (158),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (159), (161), (163), (164), (166), (168), (190),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (191), (206), (209), (212), (213), (214), (216),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (217), (218), (220), (222), (223), (224), (226),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (228), (229), (232), (233), (234), (235),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (237), (238), (247), (248), (349), (360), (7908),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (7910), (9570), (9576), (9577), (9581), (9778),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9783), (9883), (9884), (function-axioms) are
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #228.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9885)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e2, e0) = e1)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9885) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9886)  all_56_5 = e1 & op(e2, e1) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9886) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9887)  all_56_5 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9888)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (166), (9783), (9850), (9888),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #63.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9889)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9889) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9890)  all_56_6 = e2 & op(e1, e3) = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9890) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9891)  all_56_6 = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9892)  op(e1, e3) = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9893)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9893) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9894)  all_56_1 = e1 & op(e3, e2) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9780), (9894), (function-axioms) are
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #420.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9895)  all_56_3 = e1 & op(e2, e2) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9895) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9896)  all_56_3 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9897)  op(e2, e2) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (206), (212),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (213), (214), (216), (218), (224), (226), (227),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (228), (232), (234), (7908), (9576), (9577),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9783), (9790), (9887), (9896), (9897),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #246.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9898)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9898) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9899)  all_56_7 = e1 & op(e1, e2) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9899) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9900)  all_56_7 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9878), (9900) are inconsistent by sub-proof
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #987.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9901)  all_56_13 = e1 & op(e0, e2) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9901) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9902)  all_56_13 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (161), (169),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (212), (213), (214), (216), (217), (218),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (226), (227), (228), (232), (233), (234),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (7907), (7908), (7916), (9566), (9576),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9577), (9580), (9775), (9783), (9790), (9798),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9814), (9843), (9849), (9850), (9865), (9871),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9878), (9891), (9892), (9902), (function-axioms)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #62.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9903)  all_56_12 = e2 & op(e0, e3) = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9903) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9904)  all_56_12 = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9798), (9904) are inconsistent by sub-proof
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #869.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9905)  all_56_10 = e1 & op(e2, e0) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9905) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9906)  all_56_10 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9907)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (166), (9783), (9850), (9907),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #63.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9908)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9908) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9909)  all_56_6 = e2 & op(e1, e3) = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9909) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9910)  all_56_6 = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9911)  op(e1, e3) = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9912)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e2) = e1)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (164), (169), (220),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (7910), (9780), (9906), (9912),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #98.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9913)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |             e1 & op(e0, e2) = e1)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9913) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9914)  all_56_7 = e1 & op(e1, e2) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9914) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9915)  all_56_7 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9878), (9915) are inconsistent by sub-proof
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #987.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9916)  all_56_13 = e1 & op(e0, e2) = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9916) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9917)  all_56_13 = e1
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (156), (161), (169),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (207), (212), (213), (214), (216), (217), (218),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (224), (226), (227), (228), (232), (233), (234),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (7907), (7908), (7916), (9566), (9576),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9577), (9580), (9775), (9783), (9790), (9798),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9814), (9843), (9849), (9850), (9865), (9871),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9878), (9910), (9911), (9917), (function-axioms)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #62.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9918)  all_56_12 = e2 & op(e0, e3) = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9918) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9919)  all_56_12 = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9798), (9919) are inconsistent by sub-proof
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #869.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9920)  all_56_13 = e0 & op(e0, e2) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9920) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (9921)  op(e0, e2) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9813), (9921), (function-axioms) are
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |   (9922)  all_56_3 = e0 & op(e2, e2) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9922) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |   (9923)  op(e2, e2) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (45), (109), (111), (112),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            (116), (124), (125), (127), (132), (138), (139),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            (144), (145), (147), (156), (157), (158), (159),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            (161), (163), (164), (166), (168), (169), (190),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            (191), (192), (200), (206), (209), (212), (213),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            (214), (216), (217), (218), (220), (222), (223),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            (224), (225), (226), (227), (228), (229), (232),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            (233), (234), (235), (237), (238), (247), (248),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            (249), (269), (349), (360), (367), (368), (370),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            (7908), (7910), (9570), (9572), (9576), (9577),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            (9581), (9778), (9783), (9817), (9923),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |            #187.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | |   (9924)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | |             e0 & op(e2, e0) = e0)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9924) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |   (9925)  all_56_5 = e0 & op(e2, e1) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9925) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | |   (9926)  op(e2, e1) = e0
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (9927)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |             & op(e2, e3) = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (9783), (9840), (9927),
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |            #938.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |   (9928)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | |             e2 & op(e0, e3) = e2)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9928) gives:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9929)  all_56_6 = e2 & op(e1, e3) = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9929) implies:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9930)  op(e1, e3) = e2
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9566), (9580), (9926), (9930), (function-axioms)
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #164.
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.52  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9931)  all_56_12 = e2 & op(e0, e3) = e2
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9931) implies:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | |   (9932)  all_56_12 = e2
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9798), (9932) are inconsistent by sub-proof
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | |            #869.
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | |   (9933)  all_56_10 = e0 & op(e2, e0) = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9817), (9933), (function-axioms) are
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #540.
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |   (9934)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9790), (9791), (9792), (9934),
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |            #69.
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |   (9935)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |               e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |           (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |             ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | BETA: splitting (9935) gives:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |   (9936)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |               e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |           | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |               = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_9) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14))
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9783), (9936), (function-axioms) are
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |   (9937)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |               e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |             all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                   e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                   = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | |                 all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9937) gives:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |   (9938)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |           $i(all_57_13)
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9938) implies:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |   (9939)   ~ (all_57_13 = e1)
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |   (9940)  op(e1, e1) = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9791), (9939), (9940), (function-axioms) are
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #959.
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |   (9941)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |             op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |             & op(e1, e0) = e1 & $i(all_57_11) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                   e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |               (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                   = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                   e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |               (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                   = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | |                 & $i(all_57_7))))
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9941) gives:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |   (9942)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9942) implies:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |   (9943)  all_57_12 = e0
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |   (9944)   ~ (all_57_11 = e2)
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9792), (9943), (9944) are inconsistent by
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #890.
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |   (9945)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7)))
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9945) implies:
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |   (9946)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |             = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (156), (157), (7916), (9577),
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |            (9789), (9799), (9813), (9814), (9946),
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | |            #67.
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | |   (9947)  all_14_2 = e0
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | REDUCE: (340), (9947) imply:
% 149.94/21.53  | | | | | | | | | | |   (9948)   ~ (all_52_3 = e0)
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | REDUCE: (51), (9947) imply:
% 149.94/21.53  | | | | | | | | | | |   (9949)  op(e3, e3) = e0
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | BETA: splitting (237) gives:
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | |   (9950)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.94/21.53  | | | | | | | | | | | |                 e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.94/21.53  | | | | | | | | | | | |                 & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.94/21.53  | | | | | | | | | | | |             ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.94/21.53  | | | | | | | | | | | |                 (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.94/21.53  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.94/21.53  | | | | | | | | | | | |                   e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.94/21.53  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.94/21.53  | | | | | | | | | | | |           (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.94/21.53  | | | | | | | | | | | |                 e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.94/21.53  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.94/21.53  | | | | | | | | | | | |             ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.94/21.53  | | | | | | | | | | | |                 (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.94/21.53  | | | | | | | | | | | |                 $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.94/21.53  | | | | | | | | | | | |                   e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.94/21.53  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15))))
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | REF_CLOSE: (7), (9), (7916), (9949), (9950),
% 149.94/21.53  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.53  | | | | | | | | | | | |            #87.
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | |   (9951)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.94/21.53  | | | | | | | | | | | |                 e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.94/21.53  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.94/21.53  | | | | | | | | | | | |             ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.94/21.53  | | | | | | | | | | | |                 (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.94/21.53  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.94/21.53  | | | | | | | | | | | |                   e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.94/21.53  | | | | | | | | | | | |                   e0) = all_57_15 & $i(all_57_15)))) |
% 149.94/21.53  | | | | | | | | | | | |           (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.94/21.53  | | | | | | | | | | | |                 e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.94/21.53  | | | | | | | | | | | |                 & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.94/21.53  | | | | | | | | | | | |             ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.94/21.53  | | | | | | | | | | | |                 (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.94/21.53  | | | | | | | | | | | |                 $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.94/21.53  | | | | | | | | | | | |                   e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.94/21.53  | | | | | | | | | | | |                   e1) = all_57_14 & $i(all_57_14))))
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | BETA: splitting (9951) gives:
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | |   (9952)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 149.94/21.53  | | | | | | | | | | | | |               & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 149.94/21.53  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.94/21.53  | | | | | | | | | | | | |           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.94/21.53  | | | | | | | | | | | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.94/21.53  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 149.94/21.53  | | | | | | | | | | | | |               = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 149.94/21.53  | | | | | | | | | | | | |               all_57_15 & $i(all_57_15)))
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | ALPHA: (9952) implies:
% 149.94/21.53  | | | | | | | | | | | | |   (9953)  op(e1, e1) = e1
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | REF_CLOSE: (8), (9577), (9953), (function-axioms) are
% 149.94/21.53  | | | | | | | | | | | | |            inconsistent by sub-proof #734.
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | |   (9954)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 149.94/21.53  | | | | | | | | | | | | |               & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 149.94/21.53  | | | | | | | | | | | | |               op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.94/21.53  | | | | | | | | | | | | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.94/21.53  | | | | | | | | | | | | |               (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.94/21.53  | | | | | | | | | | | | |               $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.94/21.53  | | | | | | | | | | | | |                 e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.94/21.53  | | | | | | | | | | | | |                 e1) = all_57_14 & $i(all_57_14)))
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | ALPHA: (9954) implies:
% 149.94/21.53  | | | | | | | | | | | | |   (9955)  op(e0, e0) = e0
% 149.94/21.53  | | | | | | | | | | | | |   (9956)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 149.94/21.53  | | | | | | | | | | | | |             (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 149.94/21.53  | | | | | | | | | | | | |             $i(all_57_14))
% 149.94/21.53  | | | | | | | | | | | | |   (9957)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.94/21.53  | | | | | | | | | | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.94/21.53  | | | | | | | | | | | | |             $i(all_57_12))
% 149.94/21.53  | | | | | | | | | | | | |   (9958)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10
% 149.94/21.53  | | | | | | | | | | | | |               = e0) & op(e3, e3) = all_57_10 &
% 149.94/21.53  | | | | | | | | | | | | |             $i(all_57_10))
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (45), (156), (158),
% 149.94/21.53  | | | | | | | | | | | | |            (168), (169), (238), (367), (7907), (7916),
% 149.94/21.53  | | | | | | | | | | | | |            (9570), (9577), (9948), (9949), (9955), (9956),
% 149.94/21.53  | | | | | | | | | | | | |            (9957), (9958), (function-axioms) are inconsistent
% 149.94/21.53  | | | | | | | | | | | | |            by sub-proof #61.
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | |   (9959)  all_10_2 = e1
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | REDUCE: (369), (9959) imply:
% 149.94/21.53  | | | | | | | | | |   (9960)   ~ (all_52_13 = e1)
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | REDUCE: (370), (9959) imply:
% 149.94/21.53  | | | | | | | | | |   (9961)   ~ (all_52_14 = e1)
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | REDUCE: (45), (9959) imply:
% 149.94/21.53  | | | | | | | | | |   (9962)  op(e0, e0) = e1
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | BETA: splitting (211) gives:
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | |   (9963)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 149.94/21.53  | | | | | | | | | | |             e3 & op(e2, e0) = e3)
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | BETA: splitting (9963) gives:
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | |   (9964)  all_56_9 = e3 & op(e3, e0) = e3
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | ALPHA: (9964) implies:
% 149.94/21.53  | | | | | | | | | | | |   (9965)  op(e3, e0) = e3
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (51), (159), (163), (167), (209),
% 149.94/21.53  | | | | | | | | | | | |            (237), (346), (7916), (9577), (9960), (9961),
% 149.94/21.53  | | | | | | | | | | | |            (9965), (function-axioms) are inconsistent by
% 149.94/21.53  | | | | | | | | | | | |            sub-proof #70.
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | |   (9966)  all_56_10 = e3 & op(e2, e0) = e3
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | REF_CLOSE: (163), (7911), (9966), (function-axioms) are
% 149.94/21.53  | | | | | | | | | | | |            inconsistent by sub-proof #114.
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | |   (9967)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 149.94/21.53  | | | | | | | | | | |             e3 & op(e0, e0) = e3)
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | REF_CLOSE: (8), (159), (9572), (9962), (9967),
% 149.94/21.53  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.53  | | | | | | | | | | |            #60.
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | | 
% 149.94/21.53  | | | | | | | | End of split
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | |   (9968)  all_56_14 = e3 & op(e0, e1) = e3
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | | ALPHA: (9968) implies:
% 149.94/21.53  | | | | | | | |   (9969)  op(e0, e1) = e3
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | | REF_CLOSE: (156), (9571), (9969), (function-axioms) are
% 149.94/21.53  | | | | | | | |            inconsistent by sub-proof #1147.
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | End of split
% 149.94/21.53  | | | | | | | 
% 149.94/21.53  | | | | | | End of split
% 149.94/21.53  | | | | | | 
% 149.94/21.53  | | | | | End of split
% 149.94/21.53  | | | | | 
% 149.94/21.53  | | | | End of split
% 149.94/21.53  | | | | 
% 149.94/21.53  | | | Case 2:
% 149.94/21.53  | | | | 
% 149.94/21.53  | | | |   (9970)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2,
% 149.94/21.53  | | | |               e0) = e3)
% 149.94/21.53  | | | | 
% 149.94/21.53  | | | | BETA: splitting (9970) gives:
% 149.94/21.53  | | | | 
% 149.94/21.53  | | | | Case 1:
% 149.94/21.53  | | | | | 
% 149.94/21.53  | | | | |   (9971)  all_56_5 = e3 & op(e2, e1) = e3
% 149.94/21.53  | | | | | 
% 149.94/21.53  | | | | | REF_CLOSE: (164), (7910), (9971), (function-axioms) are inconsistent
% 149.94/21.53  | | | | |            by sub-proof #647.
% 149.94/21.53  | | | | | 
% 149.94/21.53  | | | | Case 2:
% 149.94/21.53  | | | | | 
% 149.94/21.53  | | | | |   (9972)  all_56_10 = e3 & op(e2, e0) = e3
% 149.94/21.53  | | | | | 
% 149.94/21.53  | | | | | REF_CLOSE: (163), (7911), (9972), (function-axioms) are inconsistent
% 149.94/21.53  | | | | |            by sub-proof #114.
% 149.94/21.53  | | | | | 
% 149.94/21.53  | | | | End of split
% 149.94/21.53  | | | | 
% 149.94/21.53  | | | End of split
% 149.94/21.53  | | | 
% 149.94/21.53  | | End of split
% 149.94/21.53  | | 
% 149.94/21.53  | Case 2:
% 149.94/21.53  | | 
% 149.94/21.53  | |   (9973)  all_4_2 = e2
% 149.94/21.53  | | 
% 149.94/21.53  | | REDUCE: (348), (9973) imply:
% 149.94/21.53  | |   (9974)   ~ (all_52_2 = e2)
% 149.94/21.53  | | 
% 149.94/21.53  | | REDUCE: (359), (9973) imply:
% 149.94/21.53  | |   (9975)   ~ (all_52_6 = e2)
% 149.94/21.53  | | 
% 149.94/21.53  | | REDUCE: (361), (9973) imply:
% 149.94/21.53  | |   (9976)   ~ (all_52_8 = e2)
% 149.94/21.53  | | 
% 149.94/21.53  | | REDUCE: (362), (9973) imply:
% 149.94/21.53  | |   (9977)   ~ (all_52_9 = e2)
% 149.94/21.53  | | 
% 149.94/21.53  | | REDUCE: (364), (9973) imply:
% 149.94/21.53  | |   (9978)   ~ (all_52_11 = e2)
% 149.94/21.53  | | 
% 149.94/21.53  | | REDUCE: (366), (9973) imply:
% 149.94/21.53  | |   (9979)   ~ (all_52_14 = e2)
% 149.94/21.53  | | 
% 149.94/21.53  | | REDUCE: (36), (9973) imply:
% 149.94/21.53  | |   (9980)  op(e1, e1) = e2
% 149.94/21.53  | | 
% 149.94/21.53  | | BETA: splitting (40) gives:
% 149.94/21.53  | | 
% 149.94/21.53  | | Case 1:
% 149.94/21.53  | | | 
% 149.94/21.53  | | |   (9981)   ~ (all_6_2 = e3)
% 149.94/21.53  | | | 
% 149.94/21.53  | | | BETA: splitting (46) gives:
% 149.94/21.53  | | | 
% 149.94/21.53  | | | Case 1:
% 149.94/21.53  | | | | 
% 149.94/21.53  | | | |   (9982)   ~ (all_10_2 = e1)
% 149.94/21.53  | | | | 
% 149.94/21.53  | | | | BETA: splitting (52) gives:
% 149.94/21.53  | | | | 
% 149.94/21.53  | | | | Case 1:
% 149.94/21.53  | | | | | 
% 149.94/21.53  | | | | |   (9983)   ~ (all_14_2 = e0)
% 149.94/21.53  | | | | | 
% 149.94/21.53  | | | | | BETA: splitting (55) gives:
% 149.94/21.53  | | | | | 
% 149.94/21.53  | | | | | Case 1:
% 149.94/21.53  | | | | | | 
% 149.94/21.53  | | | | | |   (9984)   ~ (all_16_2 = e0)
% 149.94/21.53  | | | | | | 
% 149.94/21.53  | | | | | | REDUCE: (327), (9984) imply:
% 149.94/21.53  | | | | | |   (9985)   ~ (all_6_2 = e0)
% 149.94/21.53  | | | | | | 
% 149.94/21.53  | | | | | | BETA: splitting (61) gives:
% 149.94/21.53  | | | | | | 
% 149.94/21.53  | | | | | | Case 1:
% 149.94/21.53  | | | | | | | 
% 149.94/21.53  | | | | | | |   (9986)   ~ (all_20_2 = e1)
% 149.94/21.53  | | | | | | | 
% 149.94/21.53  | | | | | | | REDUCE: (282), (9986) imply:
% 149.94/21.53  | | | | | | |   (9987)   ~ (all_6_2 = e1)
% 149.94/21.53  | | | | | | | 
% 149.94/21.53  | | | | | | | BETA: splitting (198) gives:
% 149.94/21.53  | | | | | | | 
% 149.94/21.53  | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | |   (9988)  all_54_5 = e3
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | | COMBINE_EQS: (267), (9988) imply:
% 149.94/21.53  | | | | | | | |   (9989)  all_6_2 = e3
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | | REDUCE: (9981), (9989) imply:
% 149.94/21.53  | | | | | | | |   (9990)  $false
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | | CLOSE: (9990) is inconsistent.
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | Case 2:
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | |   (9991)   ~ (all_54_5 = e3)
% 149.94/21.53  | | | | | | | |   (9992)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | | BETA: splitting (9992) gives:
% 149.94/21.53  | | | | | | | | 
% 149.94/21.53  | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | 
% 149.94/21.53  | | | | | | | | |   (9993)  all_54_5 = e2
% 149.94/21.53  | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | COMBINE_EQS: (267), (9993) imply:
% 149.94/21.53  | | | | | | | | |   (9994)  all_6_2 = e2
% 149.94/21.53  | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | REDUCE: (347), (9994) imply:
% 149.94/21.53  | | | | | | | | |   (9995)   ~ (all_52_1 = e2)
% 149.94/21.53  | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | REDUCE: (350), (9994) imply:
% 149.94/21.53  | | | | | | | | |   (9996)   ~ (all_52_4 = e2)
% 149.94/21.53  | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | REDUCE: (358), (9994) imply:
% 149.94/21.53  | | | | | | | | |   (9997)   ~ (all_52_13 = e2)
% 149.94/21.53  | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | REDUCE: (9981), (9994) imply:
% 149.94/21.53  | | | | | | | | |   (9998)   ~ (e3 = e2)
% 149.94/21.53  | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | REDUCE: (39), (9994) imply:
% 149.94/21.53  | | | | | | | | |   (9999)  op(e2, e2) = e2
% 149.94/21.53  | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | BETA: splitting (64) gives:
% 149.94/21.53  | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | |   (10000)   ~ (all_22_2 = e1)
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | REDUCE: (320), (10000) imply:
% 149.94/21.53  | | | | | | | | | |   (10001)   ~ (all_14_2 = e1)
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | BETA: splitting (67) gives:
% 149.94/21.53  | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | |   (10002)   ~ (all_24_2 = e2)
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | REDUCE: (318), (10002) imply:
% 149.94/21.53  | | | | | | | | | | |   (10003)   ~ (all_10_2 = e2)
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | BETA: splitting (207) gives:
% 149.94/21.53  | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | |   (10004)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 149.94/21.53  | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | BETA: splitting (10004) gives:
% 149.94/21.53  | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | |   (10005)  all_56_12 = e2 & op(e0, e3) = e2
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | ALPHA: (10005) implies:
% 149.94/21.53  | | | | | | | | | | | | |   (10006)  all_56_12 = e2
% 149.94/21.53  | | | | | | | | | | | | |   (10007)  op(e0, e3) = e2
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | BETA: splitting (210) gives:
% 149.94/21.53  | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | |   (10008)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 149.94/21.53  | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 149.94/21.53  | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | BETA: splitting (10008) gives:
% 149.94/21.53  | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | |   (10009)  all_56_9 = e2 & op(e3, e0) = e2
% 149.94/21.53  | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | ALPHA: (10009) implies:
% 149.94/21.53  | | | | | | | | | | | | | | |   (10010)  all_56_9 = e2
% 149.94/21.53  | | | | | | | | | | | | | | |   (10011)  op(e3, e0) = e2
% 149.94/21.53  | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 149.94/21.53  | | | | | | | | | | | | | | |              e3, e0, simplifying with (158), (10007) gives:
% 149.94/21.53  | | | | | | | | | | | | | | |   (10012)  all_52_3 = e2
% 149.94/21.53  | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 149.94/21.53  | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (167), (10011) gives:
% 149.94/21.53  | | | | | | | | | | | | | | |   (10013)  all_52_12 = e2
% 149.94/21.53  | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | REDUCE: (112), (10013) imply:
% 149.94/21.53  | | | | | | | | | | | | | | |   (10014)   ~ (all_52_13 = e2)
% 149.94/21.53  | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | REDUCE: (346), (10013) imply:
% 149.94/21.53  | | | | | | | | | | | | | | |   (10015)   ~ (all_14_2 = e2)
% 149.94/21.53  | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | SIMP: (10015) implies:
% 149.94/21.53  | | | | | | | | | | | | | | |   (10016)   ~ (all_14_2 = e2)
% 149.94/21.53  | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | REDUCE: (368), (10013) imply:
% 149.94/21.53  | | | | | | | | | | | | | | |   (10017)   ~ (all_10_2 = e2)
% 149.94/21.53  | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 149.94/21.53  | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | Case 1:
% 149.94/21.53  | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | |   (10018)  all_54_0 = e3
% 149.94/21.53  | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | COMBINE_EQS: (278), (10018) imply:
% 149.94/21.53  | | | | | | | | | | | | | | | |   (10019)  all_14_2 = e3
% 149.94/21.53  | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | REDUCE: (342), (10019) imply:
% 149.94/21.53  | | | | | | | | | | | | | | | |   (10020)   ~ (all_52_4 = e3)
% 149.94/21.53  | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | REDUCE: (344), (10019) imply:
% 149.94/21.53  | | | | | | | | | | | | | | | |   (10021)   ~ (all_52_8 = e3)
% 149.94/21.53  | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | REDUCE: (51), (10019) imply:
% 149.94/21.53  | | | | | | | | | | | | | | | |   (10022)  op(e3, e3) = e3
% 149.94/21.53  | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 149.94/21.53  | | | | | | | | | | | | | | | | 
% 149.94/21.53  | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | |   (10023)   ~ (all_42_2 = e3)
% 149.94/21.54  | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | REDUCE: (302), (10023) imply:
% 149.94/21.54  | | | | | | | | | | | | | | | | |   (10024)   ~ (all_10_2 = e3)
% 149.94/21.54  | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | |   (10025)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.94/21.54  | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.94/21.54  | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | BETA: splitting (10025) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |   (10026)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (166), (188), (245), (9982), (9995),
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |            (9999), (10003), (10024), (10026),
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |            #546.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |   (10027)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (10027) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |   (10028)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10020), (10028), (function-axioms) are
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |   (10029)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10029) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |   (10030)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10030) implies:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |   (10031)  op(e3, e3) = e2
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10022), (10031), (function-axioms) are
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |   (10032)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (209), (211),
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            (9999), (10010), (10032), (function-axioms) are
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #59.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.54  | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | |   (10033)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.94/21.54  | | | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | BETA: splitting (10033) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |   (10034)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (10034) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |   (10035)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (9977), (10021), (10035),
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |            #1083.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |   (10036)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10036) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |   (10037)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10037) implies:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |   (10038)  op(e0, e0) = e1
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (9982), (10038), (function-axioms) are
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1116.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |   (10039)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (167), (346), (10022), (10039),
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            #58.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |   (10040)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | BETA: splitting (10040) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |   (10041)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (9983), (10001), (10016),
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |            (10041), (function-axioms) are inconsistent by
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |            sub-proof #1079.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |   (10042)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10042) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |   (10043)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10043) implies:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |   (10044)  op(e2, e0) = e2
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9997), (10044), (function-axioms) are
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |   (10045)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10045) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |   (10046)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10046) implies:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |   (10047)  op(e2, e2) = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9999), (10047), (function-axioms) are
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |   (10048)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10048) implies:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |   (10049)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | |   (10050)  all_54_15 = e3
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (10024), (10050) are inconsistent by
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1049.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | |   (10051)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10051) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | |   (10052)  all_54_15 = e2
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (10003), (10052) are inconsistent by
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1048.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | |   (10053)  all_54_15 = e1 | all_54_15 = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10053) gives:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (10054)  all_54_15 = e1
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (9982), (10054) are inconsistent by
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1047.
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (10055)  all_54_15 = e0
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (10055) imply:
% 149.94/21.54  | | | | | | | | | | | | | | | | | | | | | | | | |   (10056)  all_10_2 = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10056) implies:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (10057)  all_10_2 = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (10057) imply:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (10058)   ~ (all_52_7 = e0)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (10057) imply:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (10059)   ~ (all_52_11 = e0)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10049) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10060)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10060) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10061)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10061) implies:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10062)  op(e2, e2) = e3
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9999), (10062), (function-axioms) are
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10063)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & $i(all_57_3))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10063) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10064)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_1)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10064) implies:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10065)  op(e1, e1) = e3
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (158), (245), (349), (367), (9982),
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10022), (10049), (10053), (10065),
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #694.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10066)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_3)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10066) implies:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10067)  op(e3, e3) = e2
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10022), (10067), (function-axioms) are
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10068)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (156), (157), (9999), (10058), (10059),
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            (10068), (function-axioms) are inconsistent by
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #57.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | |   (10069)  all_42_2 = e3
% 149.94/21.55  | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (10069) imply:
% 149.94/21.55  | | | | | | | | | | | | | | | | |   (10070)  all_10_2 = e3
% 149.94/21.55  | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | REDUCE: (369), (10070) imply:
% 149.94/21.55  | | | | | | | | | | | | | | | | |   (10071)   ~ (all_52_13 = e3)
% 149.94/21.55  | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | REDUCE: (370), (10070) imply:
% 149.94/21.55  | | | | | | | | | | | | | | | | |   (10072)   ~ (all_52_14 = e3)
% 149.94/21.55  | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | REDUCE: (45), (10070) imply:
% 149.94/21.55  | | | | | | | | | | | | | | | | |   (10073)  op(e0, e0) = e3
% 149.94/21.55  | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | |   (10074)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 149.94/21.55  | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | BETA: splitting (10074) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |   (10075)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |                & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | ALPHA: (10075) implies:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |   (10076)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |                = e3) & op(e0, e0) = all_57_15 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |              $i(all_57_15))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |   (10077)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = all_57_12 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | |              $i(all_57_12))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (10076) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | |   (10078)  all_57_2 = e0 & op(e0, e3) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | ALPHA: (10078) implies:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | |   (10079)  op(e0, e3) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |   (10080)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10080) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |   (10081)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10081) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |   (10082)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10082) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |   (10083)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10083) implies:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |   (10084)  op(e2, e3) = e2
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (9995), (10084), (function-axioms) are
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1181.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |   (10085)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10085) implies:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |   (10086)   ~ (all_57_2 = e0)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10073), (10076), (10086), (function-axioms) are
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #833.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |   (10087)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10076), (10077), (10087), (function-axioms) are
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |   (10088)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (51), (159), (163), (167), (169), (211),
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            (346), (9999), (10020), (10022), (10071), (10072),
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            (10088), (function-axioms) are inconsistent by
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #56.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |   (10089)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10089) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |   (10090)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (51), (164), (167), (168), (346), (9977),
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            (10021), (10022), (10073), (10090),
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            #55.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |   (10091)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10091) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |   (10092)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (9983), (10001), (10016),
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |            (10092), (function-axioms) are inconsistent by
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1079.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |   (10093)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10093) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |   (10094)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10094) implies:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |   (10095)  op(e2, e0) = e2
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9997), (10095), (function-axioms) are
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |   (10096)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10096) gives:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (10097)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10097) implies:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | |   (10098)  op(e2, e2) = e0
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9999), (10098), (function-axioms) are
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.55  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (10099)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10099) implies:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (10100)  op(e0, e0) = all_57_15
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (10101)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (139), (157), (158), (9999),
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |            (10022), (10073), (10079), (10100), (10101),
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |            #54.
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | |   (10102)   ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | |            $i(all_57_15)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (10102) implies:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | |   (10103)   ~ (all_57_15 = e3)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | |   (10104)  op(e0, e0) = all_57_15
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10073), (10103), (10104), (function-axioms) are
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1019.
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |   (10105)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |                & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | ALPHA: (10105) implies:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |   (10106)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |                = e2) & op(e1, e1) = all_57_14 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |   (10107)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |                = e2) & op(e3, e3) = all_57_10 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | BETA: splitting (10106) gives:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | |   (10108)  all_57_4 = e1 & op(e1, e2) = e1
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | ALPHA: (10108) implies:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | |   (10109)  op(e1, e2) = e1
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |   (10110)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10110) gives:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |   (10111)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (142), (161), (162), (166), (9995), (10109),
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            (10111), (function-axioms) are inconsistent by
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #53.
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |   (10112)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (51), (159), (163), (167), (169), (211),
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            (346), (9999), (10020), (10022), (10071), (10072),
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            (10112), (function-axioms) are inconsistent by
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #56.
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |   (10113)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10113) gives:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |   (10114)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (51), (164), (167), (168), (346), (9977),
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            (10021), (10022), (10073), (10114),
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            #55.
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |   (10115)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10115) gives:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |   (10116)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (9983), (10001), (10016),
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |            (10116), (function-axioms) are inconsistent by
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1079.
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |   (10117)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10117) gives:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |   (10118)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10118) implies:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |   (10119)  op(e2, e0) = e2
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9997), (10119), (function-axioms) are
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |   (10120)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10120) gives:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (10121)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10121) implies:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (10122)  op(e2, e2) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9999), (10122), (function-axioms) are
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (10123)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10123) implies:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (10124)  op(e0, e0) = all_57_15
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |   (10125)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10107) gives:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10126)  all_57_3 = e3 & op(e3, e2) = e3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10126) implies:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10127)  op(e3, e2) = e3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10020), (10127), (function-axioms) are
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1166.
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10128)   ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10128) implies:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10129)   ~ (all_57_10 = e2)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10130)  op(e3, e3) = all_57_10
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10125) gives:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10131)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10131) gives:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10132)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10132) implies:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10133)  op(e0, e3) = e0
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (139), (157), (158), (9999),
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10022), (10073), (10124), (10125), (10133),
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #54.
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10134)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & $i(all_57_3))
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10134) gives:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10135)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_1)
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.56  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10135) implies:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10136)  op(e0, e3) = e0
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (139), (157), (158), (9999),
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10022), (10073), (10124), (10125), (10136),
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #54.
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10137)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_3)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10137) implies:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10138)  op(e3, e3) = e2
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10129), (10130), (10138), (function-axioms) are
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1031.
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10139)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10139) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10140)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10140) implies:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10141)  all_57_14 = e2
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10142)   ~ (all_57_4 = e1)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10106), (10141), (10142) are inconsistent by
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1005.
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10143)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_7))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9999), (10022), (10143),
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1076.
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | |   (10144)   ~ (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | ALPHA: (10144) implies:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | |   (10145)   ~ (all_57_14 = e2)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | |   (10146)  op(e1, e1) = all_57_14
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9980), (10145), (10146), (function-axioms) are
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #52.
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | |   (10147)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 149.94/21.57  | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 149.94/21.57  | | | | | | | | | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (9980), (10073), (10147),
% 149.94/21.57  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.57  | | | | | | | | | | | | | | | | | |            #51.
% 149.94/21.57  | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | |   (10148)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | REF_CLOSE: (278), (9983), (10001), (10016), (10148) are
% 149.94/21.57  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | |   (10149)  all_56_10 = e2 & op(e2, e0) = e2
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | ALPHA: (10149) implies:
% 149.94/21.57  | | | | | | | | | | | | | | |   (10150)  op(e2, e0) = e2
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | REF_CLOSE: (163), (9997), (10150), (function-axioms) are
% 149.94/21.57  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | |   (10151)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 149.94/21.57  | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | BETA: splitting (10151) gives:
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | |   (10152)  all_56_11 = e2 & op(e1, e0) = e2
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | ALPHA: (10152) implies:
% 149.94/21.57  | | | | | | | | | | | | | | |   (10153)  op(e1, e0) = e2
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | REF_CLOSE: (159), (9979), (10153), (function-axioms) are
% 149.94/21.57  | | | | | | | | | | | | | | |            inconsistent by sub-proof #974.
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | |   (10154)  all_56_15 = e2 & op(e0, e0) = e2
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | ALPHA: (10154) implies:
% 149.94/21.57  | | | | | | | | | | | | | | |   (10155)  op(e0, e0) = e2
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (139), (157),
% 149.94/21.57  | | | | | | | | | | | | | | |            (158), (205), (206), (208), (9982), (10006),
% 149.94/21.57  | | | | | | | | | | | | | | |            (10155), (function-axioms) are inconsistent by
% 149.94/21.57  | | | | | | | | | | | | | | |            sub-proof #50.
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | |   (10156)  all_56_13 = e2 & op(e0, e2) = e2
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | ALPHA: (10156) implies:
% 149.94/21.57  | | | | | | | | | | | | |   (10157)  all_56_13 = e2
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 149.94/21.57  | | | | | | | | | | | | |            (9999), (10157), (function-axioms) are
% 149.94/21.57  | | | | | | | | | | | | |            inconsistent by sub-proof #1104.
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | |   (10158)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 149.94/21.57  | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | REF_CLOSE: (45), (156), (9978), (10003), (10158),
% 149.94/21.57  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.57  | | | | | | | | | | | |            #49.
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | |   (10159)  all_24_2 = e2
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | COMBINE_EQS: (318), (10159) imply:
% 149.94/21.57  | | | | | | | | | | |   (10160)  all_10_2 = e2
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | REDUCE: (45), (10160) imply:
% 149.94/21.57  | | | | | | | | | | |   (10161)  op(e0, e0) = e2
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | BETA: splitting (232) gives:
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | |   (10162)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 149.94/21.57  | | | | | | | | | | | |              & op(e2, e3) = e2)
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | BETA: splitting (10162) gives:
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | |   (10163)  all_56_0 = e2 & op(e3, e3) = e2
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | ALPHA: (10163) implies:
% 149.94/21.57  | | | | | | | | | | | | |   (10164)  op(e3, e3) = e2
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | REF_CLOSE: (9), (36), (45), (51), (122), (139), (142), (148),
% 149.94/21.57  | | | | | | | | | | | | |            (156), (157), (158), (159), (161), (162), (163),
% 149.94/21.57  | | | | | | | | | | | | |            (164), (166), (168), (169), (203), (214), (218),
% 149.94/21.57  | | | | | | | | | | | | |            (237), (238), (278), (336), (342), (344), (9975),
% 149.94/21.57  | | | | | | | | | | | | |            (9977), (9978), (9979), (9980), (9982), (9983),
% 149.94/21.57  | | | | | | | | | | | | |            (9997), (10001), (10161), (10164),
% 149.94/21.57  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.57  | | | | | | | | | | | | |            #48.
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | |   (10165)  all_56_2 = e2 & op(e2, e3) = e2
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | ALPHA: (10165) implies:
% 149.94/21.57  | | | | | | | | | | | | |   (10166)  op(e2, e3) = e2
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | REF_CLOSE: (166), (9995), (10166), (function-axioms) are
% 149.94/21.57  | | | | | | | | | | | | |            inconsistent by sub-proof #1181.
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | |   (10167)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 149.94/21.57  | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | BETA: splitting (10167) gives:
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | |   (10168)  all_56_6 = e2 & op(e1, e3) = e2
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | REF_CLOSE: (162), (9974), (10168), (function-axioms) are
% 149.94/21.57  | | | | | | | | | | | | |            inconsistent by sub-proof #47.
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | |   (10169)  all_56_12 = e2 & op(e0, e3) = e2
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | ALPHA: (10169) implies:
% 149.94/21.57  | | | | | | | | | | | | |   (10170)  all_56_12 = e2
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (139), (157),
% 149.94/21.57  | | | | | | | | | | | | |            (158), (205), (206), (208), (9982), (10161),
% 149.94/21.57  | | | | | | | | | | | | |            (10170), (function-axioms) are inconsistent by
% 149.94/21.57  | | | | | | | | | | | | |            sub-proof #50.
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | |   (10171)  all_22_2 = e1
% 149.94/21.57  | | | | | | | | | |   (10172)  ( ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0
% 149.94/21.57  | | | | | | | | | |              & op(e3, e1) = all_22_1 & $i(all_22_0) &
% 149.94/21.57  | | | | | | | | | |              $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e1)
% 149.94/21.57  | | | | | | | | | |              = all_22_1 & $i(all_22_1))
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | COMBINE_EQS: (320), (10171) imply:
% 149.94/21.57  | | | | | | | | | |   (10173)  all_14_2 = e1
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | COMBINE_EQS: (312), (10173) imply:
% 149.94/21.57  | | | | | | | | | |   (10174)  all_34_2 = e1
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | REDUCE: (336), (10173) imply:
% 149.94/21.57  | | | | | | | | | |   (10175)   ~ (all_52_1 = e1)
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | REDUCE: (338), (10173) imply:
% 149.94/21.57  | | | | | | | | | |   (10176)   ~ (all_52_2 = e1)
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | REDUCE: (340), (10173) imply:
% 149.94/21.57  | | | | | | | | | |   (10177)   ~ (all_52_3 = e1)
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | REDUCE: (342), (10173) imply:
% 149.94/21.57  | | | | | | | | | |   (10178)   ~ (all_52_4 = e1)
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | REDUCE: (346), (10173) imply:
% 149.94/21.57  | | | | | | | | | |   (10179)   ~ (all_52_12 = e1)
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | REDUCE: (51), (10173) imply:
% 149.94/21.57  | | | | | | | | | |   (10180)  op(e3, e3) = e1
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | BETA: splitting (232) gives:
% 149.94/21.57  | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | |   (10181)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 149.94/21.57  | | | | | | | | | | |              & op(e2, e3) = e2)
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | REF_CLOSE: (6), (166), (9995), (10180), (10181),
% 149.94/21.57  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.57  | | | | | | | | | | |            #938.
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | |   (10182)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 149.94/21.57  | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | BETA: splitting (10182) gives:
% 149.94/21.57  | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | |   (10183)  all_56_6 = e2 & op(e1, e3) = e2
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | REF_CLOSE: (162), (9974), (10183), (function-axioms) are
% 149.94/21.57  | | | | | | | | | | | |            inconsistent by sub-proof #47.
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | |   (10184)  all_56_12 = e2 & op(e0, e3) = e2
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | ALPHA: (10184) implies:
% 149.94/21.57  | | | | | | | | | | | |   (10185)  all_56_12 = e2
% 149.94/21.57  | | | | | | | | | | | |   (10186)  op(e0, e3) = e2
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | BETA: splitting (233) gives:
% 149.94/21.57  | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | |   (10187)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 149.94/21.57  | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | REF_CLOSE: (6), (169), (9996), (10180), (10187),
% 149.94/21.57  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.57  | | | | | | | | | | | | |            #968.
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | |   (10188)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 149.94/21.57  | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | BETA: splitting (10188) gives:
% 149.94/21.57  | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | |   (10189)  all_56_4 = e2 & op(e3, e1) = e2
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | REF_CLOSE: (168), (9976), (10189), (function-axioms) are
% 149.94/21.57  | | | | | | | | | | | | | |            inconsistent by sub-proof #46.
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | |   (10190)  all_56_9 = e2 & op(e3, e0) = e2
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | ALPHA: (10190) implies:
% 149.94/21.57  | | | | | | | | | | | | | |   (10191)  all_56_9 = e2
% 149.94/21.57  | | | | | | | | | | | | | |   (10192)  op(e3, e0) = e2
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 149.94/21.57  | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | |   (10193)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 149.94/21.57  | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | BETA: splitting (10193) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | |   (10194)  all_56_0 = e1 & op(e3, e3) = e1
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 149.94/21.57  | | | | | | | | | | | | | | | |              e3, e0, simplifying with (158), (10186) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | |   (10195)  all_52_3 = e2
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 149.94/21.57  | | | | | | | | | | | | | | | |              e2, e0, e3, simplifying with (167), (10192) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | |   (10196)  all_52_12 = e2
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | REDUCE: (139), (10195) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | |   (10197)   ~ (all_52_7 = e2)
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | SIMP: (10197) implies:
% 149.94/21.57  | | | | | | | | | | | | | | | |   (10198)   ~ (all_52_7 = e2)
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | REDUCE: (112), (10196) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | |   (10199)   ~ (all_52_13 = e2)
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | REDUCE: (368), (10196) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | |   (10200)   ~ (all_10_2 = e2)
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | SIMP: (10200) implies:
% 149.94/21.57  | | | | | | | | | | | | | | | |   (10201)   ~ (all_10_2 = e2)
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | BETA: splitting (81) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | |   (10202)   ~ (all_34_2 = e1)
% 149.94/21.57  | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | REDUCE: (10174), (10202) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | | |   (10203)  $false
% 149.94/21.57  | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | CLOSE: (10203) is inconsistent.
% 149.94/21.57  | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | |   (10204)  ( ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0
% 149.94/21.57  | | | | | | | | | | | | | | | | |              & op(e3, e1) = all_34_1 & $i(all_34_0) &
% 149.94/21.57  | | | | | | | | | | | | | | | | |              $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e3, e1)
% 149.94/21.57  | | | | | | | | | | | | | | | | |              = all_34_1 & $i(all_34_1))
% 149.94/21.57  | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | |   (10205)   ~ (all_42_2 = e3)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | REDUCE: (302), (10205) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | | | |   (10206)   ~ (all_10_2 = e3)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | |   (10207)  all_54_15 = e3
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (10206), (10207) are inconsistent by
% 149.94/21.57  | | | | | | | | | | | | | | | | | | |            sub-proof #1049.
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | |   (10208)   ~ (all_54_15 = e3)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | |   (10209)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | BETA: splitting (10209) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | |   (10210)  all_54_15 = e2
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (10201), (10210) are inconsistent by
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | |            sub-proof #1048.
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | |   (10211)   ~ (all_54_15 = e2)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | |   (10212)  all_54_15 = e1 | all_54_15 = e0
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10212) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | |   (10213)  all_54_15 = e1
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (9982), (10213) are inconsistent by
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1047.
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | |   (10214)  all_54_15 = e0
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (10214) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | |   (10215)  all_10_2 = e0
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | SIMP: (10215) implies:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | |   (10216)  all_10_2 = e0
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (10216) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | |   (10217)   ~ (all_52_7 = e0)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (10216) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | |   (10218)   ~ (all_52_11 = e0)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (10206), (10216) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | |   (10219)   ~ (e3 = e0)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (10201), (10216) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | |   (10220)   ~ (e2 = e0)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (9982), (10216) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | |   (10221)   ~ (e1 = e0)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (10216) imply:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | |   (10222)  op(e0, e0) = e0
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |   (10223)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10223) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |   (10224)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10224) gives:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |   (10225)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (9995), (10225), (function-axioms) are
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |   (10226)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (162), (10176), (10222), (10226),
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | |            #1045.
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 149.94/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |   (10227)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10227) gives:
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | |   (10228)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10228) gives:
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.57  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (10229)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10229) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (10230)  all_57_14 = e2
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (10231)   ~ (all_57_10 = e2)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (10232)   ~ (all_57_4 = e1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (10233)  op(e1, e2) = all_57_4
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (10234)  op(e3, e2) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10235)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10235) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10236)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10236) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10237)  op(e3, e3) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10180), (10237), (function-axioms) are
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10238)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10238) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10239)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10230), (10232), (10239) are inconsistent by
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1005.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10240)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10240) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10241)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10241) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10242)  op(e1, e1) = e1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (10242), (function-axioms) are
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10243)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14)))
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10243) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10244)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12))
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10245)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = all_57_10 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10244) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10246)  all_57_11 = e2 & op(e2, e0) = e2
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10246) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10247)  op(e2, e0) = e2
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9997), (10247), (function-axioms) are
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10248)   ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10248) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10249)   ~ (all_57_12 = e0)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10250)  op(e2, e2) = all_57_12
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10245) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10251)  all_57_9 = e3 & op(e3, e0) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10251) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10252)  op(e3, e0) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3, e0,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, simplifying with (10192), (10252) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10253)  e3 = e2
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9), (10253) imply:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10254)  $false
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (10254) is inconsistent.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10255)   ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10255) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10256)   ~ (all_57_10 = e0)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10257)  op(e3, e3) = all_57_10
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4, e2, e1, simplifying with (161), (10233)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10258)  all_57_4 = all_52_6
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12, e2, e2, simplifying with (9999),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (10250) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10259)  all_57_12 = e2
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (169), (10234) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10260)  all_52_4 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (10180),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (10257) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10261)  all_57_10 = e1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10232), (10258) imply:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10262)   ~ (all_52_6 = e1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10231), (10261) imply:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10263)   ~ (e2 = e1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (10260) imply:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10264)   ~ (all_52_6 = e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10264) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10265)   ~ (all_52_6 = e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (10260) imply:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10266)   ~ (all_52_7 = e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10266) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10267)   ~ (all_52_7 = e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (10260) imply:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10268)   ~ (all_52_8 = e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10268) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10269)   ~ (all_52_8 = e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10270)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10270) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10271)  all_56_0 = e3 & op(e3, e3) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10271) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10272)  op(e3, e3) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10180), (10272), (function-axioms) are
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10273)  all_56_1 = e3 & op(e3, e2) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10273) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10274)  all_56_1 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10275)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10275) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10276)  all_56_12 = e3 & op(e0, e3) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10276) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10277)  all_56_12 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10185), (10277) imply:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10278)  e3 = e2
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10278) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10279)  e3 = e2
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10274), (10279) imply:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10280)  all_56_1 = e2
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (224), (225),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (227), (9999), (10265), (10280), (function-axioms)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #921.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10281)  all_56_13 = e3 & op(e0, e2) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10281) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10282)  all_56_13 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (224), (225), (9999),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10274), (10282), (function-axioms) are
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #877.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10283)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10283) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10284)  all_56_14 = e3 & op(e0, e1) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10284) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10285)  all_56_14 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10286)  op(e0, e1) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10287)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10287) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10288)  all_56_4 = e1 & op(e3, e1) = e1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10288) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10289)  all_56_4 = e1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (229), (10180), (10191), (10274),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10289), (function-axioms) are inconsistent by
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #566.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10290)  all_56_5 = e1 & op(e2, e1) = e1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10290) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10291)  all_56_5 = e1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10292)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10292) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10293)  all_56_4 = e0 & op(e3, e1) = e0
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10293) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10294)  op(e3, e1) = e0
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10295)  all_54_9 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (10265), (10295) are inconsistent by
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #186.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10296)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10172) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10297)   ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_22_1 & $i(all_22_0) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_22_1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10297) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10298)   ~ (all_22_0 = e2)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10299)  op(e3, e1) = all_22_1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10300)  op(all_22_1, e3) = all_22_0
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10204) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10301)   ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_34_1 & $i(all_34_0) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_34_1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10301) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10302)  op(e3, e1) = all_34_1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9975), (10186), (10262), (10294), (10296),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10298), (10299), (10300), (10302),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #45.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10303)   ~ (all_34_1 = e2) & op(e3, e1) = all_34_1 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_34_1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10303) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10304)  op(e3, e1) = all_34_1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9975), (10186), (10262), (10294), (10296),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10298), (10299), (10300), (10304),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #45.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10305)   ~ (all_22_1 = e0) & op(e3, e1) = all_22_1 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_22_1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10305) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10306)   ~ (all_22_1 = e0)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10307)  op(e3, e1) = all_22_1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10204) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10308)   ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_34_1 & $i(all_34_0) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_34_1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10308) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10309)  op(e3, e1) = all_34_1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10294), (10306), (10307), (10309),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #44.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10310)   ~ (all_34_1 = e2) & op(e3, e1) = all_34_1 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_34_1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10310) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10311)  op(e3, e1) = all_34_1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10294), (10306), (10307), (10311),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #44.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10312)  all_56_5 = e0 & op(e2, e1) = e0
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10312) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10313)  all_56_5 = e0
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10291), (10313) are inconsistent by
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #682.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10314)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9980), (10286), (10314),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #43.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10315)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10315) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10316)  all_56_8 = e1 & op(e1, e1) = e1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10316) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10317)  op(e1, e1) = e1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (10317), (function-axioms) are
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10318)  all_56_14 = e1 & op(e0, e1) = e1
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10285), (10318) are inconsistent by
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #188.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10319)  all_56_15 = e3 & op(e0, e0) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10319) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10320)  op(e0, e0) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (124), (127),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (142), (156), (161), (162), (163), (164), (166),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (190), (237), (238), (247), (9977), (9980),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9995), (9997), (10180), (10198), (10267),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10320), (function-axioms) are inconsistent by
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #42.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10321)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10321) gives:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10322)  all_56_4 = e3 & op(e3, e1) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10322) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10323)  op(e3, e1) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10269), (10323), (function-axioms) are
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10324)  all_56_9 = e3 & op(e3, e0) = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10324) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10325)  all_56_9 = e3
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10191), (10325) are inconsistent by
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #964.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (10326)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10326) implies:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |   (10327)  op(e0, e0) = e2
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10222), (10327), (function-axioms) are
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |   (10328)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9999), (10180), (10222), (10328),
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | |            #971.
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.58  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |   (10329)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10329) gives:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |   (10330)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10330) gives:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |   (10331)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (9977), (10222), (10331),
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |            #1039.
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |   (10332)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10332) gives:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (10333)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10333) implies:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (10334)  op(e0, e0) = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10222), (10334), (function-axioms) are
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (10335)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10192), (10335), (function-axioms) are
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #40.
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |   (10336)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10336) gives:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |   (10337)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10180), (10337), (function-axioms) are
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |   (10338)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10338) gives:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (10339)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10339) implies:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (10340)  op(e2, e0) = e2
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (9997), (10340), (function-axioms) are
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |   (10341)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10341) gives:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10342)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10342) implies:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10343)  op(e2, e2) = e0
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9999), (10343), (function-axioms) are
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10344)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10344) implies:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10345)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10345) gives:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10346)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10346) gives:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10347)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10347) implies:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10348)  op(e2, e2) = e3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9999), (10348), (function-axioms) are
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10349)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & $i(all_57_3))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10349) gives:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10350)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_1)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10350) implies:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10351)  op(e1, e1) = e3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (156), (158), (245), (349), (367),
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (9982), (9999), (10180), (10201), (10209),
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10345), (10351), (function-axioms) are
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #286.
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10352)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_3)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10352) implies:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10353)  op(e3, e3) = e2
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10180), (10353), (function-axioms) are
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10354)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (156), (157), (9999), (10217), (10218),
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10354), (function-axioms) are inconsistent by
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #57.
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | |   (10355)  all_42_2 = e3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (302), (10355) imply:
% 150.13/21.59  | | | | | | | | | | | | | | | | | |   (10356)  all_10_2 = e3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | REDUCE: (360), (10356) imply:
% 150.13/21.59  | | | | | | | | | | | | | | | | | |   (10357)   ~ (all_52_7 = e3)
% 150.13/21.59  | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | REDUCE: (45), (10356) imply:
% 150.13/21.59  | | | | | | | | | | | | | | | | | |   (10358)  op(e0, e0) = e3
% 150.13/21.59  | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (124), (127),
% 150.13/21.59  | | | | | | | | | | | | | | | | | |            (142), (156), (161), (162), (163), (164), (166),
% 150.13/21.59  | | | | | | | | | | | | | | | | | |            (190), (237), (238), (247), (9977), (9980),
% 150.13/21.59  | | | | | | | | | | | | | | | | | |            (9995), (9997), (10180), (10198), (10357),
% 150.13/21.59  | | | | | | | | | | | | | | | | | |            (10358), (function-axioms) are inconsistent by
% 150.13/21.59  | | | | | | | | | | | | | | | | | |            sub-proof #42.
% 150.13/21.59  | | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | |   (10359)  all_56_2 = e1 & op(e2, e3) = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | ALPHA: (10359) implies:
% 150.13/21.59  | | | | | | | | | | | | | | | |   (10360)  op(e2, e3) = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10175), (10360), (function-axioms) are
% 150.13/21.59  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1177.
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | |   (10361)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 150.13/21.59  | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 150.13/21.59  | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | BETA: splitting (10361) gives:
% 150.13/21.59  | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | |   (10362)  all_56_6 = e1 & op(e1, e3) = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | ALPHA: (10362) implies:
% 150.13/21.59  | | | | | | | | | | | | | | | |   (10363)  all_56_6 = e1
% 150.13/21.59  | | | | | | | | | | | | | | | |   (10364)  op(e1, e3) = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (228), (232),
% 150.13/21.59  | | | | | | | | | | | | | | | |            (234), (10180), (10363), (10364),
% 150.13/21.59  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.59  | | | | | | | | | | | | | | | |            #547.
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | |   (10365)  all_56_12 = e1 & op(e0, e3) = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | ALPHA: (10365) implies:
% 150.13/21.59  | | | | | | | | | | | | | | | |   (10366)  op(e0, e3) = e1
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10177), (10366), (function-axioms) are
% 150.13/21.59  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #405.
% 150.13/21.59  | | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | | 
% 150.13/21.59  | | | | | | | | Case 2:
% 150.13/21.59  | | | | | | | | | 
% 150.13/21.59  | | | | | | | | |   (10367)  all_54_5 = e1 | all_54_5 = e0
% 150.13/21.59  | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | REF_CLOSE: (267), (9985), (9987), (10367) are inconsistent by
% 150.13/21.59  | | | | | | | | |            sub-proof #866.
% 150.13/21.59  | | | | | | | | | 
% 150.13/21.59  | | | | | | | | End of split
% 150.13/21.59  | | | | | | | | 
% 150.13/21.59  | | | | | | | End of split
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | Case 2:
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | |   (10368)  all_20_2 = e1
% 150.13/21.59  | | | | | | |   (10369)  ( ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 &
% 150.13/21.59  | | | | | | |              op(e2, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1))
% 150.13/21.59  | | | | | | |            | ( ~ (all_20_1 = e3) & op(e2, e1) = all_20_1 &
% 150.13/21.59  | | | | | | |              $i(all_20_1))
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | COMBINE_EQS: (282), (10368) imply:
% 150.13/21.59  | | | | | | |   (10370)  all_6_2 = e1
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | SIMP: (10370) implies:
% 150.13/21.59  | | | | | | |   (10371)  all_6_2 = e1
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | COMBINE_EQS: (331), (10371) imply:
% 150.13/21.59  | | | | | | |   (10372)  all_38_2 = e1
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | REDUCE: (347), (10371) imply:
% 150.13/21.59  | | | | | | |   (10373)   ~ (all_52_1 = e1)
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | REDUCE: (350), (10371) imply:
% 150.13/21.59  | | | | | | |   (10374)   ~ (all_52_4 = e1)
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | REDUCE: (352), (10371) imply:
% 150.13/21.59  | | | | | | |   (10375)   ~ (all_52_6 = e1)
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | REDUCE: (354), (10371) imply:
% 150.13/21.59  | | | | | | |   (10376)   ~ (all_52_7 = e1)
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | REDUCE: (356), (10371) imply:
% 150.13/21.59  | | | | | | |   (10377)   ~ (all_52_9 = e1)
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | REDUCE: (358), (10371) imply:
% 150.13/21.59  | | | | | | |   (10378)   ~ (all_52_13 = e1)
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | REDUCE: (9981), (10371) imply:
% 150.13/21.59  | | | | | | |   (10379)   ~ (e3 = e1)
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | REDUCE: (39), (10371) imply:
% 150.13/21.59  | | | | | | |   (10380)  op(e2, e2) = e1
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | BETA: splitting (64) gives:
% 150.13/21.59  | | | | | | | 
% 150.13/21.59  | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | 
% 150.13/21.59  | | | | | | | |   (10381)   ~ (all_22_2 = e1)
% 150.13/21.59  | | | | | | | | 
% 150.13/21.59  | | | | | | | | REDUCE: (320), (10381) imply:
% 150.13/21.59  | | | | | | | |   (10382)   ~ (all_14_2 = e1)
% 150.13/21.59  | | | | | | | | 
% 150.13/21.59  | | | | | | | | BETA: splitting (67) gives:
% 150.13/21.59  | | | | | | | | 
% 150.13/21.59  | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | 
% 150.13/21.59  | | | | | | | | |   (10383)   ~ (all_24_2 = e2)
% 150.13/21.59  | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | REDUCE: (318), (10383) imply:
% 150.13/21.59  | | | | | | | | |   (10384)   ~ (all_10_2 = e2)
% 150.13/21.59  | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | BETA: splitting (84) gives:
% 150.13/21.59  | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | |   (10385)   ~ (all_36_2 = e2)
% 150.13/21.59  | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | REDUCE: (304), (10385) imply:
% 150.13/21.59  | | | | | | | | | |   (10386)   ~ (all_14_2 = e2)
% 150.13/21.59  | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | BETA: splitting (203) gives:
% 150.13/21.59  | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | Case 1:
% 150.13/21.59  | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | |   (10387)  all_54_0 = e3
% 150.13/21.59  | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | COMBINE_EQS: (278), (10387) imply:
% 150.13/21.59  | | | | | | | | | | |   (10388)  all_14_2 = e3
% 150.13/21.59  | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | SIMP: (10388) implies:
% 150.13/21.59  | | | | | | | | | | |   (10389)  all_14_2 = e3
% 150.13/21.59  | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | REDUCE: (338), (10389) imply:
% 150.13/21.59  | | | | | | | | | | |   (10390)   ~ (all_52_2 = e3)
% 150.13/21.59  | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | REDUCE: (342), (10389) imply:
% 150.13/21.59  | | | | | | | | | | |   (10391)   ~ (all_52_4 = e3)
% 150.13/21.59  | | | | | | | | | | | 
% 150.13/21.59  | | | | | | | | | | | REDUCE: (344), (10389) imply:
% 150.13/21.60  | | | | | | | | | | |   (10392)   ~ (all_52_8 = e3)
% 150.13/21.60  | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | REDUCE: (346), (10389) imply:
% 150.13/21.60  | | | | | | | | | | |   (10393)   ~ (all_52_12 = e3)
% 150.13/21.60  | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | REDUCE: (51), (10389) imply:
% 150.13/21.60  | | | | | | | | | | |   (10394)  op(e3, e3) = e3
% 150.13/21.60  | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | BETA: splitting (87) gives:
% 150.13/21.60  | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | |   (10395)   ~ (all_38_2 = e1)
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | REDUCE: (10372), (10395) imply:
% 150.13/21.60  | | | | | | | | | | | |   (10396)  $false
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | CLOSE: (10396) is inconsistent.
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | |   (10397)  ( ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0
% 150.13/21.60  | | | | | | | | | | | |              & op(e2, e1) = all_38_1 & $i(all_38_0) &
% 150.13/21.60  | | | | | | | | | | | |              $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e2, e1)
% 150.13/21.60  | | | | | | | | | | | |              = all_38_1 & $i(all_38_1))
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | BETA: splitting (93) gives:
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | |   (10398)   ~ (all_42_2 = e3)
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | REDUCE: (302), (10398) imply:
% 150.13/21.60  | | | | | | | | | | | | |   (10399)   ~ (all_10_2 = e3)
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | BETA: splitting (188) gives:
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | |   (10400)  all_54_15 = e3
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | REF_CLOSE: (245), (10399), (10400) are inconsistent by
% 150.13/21.60  | | | | | | | | | | | | | |            sub-proof #1049.
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | |   (10401)   ~ (all_54_15 = e3)
% 150.13/21.60  | | | | | | | | | | | | | |   (10402)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (45), (156), (157),
% 150.13/21.60  | | | | | | | | | | | | | |            (158), (164), (167), (168), (169), (238), (245),
% 150.13/21.60  | | | | | | | | | | | | | |            (349), (360), (367), (9977), (9980), (9982),
% 150.13/21.60  | | | | | | | | | | | | | |            (10380), (10384), (10391), (10392), (10393),
% 150.13/21.60  | | | | | | | | | | | | | |            (10394), (10399), (10402), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | |            inconsistent by sub-proof #37.
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | End of split
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | |   (10403)  all_42_2 = e3
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | COMBINE_EQS: (302), (10403) imply:
% 150.13/21.60  | | | | | | | | | | | | |   (10404)  all_10_2 = e3
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | REDUCE: (367), (10404) imply:
% 150.13/21.60  | | | | | | | | | | | | |   (10405)   ~ (all_52_11 = e3)
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | REDUCE: (45), (10404) imply:
% 150.13/21.60  | | | | | | | | | | | | |   (10406)  op(e0, e0) = e3
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | BETA: splitting (219) gives:
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | |   (10407)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 150.13/21.60  | | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | BETA: splitting (10407) gives:
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | |   (10408)  all_56_4 = e3 & op(e3, e1) = e3
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | ALPHA: (10408) implies:
% 150.13/21.60  | | | | | | | | | | | | | | |   (10409)  op(e3, e1) = e3
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | REF_CLOSE: (168), (10392), (10409), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1164.
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | |   (10410)  all_56_5 = e3 & op(e2, e1) = e3
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | ALPHA: (10410) implies:
% 150.13/21.60  | | | | | | | | | | | | | | |   (10411)  all_56_5 = e3
% 150.13/21.60  | | | | | | | | | | | | | | |   (10412)  op(e2, e1) = e3
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10413)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 150.13/21.60  | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | BETA: splitting (10413) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | |   (10414)  all_56_6 = e3 & op(e1, e3) = e3
% 150.13/21.60  | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (10390), (10414), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #132.
% 150.13/21.60  | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | |   (10415)  all_56_7 = e3 & op(e1, e2) = e3
% 150.13/21.60  | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | ALPHA: (10415) implies:
% 150.13/21.60  | | | | | | | | | | | | | | | | |   (10416)  all_56_7 = e3
% 150.13/21.60  | | | | | | | | | | | | | | | | |   (10417)  op(e1, e2) = e3
% 150.13/21.60  | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (122), (124), (127),
% 150.13/21.60  | | | | | | | | | | | | | | | | |            (134), (135), (138), (139), (144), (145), (147),
% 150.13/21.60  | | | | | | | | | | | | | | | | |            (156), (157), (158), (161), (162), (163), (164),
% 150.13/21.60  | | | | | | | | | | | | | | | | |            (166), (167), (168), (169), (190), (199), (202),
% 150.13/21.60  | | | | | | | | | | | | | | | | |            (205), (206), (208), (209), (211), (212), (214),
% 150.13/21.60  | | | | | | | | | | | | | | | | |            (216), (218), (220), (224), (226), (228), (229),
% 150.13/21.60  | | | | | | | | | | | | | | | | |            (230), (231), (232), (233), (235), (237), (238),
% 150.13/21.60  | | | | | | | | | | | | | | | | |            (247), (268), (271), (10369), (10373), (10374),
% 150.13/21.60  | | | | | | | | | | | | | | | | |            (10376), (10377), (10378), (10380), (10393),
% 150.13/21.60  | | | | | | | | | | | | | | | | |            (10394), (10397), (10405), (10411), (10412),
% 150.13/21.60  | | | | | | | | | | | | | | | | |            (10416), (10417), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #793.
% 150.13/21.60  | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | End of split
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10418)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 150.13/21.60  | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (163), (205),
% 150.13/21.60  | | | | | | | | | | | | | | | |            (209), (210), (9980), (10384), (10406), (10418),
% 150.13/21.60  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.60  | | | | | | | | | | | | | | | |            #36.
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | End of split
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | End of split
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | |   (10419)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 150.13/21.60  | | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | BETA: splitting (10419) gives:
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | |   (10420)  all_56_8 = e3 & op(e1, e1) = e3
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | ALPHA: (10420) implies:
% 150.13/21.60  | | | | | | | | | | | | | | |   (10421)  op(e1, e1) = e3
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | REF_CLOSE: (9), (9980), (10421), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | |   (10422)  all_56_14 = e3 & op(e0, e1) = e3
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | ALPHA: (10422) implies:
% 150.13/21.60  | | | | | | | | | | | | | | |   (10423)  op(e0, e1) = e3
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | REF_CLOSE: (156), (10405), (10423), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1147.
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | End of split
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | End of split
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | End of split
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | End of split
% 150.13/21.60  | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | |   (10424)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 150.13/21.60  | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | REF_CLOSE: (278), (9983), (10382), (10386), (10424) are
% 150.13/21.60  | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 150.13/21.60  | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | End of split
% 150.13/21.60  | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | |   (10425)  all_36_2 = e2
% 150.13/21.60  | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | COMBINE_EQS: (304), (10425) imply:
% 150.13/21.60  | | | | | | | | | |   (10426)  all_14_2 = e2
% 150.13/21.60  | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | SIMP: (10426) implies:
% 150.13/21.60  | | | | | | | | | |   (10427)  all_14_2 = e2
% 150.13/21.60  | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | REDUCE: (336), (10427) imply:
% 150.13/21.60  | | | | | | | | | |   (10428)   ~ (all_52_1 = e2)
% 150.13/21.60  | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | REDUCE: (51), (10427) imply:
% 150.13/21.60  | | | | | | | | | |   (10429)  op(e3, e3) = e2
% 150.13/21.60  | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | BETA: splitting (207) gives:
% 150.13/21.60  | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | |   (10430)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 150.13/21.60  | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 150.13/21.60  | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | BETA: splitting (10430) gives:
% 150.13/21.60  | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | |   (10431)  all_56_12 = e2 & op(e0, e3) = e2
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | ALPHA: (10431) implies:
% 150.13/21.60  | | | | | | | | | | | |   (10432)  all_56_12 = e2
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230), (234),
% 150.13/21.60  | | | | | | | | | | | |            (10429), (10432), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | |            inconsistent by sub-proof #781.
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | |   (10433)  all_56_13 = e2 & op(e0, e2) = e2
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | ALPHA: (10433) implies:
% 150.13/21.60  | | | | | | | | | | | |   (10434)  all_56_13 = e2
% 150.13/21.60  | | | | | | | | | | | |   (10435)  op(e0, e2) = e2
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | BETA: splitting (222) gives:
% 150.13/21.60  | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | |   (10436)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 150.13/21.60  | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (224), (225),
% 150.13/21.60  | | | | | | | | | | | | |            (227), (10428), (10434), (10436),
% 150.13/21.60  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.60  | | | | | | | | | | | | |            #35.
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | |   (10437)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 150.13/21.60  | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | BETA: splitting (10437) gives:
% 150.13/21.60  | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | |   (10438)  all_56_5 = e2 & op(e2, e1) = e2
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | ALPHA: (10438) implies:
% 150.13/21.60  | | | | | | | | | | | | | |   (10439)  op(e2, e1) = e2
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | REF_CLOSE: (164), (9977), (10439), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | |   (10440)  all_56_10 = e2 & op(e2, e0) = e2
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | ALPHA: (10440) implies:
% 150.13/21.60  | | | | | | | | | | | | | |   (10441)  op(e2, e0) = e2
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 150.13/21.60  | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | |   (10442)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.13/21.60  | | | | | | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.13/21.60  | | | | | | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.13/21.60  | | | | | | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.13/21.60  | | | | | | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.60  | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.13/21.60  | | | | | | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.13/21.60  | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.60  | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.13/21.60  | | | | | | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.13/21.60  | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.60  | | | | | | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.13/21.60  | | | | | | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.60  | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.13/21.60  | | | | | | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.13/21.60  | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 150.13/21.60  | | | | | | | | | | | | | | |            (10429), (10434), (10442), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | |            inconsistent by sub-proof #34.
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | |   (10443)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.13/21.60  | | | | | | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.13/21.60  | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.60  | | | | | | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.60  | | | | | | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.60  | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.13/21.60  | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.13/21.60  | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.60  | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.13/21.60  | | | | | | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.13/21.60  | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.60  | | | | | | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.60  | | | | | | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.60  | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.60  | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.60  | | | | | | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | BETA: splitting (10443) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10444)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.13/21.60  | | | | | | | | | | | | | | | |                & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.13/21.60  | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.60  | | | | | | | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.60  | | | | | | | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.60  | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.13/21.60  | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.13/21.60  | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | ALPHA: (10444) implies:
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10445)  op(e1, e1) = e1
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (10445), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10446)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.13/21.60  | | | | | | | | | | | | | | | |                & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.13/21.60  | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.60  | | | | | | | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.60  | | | | | | | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.60  | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.60  | | | | | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.60  | | | | | | | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14)))
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | ALPHA: (10446) implies:
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10447)  all_57_15 = e0
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10448)  op(e0, e0) = e0
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10449)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 150.13/21.60  | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.13/21.60  | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10450)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.60  | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.60  | | | | | | | | | | | | | | | |              $i(all_57_12))
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 150.13/21.60  | | | | | | | | | | | | | | | |              e0, e0, simplifying with (45), (10448) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10451)  all_10_2 = e0
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 150.13/21.60  | | | | | | | | | | | | | | | |              e2, e0, simplifying with (157), (10435) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10452)  all_52_7 = e2
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 150.13/21.60  | | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (163), (10441) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10453)  all_52_13 = e2
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | REDUCE: (349), (10451) imply:
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10454)   ~ (all_52_3 = e0)
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | REDUCE: (367), (10451) imply:
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10455)   ~ (all_52_11 = e0)
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | REDUCE: (10384), (10451) imply:
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10456)   ~ (e2 = e0)
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | REDUCE: (9982), (10451) imply:
% 150.13/21.60  | | | | | | | | | | | | | | | |   (10457)   ~ (e1 = e0)
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | |   (10458)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.60  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.60  | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.60  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.60  | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.60  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.60  | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.60  | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.13/21.60  | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.13/21.60  | | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.13/21.60  | | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.60  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.60  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.13/21.60  | | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.13/21.60  | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.13/21.60  | | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.13/21.60  | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.13/21.60  | | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.13/21.60  | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.13/21.60  | | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.60  | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.60  | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.60  | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.13/21.60  | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | BETA: splitting (10458) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | |   (10459)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.60  | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.60  | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.13/21.60  | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | BETA: splitting (10459) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |   (10460)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10428), (10460), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |   (10461)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (10380), (10448), (10461),
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |            #864.
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.60  | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | |   (10462)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.13/21.60  | | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.13/21.60  | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.13/21.60  | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | BETA: splitting (10462) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |   (10463)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | BETA: splitting (10463) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |   (10464)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | ALPHA: (10464) implies:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |   (10465)   ~ (all_57_10 = e2)
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |   (10466)  op(e3, e3) = all_57_10
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10429), (10465), (10466), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1031.
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |   (10467)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | ALPHA: (10467) implies:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |   (10468)  op(e0, e0) = e2
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (237), (9980), (10380),
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            (10429), (10468), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #706.
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |   (10469)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | BETA: splitting (10469) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |   (10470)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | ALPHA: (10470) implies:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |   (10471)  op(e1, e2) = e1
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (10375), (10471), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |   (10472)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10472) gives:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |   (10473)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10473) implies:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |   (10474)  op(e0, e0) = e2
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (237), (9980), (10380),
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |            (10429), (10474), (function-axioms) are
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #706.
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |   (10475)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.60  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10475) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |   (10476)   ~ (all_57_10 = e1)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |   (10477)  op(e2, e1) = all_57_7
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |   (10478)  op(e3, e1) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |   (10479)  op(e3, e3) = all_57_10
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |              all_57_7, e1, e2, simplifying with (164), (10477)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |              gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |   (10480)  all_57_7 = all_52_9
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (10478) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |   (10481)  all_52_8 = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (10429),
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |              (10479) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |   (10482)  all_57_10 = e2
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (10481) imply:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |   (10483)   ~ (all_52_9 = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | SIMP: (10483) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |   (10484)   ~ (all_52_9 = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (10481) imply:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |   (10485)   ~ (all_52_11 = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | SIMP: (10485) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | |   (10486)   ~ (all_52_11 = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | |   (10487)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10487) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | |   (10488)  all_56_0 = e1 & op(e3, e3) = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10488) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | |   (10489)  op(e3, e3) = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10476), (10479), (10489), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #893.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | |   (10490)  all_56_1 = e1 & op(e3, e2) = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10374), (10490), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #420.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | |   (10491)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10491) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | |   (10492)  all_56_4 = e1 & op(e3, e1) = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10492) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | |   (10493)  op(e3, e1) = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (10478), (10493), (function-axioms)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #439.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | |   (10494)  all_56_9 = e1 & op(e3, e0) = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10494) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | |   (10495)  op(e3, e0) = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | |   (10496)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10496) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (10497)  all_56_12 = e3 & op(e0, e3) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10497) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (10498)  all_56_12 = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10499)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10499) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10500)  all_56_2 = e3 & op(e2, e3) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10500) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10501)  all_56_2 = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10502)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10502) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10503)  all_56_9 = e3 & op(e3, e0) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10503) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10504)  op(e3, e0) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (10495), (10504), (function-axioms)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #512.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10505)  all_56_10 = e3 & op(e2, e0) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10505) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10506)  op(e2, e0) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10441), (10506), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #854.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10507)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10507) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10508)  all_56_11 = e3 & op(e1, e0) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10508) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10509)  all_56_11 = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10510)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10510) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10511)  all_56_6 = e1 & op(e1, e3) = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10511) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10512)  all_56_6 = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10513)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10513) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10514)  all_56_0 = e0 & op(e3, e3) = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10514) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10515)  op(e3, e3) = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10429), (10515), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10516)  all_56_2 = e0 & op(e2, e3) = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10516) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10517)  all_56_2 = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10501), (10517) are inconsistent by
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1137.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10518)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10518) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10519)  all_56_6 = e0 & op(e1, e3) = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10519) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10520)  all_56_6 = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10512), (10520) are inconsistent by
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #790.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10521)  all_56_12 = e0 & op(e0, e3) = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10521) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10522)  all_56_12 = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10498), (10522) are inconsistent by
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1052.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10523)  all_56_7 = e1 & op(e1, e2) = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10523) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10524)  op(e1, e2) = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (10375), (10524), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10525)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (9980), (10509), (10525),
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #33.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10526)  all_56_15 = e3 & op(e0, e0) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10526) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10527)  op(e0, e0) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10448), (10527), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10528)  all_56_3 = e3 & op(e2, e2) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10528) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10529)  op(e2, e2) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10380), (10529), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10530)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (10441), (10484), (10530),
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | |            #224.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (10531)  all_56_13 = e3 & op(e0, e2) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10434), (10531) are inconsistent by
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #563.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | |   (10532)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10532) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (10533)  all_56_14 = e3 & op(e0, e1) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10533) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (10534)  op(e0, e1) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (10486), (10534), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1147.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (10535)  all_56_15 = e3 & op(e0, e0) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10535) implies:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |   (10536)  op(e0, e0) = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10448), (10536), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | |   (10537)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.61  | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.61  | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.13/21.61  | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.13/21.61  | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.13/21.61  | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.13/21.61  | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.13/21.61  | | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.13/21.61  | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.13/21.61  | | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.13/21.61  | | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.13/21.61  | | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.61  | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.61  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.61  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.61  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.61  | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (116), (156), (158), (163), (164),
% 150.13/21.61  | | | | | | | | | | | | | | | | |            (10429), (10435), (10441), (10447), (10448),
% 150.13/21.61  | | | | | | | | | | | | | | | | |            (10449), (10450), (10454), (10455), (10537),
% 150.13/21.61  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.61  | | | | | | | | | | | | | | | | |            #30.
% 150.13/21.61  | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | |   (10538)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 150.13/21.61  | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 150.13/21.61  | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | BETA: splitting (10538) gives:
% 150.13/21.61  | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | |   (10539)  all_56_14 = e2 & op(e0, e1) = e2
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | ALPHA: (10539) implies:
% 150.13/21.61  | | | | | | | | | | | |   (10540)  op(e0, e1) = e2
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | REF_CLOSE: (156), (9978), (10540), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | |            inconsistent by sub-proof #1092.
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | |   (10541)  all_56_15 = e2 & op(e0, e0) = e2
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | ALPHA: (10541) implies:
% 150.13/21.61  | | | | | | | | | | | |   (10542)  op(e0, e0) = e2
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (237), (9980), (10380),
% 150.13/21.61  | | | | | | | | | | | |            (10429), (10542), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | |            inconsistent by sub-proof #706.
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | 
% 150.13/21.61  | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | 
% 150.13/21.61  | | | | | | | | |   (10543)  all_24_2 = e2
% 150.13/21.61  | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | COMBINE_EQS: (318), (10543) imply:
% 150.13/21.61  | | | | | | | | |   (10544)  all_10_2 = e2
% 150.13/21.61  | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | SIMP: (10544) implies:
% 150.13/21.61  | | | | | | | | |   (10545)  all_10_2 = e2
% 150.13/21.61  | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | REDUCE: (360), (10545) imply:
% 150.13/21.61  | | | | | | | | |   (10546)   ~ (all_52_7 = e2)
% 150.13/21.61  | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | REDUCE: (369), (10545) imply:
% 150.13/21.61  | | | | | | | | |   (10547)   ~ (all_52_13 = e2)
% 150.13/21.61  | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | REDUCE: (45), (10545) imply:
% 150.13/21.61  | | | | | | | | |   (10548)  op(e0, e0) = e2
% 150.13/21.61  | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | BETA: splitting (237) gives:
% 150.13/21.61  | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | |   (10549)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.13/21.61  | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.13/21.61  | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.13/21.61  | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.13/21.61  | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.61  | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.13/21.61  | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.13/21.61  | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.61  | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.13/21.61  | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.13/21.61  | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.61  | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.13/21.61  | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.61  | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.13/21.61  | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.13/21.61  | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.13/21.61  | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | BETA: splitting (10549) gives:
% 150.13/21.61  | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | |   (10550)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.13/21.61  | | | | | | | | | | |                & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.13/21.61  | | | | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.13/21.61  | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.13/21.61  | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.61  | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 150.13/21.61  | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 150.13/21.61  | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.61  | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | ALPHA: (10550) implies:
% 150.13/21.61  | | | | | | | | | | |   (10551)  op(e3, e3) = e3
% 150.13/21.61  | | | | | | | | | | |   (10552)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 150.13/21.61  | | | | | | | | | | |                = e3) & op(e0, e0) = all_57_15 &
% 150.13/21.61  | | | | | | | | | | |              $i(all_57_15))
% 150.13/21.61  | | | | | | | | | | |   (10553)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 150.13/21.61  | | | | | | | | | | |                = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.61  | | | | | | | | | | |              $i(all_57_14))
% 150.13/21.61  | | | | | | | | | | |   (10554)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 150.13/21.61  | | | | | | | | | | |                = e3) & op(e2, e2) = all_57_12 &
% 150.13/21.61  | | | | | | | | | | |              $i(all_57_12))
% 150.13/21.61  | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | BETA: splitting (222) gives:
% 150.13/21.61  | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | |   (10555)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 150.13/21.61  | | | | | | | | | | | |              & op(e2, e2) = e2)
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | BETA: splitting (10555) gives:
% 150.13/21.61  | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | |   (10556)  all_56_2 = e2 & op(e2, e3) = e2
% 150.13/21.61  | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | ALPHA: (10556) implies:
% 150.13/21.61  | | | | | | | | | | | | |   (10557)  all_56_2 = e2
% 150.13/21.61  | | | | | | | | | | | | |   (10558)  op(e2, e3) = e2
% 150.13/21.61  | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | BETA: splitting (226) gives:
% 150.13/21.61  | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | |   (10559)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 150.13/21.61  | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 150.13/21.61  | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | BETA: splitting (10559) gives:
% 150.13/21.61  | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | |   (10560)  all_56_1 = e2 & op(e3, e2) = e2
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | ALPHA: (10560) implies:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10561)  op(e3, e2) = e2
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 150.13/21.61  | | | | | | | | | | | | | | |              e3, e2, simplifying with (166), (10558) gives:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10562)  all_52_1 = e2
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 150.13/21.61  | | | | | | | | | | | | | | |              e2, e3, simplifying with (169), (10561) gives:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10563)  all_52_4 = e2
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e3,
% 150.13/21.61  | | | | | | | | | | | | | | |              e3, e3, simplifying with (51), (10551) gives:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10564)  all_14_2 = e3
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | REDUCE: (148), (10562) imply:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10565)   ~ (all_52_2 = e2)
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | REDUCE: (145), (10562) imply:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10566)   ~ (all_52_9 = e2)
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | REDUCE: (144), (10562) imply:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10567)   ~ (all_52_13 = e2)
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | REDUCE: (338), (10564) imply:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10568)   ~ (all_52_2 = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | REDUCE: (135), (10563) imply:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10569)   ~ (all_52_6 = e2)
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | REDUCE: (134), (10563) imply:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10570)   ~ (all_52_7 = e2)
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | REDUCE: (342), (10563), (10564) imply:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10571)   ~ (e3 = e2)
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | REDUCE: (344), (10564) imply:
% 150.13/21.61  | | | | | | | | | | | | | | |   (10572)   ~ (all_52_8 = e3)
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | |   (10573)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.61  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.61  | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.61  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.61  | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.61  | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.61  | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.61  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.61  | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.61  | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.13/21.61  | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.13/21.61  | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.13/21.61  | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.61  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.61  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.13/21.61  | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.13/21.61  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.13/21.61  | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.13/21.61  | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.13/21.61  | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.13/21.61  | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.13/21.61  | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.13/21.61  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.13/21.61  | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.61  | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.61  | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.61  | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.13/21.61  | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | BETA: splitting (10573) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | |   (10574)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.61  | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.61  | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.13/21.61  | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | BETA: splitting (10574) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | |   (10575)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.61  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.61  | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.61  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.61  | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | REF_CLOSE: (10552), (10553), (10575), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #814.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | |   (10576)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.61  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.13/21.61  | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | | REF_CLOSE: (10552), (10554), (10576), (function-axioms) are
% 150.13/21.61  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 150.13/21.61  | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.61  | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.61  | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | |   (10577)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.13/21.61  | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.61  | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.61  | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.13/21.61  | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.13/21.61  | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.13/21.61  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.61  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.13/21.61  | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.13/21.61  | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | BETA: splitting (10577) gives:
% 150.13/21.61  | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.61  | | | | | | | | | | | | | | | | | | 
% 150.13/21.61  | | | | | | | | | | | | | | | | | |   (10578)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.61  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.13/21.61  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10561), (10578), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #28.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | |   (10579)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (161), (168), (10375), (10551), (10572),
% 150.13/21.62  | | | | | | | | | | | | | | | | | |            (10579), (function-axioms) are inconsistent by
% 150.13/21.62  | | | | | | | | | | | | | | | | | |            sub-proof #729.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | |   (10580)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.62  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.62  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.62  | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.62  | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.62  | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.62  | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.13/21.62  | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.62  | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.13/21.62  | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.13/21.62  | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.62  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.62  | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.62  | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.62  | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.62  | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.62  | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.13/21.62  | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.13/21.62  | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.13/21.62  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.13/21.62  | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.13/21.62  | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.13/21.62  | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.13/21.62  | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.13/21.62  | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.62  | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.62  | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.13/21.62  | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.13/21.62  | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.62  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.13/21.62  | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.13/21.62  | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.13/21.62  | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.62  | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.62  | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.62  | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.62  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.62  | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.62  | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.62  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.62  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.62  | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.62  | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.62  | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | BETA: splitting (10580) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | |   (10581)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.62  | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.13/21.62  | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.13/21.62  | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.13/21.62  | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | BETA: splitting (10581) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | |   (10582)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (9977), (10572), (10582),
% 150.13/21.62  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.62  | | | | | | | | | | | | | | | | | |            #1083.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | |   (10583)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (51), (167), (346), (10548), (10551),
% 150.13/21.62  | | | | | | | | | | | | | | | | | |            (10583), (function-axioms) are inconsistent by
% 150.13/21.62  | | | | | | | | | | | | | | | | | |            sub-proof #27.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | |   (10584)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.13/21.62  | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.13/21.62  | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.13/21.62  | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.13/21.62  | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.13/21.62  | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.13/21.62  | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.13/21.62  | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.13/21.62  | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.13/21.62  | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.62  | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.62  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.62  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.62  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.62  | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | BETA: splitting (10584) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | |   (10585)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.13/21.62  | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10551), (10585), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | |   (10586)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | BETA: splitting (10586) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |   (10587)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | ALPHA: (10587) implies:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |   (10588)  op(e2, e0) = e2
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (10547), (10588), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |   (10589)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | BETA: splitting (10589) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |   (10590)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (10590) implies:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |   (10591)  op(e2, e2) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10380), (10591), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |   (10592)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | ALPHA: (10592) implies:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |   (10593)  op(e0, e0) = all_57_15
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |   (10594)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (10548),
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |              (10593) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | |   (10595)  all_57_15 = e2
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10594) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |   (10596)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10548), (10553), (10554), (10593), (10596),
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |            #627.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |   (10597)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10597) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |   (10598)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10598) implies:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |   (10599)   ~ (all_57_15 = e2)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10548), (10593), (10599), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #901.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |   (10600)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_7))
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10600) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |   (10601)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10601) implies:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |   (10602)  op(e3, e3) = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10551), (10602), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |   (10603)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_7)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10603) implies:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |   (10604)   ~ (all_57_15 = e1)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |   (10605)  op(e0, e1) = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |              e0, e1, e0, simplifying with (156), (10605) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |   (10606)  all_52_11 = e0
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (10606) imply:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |   (10607)   ~ (all_52_3 = e0)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (124), (10606) imply:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |   (10608)   ~ (all_52_7 = e0)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9978), (10606) imply:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | |   (10609)   ~ (e2 = e0)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | |   (10610)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10610) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (10611)  all_56_6 = e1 & op(e1, e3) = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10611) implies:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (10612)  op(e1, e3) = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (158), (162), (228), (10551),
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |            (10557), (10607), (10612), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #26.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (10613)  all_56_7 = e1 & op(e1, e2) = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10613) implies:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (10614)  op(e1, e2) = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (10375), (10614), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | |   (10615)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10615) gives:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (10616)  all_56_8 = e1 & op(e1, e1) = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10616) implies:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (10617)  op(e1, e1) = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (10617), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (10618)  all_56_11 = e1 & op(e1, e0) = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10618) implies:
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |   (10619)  op(e1, e0) = e1
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (127), (139), (140), (142), (158), (159),
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |            (162), (166), (190), (194), (195), (230), (247),
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |            (257), (258), (9974), (9975), (9979), (10546),
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |            (10551), (10558), (10568), (10608), (10619),
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | |            #25.
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | |   (10620)  all_56_3 = e2 & op(e2, e2) = e2
% 150.13/21.62  | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | ALPHA: (10620) implies:
% 150.13/21.62  | | | | | | | | | | | | | | |   (10621)  op(e2, e2) = e2
% 150.13/21.62  | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | | REF_CLOSE: (6), (10380), (10621), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 150.13/21.62  | | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | |   (10622)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 150.13/21.62  | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 150.13/21.62  | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | | REF_CLOSE: (157), (161), (9975), (10546), (10622),
% 150.13/21.62  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.62  | | | | | | | | | | | | | |            #24.
% 150.13/21.62  | | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | |   (10623)  all_56_3 = e2 & op(e2, e2) = e2
% 150.13/21.62  | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | ALPHA: (10623) implies:
% 150.13/21.62  | | | | | | | | | | | | |   (10624)  op(e2, e2) = e2
% 150.13/21.62  | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | | REF_CLOSE: (6), (10380), (10624), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 150.13/21.62  | | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | |   (10625)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 150.13/21.62  | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 150.13/21.62  | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | | REF_CLOSE: (163), (164), (9977), (10547), (10625),
% 150.13/21.62  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.62  | | | | | | | | | | | |            #1155.
% 150.13/21.62  | | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | |   (10626)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.13/21.62  | | | | | | | | | | |                & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.13/21.62  | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.62  | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.13/21.62  | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.62  | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 150.13/21.62  | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 150.13/21.62  | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.62  | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | ALPHA: (10626) implies:
% 150.13/21.62  | | | | | | | | | | |   (10627)  op(e2, e2) = e2
% 150.13/21.62  | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | | REF_CLOSE: (6), (10380), (10627), (function-axioms) are
% 150.13/21.62  | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 150.13/21.62  | | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | |   (10628)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.13/21.62  | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.13/21.62  | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.62  | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.62  | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.62  | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.13/21.62  | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.13/21.62  | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.62  | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.13/21.62  | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.13/21.62  | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.62  | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.62  | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.62  | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.62  | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.62  | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.13/21.62  | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | | REF_CLOSE: (5), (6), (36), (9980), (10548), (10628),
% 150.13/21.62  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.62  | | | | | | | | | |            #707.
% 150.13/21.62  | | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | | 
% 150.13/21.62  | | | | | | | | End of split
% 150.13/21.62  | | | | | | | | 
% 150.13/21.62  | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | 
% 150.13/21.62  | | | | | | | |   (10629)  all_22_2 = e1
% 150.13/21.62  | | | | | | | | 
% 150.13/21.62  | | | | | | | | COMBINE_EQS: (320), (10629) imply:
% 150.13/21.62  | | | | | | | |   (10630)  all_14_2 = e1
% 150.13/21.62  | | | | | | | | 
% 150.13/21.62  | | | | | | | | SIMP: (10630) implies:
% 150.13/21.62  | | | | | | | |   (10631)  all_14_2 = e1
% 150.13/21.62  | | | | | | | | 
% 150.13/21.62  | | | | | | | | REDUCE: (340), (10631) imply:
% 150.13/21.62  | | | | | | | |   (10632)   ~ (all_52_3 = e1)
% 150.13/21.62  | | | | | | | | 
% 150.13/21.62  | | | | | | | | REDUCE: (346), (10631) imply:
% 150.13/21.62  | | | | | | | |   (10633)   ~ (all_52_12 = e1)
% 150.13/21.62  | | | | | | | | 
% 150.13/21.62  | | | | | | | | REDUCE: (51), (10631) imply:
% 150.13/21.62  | | | | | | | |   (10634)  op(e3, e3) = e1
% 150.13/21.62  | | | | | | | | 
% 150.13/21.62  | | | | | | | | BETA: splitting (237) gives:
% 150.13/21.62  | | | | | | | | 
% 150.13/21.62  | | | | | | | | Case 1:
% 150.13/21.62  | | | | | | | | | 
% 150.13/21.62  | | | | | | | | |   (10635)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.13/21.62  | | | | | | | | |                  & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.13/21.62  | | | | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.13/21.62  | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.13/21.62  | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.62  | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.13/21.62  | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.13/21.62  | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.62  | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.13/21.62  | | | | | | | | |                  & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.13/21.62  | | | | | | | | |                  op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.62  | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.13/21.62  | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.62  | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.13/21.62  | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.13/21.62  | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.13/21.62  | | | | | | | | | 
% 150.13/21.62  | | | | | | | | | REF_CLOSE: (6), (8), (10380), (10634), (10635),
% 150.13/21.62  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.62  | | | | | | | | |            #898.
% 150.13/21.62  | | | | | | | | | 
% 150.13/21.62  | | | | | | | | Case 2:
% 150.13/21.62  | | | | | | | | | 
% 150.13/21.63  | | | | | | | | |   (10636)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.13/21.63  | | | | | | | | |                  & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.13/21.63  | | | | | | | | |                  op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.63  | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.63  | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.63  | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.13/21.63  | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.13/21.63  | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.63  | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.13/21.63  | | | | | | | | |                  & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.13/21.63  | | | | | | | | |                  op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.63  | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.63  | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.63  | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.63  | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.63  | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.13/21.63  | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | BETA: splitting (10636) gives:
% 150.13/21.63  | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | |   (10637)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.13/21.63  | | | | | | | | | |                & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.13/21.63  | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.63  | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.63  | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.63  | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.13/21.63  | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.13/21.63  | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.63  | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | ALPHA: (10637) implies:
% 150.13/21.63  | | | | | | | | | |   (10638)  op(e1, e1) = e1
% 150.13/21.63  | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (10638), (function-axioms) are
% 150.13/21.63  | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.13/21.63  | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | |   (10639)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.13/21.63  | | | | | | | | | |                & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.13/21.63  | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.63  | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.63  | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.63  | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.63  | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.63  | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14)))
% 150.13/21.63  | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | ALPHA: (10639) implies:
% 150.13/21.63  | | | | | | | | | |   (10640)  op(e0, e0) = e0
% 150.13/21.63  | | | | | | | | | |   (10641)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 150.13/21.63  | | | | | | | | | |              (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.13/21.63  | | | | | | | | | |              $i(all_57_14))
% 150.13/21.63  | | | | | | | | | |   (10642)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.63  | | | | | | | | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.63  | | | | | | | | | |              $i(all_57_12))
% 150.13/21.63  | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | BETA: splitting (209) gives:
% 150.13/21.63  | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | |   (10643)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 150.13/21.63  | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 150.13/21.63  | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | BETA: splitting (10643) gives:
% 150.13/21.63  | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | |   (10644)  all_56_9 = e1 & op(e3, e0) = e1
% 150.13/21.63  | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | REF_CLOSE: (167), (10633), (10644), (function-axioms) are
% 150.13/21.63  | | | | | | | | | | | |            inconsistent by sub-proof #970.
% 150.13/21.63  | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | |   (10645)  all_56_10 = e1 & op(e2, e0) = e1
% 150.13/21.63  | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | REF_CLOSE: (163), (10378), (10645), (function-axioms) are
% 150.13/21.63  | | | | | | | | | | | |            inconsistent by sub-proof #810.
% 150.13/21.63  | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | End of split
% 150.13/21.63  | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | |   (10646)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 150.13/21.63  | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 150.13/21.63  | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | BETA: splitting (10646) gives:
% 150.13/21.63  | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | |   (10647)  all_56_11 = e1 & op(e1, e0) = e1
% 150.13/21.63  | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | ALPHA: (10647) implies:
% 150.13/21.63  | | | | | | | | | | | |   (10648)  op(e1, e0) = e1
% 150.13/21.63  | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | BETA: splitting (206) gives:
% 150.13/21.63  | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | |   (10649)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 150.13/21.63  | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 150.13/21.63  | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | REF_CLOSE: (157), (158), (10376), (10632), (10649),
% 150.13/21.63  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.63  | | | | | | | | | | | | |            #23.
% 150.13/21.63  | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | |   (10650)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 150.13/21.63  | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 150.13/21.63  | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | BETA: splitting (10650) gives:
% 150.13/21.63  | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | |   (10651)  all_56_14 = e1 & op(e0, e1) = e1
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | ALPHA: (10651) implies:
% 150.13/21.63  | | | | | | | | | | | | | |   (10652)  op(e0, e1) = e1
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 150.13/21.63  | | | | | | | | | | | | | |              e0, e0, simplifying with (45), (10640) gives:
% 150.13/21.63  | | | | | | | | | | | | | |   (10653)  all_10_2 = e0
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 150.13/21.63  | | | | | | | | | | | | | |              e1, e1, e0, simplifying with (156), (10652) gives:
% 150.13/21.63  | | | | | | | | | | | | | |   (10654)  all_52_11 = e1
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 150.13/21.63  | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (159), (10648) gives:
% 150.13/21.63  | | | | | | | | | | | | | |   (10655)  all_52_14 = e1
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | REDUCE: (140), (10655) imply:
% 150.13/21.63  | | | | | | | | | | | | | |   (10656)   ~ (all_52_2 = e1)
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | REDUCE: (349), (10653) imply:
% 150.13/21.63  | | | | | | | | | | | | | |   (10657)   ~ (all_52_3 = e0)
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | REDUCE: (360), (10653) imply:
% 150.13/21.63  | | | | | | | | | | | | | |   (10658)   ~ (all_52_7 = e0)
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | REDUCE: (9979), (10655) imply:
% 150.13/21.63  | | | | | | | | | | | | | |   (10659)   ~ (e2 = e1)
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | REDUCE: (9982), (10653) imply:
% 150.13/21.63  | | | | | | | | | | | | | |   (10660)   ~ (e1 = e0)
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.13/21.63  | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | |   (10661)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.63  | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.63  | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.63  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.63  | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.63  | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.63  | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.63  | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.63  | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.13/21.63  | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.13/21.63  | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.63  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.13/21.63  | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.13/21.63  | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.13/21.63  | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.63  | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.13/21.63  | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.13/21.63  | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.13/21.63  | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.13/21.63  | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | BETA: splitting (10661) gives:
% 150.13/21.63  | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | |   (10662)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.63  | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.63  | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.63  | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (162), (9980), (10640), (10656),
% 150.13/21.63  | | | | | | | | | | | | | | | |            (10662), (function-axioms) are inconsistent by
% 150.13/21.63  | | | | | | | | | | | | | | | |            sub-proof #22.
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | |   (10663)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.13/21.63  | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.63  | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.13/21.63  | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.13/21.63  | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | BETA: splitting (10663) gives:
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | |   (10664)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.13/21.63  | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | BETA: splitting (10664) gives:
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10665)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | ALPHA: (10665) implies:
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10666)   ~ (all_57_4 = e1)
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10667)  op(e1, e2) = all_57_4
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10668)  op(e3, e2) = e3
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 150.13/21.63  | | | | | | | | | | | | | | | | | |              all_57_4, e2, e1, simplifying with (161), (10667)
% 150.13/21.63  | | | | | | | | | | | | | | | | | |              gives:
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10669)  all_57_4 = all_52_6
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 150.13/21.63  | | | | | | | | | | | | | | | | | |              e2, e3, simplifying with (169), (10668) gives:
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10670)  all_52_4 = e3
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | REDUCE: (135), (10670) imply:
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10671)   ~ (all_52_6 = e3)
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | SIMP: (10671) implies:
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10672)   ~ (all_52_6 = e3)
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | REDUCE: (134), (10670) imply:
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10673)   ~ (all_52_7 = e3)
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | SIMP: (10673) implies:
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10674)   ~ (all_52_7 = e3)
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (127), (139), (142), (143), (190), (191), (194),
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            (195), (247), (248), (257), (258), (9974),
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            (10375), (10376), (10632), (10656), (10657),
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            (10658), (10672), (10674) are inconsistent by
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            sub-proof #78.
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10675)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | ALPHA: (10675) implies:
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10676)  op(e0, e0) = e2
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10640), (10676), (function-axioms) are
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | |   (10677)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.13/21.63  | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.13/21.63  | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (10634), (10640), (10677),
% 150.13/21.63  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.63  | | | | | | | | | | | | | | | | |            #892.
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | End of split
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | End of split
% 150.13/21.63  | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | |   (10678)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.63  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.63  | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.63  | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.63  | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.13/21.63  | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.13/21.63  | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.63  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.63  | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.63  | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.63  | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.13/21.63  | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.13/21.63  | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.13/21.63  | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.13/21.63  | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.13/21.63  | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.13/21.63  | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.13/21.63  | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.63  | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.13/21.63  | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.63  | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.13/21.63  | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.13/21.63  | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.13/21.63  | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.63  | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.63  | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.63  | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.63  | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.63  | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.63  | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.63  | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.63  | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.63  | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.63  | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.63  | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.63  | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.63  | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | BETA: splitting (10678) gives:
% 150.13/21.63  | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | |   (10679)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.63  | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.63  | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.13/21.63  | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.13/21.63  | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.63  | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | BETA: splitting (10679) gives:
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | |   (10680)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.63  | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.63  | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (9977), (10640), (10680),
% 150.13/21.63  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.63  | | | | | | | | | | | | | | | | |            #1039.
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | |   (10681)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.13/21.63  | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.13/21.63  | | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10640), (10641), (10642), (10681),
% 150.13/21.63  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.63  | | | | | | | | | | | | | | | | |            #69.
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | End of split
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | |   (10682)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.13/21.63  | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.13/21.63  | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.13/21.63  | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.13/21.63  | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.13/21.63  | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.63  | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.13/21.63  | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.13/21.63  | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.13/21.63  | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.13/21.63  | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.13/21.63  | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.13/21.63  | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.13/21.63  | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.13/21.63  | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.63  | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.63  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.63  | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.63  | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.63  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.63  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.63  | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.63  | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.63  | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | BETA: splitting (10682) gives:
% 150.13/21.63  | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | |   (10683)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.13/21.63  | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.13/21.63  | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.13/21.63  | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.13/21.63  | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10634), (10683), (function-axioms) are
% 150.13/21.63  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | |   (10684)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.13/21.63  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.63  | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.63  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.63  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.63  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | BETA: splitting (10684) gives:
% 150.13/21.63  | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10685)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | ALPHA: (10685) implies:
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10686)   ~ (all_57_13 = e1)
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10687)  op(e1, e1) = e0
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | REF_CLOSE: (10641), (10686), (10687), (function-axioms) are
% 150.13/21.63  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #959.
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | |   (10688)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.13/21.63  | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.13/21.63  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.13/21.63  | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.13/21.63  | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | BETA: splitting (10688) gives:
% 150.13/21.63  | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.63  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | |   (10689)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.13/21.63  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.13/21.63  | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.13/21.63  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.13/21.63  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | | ALPHA: (10689) implies:
% 150.13/21.63  | | | | | | | | | | | | | | | | | | |   (10690)  all_57_12 = e0
% 150.13/21.63  | | | | | | | | | | | | | | | | | | |   (10691)   ~ (all_57_11 = e2)
% 150.13/21.63  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10642), (10690), (10691) are inconsistent by
% 150.13/21.63  | | | | | | | | | | | | | | | | | | |            sub-proof #890.
% 150.13/21.63  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.63  | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.63  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |   (10692)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | ALPHA: (10692) implies:
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |   (10693)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.13/21.64  | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | BETA: splitting (10693) gives:
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |   (10694)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (158), (10634), (10657), (10694),
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |            #955.
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |   (10695)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10695) gives:
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |   (10696)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10696) implies:
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |   (10697)  op(e0, e2) = e0
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (10658), (10697), (function-axioms) are
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |   (10698)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_7))
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10652), (10698), (function-axioms) are
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #800.
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | |   (10699)  all_56_15 = e1 & op(e0, e0) = e1
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | ALPHA: (10699) implies:
% 150.13/21.64  | | | | | | | | | | | | | |   (10700)  op(e0, e0) = e1
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | REF_CLOSE: (4), (10640), (10700), (function-axioms) are
% 150.13/21.64  | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | |   (10701)  all_56_15 = e1 & op(e0, e0) = e1
% 150.13/21.64  | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | ALPHA: (10701) implies:
% 150.13/21.64  | | | | | | | | | | | |   (10702)  op(e0, e0) = e1
% 150.13/21.64  | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | REF_CLOSE: (4), (10640), (10702), (function-axioms) are
% 150.13/21.64  | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 150.13/21.64  | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | 
% 150.13/21.64  | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | 
% 150.13/21.64  | | | | | | | End of split
% 150.13/21.64  | | | | | | | 
% 150.13/21.64  | | | | | | End of split
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | Case 2:
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | |   (10703)  all_16_2 = e0
% 150.13/21.64  | | | | | |   (10704)  ( ~ (all_16_0 = e3) & op(all_16_1, e2) = all_16_0 &
% 150.13/21.64  | | | | | |              op(e2, e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)) |
% 150.13/21.64  | | | | | |            ( ~ (all_16_1 = e1) & op(e2, e0) = all_16_1 &
% 150.13/21.64  | | | | | |              $i(all_16_1))
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | | COMBINE_EQS: (327), (10703) imply:
% 150.13/21.64  | | | | | |   (10705)  all_6_2 = e0
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | | COMBINE_EQS: (325), (10705) imply:
% 150.13/21.64  | | | | | |   (10706)  all_18_2 = e0
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | | REDUCE: (347), (10705) imply:
% 150.13/21.64  | | | | | |   (10707)   ~ (all_52_1 = e0)
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | | REDUCE: (350), (10705) imply:
% 150.13/21.64  | | | | | |   (10708)   ~ (all_52_4 = e0)
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | | REDUCE: (352), (10705) imply:
% 150.13/21.64  | | | | | |   (10709)   ~ (all_52_6 = e0)
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | | REDUCE: (354), (10705) imply:
% 150.13/21.64  | | | | | |   (10710)   ~ (all_52_7 = e0)
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | | REDUCE: (9981), (10705) imply:
% 150.13/21.64  | | | | | |   (10711)   ~ (e3 = e0)
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | | REDUCE: (39), (10705) imply:
% 150.13/21.64  | | | | | |   (10712)  op(e2, e2) = e0
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | | BETA: splitting (58) gives:
% 150.13/21.64  | | | | | | 
% 150.13/21.64  | | | | | | Case 1:
% 150.13/21.64  | | | | | | | 
% 150.13/21.64  | | | | | | |   (10713)   ~ (all_18_2 = e0)
% 150.13/21.64  | | | | | | | 
% 150.13/21.64  | | | | | | | REDUCE: (10706), (10713) imply:
% 150.13/21.64  | | | | | | |   (10714)  $false
% 150.13/21.64  | | | | | | | 
% 150.13/21.64  | | | | | | | CLOSE: (10714) is inconsistent.
% 150.13/21.64  | | | | | | | 
% 150.13/21.64  | | | | | | Case 2:
% 150.13/21.64  | | | | | | | 
% 150.13/21.64  | | | | | | |   (10715)  ( ~ (all_18_0 = e1) & op(all_18_1, e2) = all_18_0 &
% 150.13/21.64  | | | | | | |              op(e2, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1))
% 150.13/21.64  | | | | | | |            | ( ~ (all_18_1 = e3) & op(e2, e0) = all_18_1 &
% 150.13/21.64  | | | | | | |              $i(all_18_1))
% 150.13/21.64  | | | | | | | 
% 150.13/21.64  | | | | | | | BETA: splitting (64) gives:
% 150.13/21.64  | | | | | | | 
% 150.13/21.64  | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | 
% 150.13/21.64  | | | | | | | |   (10716)   ~ (all_22_2 = e1)
% 150.13/21.64  | | | | | | | | 
% 150.13/21.64  | | | | | | | | REDUCE: (320), (10716) imply:
% 150.13/21.64  | | | | | | | |   (10717)   ~ (all_14_2 = e1)
% 150.13/21.64  | | | | | | | | 
% 150.13/21.64  | | | | | | | | BETA: splitting (67) gives:
% 150.13/21.64  | | | | | | | | 
% 150.13/21.64  | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | 
% 150.13/21.64  | | | | | | | | |   (10718)   ~ (all_24_2 = e2)
% 150.13/21.64  | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | REDUCE: (318), (10718) imply:
% 150.13/21.64  | | | | | | | | |   (10719)   ~ (all_10_2 = e2)
% 150.13/21.64  | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | BETA: splitting (84) gives:
% 150.13/21.64  | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | |   (10720)   ~ (all_36_2 = e2)
% 150.13/21.64  | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | REDUCE: (304), (10720) imply:
% 150.13/21.64  | | | | | | | | | |   (10721)   ~ (all_14_2 = e2)
% 150.13/21.64  | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | BETA: splitting (203) gives:
% 150.13/21.64  | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | |   (10722)  all_54_0 = e3
% 150.13/21.64  | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | COMBINE_EQS: (278), (10722) imply:
% 150.13/21.64  | | | | | | | | | | |   (10723)  all_14_2 = e3
% 150.13/21.64  | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | SIMP: (10723) implies:
% 150.13/21.64  | | | | | | | | | | |   (10724)  all_14_2 = e3
% 150.13/21.64  | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | REDUCE: (342), (10724) imply:
% 150.13/21.64  | | | | | | | | | | |   (10725)   ~ (all_52_4 = e3)
% 150.13/21.64  | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | REDUCE: (344), (10724) imply:
% 150.13/21.64  | | | | | | | | | | |   (10726)   ~ (all_52_8 = e3)
% 150.13/21.64  | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | REDUCE: (346), (10724) imply:
% 150.13/21.64  | | | | | | | | | | |   (10727)   ~ (all_52_12 = e3)
% 150.13/21.64  | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | REDUCE: (51), (10724) imply:
% 150.13/21.64  | | | | | | | | | | |   (10728)  op(e3, e3) = e3
% 150.13/21.64  | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | BETA: splitting (93) gives:
% 150.13/21.64  | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | |   (10729)   ~ (all_42_2 = e3)
% 150.13/21.64  | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | REDUCE: (302), (10729) imply:
% 150.13/21.64  | | | | | | | | | | | |   (10730)   ~ (all_10_2 = e3)
% 150.13/21.64  | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | BETA: splitting (188) gives:
% 150.13/21.64  | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | |   (10731)  all_54_15 = e3
% 150.13/21.64  | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | REF_CLOSE: (245), (10730), (10731) are inconsistent by
% 150.13/21.64  | | | | | | | | | | | | |            sub-proof #1049.
% 150.13/21.64  | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | |   (10732)   ~ (all_54_15 = e3)
% 150.13/21.64  | | | | | | | | | | | | |   (10733)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 150.13/21.64  | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.13/21.64  | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | |   (10734)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.64  | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.64  | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.64  | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.64  | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.64  | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.64  | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.64  | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.64  | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.13/21.64  | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.13/21.64  | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.13/21.64  | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.64  | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.13/21.64  | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.13/21.64  | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.13/21.64  | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.64  | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.13/21.64  | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.13/21.64  | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.13/21.64  | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.13/21.64  | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.64  | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | BETA: splitting (10734) gives:
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | |   (10735)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.64  | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.64  | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.64  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.64  | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.64  | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.64  | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.64  | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.64  | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | BETA: splitting (10735) gives:
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | |   (10736)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.64  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.64  | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.64  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | REF_CLOSE: (9), (45), (245), (9980), (9982), (10719),
% 150.13/21.64  | | | | | | | | | | | | | | | |            (10730), (10733), (10736), (function-axioms) are
% 150.13/21.64  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #39.
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | |   (10737)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.64  | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.64  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.64  | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | BETA: splitting (10737) gives:
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | |   (10738)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.64  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.64  | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.64  | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 150.13/21.64  | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | ALPHA: (10738) implies:
% 150.13/21.64  | | | | | | | | | | | | | | | | |   (10739)  op(e2, e2) = e3
% 150.13/21.64  | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10712), (10739), (function-axioms) are
% 150.13/21.64  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 150.13/21.64  | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | |   (10740)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.64  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.13/21.64  | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 150.13/21.64  | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 150.13/21.64  | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | ALPHA: (10740) implies:
% 150.13/21.64  | | | | | | | | | | | | | | | | |   (10741)  op(e0, e0) = e3
% 150.13/21.64  | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (245), (9982), (10719), (10730), (10733),
% 150.13/21.64  | | | | | | | | | | | | | | | | |            (10741), (function-axioms) are inconsistent by
% 150.13/21.64  | | | | | | | | | | | | | | | | |            sub-proof #702.
% 150.13/21.64  | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | |   (10742)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.64  | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.64  | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.64  | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.13/21.64  | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.13/21.64  | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.64  | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.64  | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.13/21.64  | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.13/21.64  | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.64  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.13/21.64  | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.13/21.64  | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.13/21.64  | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (45), (169), (10712), (10719), (10725),
% 150.13/21.64  | | | | | | | | | | | | | | |            (10728), (10742), (function-axioms) are
% 150.13/21.64  | | | | | | | | | | | | | | |            inconsistent by sub-proof #699.
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | |   (10743)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.64  | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.64  | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.64  | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.64  | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.13/21.64  | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.13/21.64  | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.13/21.64  | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.64  | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.64  | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.64  | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.64  | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.13/21.64  | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.13/21.64  | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.13/21.64  | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.13/21.64  | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.13/21.64  | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.13/21.64  | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.13/21.64  | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.13/21.64  | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.64  | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.13/21.64  | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.64  | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.13/21.64  | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.13/21.64  | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.13/21.64  | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.13/21.64  | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.13/21.64  | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.64  | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.64  | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.64  | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.64  | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.64  | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.64  | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.64  | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.64  | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.64  | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.64  | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.64  | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.64  | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.64  | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.64  | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.64  | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | BETA: splitting (10743) gives:
% 150.13/21.64  | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | |   (10744)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.64  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.64  | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.64  | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.64  | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.64  | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.13/21.64  | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.13/21.64  | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.13/21.64  | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.13/21.64  | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.64  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.64  | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.64  | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.64  | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | BETA: splitting (10744) gives:
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | |   (10745)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.64  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.64  | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.64  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.64  | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.64  | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (9977), (10726), (10745),
% 150.13/21.64  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.64  | | | | | | | | | | | | | | | |            #1083.
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | |   (10746)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.64  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.13/21.64  | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.13/21.64  | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.64  | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.13/21.64  | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.13/21.64  | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.13/21.64  | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.13/21.64  | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | REF_CLOSE: (45), (167), (9982), (10727), (10746),
% 150.13/21.64  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.64  | | | | | | | | | | | | | | | |            #1080.
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | End of split
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | |   (10747)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.13/21.64  | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.13/21.64  | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.13/21.64  | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.13/21.64  | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.13/21.64  | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.13/21.64  | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.13/21.64  | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.13/21.64  | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.64  | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.13/21.64  | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.13/21.64  | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.13/21.64  | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.13/21.64  | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.13/21.64  | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.13/21.64  | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.13/21.64  | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.13/21.64  | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.13/21.64  | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.64  | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.64  | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.64  | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.64  | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.64  | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.64  | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.64  | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.64  | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.64  | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.64  | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.64  | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.64  | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.64  | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.64  | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | BETA: splitting (10747) gives:
% 150.13/21.64  | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | |   (10748)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.13/21.64  | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.13/21.64  | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.13/21.64  | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.13/21.64  | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.13/21.64  | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.13/21.64  | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (9983), (10717), (10721),
% 150.13/21.64  | | | | | | | | | | | | | | | |            (10748), (function-axioms) are inconsistent by
% 150.13/21.64  | | | | | | | | | | | | | | | |            sub-proof #1079.
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | |   (10749)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.13/21.64  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.64  | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.64  | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.13/21.64  | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.13/21.64  | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.13/21.64  | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.13/21.64  | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.13/21.64  | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.64  | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.64  | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.64  | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.64  | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.64  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.64  | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.64  | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.64  | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.64  | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.64  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.64  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.64  | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.64  | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.64  | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.64  | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.64  | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | BETA: splitting (10749) gives:
% 150.13/21.64  | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.64  | | | | | | | | | | | | | | | | | 
% 150.13/21.64  | | | | | | | | | | | | | | | | |   (10750)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.13/21.64  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.64  | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.64  | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.64  | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.13/21.65  | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | ALPHA: (10750) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | |   (10751)  op(e1, e1) = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9980), (10751), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 150.13/21.65  | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | |   (10752)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.13/21.65  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.13/21.65  | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.13/21.65  | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.13/21.65  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.13/21.65  | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.13/21.65  | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.13/21.65  | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.13/21.65  | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.13/21.65  | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.13/21.65  | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.13/21.65  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.13/21.65  | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.13/21.65  | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | BETA: splitting (10752) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | |   (10753)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.13/21.65  | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.13/21.65  | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | ALPHA: (10753) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | |   (10754)  all_57_12 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | |   (10755)   ~ (all_57_11 = e2)
% 150.13/21.65  | | | | | | | | | | | | | | | | | |   (10756)  op(e1, e0) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | |   (10757)  op(e2, e0) = all_57_11
% 150.13/21.65  | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | BETA: splitting (10733) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | |   (10758)  all_54_15 = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (10719), (10758) are inconsistent by
% 150.13/21.65  | | | | | | | | | | | | | | | | | | |            sub-proof #1048.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | |   (10759)   ~ (all_54_15 = e2)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | |   (10760)  all_54_15 = e1 | all_54_15 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |   (10761)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10761) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | |   (10762)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | |                & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10762) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | |   (10763)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e0, e0) = all_57_15 &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_15))
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10760) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | |   (10764)  all_54_15 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (9982), (10764) are inconsistent by
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1047.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | |   (10765)  all_54_15 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (10765) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | |   (10766)  all_10_2 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | SIMP: (10766) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | |   (10767)  all_10_2 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (10767) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | |   (10768)   ~ (all_52_3 = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (10767) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | |   (10769)   ~ (all_52_12 = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (10767) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | |   (10770)   ~ (all_52_13 = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (10767) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | |   (10771)   ~ (all_52_14 = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (10767) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | |   (10772)  op(e0, e0) = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | |   (10773)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (169), (203), (278), (9983), (10708),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | |            (10717), (10721), (10773), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #698.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | |   (10774)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10774) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | |   (10775)  all_56_4 = e0 & op(e3, e1) = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10775) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | |   (10776)  all_56_4 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | |   (10777)  op(e3, e1) = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (10778)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (166), (203), (278), (9983), (10707),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | |            (10717), (10721), (10778), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #692.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | |   (10779)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10779) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10780)  all_56_6 = e0 & op(e1, e3) = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10780) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10781)  all_56_6 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10782)  op(e1, e3) = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10763) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10783)  all_57_2 = e0 & op(e0, e3) = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10783) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10784)  op(e0, e3) = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10768), (10784), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10785)   ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_15)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10785) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10786)  op(e0, e0) = all_57_15
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (10772),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |              (10786) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10787)  all_57_15 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (159), (10756) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10788)  all_52_14 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (10782) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10789)  all_52_2 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_11, e0, e2, simplifying with (163), (10757)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |              gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10790)  all_57_11 = all_52_13
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1, e3, simplifying with (168), (10777) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10791)  all_52_8 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (10755), (10790) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10792)   ~ (all_52_13 = e2)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (10789) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10793)   ~ (all_52_3 = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (10789) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10794)   ~ (all_52_6 = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (10788) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10795)   ~ (all_52_6 = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (122), (10791) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10796)   ~ (all_52_9 = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10796) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10797)   ~ (all_52_9 = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9976), (10791) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10798)   ~ (e2 = e0)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (111), (10788) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10799)   ~ (all_52_12 = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (109), (10788) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10800)   ~ (all_52_13 = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9979), (10788) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10801)   ~ (e2 = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10802)  all_54_9 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (10802) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10803)  all_52_6 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10803) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10804)  all_52_6 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (10804) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10805)  op(e1, e2) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10806)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10806) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10807)  all_56_9 = e3 & op(e3, e0) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10807) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10808)  op(e3, e0) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10727), (10808), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1082.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10809)  all_56_10 = e3 & op(e2, e0) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10809) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10810)  all_56_10 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10811)  op(e2, e0) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10812)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10812) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10813)  all_56_2 = e2 & op(e2, e3) = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10813) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10814)  op(e2, e3) = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10815)  all_54_7 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (10815) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10816)  all_52_13 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10816) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10817)  all_52_13 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (10817) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10818)   ~ (all_52_1 = e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (10817) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10819)   ~ (all_52_9 = e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10820)  all_54_6 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (10819), (10820) are inconsistent by
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #650.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10821)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10822)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10822) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10823)  all_56_0 = e1 & op(e3, e3) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10823) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10824)  op(e3, e3) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (167), (169), (235), (10725), (10727),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10776), (10824), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #90.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10825)  all_56_2 = e1 & op(e2, e3) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10825) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10826)  op(e2, e3) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (10814), (10826), (function-axioms)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #842.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10827)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10827) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10828)  all_56_6 = e1 & op(e1, e3) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10828) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10829)  op(e1, e3) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (51), (158), (162),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (203), (221), (222), (228), (278), (9983),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10712), (10717), (10721), (10768), (10810),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10811), (10829), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #668.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10830)  all_56_12 = e1 & op(e0, e3) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10830) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10831)  all_56_12 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10832)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10832) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10833)  all_56_0 = e1 & op(e3, e3) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10833) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10834)  op(e3, e3) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10835)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (232),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10831), (10834), (10835), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #927.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10836)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10836) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10837)  all_56_6 = e3 & op(e1, e3) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10781), (10837) are inconsistent by
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #576.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10838)  all_56_12 = e3 & op(e0, e3) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10838) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10839)  all_56_12 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10831), (10839) are inconsistent by
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1056.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10840)  all_56_1 = e1 & op(e3, e2) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10840) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10841)  op(e3, e2) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10704) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10842)   ~ (all_16_0 = e3) & op(all_16_1, e2) = all_16_0 &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_16_1 & $i(all_16_0) &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_16_1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10842) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10843)  op(e2, e0) = all_16_1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (199), (260), (268), (9977), (10707),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10715), (10797), (10811), (10818), (10821),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10841), (10843), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #21.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10844)   ~ (all_16_1 = e1) & op(e2, e0) = all_16_1 &
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_16_1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10844) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10845)  op(e2, e0) = all_16_1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (145), (199), (260), (268), (9977), (10707),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10715), (10797), (10811), (10818), (10821),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10841), (10845), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #21.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10846)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10846) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10847)  all_56_4 = e1 & op(e3, e1) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10847) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10848)  all_56_4 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10776), (10848) are inconsistent by
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #657.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10849)  all_56_9 = e1 & op(e3, e0) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10799), (10849), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #970.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10850)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (10770), (10792), (10800), (10850) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #449.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10851)  all_56_3 = e2 & op(e2, e2) = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10851) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10852)  op(e2, e2) = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10712), (10852), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10853)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (9977), (10811), (10853),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #190.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10854)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10854) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10855)  all_56_11 = e3 & op(e1, e0) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10855) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10856)  all_56_11 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10857)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10857) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10858)  all_56_2 = e2 & op(e2, e3) = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10858) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10859)  op(e2, e3) = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10860)  all_54_7 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (10860) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10861)  all_52_13 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (10861) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10862)  all_52_13 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (10862) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10863)   ~ (all_52_1 = e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (116), (10862) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10864)   ~ (all_52_9 = e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10865)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (166), (10712), (10863), (10865),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #690.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10866)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10866) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10867)  all_56_5 = e3 & op(e2, e1) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (10864), (10867), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #647.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10868)  all_56_10 = e3 & op(e2, e0) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10868) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10869)  all_56_10 = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10870)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (166), (10712), (10859), (10870),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #686.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10871)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10871) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10872)  all_56_5 = e1 & op(e2, e1) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10872) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10873)  all_56_5 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10874)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10874) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10875)  all_56_9 = e1 & op(e3, e0) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10799), (10875), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #970.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10876)  all_56_10 = e1 & op(e2, e0) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10876) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10877)  all_56_10 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (220), (222), (223),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10712), (10873), (10877), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #676.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10878)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10878) gives:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10879)  all_56_11 = e1 & op(e1, e0) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10879) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10880)  all_56_11 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10856), (10880) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10881)  e3 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10869), (10881) imply:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10882)  all_56_10 = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (220), (222), (223),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10712), (10873), (10882), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #676.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10883)  all_56_15 = e1 & op(e0, e0) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10883) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10884)  op(e0, e0) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10772), (10884), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10885)  all_56_10 = e1 & op(e2, e0) = e1
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10704), (10715), (10805), (10885),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #688.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10886)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (10770), (10792), (10800), (10886) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #449.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10887)  all_56_3 = e2 & op(e2, e2) = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10887) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10888)  op(e2, e2) = e2
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10712), (10888), (function-axioms) are
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10889)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (164), (9977), (10792), (10889),
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1155.
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10890)  all_56_15 = e3 & op(e0, e0) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10890) implies:
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10891)  op(e0, e0) = e3
% 150.13/21.65  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (245), (9982), (10719), (10730), (10733),
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (10891), (function-axioms) are inconsistent by
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #702.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (10892)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9975), (10709), (10795), (10892) are
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #20.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10893)  all_56_12 = e0 & op(e0, e3) = e0
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10893) implies:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |   (10894)  op(e0, e3) = e0
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (10768), (10894), (function-axioms) are
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1142.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | |   (10895)  all_56_9 = e0 & op(e3, e0) = e0
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (10769), (10895), (function-axioms) are
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |   (10896)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10896) implies:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |   (10897)  op(e2, e2) = e2
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10712), (10897), (function-axioms) are
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |   (10898)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | BETA: splitting (10898) gives:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |   (10899)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10899) implies:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |   (10900)  op(e1, e1) = e1
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (10900), (function-axioms) are
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |   (10901)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14)))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | ALPHA: (10901) implies:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |   (10902)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10754), (10755), (10902) are inconsistent by
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | |            sub-proof #890.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | |   (10903)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | ALPHA: (10903) implies:
% 150.13/21.66  | | | | | | | | | | | | | | | | | |   (10904)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (9), (156), (157), (158), (188),
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            (245), (349), (367), (9982), (10710), (10712),
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            (10719), (10728), (10730), (10904),
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            #693.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | |   (10905)  all_42_2 = e3
% 150.13/21.66  | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | COMBINE_EQS: (302), (10905) imply:
% 150.13/21.66  | | | | | | | | | | | |   (10906)  all_10_2 = e3
% 150.13/21.66  | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | REDUCE: (369), (10906) imply:
% 150.13/21.66  | | | | | | | | | | | |   (10907)   ~ (all_52_13 = e3)
% 150.13/21.66  | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | REDUCE: (370), (10906) imply:
% 150.13/21.66  | | | | | | | | | | | |   (10908)   ~ (all_52_14 = e3)
% 150.13/21.66  | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | REDUCE: (45), (10906) imply:
% 150.13/21.66  | | | | | | | | | | | |   (10909)  op(e0, e0) = e3
% 150.13/21.66  | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | BETA: splitting (237) gives:
% 150.13/21.66  | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | |   (10910)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.13/21.66  | | | | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.13/21.66  | | | | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.13/21.66  | | | | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.13/21.66  | | | | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.66  | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.13/21.66  | | | | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.13/21.66  | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.66  | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.13/21.66  | | | | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.13/21.66  | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.66  | | | | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.13/21.66  | | | | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.66  | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.13/21.66  | | | | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.13/21.66  | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.13/21.66  | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | BETA: splitting (10910) gives:
% 150.13/21.66  | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | |   (10911)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.13/21.66  | | | | | | | | | | | | | |                & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.13/21.66  | | | | | | | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.13/21.66  | | | | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.13/21.66  | | | | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.66  | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 150.13/21.66  | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 150.13/21.66  | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.66  | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | ALPHA: (10911) implies:
% 150.13/21.66  | | | | | | | | | | | | | |   (10912)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 150.13/21.66  | | | | | | | | | | | | | |                = e3) & op(e0, e0) = all_57_15 &
% 150.13/21.66  | | | | | | | | | | | | | |              $i(all_57_15))
% 150.13/21.66  | | | | | | | | | | | | | |   (10913)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 150.13/21.66  | | | | | | | | | | | | | |                = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.66  | | | | | | | | | | | | | |              $i(all_57_14))
% 150.13/21.66  | | | | | | | | | | | | | |   (10914)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 150.13/21.66  | | | | | | | | | | | | | |                = e3) & op(e2, e2) = all_57_12 &
% 150.13/21.66  | | | | | | | | | | | | | |              $i(all_57_12))
% 150.13/21.66  | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | BETA: splitting (10912) gives:
% 150.13/21.66  | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | |   (10915)  all_57_2 = e0 & op(e0, e3) = e0
% 150.13/21.66  | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | ALPHA: (10915) implies:
% 150.13/21.66  | | | | | | | | | | | | | | |   (10916)  op(e0, e3) = e0
% 150.13/21.66  | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.13/21.66  | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | |   (10917)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.66  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.66  | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.66  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.66  | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.66  | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.66  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.66  | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.13/21.66  | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.13/21.66  | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.66  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.13/21.66  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.13/21.66  | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.13/21.66  | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.13/21.66  | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.13/21.66  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.13/21.66  | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.13/21.66  | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | BETA: splitting (10917) gives:
% 150.13/21.66  | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | |   (10918)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.66  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.66  | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.66  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.66  | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.66  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.66  | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | BETA: splitting (10918) gives:
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | |   (10919)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (10912), (10913), (10919), (function-axioms) are
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #814.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | |   (10920)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (10912), (10914), (10920), (function-axioms) are
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | |   (10921)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.66  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.66  | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.13/21.66  | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.66  | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.13/21.66  | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.13/21.66  | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.66  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.13/21.66  | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.13/21.66  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | BETA: splitting (10921) gives:
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | |   (10922)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (10725), (10922), (function-axioms) are
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | |   (10923)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | BETA: splitting (10923) gives:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |   (10924)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | ALPHA: (10924) implies:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |   (10925)  op(e3, e3) = e2
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10728), (10925), (function-axioms) are
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |   (10926)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | BETA: splitting (10926) gives:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |   (10927)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | ALPHA: (10927) implies:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |   (10928)  op(e0, e0) = e2
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (51), (159), (163), (167), (211), (346),
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |            (10728), (10907), (10908), (10928),
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |            #65.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |   (10929)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | ALPHA: (10929) implies:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |   (10930)  op(e2, e2) = e1
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10712), (10930), (function-axioms) are
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | |   (10931)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.66  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.66  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.66  | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.66  | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.13/21.66  | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.13/21.66  | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.66  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.66  | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.66  | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.13/21.66  | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.13/21.66  | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.13/21.66  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.13/21.66  | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.13/21.66  | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.13/21.66  | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.13/21.66  | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.66  | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.13/21.66  | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.13/21.66  | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.13/21.66  | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.13/21.66  | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.66  | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.66  | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.66  | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.66  | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.66  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.66  | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.66  | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.66  | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.66  | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.66  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.66  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.66  | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.66  | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.66  | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.66  | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.66  | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | BETA: splitting (10931) gives:
% 150.13/21.66  | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | |   (10932)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.66  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.66  | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.66  | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.66  | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.13/21.66  | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.13/21.66  | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.13/21.66  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.13/21.66  | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.66  | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | BETA: splitting (10932) gives:
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | |   (10933)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (9977), (10726), (10933),
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            #1083.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | |   (10934)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.13/21.66  | | | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (10727), (10909), (10934),
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.66  | | | | | | | | | | | | | | | | | |            #1020.
% 150.13/21.66  | | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.66  | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.66  | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | |   (10935)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.13/21.67  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.13/21.67  | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.13/21.67  | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.13/21.67  | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.13/21.67  | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.13/21.67  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.13/21.67  | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.13/21.67  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.13/21.67  | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.13/21.67  | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.13/21.67  | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.13/21.67  | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.13/21.67  | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.13/21.67  | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.13/21.67  | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.13/21.67  | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.67  | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.67  | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.67  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.67  | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.67  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.67  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.67  | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.67  | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.67  | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | BETA: splitting (10935) gives:
% 150.13/21.67  | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | |   (10936)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.13/21.67  | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.13/21.67  | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (9983), (10717), (10721),
% 150.13/21.67  | | | | | | | | | | | | | | | | | |            (10936), (function-axioms) are inconsistent by
% 150.13/21.67  | | | | | | | | | | | | | | | | | |            sub-proof #1079.
% 150.13/21.67  | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | |   (10937)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.13/21.67  | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | BETA: splitting (10937) gives:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |   (10938)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | ALPHA: (10938) implies:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |   (10939)  op(e1, e1) = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9980), (10939), (function-axioms) are
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |   (10940)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | BETA: splitting (10940) gives:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |   (10941)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | ALPHA: (10941) implies:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |   (10942)  op(e1, e0) = e1
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | |   (10943)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10943) gives:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |   (10944)  all_56_6 = e3 & op(e1, e3) = e3
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10944) implies:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |   (10945)  all_56_6 = e3
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (51), (166), (203),
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |            (228), (230), (232), (278), (9983), (10707),
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |            (10717), (10721), (10728), (10945),
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |            #691.
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |   (10946)  all_56_7 = e3 & op(e1, e2) = e3
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (10946) implies:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |   (10947)  op(e1, e2) = e3
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |              e3, e0, simplifying with (158), (10916) gives:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |   (10948)  all_52_3 = e0
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |              e1, e0, e1, simplifying with (159), (10942) gives:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |   (10949)  all_52_14 = e1
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e3,
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |              e2, e1, simplifying with (161), (10947) gives:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |   (10950)  all_52_6 = e3
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (10948) imply:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |   (10951)   ~ (all_52_2 = e0)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (10950) imply:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |   (10952)   ~ (all_52_2 = e3)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (10949) imply:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |   (10953)   ~ (all_52_2 = e1)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (195), (258), (9974), (10951), (10952), (10953)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #102.
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | |   (10954)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (163), (205),
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | |            (209), (210), (9980), (10719), (10909), (10954),
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | |            #36.
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |   (10955)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | ALPHA: (10955) implies:
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |   (10956)  op(e0, e0) = all_57_15
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |   (10957)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (157), (10710), (10712), (10728),
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |            (10909), (10956), (10957), (function-axioms) are
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #822.
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | |   (10958)   ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 150.13/21.67  | | | | | | | | | | | | | | |            $i(all_57_15)
% 150.13/21.67  | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | ALPHA: (10958) implies:
% 150.13/21.67  | | | | | | | | | | | | | | |   (10959)   ~ (all_57_15 = e3)
% 150.13/21.67  | | | | | | | | | | | | | | |   (10960)  op(e0, e0) = all_57_15
% 150.13/21.67  | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | REF_CLOSE: (10909), (10959), (10960), (function-axioms) are
% 150.13/21.67  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1019.
% 150.13/21.67  | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | |   (10961)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.13/21.67  | | | | | | | | | | | | | |                & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.13/21.67  | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.67  | | | | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.13/21.67  | | | | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.67  | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 150.13/21.67  | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 150.13/21.67  | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.67  | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | ALPHA: (10961) implies:
% 150.13/21.67  | | | | | | | | | | | | | |   (10962)  op(e2, e2) = e2
% 150.13/21.67  | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | REF_CLOSE: (5), (10712), (10962), (function-axioms) are
% 150.13/21.67  | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 150.13/21.67  | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | |   (10963)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.13/21.67  | | | | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.13/21.67  | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.67  | | | | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.67  | | | | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.67  | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.13/21.67  | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.13/21.67  | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.67  | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.13/21.67  | | | | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.13/21.67  | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.67  | | | | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.67  | | | | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.67  | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.67  | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.67  | | | | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.13/21.67  | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (9980), (10909), (10963),
% 150.13/21.67  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.67  | | | | | | | | | | | | |            #51.
% 150.13/21.67  | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | |   (10964)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 150.13/21.67  | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | REF_CLOSE: (278), (9983), (10717), (10721), (10964) are
% 150.13/21.67  | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 150.13/21.67  | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | End of split
% 150.13/21.67  | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | |   (10965)  all_36_2 = e2
% 150.13/21.67  | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | COMBINE_EQS: (304), (10965) imply:
% 150.13/21.67  | | | | | | | | | |   (10966)  all_14_2 = e2
% 150.13/21.67  | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | SIMP: (10966) implies:
% 150.13/21.67  | | | | | | | | | |   (10967)  all_14_2 = e2
% 150.13/21.67  | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | REDUCE: (336), (10967) imply:
% 150.13/21.67  | | | | | | | | | |   (10968)   ~ (all_52_1 = e2)
% 150.13/21.67  | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | REDUCE: (51), (10967) imply:
% 150.13/21.67  | | | | | | | | | |   (10969)  op(e3, e3) = e2
% 150.13/21.67  | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | BETA: splitting (237) gives:
% 150.13/21.67  | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | Case 1:
% 150.13/21.67  | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | |   (10970)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.13/21.67  | | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.13/21.67  | | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.13/21.67  | | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.13/21.67  | | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.13/21.67  | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.13/21.67  | | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.13/21.67  | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.67  | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.13/21.67  | | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.13/21.67  | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.67  | | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.13/21.67  | | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.13/21.67  | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.13/21.67  | | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.13/21.67  | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.13/21.67  | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | REF_CLOSE: (5), (7), (9), (157), (161), (169), (224),
% 150.13/21.67  | | | | | | | | | | |            (10709), (10710), (10969), (10970),
% 150.13/21.67  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.13/21.67  | | | | | | | | | | |            #385.
% 150.13/21.67  | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | |   (10971)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.13/21.67  | | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.13/21.67  | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.67  | | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.67  | | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.67  | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.13/21.67  | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.13/21.67  | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.13/21.67  | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.13/21.67  | | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.13/21.67  | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.67  | | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.67  | | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.67  | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.67  | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.67  | | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.13/21.67  | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | BETA: splitting (10971) gives:
% 150.13/21.67  | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | Case 1:
% 150.13/21.67  | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | |   (10972)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.13/21.67  | | | | | | | | | | | |                & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.13/21.67  | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.67  | | | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.13/21.67  | | | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.13/21.67  | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.13/21.67  | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.13/21.67  | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.13/21.67  | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | ALPHA: (10972) implies:
% 150.13/21.67  | | | | | | | | | | | |   (10973)  op(e1, e1) = e1
% 150.13/21.67  | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (10973), (function-axioms) are
% 150.13/21.67  | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.13/21.67  | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | |   (10974)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.13/21.67  | | | | | | | | | | | |                & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.13/21.67  | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.13/21.67  | | | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.67  | | | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.67  | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.13/21.67  | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.13/21.67  | | | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14)))
% 150.13/21.67  | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | ALPHA: (10974) implies:
% 150.13/21.67  | | | | | | | | | | | |   (10975)  all_57_15 = e0
% 150.13/21.67  | | | | | | | | | | | |   (10976)  op(e0, e0) = e0
% 150.13/21.67  | | | | | | | | | | | |   (10977)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 150.13/21.67  | | | | | | | | | | | |              (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.13/21.67  | | | | | | | | | | | |              $i(all_57_14))
% 150.13/21.67  | | | | | | | | | | | |   (10978)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.13/21.67  | | | | | | | | | | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.13/21.67  | | | | | | | | | | | |              $i(all_57_12))
% 150.13/21.67  | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | BETA: splitting (10978) gives:
% 150.13/21.67  | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | Case 1:
% 150.13/21.67  | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | |   (10979)  all_57_11 = e2 & op(e2, e0) = e2
% 150.13/21.67  | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | ALPHA: (10979) implies:
% 150.13/21.67  | | | | | | | | | | | | |   (10980)  op(e2, e0) = e2
% 150.13/21.67  | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.13/21.67  | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | Case 1:
% 150.13/21.67  | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | |   (10981)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.67  | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.67  | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.67  | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.67  | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.67  | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.67  | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.67  | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.67  | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.67  | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.67  | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.67  | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.67  | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.67  | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.67  | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.67  | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.67  | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.13/21.67  | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.13/21.67  | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.13/21.67  | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.13/21.67  | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.13/21.67  | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.13/21.67  | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.13/21.67  | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.13/21.67  | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.13/21.67  | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.13/21.67  | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.13/21.67  | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.13/21.67  | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.67  | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.13/21.67  | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.13/21.67  | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.13/21.67  | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.13/21.67  | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.13/21.67  | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.13/21.67  | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.13/21.67  | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.13/21.67  | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.13/21.67  | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | BETA: splitting (10981) gives:
% 150.13/21.67  | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | Case 1:
% 150.13/21.67  | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | |   (10982)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.67  | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.67  | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.67  | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.67  | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.67  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.67  | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.67  | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.67  | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.13/21.67  | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.13/21.67  | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.13/21.67  | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.13/21.67  | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.13/21.67  | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.13/21.67  | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.13/21.67  | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.13/21.67  | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.13/21.67  | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | BETA: splitting (10982) gives:
% 150.13/21.67  | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | Case 1:
% 150.13/21.67  | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | |   (10983)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.13/21.67  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.67  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.13/21.67  | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.13/21.67  | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.13/21.67  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.13/21.67  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.13/21.67  | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.13/21.67  | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | | REF_CLOSE: (166), (10968), (10983), (function-axioms) are
% 150.13/21.67  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 150.13/21.67  | | | | | | | | | | | | | | | | 
% 150.13/21.67  | | | | | | | | | | | | | | | Case 2:
% 150.13/21.67  | | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | | |   (10984)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.53/21.67  | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.53/21.67  | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.53/21.67  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.53/21.67  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.53/21.67  | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.53/21.67  | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.53/21.67  | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.53/21.67  | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.53/21.67  | | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10712), (10976), (10984), (function-axioms)
% 150.53/21.67  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #474.
% 150.53/21.67  | | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | | End of split
% 150.53/21.67  | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | Case 2:
% 150.53/21.67  | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | |   (10985)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.67  | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.53/21.67  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.53/21.67  | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.53/21.67  | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.53/21.67  | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.53/21.67  | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.53/21.67  | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.53/21.67  | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.53/21.67  | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.53/21.67  | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.53/21.67  | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.53/21.67  | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.53/21.67  | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.53/21.67  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.53/21.67  | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.53/21.67  | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.53/21.67  | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.53/21.67  | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.53/21.67  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.53/21.67  | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.53/21.67  | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.53/21.67  | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | | BETA: splitting (10985) gives:
% 150.53/21.67  | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | | Case 1:
% 150.53/21.67  | | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | | |   (10986)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.67  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.53/21.67  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.53/21.67  | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.53/21.67  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.53/21.67  | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.53/21.67  | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.53/21.67  | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.53/21.67  | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.53/21.67  | | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | | | BETA: splitting (10986) gives:
% 150.53/21.67  | | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.67  | | | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | | | |   (10987)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.67  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.53/21.67  | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.53/21.67  | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.53/21.67  | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.53/21.67  | | | | | | | | | | | | | | | | | 
% 150.53/21.67  | | | | | | | | | | | | | | | | | ALPHA: (10987) implies:
% 150.53/21.67  | | | | | | | | | | | | | | | | |   (10988)   ~ (all_57_10 = e2)
% 150.53/21.67  | | | | | | | | | | | | | | | | |   (10989)  op(e3, e3) = all_57_10
% 150.53/21.67  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (10969), (10988), (10989), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1031.
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | |   (10990)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.53/21.68  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.53/21.68  | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.53/21.68  | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | ALPHA: (10990) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | |   (10991)  op(e0, e0) = e2
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (237), (9980), (10712),
% 150.53/21.68  | | | | | | | | | | | | | | | | |            (10969), (10991), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #629.
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | |   (10992)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.53/21.68  | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.53/21.68  | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.53/21.68  | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.53/21.68  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.53/21.68  | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.53/21.68  | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.53/21.68  | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.53/21.68  | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.53/21.68  | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.53/21.68  | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.53/21.68  | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.53/21.68  | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | BETA: splitting (10992) gives:
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | |   (10993)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.53/21.68  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.53/21.68  | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.53/21.68  | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | ALPHA: (10993) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | |   (10994)   ~ (all_57_14 = e2)
% 150.53/21.68  | | | | | | | | | | | | | | | | |   (10995)  op(e1, e1) = all_57_14
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (9980), (10994), (10995), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #52.
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | |   (10996)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.53/21.68  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.53/21.68  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.53/21.68  | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.53/21.68  | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.53/21.68  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.53/21.68  | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.53/21.68  | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | BETA: splitting (10996) gives:
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | |   (10997)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | ALPHA: (10997) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | | |   (10998)  op(e0, e0) = e2
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (237), (9980), (10712),
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            (10969), (10998), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #629.
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | |   (10999)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | ALPHA: (10999) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | | |   (11000)  op(e2, e2) = e1
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10712), (11000), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | |   (11001)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.53/21.68  | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.53/21.68  | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.53/21.68  | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.53/21.68  | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.53/21.68  | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.53/21.68  | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.53/21.68  | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.53/21.68  | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.53/21.68  | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.53/21.68  | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.53/21.68  | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.53/21.68  | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.53/21.68  | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.53/21.68  | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.53/21.68  | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.53/21.68  | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.53/21.68  | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.53/21.68  | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.53/21.68  | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.53/21.68  | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.53/21.68  | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.53/21.68  | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.53/21.68  | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.53/21.68  | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.53/21.68  | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.53/21.68  | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.53/21.68  | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.53/21.68  | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.53/21.68  | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.53/21.68  | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.53/21.68  | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.53/21.68  | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.53/21.68  | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.53/21.68  | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.53/21.68  | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.53/21.68  | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.53/21.68  | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.53/21.68  | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.53/21.68  | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.53/21.68  | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.53/21.68  | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.53/21.68  | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.53/21.68  | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.53/21.68  | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.53/21.68  | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.53/21.68  | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.53/21.68  | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.53/21.68  | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.53/21.68  | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.53/21.68  | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.53/21.68  | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.53/21.68  | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | BETA: splitting (11001) gives:
% 150.53/21.68  | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | |   (11002)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.53/21.68  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.53/21.68  | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.53/21.68  | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.53/21.68  | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.53/21.68  | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.53/21.68  | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.53/21.68  | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.53/21.68  | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.53/21.68  | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.53/21.68  | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.53/21.68  | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.53/21.68  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.53/21.68  | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.53/21.68  | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.53/21.68  | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.53/21.68  | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.53/21.68  | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.53/21.68  | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | REF_CLOSE: (4), (116), (163), (164), (10976), (10977),
% 150.53/21.68  | | | | | | | | | | | | | | |            (10978), (10980), (11002), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | |            inconsistent by sub-proof #32.
% 150.53/21.68  | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | |   (11003)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.53/21.68  | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.53/21.68  | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.53/21.68  | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.53/21.68  | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.53/21.68  | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.53/21.68  | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.53/21.68  | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.53/21.68  | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.53/21.68  | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.53/21.68  | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.53/21.68  | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.53/21.68  | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.53/21.68  | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.53/21.68  | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.53/21.68  | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.53/21.68  | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.53/21.68  | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.53/21.68  | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.53/21.68  | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.53/21.68  | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.53/21.68  | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.53/21.68  | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.53/21.68  | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.53/21.68  | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.53/21.68  | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.53/21.68  | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.53/21.68  | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.53/21.68  | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.53/21.68  | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.53/21.68  | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.53/21.68  | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.53/21.68  | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.53/21.68  | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.53/21.68  | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.53/21.68  | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | BETA: splitting (11003) gives:
% 150.53/21.68  | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | |   (11004)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.53/21.68  | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.53/21.68  | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.53/21.68  | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.53/21.68  | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.53/21.68  | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.53/21.68  | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.53/21.68  | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (10969), (11004), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1037.
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | |   (11005)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.53/21.68  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.53/21.68  | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.53/21.68  | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.53/21.68  | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.53/21.68  | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.53/21.68  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.53/21.68  | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.53/21.68  | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.53/21.68  | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.53/21.68  | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.53/21.68  | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.53/21.68  | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.53/21.68  | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.53/21.68  | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.53/21.68  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.53/21.68  | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.53/21.68  | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.53/21.68  | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.53/21.68  | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.53/21.68  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.53/21.68  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.53/21.68  | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.53/21.68  | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.53/21.68  | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.53/21.68  | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | BETA: splitting (11005) gives:
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | |   (11006)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.53/21.68  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.53/21.68  | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.53/21.68  | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | ALPHA: (11006) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | |   (11007)   ~ (all_57_13 = e1)
% 150.53/21.68  | | | | | | | | | | | | | | | | |   (11008)  op(e1, e1) = e0
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | REF_CLOSE: (10977), (11007), (11008), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #959.
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | |   (11009)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.53/21.68  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.53/21.68  | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.53/21.68  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.53/21.68  | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.53/21.68  | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.53/21.68  | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.53/21.68  | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.53/21.68  | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.53/21.68  | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.53/21.68  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.53/21.68  | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.53/21.68  | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | BETA: splitting (11009) gives:
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | |   (11010)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | ALPHA: (11010) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | | |   (11011)  all_57_12 = e0
% 150.53/21.68  | | | | | | | | | | | | | | | | | |   (11012)   ~ (all_57_11 = e2)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | REF_CLOSE: (10978), (11011), (11012) are inconsistent by
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            sub-proof #890.
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | |   (11013)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | ALPHA: (11013) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | | |   (11014)  op(e0, e0) = all_57_15
% 150.53/21.68  | | | | | | | | | | | | | | | | | |   (11015)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.53/21.68  | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.53/21.68  | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | BETA: splitting (11015) gives:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |   (11016)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | BETA: splitting (11016) gives:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |   (11017)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | ALPHA: (11017) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |   (11018)  op(e2, e2) = e3
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10712), (11018), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |   (11019)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |              all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |              $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |                e2) = e0 & $i(all_57_3))
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11019) gives:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |   (11020)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_1)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11020) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |   (11021)  op(e1, e1) = e3
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9980), (11021), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |   (11022)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_3)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11022) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |   (11023)  op(e0, e2) = e0
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (10710), (11023), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |   (11024)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | BETA: splitting (11024) gives:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |   (11025)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | ALPHA: (11025) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |   (11026)  op(e0, e2) = e0
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (10710), (11026), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |   (11027)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_7))
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11027) gives:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |   (11028)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11028) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |   (11029)  op(e0, e1) = e0
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (156), (367), (10976), (11029),
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            #1034.
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |   (11030)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_7)
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11030) implies:
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |   (11031)  op(e2, e2) = e1
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10712), (11031), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | |   (11032)   ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.53/21.68  | | | | | | | | | | | | |            $i(all_57_12)
% 150.53/21.68  | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | ALPHA: (11032) implies:
% 150.53/21.68  | | | | | | | | | | | | |   (11033)   ~ (all_57_12 = e0)
% 150.53/21.68  | | | | | | | | | | | | |   (11034)  op(e2, e2) = all_57_12
% 150.53/21.68  | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | REF_CLOSE: (10712), (11033), (11034), (function-axioms) are
% 150.53/21.68  | | | | | | | | | | | | |            inconsistent by sub-proof #856.
% 150.53/21.68  | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | End of split
% 150.53/21.68  | | | | | | | | | 
% 150.53/21.68  | | | | | | | | Case 2:
% 150.53/21.68  | | | | | | | | | 
% 150.53/21.68  | | | | | | | | |   (11035)  all_24_2 = e2
% 150.53/21.68  | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | COMBINE_EQS: (318), (11035) imply:
% 150.53/21.68  | | | | | | | | |   (11036)  all_10_2 = e2
% 150.53/21.68  | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | REDUCE: (360), (11036) imply:
% 150.53/21.68  | | | | | | | | |   (11037)   ~ (all_52_7 = e2)
% 150.53/21.68  | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | REDUCE: (369), (11036) imply:
% 150.53/21.68  | | | | | | | | |   (11038)   ~ (all_52_13 = e2)
% 150.53/21.68  | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | REDUCE: (45), (11036) imply:
% 150.53/21.68  | | | | | | | | |   (11039)  op(e0, e0) = e2
% 150.53/21.68  | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | BETA: splitting (222) gives:
% 150.53/21.68  | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | |   (11040)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 150.53/21.68  | | | | | | | | | |              & op(e2, e2) = e2)
% 150.53/21.68  | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | BETA: splitting (11040) gives:
% 150.53/21.68  | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | |   (11041)  all_56_2 = e2 & op(e2, e3) = e2
% 150.53/21.68  | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | ALPHA: (11041) implies:
% 150.53/21.68  | | | | | | | | | | |   (11042)  op(e2, e3) = e2
% 150.53/21.68  | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | BETA: splitting (226) gives:
% 150.53/21.68  | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | |   (11043)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 150.53/21.68  | | | | | | | | | | | |              & op(e2, e2) = e2)
% 150.53/21.68  | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | BETA: splitting (11043) gives:
% 150.53/21.68  | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | |   (11044)  all_56_1 = e2 & op(e3, e2) = e2
% 150.53/21.68  | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | ALPHA: (11044) implies:
% 150.53/21.68  | | | | | | | | | | | | |   (11045)  op(e3, e2) = e2
% 150.53/21.68  | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | BETA: splitting (237) gives:
% 150.53/21.68  | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | |   (11046)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.53/21.68  | | | | | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.53/21.68  | | | | | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.53/21.68  | | | | | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.53/21.68  | | | | | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.53/21.68  | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.53/21.68  | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.53/21.68  | | | | | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.53/21.68  | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.53/21.68  | | | | | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.53/21.68  | | | | | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.53/21.68  | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.53/21.68  | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.53/21.68  | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | BETA: splitting (11046) gives:
% 150.53/21.68  | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | Case 1:
% 150.53/21.68  | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | |   (11047)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.53/21.68  | | | | | | | | | | | | | | |                & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.53/21.68  | | | | | | | | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.53/21.68  | | | | | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.53/21.68  | | | | | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.53/21.68  | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 150.53/21.68  | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 150.53/21.68  | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.53/21.68  | | | | | | | | | | | | | | | 
% 150.53/21.68  | | | | | | | | | | | | | | | ALPHA: (11047) implies:
% 150.53/21.68  | | | | | | | | | | | | | | |   (11048)  all_57_10 = e3
% 150.53/21.68  | | | | | | | | | | | | | | |   (11049)  op(e3, e3) = e3
% 150.53/21.68  | | | | | | | | | | | | | | |   (11050)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 150.53/21.68  | | | | | | | | | | | | | | |                = e3) & op(e0, e0) = all_57_15 &
% 150.53/21.68  | | | | | | | | | | | | | | |              $i(all_57_15))
% 150.53/21.68  | | | | | | | | | | | | | | |   (11051)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 150.53/21.68  | | | | | | | | | | | | | | |                = e3) & op(e1, e1) = all_57_14 &
% 150.53/21.68  | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.53/21.69  | | | | | | | | | | | | | | |   (11052)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 150.53/21.69  | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = all_57_12 &
% 150.53/21.69  | | | | | | | | | | | | | | |              $i(all_57_12))
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 150.53/21.69  | | | | | | | | | | | | | | |              e3, e2, simplifying with (166), (11042) gives:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11053)  all_52_1 = e2
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 150.53/21.69  | | | | | | | | | | | | | | |              e2, e3, simplifying with (169), (11045) gives:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11054)  all_52_4 = e2
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e3,
% 150.53/21.69  | | | | | | | | | | | | | | |              e3, e3, simplifying with (51), (11049) gives:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11055)  all_14_2 = e3
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | REDUCE: (148), (11053) imply:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11056)   ~ (all_52_2 = e2)
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | REDUCE: (145), (11053) imply:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11057)   ~ (all_52_9 = e2)
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | REDUCE: (144), (11053) imply:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11058)   ~ (all_52_13 = e2)
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | REDUCE: (338), (11055) imply:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11059)   ~ (all_52_2 = e3)
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | REDUCE: (135), (11054) imply:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11060)   ~ (all_52_6 = e2)
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | REDUCE: (134), (11054) imply:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11061)   ~ (all_52_7 = e2)
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | REDUCE: (342), (11054), (11055) imply:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11062)   ~ (e3 = e2)
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | REDUCE: (344), (11055) imply:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11063)   ~ (all_52_8 = e3)
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | REDUCE: (346), (11055) imply:
% 150.53/21.69  | | | | | | | | | | | | | | |   (11064)   ~ (all_52_12 = e3)
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | |   (11065)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.53/21.69  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.53/21.69  | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.53/21.69  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.53/21.69  | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.53/21.69  | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.53/21.69  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.53/21.69  | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.53/21.69  | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.53/21.69  | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.53/21.69  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.53/21.69  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.53/21.69  | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.53/21.69  | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.53/21.69  | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.53/21.69  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.53/21.69  | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.53/21.69  | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | BETA: splitting (11065) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | |   (11066)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.53/21.69  | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.53/21.69  | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.53/21.69  | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | BETA: splitting (11066) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | |   (11067)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.53/21.69  | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11050), (11051), (11067), (function-axioms) are
% 150.53/21.69  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #814.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | |   (11068)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | REF_CLOSE: (11050), (11052), (11068), (function-axioms) are
% 150.53/21.69  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | End of split
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | |   (11069)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.53/21.69  | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.53/21.69  | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.53/21.69  | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.53/21.69  | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | BETA: splitting (11069) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | |   (11070)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | BETA: splitting (11070) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11071)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | ALPHA: (11071) implies:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11072)  op(e3, e2) = e3
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11045), (11072), (function-axioms) are
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #29.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11073)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | ALPHA: (11073) implies:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11074)   ~ (all_57_10 = e2)
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11075)  op(e3, e2) = e3
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e3, e2,
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              e3, simplifying with (11045), (11075) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11076)  e3 = e2
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | REDUCE: (9), (11076) imply:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11077)  $false
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | CLOSE: (11077) is inconsistent.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | |   (11078)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | BETA: splitting (11078) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11079)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | ALPHA: (11079) implies:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11080)  op(e3, e3) = e2
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (36), (237), (9980), (10712),
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            (11039), (11080), (function-axioms) are
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #629.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11081)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | BETA: splitting (11081) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |   (11082)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | ALPHA: (11082) implies:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |   (11083)   ~ (all_57_14 = e2)
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |   (11084)  op(e1, e1) = all_57_14
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9980), (11083), (11084), (function-axioms) are
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #52.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |   (11085)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | ALPHA: (11085) implies:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |   (11086)  op(e2, e2) = e1
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10712), (11086), (function-axioms) are
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #853.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | End of split
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | End of split
% 150.53/21.69  | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | |   (11087)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.53/21.69  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.53/21.69  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.53/21.69  | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.53/21.69  | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.53/21.69  | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.53/21.69  | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.53/21.69  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.53/21.69  | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.53/21.69  | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.53/21.69  | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.53/21.69  | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.53/21.69  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.53/21.69  | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.53/21.69  | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.53/21.69  | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.53/21.69  | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.53/21.69  | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.53/21.69  | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.53/21.69  | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.53/21.69  | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.53/21.69  | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.53/21.69  | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.53/21.69  | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.53/21.69  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.53/21.69  | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.53/21.69  | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.53/21.69  | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.53/21.69  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.53/21.69  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.53/21.69  | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.53/21.69  | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.53/21.69  | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.53/21.69  | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | BETA: splitting (11087) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | |   (11088)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.53/21.69  | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.53/21.69  | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | BETA: splitting (11088) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | |   (11089)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (9977), (11063), (11089),
% 150.53/21.69  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.53/21.69  | | | | | | | | | | | | | | | | | |            #1083.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | |   (11090)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (11039), (11064), (11090),
% 150.53/21.69  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.53/21.69  | | | | | | | | | | | | | | | | | |            #976.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | End of split
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | |   (11091)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.53/21.69  | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.53/21.69  | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.53/21.69  | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.53/21.69  | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.53/21.69  | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.53/21.69  | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.53/21.69  | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.53/21.69  | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.53/21.69  | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.53/21.69  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.53/21.69  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.53/21.69  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | BETA: splitting (11091) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | |   (11092)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.53/21.69  | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11049), (11092), (function-axioms) are
% 150.53/21.69  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | |   (11093)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | BETA: splitting (11093) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11094)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | ALPHA: (11094) implies:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11095)  op(e2, e0) = e2
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (11038), (11095), (function-axioms) are
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |   (11096)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.53/21.69  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | BETA: splitting (11096) gives:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |   (11097)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | ALPHA: (11097) implies:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |   (11098)  op(e1, e0) = e1
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (125), (127), (139), (140), (142), (158), (159),
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            (162), (166), (190), (194), (195), (230), (247),
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            (257), (258), (9974), (9975), (9979), (10710),
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            (11037), (11042), (11049), (11059), (11098),
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | |            #25.
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.69  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |   (11099)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | ALPHA: (11099) implies:
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |   (11100)  op(e0, e0) = all_57_15
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |   (11101)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11101) gives:
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |   (11102)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11039), (11051), (11052), (11100), (11102),
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |            #627.
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |   (11103)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11103) gives:
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |   (11104)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11104) implies:
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |   (11105)   ~ (all_57_15 = e2)
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11039), (11100), (11105), (function-axioms) are
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #901.
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |   (11106)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_7))
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (10712), (11049), (11106),
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | |            #824.
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | | End of split
% 150.53/21.70  | | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | | End of split
% 150.53/21.70  | | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | | End of split
% 150.53/21.70  | | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | End of split
% 150.53/21.70  | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | Case 2:
% 150.53/21.70  | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | |   (11107)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.53/21.70  | | | | | | | | | | | | | | |                & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.53/21.70  | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.53/21.70  | | | | | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.53/21.70  | | | | | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.53/21.70  | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 150.53/21.70  | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 150.53/21.70  | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.53/21.70  | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | ALPHA: (11107) implies:
% 150.53/21.70  | | | | | | | | | | | | | | |   (11108)  op(e2, e2) = e2
% 150.53/21.70  | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | | REF_CLOSE: (5), (10712), (11108), (function-axioms) are
% 150.53/21.70  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 150.53/21.70  | | | | | | | | | | | | | | | 
% 150.53/21.70  | | | | | | | | | | | | | | End of split
% 150.53/21.70  | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | |   (11109)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.63/21.70  | | | | | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.63/21.70  | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.70  | | | | | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.63/21.70  | | | | | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.63/21.70  | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.63/21.70  | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.63/21.70  | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.63/21.70  | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.63/21.70  | | | | | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.63/21.70  | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.70  | | | | | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.63/21.70  | | | | | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.63/21.70  | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.63/21.70  | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.63/21.70  | | | | | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.63/21.70  | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (9980), (11039), (11109),
% 150.63/21.70  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.70  | | | | | | | | | | | | | |            #707.
% 150.63/21.70  | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | End of split
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | |   (11110)  all_56_3 = e2 & op(e2, e2) = e2
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | ALPHA: (11110) implies:
% 150.63/21.70  | | | | | | | | | | | | |   (11111)  op(e2, e2) = e2
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | REF_CLOSE: (5), (10712), (11111), (function-axioms) are
% 150.63/21.70  | | | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | End of split
% 150.63/21.70  | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | |   (11112)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 150.63/21.70  | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 150.63/21.70  | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | REF_CLOSE: (157), (161), (9975), (11037), (11112),
% 150.63/21.70  | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.70  | | | | | | | | | | | |            #24.
% 150.63/21.70  | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | End of split
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | |   (11113)  all_56_3 = e2 & op(e2, e2) = e2
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | ALPHA: (11113) implies:
% 150.63/21.70  | | | | | | | | | | |   (11114)  op(e2, e2) = e2
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | REF_CLOSE: (5), (10712), (11114), (function-axioms) are
% 150.63/21.70  | | | | | | | | | | |            inconsistent by sub-proof #1145.
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | End of split
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | |   (11115)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 150.63/21.70  | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | REF_CLOSE: (163), (164), (9977), (11038), (11115),
% 150.63/21.70  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.70  | | | | | | | | | |            #1155.
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | End of split
% 150.63/21.70  | | | | | | | | | 
% 150.63/21.70  | | | | | | | | End of split
% 150.63/21.70  | | | | | | | | 
% 150.63/21.70  | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | 
% 150.63/21.70  | | | | | | | |   (11116)  all_22_2 = e1
% 150.63/21.70  | | | | | | | | 
% 150.63/21.70  | | | | | | | | COMBINE_EQS: (320), (11116) imply:
% 150.63/21.70  | | | | | | | |   (11117)  all_14_2 = e1
% 150.63/21.70  | | | | | | | | 
% 150.63/21.70  | | | | | | | | REDUCE: (336), (11117) imply:
% 150.63/21.70  | | | | | | | |   (11118)   ~ (all_52_1 = e1)
% 150.63/21.70  | | | | | | | | 
% 150.63/21.70  | | | | | | | | REDUCE: (344), (11117) imply:
% 150.63/21.70  | | | | | | | |   (11119)   ~ (all_52_8 = e1)
% 150.63/21.70  | | | | | | | | 
% 150.63/21.70  | | | | | | | | REDUCE: (346), (11117) imply:
% 150.63/21.70  | | | | | | | |   (11120)   ~ (all_52_12 = e1)
% 150.63/21.70  | | | | | | | | 
% 150.63/21.70  | | | | | | | | REDUCE: (51), (11117) imply:
% 150.63/21.70  | | | | | | | |   (11121)  op(e3, e3) = e1
% 150.63/21.70  | | | | | | | | 
% 150.63/21.70  | | | | | | | | BETA: splitting (237) gives:
% 150.63/21.70  | | | | | | | | 
% 150.63/21.70  | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | 
% 150.63/21.70  | | | | | | | | |   (11122)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.63/21.70  | | | | | | | | |                  & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.63/21.70  | | | | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.63/21.70  | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.63/21.70  | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.63/21.70  | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.63/21.70  | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.63/21.70  | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.63/21.70  | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.63/21.70  | | | | | | | | |                  & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.63/21.70  | | | | | | | | |                  op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.70  | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.63/21.70  | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.63/21.70  | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.63/21.70  | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.63/21.70  | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.63/21.70  | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | REF_CLOSE: (5), (8), (10712), (11121), (11122),
% 150.63/21.70  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.70  | | | | | | | | |            #602.
% 150.63/21.70  | | | | | | | | | 
% 150.63/21.70  | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | 
% 150.63/21.70  | | | | | | | | |   (11123)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.63/21.70  | | | | | | | | |                  & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.63/21.70  | | | | | | | | |                  op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.70  | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.63/21.70  | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.63/21.70  | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.63/21.70  | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.63/21.70  | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.63/21.70  | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.63/21.70  | | | | | | | | |                  & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.63/21.70  | | | | | | | | |                  op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.70  | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.63/21.70  | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.63/21.70  | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.63/21.70  | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.63/21.70  | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.63/21.70  | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | BETA: splitting (11123) gives:
% 150.63/21.70  | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | |   (11124)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.63/21.70  | | | | | | | | | |                & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.63/21.70  | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.70  | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.63/21.70  | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.63/21.70  | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.63/21.70  | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.63/21.70  | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | ALPHA: (11124) implies:
% 150.63/21.70  | | | | | | | | | |   (11125)  op(e1, e1) = e1
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (11125), (function-axioms) are
% 150.63/21.70  | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | |   (11126)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.63/21.70  | | | | | | | | | |                & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.63/21.70  | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.70  | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.63/21.70  | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.63/21.70  | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.63/21.70  | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.63/21.70  | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14)))
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | ALPHA: (11126) implies:
% 150.63/21.70  | | | | | | | | | |   (11127)  op(e0, e0) = e0
% 150.63/21.70  | | | | | | | | | |   (11128)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 150.63/21.70  | | | | | | | | | |              (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.63/21.70  | | | | | | | | | |              $i(all_57_14))
% 150.63/21.70  | | | | | | | | | |   (11129)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.63/21.70  | | | | | | | | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.63/21.70  | | | | | | | | | |              $i(all_57_12))
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | BETA: splitting (11129) gives:
% 150.63/21.70  | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | |   (11130)  all_57_11 = e2 & op(e2, e0) = e2
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | ALPHA: (11130) implies:
% 150.63/21.70  | | | | | | | | | | |   (11131)  op(e2, e0) = e2
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 150.63/21.70  | | | | | | | | | | |              e0, e0, simplifying with (45), (11127) gives:
% 150.63/21.70  | | | | | | | | | | |   (11132)  all_10_2 = e0
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 150.63/21.70  | | | | | | | | | | |              e2, e0, e2, simplifying with (163), (11131) gives:
% 150.63/21.70  | | | | | | | | | | |   (11133)  all_52_13 = e2
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | REDUCE: (144), (11133) imply:
% 150.63/21.70  | | | | | | | | | | |   (11134)   ~ (all_52_1 = e2)
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | REDUCE: (349), (11132) imply:
% 150.63/21.70  | | | | | | | | | | |   (11135)   ~ (all_52_3 = e0)
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | REDUCE: (112), (11133) imply:
% 150.63/21.70  | | | | | | | | | | |   (11136)   ~ (all_52_12 = e2)
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | REDUCE: (368), (11132) imply:
% 150.63/21.70  | | | | | | | | | | |   (11137)   ~ (all_52_12 = e0)
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | BETA: splitting (199) gives:
% 150.63/21.70  | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | |   (11138)  all_54_4 = e3
% 150.63/21.70  | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | COMBINE_EQS: (268), (11138) imply:
% 150.63/21.70  | | | | | | | | | | | |   (11139)  all_52_1 = e3
% 150.63/21.70  | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | SIMP: (11139) implies:
% 150.63/21.70  | | | | | | | | | | | |   (11140)  all_52_1 = e3
% 150.63/21.70  | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | REDUCE: (145), (11140) imply:
% 150.63/21.70  | | | | | | | | | | | |   (11141)   ~ (all_52_9 = e3)
% 150.63/21.70  | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | SIMP: (11141) implies:
% 150.63/21.70  | | | | | | | | | | | |   (11142)   ~ (all_52_9 = e3)
% 150.63/21.70  | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | BETA: splitting (200) gives:
% 150.63/21.70  | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | |   (11143)  all_54_3 = e3
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | COMBINE_EQS: (269), (11143) imply:
% 150.63/21.70  | | | | | | | | | | | | |   (11144)  all_52_12 = e3
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | SIMP: (11144) implies:
% 150.63/21.70  | | | | | | | | | | | | |   (11145)  all_52_12 = e3
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | REDUCE: (132), (11145) imply:
% 150.63/21.70  | | | | | | | | | | | | |   (11146)   ~ (all_52_4 = e3)
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | REDUCE: (119), (11145) imply:
% 150.63/21.70  | | | | | | | | | | | | |   (11147)   ~ (all_52_8 = e3)
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | BETA: splitting (201) gives:
% 150.63/21.70  | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | |   (11148)  all_54_2 = e3
% 150.63/21.70  | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | REF_CLOSE: (270), (11147), (11148) are inconsistent by
% 150.63/21.70  | | | | | | | | | | | | | |            sub-proof #184.
% 150.63/21.70  | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | |   (11149)   ~ (all_54_2 = e3)
% 150.63/21.70  | | | | | | | | | | | | | |   (11150)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 150.63/21.70  | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | BETA: splitting (11150) gives:
% 150.63/21.70  | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | |   (11151)  all_54_2 = e2
% 150.63/21.70  | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | REF_CLOSE: (270), (9976), (11151) are inconsistent by
% 150.63/21.70  | | | | | | | | | | | | | | |            sub-proof #183.
% 150.63/21.70  | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | |   (11152)   ~ (all_54_2 = e2)
% 150.63/21.70  | | | | | | | | | | | | | | |   (11153)  all_54_2 = e1 | all_54_2 = e0
% 150.63/21.70  | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | BETA: splitting (11153) gives:
% 150.63/21.70  | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | |   (11154)  all_54_2 = e1
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | REF_CLOSE: (270), (11119), (11154) are inconsistent by
% 150.63/21.70  | | | | | | | | | | | | | | | |            sub-proof #384.
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | |   (11155)  all_54_2 = e0
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (11155) imply:
% 150.63/21.70  | | | | | | | | | | | | | | | |   (11156)  all_52_8 = e0
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | SIMP: (11156) implies:
% 150.63/21.70  | | | | | | | | | | | | | | | |   (11157)  all_52_8 = e0
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | REDUCE: (120), (11157) imply:
% 150.63/21.70  | | | | | | | | | | | | | | | |   (11158)   ~ (all_52_11 = e0)
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | SIMP: (11158) implies:
% 150.63/21.70  | | | | | | | | | | | | | | | |   (11159)   ~ (all_52_11 = e0)
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | REDUCE: (9976), (11157) imply:
% 150.63/21.70  | | | | | | | | | | | | | | | |   (11160)   ~ (e2 = e0)
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | REDUCE: (11119), (11157) imply:
% 150.63/21.70  | | | | | | | | | | | | | | | |   (11161)   ~ (e1 = e0)
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | REDUCE: (168), (11157) imply:
% 150.63/21.70  | | | | | | | | | | | | | | | |   (11162)  op(e3, e1) = e0
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.63/21.70  | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | |   (11163)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.63/21.70  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.63/21.70  | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.63/21.70  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.63/21.70  | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.70  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.63/21.70  | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.63/21.70  | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.63/21.70  | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.63/21.70  | | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.63/21.70  | | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.63/21.70  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.63/21.70  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.63/21.70  | | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.63/21.70  | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.63/21.70  | | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.63/21.70  | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.63/21.70  | | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.63/21.70  | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.63/21.70  | | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.63/21.70  | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.63/21.70  | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.63/21.70  | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | BETA: splitting (11163) gives:
% 150.63/21.70  | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | |   (11164)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.63/21.70  | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.63/21.70  | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.63/21.70  | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | BETA: splitting (11164) gives:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |   (11165)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (11134), (11165), (function-axioms) are
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |   (11166)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | BETA: splitting (11166) gives:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |   (11167)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | ALPHA: (11167) implies:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |   (11168)  op(e1, e3) = e1
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (162), (164),
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            (221), (222), (223), (228), (10712), (11121),
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            (11135), (11142), (11168), (function-axioms) are
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #598.
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |   (11169)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | ALPHA: (11169) implies:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |   (11170)  op(e0, e0) = e3
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11127), (11170), (function-axioms) are
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.70  | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | |   (11171)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.63/21.70  | | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.63/21.70  | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.63/21.70  | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | BETA: splitting (11171) gives:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |   (11172)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11146), (11172), (function-axioms) are
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |   (11173)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | BETA: splitting (11173) gives:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |   (11174)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | ALPHA: (11174) implies:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |   (11175)  op(e3, e3) = e2
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11121), (11175), (function-axioms) are
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1074.
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |   (11176)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10712), (11127), (11176),
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | |            #664.
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.70  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.70  | | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | | End of split
% 150.63/21.70  | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.70  | | | | | | | | | | | | | | | | | 
% 150.63/21.70  | | | | | | | | | | | | | | | | |   (11177)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.63/21.70  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.63/21.70  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.63/21.70  | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.63/21.70  | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.63/21.70  | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.63/21.71  | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.63/21.71  | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.63/21.71  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.63/21.71  | | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.63/21.71  | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.63/21.71  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.63/21.71  | | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.63/21.71  | | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.63/21.71  | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.63/21.71  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.63/21.71  | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.63/21.71  | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.63/21.71  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.63/21.71  | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.63/21.71  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.63/21.71  | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.63/21.71  | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | BETA: splitting (11177) gives:
% 150.63/21.71  | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | |   (11178)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | BETA: splitting (11178) gives:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |   (11179)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (11179) gives:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |   (11180)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | ALPHA: (11180) implies:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |   (11181)  op(e3, e1) = e3
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11162), (11181), (function-axioms) are
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #663.
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |   (11182)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | ALPHA: (11182) implies:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |   (11183)  op(e2, e1) = e2
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (116), (163), (164), (11131), (11183),
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            #400.
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |   (11184)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11127), (11128), (11129), (11184),
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |            #69.
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | |   (11185)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.63/21.71  | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | BETA: splitting (11185) gives:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |   (11186)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11121), (11186), (function-axioms) are
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #956.
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |   (11187)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | BETA: splitting (11187) gives:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |   (11188)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | ALPHA: (11188) implies:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |   (11189)   ~ (all_57_13 = e1)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |   (11190)  op(e1, e1) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11128), (11189), (11190), (function-axioms) are
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #959.
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |   (11191)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11191) gives:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |   (11192)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11192) implies:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |   (11193)  all_57_12 = e0
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |   (11194)   ~ (all_57_11 = e2)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11129), (11193), (11194) are inconsistent by
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |            sub-proof #890.
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |   (11195)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11195) implies:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |   (11196)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11196) gives:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |   (11197)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (10710), (11135), (11197),
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |            #1035.
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |   (11198)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (156), (157), (10710), (10712), (11159),
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |            (11198), (function-axioms) are inconsistent by
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #803.
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | |   (11199)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | REF_CLOSE: (269), (11120), (11136), (11137), (11199) are
% 150.63/21.71  | | | | | | | | | | | | |            inconsistent by sub-proof #758.
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | |   (11200)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | REF_CLOSE: (268), (10707), (11118), (11134), (11200) are
% 150.63/21.71  | | | | | | | | | | | |            inconsistent by sub-proof #636.
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | |   (11201)   ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.63/21.71  | | | | | | | | | | |            $i(all_57_12)
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | ALPHA: (11201) implies:
% 150.63/21.71  | | | | | | | | | | |   (11202)   ~ (all_57_12 = e0)
% 150.63/21.71  | | | | | | | | | | |   (11203)  op(e2, e2) = all_57_12
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | REF_CLOSE: (10712), (11202), (11203), (function-axioms) are
% 150.63/21.71  | | | | | | | | | | |            inconsistent by sub-proof #856.
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | End of split
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | End of split
% 150.63/21.71  | | | | | | 
% 150.63/21.71  | | | | | End of split
% 150.63/21.71  | | | | | 
% 150.63/21.71  | | | | Case 2:
% 150.63/21.71  | | | | | 
% 150.63/21.71  | | | | |   (11204)  all_14_2 = e0
% 150.63/21.71  | | | | |   (11205)  ( ~ (all_14_0 = e2) & op(all_14_1, e3) = all_14_0 & op(e3,
% 150.63/21.71  | | | | |                e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 150.63/21.71  | | | | |              (all_14_1 = e1) & op(e3, e0) = all_14_1 & $i(all_14_1))
% 150.63/21.71  | | | | | 
% 150.63/21.71  | | | | | REDUCE: (336), (11204) imply:
% 150.63/21.71  | | | | |   (11206)   ~ (all_52_1 = e0)
% 150.63/21.71  | | | | | 
% 150.63/21.71  | | | | | REDUCE: (338), (11204) imply:
% 150.63/21.71  | | | | |   (11207)   ~ (all_52_2 = e0)
% 150.63/21.71  | | | | | 
% 150.63/21.71  | | | | | REDUCE: (342), (11204) imply:
% 150.63/21.71  | | | | |   (11208)   ~ (all_52_4 = e0)
% 150.63/21.71  | | | | | 
% 150.63/21.71  | | | | | REDUCE: (344), (11204) imply:
% 150.63/21.71  | | | | |   (11209)   ~ (all_52_8 = e0)
% 150.63/21.71  | | | | | 
% 150.63/21.71  | | | | | REDUCE: (346), (11204) imply:
% 150.63/21.71  | | | | |   (11210)   ~ (all_52_12 = e0)
% 150.63/21.71  | | | | | 
% 150.63/21.71  | | | | | REDUCE: (51), (11204) imply:
% 150.63/21.71  | | | | |   (11211)  op(e3, e3) = e0
% 150.63/21.71  | | | | | 
% 150.63/21.71  | | | | | BETA: splitting (55) gives:
% 150.63/21.71  | | | | | 
% 150.63/21.71  | | | | | Case 1:
% 150.63/21.71  | | | | | | 
% 150.63/21.71  | | | | | |   (11212)   ~ (all_16_2 = e0)
% 150.63/21.71  | | | | | | 
% 150.63/21.71  | | | | | | REDUCE: (327), (11212) imply:
% 150.63/21.71  | | | | | |   (11213)   ~ (all_6_2 = e0)
% 150.63/21.71  | | | | | | 
% 150.63/21.71  | | | | | | BETA: splitting (61) gives:
% 150.63/21.71  | | | | | | 
% 150.63/21.71  | | | | | | Case 1:
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | |   (11214)   ~ (all_20_2 = e1)
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | REDUCE: (282), (11214) imply:
% 150.63/21.71  | | | | | | |   (11215)   ~ (all_6_2 = e1)
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | BETA: splitting (198) gives:
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | |   (11216)  all_54_5 = e3
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | | REF_CLOSE: (267), (9981), (11216) are inconsistent by sub-proof
% 150.63/21.71  | | | | | | | |            #443.
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | |   (11217)   ~ (all_54_5 = e3)
% 150.63/21.71  | | | | | | | |   (11218)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | | BETA: splitting (11218) gives:
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | |   (11219)  all_54_5 = e2
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | COMBINE_EQS: (267), (11219) imply:
% 150.63/21.71  | | | | | | | | |   (11220)  all_6_2 = e2
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | SIMP: (11220) implies:
% 150.63/21.71  | | | | | | | | |   (11221)  all_6_2 = e2
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | REDUCE: (347), (11221) imply:
% 150.63/21.71  | | | | | | | | |   (11222)   ~ (all_52_1 = e2)
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | REDUCE: (350), (11221) imply:
% 150.63/21.71  | | | | | | | | |   (11223)   ~ (all_52_4 = e2)
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | REDUCE: (9981), (11221) imply:
% 150.63/21.71  | | | | | | | | |   (11224)   ~ (e3 = e2)
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | BETA: splitting (232) gives:
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | |   (11225)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 150.63/21.71  | | | | | | | | | |              & op(e2, e3) = e2)
% 150.63/21.71  | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | REF_CLOSE: (5), (166), (11211), (11222), (11225),
% 150.63/21.71  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.71  | | | | | | | | | |            #526.
% 150.63/21.71  | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | |   (11226)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 150.63/21.71  | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 150.63/21.71  | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | BETA: splitting (11226) gives:
% 150.63/21.71  | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | |   (11227)  all_56_6 = e2 & op(e1, e3) = e2
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | REF_CLOSE: (162), (9974), (11227), (function-axioms) are
% 150.63/21.71  | | | | | | | | | | |            inconsistent by sub-proof #47.
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | |   (11228)  all_56_12 = e2 & op(e0, e3) = e2
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | ALPHA: (11228) implies:
% 150.63/21.71  | | | | | | | | | | |   (11229)  all_56_12 = e2
% 150.63/21.71  | | | | | | | | | | |   (11230)  op(e0, e3) = e2
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | BETA: splitting (233) gives:
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | |   (11231)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 150.63/21.71  | | | | | | | | | | | |              & op(e3, e2) = e2)
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | BETA: splitting (11231) gives:
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | |   (11232)  all_56_0 = e2 & op(e3, e3) = e2
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | ALPHA: (11232) implies:
% 150.63/21.71  | | | | | | | | | | | | |   (11233)  op(e3, e3) = e2
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230), (234),
% 150.63/21.71  | | | | | | | | | | | | |            (11229), (11233), (function-axioms) are
% 150.63/21.71  | | | | | | | | | | | | |            inconsistent by sub-proof #781.
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | |   (11234)  all_56_1 = e2 & op(e3, e2) = e2
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | REF_CLOSE: (169), (11223), (11234), (function-axioms) are
% 150.63/21.71  | | | | | | | | | | | | |            inconsistent by sub-proof #969.
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | |   (11235)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 150.63/21.71  | | | | | | | | | | | |              & op(e3, e0) = e2)
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | BETA: splitting (11235) gives:
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | |   (11236)  all_56_4 = e2 & op(e3, e1) = e2
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | REF_CLOSE: (168), (9976), (11236), (function-axioms) are
% 150.63/21.71  | | | | | | | | | | | | |            inconsistent by sub-proof #46.
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | |   (11237)  all_56_9 = e2 & op(e3, e0) = e2
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | ALPHA: (11237) implies:
% 150.63/21.71  | | | | | | | | | | | | |   (11238)  all_56_9 = e2
% 150.63/21.71  | | | | | | | | | | | | |   (11239)  op(e3, e0) = e2
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 150.63/21.71  | | | | | | | | | | | | |              e3, e0, simplifying with (158), (11230) gives:
% 150.63/21.71  | | | | | | | | | | | | |   (11240)  all_52_3 = e2
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 150.63/21.71  | | | | | | | | | | | | |              e2, e0, e3, simplifying with (167), (11239) gives:
% 150.63/21.71  | | | | | | | | | | | | |   (11241)  all_52_12 = e2
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | REDUCE: (112), (11241) imply:
% 150.63/21.71  | | | | | | | | | | | | |   (11242)   ~ (all_52_13 = e2)
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | SIMP: (11242) implies:
% 150.63/21.71  | | | | | | | | | | | | |   (11243)   ~ (all_52_13 = e2)
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | REDUCE: (368), (11241) imply:
% 150.63/21.71  | | | | | | | | | | | | |   (11244)   ~ (all_10_2 = e2)
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | SIMP: (11244) implies:
% 150.63/21.71  | | | | | | | | | | | | |   (11245)   ~ (all_10_2 = e2)
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | BETA: splitting (11205) gives:
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | |   (11246)   ~ (all_14_0 = e2) & op(all_14_1, e3) = all_14_0 &
% 150.63/21.71  | | | | | | | | | | | | | |            op(e3, e0) = all_14_1 & $i(all_14_0) &
% 150.63/21.71  | | | | | | | | | | | | | |            $i(all_14_1)
% 150.63/21.71  | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | ALPHA: (11246) implies:
% 150.63/21.71  | | | | | | | | | | | | | |   (11247)  op(e3, e0) = all_14_1
% 150.63/21.71  | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (45), (125), (127),
% 150.63/21.71  | | | | | | | | | | | | | |            (133), (135), (142), (157), (159), (161), (162),
% 150.63/21.71  | | | | | | | | | | | | | |            (163), (166), (168), (169), (195), (202), (205),
% 150.63/21.71  | | | | | | | | | | | | | |            (206), (208), (209), (210), (211), (213), (216),
% 150.63/21.71  | | | | | | | | | | | | | |            (223), (224), (228), (230), (231), (232), (233),
% 150.63/21.71  | | | | | | | | | | | | | |            (234), (235), (237), (258), (271), (9974), (9975),
% 150.63/21.71  | | | | | | | | | | | | | |            (9980), (9982), (11207), (11208), (11209),
% 150.63/21.71  | | | | | | | | | | | | | |            (11211), (11223), (11229), (11238), (11239),
% 150.63/21.71  | | | | | | | | | | | | | |            (11243), (11245), (11247), (function-axioms) are
% 150.63/21.71  | | | | | | | | | | | | | |            inconsistent by sub-proof #13.
% 150.63/21.71  | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | |   (11248)   ~ (all_14_1 = e1) & op(e3, e0) = all_14_1 &
% 150.63/21.71  | | | | | | | | | | | | | |            $i(all_14_1)
% 150.63/21.71  | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | ALPHA: (11248) implies:
% 150.63/21.71  | | | | | | | | | | | | | |   (11249)  op(e3, e0) = all_14_1
% 150.63/21.71  | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (45), (125), (127),
% 150.63/21.71  | | | | | | | | | | | | | |            (133), (135), (142), (157), (159), (161), (162),
% 150.63/21.71  | | | | | | | | | | | | | |            (163), (166), (168), (169), (195), (202), (205),
% 150.63/21.71  | | | | | | | | | | | | | |            (206), (208), (209), (210), (211), (213), (216),
% 150.63/21.71  | | | | | | | | | | | | | |            (223), (224), (228), (230), (231), (232), (233),
% 150.63/21.71  | | | | | | | | | | | | | |            (234), (235), (237), (258), (271), (9974), (9975),
% 150.63/21.71  | | | | | | | | | | | | | |            (9980), (9982), (11207), (11208), (11209),
% 150.63/21.71  | | | | | | | | | | | | | |            (11211), (11223), (11229), (11238), (11239),
% 150.63/21.71  | | | | | | | | | | | | | |            (11243), (11245), (11249), (function-axioms) are
% 150.63/21.71  | | | | | | | | | | | | | |            inconsistent by sub-proof #13.
% 150.63/21.71  | | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | |   (11250)  all_54_5 = e1 | all_54_5 = e0
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | | REF_CLOSE: (267), (11213), (11215), (11250) are inconsistent
% 150.63/21.71  | | | | | | | | |            by sub-proof #866.
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | End of split
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | End of split
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | Case 2:
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | |   (11251)  all_20_2 = e1
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | COMBINE_EQS: (282), (11251) imply:
% 150.63/21.71  | | | | | | |   (11252)  all_6_2 = e1
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | SIMP: (11252) implies:
% 150.63/21.71  | | | | | | |   (11253)  all_6_2 = e1
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | REDUCE: (347), (11253) imply:
% 150.63/21.71  | | | | | | |   (11254)   ~ (all_52_1 = e1)
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | REDUCE: (350), (11253) imply:
% 150.63/21.71  | | | | | | |   (11255)   ~ (all_52_4 = e1)
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | REDUCE: (352), (11253) imply:
% 150.63/21.71  | | | | | | |   (11256)   ~ (all_52_6 = e1)
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | REDUCE: (9981), (11253) imply:
% 150.63/21.71  | | | | | | |   (11257)   ~ (e3 = e1)
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | REDUCE: (39), (11253) imply:
% 150.63/21.71  | | | | | | |   (11258)  op(e2, e2) = e1
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | BETA: splitting (237) gives:
% 150.63/21.71  | | | | | | | 
% 150.63/21.71  | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | |   (11259)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 &
% 150.63/21.71  | | | | | | | |                  op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.63/21.71  | | | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.63/21.71  | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 150.63/21.71  | | | | | | | |                    = e3) & op(e1, e1) = all_57_14 &
% 150.63/21.71  | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 150.63/21.71  | | | | | | | |                  = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 150.63/21.71  | | | | | | | |                  all_57_15 & $i(all_57_15)))) | (all_57_12 = e2
% 150.63/21.71  | | | | | | | |              & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 150.63/21.71  | | | | | | | |                  e3) | ( ~ (all_57_10 = e2) & op(e3, e3) =
% 150.63/21.71  | | | | | | | |                  all_57_10 & $i(all_57_10))) & ((all_57_4 = e1 &
% 150.63/21.71  | | | | | | | |                  op(e1, e2) = e1) | ( ~ (all_57_14 = e2) &
% 150.63/21.71  | | | | | | | |                  op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.63/21.71  | | | | | | | |              ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15
% 150.63/21.71  | | | | | | | |                    = e2) & op(e0, e0) = all_57_15 &
% 150.63/21.71  | | | | | | | |                  $i(all_57_15))))
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | | REF_CLOSE: (6), (7), (11211), (11258), (11259),
% 150.63/21.71  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #515.
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | Case 2:
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | |   (11260)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 &
% 150.63/21.71  | | | | | | | |                  op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.63/21.71  | | | | | | | |                  op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.71  | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 150.63/21.71  | | | | | | | |                    = e1) & op(e2, e2) = all_57_12 &
% 150.63/21.71  | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.63/21.71  | | | | | | | |                  = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.63/21.71  | | | | | | | |                  all_57_15 & $i(all_57_15)))) | (all_57_15 = e0
% 150.63/21.71  | | | | | | | |              & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 150.63/21.71  | | | | | | | |                  e3) | ( ~ (all_57_10 = e0) & op(e3, e3) =
% 150.63/21.71  | | | | | | | |                  all_57_10 & $i(all_57_10))) & ((all_57_11 = e2
% 150.63/21.71  | | | | | | | |                  & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 150.63/21.71  | | | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.63/21.71  | | | | | | | |              ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 150.63/21.71  | | | | | | | |                  (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.63/21.71  | | | | | | | |                  $i(all_57_14))))
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | | BETA: splitting (11260) gives:
% 150.63/21.71  | | | | | | | | 
% 150.63/21.71  | | | | | | | | Case 1:
% 150.63/21.71  | | | | | | | | | 
% 150.63/21.71  | | | | | | | | |   (11261)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.63/21.71  | | | | | | | | |                & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.63/21.71  | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.71  | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12
% 150.63/21.71  | | | | | | | | |                  = e1) & op(e2, e2) = all_57_12 &
% 150.63/21.71  | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.63/21.71  | | | | | | | | |                = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.63/21.71  | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | ALPHA: (11261) implies:
% 150.63/21.72  | | | | | | | | |   (11262)  op(e1, e1) = e1
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | REF_CLOSE: (6), (36), (9980), (11262), (function-axioms) are
% 150.63/21.72  | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | |   (11263)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.63/21.72  | | | | | | | | |                & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.63/21.72  | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.72  | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.63/21.72  | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.63/21.72  | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0)
% 150.63/21.72  | | | | | | | | |                = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 150.63/21.72  | | | | | | | | |                all_57_14 & $i(all_57_14)))
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | ALPHA: (11263) implies:
% 150.63/21.72  | | | | | | | | |   (11264)  op(e0, e0) = e0
% 150.63/21.72  | | | | | | | | |   (11265)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10
% 150.63/21.72  | | | | | | | | |                = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | BETA: splitting (225) gives:
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | |   (11266)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 150.63/21.72  | | | | | | | | | |              & op(e2, e2) = e1)
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | BETA: splitting (11266) gives:
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | |   (11267)  all_56_1 = e1 & op(e3, e2) = e1
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | REF_CLOSE: (169), (11255), (11267), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | |            inconsistent by sub-proof #420.
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | |   (11268)  all_56_3 = e1 & op(e2, e2) = e1
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | ALPHA: (11268) implies:
% 150.63/21.72  | | | | | | | | | | |   (11269)  all_56_3 = e1
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | BETA: splitting (11265) gives:
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | |   (11270)  all_57_9 = e3 & op(e3, e0) = e3
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | ALPHA: (11270) implies:
% 150.63/21.72  | | | | | | | | | | | |   (11271)  op(e3, e0) = e3
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 150.63/21.72  | | | | | | | | | | | |              e0, e0, simplifying with (45), (11264) gives:
% 150.63/21.72  | | | | | | | | | | | |   (11272)  all_10_2 = e0
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 150.63/21.72  | | | | | | | | | | | |              e3, e0, e3, simplifying with (167), (11271) gives:
% 150.63/21.72  | | | | | | | | | | | |   (11273)  all_52_12 = e3
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | REDUCE: (360), (11272) imply:
% 150.63/21.72  | | | | | | | | | | | |   (11274)   ~ (all_52_7 = e0)
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | REDUCE: (367), (11272) imply:
% 150.63/21.72  | | | | | | | | | | | |   (11275)   ~ (all_52_11 = e0)
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | REDUCE: (112), (11273) imply:
% 150.63/21.72  | | | | | | | | | | | |   (11276)   ~ (all_52_13 = e3)
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | SIMP: (11276) implies:
% 150.63/21.72  | | | | | | | | | | | |   (11277)   ~ (all_52_13 = e3)
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | REDUCE: (111), (11273) imply:
% 150.63/21.72  | | | | | | | | | | | |   (11278)   ~ (all_52_14 = e3)
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | SIMP: (11278) implies:
% 150.63/21.72  | | | | | | | | | | | |   (11279)   ~ (all_52_14 = e3)
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | REDUCE: (369), (11272) imply:
% 150.63/21.72  | | | | | | | | | | | |   (11280)   ~ (all_52_13 = e0)
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | REDUCE: (370), (11272) imply:
% 150.63/21.72  | | | | | | | | | | | |   (11281)   ~ (all_52_14 = e0)
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | BETA: splitting (233) gives:
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | |   (11282)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 150.63/21.72  | | | | | | | | | | | | |              & op(e3, e2) = e2)
% 150.63/21.72  | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | BETA: splitting (11282) gives:
% 150.63/21.72  | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | |   (11283)  all_56_0 = e2 & op(e3, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | ALPHA: (11283) implies:
% 150.63/21.72  | | | | | | | | | | | | | |   (11284)  op(e3, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | REF_CLOSE: (5), (11211), (11284), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | |   (11285)  all_56_1 = e2 & op(e3, e2) = e2
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | ALPHA: (11285) implies:
% 150.63/21.72  | | | | | | | | | | | | | |   (11286)  all_56_1 = e2
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | |   (11287)  all_54_11 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | REF_CLOSE: (249), (11279), (11287) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | |            sub-proof #661.
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | |   (11288)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | BETA: splitting (11288) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | |   (11289)  all_54_11 = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | REF_CLOSE: (249), (9979), (11289) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | | |            sub-proof #393.
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | |   (11290)   ~ (all_54_11 = e2)
% 150.63/21.72  | | | | | | | | | | | | | | | |   (11291)  all_54_11 = e1 | all_54_11 = e0
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | BETA: splitting (11291) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11292)  all_54_11 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (11292) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11293)  all_52_14 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | SIMP: (11293) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11294)  all_52_14 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | REDUCE: (140), (11294) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11295)   ~ (all_52_2 = e1)
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | REDUCE: (109), (11294) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11296)   ~ (all_52_13 = e1)
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | REDUCE: (9979), (11294) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11297)   ~ (e2 = e1)
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | |   (11298)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (166), (11211), (11254), (11298),
% 150.63/21.72  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.72  | | | | | | | | | | | | | | | | | |            #12.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | |   (11299)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 150.63/21.72  | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | BETA: splitting (11299) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |   (11300)  all_56_6 = e1 & op(e1, e3) = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | ALPHA: (11300) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |   (11301)  op(e1, e3) = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11295), (11301), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |   (11302)  all_56_12 = e1 & op(e0, e3) = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | ALPHA: (11302) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |   (11303)  all_56_12 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |   (11304)  all_54_8 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11304) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |   (11305)  all_52_2 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | SIMP: (11305) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |   (11306)  all_52_2 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (11306) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |   (11307)   ~ (all_52_1 = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (11306) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |   (11308)   ~ (all_52_3 = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | SIMP: (11308) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |   (11309)   ~ (all_52_3 = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | REDUCE: (142), (11306) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |   (11310)   ~ (all_52_6 = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | SIMP: (11310) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |   (11311)   ~ (all_52_6 = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | |   (11312)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11312) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11313)  all_56_0 = e2 & op(e3, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11313) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11314)  op(e3, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11211), (11314), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11315)  all_56_2 = e2 & op(e2, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11315) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11316)  op(e2, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (166), (196), (259), (11277), (11280),
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |            (11296), (11316), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #168.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | |   (11317)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11317) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11318)  all_56_6 = e2 & op(e1, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11318) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11319)  all_56_6 = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | |   (11320)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (166), (228), (11206), (11303),
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | |            (11307), (11319), (11320), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #11.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | |   (11321)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11321) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |   (11322)  all_56_6 = e3 & op(e1, e3) = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11319), (11322) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #570.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |   (11323)  all_56_12 = e3 & op(e0, e3) = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11309), (11323), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #73.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11324)  all_56_12 = e2 & op(e0, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11324) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11325)  all_56_12 = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11303), (11325) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11326)  e2 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11286), (11326) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11327)  all_56_1 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (224), (226),
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |            (227), (11258), (11269), (11311), (11327),
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |            #268.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |   (11328)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (9974), (11207), (11295), (11328) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #460.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11329)  all_54_11 = e0
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (11281), (11329) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | | | |            sub-proof #211.
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | |   (11330)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 150.63/21.72  | | | | | | | | | | | | |              & op(e3, e0) = e2)
% 150.63/21.72  | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | BETA: splitting (11330) gives:
% 150.63/21.72  | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | |   (11331)  all_56_4 = e2 & op(e3, e1) = e2
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | ALPHA: (11331) implies:
% 150.63/21.72  | | | | | | | | | | | | | |   (11332)  all_56_4 = e2
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | |   (11333)  all_54_11 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | REF_CLOSE: (249), (11279), (11333) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | |            sub-proof #661.
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | |   (11334)   ~ (all_54_11 = e3)
% 150.63/21.72  | | | | | | | | | | | | | | |   (11335)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | |   (11336)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 150.63/21.72  | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | BETA: splitting (11336) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11337)  all_56_9 = e3 & op(e3, e0) = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | ALPHA: (11337) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11338)  all_56_9 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | BETA: splitting (11335) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | |   (11339)  all_54_11 = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (9979), (11339) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | | | | |            sub-proof #393.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | |   (11340)   ~ (all_54_11 = e2)
% 150.63/21.72  | | | | | | | | | | | | | | | | | |   (11341)  all_54_11 = e1 | all_54_11 = e0
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | BETA: splitting (11341) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |   (11342)  all_54_11 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (11342) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |   (11343)  all_52_14 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | SIMP: (11343) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |   (11344)  all_52_14 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | REDUCE: (140), (11344) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |   (11345)   ~ (all_52_2 = e1)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | REDUCE: (109), (11344) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |   (11346)   ~ (all_52_13 = e1)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | REDUCE: (9979), (11344) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |   (11347)   ~ (e2 = e1)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |   (11348)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (166), (11211), (11254), (11348),
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |            #12.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |   (11349)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11349) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | |   (11350)  all_56_6 = e1 & op(e1, e3) = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11350) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | |   (11351)  op(e1, e3) = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11345), (11351), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | |   (11352)  all_56_12 = e1 & op(e0, e3) = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11352) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | |   (11353)  all_56_12 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11354)  all_54_8 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11354) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11355)  all_52_2 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | SIMP: (11355) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11356)  all_52_2 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (11356) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11357)   ~ (all_52_1 = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (11356) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11358)   ~ (all_52_3 = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | SIMP: (11358) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11359)   ~ (all_52_3 = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | |   (11360)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e2)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11360) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |   (11361)  all_56_0 = e2 & op(e3, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11361) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |   (11362)  op(e3, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (229), (231), (235),
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |            (11332), (11362), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1062.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |   (11363)  all_56_2 = e2 & op(e2, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11363) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |   (11364)  op(e2, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (166), (196), (259), (11277), (11280),
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |            (11346), (11364), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #168.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | |   (11365)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e0, e3) = e2)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11365) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |   (11366)  all_56_6 = e2 & op(e1, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11366) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |   (11367)  all_56_6 = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (11368)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (166), (228), (11206), (11353),
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | |            (11357), (11367), (11368), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #11.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | |   (11369)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e3) = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11369) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11370)  all_56_6 = e3 & op(e1, e3) = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11370) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11371)  all_56_6 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11367), (11371) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11372)  e3 = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11338), (11372) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11373)  all_56_9 = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (156), (157), (159), (162), (163),
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            (166), (205), (211), (230), (11211), (11254),
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            (11274), (11275), (11277), (11279), (11345),
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            (11373), (function-axioms) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #10.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11374)  all_56_12 = e3 & op(e0, e3) = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11359), (11374), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #73.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |   (11375)  all_56_12 = e2 & op(e0, e3) = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11375) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |   (11376)  all_56_12 = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11353), (11376) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1122.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |   (11377)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (9974), (11207), (11345), (11377) are
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #460.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |   (11378)  all_54_11 = e0
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (11281), (11378) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | | | | | |            sub-proof #211.
% 150.63/21.72  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11379)  all_56_10 = e3 & op(e2, e0) = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (11277), (11379), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #114.
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | |   (11380)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 150.63/21.72  | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | BETA: splitting (11380) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11381)  all_56_11 = e3 & op(e1, e0) = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11279), (11381), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #66.
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11382)  all_56_15 = e3 & op(e0, e0) = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | ALPHA: (11382) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11383)  op(e0, e0) = e3
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11264), (11383), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | |   (11384)  all_56_9 = e2 & op(e3, e0) = e2
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | ALPHA: (11384) implies:
% 150.63/21.72  | | | | | | | | | | | | | |   (11385)  all_56_9 = e2
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | |   (11386)  all_54_11 = e3
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | REF_CLOSE: (249), (11279), (11386) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | |            sub-proof #661.
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | |   (11387)   ~ (all_54_11 = e3)
% 150.63/21.72  | | | | | | | | | | | | | | |   (11388)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | BETA: splitting (11388) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | |   (11389)  all_54_11 = e2
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | REF_CLOSE: (249), (9979), (11389) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | | |            sub-proof #393.
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | |   (11390)  all_54_11 = e1 | all_54_11 = e0
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | BETA: splitting (11390) gives:
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11391)  all_54_11 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (11391) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11392)  all_52_14 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | SIMP: (11392) implies:
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11393)  all_52_14 = e1
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | REDUCE: (140), (11393) imply:
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11394)   ~ (all_52_2 = e1)
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (9), (156), (157), (159), (162), (163),
% 150.63/21.72  | | | | | | | | | | | | | | | | |            (166), (205), (211), (230), (11211), (11254),
% 150.63/21.72  | | | | | | | | | | | | | | | | |            (11274), (11275), (11277), (11279), (11385),
% 150.63/21.72  | | | | | | | | | | | | | | | | |            (11394), (function-axioms) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | | | |            sub-proof #10.
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | |   (11395)  all_54_11 = e0
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (11281), (11395) are inconsistent by
% 150.63/21.72  | | | | | | | | | | | | | | | | |            sub-proof #211.
% 150.63/21.72  | | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | |   (11396)   ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.63/21.72  | | | | | | | | | | | |            $i(all_57_10)
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | ALPHA: (11396) implies:
% 150.63/21.72  | | | | | | | | | | | |   (11397)   ~ (all_57_10 = e0)
% 150.63/21.72  | | | | | | | | | | | |   (11398)  op(e3, e3) = all_57_10
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | | REF_CLOSE: (11211), (11397), (11398), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | | |            inconsistent by sub-proof #543.
% 150.63/21.72  | | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | |   (11399)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 150.63/21.72  | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | BETA: splitting (11399) gives:
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | |   (11400)  all_56_7 = e1 & op(e1, e2) = e1
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | ALPHA: (11400) implies:
% 150.63/21.72  | | | | | | | | | | |   (11401)  op(e1, e2) = e1
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | REF_CLOSE: (161), (11256), (11401), (function-axioms) are
% 150.63/21.72  | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | |   (11402)  all_56_13 = e1 & op(e0, e2) = e1
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (224), (226),
% 150.63/21.72  | | | | | | | | | | |            (227), (11208), (11258), (11402),
% 150.63/21.72  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.72  | | | | | | | | | | |            #499.
% 150.63/21.72  | | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | End of split
% 150.63/21.72  | | | | | | | 
% 150.63/21.72  | | | | | | End of split
% 150.63/21.72  | | | | | | 
% 150.63/21.72  | | | | | Case 2:
% 150.63/21.72  | | | | | | 
% 150.63/21.72  | | | | | |   (11403)  all_16_2 = e0
% 150.63/21.72  | | | | | | 
% 150.63/21.72  | | | | | | COMBINE_EQS: (327), (11403) imply:
% 150.63/21.72  | | | | | |   (11404)  all_6_2 = e0
% 150.63/21.72  | | | | | | 
% 150.63/21.72  | | | | | | SIMP: (11404) implies:
% 150.63/21.72  | | | | | |   (11405)  all_6_2 = e0
% 150.63/21.72  | | | | | | 
% 150.63/21.72  | | | | | | REDUCE: (356), (11405) imply:
% 150.63/21.72  | | | | | |   (11406)   ~ (all_52_9 = e0)
% 150.63/21.72  | | | | | | 
% 150.63/21.72  | | | | | | REDUCE: (9981), (11405) imply:
% 150.63/21.72  | | | | | |   (11407)   ~ (e3 = e0)
% 150.63/21.72  | | | | | | 
% 150.63/21.72  | | | | | | REDUCE: (39), (11405) imply:
% 150.63/21.72  | | | | | |   (11408)  op(e2, e2) = e0
% 150.63/21.72  | | | | | | 
% 150.63/21.72  | | | | | | BETA: splitting (216) gives:
% 150.63/21.72  | | | | | | 
% 150.63/21.72  | | | | | | Case 1:
% 150.63/21.72  | | | | | | | 
% 150.63/21.72  | | | | | | |   (11409)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 &
% 150.63/21.72  | | | | | | |              op(e2, e1) = e0)
% 150.63/21.72  | | | | | | | 
% 150.63/21.72  | | | | | | | BETA: splitting (11409) gives:
% 150.63/21.72  | | | | | | | 
% 150.63/21.72  | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | |   (11410)  all_56_4 = e0 & op(e3, e1) = e0
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | | REF_CLOSE: (168), (11209), (11410), (function-axioms) are
% 150.63/21.72  | | | | | | | |            inconsistent by sub-proof #1130.
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | |   (11411)  all_56_5 = e0 & op(e2, e1) = e0
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | | REF_CLOSE: (164), (11406), (11411), (function-axioms) are
% 150.63/21.72  | | | | | | | |            inconsistent by sub-proof #1144.
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | End of split
% 150.63/21.72  | | | | | | | 
% 150.63/21.72  | | | | | | Case 2:
% 150.63/21.72  | | | | | | | 
% 150.63/21.72  | | | | | | |   (11412)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 &
% 150.63/21.72  | | | | | | |              op(e0, e1) = e0)
% 150.63/21.72  | | | | | | | 
% 150.63/21.72  | | | | | | | BETA: splitting (11412) gives:
% 150.63/21.72  | | | | | | | 
% 150.63/21.72  | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | |   (11413)  all_56_8 = e0 & op(e1, e1) = e0
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | | ALPHA: (11413) implies:
% 150.63/21.72  | | | | | | | |   (11414)  op(e1, e1) = e0
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | | REF_CLOSE: (5), (9980), (11414), (function-axioms) are
% 150.63/21.72  | | | | | | | |            inconsistent by sub-proof #1006.
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | |   (11415)  all_56_14 = e0 & op(e0, e1) = e0
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | | ALPHA: (11415) implies:
% 150.63/21.72  | | | | | | | |   (11416)  op(e0, e1) = e0
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | | BETA: splitting (237) gives:
% 150.63/21.72  | | | | | | | | 
% 150.63/21.72  | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | |   (11417)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.63/21.72  | | | | | | | | |                  & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.63/21.72  | | | | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.63/21.72  | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.63/21.72  | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.63/21.72  | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.63/21.72  | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.63/21.72  | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.63/21.72  | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.63/21.72  | | | | | | | | |                  & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.63/21.72  | | | | | | | | |                  op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.72  | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.63/21.72  | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.63/21.72  | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.63/21.72  | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.63/21.72  | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | REF_CLOSE: (5), (7), (11211), (11408), (11417),
% 150.63/21.72  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.72  | | | | | | | | |            #477.
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | |   (11418)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.63/21.72  | | | | | | | | |                  & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.63/21.72  | | | | | | | | |                  op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.72  | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.63/21.72  | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.63/21.72  | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.63/21.72  | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.63/21.72  | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.63/21.72  | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.63/21.72  | | | | | | | | |                  & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.63/21.72  | | | | | | | | |                  op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.72  | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.63/21.72  | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.63/21.72  | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.63/21.72  | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.63/21.72  | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | BETA: splitting (11418) gives:
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | Case 1:
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | |   (11419)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.63/21.72  | | | | | | | | | |                & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.63/21.72  | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.72  | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.63/21.72  | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.63/21.72  | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.63/21.72  | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.63/21.72  | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | ALPHA: (11419) implies:
% 150.63/21.72  | | | | | | | | | |   (11420)  op(e1, e1) = e1
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (11420), (function-axioms) are
% 150.63/21.72  | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | Case 2:
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | |   (11421)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.63/21.72  | | | | | | | | | |                & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.63/21.72  | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.72  | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.63/21.72  | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.63/21.72  | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.63/21.72  | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.63/21.72  | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14)))
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | ALPHA: (11421) implies:
% 150.63/21.72  | | | | | | | | | |   (11422)  op(e0, e0) = e0
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | | REF_CLOSE: (45), (156), (367), (11416), (11422),
% 150.63/21.72  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.72  | | | | | | | | | |            #1034.
% 150.63/21.72  | | | | | | | | | | 
% 150.63/21.72  | | | | | | | | | End of split
% 150.63/21.72  | | | | | | | | | 
% 150.63/21.73  | | | | | | | | End of split
% 150.63/21.73  | | | | | | | | 
% 150.63/21.73  | | | | | | | End of split
% 150.63/21.73  | | | | | | | 
% 150.63/21.73  | | | | | | End of split
% 150.63/21.73  | | | | | | 
% 150.63/21.73  | | | | | End of split
% 150.63/21.73  | | | | | 
% 150.63/21.73  | | | | End of split
% 150.63/21.73  | | | | 
% 150.63/21.73  | | | Case 2:
% 150.63/21.73  | | | | 
% 150.63/21.73  | | | |   (11423)  all_10_2 = e1
% 150.63/21.73  | | | |   (11424)  ( ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 & op(e0,
% 150.63/21.73  | | | |                e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 150.63/21.73  | | | |              (all_10_1 = e2) & op(e0, e1) = all_10_1 & $i(all_10_1))
% 150.63/21.73  | | | | 
% 150.63/21.73  | | | | COMBINE_EQS: (308), (11423) imply:
% 150.63/21.73  | | | |   (11425)  all_30_2 = e1
% 150.63/21.73  | | | | 
% 150.63/21.73  | | | | REDUCE: (349), (11423) imply:
% 150.63/21.73  | | | |   (11426)   ~ (all_52_3 = e1)
% 150.63/21.73  | | | | 
% 150.63/21.73  | | | | REDUCE: (367), (11423) imply:
% 150.63/21.73  | | | |   (11427)   ~ (all_52_11 = e1)
% 150.63/21.73  | | | | 
% 150.63/21.73  | | | | REDUCE: (368), (11423) imply:
% 150.63/21.73  | | | |   (11428)   ~ (all_52_12 = e1)
% 150.63/21.73  | | | | 
% 150.63/21.73  | | | | REDUCE: (370), (11423) imply:
% 150.63/21.73  | | | |   (11429)   ~ (all_52_14 = e1)
% 150.63/21.73  | | | | 
% 150.63/21.73  | | | | REDUCE: (45), (11423) imply:
% 150.63/21.73  | | | |   (11430)  op(e0, e0) = e1
% 150.63/21.73  | | | | 
% 150.63/21.73  | | | | BETA: splitting (52) gives:
% 150.63/21.73  | | | | 
% 150.63/21.73  | | | | Case 1:
% 150.63/21.73  | | | | | 
% 150.63/21.73  | | | | |   (11431)   ~ (all_14_2 = e0)
% 150.63/21.73  | | | | | 
% 150.63/21.73  | | | | | BETA: splitting (55) gives:
% 150.63/21.73  | | | | | 
% 150.63/21.73  | | | | | Case 1:
% 150.63/21.73  | | | | | | 
% 150.63/21.73  | | | | | |   (11432)   ~ (all_16_2 = e0)
% 150.63/21.73  | | | | | | 
% 150.63/21.73  | | | | | | REDUCE: (327), (11432) imply:
% 150.63/21.73  | | | | | |   (11433)   ~ (all_6_2 = e0)
% 150.63/21.73  | | | | | | 
% 150.63/21.73  | | | | | | BETA: splitting (61) gives:
% 150.63/21.73  | | | | | | 
% 150.63/21.73  | | | | | | Case 1:
% 150.63/21.73  | | | | | | | 
% 150.63/21.73  | | | | | | |   (11434)   ~ (all_20_2 = e1)
% 150.63/21.73  | | | | | | | 
% 150.63/21.73  | | | | | | | REDUCE: (282), (11434) imply:
% 150.63/21.73  | | | | | | |   (11435)   ~ (all_6_2 = e1)
% 150.63/21.73  | | | | | | | 
% 150.63/21.73  | | | | | | | BETA: splitting (198) gives:
% 150.63/21.73  | | | | | | | 
% 150.63/21.73  | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | 
% 150.63/21.73  | | | | | | | |   (11436)  all_54_5 = e3
% 150.63/21.73  | | | | | | | | 
% 150.63/21.73  | | | | | | | | COMBINE_EQS: (267), (11436) imply:
% 150.63/21.73  | | | | | | | |   (11437)  all_6_2 = e3
% 150.63/21.73  | | | | | | | | 
% 150.63/21.73  | | | | | | | | REDUCE: (9981), (11437) imply:
% 150.63/21.73  | | | | | | | |   (11438)  $false
% 150.63/21.73  | | | | | | | | 
% 150.63/21.73  | | | | | | | | CLOSE: (11438) is inconsistent.
% 150.63/21.73  | | | | | | | | 
% 150.63/21.73  | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | 
% 150.63/21.73  | | | | | | | |   (11439)   ~ (all_54_5 = e3)
% 150.63/21.73  | | | | | | | |   (11440)  all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 150.63/21.73  | | | | | | | | 
% 150.63/21.73  | | | | | | | | BETA: splitting (11440) gives:
% 150.63/21.73  | | | | | | | | 
% 150.63/21.73  | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | 
% 150.63/21.73  | | | | | | | | |   (11441)  all_54_5 = e2
% 150.63/21.73  | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | COMBINE_EQS: (267), (11441) imply:
% 150.63/21.73  | | | | | | | | |   (11442)  all_6_2 = e2
% 150.63/21.73  | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | REDUCE: (358), (11442) imply:
% 150.63/21.73  | | | | | | | | |   (11443)   ~ (all_52_13 = e2)
% 150.63/21.73  | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | REDUCE: (9981), (11442) imply:
% 150.63/21.73  | | | | | | | | |   (11444)   ~ (e3 = e2)
% 150.63/21.73  | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | REDUCE: (39), (11442) imply:
% 150.63/21.73  | | | | | | | | |   (11445)  op(e2, e2) = e2
% 150.63/21.73  | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | BETA: splitting (210) gives:
% 150.63/21.73  | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | |   (11446)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 150.63/21.73  | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 150.63/21.73  | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | BETA: splitting (11446) gives:
% 150.63/21.73  | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | |   (11447)  all_56_9 = e2 & op(e3, e0) = e2
% 150.63/21.73  | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | ALPHA: (11447) implies:
% 150.63/21.73  | | | | | | | | | | |   (11448)  all_56_9 = e2
% 150.63/21.73  | | | | | | | | | | |   (11449)  op(e3, e0) = e2
% 150.63/21.73  | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | BETA: splitting (207) gives:
% 150.63/21.73  | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | |   (11450)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 150.63/21.73  | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 150.63/21.73  | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | BETA: splitting (11450) gives:
% 150.63/21.73  | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | |   (11451)  all_56_12 = e2 & op(e0, e3) = e2
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | ALPHA: (11451) implies:
% 150.63/21.73  | | | | | | | | | | | | |   (11452)  op(e0, e3) = e2
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 150.63/21.73  | | | | | | | | | | | | |              e3, e0, simplifying with (158), (11452) gives:
% 150.63/21.73  | | | | | | | | | | | | |   (11453)  all_52_3 = e2
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 150.63/21.73  | | | | | | | | | | | | |              e2, e0, e3, simplifying with (167), (11449) gives:
% 150.63/21.73  | | | | | | | | | | | | |   (11454)  all_52_12 = e2
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | REDUCE: (147), (11453) imply:
% 150.63/21.73  | | | | | | | | | | | | |   (11455)   ~ (all_52_1 = e2)
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | REDUCE: (138), (11453) imply:
% 150.63/21.73  | | | | | | | | | | | | |   (11456)   ~ (all_52_11 = e2)
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | REDUCE: (112), (11454) imply:
% 150.63/21.73  | | | | | | | | | | | | |   (11457)   ~ (all_52_13 = e2)
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | REDUCE: (111), (11454) imply:
% 150.63/21.73  | | | | | | | | | | | | |   (11458)   ~ (all_52_14 = e2)
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | REDUCE: (346), (11454) imply:
% 150.63/21.73  | | | | | | | | | | | | |   (11459)   ~ (all_14_2 = e2)
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | SIMP: (11459) implies:
% 150.63/21.73  | | | | | | | | | | | | |   (11460)   ~ (all_14_2 = e2)
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | BETA: splitting (64) gives:
% 150.63/21.73  | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | |   (11461)   ~ (all_22_2 = e1)
% 150.63/21.73  | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | REDUCE: (320), (11461) imply:
% 150.63/21.73  | | | | | | | | | | | | | |   (11462)   ~ (all_14_2 = e1)
% 150.63/21.73  | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 150.63/21.73  | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | |   (11463)  all_54_0 = e3
% 150.63/21.73  | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | COMBINE_EQS: (278), (11463) imply:
% 150.63/21.73  | | | | | | | | | | | | | | |   (11464)  all_14_2 = e3
% 150.63/21.73  | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | SIMP: (11464) implies:
% 150.63/21.73  | | | | | | | | | | | | | | |   (11465)  all_14_2 = e3
% 150.63/21.73  | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | REDUCE: (342), (11465) imply:
% 150.63/21.73  | | | | | | | | | | | | | | |   (11466)   ~ (all_52_4 = e3)
% 150.63/21.73  | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | REDUCE: (344), (11465) imply:
% 150.63/21.73  | | | | | | | | | | | | | | |   (11467)   ~ (all_52_8 = e3)
% 150.63/21.73  | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | REDUCE: (51), (11465) imply:
% 150.63/21.73  | | | | | | | | | | | | | | |   (11468)  op(e3, e3) = e3
% 150.63/21.73  | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | |   (11469)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.63/21.73  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.63/21.73  | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.63/21.73  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.63/21.73  | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.73  | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.63/21.73  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.63/21.73  | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.63/21.73  | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.63/21.73  | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.63/21.73  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.63/21.73  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.63/21.73  | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.63/21.73  | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.63/21.73  | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.63/21.73  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.63/21.73  | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.63/21.73  | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | BETA: splitting (11469) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | |   (11470)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.63/21.73  | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.63/21.73  | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.63/21.73  | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (166), (11430), (11445), (11455),
% 150.63/21.73  | | | | | | | | | | | | | | | | |            (11470), (function-axioms) are inconsistent by
% 150.63/21.73  | | | | | | | | | | | | | | | | |            sub-proof #442.
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | |   (11471)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.63/21.73  | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.63/21.73  | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.63/21.73  | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.63/21.73  | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | BETA: splitting (11471) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | |   (11472)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11466), (11472), (function-axioms) are
% 150.63/21.73  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | |   (11473)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | BETA: splitting (11473) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |   (11474)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | ALPHA: (11474) implies:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |   (11475)  op(e3, e3) = e2
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (11431), (11460), (11462),
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |            (11475), (function-axioms) are inconsistent by
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |            sub-proof #366.
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |   (11476)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (209), (211),
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |            (11445), (11448), (11476), (function-axioms) are
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #59.
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | End of split
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | End of split
% 150.63/21.73  | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | |   (11477)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.63/21.73  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.63/21.73  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.63/21.73  | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.63/21.73  | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.63/21.73  | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.63/21.73  | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.63/21.73  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.63/21.73  | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.63/21.73  | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.63/21.73  | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.63/21.73  | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.63/21.73  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.63/21.73  | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.63/21.73  | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.63/21.73  | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.63/21.73  | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.63/21.73  | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.63/21.73  | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.63/21.73  | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.63/21.73  | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.63/21.73  | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.63/21.73  | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.63/21.73  | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.63/21.73  | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.63/21.73  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.63/21.73  | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.63/21.73  | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.63/21.73  | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.63/21.73  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.63/21.73  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.63/21.73  | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.63/21.73  | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.63/21.73  | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.63/21.73  | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | BETA: splitting (11477) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | |   (11478)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.63/21.73  | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.63/21.73  | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | BETA: splitting (11478) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | |   (11479)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (9977), (11467), (11479),
% 150.63/21.73  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.73  | | | | | | | | | | | | | | | | | |            #1083.
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | |   (11480)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (9977), (11449), (11480),
% 150.63/21.73  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.73  | | | | | | | | | | | | | | | | | |            #9.
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | End of split
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | |   (11481)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.63/21.73  | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.63/21.73  | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.63/21.73  | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.63/21.73  | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.63/21.73  | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.63/21.73  | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.63/21.73  | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.63/21.73  | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.63/21.73  | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.63/21.73  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.63/21.73  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.63/21.73  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | BETA: splitting (11481) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | |   (11482)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.63/21.73  | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (11431), (11460), (11462),
% 150.63/21.73  | | | | | | | | | | | | | | | | | |            (11482), (function-axioms) are inconsistent by
% 150.63/21.73  | | | | | | | | | | | | | | | | | |            sub-proof #1079.
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | |   (11483)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | BETA: splitting (11483) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |   (11484)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | ALPHA: (11484) implies:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |   (11485)  op(e2, e0) = e2
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (11443), (11485), (function-axioms) are
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |   (11486)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.63/21.73  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | BETA: splitting (11486) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |   (11487)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | ALPHA: (11487) implies:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |   (11488)  op(e1, e0) = e1
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11429), (11488), (function-axioms) are
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |   (11489)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | ALPHA: (11489) implies:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |   (11490)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11490) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | |   (11491)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11491) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |   (11492)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11492) implies:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |   (11493)  op(e2, e2) = e3
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11445), (11493), (function-axioms) are
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |   (11494)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |              all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & $i(all_57_3))
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11494) gives:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |   (11495)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_1)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11495) implies:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |   (11496)  op(e1, e1) = e3
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9980), (11496), (function-axioms) are
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |   (11497)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_3)
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11497) implies:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |   (11498)  op(e3, e3) = e2
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (203), (278), (11431), (11460), (11462),
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |            (11498), (function-axioms) are inconsistent by
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #366.
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.73  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | |   (11499)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11499) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |   (11500)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11500) implies:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |   (11501)   ~ (all_57_4 = e1)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |   (11502)  op(e0, e2) = e0
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |   (11503)  op(e1, e2) = all_57_4
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (157), (11502) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |   (11504)  all_52_7 = e0
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |              all_57_4, e2, e1, simplifying with (161), (11503)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |              gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |   (11505)  all_57_4 = all_52_6
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11501), (11505) imply:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |   (11506)   ~ (all_52_6 = e1)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (11504) imply:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |   (11507)   ~ (all_52_6 = e0)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | |   (11508)  all_54_14 = e3
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (11508) imply:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | |   (11509)  all_52_11 = e3
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (156), (11509) imply:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | |   (11510)  op(e0, e1) = e3
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | |   (11511)   ~ (all_30_2 = e1)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11425), (11511) imply:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | |   (11512)  $false
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (11512) is inconsistent.
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | |   (11513)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | |              = all_30_1 & $i(all_30_1))
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11513) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (11514)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = all_30_1 & $i(all_30_0) &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11514) implies:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (11515)   ~ (all_30_0 = e2)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (11516)  op(e0, e1) = all_30_1
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (11517)  op(all_30_1, e0) = all_30_0
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11518)  all_54_9 = e3
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11518) imply:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11519)  all_52_6 = e3
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11519) implies:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11520)  all_52_6 = e3
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (11520) imply:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11521)   ~ (all_52_14 = e3)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11521) implies:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11522)   ~ (all_52_14 = e3)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11523)  all_54_11 = e3
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (11522), (11523) are inconsistent by
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #661.
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11524)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11424) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11525)   ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = all_10_1 & $i(all_10_0) &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11525) implies:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11526)  op(e0, e1) = all_10_1
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (9979), (11429), (11449), (11510), (11515),
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11516), (11517), (11524), (11526),
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #392.
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11527)   ~ (all_10_1 = e2) & op(e0, e1) = all_10_1 &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11527) implies:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11528)  op(e0, e1) = all_10_1
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (9979), (11429), (11449), (11510), (11515),
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11516), (11517), (11524), (11528),
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #392.
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11529)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9975), (11506), (11507), (11529) are
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #20.
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |   (11530)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11424), (11510), (11530), (function-axioms) are
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #8.
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | |   (11531)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11531) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | |   (11532)  all_54_14 = e2
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (9978), (11532) are inconsistent by
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #902.
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | |   (11533)  all_54_14 = e1 | all_54_14 = e0
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (124), (157), (246), (11427), (11502), (11533),
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | |            #752.
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |   (11534)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_7))
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (11445), (11468), (11534),
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | |            #1076.
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | Case 2:
% 150.63/21.74  | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | |   (11535)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 150.63/21.74  | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | REF_CLOSE: (278), (11431), (11460), (11462), (11535) are
% 150.63/21.74  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1140.
% 150.63/21.74  | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | End of split
% 150.63/21.74  | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | Case 2:
% 150.63/21.74  | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | |   (11536)  all_22_2 = e1
% 150.63/21.74  | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | COMBINE_EQS: (320), (11536) imply:
% 150.63/21.74  | | | | | | | | | | | | | |   (11537)  all_14_2 = e1
% 150.63/21.74  | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | SIMP: (11537) implies:
% 150.63/21.74  | | | | | | | | | | | | | |   (11538)  all_14_2 = e1
% 150.63/21.74  | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | REDUCE: (11460), (11538) imply:
% 150.63/21.74  | | | | | | | | | | | | | |   (11539)   ~ (e2 = e1)
% 150.63/21.74  | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | REDUCE: (51), (11538) imply:
% 150.63/21.74  | | | | | | | | | | | | | |   (11540)  op(e3, e3) = e1
% 150.63/21.74  | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 150.63/21.74  | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | |   (11541)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.63/21.74  | | | | | | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.63/21.74  | | | | | | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.63/21.74  | | | | | | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.63/21.74  | | | | | | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.63/21.74  | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.63/21.74  | | | | | | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.63/21.74  | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.63/21.74  | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.63/21.74  | | | | | | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.63/21.74  | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.74  | | | | | | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.63/21.74  | | | | | | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.63/21.74  | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.63/21.74  | | | | | | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.63/21.74  | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.63/21.74  | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | BETA: splitting (11541) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | |   (11542)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.63/21.74  | | | | | | | | | | | | | | | |                & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.63/21.74  | | | | | | | | | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.63/21.74  | | | | | | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.63/21.74  | | | | | | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.63/21.74  | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 150.63/21.74  | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 150.63/21.74  | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.63/21.74  | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | ALPHA: (11542) implies:
% 150.63/21.74  | | | | | | | | | | | | | | | |   (11543)  op(e3, e3) = e3
% 150.63/21.74  | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11540), (11543), (function-axioms) are
% 150.63/21.74  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 150.63/21.74  | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | Case 2:
% 150.63/21.74  | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | |   (11544)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.63/21.74  | | | | | | | | | | | | | | | |                & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.63/21.74  | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.63/21.74  | | | | | | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.63/21.74  | | | | | | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.63/21.74  | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 150.63/21.74  | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 150.63/21.74  | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.63/21.74  | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | ALPHA: (11544) implies:
% 150.63/21.74  | | | | | | | | | | | | | | | |   (11545)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14
% 150.63/21.74  | | | | | | | | | | | | | | | |                = e2) & op(e1, e1) = all_57_14 &
% 150.63/21.74  | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.63/21.74  | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | |   (11546)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 150.63/21.74  | | | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 150.63/21.74  | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | BETA: splitting (11546) gives:
% 150.63/21.74  | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | Case 1:
% 150.63/21.74  | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | |   (11547)  all_56_6 = e1 & op(e1, e3) = e1
% 150.63/21.74  | | | | | | | | | | | | | | | | | | 
% 150.63/21.74  | | | | | | | | | | | | | | | | | | ALPHA: (11547) implies:
% 150.63/21.74  | | | | | | | | | | | | | | | | | |   (11548)  all_56_6 = e1
% 150.63/21.74  | | | | | | | | | | | | | | | | | |   (11549)  op(e1, e3) = e1
% 150.63/21.74  | | | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (228), (232),
% 150.68/21.74  | | | | | | | | | | | | | | | | | |            (234), (11540), (11548), (11549),
% 150.68/21.74  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.74  | | | | | | | | | | | | | | | | | |            #547.
% 150.68/21.74  | | | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | | |   (11550)  all_56_7 = e1 & op(e1, e2) = e1
% 150.68/21.74  | | | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | | | ALPHA: (11550) implies:
% 150.68/21.74  | | | | | | | | | | | | | | | | | |   (11551)  op(e1, e2) = e1
% 150.68/21.74  | | | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (142), (159), (161),
% 150.68/21.74  | | | | | | | | | | | | | | | | | |            (162), (163), (164), (166), (205), (209), (211),
% 150.68/21.74  | | | | | | | | | | | | | | | | | |            (238), (9977), (9980), (11429), (11430), (11443),
% 150.68/21.74  | | | | | | | | | | | | | | | | | |            (11445), (11448), (11449), (11455), (11540),
% 150.68/21.74  | | | | | | | | | | | | | | | | | |            (11545), (11551), (function-axioms) are
% 150.68/21.74  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #7.
% 150.68/21.74  | | | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | |   (11552)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 150.68/21.74  | | | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 150.68/21.74  | | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (159), (9980), (11429), (11552),
% 150.68/21.74  | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.74  | | | | | | | | | | | | | | | | |            #17.
% 150.68/21.74  | | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | |   (11553)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.68/21.74  | | | | | | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.68/21.74  | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.74  | | | | | | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.68/21.74  | | | | | | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.74  | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.68/21.74  | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.68/21.74  | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.74  | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.68/21.74  | | | | | | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.68/21.74  | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.74  | | | | | | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.68/21.74  | | | | | | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.68/21.74  | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.68/21.74  | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.68/21.74  | | | | | | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (36), (9980), (11430), (11553),
% 150.68/21.74  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.74  | | | | | | | | | | | | | | |            #6.
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | |   (11554)  all_56_13 = e2 & op(e0, e2) = e2
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | ALPHA: (11554) implies:
% 150.68/21.74  | | | | | | | | | | | | |   (11555)  all_56_13 = e2
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 150.68/21.74  | | | | | | | | | | | | |            (11445), (11555), (function-axioms) are
% 150.68/21.74  | | | | | | | | | | | | |            inconsistent by sub-proof #1104.
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | |   (11556)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 150.68/21.74  | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 150.68/21.74  | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | BETA: splitting (11556) gives:
% 150.68/21.74  | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | Case 1:
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | |   (11557)  all_56_14 = e2 & op(e0, e1) = e2
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | ALPHA: (11557) implies:
% 150.68/21.74  | | | | | | | | | | | | |   (11558)  op(e0, e1) = e2
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | REF_CLOSE: (156), (9978), (11558), (function-axioms) are
% 150.68/21.74  | | | | | | | | | | | | |            inconsistent by sub-proof #1092.
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | |   (11559)  all_56_15 = e2 & op(e0, e0) = e2
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | ALPHA: (11559) implies:
% 150.68/21.74  | | | | | | | | | | | | |   (11560)  op(e0, e0) = e2
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (209), (211),
% 150.68/21.74  | | | | | | | | | | | | |            (11448), (11560), (function-axioms) are
% 150.68/21.74  | | | | | | | | | | | | |            inconsistent by sub-proof #486.
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | |   (11561)  all_56_10 = e2 & op(e2, e0) = e2
% 150.68/21.74  | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | ALPHA: (11561) implies:
% 150.68/21.74  | | | | | | | | | | |   (11562)  op(e2, e0) = e2
% 150.68/21.74  | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | REF_CLOSE: (163), (11443), (11562), (function-axioms) are
% 150.68/21.74  | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 150.68/21.74  | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | |   (11563)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 150.68/21.74  | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 150.68/21.74  | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | REF_CLOSE: (6), (159), (9979), (11430), (11563),
% 150.68/21.74  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.74  | | | | | | | | | |            #5.
% 150.68/21.74  | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | 
% 150.68/21.74  | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | 
% 150.68/21.74  | | | | | | | | |   (11564)  all_54_5 = e1 | all_54_5 = e0
% 150.68/21.74  | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | REF_CLOSE: (267), (11433), (11435), (11564) are inconsistent
% 150.68/21.74  | | | | | | | | |            by sub-proof #866.
% 150.68/21.74  | | | | | | | | | 
% 150.68/21.74  | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | 
% 150.68/21.74  | | | | | | | End of split
% 150.68/21.74  | | | | | | | 
% 150.68/21.74  | | | | | | Case 2:
% 150.68/21.74  | | | | | | | 
% 150.68/21.74  | | | | | | |   (11565)  all_20_2 = e1
% 150.68/21.74  | | | | | | | 
% 150.68/21.74  | | | | | | | COMBINE_EQS: (282), (11565) imply:
% 150.68/21.74  | | | | | | |   (11566)  all_6_2 = e1
% 150.68/21.74  | | | | | | | 
% 150.68/21.74  | | | | | | | SIMP: (11566) implies:
% 150.68/21.74  | | | | | | |   (11567)  all_6_2 = e1
% 150.68/21.74  | | | | | | | 
% 150.68/21.74  | | | | | | | REDUCE: (352), (11567) imply:
% 150.68/21.74  | | | | | | |   (11568)   ~ (all_52_6 = e1)
% 150.68/21.74  | | | | | | | 
% 150.68/21.74  | | | | | | | REDUCE: (354), (11567) imply:
% 150.68/21.74  | | | | | | |   (11569)   ~ (all_52_7 = e1)
% 150.68/21.74  | | | | | | | 
% 150.68/21.74  | | | | | | | REDUCE: (356), (11567) imply:
% 150.68/21.74  | | | | | | |   (11570)   ~ (all_52_9 = e1)
% 150.68/21.74  | | | | | | | 
% 150.68/21.74  | | | | | | | REDUCE: (9981), (11567) imply:
% 150.68/21.74  | | | | | | |   (11571)   ~ (e3 = e1)
% 150.68/21.74  | | | | | | | 
% 150.68/21.74  | | | | | | | REDUCE: (39), (11567) imply:
% 150.68/21.74  | | | | | | |   (11572)  op(e2, e2) = e1
% 150.68/21.74  | | | | | | | 
% 150.68/21.74  | | | | | | | BETA: splitting (213) gives:
% 150.68/21.74  | | | | | | | 
% 150.68/21.74  | | | | | | | Case 1:
% 150.68/21.74  | | | | | | | | 
% 150.68/21.74  | | | | | | | |   (11573)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 &
% 150.68/21.74  | | | | | | | |              op(e1, e2) = e1)
% 150.68/21.74  | | | | | | | | 
% 150.68/21.74  | | | | | | | | BETA: splitting (11573) gives:
% 150.68/21.74  | | | | | | | | 
% 150.68/21.74  | | | | | | | | Case 1:
% 150.68/21.74  | | | | | | | | | 
% 150.68/21.74  | | | | | | | | |   (11574)  all_56_6 = e1 & op(e1, e3) = e1
% 150.68/21.74  | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | ALPHA: (11574) implies:
% 150.68/21.74  | | | | | | | | |   (11575)  op(e1, e3) = e1
% 150.68/21.74  | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | BETA: splitting (217) gives:
% 150.68/21.74  | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | Case 1:
% 150.68/21.74  | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | |   (11576)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 150.68/21.74  | | | | | | | | | |              & op(e2, e1) = e1)
% 150.68/21.74  | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | BETA: splitting (11576) gives:
% 150.68/21.74  | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | Case 1:
% 150.68/21.74  | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | |   (11577)  all_56_4 = e1 & op(e3, e1) = e1
% 150.68/21.74  | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | ALPHA: (11577) implies:
% 150.68/21.74  | | | | | | | | | | |   (11578)  all_56_4 = e1
% 150.68/21.74  | | | | | | | | | | |   (11579)  op(e3, e1) = e1
% 150.68/21.74  | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | BETA: splitting (237) gives:
% 150.68/21.74  | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | Case 1:
% 150.68/21.74  | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | |   (11580)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.68/21.74  | | | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.68/21.74  | | | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.74  | | | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.68/21.74  | | | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.68/21.74  | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.68/21.74  | | | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.68/21.74  | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.74  | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.68/21.74  | | | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.68/21.74  | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.74  | | | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.68/21.74  | | | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.68/21.74  | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.68/21.74  | | | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.68/21.74  | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.74  | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | BETA: splitting (11580) gives:
% 150.68/21.74  | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | Case 1:
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | |   (11581)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.68/21.74  | | | | | | | | | | | | |                & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.68/21.74  | | | | | | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.74  | | | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.68/21.74  | | | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.68/21.74  | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 150.68/21.74  | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 150.68/21.74  | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | ALPHA: (11581) implies:
% 150.68/21.74  | | | | | | | | | | | | |   (11582)  op(e3, e3) = e3
% 150.68/21.74  | | | | | | | | | | | | |   (11583)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15
% 150.68/21.74  | | | | | | | | | | | | |                = e3) & op(e0, e0) = all_57_15 &
% 150.68/21.74  | | | | | | | | | | | | |              $i(all_57_15))
% 150.68/21.74  | | | | | | | | | | | | |   (11584)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 150.68/21.74  | | | | | | | | | | | | |                = e3) & op(e1, e1) = all_57_14 &
% 150.68/21.74  | | | | | | | | | | | | |              $i(all_57_14))
% 150.68/21.74  | | | | | | | | | | | | |   (11585)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 150.68/21.74  | | | | | | | | | | | | |                = e3) & op(e2, e2) = all_57_12 &
% 150.68/21.74  | | | | | | | | | | | | |              $i(all_57_12))
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 150.68/21.74  | | | | | | | | | | | | |              e3, e1, simplifying with (162), (11575) gives:
% 150.68/21.74  | | | | | | | | | | | | |   (11586)  all_52_2 = e1
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 150.68/21.74  | | | | | | | | | | | | |              e1, e3, simplifying with (168), (11579) gives:
% 150.68/21.74  | | | | | | | | | | | | |   (11587)  all_52_8 = e1
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e3,
% 150.68/21.74  | | | | | | | | | | | | |              e3, e3, simplifying with (51), (11582) gives:
% 150.68/21.74  | | | | | | | | | | | | |   (11588)  all_14_2 = e3
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | REDUCE: (140), (11586) imply:
% 150.68/21.74  | | | | | | | | | | | | |   (11589)   ~ (all_52_14 = e1)
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | REDUCE: (342), (11588) imply:
% 150.68/21.74  | | | | | | | | | | | | |   (11590)   ~ (all_52_4 = e3)
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | REDUCE: (9976), (11587) imply:
% 150.68/21.74  | | | | | | | | | | | | |   (11591)   ~ (e2 = e1)
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.68/21.74  | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | Case 1:
% 150.68/21.74  | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | |   (11592)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.74  | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.74  | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.74  | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.74  | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.74  | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.74  | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.74  | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.74  | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.74  | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.74  | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.74  | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.74  | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.74  | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.74  | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.74  | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.74  | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.68/21.74  | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.68/21.74  | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.68/21.74  | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.68/21.74  | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.68/21.74  | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.74  | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.74  | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.68/21.74  | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.68/21.74  | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.68/21.74  | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.68/21.74  | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.68/21.74  | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.74  | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.68/21.74  | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.68/21.74  | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.68/21.74  | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.68/21.74  | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.68/21.74  | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.74  | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.74  | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.74  | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.74  | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | BETA: splitting (11592) gives:
% 150.68/21.74  | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | Case 1:
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | |   (11593)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.74  | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.74  | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.74  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.74  | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.74  | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.74  | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.74  | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.74  | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.74  | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | BETA: splitting (11593) gives:
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | |   (11594)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.74  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.74  | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.74  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | REF_CLOSE: (11583), (11584), (11594), (function-axioms) are
% 150.68/21.74  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #814.
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | |   (11595)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.74  | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.74  | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.74  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.74  | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | REF_CLOSE: (11583), (11585), (11595), (function-axioms) are
% 150.68/21.74  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | |   (11596)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.74  | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.74  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.74  | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.74  | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.74  | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.74  | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.68/21.74  | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.74  | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.74  | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.68/21.74  | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.68/21.74  | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.74  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.68/21.74  | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.74  | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.74  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.74  | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.74  | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | BETA: splitting (11596) gives:
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | |   (11597)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.74  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.74  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.74  | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.74  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.74  | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11590), (11597), (function-axioms) are
% 150.68/21.74  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | |   (11598)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.68/21.74  | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.68/21.74  | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.68/21.74  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.68/21.74  | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.74  | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.74  | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.74  | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (168), (11430), (11579), (11582),
% 150.68/21.74  | | | | | | | | | | | | | | | |            (11598), (function-axioms) are inconsistent by
% 150.68/21.74  | | | | | | | | | | | | | | | |            sub-proof #411.
% 150.68/21.74  | | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | | End of split
% 150.68/21.74  | | | | | | | | | | | | | | 
% 150.68/21.74  | | | | | | | | | | | | | Case 2:
% 150.68/21.74  | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | |   (11599)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.75  | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.75  | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.75  | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.75  | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.75  | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.75  | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.75  | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.75  | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.75  | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.75  | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.75  | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.75  | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.75  | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.75  | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.75  | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.75  | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.75  | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.75  | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.68/21.75  | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.68/21.75  | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.68/21.75  | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.68/21.75  | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.68/21.75  | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.68/21.75  | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.68/21.75  | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.68/21.75  | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.68/21.75  | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.75  | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.75  | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.68/21.75  | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.68/21.75  | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.75  | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.68/21.75  | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.68/21.75  | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.68/21.75  | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.68/21.75  | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.68/21.75  | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.75  | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.75  | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.75  | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.75  | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.75  | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.75  | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.75  | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.75  | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.75  | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.75  | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.75  | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.75  | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.75  | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.75  | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.75  | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.75  | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | BETA: splitting (11599) gives:
% 150.68/21.75  | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | |   (11600)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.75  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.75  | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.75  | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.75  | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.75  | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.75  | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.75  | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.75  | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.75  | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.75  | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.75  | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.75  | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.75  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.75  | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.75  | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.75  | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.75  | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.75  | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.68/21.75  | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | BETA: splitting (11600) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | |   (11601)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.75  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.75  | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.75  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.75  | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.75  | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.75  | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.75  | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | BETA: splitting (11601) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | |   (11602)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.75  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.75  | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.75  | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | ALPHA: (11602) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | |   (11603)  op(e3, e1) = e3
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (11579), (11603), (function-axioms)
% 150.68/21.75  | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #439.
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | |   (11604)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.68/21.75  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 150.68/21.75  | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 150.68/21.75  | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | ALPHA: (11604) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | |   (11605)  op(e2, e1) = e2
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9977), (11605), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | |   (11606)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.75  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.68/21.75  | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.68/21.75  | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.75  | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.68/21.75  | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.68/21.75  | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.75  | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.75  | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.68/21.75  | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.68/21.75  | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.75  | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.68/21.75  | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | REF_CLOSE: (51), (164), (167), (346), (9977), (11582),
% 150.68/21.75  | | | | | | | | | | | | | | | |            (11606), (function-axioms) are inconsistent by
% 150.68/21.75  | | | | | | | | | | | | | | | |            sub-proof #4.
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | |   (11607)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.75  | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.75  | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.75  | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.75  | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.75  | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.75  | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.75  | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.68/21.75  | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.75  | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.68/21.75  | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.75  | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.68/21.75  | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.68/21.75  | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.68/21.75  | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.68/21.75  | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.68/21.75  | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.75  | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.68/21.75  | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.68/21.75  | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.68/21.75  | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.75  | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.75  | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.75  | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.75  | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.75  | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.75  | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.75  | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.75  | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.75  | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.75  | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.75  | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.75  | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.75  | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.75  | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.75  | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | BETA: splitting (11607) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | |   (11608)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.75  | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.75  | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.75  | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.75  | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.75  | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.75  | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.75  | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11582), (11608), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | |   (11609)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.75  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.75  | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.75  | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.68/21.75  | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.68/21.75  | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.75  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.68/21.75  | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.68/21.75  | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.68/21.75  | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.68/21.75  | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.75  | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.75  | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.75  | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.75  | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.75  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.75  | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.75  | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.75  | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.75  | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.75  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.75  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.75  | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.75  | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.75  | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.75  | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | BETA: splitting (11609) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | |   (11610)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.75  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.75  | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.75  | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | ALPHA: (11610) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | |   (11611)  op(e1, e1) = e0
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9980), (11611), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | |   (11612)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.75  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.68/21.75  | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.68/21.75  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.68/21.75  | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.68/21.75  | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.68/21.75  | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.75  | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.68/21.75  | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.68/21.75  | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.68/21.75  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.68/21.75  | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.68/21.75  | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | BETA: splitting (11612) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | |   (11613)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | ALPHA: (11613) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | | |   (11614)  op(e1, e0) = e1
% 150.68/21.75  | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (11429), (11614), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 150.68/21.75  | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | |   (11615)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.68/21.75  | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | ALPHA: (11615) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | | |   (11616)  op(e0, e0) = all_57_15
% 150.68/21.75  | | | | | | | | | | | | | | | | | |   (11617)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.75  | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.68/21.75  | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.68/21.75  | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              all_57_15, e0, e0, simplifying with (11430),
% 150.68/21.75  | | | | | | | | | | | | | | | | | |              (11616) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | |   (11618)  all_57_15 = e1
% 150.68/21.75  | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | BETA: splitting (11617) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |   (11619)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11582), (11584), (11585), (11619),
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |            #406.
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |   (11620)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | BETA: splitting (11620) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |   (11621)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | ALPHA: (11621) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |   (11622)   ~ (all_57_15 = e2)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |   (11623)   ~ (all_57_4 = e1)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |   (11624)  op(e0, e2) = e0
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |   (11625)  op(e1, e2) = all_57_4
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |              e2, e0, simplifying with (157), (11624) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |   (11626)  all_52_7 = e0
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |              all_57_4, e2, e1, simplifying with (161), (11625)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |              gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |   (11627)  all_57_4 = all_52_6
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (11626) imply:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |   (11628)   ~ (all_52_3 = e0)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (127), (11626) imply:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |   (11629)   ~ (all_52_6 = e0)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | REDUCE: (11569), (11626) imply:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |   (11630)   ~ (e1 = e0)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |   (11631)  all_54_9 = e3
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (257), (11631) imply:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |   (11632)  all_52_6 = e3
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | SIMP: (11632) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |   (11633)  all_52_6 = e3
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (11633) imply:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |   (11634)   ~ (all_52_14 = e3)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | SIMP: (11634) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |   (11635)   ~ (all_52_14 = e3)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | |   (11636)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11636) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | |   (11637)  all_56_9 = e3 & op(e3, e0) = e3
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11637) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | |   (11638)  op(e3, e0) = e3
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (167), (346), (11582), (11638),
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | |            #71.
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | |   (11639)  all_56_10 = e3 & op(e2, e0) = e3
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11639) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | |   (11640)  all_56_10 = e3
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | |   (11641)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11641) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (11642)  all_56_2 = e2 & op(e2, e3) = e2
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11642) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (11643)  all_56_2 = e2
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (158), (162), (228), (11575),
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | |            (11582), (11628), (11643), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #26.
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (11644)  all_56_3 = e2 & op(e2, e2) = e2
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11644) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | |   (11645)  op(e2, e2) = e2
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (11572), (11645), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | |   (11646)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (9977), (11640), (11646),
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | |            #258.
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | |   (11647)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (159), (11430), (11635), (11647),
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | |            #60.
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |   (11648)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (257), (9975), (11568), (11629), (11648) are
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #20.
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |   (11649)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_7))
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11649) gives:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |   (11650)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11650) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |   (11651)  op(e3, e3) = e1
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11582), (11651), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1178.
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |   (11652)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_7)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11652) implies:
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |   (11653)   ~ (all_57_15 = e1)
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11430), (11616), (11653), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #940.
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | |   (11654)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.68/21.75  | | | | | | | | | | | | |                & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.68/21.75  | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.75  | | | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.68/21.75  | | | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.68/21.75  | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 150.68/21.75  | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 150.68/21.75  | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | ALPHA: (11654) implies:
% 150.68/21.75  | | | | | | | | | | | | |   (11655)  op(e2, e2) = e2
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | REF_CLOSE: (6), (11572), (11655), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | | | |            inconsistent by sub-proof #1158.
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | |   (11656)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.68/21.75  | | | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.68/21.75  | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.75  | | | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.68/21.75  | | | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.75  | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.68/21.75  | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.68/21.75  | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.75  | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.68/21.75  | | | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.68/21.75  | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.75  | | | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.68/21.75  | | | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.68/21.75  | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.68/21.75  | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.68/21.75  | | | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.68/21.75  | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | BETA: splitting (11656) gives:
% 150.68/21.75  | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | |   (11657)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.68/21.75  | | | | | | | | | | | | |                & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.68/21.75  | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.75  | | | | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.68/21.75  | | | | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.75  | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.68/21.75  | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.68/21.75  | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | ALPHA: (11657) implies:
% 150.68/21.75  | | | | | | | | | | | | |   (11658)  op(e1, e1) = e1
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (11658), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | |   (11659)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.68/21.75  | | | | | | | | | | | | |                & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.68/21.75  | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.75  | | | | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.68/21.75  | | | | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.68/21.75  | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.68/21.75  | | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.68/21.75  | | | | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14)))
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | ALPHA: (11659) implies:
% 150.68/21.75  | | | | | | | | | | | | |   (11660)  op(e0, e0) = e0
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (158), (168),
% 150.68/21.75  | | | | | | | | | | | | |            (206), (216), (218), (219), (9980), (11426),
% 150.68/21.75  | | | | | | | | | | | | |            (11569), (11578), (11579), (11660),
% 150.68/21.75  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.75  | | | | | | | | | | | | |            #3.
% 150.68/21.75  | | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | |   (11661)  all_56_5 = e1 & op(e2, e1) = e1
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | ALPHA: (11661) implies:
% 150.68/21.75  | | | | | | | | | | |   (11662)  op(e2, e1) = e1
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | REF_CLOSE: (164), (11570), (11662), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | |            inconsistent by sub-proof #704.
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | |   (11663)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 150.68/21.75  | | | | | | | | | |              e1 & op(e0, e1) = e1)
% 150.68/21.75  | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | BETA: splitting (11663) gives:
% 150.68/21.75  | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | Case 1:
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | |   (11664)  all_56_8 = e1 & op(e1, e1) = e1
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | ALPHA: (11664) implies:
% 150.68/21.75  | | | | | | | | | | |   (11665)  op(e1, e1) = e1
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (11665), (function-axioms) are
% 150.68/21.75  | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | |   (11666)  all_56_14 = e1 & op(e0, e1) = e1
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | ALPHA: (11666) implies:
% 150.68/21.75  | | | | | | | | | | |   (11667)  op(e0, e1) = e1
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 150.68/21.75  | | | | | | | | | | |              e1, e1, e0, simplifying with (156), (11667) gives:
% 150.68/21.75  | | | | | | | | | | |   (11668)  all_52_11 = e1
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | REDUCE: (11427), (11668) imply:
% 150.68/21.75  | | | | | | | | | | |   (11669)  $false
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | | CLOSE: (11669) is inconsistent.
% 150.68/21.75  | | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | | 
% 150.68/21.75  | | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | | 
% 150.68/21.75  | | | | | | | | |   (11670)  all_56_7 = e1 & op(e1, e2) = e1
% 150.68/21.75  | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | ALPHA: (11670) implies:
% 150.68/21.75  | | | | | | | | |   (11671)  op(e1, e2) = e1
% 150.68/21.75  | | | | | | | | | 
% 150.68/21.75  | | | | | | | | | REF_CLOSE: (161), (11568), (11671), (function-axioms) are
% 150.68/21.75  | | | | | | | | |            inconsistent by sub-proof #1042.
% 150.68/21.75  | | | | | | | | | 
% 150.68/21.75  | | | | | | | | End of split
% 150.68/21.75  | | | | | | | | 
% 150.68/21.75  | | | | | | | Case 2:
% 150.68/21.75  | | | | | | | | 
% 150.68/21.75  | | | | | | | |   (11672)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 &
% 150.68/21.75  | | | | | | | |              op(e1, e0) = e1)
% 150.68/21.75  | | | | | | | | 
% 150.68/21.75  | | | | | | | | REF_CLOSE: (6), (36), (159), (9980), (11429), (11672),
% 150.68/21.75  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #17.
% 150.68/21.75  | | | | | | | | 
% 150.68/21.75  | | | | | | | End of split
% 150.68/21.75  | | | | | | | 
% 150.68/21.75  | | | | | | End of split
% 150.68/21.75  | | | | | | 
% 150.68/21.75  | | | | | Case 2:
% 150.68/21.75  | | | | | | 
% 150.68/21.75  | | | | | |   (11673)  all_16_2 = e0
% 150.68/21.75  | | | | | | 
% 150.68/21.75  | | | | | | COMBINE_EQS: (327), (11673) imply:
% 150.68/21.75  | | | | | |   (11674)  all_6_2 = e0
% 150.68/21.75  | | | | | | 
% 150.68/21.75  | | | | | | SIMP: (11674) implies:
% 150.68/21.75  | | | | | |   (11675)  all_6_2 = e0
% 150.68/21.75  | | | | | | 
% 150.68/21.75  | | | | | | REDUCE: (354), (11675) imply:
% 150.68/21.75  | | | | | |   (11676)   ~ (all_52_7 = e0)
% 150.68/21.75  | | | | | | 
% 150.68/21.75  | | | | | | REDUCE: (39), (11675) imply:
% 150.68/21.75  | | | | | |   (11677)  op(e2, e2) = e0
% 150.68/21.75  | | | | | | 
% 150.68/21.75  | | | | | | BETA: splitting (237) gives:
% 150.68/21.75  | | | | | | 
% 150.68/21.75  | | | | | | Case 1:
% 150.68/21.75  | | | | | | | 
% 150.68/21.75  | | | | | | |   (11678)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 &
% 150.68/21.75  | | | | | | |                  op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2,
% 150.68/21.75  | | | | | | |                    e2) = all_57_12 & $i(all_57_12))) & ((all_57_1
% 150.68/21.75  | | | | | | |                  = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) &
% 150.68/21.75  | | | | | | |                  op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.75  | | | | | | |              ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 =
% 150.68/21.75  | | | | | | |                    e3) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.75  | | | | | | |            | (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 &
% 150.68/21.75  | | | | | | |                  op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3,
% 150.68/21.75  | | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_4
% 150.68/21.75  | | | | | | |                  = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) &
% 150.68/21.75  | | | | | | |                  op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.75  | | | | | | |              ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 =
% 150.68/21.75  | | | | | | |                    e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.75  | | | | | | | 
% 150.68/21.75  | | | | | | | BETA: splitting (11678) gives:
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | |   (11679)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 &
% 150.68/21.76  | | | | | | | |                op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2,
% 150.68/21.76  | | | | | | | |                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_1
% 150.68/21.76  | | | | | | | |                = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) &
% 150.68/21.76  | | | | | | | |                op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.76  | | | | | | | |            ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 =
% 150.68/21.76  | | | | | | | |                  e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | ALPHA: (11679) implies:
% 150.68/21.76  | | | | | | | |   (11680)  op(e3, e3) = e3
% 150.68/21.76  | | | | | | | |   (11681)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 =
% 150.68/21.76  | | | | | | | |                e3) & op(e0, e0) = all_57_15 & $i(all_57_15))
% 150.68/21.76  | | | | | | | |   (11682)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 =
% 150.68/21.76  | | | | | | | |                e3) & op(e1, e1) = all_57_14 & $i(all_57_14))
% 150.68/21.76  | | | | | | | |   (11683)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 =
% 150.68/21.76  | | | | | | | |                e3) & op(e2, e2) = all_57_12 & $i(all_57_12))
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e3,
% 150.68/21.76  | | | | | | | |              e3, e3, simplifying with (51), (11680) gives:
% 150.68/21.76  | | | | | | | |   (11684)  all_14_2 = e3
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | REDUCE: (342), (11684) imply:
% 150.68/21.76  | | | | | | | |   (11685)   ~ (all_52_4 = e3)
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | REDUCE: (344), (11684) imply:
% 150.68/21.76  | | | | | | | |   (11686)   ~ (all_52_8 = e3)
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | BETA: splitting (238) gives:
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | | 
% 150.68/21.76  | | | | | | | | |   (11687)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.76  | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.76  | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.76  | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 150.68/21.76  | | | | | | | | |            (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.76  | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.76  | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.76  | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 150.68/21.76  | | | | | | | | |            (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.76  | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.76  | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.76  | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.76  | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.76  | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.76  | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 150.68/21.76  | | | | | | | | |                e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2)
% 150.68/21.76  | | | | | | | | |              & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 =
% 150.68/21.76  | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 = e2) &
% 150.68/21.76  | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 150.68/21.76  | | | | | | | | |                e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4)
% 150.68/21.76  | | | | | | | | |              & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 =
% 150.68/21.76  | | | | | | | | |              e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.76  | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 150.68/21.76  | | | | | | | | |                e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5)
% 150.68/21.76  | | | | | | | | |              & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 =
% 150.68/21.76  | | | | | | | | |              e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.68/21.76  | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.68/21.76  | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.76  | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.68/21.76  | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.68/21.76  | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 150.68/21.76  | | | | | | | | |              all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 150.68/21.76  | | | | | | | | |              e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 =
% 150.68/21.76  | | | | | | | | |              e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.76  | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.76  | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.76  | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.76  | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | BETA: splitting (11687) gives:
% 150.68/21.76  | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | |   (11688)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.76  | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.76  | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.76  | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.76  | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.76  | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.76  | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.76  | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.76  | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.76  | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.76  | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.76  | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.76  | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.76  | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.76  | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.76  | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.76  | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | BETA: splitting (11688) gives:
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | |   (11689)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.76  | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.76  | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.76  | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.76  | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.76  | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.76  | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.76  | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | REF_CLOSE: (11681), (11682), (11689), (function-axioms) are
% 150.68/21.76  | | | | | | | | | | |            inconsistent by sub-proof #814.
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | Case 2:
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | |   (11690)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.76  | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.76  | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.76  | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.76  | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.76  | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.76  | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | REF_CLOSE: (11681), (11683), (11690), (function-axioms) are
% 150.68/21.76  | | | | | | | | | | |            inconsistent by sub-proof #831.
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | End of split
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | Case 2:
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | |   (11691)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.76  | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.76  | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.76  | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.76  | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.76  | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.76  | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.76  | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.68/21.76  | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.76  | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.76  | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.68/21.76  | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.68/21.76  | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.76  | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.76  | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.76  | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.68/21.76  | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.76  | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.76  | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.76  | | | | | | | | | |              $i(all_57_10))
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | BETA: splitting (11691) gives:
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | |   (11692)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.76  | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.76  | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.76  | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.76  | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.76  | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | REF_CLOSE: (169), (11685), (11692), (function-axioms) are
% 150.68/21.76  | | | | | | | | | | |            inconsistent by sub-proof #863.
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | Case 2:
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | |   (11693)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.68/21.76  | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.68/21.76  | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.68/21.76  | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.68/21.76  | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.68/21.76  | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.76  | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.68/21.76  | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.76  | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.76  | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.76  | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (11430), (11677), (11680), (11693),
% 150.68/21.76  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.76  | | | | | | | | | | |            #395.
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | End of split
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | End of split
% 150.68/21.76  | | | | | | | | | 
% 150.68/21.76  | | | | | | | | Case 2:
% 150.68/21.76  | | | | | | | | | 
% 150.68/21.76  | | | | | | | | |   (11694)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.76  | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.76  | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.76  | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.76  | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.76  | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.76  | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.76  | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.76  | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.76  | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.76  | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.76  | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.76  | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.76  | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.76  | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.76  | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.76  | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.76  | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1,
% 150.68/21.76  | | | | | | | | |                e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.76  | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.68/21.76  | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.68/21.76  | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.68/21.76  | | | | | | | | |              all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) =
% 150.68/21.76  | | | | | | | | |              e2 & $i(all_57_9) & $i(all_57_12)) | (all_57_10 =
% 150.68/21.76  | | | | | | | | |              e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 150.68/21.76  | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.68/21.76  | | | | | | | | |              all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.68/21.76  | | | | | | | | |              e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 =
% 150.68/21.76  | | | | | | | | |              e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 150.68/21.76  | | | | | | | | |              (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.76  | | | | | | | | |              op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 150.68/21.76  | | | | | | | | |              all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 150.68/21.76  | | | | | | | | |            (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.76  | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.76  | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.68/21.76  | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14))
% 150.68/21.76  | | | | | | | | |            | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.76  | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.76  | | | | | | | | |                    e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.76  | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.68/21.76  | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.68/21.76  | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.76  | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.76  | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.76  | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.76  | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.76  | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.76  | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.76  | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.76  | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.76  | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.76  | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.76  | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.76  | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.76  | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.76  | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.76  | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | BETA: splitting (11694) gives:
% 150.68/21.76  | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | |   (11695)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.76  | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.76  | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.76  | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.76  | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.76  | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.76  | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.76  | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.76  | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.76  | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.76  | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.76  | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.76  | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.76  | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.76  | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.76  | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.76  | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.76  | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.76  | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.76  | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | BETA: splitting (11695) gives:
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | |   (11696)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.76  | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.76  | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.76  | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.76  | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.76  | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | REF_CLOSE: (164), (168), (9977), (11686), (11696),
% 150.68/21.76  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.76  | | | | | | | | | | |            #1083.
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | Case 2:
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | |   (11697)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.76  | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.68/21.76  | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.68/21.76  | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.68/21.76  | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.68/21.76  | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.76  | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.68/21.76  | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.68/21.76  | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.76  | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.68/21.76  | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | REF_CLOSE: (51), (164), (167), (346), (9977), (11680),
% 150.68/21.76  | | | | | | | | | | |            (11697), (function-axioms) are inconsistent by
% 150.68/21.76  | | | | | | | | | | |            sub-proof #4.
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | End of split
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | Case 2:
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | |   (11698)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.76  | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.76  | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.76  | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.76  | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.76  | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.76  | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.76  | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.76  | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.68/21.76  | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.76  | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.68/21.76  | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.76  | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.68/21.76  | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.68/21.76  | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.68/21.76  | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.68/21.76  | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.68/21.76  | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.76  | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.68/21.76  | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.76  | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.68/21.76  | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.68/21.76  | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.76  | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.76  | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.76  | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.76  | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.76  | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.76  | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.76  | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.76  | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.76  | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.76  | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.76  | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.76  | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.76  | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.76  | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | BETA: splitting (11698) gives:
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | |   (11699)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.76  | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.76  | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.76  | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.76  | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.76  | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.76  | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.76  | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_14))
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | REF_CLOSE: (7), (11680), (11699), (function-axioms) are
% 150.68/21.76  | | | | | | | | | | |            inconsistent by sub-proof #975.
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | Case 2:
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | |   (11700)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.76  | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.76  | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.76  | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.68/21.76  | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.68/21.76  | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.76  | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.68/21.76  | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.68/21.76  | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.68/21.76  | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.68/21.76  | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.68/21.76  | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.76  | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.76  | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.76  | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.76  | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.76  | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.76  | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.76  | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.76  | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.76  | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.76  | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.76  | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.76  | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.76  | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.76  | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.76  | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.76  | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.76  | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | BETA: splitting (11700) gives:
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | |   (11701)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.76  | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.76  | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.76  | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.76  | | | | | | | | | | | |            $i(all_57_13)
% 150.68/21.76  | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | ALPHA: (11701) implies:
% 150.68/21.76  | | | | | | | | | | | |   (11702)  op(e1, e1) = e0
% 150.68/21.76  | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | REF_CLOSE: (5), (9980), (11702), (function-axioms) are
% 150.68/21.76  | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 150.68/21.76  | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | Case 2:
% 150.68/21.76  | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | |   (11703)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.76  | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.76  | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.68/21.76  | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.68/21.76  | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.68/21.76  | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.68/21.76  | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.68/21.76  | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.68/21.76  | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.68/21.76  | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.68/21.76  | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.68/21.76  | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.68/21.76  | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.68/21.76  | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.68/21.76  | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.68/21.76  | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.76  | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.68/21.76  | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.76  | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.68/21.76  | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.68/21.76  | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.68/21.76  | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.68/21.76  | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.68/21.76  | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.68/21.76  | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.68/21.76  | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.68/21.76  | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.68/21.76  | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | BETA: splitting (11703) gives:
% 150.68/21.76  | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | |   (11704)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.76  | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.76  | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.68/21.76  | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.68/21.76  | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | | ALPHA: (11704) implies:
% 150.68/21.76  | | | | | | | | | | | | |   (11705)  op(e1, e0) = e1
% 150.68/21.76  | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | | REF_CLOSE: (159), (11429), (11705), (function-axioms) are
% 150.68/21.76  | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 150.68/21.76  | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | Case 2:
% 150.68/21.76  | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | |   (11706)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.76  | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.76  | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.76  | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.76  | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.76  | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.68/21.76  | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.68/21.76  | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.68/21.76  | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.76  | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.68/21.76  | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.68/21.76  | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.68/21.76  | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.68/21.76  | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.68/21.76  | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.68/21.76  | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.68/21.76  | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.68/21.76  | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.76  | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.68/21.76  | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.68/21.76  | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.68/21.76  | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.68/21.76  | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | | ALPHA: (11706) implies:
% 150.68/21.76  | | | | | | | | | | | | |   (11707)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.76  | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.76  | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.76  | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.68/21.76  | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.68/21.76  | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.68/21.76  | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.68/21.76  | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.76  | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.76  | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.76  | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.76  | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.76  | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.76  | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.68/21.76  | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.68/21.76  | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.68/21.76  | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.68/21.76  | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.76  | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.68/21.76  | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.68/21.76  | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | | BETA: splitting (11707) gives:
% 150.68/21.76  | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | | |   (11708)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.76  | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.76  | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.76  | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.68/21.76  | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.68/21.76  | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.68/21.76  | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.68/21.76  | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.76  | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.76  | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.68/21.76  | | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | | | REF_CLOSE: (9), (11680), (11682), (11683), (11708),
% 150.68/21.76  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.76  | | | | | | | | | | | | | |            #406.
% 150.68/21.76  | | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | | Case 2:
% 150.68/21.76  | | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | | |   (11709)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.76  | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.76  | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.76  | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.68/21.76  | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.68/21.76  | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.68/21.76  | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.68/21.76  | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.76  | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.68/21.76  | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.68/21.76  | | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (157), (11676), (11677), (11680),
% 150.68/21.76  | | | | | | | | | | | | | |            (11709), (function-axioms) are inconsistent by
% 150.68/21.76  | | | | | | | | | | | | | |            sub-proof #823.
% 150.68/21.76  | | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | | End of split
% 150.68/21.76  | | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | | End of split
% 150.68/21.76  | | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | | End of split
% 150.68/21.76  | | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | | End of split
% 150.68/21.76  | | | | | | | | | | 
% 150.68/21.76  | | | | | | | | | End of split
% 150.68/21.76  | | | | | | | | | 
% 150.68/21.76  | | | | | | | | End of split
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | Case 2:
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | |   (11710)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 &
% 150.68/21.76  | | | | | | | |                op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3,
% 150.68/21.76  | | | | | | | |                  e3) = all_57_10 & $i(all_57_10))) & ((all_57_4
% 150.68/21.76  | | | | | | | |                = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) &
% 150.68/21.76  | | | | | | | |                op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.76  | | | | | | | |            ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 =
% 150.68/21.76  | | | | | | | |                  e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | ALPHA: (11710) implies:
% 150.68/21.76  | | | | | | | |   (11711)  op(e2, e2) = e2
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | REF_CLOSE: (5), (11677), (11711), (function-axioms) are
% 150.68/21.76  | | | | | | | |            inconsistent by sub-proof #1145.
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | End of split
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | Case 2:
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | |   (11712)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 &
% 150.68/21.76  | | | | | | |                  op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3,
% 150.68/21.76  | | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_7
% 150.68/21.76  | | | | | | |                  = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) &
% 150.68/21.76  | | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.76  | | | | | | |              ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 =
% 150.68/21.76  | | | | | | |                    e1) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.76  | | | | | | |            | (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 &
% 150.68/21.76  | | | | | | |                  op(e3, e0) = e3) | ( ~ (all_57_10 = e0) & op(e3,
% 150.68/21.76  | | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_11
% 150.68/21.76  | | | | | | |                  = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 150.68/21.76  | | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.76  | | | | | | |              ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14
% 150.68/21.76  | | | | | | |                    = e0) & op(e1, e1) = all_57_14 &
% 150.68/21.76  | | | | | | |                  $i(all_57_14))))
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | | REF_CLOSE: (4), (6), (36), (9980), (11430), (11712),
% 150.68/21.76  | | | | | | |            (function-axioms) are inconsistent by sub-proof #6.
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | End of split
% 150.68/21.76  | | | | | | 
% 150.68/21.76  | | | | | End of split
% 150.68/21.76  | | | | | 
% 150.68/21.76  | | | | Case 2:
% 150.68/21.76  | | | | | 
% 150.68/21.76  | | | | |   (11713)  all_14_2 = e0
% 150.68/21.76  | | | | |   (11714)  ( ~ (all_14_0 = e2) & op(all_14_1, e3) = all_14_0 & op(e3,
% 150.68/21.76  | | | | |                e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 150.68/21.76  | | | | |              (all_14_1 = e1) & op(e3, e0) = all_14_1 & $i(all_14_1))
% 150.68/21.76  | | | | | 
% 150.68/21.76  | | | | | REDUCE: (338), (11713) imply:
% 150.68/21.76  | | | | |   (11715)   ~ (all_52_2 = e0)
% 150.68/21.76  | | | | | 
% 150.68/21.76  | | | | | REDUCE: (342), (11713) imply:
% 150.68/21.76  | | | | |   (11716)   ~ (all_52_4 = e0)
% 150.68/21.76  | | | | | 
% 150.68/21.76  | | | | | REDUCE: (344), (11713) imply:
% 150.68/21.76  | | | | |   (11717)   ~ (all_52_8 = e0)
% 150.68/21.76  | | | | | 
% 150.68/21.76  | | | | | REDUCE: (51), (11713) imply:
% 150.68/21.76  | | | | |   (11718)  op(e3, e3) = e0
% 150.68/21.76  | | | | | 
% 150.68/21.76  | | | | | BETA: splitting (237) gives:
% 150.68/21.76  | | | | | 
% 150.68/21.76  | | | | | Case 1:
% 150.68/21.76  | | | | | | 
% 150.68/21.76  | | | | | |   (11719)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 &
% 150.68/21.76  | | | | | |                  op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2,
% 150.68/21.76  | | | | | |                    e2) = all_57_12 & $i(all_57_12))) & ((all_57_1 =
% 150.68/21.76  | | | | | |                  e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) &
% 150.68/21.76  | | | | | |                  op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.76  | | | | | |              ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 =
% 150.68/21.76  | | | | | |                    e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.76  | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 &
% 150.68/21.76  | | | | | |                  op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3,
% 150.68/21.76  | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_4 =
% 150.68/21.76  | | | | | |                  e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) &
% 150.68/21.76  | | | | | |                  op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.76  | | | | | |              ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 =
% 150.68/21.76  | | | | | |                    e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.76  | | | | | | 
% 150.68/21.76  | | | | | | BETA: splitting (11719) gives:
% 150.68/21.76  | | | | | | 
% 150.68/21.76  | | | | | | Case 1:
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | |   (11720)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 &
% 150.68/21.76  | | | | | | |                op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2,
% 150.68/21.76  | | | | | | |                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_1 =
% 150.68/21.76  | | | | | | |                e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) &
% 150.68/21.76  | | | | | | |                op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.76  | | | | | | |            ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 =
% 150.68/21.76  | | | | | | |                  e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | | ALPHA: (11720) implies:
% 150.68/21.76  | | | | | | |   (11721)  op(e3, e3) = e3
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | | REF_CLOSE: (7), (11718), (11721), (function-axioms) are
% 150.68/21.76  | | | | | | |            inconsistent by sub-proof #1141.
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | Case 2:
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | |   (11722)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 &
% 150.68/21.76  | | | | | | |                op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3,
% 150.68/21.76  | | | | | | |                  e3) = all_57_10 & $i(all_57_10))) & ((all_57_4 =
% 150.68/21.76  | | | | | | |                e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) &
% 150.68/21.76  | | | | | | |                op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.76  | | | | | | |            ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 =
% 150.68/21.76  | | | | | | |                  e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | | ALPHA: (11722) implies:
% 150.68/21.76  | | | | | | |   (11723)  op(e2, e2) = e2
% 150.68/21.76  | | | | | | |   (11724)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 =
% 150.68/21.76  | | | | | | |                e2) & op(e1, e1) = all_57_14 & $i(all_57_14))
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | | BETA: splitting (11724) gives:
% 150.68/21.76  | | | | | | | 
% 150.68/21.76  | | | | | | | Case 1:
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | |   (11725)  all_57_4 = e1 & op(e1, e2) = e1
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | ALPHA: (11725) implies:
% 150.68/21.76  | | | | | | | |   (11726)  op(e1, e2) = e1
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 150.68/21.76  | | | | | | | |              e2, e1, simplifying with (161), (11726) gives:
% 150.68/21.76  | | | | | | | |   (11727)  all_52_6 = e1
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_6_2, e2,
% 150.68/21.76  | | | | | | | |              e2, e2, simplifying with (39), (11723) gives:
% 150.68/21.76  | | | | | | | |   (11728)  all_6_2 = e2
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | REDUCE: (347), (11728) imply:
% 150.68/21.76  | | | | | | | |   (11729)   ~ (all_52_1 = e2)
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | REDUCE: (142), (11727) imply:
% 150.68/21.76  | | | | | | | |   (11730)   ~ (all_52_2 = e1)
% 150.68/21.76  | | | | | | | | 
% 150.68/21.76  | | | | | | | | REDUCE: (135), (11727) imply:
% 150.68/21.76  | | | | | | | |   (11731)   ~ (all_52_4 = e1)
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | REDUCE: (350), (11728) imply:
% 150.68/21.77  | | | | | | | |   (11732)   ~ (all_52_4 = e2)
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | REDUCE: (127), (11727) imply:
% 150.68/21.77  | | | | | | | |   (11733)   ~ (all_52_7 = e1)
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | SIMP: (11733) implies:
% 150.68/21.77  | | | | | | | |   (11734)   ~ (all_52_7 = e1)
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | REDUCE: (125), (11727) imply:
% 150.68/21.77  | | | | | | | |   (11735)   ~ (all_52_14 = e1)
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | REDUCE: (9975), (11727) imply:
% 150.68/21.77  | | | | | | | |   (11736)   ~ (e2 = e1)
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | REDUCE: (358), (11728) imply:
% 150.68/21.77  | | | | | | | |   (11737)   ~ (all_52_13 = e2)
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | REDUCE: (9981), (11728) imply:
% 150.68/21.77  | | | | | | | |   (11738)   ~ (e3 = e2)
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | BETA: splitting (232) gives:
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | 
% 150.68/21.77  | | | | | | | | |   (11739)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 150.68/21.77  | | | | | | | | |              & op(e2, e3) = e2)
% 150.68/21.77  | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | REF_CLOSE: (5), (166), (11718), (11729), (11739),
% 150.68/21.77  | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.77  | | | | | | | | |            #526.
% 150.68/21.77  | | | | | | | | | 
% 150.68/21.77  | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | 
% 150.68/21.77  | | | | | | | | |   (11740)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2
% 150.68/21.77  | | | | | | | | |              & op(e0, e3) = e2)
% 150.68/21.77  | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | BETA: splitting (11740) gives:
% 150.68/21.77  | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | |   (11741)  all_56_6 = e2 & op(e1, e3) = e2
% 150.68/21.77  | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | REF_CLOSE: (162), (9974), (11741), (function-axioms) are
% 150.68/21.77  | | | | | | | | | |            inconsistent by sub-proof #47.
% 150.68/21.77  | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | |   (11742)  all_56_12 = e2 & op(e0, e3) = e2
% 150.68/21.77  | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | ALPHA: (11742) implies:
% 150.68/21.77  | | | | | | | | | |   (11743)  all_56_12 = e2
% 150.68/21.77  | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | BETA: splitting (210) gives:
% 150.68/21.77  | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | |   (11744)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 150.68/21.77  | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 150.68/21.77  | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | BETA: splitting (11744) gives:
% 150.68/21.77  | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | |   (11745)  all_56_9 = e2 & op(e3, e0) = e2
% 150.68/21.77  | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | ALPHA: (11745) implies:
% 150.68/21.77  | | | | | | | | | | | |   (11746)  all_56_9 = e2
% 150.68/21.77  | | | | | | | | | | | |   (11747)  op(e3, e0) = e2
% 150.68/21.77  | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | BETA: splitting (212) gives:
% 150.68/21.77  | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | |   (11748)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 150.68/21.77  | | | | | | | | | | | | |              & op(e1, e2) = e0)
% 150.68/21.77  | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | BETA: splitting (11748) gives:
% 150.68/21.77  | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | |   (11749)  all_56_6 = e0 & op(e1, e3) = e0
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | ALPHA: (11749) implies:
% 150.68/21.77  | | | | | | | | | | | | | |   (11750)  all_56_6 = e0
% 150.68/21.77  | | | | | | | | | | | | | |   (11751)  op(e1, e3) = e0
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (162), (230), (234),
% 150.68/21.77  | | | | | | | | | | | | | |            (11718), (11743), (11750), (11751),
% 150.68/21.77  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.77  | | | | | | | | | | | | | |            #619.
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | |   (11752)  all_56_7 = e0 & op(e1, e2) = e0
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | ALPHA: (11752) implies:
% 150.68/21.77  | | | | | | | | | | | | | |   (11753)  all_56_7 = e0
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | |   (11754)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 150.68/21.77  | | | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | BETA: splitting (11754) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | |   (11755)  all_56_6 = e1 & op(e1, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | ALPHA: (11755) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | |   (11756)  op(e1, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11730), (11756), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | |   (11757)  all_56_7 = e1 & op(e1, e2) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11753), (11757) are inconsistent by
% 150.68/21.77  | | | | | | | | | | | | | | | |            sub-proof #1111.
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | |   (11758)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 150.68/21.77  | | | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (159), (9980), (11429), (11758),
% 150.68/21.77  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.77  | | | | | | | | | | | | | | |            #17.
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | |   (11759)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 150.68/21.77  | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 150.68/21.77  | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | BETA: splitting (11759) gives:
% 150.68/21.77  | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | |   (11760)  all_56_8 = e0 & op(e1, e1) = e0
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | ALPHA: (11760) implies:
% 150.68/21.77  | | | | | | | | | | | | | |   (11761)  op(e1, e1) = e0
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | REF_CLOSE: (5), (9980), (11761), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | |   (11762)  all_56_11 = e0 & op(e1, e0) = e0
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | ALPHA: (11762) implies:
% 150.68/21.77  | | | | | | | | | | | | | |   (11763)  op(e1, e0) = e0
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | |   (11764)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 150.68/21.77  | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | BETA: splitting (11764) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | |   (11765)  all_56_0 = e1 & op(e3, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | ALPHA: (11765) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | |   (11766)  op(e3, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (142), (159), (161),
% 150.68/21.77  | | | | | | | | | | | | | | | |            (162), (163), (164), (166), (205), (209), (211),
% 150.68/21.77  | | | | | | | | | | | | | | | |            (238), (9977), (9980), (11429), (11430), (11723),
% 150.68/21.77  | | | | | | | | | | | | | | | |            (11724), (11726), (11729), (11737), (11746),
% 150.68/21.77  | | | | | | | | | | | | | | | |            (11747), (11766), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #7.
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | |   (11767)  all_56_2 = e1 & op(e2, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | ALPHA: (11767) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | |   (11768)  op(e2, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | |   (11769)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 150.68/21.77  | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | BETA: splitting (11769) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | |   (11770)  all_56_0 = e1 & op(e3, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | ALPHA: (11770) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | |   (11771)  op(e3, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (142), (159), (161),
% 150.68/21.77  | | | | | | | | | | | | | | | | | |            (162), (163), (164), (166), (205), (209), (211),
% 150.68/21.77  | | | | | | | | | | | | | | | | | |            (238), (9977), (9980), (11429), (11430), (11723),
% 150.68/21.77  | | | | | | | | | | | | | | | | | |            (11724), (11726), (11729), (11737), (11746),
% 150.68/21.77  | | | | | | | | | | | | | | | | | |            (11747), (11771), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #7.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | |   (11772)  all_56_1 = e1 & op(e3, e2) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11731), (11772), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #420.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | |   (11773)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 150.68/21.77  | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | BETA: splitting (11773) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | |   (11774)  all_56_4 = e1 & op(e3, e1) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | ALPHA: (11774) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | |   (11775)  all_56_4 = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | | |   (11776)  op(e3, e1) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | |   (11777)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e3)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (11777) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | |   (11778)  all_56_0 = e3 & op(e3, e3) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | ALPHA: (11778) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | |   (11779)  op(e3, e3) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11718), (11779), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | |   (11780)  all_56_1 = e3 & op(e3, e2) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | ALPHA: (11780) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | |   (11781)  all_56_1 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | |   (11782)  all_54_1 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (11782) imply:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | |   (11783)  all_52_4 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | SIMP: (11783) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | |   (11784)  all_52_4 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (11784) imply:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | |   (11785)   ~ (all_52_8 = e3)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | SIMP: (11785) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | |   (11786)   ~ (all_52_8 = e3)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (208) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | |   (11787)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e2) = e3)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11787) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |   (11788)  all_56_12 = e3 & op(e0, e3) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11743), (11788) are inconsistent by
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #575.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |   (11789)  all_56_13 = e3 & op(e0, e2) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11789) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |   (11790)  all_56_13 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (224), (225), (11723),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |            (11781), (11790), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #877.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | |   (11791)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e0, e0) = e3)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11791) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |   (11792)  all_56_14 = e3 & op(e0, e1) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11792) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |   (11793)  all_56_14 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |   (11794)  op(e0, e1) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | |   (11795)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11795) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (11796)  all_56_4 = e0 & op(e3, e1) = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (11717), (11796), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1130.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (11797)  all_56_5 = e0 & op(e2, e1) = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11797) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | |   (11798)  all_56_5 = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11799)  all_54_8 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (258), (11799) imply:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11800)  all_52_2 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11800) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11801)  all_52_2 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (162), (11801) imply:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11802)  op(e1, e3) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11803)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e3)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11803) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11804)  all_56_2 = e3 & op(e2, e3) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (230), (11718), (11743), (11802),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11804), (function-axioms) are inconsistent by
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #18.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11805)  all_56_3 = e3 & op(e2, e2) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11805) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11806)  op(e2, e2) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11723), (11806), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11807)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 & op(e2, e0) = e3)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11807) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11808)  all_56_5 = e3 & op(e2, e1) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11808) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11809)  all_56_5 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11798), (11809) imply:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11810)  e3 = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (11781), (11810) imply:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11811)  all_56_1 = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (231), (233),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (11718), (11786), (11811),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #492.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11812)  all_56_10 = e3 & op(e2, e0) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11812) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11813)  all_56_10 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11814)  op(e2, e0) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11815)  all_56_15 = e0 & op(e0, e0) = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11815) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11816)  op(e0, e0) = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (157), (158), (168),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (206), (216), (218), (219), (9980), (11426),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11734), (11775), (11776), (11816),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #3.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11817)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11817) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11818)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11819)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11819) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11820)  all_56_1 = e0 & op(e3, e2) = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11820) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11821)  all_56_1 = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (168), (231), (233),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (235), (11718), (11786), (11821),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #492.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11822)  all_56_3 = e0 & op(e2, e2) = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11822) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11823)  op(e2, e2) = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (166), (222), (11768), (11798),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11814), (11823), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #191.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11824)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11824) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11825)  all_56_7 = e0 & op(e1, e2) = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (36), (159), (213), (9980),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11429), (11802), (11825), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #16.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11826)  all_56_13 = e0 & op(e0, e2) = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11826) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11827)  op(e0, e2) = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11714) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11828)   ~ (all_14_0 = e2) & op(all_14_1, e3) = all_14_0 &
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_14_1 & $i(all_14_0) &
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_14_1)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11828) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11829)  op(e3, e0) = all_14_1
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (139), (157), (158),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (168), (206), (221), (222), (229),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (238), (9977), (11430), (11723), (11724),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11743), (11746), (11747), (11763), (11768),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11781), (11786), (11793), (11794), (11798),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11802), (11813), (11814), (11818), (11827),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11829), (function-axioms) are inconsistent by
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11830)   ~ (all_14_1 = e1) & op(e3, e0) = all_14_1 &
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_14_1)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11830) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11831)  op(e3, e0) = all_14_1
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (139), (157), (158),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (164), (166), (168), (206), (221), (222), (229),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (231), (238), (9977), (11430), (11723), (11724),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11743), (11746), (11747), (11763), (11768),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11781), (11786), (11793), (11794), (11798),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11802), (11813), (11814), (11818), (11827),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11831), (function-axioms) are inconsistent by
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #2.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11832)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (258), (9974), (11715), (11730), (11832) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #460.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | |   (11833)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (9980), (11794), (11833),
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | |            #43.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |   (11834)  all_56_15 = e3 & op(e0, e0) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11834) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |   (11835)  op(e0, e0) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11430), (11835), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1022.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | |   (11836)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (11716), (11731), (11732), (11836) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #875.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | |   (11837)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e3)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | BETA: splitting (11837) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | |   (11838)  all_56_4 = e3 & op(e3, e1) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | ALPHA: (11838) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | |   (11839)  op(e3, e1) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (168), (11776), (11839), (function-axioms)
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #439.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | |   (11840)  all_56_9 = e3 & op(e3, e0) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | ALPHA: (11840) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | |   (11841)  op(e3, e0) = e3
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11747), (11841), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #41.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | |   (11842)  all_56_9 = e1 & op(e3, e0) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | ALPHA: (11842) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | | | |   (11843)  all_56_9 = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (205), (210), (211),
% 150.68/21.77  | | | | | | | | | | | | | | | | | |            (11430), (11843), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #496.
% 150.68/21.77  | | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | |   (11844)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 150.68/21.77  | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | BETA: splitting (11844) gives:
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | |   (11845)  all_56_6 = e1 & op(e1, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | ALPHA: (11845) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | |   (11846)  op(e1, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | REF_CLOSE: (162), (11730), (11846), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1046.
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | |   (11847)  all_56_12 = e1 & op(e0, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | ALPHA: (11847) implies:
% 150.68/21.77  | | | | | | | | | | | | | | | |   (11848)  op(e0, e3) = e1
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11426), (11848), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #405.
% 150.68/21.77  | | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | |   (11849)  all_56_10 = e2 & op(e2, e0) = e2
% 150.68/21.77  | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | ALPHA: (11849) implies:
% 150.68/21.77  | | | | | | | | | | | |   (11850)  op(e2, e0) = e2
% 150.68/21.77  | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | | REF_CLOSE: (163), (11737), (11850), (function-axioms) are
% 150.68/21.77  | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 150.68/21.77  | | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | |   (11851)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 150.68/21.77  | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 150.68/21.77  | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | | REF_CLOSE: (6), (159), (9979), (11430), (11851),
% 150.68/21.77  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.77  | | | | | | | | | | |            #5.
% 150.68/21.77  | | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | | 
% 150.68/21.77  | | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | | 
% 150.68/21.77  | | | | | | | | End of split
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | |   (11852)   ~ (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.68/21.77  | | | | | | | |            $i(all_57_14)
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | ALPHA: (11852) implies:
% 150.68/21.77  | | | | | | | |   (11853)   ~ (all_57_14 = e2)
% 150.68/21.77  | | | | | | | |   (11854)  op(e1, e1) = all_57_14
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | REF_CLOSE: (9980), (11853), (11854), (function-axioms) are
% 150.68/21.77  | | | | | | | |            inconsistent by sub-proof #52.
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | End of split
% 150.68/21.77  | | | | | | | 
% 150.68/21.77  | | | | | | End of split
% 150.68/21.77  | | | | | | 
% 150.68/21.77  | | | | | Case 2:
% 150.68/21.77  | | | | | | 
% 150.68/21.77  | | | | | |   (11855)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 &
% 150.68/21.77  | | | | | |                  op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3,
% 150.68/21.77  | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_7 =
% 150.68/21.77  | | | | | |                  e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) &
% 150.68/21.77  | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.77  | | | | | |              ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 =
% 150.68/21.77  | | | | | |                    e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.77  | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 &
% 150.68/21.77  | | | | | |                  op(e3, e0) = e3) | ( ~ (all_57_10 = e0) & op(e3,
% 150.68/21.77  | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_11 =
% 150.68/21.77  | | | | | |                  e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 150.68/21.77  | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.77  | | | | | |              ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 =
% 150.68/21.77  | | | | | |                    e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 150.68/21.77  | | | | | | 
% 150.68/21.77  | | | | | | REF_CLOSE: (4), (6), (36), (9980), (11430), (11855),
% 150.68/21.77  | | | | | |            (function-axioms) are inconsistent by sub-proof #6.
% 150.68/21.77  | | | | | | 
% 150.68/21.77  | | | | | End of split
% 150.68/21.77  | | | | | 
% 150.68/21.77  | | | | End of split
% 150.68/21.77  | | | | 
% 150.68/21.77  | | | End of split
% 150.68/21.77  | | | 
% 150.68/21.77  | | Case 2:
% 150.68/21.77  | | | 
% 150.68/21.77  | | |   (11856)  all_6_2 = e3
% 150.68/21.77  | | |   (11857)  ( ~ (all_6_0 = e1) & op(all_6_1, e2) = all_6_0 & op(e2, e3) =
% 150.68/21.77  | | |              all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) &
% 150.68/21.77  | | |              op(e2, e3) = all_6_1 & $i(all_6_1))
% 150.68/21.77  | | | 
% 150.68/21.77  | | | COMBINE_EQS: (330), (11856) imply:
% 150.68/21.77  | | |   (11858)  all_26_2 = e3
% 150.68/21.77  | | | 
% 150.68/21.77  | | | REDUCE: (347), (11856) imply:
% 150.68/21.77  | | |   (11859)   ~ (all_52_1 = e3)
% 150.68/21.77  | | | 
% 150.68/21.77  | | | REDUCE: (350), (11856) imply:
% 150.68/21.77  | | |   (11860)   ~ (all_52_4 = e3)
% 150.68/21.77  | | | 
% 150.68/21.77  | | | REDUCE: (352), (11856) imply:
% 150.68/21.77  | | |   (11861)   ~ (all_52_6 = e3)
% 150.68/21.77  | | | 
% 150.68/21.77  | | | REDUCE: (354), (11856) imply:
% 150.68/21.77  | | |   (11862)   ~ (all_52_7 = e3)
% 150.68/21.77  | | | 
% 150.68/21.77  | | | REDUCE: (356), (11856) imply:
% 150.68/21.77  | | |   (11863)   ~ (all_52_9 = e3)
% 150.68/21.77  | | | 
% 150.68/21.77  | | | REDUCE: (358), (11856) imply:
% 150.68/21.77  | | |   (11864)   ~ (all_52_13 = e3)
% 150.68/21.77  | | | 
% 150.68/21.77  | | | REDUCE: (39), (11856) imply:
% 150.68/21.77  | | |   (11865)  op(e2, e2) = e3
% 150.68/21.77  | | | 
% 150.68/21.77  | | | BETA: splitting (46) gives:
% 150.68/21.77  | | | 
% 150.68/21.77  | | | Case 1:
% 150.68/21.77  | | | | 
% 150.68/21.77  | | | |   (11866)   ~ (all_10_2 = e1)
% 150.68/21.77  | | | | 
% 150.68/21.77  | | | | BETA: splitting (52) gives:
% 150.68/21.77  | | | | 
% 150.68/21.77  | | | | Case 1:
% 150.68/21.77  | | | | | 
% 150.68/21.77  | | | | |   (11867)   ~ (all_14_2 = e0)
% 150.68/21.77  | | | | | 
% 150.68/21.77  | | | | | BETA: splitting (64) gives:
% 150.68/21.77  | | | | | 
% 150.68/21.77  | | | | | Case 1:
% 150.68/21.77  | | | | | | 
% 150.68/21.77  | | | | | |   (11868)   ~ (all_22_2 = e1)
% 150.68/21.77  | | | | | | 
% 150.68/21.77  | | | | | | REDUCE: (320), (11868) imply:
% 150.68/21.77  | | | | | |   (11869)   ~ (all_14_2 = e1)
% 150.68/21.77  | | | | | | 
% 150.68/21.77  | | | | | | BETA: splitting (67) gives:
% 150.68/21.77  | | | | | | 
% 150.68/21.77  | | | | | | Case 1:
% 150.68/21.77  | | | | | | | 
% 150.68/21.77  | | | | | | |   (11870)   ~ (all_24_2 = e2)
% 150.68/21.77  | | | | | | | 
% 150.68/21.77  | | | | | | | REDUCE: (318), (11870) imply:
% 150.68/21.77  | | | | | | |   (11871)   ~ (all_10_2 = e2)
% 150.68/21.77  | | | | | | | 
% 150.68/21.77  | | | | | | | BETA: splitting (70) gives:
% 150.68/21.77  | | | | | | | 
% 150.68/21.77  | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | |   (11872)   ~ (all_26_2 = e3)
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | REDUCE: (11858), (11872) imply:
% 150.68/21.77  | | | | | | | |   (11873)  $false
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | CLOSE: (11873) is inconsistent.
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | Case 2:
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | |   (11874)  ( ~ (all_26_0 = e0) & op(all_26_1, e2) = all_26_0 &
% 150.68/21.77  | | | | | | | |              op(e2, e3) = all_26_1 & $i(all_26_0) &
% 150.68/21.77  | | | | | | | |              $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e2, e3) =
% 150.68/21.77  | | | | | | | |              all_26_1 & $i(all_26_1))
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | BETA: splitting (84) gives:
% 150.68/21.77  | | | | | | | | 
% 150.68/21.77  | | | | | | | | Case 1:
% 150.68/21.77  | | | | | | | | | 
% 150.68/21.78  | | | | | | | | |   (11875)   ~ (all_36_2 = e2)
% 150.68/21.78  | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | REDUCE: (304), (11875) imply:
% 150.68/21.78  | | | | | | | | |   (11876)   ~ (all_14_2 = e2)
% 150.68/21.78  | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | BETA: splitting (203) gives:
% 150.68/21.78  | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | |   (11877)  all_54_0 = e3
% 150.68/21.78  | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | COMBINE_EQS: (278), (11877) imply:
% 150.68/21.78  | | | | | | | | | |   (11878)  all_14_2 = e3
% 150.68/21.78  | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | SIMP: (11878) implies:
% 150.68/21.78  | | | | | | | | | |   (11879)  all_14_2 = e3
% 150.68/21.78  | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | REDUCE: (338), (11879) imply:
% 150.68/21.78  | | | | | | | | | |   (11880)   ~ (all_52_2 = e3)
% 150.68/21.78  | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | REDUCE: (344), (11879) imply:
% 150.68/21.78  | | | | | | | | | |   (11881)   ~ (all_52_8 = e3)
% 150.68/21.78  | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | REDUCE: (51), (11879) imply:
% 150.68/21.78  | | | | | | | | | |   (11882)  op(e3, e3) = e3
% 150.68/21.78  | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | BETA: splitting (219) gives:
% 150.68/21.78  | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | |   (11883)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 150.68/21.78  | | | | | | | | | | |              & op(e2, e1) = e3)
% 150.68/21.78  | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | REF_CLOSE: (164), (168), (11863), (11881), (11883),
% 150.68/21.78  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.78  | | | | | | | | | | |            #369.
% 150.68/21.78  | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | |   (11884)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 150.68/21.78  | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 150.68/21.78  | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | BETA: splitting (11884) gives:
% 150.68/21.78  | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | |   (11885)  all_56_8 = e3 & op(e1, e1) = e3
% 150.68/21.78  | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | ALPHA: (11885) implies:
% 150.68/21.78  | | | | | | | | | | | |   (11886)  op(e1, e1) = e3
% 150.68/21.78  | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | REF_CLOSE: (9), (9980), (11886), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 150.68/21.78  | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | |   (11887)  all_56_14 = e3 & op(e0, e1) = e3
% 150.68/21.78  | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | ALPHA: (11887) implies:
% 150.68/21.78  | | | | | | | | | | | |   (11888)  all_56_14 = e3
% 150.68/21.78  | | | | | | | | | | | |   (11889)  op(e0, e1) = e3
% 150.68/21.78  | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | BETA: splitting (215) gives:
% 150.68/21.78  | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | |   (11890)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 150.68/21.78  | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 150.68/21.78  | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | BETA: splitting (11890) gives:
% 150.68/21.78  | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | |   (11891)  all_56_6 = e3 & op(e1, e3) = e3
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | REF_CLOSE: (162), (11880), (11891), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | |            inconsistent by sub-proof #132.
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | |   (11892)  all_56_7 = e3 & op(e1, e2) = e3
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | REF_CLOSE: (161), (11861), (11892), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | |   (11893)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 150.68/21.78  | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 150.68/21.78  | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | BETA: splitting (11893) gives:
% 150.68/21.78  | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | |   (11894)  all_56_8 = e3 & op(e1, e1) = e3
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | ALPHA: (11894) implies:
% 150.68/21.78  | | | | | | | | | | | | | |   (11895)  op(e1, e1) = e3
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | REF_CLOSE: (9), (9980), (11895), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | |   (11896)  all_56_11 = e3 & op(e1, e0) = e3
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | ALPHA: (11896) implies:
% 150.68/21.78  | | | | | | | | | | | | | |   (11897)  op(e1, e0) = e3
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 150.68/21.78  | | | | | | | | | | | | | |              e3, e1, e0, simplifying with (156), (11889) gives:
% 150.68/21.78  | | | | | | | | | | | | | |   (11898)  all_52_11 = e3
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 150.68/21.78  | | | | | | | | | | | | | |              e3, e0, e1, simplifying with (159), (11897) gives:
% 150.68/21.78  | | | | | | | | | | | | | |   (11899)  all_52_14 = e3
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | REDUCE: (111), (11899) imply:
% 150.68/21.78  | | | | | | | | | | | | | |   (11900)   ~ (all_52_12 = e3)
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | REDUCE: (370), (11899) imply:
% 150.68/21.78  | | | | | | | | | | | | | |   (11901)   ~ (all_10_2 = e3)
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | SIMP: (11901) implies:
% 150.68/21.78  | | | | | | | | | | | | | |   (11902)   ~ (all_10_2 = e3)
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 150.68/21.78  | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | |   (11903)  all_54_15 = e3
% 150.68/21.78  | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | REF_CLOSE: (245), (11902), (11903) are inconsistent by
% 150.68/21.78  | | | | | | | | | | | | | | |            sub-proof #1049.
% 150.68/21.78  | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | |   (11904)   ~ (all_54_15 = e3)
% 150.68/21.78  | | | | | | | | | | | | | | |   (11905)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 150.68/21.78  | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | BETA: splitting (11905) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | |   (11906)  all_54_15 = e2
% 150.68/21.78  | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | REF_CLOSE: (245), (11871), (11906) are inconsistent by
% 150.68/21.78  | | | | | | | | | | | | | | | |            sub-proof #1048.
% 150.68/21.78  | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | |   (11907)   ~ (all_54_15 = e2)
% 150.68/21.78  | | | | | | | | | | | | | | | |   (11908)  all_54_15 = e1 | all_54_15 = e0
% 150.68/21.78  | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | BETA: splitting (11908) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | |   (11909)  all_54_15 = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | REF_CLOSE: (245), (11866), (11909) are inconsistent by
% 150.68/21.78  | | | | | | | | | | | | | | | | |            sub-proof #1047.
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | |   (11910)  all_54_15 = e0
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | COMBINE_EQS: (245), (11910) imply:
% 150.68/21.78  | | | | | | | | | | | | | | | | |   (11911)  all_10_2 = e0
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | SIMP: (11911) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | |   (11912)  all_10_2 = e0
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | REDUCE: (349), (11912) imply:
% 150.68/21.78  | | | | | | | | | | | | | | | | |   (11913)   ~ (all_52_3 = e0)
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | REDUCE: (11902), (11912) imply:
% 150.68/21.78  | | | | | | | | | | | | | | | | |   (11914)   ~ (e3 = e0)
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | REDUCE: (11871), (11912) imply:
% 150.68/21.78  | | | | | | | | | | | | | | | | |   (11915)   ~ (e2 = e0)
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | REDUCE: (11866), (11912) imply:
% 150.68/21.78  | | | | | | | | | | | | | | | | |   (11916)   ~ (e1 = e0)
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | REDUCE: (45), (11912) imply:
% 150.68/21.78  | | | | | | | | | | | | | | | | |   (11917)  op(e0, e0) = e0
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | |   (11918)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.78  | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.78  | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.68/21.78  | | | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.68/21.78  | | | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.68/21.78  | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | BETA: splitting (11918) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |   (11919)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | BETA: splitting (11919) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |   (11920)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11920) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11921)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11921) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11922)  op(e1, e1) = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9980), (11922), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11923)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11923) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11924)  op(e0, e0) = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (245), (11866), (11902), (11908), (11924),
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            #703.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |   (11925)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11925) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11926)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11926) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11927)  all_57_12 = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11928)   ~ (all_57_0 = e2)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11929)  op(e1, e3) = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |   (11930)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11930) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |   (11931)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11931) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |   (11932)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                = e3) & op(e2, e2) = all_57_12 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11927), (11928), (11932) are inconsistent by
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #832.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |   (11933)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11933) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |   (11934)  op(e2, e2) = e2
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11865), (11934), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1179.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |   (11935)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11935) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |   (11936)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11936) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |   (11937)  op(e1, e1) = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (11937), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |   (11938)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14)))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11938) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |   (11939)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |                = e0) & op(e3, e3) = all_57_10 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11939) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (11940)  all_57_9 = e3 & op(e3, e0) = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11940) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (11941)  op(e3, e0) = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (11900), (11941), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1082.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (11942)   ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11942) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (11943)   ~ (all_57_10 = e0)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (11944)  op(e3, e3) = all_57_10
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (11929) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (11945)  all_52_2 = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10, e3, e3, simplifying with (11882),
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |              (11944) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (11946)  all_57_10 = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (11945) imply:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (11947)   ~ (all_52_3 = e1)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (11947) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (11948)   ~ (all_52_3 = e1)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (11880), (11945) imply:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | |   (11949)   ~ (e3 = e1)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (11950)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11950) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11951)  all_56_12 = e1 & op(e0, e3) = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11951) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11952)  op(e0, e3) = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (11948), (11952), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #405.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11953)  all_56_13 = e1 & op(e0, e2) = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11953) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11954)  op(e0, e2) = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11955)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e3) = e0)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11955) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11956)  all_56_0 = e0 & op(e3, e3) = e0
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11956) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11957)  op(e3, e3) = e0
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11882), (11957), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1141.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11958)  all_56_2 = e0 & op(e2, e3) = e0
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11857), (11874), (11954), (11958),
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #95.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (11959)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e3) = e0)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (158), (162), (11913), (11929), (11959),
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #669.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |   (11960)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e0) = e1)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11960) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11961)  all_56_14 = e1 & op(e0, e1) = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11888), (11961) are inconsistent by
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #188.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11962)  all_56_15 = e1 & op(e0, e0) = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11962) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | |   (11963)  op(e0, e0) = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11917), (11963), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11964)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11964) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11965)  op(e0, e0) = e3
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (245), (11866), (11902), (11908), (11965),
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            #703.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |   (11966)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | BETA: splitting (11966) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |   (11967)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11860), (11967), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |   (11968)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11968) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11969)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11969) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11970)  op(e3, e3) = e2
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11882), (11970), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1085.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |   (11971)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11971) gives:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |   (11972)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11972) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |   (11973)  op(e0, e0) = e2
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11917), (11973), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |   (11974)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11974) implies:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |   (11975)  op(e2, e2) = e1
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (45), (156), (157),
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            (158), (164), (167), (168), (169), (238), (245),
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            (349), (360), (367), (9977), (9980), (11860),
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            (11866), (11871), (11881), (11882), (11900),
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            (11902), (11905), (11975), (function-axioms) are
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #37.
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.78  | | | | | | | | | | | | | | | | | | 
% 150.68/21.78  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.78  | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | |   (11976)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.68/21.79  | | | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | BETA: splitting (11976) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (11977)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | BETA: splitting (11977) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |   (11978)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (9977), (11881), (11978),
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |            #1083.
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |   (11979)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (11900), (11917), (11979),
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |            #859.
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (11980)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | BETA: splitting (11980) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |   (11981)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11882), (11981), (function-axioms) are
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |   (11982)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | BETA: splitting (11982) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |   (11983)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (11983) implies:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |   (11984)  op(e1, e1) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9980), (11984), (function-axioms) are
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |   (11985)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11985) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |   (11986)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11986) implies:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |   (11987)  op(e2, e2) = e0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11865), (11987), (function-axioms) are
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |   (11988)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (11988) implies:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |   (11989)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (156), (157), (158), (245), (349), (360),
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |            (367), (11866), (11882), (11908), (11989),
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |            #38.
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | |   (11990)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 150.68/21.79  | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | REF_CLOSE: (278), (11867), (11869), (11876), (11990) are
% 150.68/21.79  | | | | | | | | | |            inconsistent by sub-proof #1140.
% 150.68/21.79  | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | 
% 150.68/21.79  | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | 
% 150.68/21.79  | | | | | | | | |   (11991)  all_36_2 = e2
% 150.68/21.79  | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | COMBINE_EQS: (304), (11991) imply:
% 150.68/21.79  | | | | | | | | |   (11992)  all_14_2 = e2
% 150.68/21.79  | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | SIMP: (11992) implies:
% 150.68/21.79  | | | | | | | | |   (11993)  all_14_2 = e2
% 150.68/21.79  | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | REDUCE: (336), (11993) imply:
% 150.68/21.79  | | | | | | | | |   (11994)   ~ (all_52_1 = e2)
% 150.68/21.79  | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | REDUCE: (51), (11993) imply:
% 150.68/21.79  | | | | | | | | |   (11995)  op(e3, e3) = e2
% 150.68/21.79  | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | BETA: splitting (207) gives:
% 150.68/21.79  | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | |   (11996)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 150.68/21.79  | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 150.68/21.79  | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | BETA: splitting (11996) gives:
% 150.68/21.79  | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | |   (11997)  all_56_12 = e2 & op(e0, e3) = e2
% 150.68/21.79  | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | ALPHA: (11997) implies:
% 150.68/21.79  | | | | | | | | | | |   (11998)  all_56_12 = e2
% 150.68/21.79  | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (230), (234),
% 150.68/21.79  | | | | | | | | | | |            (11995), (11998), (function-axioms) are
% 150.68/21.79  | | | | | | | | | | |            inconsistent by sub-proof #781.
% 150.68/21.79  | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | |   (11999)  all_56_13 = e2 & op(e0, e2) = e2
% 150.68/21.79  | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | ALPHA: (11999) implies:
% 150.68/21.79  | | | | | | | | | | |   (12000)  all_56_13 = e2
% 150.68/21.79  | | | | | | | | | | |   (12001)  op(e0, e2) = e2
% 150.68/21.79  | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | BETA: splitting (237) gives:
% 150.68/21.79  | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | |   (12002)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.68/21.79  | | | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.68/21.79  | | | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.79  | | | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.68/21.79  | | | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.68/21.79  | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.68/21.79  | | | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.68/21.79  | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.79  | | | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.68/21.79  | | | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.68/21.79  | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.79  | | | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.68/21.79  | | | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.68/21.79  | | | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.68/21.79  | | | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.68/21.79  | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.79  | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (224), (225), (227),
% 150.68/21.79  | | | | | | | | | | | |            (11995), (12000), (12002), (function-axioms) are
% 150.68/21.79  | | | | | | | | | | | |            inconsistent by sub-proof #34.
% 150.68/21.79  | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | |   (12003)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.68/21.79  | | | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.68/21.79  | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.79  | | | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.68/21.79  | | | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.79  | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.68/21.79  | | | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.68/21.79  | | | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.79  | | | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.68/21.79  | | | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.68/21.79  | | | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.79  | | | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.68/21.79  | | | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.68/21.79  | | | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.68/21.79  | | | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.68/21.79  | | | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.68/21.79  | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | BETA: splitting (12003) gives:
% 150.68/21.79  | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | |   (12004)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3
% 150.68/21.79  | | | | | | | | | | | | |                & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) &
% 150.68/21.79  | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.79  | | | | | | | | | | | | |            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.68/21.79  | | | | | | | | | | | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.79  | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1)
% 150.68/21.79  | | | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 150.68/21.79  | | | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.68/21.79  | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | ALPHA: (12004) implies:
% 150.68/21.79  | | | | | | | | | | | | |   (12005)  op(e1, e1) = e1
% 150.68/21.79  | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | REF_CLOSE: (6), (36), (9980), (12005), (function-axioms) are
% 150.68/21.79  | | | | | | | | | | | | |            inconsistent by sub-proof #1044.
% 150.68/21.79  | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | |   (12006)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3
% 150.68/21.79  | | | | | | | | | | | | |                & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) &
% 150.68/21.79  | | | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.79  | | | | | | | | | | | | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.68/21.79  | | | | | | | | | | | | |                (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.68/21.79  | | | | | | | | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.68/21.79  | | | | | | | | | | | | |                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.68/21.79  | | | | | | | | | | | | |                  e1) = all_57_14 & $i(all_57_14)))
% 150.68/21.79  | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | ALPHA: (12006) implies:
% 150.68/21.79  | | | | | | | | | | | | |   (12007)  all_57_15 = e0
% 150.68/21.79  | | | | | | | | | | | | |   (12008)  op(e0, e0) = e0
% 150.68/21.79  | | | | | | | | | | | | |   (12009)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~
% 150.68/21.79  | | | | | | | | | | | | |              (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.68/21.79  | | | | | | | | | | | | |              $i(all_57_14))
% 150.68/21.79  | | | | | | | | | | | | |   (12010)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.68/21.79  | | | | | | | | | | | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.68/21.79  | | | | | | | | | | | | |              $i(all_57_12))
% 150.68/21.79  | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | BETA: splitting (222) gives:
% 150.68/21.79  | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | |   (12011)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 150.68/21.79  | | | | | | | | | | | | | |              & op(e2, e2) = e2)
% 150.68/21.79  | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (166), (224), (225),
% 150.68/21.79  | | | | | | | | | | | | | |            (227), (11994), (12000), (12011),
% 150.68/21.79  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.79  | | | | | | | | | | | | | |            #35.
% 150.68/21.79  | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | |   (12012)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 150.68/21.79  | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 150.68/21.79  | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | BETA: splitting (12012) gives:
% 150.68/21.79  | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | |   (12013)  all_56_5 = e2 & op(e2, e1) = e2
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | ALPHA: (12013) implies:
% 150.68/21.79  | | | | | | | | | | | | | | |   (12014)  op(e2, e1) = e2
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | REF_CLOSE: (164), (9977), (12014), (function-axioms) are
% 150.68/21.79  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | |   (12015)  all_56_10 = e2 & op(e2, e0) = e2
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | ALPHA: (12015) implies:
% 150.68/21.79  | | | | | | | | | | | | | | |   (12016)  op(e2, e0) = e2
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 150.68/21.79  | | | | | | | | | | | | | | |              e0, e0, simplifying with (45), (12008) gives:
% 150.68/21.79  | | | | | | | | | | | | | | |   (12017)  all_10_2 = e0
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e2,
% 150.68/21.79  | | | | | | | | | | | | | | |              e2, e0, simplifying with (157), (12001) gives:
% 150.68/21.79  | | | | | | | | | | | | | | |   (12018)  all_52_7 = e2
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 150.68/21.79  | | | | | | | | | | | | | | |              e2, e0, e2, simplifying with (163), (12016) gives:
% 150.68/21.79  | | | | | | | | | | | | | | |   (12019)  all_52_13 = e2
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | REDUCE: (139), (12018) imply:
% 150.68/21.79  | | | | | | | | | | | | | | |   (12020)   ~ (all_52_3 = e2)
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | REDUCE: (349), (12017) imply:
% 150.68/21.79  | | | | | | | | | | | | | | |   (12021)   ~ (all_52_3 = e0)
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | REDUCE: (124), (12018) imply:
% 150.68/21.79  | | | | | | | | | | | | | | |   (12022)   ~ (all_52_11 = e2)
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | REDUCE: (367), (12017) imply:
% 150.68/21.79  | | | | | | | | | | | | | | |   (12023)   ~ (all_52_11 = e0)
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | REDUCE: (11871), (12017) imply:
% 150.68/21.79  | | | | | | | | | | | | | | |   (12024)   ~ (e2 = e0)
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | REDUCE: (11866), (12017) imply:
% 150.68/21.79  | | | | | | | | | | | | | | |   (12025)   ~ (e1 = e0)
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | |   (12026)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.79  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.79  | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.79  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.79  | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.79  | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.79  | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.79  | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.79  | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.68/21.79  | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.68/21.79  | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.79  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.68/21.79  | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.68/21.79  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.68/21.79  | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.68/21.79  | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.68/21.79  | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.68/21.79  | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.68/21.79  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.68/21.79  | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.79  | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.79  | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.79  | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.79  | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | BETA: splitting (12026) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | |   (12027)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.79  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.79  | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.79  | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.79  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.79  | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.79  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.79  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.79  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.79  | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.79  | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.79  | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.79  | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.79  | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | BETA: splitting (12027) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | |   (12028)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.79  | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (11994), (12028), (function-axioms) are
% 150.68/21.79  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1180.
% 150.68/21.79  | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | |   (12029)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.79  | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | BETA: splitting (12029) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12030)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | ALPHA: (12030) implies:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12031)   ~ (all_57_14 = e3)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12032)  op(e1, e1) = all_57_14
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12033)  op(e1, e3) = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12034)  op(e2, e3) = all_57_0
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              all_57_14, e1, e1, simplifying with (9980),
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              (12032) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12035)  all_57_14 = e2
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              e3, e1, simplifying with (162), (12033) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12036)  all_52_2 = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              all_57_0, e3, e2, simplifying with (166), (12034)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |              gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12037)  all_57_0 = all_52_1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | REDUCE: (12031), (12035) imply:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12038)   ~ (e3 = e2)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | REDUCE: (148), (12036) imply:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12039)   ~ (all_52_1 = e1)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | REDUCE: (143), (12036) imply:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12040)   ~ (all_52_3 = e1)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | SIMP: (12040) implies:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12041)   ~ (all_52_3 = e1)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | REDUCE: (142), (12036) imply:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12042)   ~ (all_52_6 = e1)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | SIMP: (12042) implies:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12043)   ~ (all_52_6 = e1)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | REDUCE: (9974), (12036) imply:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | |   (12044)   ~ (e2 = e1)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |   (12045)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12045) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |   (12046)  all_56_1 = e1 & op(e3, e2) = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12046) implies:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | |   (12047)  all_56_1 = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |   (12048)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12048) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | |   (12049)  all_56_2 = e1 & op(e2, e3) = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12049) implies:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | |   (12050)  op(e2, e3) = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (166), (12039), (12050), (function-axioms) are
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1177.
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | |   (12051)  all_56_3 = e1 & op(e2, e2) = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12051) implies:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | |   (12052)  all_56_3 = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (161), (227), (11861), (12000), (12047),
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | |            (12052), (function-axioms) are inconsistent by
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #269.
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |   (12053)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12053) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | |   (12054)  all_56_5 = e1 & op(e2, e1) = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12054) implies:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | |   (12055)  op(e2, e1) = e1
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | |   (12056)  all_54_12 = e3
% 150.68/21.79  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (12056) imply:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | |   (12057)  all_52_3 = e3
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12057) implies:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | |   (12058)  all_52_3 = e3
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (138), (12058) imply:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | |   (12059)   ~ (all_52_11 = e3)
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12059) implies:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | |   (12060)   ~ (all_52_11 = e3)
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (12061)  all_54_14 = e3
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (12060), (12061) are inconsistent by
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #903.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | |   (12062)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12062) gives:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12063)  all_54_14 = e2
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (9978), (12063) are inconsistent by
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #902.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12064)  all_54_14 = e1 | all_54_14 = e0
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12064) gives:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12065)  all_54_14 = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (12065) imply:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12066)  all_52_11 = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (12066) implies:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12067)  all_52_11 = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (12067) imply:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12068)   ~ (all_52_9 = e1)
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (12055), (12068), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #704.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12069)  all_54_14 = e0
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (12023), (12069) are inconsistent by
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #886.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | |   (12070)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (12020), (12021), (12041), (12070) are
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #881.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | |   (12071)  all_56_10 = e1 & op(e2, e0) = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12071) implies:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | |   (12072)  op(e2, e0) = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (163), (12016), (12072), (function-axioms)
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #904.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | |   (12073)  all_56_3 = e1 & op(e2, e2) = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12073) implies:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | |   (12074)  op(e2, e2) = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11865), (12074), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | |   (12075)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | |              e1 & op(e0, e2) = e1)
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12075) gives:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | |   (12076)  all_56_7 = e1 & op(e1, e2) = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12076) implies:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | |   (12077)  op(e1, e2) = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (161), (12043), (12077), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1042.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | |   (12078)  all_56_13 = e1 & op(e0, e2) = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12078) implies:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | |   (12079)  all_56_13 = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12000), (12079) are inconsistent by
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1110.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |   (12080)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | ALPHA: (12080) implies:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |   (12081)  op(e0, e0) = e3
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12008), (12081), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | |   (12082)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.80  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.80  | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.80  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.80  | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.80  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.80  | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.80  | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.80  | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.68/21.80  | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.68/21.80  | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.80  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.80  | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.68/21.80  | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.80  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.80  | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.68/21.80  | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | BETA: splitting (12082) gives:
% 150.68/21.80  | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | |   (12083)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.80  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.68/21.80  | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11860), (12083), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | |   (12084)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.68/21.80  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.68/21.80  | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.80  | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.80  | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | BETA: splitting (12084) gives:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |   (12085)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | ALPHA: (12085) implies:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |   (12086)   ~ (all_57_14 = e2)
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |   (12087)  op(e1, e1) = all_57_14
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9980), (12086), (12087), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #52.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |   (12088)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (11865), (12008), (12088),
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.80  | | | | | | | | | | | | | | | | | | |            #130.
% 150.68/21.80  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | |   (12089)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.80  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.80  | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.80  | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.80  | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.80  | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.80  | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.80  | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.80  | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.80  | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.80  | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.80  | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.80  | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.80  | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.80  | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.80  | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.80  | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.80  | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.80  | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.68/21.80  | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.68/21.80  | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.68/21.80  | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.68/21.80  | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.68/21.80  | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.68/21.80  | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.68/21.80  | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.68/21.80  | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.68/21.80  | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.68/21.80  | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.80  | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.80  | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.80  | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.68/21.80  | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.68/21.80  | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.80  | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.68/21.80  | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.68/21.80  | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.68/21.80  | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.68/21.80  | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.80  | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.80  | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.80  | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.80  | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.80  | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.80  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.80  | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.80  | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.80  | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.80  | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.80  | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.80  | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.80  | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.80  | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.80  | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.80  | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (116), (156), (158), (163), (164),
% 150.68/21.80  | | | | | | | | | | | | | | | |            (11995), (12001), (12007), (12008), (12009),
% 150.68/21.80  | | | | | | | | | | | | | | | |            (12010), (12016), (12021), (12023), (12089),
% 150.68/21.80  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.80  | | | | | | | | | | | | | | | |            #30.
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | |   (12090)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 150.68/21.80  | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 150.68/21.80  | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | REF_CLOSE: (45), (156), (9978), (11871), (12090),
% 150.68/21.80  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.80  | | | | | | | | | |            #49.
% 150.68/21.80  | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | 
% 150.68/21.80  | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | 
% 150.68/21.80  | | | | | | | End of split
% 150.68/21.80  | | | | | | | 
% 150.68/21.80  | | | | | | Case 2:
% 150.68/21.80  | | | | | | | 
% 150.68/21.80  | | | | | | |   (12091)  all_24_2 = e2
% 150.68/21.80  | | | | | | | 
% 150.68/21.80  | | | | | | | COMBINE_EQS: (318), (12091) imply:
% 150.68/21.80  | | | | | | |   (12092)  all_10_2 = e2
% 150.68/21.80  | | | | | | | 
% 150.68/21.80  | | | | | | | SIMP: (12092) implies:
% 150.68/21.80  | | | | | | |   (12093)  all_10_2 = e2
% 150.68/21.80  | | | | | | | 
% 150.68/21.80  | | | | | | | REDUCE: (360), (12093) imply:
% 150.68/21.80  | | | | | | |   (12094)   ~ (all_52_7 = e2)
% 150.68/21.80  | | | | | | | 
% 150.68/21.80  | | | | | | | REDUCE: (369), (12093) imply:
% 150.68/21.80  | | | | | | |   (12095)   ~ (all_52_13 = e2)
% 150.68/21.80  | | | | | | | 
% 150.68/21.80  | | | | | | | REDUCE: (45), (12093) imply:
% 150.68/21.80  | | | | | | |   (12096)  op(e0, e0) = e2
% 150.68/21.80  | | | | | | | 
% 150.68/21.80  | | | | | | | BETA: splitting (226) gives:
% 150.68/21.80  | | | | | | | 
% 150.68/21.80  | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | 
% 150.68/21.80  | | | | | | | |   (12097)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 &
% 150.68/21.80  | | | | | | | |              op(e2, e2) = e2)
% 150.68/21.80  | | | | | | | | 
% 150.68/21.80  | | | | | | | | BETA: splitting (12097) gives:
% 150.68/21.80  | | | | | | | | 
% 150.68/21.80  | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | 
% 150.68/21.80  | | | | | | | | |   (12098)  all_56_1 = e2 & op(e3, e2) = e2
% 150.68/21.80  | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | ALPHA: (12098) implies:
% 150.68/21.80  | | | | | | | | |   (12099)  all_56_1 = e2
% 150.68/21.80  | | | | | | | | |   (12100)  op(e3, e2) = e2
% 150.68/21.80  | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | BETA: splitting (237) gives:
% 150.68/21.80  | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | |   (12101)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 =
% 150.68/21.80  | | | | | | | | | |                  e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.68/21.80  | | | | | | | | | |                  & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.80  | | | | | | | | | |              ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.68/21.80  | | | | | | | | | |                  (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.68/21.80  | | | | | | | | | |                  $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 150.68/21.80  | | | | | | | | | |                    e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.68/21.80  | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.80  | | | | | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 =
% 150.68/21.80  | | | | | | | | | |                  e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2)
% 150.68/21.80  | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.80  | | | | | | | | | |              ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.68/21.80  | | | | | | | | | |                  (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.68/21.80  | | | | | | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.68/21.80  | | | | | | | | | |                    e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.68/21.80  | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.80  | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | BETA: splitting (12101) gives:
% 150.68/21.80  | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | |   (12102)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2
% 150.68/21.80  | | | | | | | | | | |                & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) &
% 150.68/21.80  | | | | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.80  | | | | | | | | | | |            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.68/21.80  | | | | | | | | | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 150.68/21.80  | | | | | | | | | | |                $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3)
% 150.68/21.80  | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 150.68/21.80  | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.68/21.80  | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | ALPHA: (12102) implies:
% 150.68/21.80  | | | | | | | | | | |   (12103)  op(e3, e3) = e3
% 150.68/21.80  | | | | | | | | | | |   (12104)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14
% 150.68/21.80  | | | | | | | | | | |                = e3) & op(e1, e1) = all_57_14 &
% 150.68/21.80  | | | | | | | | | | |              $i(all_57_14))
% 150.68/21.80  | | | | | | | | | | |   (12105)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12
% 150.68/21.80  | | | | | | | | | | |                = e3) & op(e2, e2) = all_57_12 &
% 150.68/21.80  | | | | | | | | | | |              $i(all_57_12))
% 150.68/21.80  | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | BETA: splitting (238) gives:
% 150.68/21.80  | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | |   (12106)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.80  | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.80  | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.80  | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.80  | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.80  | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.80  | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.80  | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.80  | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.80  | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.80  | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.80  | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.80  | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.80  | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.80  | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.68/21.80  | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.68/21.80  | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.68/21.80  | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.68/21.80  | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.68/21.80  | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.80  | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.68/21.80  | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.68/21.80  | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.68/21.80  | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.68/21.80  | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.68/21.80  | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.80  | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.68/21.80  | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.68/21.80  | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.68/21.80  | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.68/21.80  | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.68/21.80  | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.80  | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.80  | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.80  | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.80  | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | BETA: splitting (12106) gives:
% 150.68/21.80  | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | |   (12107)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.80  | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.80  | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.80  | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.80  | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.80  | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.80  | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.80  | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.80  | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.80  | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.80  | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.80  | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.80  | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.80  | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.80  | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.80  | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | BETA: splitting (12107) gives:
% 150.68/21.80  | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | |   (12108)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.80  | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.80  | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.80  | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | BETA: splitting (12108) gives:
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | |   (12109)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.80  | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.80  | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | ALPHA: (12109) implies:
% 150.68/21.80  | | | | | | | | | | | | | | |   (12110)   ~ (all_57_1 = e1)
% 150.68/21.80  | | | | | | | | | | | | | | |   (12111)  op(e1, e1) = e3
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | REF_CLOSE: (12104), (12110), (12111), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | | |            inconsistent by sub-proof #815.
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | |   (12112)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.80  | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.80  | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | ALPHA: (12112) implies:
% 150.68/21.80  | | | | | | | | | | | | | | |   (12113)  op(e0, e0) = e3
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (12113), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | |   (12114)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.80  | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.80  | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.80  | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.80  | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.80  | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | BETA: splitting (12114) gives:
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | |   (12115)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.80  | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.80  | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.80  | | | | | | | | | | | | | | |            $i(all_57_14)
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | ALPHA: (12115) implies:
% 150.68/21.80  | | | | | | | | | | | | | | |   (12116)  all_57_12 = e3
% 150.68/21.80  | | | | | | | | | | | | | | |   (12117)   ~ (all_57_0 = e2)
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | REF_CLOSE: (12105), (12116), (12117) are inconsistent by
% 150.68/21.80  | | | | | | | | | | | | | | |            sub-proof #832.
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | |   (12118)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.80  | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 150.68/21.80  | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | ALPHA: (12118) implies:
% 150.68/21.80  | | | | | | | | | | | | | | |   (12119)  op(e0, e0) = e3
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | REF_CLOSE: (9), (12096), (12119), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1087.
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | |   (12120)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.80  | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.80  | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.80  | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.80  | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.80  | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.80  | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.80  | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.68/21.80  | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.80  | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.80  | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.68/21.80  | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.68/21.80  | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.80  | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.80  | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.80  | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.68/21.80  | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.80  | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.80  | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.80  | | | | | | | | | | | | |              $i(all_57_10))
% 150.68/21.80  | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | BETA: splitting (12120) gives:
% 150.68/21.80  | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | |   (12121)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.80  | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.80  | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.80  | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.80  | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | REF_CLOSE: (9), (12100), (12121), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | |            inconsistent by sub-proof #28.
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | |   (12122)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.68/21.80  | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.68/21.80  | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.68/21.80  | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.68/21.80  | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.68/21.80  | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.80  | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.80  | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.80  | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | BETA: splitting (12122) gives:
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | |   (12123)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.68/21.80  | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.68/21.80  | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.68/21.80  | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | ALPHA: (12123) implies:
% 150.68/21.80  | | | | | | | | | | | | | | |   (12124)  op(e3, e3) = e2
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (45), (51), (122), (139), (142), (148),
% 150.68/21.80  | | | | | | | | | | | | | | |            (156), (157), (158), (159), (161), (162), (163),
% 150.68/21.80  | | | | | | | | | | | | | | |            (164), (166), (168), (169), (203), (214), (218),
% 150.68/21.80  | | | | | | | | | | | | | | |            (237), (238), (278), (336), (342), (344), (9975),
% 150.68/21.80  | | | | | | | | | | | | | | |            (9977), (9978), (9979), (9980), (11866), (11867),
% 150.68/21.80  | | | | | | | | | | | | | | |            (11869), (12095), (12096), (12124),
% 150.68/21.80  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.80  | | | | | | | | | | | | | | |            #48.
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | |   (12125)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.80  | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.80  | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.68/21.80  | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.80  | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.80  | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | BETA: splitting (12125) gives:
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | |   (12126)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.80  | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.80  | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | ALPHA: (12126) implies:
% 150.68/21.80  | | | | | | | | | | | | | | | |   (12127)   ~ (all_57_14 = e2)
% 150.68/21.80  | | | | | | | | | | | | | | | |   (12128)  op(e1, e1) = all_57_14
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | REF_CLOSE: (9980), (12127), (12128), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #52.
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | |   (12129)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.80  | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.80  | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.80  | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | ALPHA: (12129) implies:
% 150.68/21.80  | | | | | | | | | | | | | | | |   (12130)  op(e2, e2) = e1
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11865), (12130), (function-axioms) are
% 150.68/21.80  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 150.68/21.80  | | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | | End of split
% 150.68/21.80  | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | Case 2:
% 150.68/21.80  | | | | | | | | | | | | 
% 150.68/21.80  | | | | | | | | | | | |   (12131)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.80  | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.80  | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.80  | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.80  | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.80  | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.80  | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.80  | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.80  | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.80  | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.80  | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.80  | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.80  | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.80  | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.80  | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.81  | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.81  | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.81  | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.81  | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.81  | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.81  | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.68/21.81  | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.68/21.81  | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.68/21.81  | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.68/21.81  | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.68/21.81  | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.68/21.81  | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.68/21.81  | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.68/21.81  | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.68/21.81  | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.81  | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.81  | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.81  | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.68/21.81  | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.68/21.81  | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.81  | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.68/21.81  | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.68/21.81  | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.68/21.81  | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.68/21.81  | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.68/21.81  | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.81  | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.81  | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.81  | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.81  | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.81  | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.81  | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.81  | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.81  | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.81  | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.81  | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.81  | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.81  | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.81  | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.81  | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.81  | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.81  | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.81  | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.81  | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | BETA: splitting (12131) gives:
% 150.68/21.81  | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | |   (12132)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.81  | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.81  | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.81  | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.81  | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.81  | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.81  | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.81  | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.81  | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.81  | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.81  | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.81  | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.81  | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.81  | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.81  | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.81  | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.81  | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.81  | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.81  | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.81  | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.81  | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.81  | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.68/21.81  | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | BETA: splitting (12132) gives:
% 150.68/21.81  | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | |   (12133)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.81  | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.81  | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.81  | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.81  | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.81  | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.81  | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.81  | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.81  | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (9977), (12096), (12133),
% 150.68/21.81  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.81  | | | | | | | | | | | | | |            #977.
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | |   (12134)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.81  | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.68/21.81  | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.68/21.81  | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.81  | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.68/21.81  | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.68/21.81  | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.81  | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.81  | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.68/21.81  | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.68/21.81  | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.81  | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.68/21.81  | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | REF_CLOSE: (6), (51), (167), (346), (12096), (12103),
% 150.68/21.81  | | | | | | | | | | | | | |            (12134), (function-axioms) are inconsistent by
% 150.68/21.81  | | | | | | | | | | | | | |            sub-proof #27.
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | |   (12135)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.81  | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.81  | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.81  | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.81  | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.81  | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.81  | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.81  | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.68/21.81  | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.81  | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.68/21.81  | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.81  | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.68/21.81  | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.68/21.81  | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.68/21.81  | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.68/21.81  | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.68/21.81  | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.81  | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.68/21.81  | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.81  | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.68/21.81  | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.68/21.81  | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.81  | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.81  | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.81  | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.81  | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.81  | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.81  | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.81  | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.81  | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.81  | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.81  | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.81  | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.81  | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.81  | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.81  | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.81  | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.81  | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.81  | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | BETA: splitting (12135) gives:
% 150.68/21.81  | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | |   (12136)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.81  | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.81  | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.81  | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.81  | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.81  | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.81  | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.81  | | | | | | | | | | | | | |              $i(all_57_14))
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | REF_CLOSE: (7), (12103), (12136), (function-axioms) are
% 150.68/21.81  | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | |   (12137)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.81  | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.81  | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.81  | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.68/21.81  | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.68/21.81  | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.81  | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.68/21.81  | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.68/21.81  | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.68/21.81  | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.68/21.81  | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.68/21.81  | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.81  | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.81  | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.81  | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.81  | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.81  | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.81  | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.81  | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.81  | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.81  | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.81  | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.81  | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.81  | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.81  | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.81  | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.81  | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.81  | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.81  | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | BETA: splitting (12137) gives:
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | |   (12138)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.81  | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.81  | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.81  | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.68/21.81  | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | ALPHA: (12138) implies:
% 150.68/21.81  | | | | | | | | | | | | | | |   (12139)  op(e2, e0) = e2
% 150.68/21.81  | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | REF_CLOSE: (163), (12095), (12139), (function-axioms) are
% 150.68/21.81  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 150.68/21.81  | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | |   (12140)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.81  | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.68/21.81  | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.68/21.81  | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.68/21.81  | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.68/21.81  | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.68/21.81  | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.68/21.81  | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.68/21.81  | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.68/21.81  | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.68/21.81  | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.68/21.81  | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.68/21.81  | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.68/21.81  | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.81  | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.68/21.81  | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.81  | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.68/21.81  | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.68/21.81  | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.68/21.81  | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.68/21.81  | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.68/21.81  | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.68/21.81  | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.68/21.81  | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.68/21.81  | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.68/21.81  | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | BETA: splitting (12140) gives:
% 150.68/21.81  | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | |   (12141)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.81  | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.68/21.81  | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.68/21.81  | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | ALPHA: (12141) implies:
% 150.68/21.81  | | | | | | | | | | | | | | | |   (12142)  op(e2, e2) = e0
% 150.68/21.81  | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11865), (12142), (function-axioms) are
% 150.68/21.81  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #719.
% 150.68/21.81  | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | |   (12143)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.81  | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.81  | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.81  | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.81  | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.68/21.81  | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.68/21.81  | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.68/21.81  | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.81  | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.68/21.81  | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.68/21.81  | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.68/21.81  | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.68/21.81  | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.68/21.81  | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.68/21.81  | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.68/21.81  | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.68/21.81  | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.68/21.81  | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.68/21.81  | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.68/21.81  | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | ALPHA: (12143) implies:
% 150.68/21.81  | | | | | | | | | | | | | | | |   (12144)  op(e0, e0) = all_57_15
% 150.68/21.81  | | | | | | | | | | | | | | | |   (12145)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.81  | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.81  | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.68/21.81  | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.68/21.81  | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.68/21.81  | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.81  | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.81  | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.81  | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.81  | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.81  | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.68/21.81  | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.68/21.81  | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.68/21.81  | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.81  | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.68/21.81  | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.68/21.81  | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | BETA: splitting (12145) gives:
% 150.68/21.81  | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | |   (12146)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.81  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.81  | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.68/21.81  | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.68/21.81  | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.68/21.81  | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.81  | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.81  | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.68/21.81  | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | BETA: splitting (12146) gives:
% 150.68/21.81  | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | |   (12147)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.81  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.81  | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | |            $i(all_57_0)
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | ALPHA: (12147) implies:
% 150.68/21.81  | | | | | | | | | | | | | | | | | |   (12148)  all_57_12 = e3
% 150.68/21.81  | | | | | | | | | | | | | | | | | |   (12149)   ~ (all_57_0 = e2)
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | REF_CLOSE: (12105), (12148), (12149) are inconsistent by
% 150.68/21.81  | | | | | | | | | | | | | | | | | |            sub-proof #832.
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | |   (12150)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.81  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.68/21.81  | | | | | | | | | | | | | | | | | |              all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | |              $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 150.68/21.81  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 150.68/21.81  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 150.68/21.81  | | | | | | | | | | | | | | | | | |                e2) = e0 & $i(all_57_3))
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | BETA: splitting (12150) gives:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |   (12151)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            $i(all_57_1)
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | ALPHA: (12151) implies:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |   (12152)  op(e1, e1) = e3
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (11865), (12103), (12104), (12105),
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            (12145), (12152), (function-axioms) are
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #72.
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |   (12153)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            $i(all_57_3)
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | ALPHA: (12153) implies:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |   (12154)   ~ (all_57_15 = e2)
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12096), (12144), (12154), (function-axioms) are
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #901.
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | |   (12155)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.81  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.81  | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.68/21.81  | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.68/21.81  | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.68/21.81  | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.81  | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.68/21.81  | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.68/21.81  | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | BETA: splitting (12155) gives:
% 150.68/21.81  | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | |   (12156)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.81  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.81  | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | |            $i(all_57_4)
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | ALPHA: (12156) implies:
% 150.68/21.81  | | | | | | | | | | | | | | | | | |   (12157)   ~ (all_57_15 = e2)
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | REF_CLOSE: (12096), (12144), (12157), (function-axioms) are
% 150.68/21.81  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #901.
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | |   (12158)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.68/21.81  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 150.68/21.81  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.68/21.81  | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 150.68/21.81  | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_7))
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | BETA: splitting (12158) gives:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |   (12159)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            $i(all_57_6)
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | ALPHA: (12159) implies:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |   (12160)  op(e3, e3) = e1
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (11869), (12160), (function-axioms) are
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #413.
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |   (12161)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            $i(all_57_7)
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | ALPHA: (12161) implies:
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |   (12162)  op(e2, e2) = e1
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11865), (12162), (function-axioms) are
% 150.68/21.81  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 150.68/21.81  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | |   (12163)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3
% 150.68/21.81  | | | | | | | | | | |                & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) &
% 150.68/21.81  | | | | | | | | | | |                op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.81  | | | | | | | | | | |            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.68/21.81  | | | | | | | | | | |                (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.68/21.81  | | | | | | | | | | |                $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2)
% 150.68/21.81  | | | | | | | | | | |                = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 150.68/21.81  | | | | | | | | | | |                all_57_15 & $i(all_57_15)))
% 150.68/21.81  | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | ALPHA: (12163) implies:
% 150.68/21.81  | | | | | | | | | | |   (12164)  op(e2, e2) = e2
% 150.68/21.81  | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (224), (225),
% 150.68/21.81  | | | | | | | | | | |            (227), (11861), (12099), (12164),
% 150.68/21.81  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.81  | | | | | | | | | | |            #921.
% 150.68/21.81  | | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | |   (12165)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 =
% 150.68/21.81  | | | | | | | | | |                  e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1)
% 150.68/21.81  | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.81  | | | | | | | | | |              ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.68/21.81  | | | | | | | | | |                  (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.81  | | | | | | | | | |                  $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.68/21.81  | | | | | | | | | |                    e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.68/21.81  | | | | | | | | | |                    e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.81  | | | | | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 =
% 150.68/21.81  | | | | | | | | | |                  e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0)
% 150.68/21.81  | | | | | | | | | |                  & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.68/21.81  | | | | | | | | | |              ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.68/21.81  | | | | | | | | | |                  (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.68/21.81  | | | | | | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.68/21.81  | | | | | | | | | |                    e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.68/21.81  | | | | | | | | | |                    e1) = all_57_14 & $i(all_57_14))))
% 150.68/21.81  | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | REF_CLOSE: (5), (6), (36), (9980), (12096), (12165),
% 150.68/21.81  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.81  | | | | | | | | | |            #707.
% 150.68/21.81  | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | | 
% 150.68/21.81  | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | 
% 150.68/21.81  | | | | | | | | |   (12166)  all_56_3 = e2 & op(e2, e2) = e2
% 150.68/21.81  | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | ALPHA: (12166) implies:
% 150.68/21.81  | | | | | | | | |   (12167)  op(e2, e2) = e2
% 150.68/21.81  | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | REF_CLOSE: (9), (11865), (12167), (function-axioms) are
% 150.68/21.81  | | | | | | | | |            inconsistent by sub-proof #1179.
% 150.68/21.81  | | | | | | | | | 
% 150.68/21.81  | | | | | | | | End of split
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | |   (12168)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 &
% 150.68/21.81  | | | | | | | |              op(e0, e2) = e2)
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | | REF_CLOSE: (157), (161), (9975), (12094), (12168),
% 150.68/21.81  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #24.
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | End of split
% 150.68/21.81  | | | | | | | 
% 150.68/21.81  | | | | | | End of split
% 150.68/21.81  | | | | | | 
% 150.68/21.81  | | | | | Case 2:
% 150.68/21.81  | | | | | | 
% 150.68/21.81  | | | | | |   (12169)  all_22_2 = e1
% 150.68/21.81  | | | | | | 
% 150.68/21.81  | | | | | | COMBINE_EQS: (320), (12169) imply:
% 150.68/21.81  | | | | | |   (12170)  all_14_2 = e1
% 150.68/21.81  | | | | | | 
% 150.68/21.81  | | | | | | SIMP: (12170) implies:
% 150.68/21.81  | | | | | |   (12171)  all_14_2 = e1
% 150.68/21.81  | | | | | | 
% 150.68/21.81  | | | | | | REDUCE: (338), (12171) imply:
% 150.68/21.81  | | | | | |   (12172)   ~ (all_52_2 = e1)
% 150.68/21.81  | | | | | | 
% 150.68/21.81  | | | | | | REDUCE: (51), (12171) imply:
% 150.68/21.81  | | | | | |   (12173)  op(e3, e3) = e1
% 150.68/21.81  | | | | | | 
% 150.68/21.81  | | | | | | BETA: splitting (237) gives:
% 150.68/21.81  | | | | | | 
% 150.68/21.81  | | | | | | Case 1:
% 150.68/21.81  | | | | | | | 
% 150.68/21.81  | | | | | | |   (12174)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 &
% 150.68/21.81  | | | | | | |                  op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2,
% 150.68/21.81  | | | | | | |                    e2) = all_57_12 & $i(all_57_12))) & ((all_57_1
% 150.68/21.81  | | | | | | |                  = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) &
% 150.68/21.81  | | | | | | |                  op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.81  | | | | | | |              ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 =
% 150.68/21.81  | | | | | | |                    e3) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.81  | | | | | | |            | (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 &
% 150.68/21.81  | | | | | | |                  op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3,
% 150.68/21.81  | | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_4
% 150.68/21.81  | | | | | | |                  = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) &
% 150.68/21.81  | | | | | | |                  op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.81  | | | | | | |              ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 =
% 150.68/21.81  | | | | | | |                    e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.81  | | | | | | | 
% 150.68/21.81  | | | | | | | REF_CLOSE: (8), (9), (11865), (12173), (12174), (function-axioms)
% 150.68/21.81  | | | | | | |            are inconsistent by sub-proof #100.
% 150.68/21.81  | | | | | | | 
% 150.68/21.81  | | | | | | Case 2:
% 150.68/21.81  | | | | | | | 
% 150.68/21.81  | | | | | | |   (12175)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 &
% 150.68/21.81  | | | | | | |                  op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3,
% 150.68/21.81  | | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_7
% 150.68/21.81  | | | | | | |                  = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) &
% 150.68/21.81  | | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.81  | | | | | | |              ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 =
% 150.68/21.81  | | | | | | |                    e1) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.81  | | | | | | |            | (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 &
% 150.68/21.81  | | | | | | |                  op(e3, e0) = e3) | ( ~ (all_57_10 = e0) & op(e3,
% 150.68/21.81  | | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_11
% 150.68/21.81  | | | | | | |                  = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 150.68/21.81  | | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.81  | | | | | | |              ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14
% 150.68/21.81  | | | | | | |                    = e0) & op(e1, e1) = all_57_14 &
% 150.68/21.81  | | | | | | |                  $i(all_57_14))))
% 150.68/21.81  | | | | | | | 
% 150.68/21.81  | | | | | | | BETA: splitting (12175) gives:
% 150.68/21.81  | | | | | | | 
% 150.68/21.81  | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | |   (12176)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 &
% 150.68/21.81  | | | | | | | |                op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3,
% 150.68/21.81  | | | | | | | |                  e3) = all_57_10 & $i(all_57_10))) & ((all_57_7
% 150.68/21.81  | | | | | | | |                = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) &
% 150.68/21.81  | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.81  | | | | | | | |            ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 =
% 150.68/21.81  | | | | | | | |                  e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | | ALPHA: (12176) implies:
% 150.68/21.81  | | | | | | | |   (12177)  op(e1, e1) = e1
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | | REF_CLOSE: (6), (36), (9980), (12177), (function-axioms) are
% 150.68/21.81  | | | | | | | |            inconsistent by sub-proof #1044.
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | |   (12178)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 &
% 150.68/21.81  | | | | | | | |                op(e3, e0) = e3) | ( ~ (all_57_10 = e0) & op(e3,
% 150.68/21.81  | | | | | | | |                  e3) = all_57_10 & $i(all_57_10))) & ((all_57_11
% 150.68/21.81  | | | | | | | |                = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 150.68/21.81  | | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.81  | | | | | | | |            ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14
% 150.68/21.81  | | | | | | | |                  = e0) & op(e1, e1) = all_57_14 &
% 150.68/21.81  | | | | | | | |                $i(all_57_14)))
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | | ALPHA: (12178) implies:
% 150.68/21.81  | | | | | | | |   (12179)  all_57_15 = e0
% 150.68/21.81  | | | | | | | |   (12180)  op(e0, e0) = e0
% 150.68/21.81  | | | | | | | |   (12181)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 =
% 150.68/21.81  | | | | | | | |                e0) & op(e1, e1) = all_57_14 & $i(all_57_14))
% 150.68/21.81  | | | | | | | |   (12182)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 =
% 150.68/21.81  | | | | | | | |                e0) & op(e2, e2) = all_57_12 & $i(all_57_12))
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | | BETA: splitting (238) gives:
% 150.68/21.81  | | | | | | | | 
% 150.68/21.81  | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | 
% 150.68/21.81  | | | | | | | | |   (12183)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.81  | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.81  | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.81  | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 150.68/21.81  | | | | | | | | |            (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.81  | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.81  | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.81  | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 150.68/21.81  | | | | | | | | |            (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.81  | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.81  | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.81  | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.81  | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.81  | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.81  | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 150.68/21.81  | | | | | | | | |                e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2)
% 150.68/21.81  | | | | | | | | |              & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 =
% 150.68/21.81  | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 = e2) &
% 150.68/21.81  | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 150.68/21.81  | | | | | | | | |                e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4)
% 150.68/21.81  | | | | | | | | |              & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 =
% 150.68/21.81  | | | | | | | | |              e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.81  | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 150.68/21.81  | | | | | | | | |                e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5)
% 150.68/21.81  | | | | | | | | |              & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 =
% 150.68/21.81  | | | | | | | | |              e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.68/21.81  | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.68/21.81  | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.81  | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.68/21.81  | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.68/21.81  | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 150.68/21.81  | | | | | | | | |              all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 150.68/21.81  | | | | | | | | |              e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 =
% 150.68/21.81  | | | | | | | | |              e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.81  | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.81  | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.81  | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.81  | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | BETA: splitting (12183) gives:
% 150.68/21.81  | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | |   (12184)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.81  | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.81  | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.81  | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.81  | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.81  | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.81  | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.81  | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.81  | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.81  | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.81  | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.81  | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.81  | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.81  | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.81  | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.81  | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.81  | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.81  | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | REF_CLOSE: (7), (9), (162), (9980), (12172), (12180),
% 150.68/21.81  | | | | | | | | | |            (12184), (function-axioms) are inconsistent by
% 150.68/21.81  | | | | | | | | | |            sub-proof #22.
% 150.68/21.81  | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | Case 2:
% 150.68/21.81  | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | |   (12185)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.81  | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.81  | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.81  | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.81  | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.81  | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.81  | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.81  | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.81  | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.68/21.81  | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.81  | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.81  | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.68/21.81  | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.68/21.81  | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.81  | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.81  | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.81  | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.68/21.81  | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.81  | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.81  | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.81  | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.81  | | | | | | | | | |              $i(all_57_10))
% 150.68/21.81  | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | BETA: splitting (12185) gives:
% 150.68/21.81  | | | | | | | | | | 
% 150.68/21.81  | | | | | | | | | | Case 1:
% 150.68/21.81  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | |   (12186)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.82  | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.82  | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.82  | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.82  | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.82  | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.82  | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.82  | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | REF_CLOSE: (169), (11860), (12186), (function-axioms) are
% 150.68/21.82  | | | | | | | | | | |            inconsistent by sub-proof #863.
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | |   (12187)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.68/21.82  | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.68/21.82  | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.68/21.82  | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.68/21.82  | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.68/21.82  | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.68/21.82  | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.82  | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.82  | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.68/21.82  | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.82  | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.82  | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.82  | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (11865), (12173), (12180), (12187),
% 150.68/21.82  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.82  | | | | | | | | | | |            #101.
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | End of split
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | End of split
% 150.68/21.82  | | | | | | | | | 
% 150.68/21.82  | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | 
% 150.68/21.82  | | | | | | | | |   (12188)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.82  | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.82  | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.82  | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.82  | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.82  | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.82  | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.82  | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.82  | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.82  | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.82  | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.82  | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.82  | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.82  | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.82  | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.82  | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.82  | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.82  | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1,
% 150.68/21.82  | | | | | | | | |                e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.82  | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.68/21.82  | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.68/21.82  | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.68/21.82  | | | | | | | | |              all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) =
% 150.68/21.82  | | | | | | | | |              e2 & $i(all_57_9) & $i(all_57_12)) | (all_57_10 =
% 150.68/21.82  | | | | | | | | |              e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 150.68/21.82  | | | | | | | | |              (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.68/21.82  | | | | | | | | |              all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.68/21.82  | | | | | | | | |              e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 =
% 150.68/21.82  | | | | | | | | |              e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 150.68/21.82  | | | | | | | | |              (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.82  | | | | | | | | |              op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 150.68/21.82  | | | | | | | | |              all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 150.68/21.82  | | | | | | | | |            (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.82  | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.82  | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.68/21.82  | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14))
% 150.68/21.82  | | | | | | | | |            | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.82  | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.82  | | | | | | | | |                    e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.82  | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.68/21.82  | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.68/21.82  | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.82  | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.82  | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.82  | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.82  | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.82  | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.82  | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.82  | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.82  | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.82  | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.82  | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.82  | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.82  | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.82  | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.82  | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.82  | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | BETA: splitting (12188) gives:
% 150.68/21.82  | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | |   (12189)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.82  | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.82  | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.82  | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.82  | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.82  | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.82  | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.82  | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.82  | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.82  | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.82  | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.82  | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.82  | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.82  | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.82  | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.82  | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.82  | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.82  | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.82  | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.82  | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | BETA: splitting (12189) gives:
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | |   (12190)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.82  | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.82  | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.82  | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.82  | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.82  | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.82  | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.82  | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | REF_CLOSE: (4), (164), (9977), (12180), (12190),
% 150.68/21.82  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.82  | | | | | | | | | | |            #1039.
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | |   (12191)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.82  | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.68/21.82  | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.68/21.82  | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.82  | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.68/21.82  | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.68/21.82  | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.82  | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.82  | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.68/21.82  | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.68/21.82  | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.82  | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.68/21.82  | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | REF_CLOSE: (4), (12180), (12181), (12182), (12191),
% 150.68/21.82  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.82  | | | | | | | | | | |            #69.
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | End of split
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | |   (12192)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.82  | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.82  | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.82  | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.82  | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.82  | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.82  | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.82  | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.82  | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.68/21.82  | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.82  | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.68/21.82  | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.82  | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.68/21.82  | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.68/21.82  | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.68/21.82  | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.68/21.82  | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.68/21.82  | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.82  | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.68/21.82  | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.82  | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.68/21.82  | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.68/21.82  | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.82  | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.82  | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.82  | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.82  | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.82  | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.82  | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.82  | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.82  | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.82  | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.82  | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.82  | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.82  | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.82  | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.82  | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | BETA: splitting (12192) gives:
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | |   (12193)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.82  | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.82  | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.82  | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.82  | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.82  | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.82  | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.82  | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.82  | | | | | | | | | | |              $i(all_57_14))
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | REF_CLOSE: (4), (12173), (12193), (function-axioms) are
% 150.68/21.82  | | | | | | | | | | |            inconsistent by sub-proof #956.
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | |   (12194)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.82  | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.82  | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.82  | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.82  | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.68/21.82  | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.68/21.82  | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.82  | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.68/21.82  | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.68/21.82  | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.68/21.82  | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.68/21.82  | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.68/21.82  | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.82  | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.82  | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.82  | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.82  | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.82  | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.82  | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.82  | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.82  | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.82  | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.82  | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.82  | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.82  | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.82  | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.82  | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.82  | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.82  | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | BETA: splitting (12194) gives:
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | |   (12195)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.82  | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.82  | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.82  | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.82  | | | | | | | | | | | |            $i(all_57_13)
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | ALPHA: (12195) implies:
% 150.68/21.82  | | | | | | | | | | | |   (12196)   ~ (all_57_13 = e1)
% 150.68/21.82  | | | | | | | | | | | |   (12197)  op(e1, e1) = e0
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | REF_CLOSE: (12181), (12196), (12197), (function-axioms) are
% 150.68/21.82  | | | | | | | | | | | |            inconsistent by sub-proof #959.
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | |   (12198)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.82  | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.82  | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.68/21.82  | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.68/21.82  | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.68/21.82  | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.68/21.82  | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.68/21.82  | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.68/21.82  | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.68/21.82  | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.68/21.82  | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.68/21.82  | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.68/21.82  | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.68/21.82  | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.68/21.82  | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.68/21.82  | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.82  | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.68/21.82  | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.82  | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.68/21.82  | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.68/21.82  | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.68/21.82  | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.68/21.82  | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.68/21.82  | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.68/21.82  | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.68/21.82  | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.68/21.82  | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | BETA: splitting (12198) gives:
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | |   (12199)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.82  | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.82  | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.68/21.82  | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | ALPHA: (12199) implies:
% 150.68/21.82  | | | | | | | | | | | | |   (12200)  all_57_12 = e0
% 150.68/21.82  | | | | | | | | | | | | |   (12201)   ~ (all_57_11 = e2)
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | REF_CLOSE: (12182), (12200), (12201) are inconsistent by
% 150.68/21.82  | | | | | | | | | | | | |            sub-proof #890.
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | |   (12202)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.82  | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.82  | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.82  | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.82  | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.82  | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.68/21.82  | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.68/21.82  | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.68/21.82  | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.82  | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.68/21.82  | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.68/21.82  | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.68/21.82  | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.68/21.82  | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.68/21.82  | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.68/21.82  | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.68/21.82  | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.68/21.82  | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.82  | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.68/21.82  | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.68/21.82  | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.68/21.82  | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | ALPHA: (12202) implies:
% 150.68/21.82  | | | | | | | | | | | | |   (12203)  op(e0, e0) = all_57_15
% 150.68/21.82  | | | | | | | | | | | | |   (12204)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.82  | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.82  | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.82  | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.68/21.82  | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.68/21.82  | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.68/21.82  | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.68/21.82  | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.82  | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.82  | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.82  | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.82  | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.82  | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.82  | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.68/21.82  | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.68/21.82  | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.68/21.82  | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.68/21.82  | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.82  | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.68/21.82  | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 150.68/21.82  | | | | | | | | | | | | |              e0, e0, simplifying with (45), (12180) gives:
% 150.68/21.82  | | | | | | | | | | | | |   (12205)  all_10_2 = e0
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | REDUCE: (349), (12205) imply:
% 150.68/21.82  | | | | | | | | | | | | |   (12206)   ~ (all_52_3 = e0)
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | REDUCE: (360), (12205) imply:
% 150.68/21.82  | | | | | | | | | | | | |   (12207)   ~ (all_52_7 = e0)
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | REDUCE: (367), (12205) imply:
% 150.68/21.82  | | | | | | | | | | | | |   (12208)   ~ (all_52_11 = e0)
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | BETA: splitting (12204) gives:
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | |   (12209)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.82  | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.82  | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.82  | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.68/21.82  | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.68/21.82  | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.68/21.82  | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.68/21.82  | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.82  | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.82  | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | REF_CLOSE: (6), (158), (12173), (12206), (12209),
% 150.68/21.82  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.82  | | | | | | | | | | | | | |            #955.
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | |   (12210)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.82  | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.82  | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.82  | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.68/21.82  | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.68/21.82  | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.68/21.82  | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.68/21.82  | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.82  | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.68/21.82  | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | BETA: splitting (12210) gives:
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | |   (12211)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.82  | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.82  | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.82  | | | | | | | | | | | | | | |            $i(all_57_4)
% 150.68/21.82  | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | ALPHA: (12211) implies:
% 150.68/21.82  | | | | | | | | | | | | | | |   (12212)  op(e0, e2) = e0
% 150.68/21.82  | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | REF_CLOSE: (157), (12207), (12212), (function-axioms) are
% 150.68/21.82  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 150.68/21.82  | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | |   (12213)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.68/21.82  | | | | | | | | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.68/21.82  | | | | | | | | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.82  | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 150.68/21.82  | | | | | | | | | | | | | | |              &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.68/21.82  | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 150.68/21.82  | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_7))
% 150.68/21.82  | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | REF_CLOSE: (8), (156), (11865), (12208), (12213),
% 150.68/21.82  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.82  | | | | | | | | | | | | | | |            #68.
% 150.68/21.82  | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | End of split
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | End of split
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | End of split
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | End of split
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | End of split
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | End of split
% 150.68/21.82  | | | | | | | | | 
% 150.68/21.82  | | | | | | | | End of split
% 150.68/21.82  | | | | | | | | 
% 150.68/21.82  | | | | | | | End of split
% 150.68/21.82  | | | | | | | 
% 150.68/21.82  | | | | | | End of split
% 150.68/21.82  | | | | | | 
% 150.68/21.82  | | | | | End of split
% 150.68/21.82  | | | | | 
% 150.68/21.82  | | | | Case 2:
% 150.68/21.82  | | | | | 
% 150.68/21.82  | | | | |   (12214)  all_14_2 = e0
% 150.68/21.82  | | | | | 
% 150.68/21.82  | | | | | REDUCE: (336), (12214) imply:
% 150.68/21.82  | | | | |   (12215)   ~ (all_52_1 = e0)
% 150.68/21.82  | | | | | 
% 150.68/21.82  | | | | | REDUCE: (340), (12214) imply:
% 150.68/21.82  | | | | |   (12216)   ~ (all_52_3 = e0)
% 150.68/21.82  | | | | | 
% 150.68/21.82  | | | | | REDUCE: (342), (12214) imply:
% 150.68/21.82  | | | | |   (12217)   ~ (all_52_4 = e0)
% 150.68/21.82  | | | | | 
% 150.68/21.82  | | | | | REDUCE: (346), (12214) imply:
% 150.68/21.82  | | | | |   (12218)   ~ (all_52_12 = e0)
% 150.68/21.82  | | | | | 
% 150.68/21.82  | | | | | REDUCE: (51), (12214) imply:
% 150.68/21.82  | | | | |   (12219)  op(e3, e3) = e0
% 150.68/21.82  | | | | | 
% 150.68/21.82  | | | | | BETA: splitting (237) gives:
% 150.68/21.82  | | | | | 
% 150.68/21.82  | | | | | Case 1:
% 150.68/21.82  | | | | | | 
% 150.68/21.82  | | | | | |   (12220)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 &
% 150.68/21.82  | | | | | |                  op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2,
% 150.68/21.82  | | | | | |                    e2) = all_57_12 & $i(all_57_12))) & ((all_57_1 =
% 150.68/21.82  | | | | | |                  e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) &
% 150.68/21.82  | | | | | |                  op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.82  | | | | | |              ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 =
% 150.68/21.82  | | | | | |                    e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.82  | | | | | |            (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 &
% 150.68/21.82  | | | | | |                  op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3,
% 150.68/21.82  | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_4 =
% 150.68/21.82  | | | | | |                  e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) &
% 150.68/21.82  | | | | | |                  op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.68/21.82  | | | | | |              ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 =
% 150.68/21.82  | | | | | |                    e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 150.68/21.82  | | | | | | 
% 150.68/21.82  | | | | | | REF_CLOSE: (7), (9), (11865), (12219), (12220), (function-axioms)
% 150.68/21.82  | | | | | |            are inconsistent by sub-proof #87.
% 150.68/21.82  | | | | | | 
% 150.68/21.82  | | | | | Case 2:
% 150.68/21.82  | | | | | | 
% 150.68/21.82  | | | | | |   (12221)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 &
% 150.68/21.82  | | | | | |                  op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3,
% 150.68/21.82  | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_7 =
% 150.68/21.82  | | | | | |                  e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) &
% 150.68/21.82  | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.82  | | | | | |              ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 =
% 150.68/21.82  | | | | | |                    e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.68/21.82  | | | | | |            (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 &
% 150.68/21.82  | | | | | |                  op(e3, e0) = e3) | ( ~ (all_57_10 = e0) & op(e3,
% 150.68/21.82  | | | | | |                    e3) = all_57_10 & $i(all_57_10))) & ((all_57_11 =
% 150.68/21.82  | | | | | |                  e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 150.68/21.82  | | | | | |                  op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.82  | | | | | |              ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 =
% 150.68/21.82  | | | | | |                    e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 150.68/21.82  | | | | | | 
% 150.68/21.82  | | | | | | BETA: splitting (12221) gives:
% 150.68/21.82  | | | | | | 
% 150.68/21.82  | | | | | | Case 1:
% 150.68/21.82  | | | | | | | 
% 150.68/21.82  | | | | | | |   (12222)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 &
% 150.68/21.82  | | | | | | |                op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3,
% 150.68/21.82  | | | | | | |                  e3) = all_57_10 & $i(all_57_10))) & ((all_57_7 =
% 150.68/21.82  | | | | | | |                e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) &
% 150.68/21.82  | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.82  | | | | | | |            ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 =
% 150.68/21.82  | | | | | | |                  e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))
% 150.68/21.82  | | | | | | | 
% 150.68/21.82  | | | | | | | ALPHA: (12222) implies:
% 150.68/21.82  | | | | | | |   (12223)  op(e1, e1) = e1
% 150.68/21.82  | | | | | | | 
% 150.68/21.82  | | | | | | | REF_CLOSE: (6), (36), (9980), (12223), (function-axioms) are
% 150.68/21.82  | | | | | | |            inconsistent by sub-proof #1044.
% 150.68/21.82  | | | | | | | 
% 150.68/21.82  | | | | | | Case 2:
% 150.68/21.82  | | | | | | | 
% 150.68/21.82  | | | | | | |   (12224)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 &
% 150.68/21.82  | | | | | | |                op(e3, e0) = e3) | ( ~ (all_57_10 = e0) & op(e3,
% 150.68/21.82  | | | | | | |                  e3) = all_57_10 & $i(all_57_10))) & ((all_57_11 =
% 150.68/21.82  | | | | | | |                e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 150.68/21.82  | | | | | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.68/21.82  | | | | | | |            ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 =
% 150.68/21.82  | | | | | | |                  e0) & op(e1, e1) = all_57_14 & $i(all_57_14)))
% 150.68/21.82  | | | | | | | 
% 150.68/21.82  | | | | | | | ALPHA: (12224) implies:
% 150.68/21.82  | | | | | | |   (12225)  op(e0, e0) = e0
% 150.68/21.82  | | | | | | |   (12226)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 =
% 150.68/21.82  | | | | | | |                e0) & op(e1, e1) = all_57_14 & $i(all_57_14))
% 150.68/21.82  | | | | | | |   (12227)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 =
% 150.68/21.82  | | | | | | |                e0) & op(e2, e2) = all_57_12 & $i(all_57_12))
% 150.68/21.82  | | | | | | |   (12228)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10 =
% 150.68/21.82  | | | | | | |                e0) & op(e3, e3) = all_57_10 & $i(all_57_10))
% 150.68/21.82  | | | | | | | 
% 150.68/21.82  | | | | | | | BETA: splitting (12228) gives:
% 150.68/21.82  | | | | | | | 
% 150.68/21.82  | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | 
% 150.68/21.82  | | | | | | | |   (12229)  all_57_9 = e3 & op(e3, e0) = e3
% 150.68/21.82  | | | | | | | | 
% 150.68/21.82  | | | | | | | | ALPHA: (12229) implies:
% 150.68/21.82  | | | | | | | |   (12230)  op(e3, e0) = e3
% 150.68/21.82  | | | | | | | | 
% 150.68/21.82  | | | | | | | | BETA: splitting (228) gives:
% 150.68/21.82  | | | | | | | | 
% 150.68/21.82  | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | 
% 150.68/21.82  | | | | | | | | |   (12231)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 150.68/21.82  | | | | | | | | |              & op(e2, e3) = e0)
% 150.68/21.82  | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | BETA: splitting (12231) gives:
% 150.68/21.82  | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | |   (12232)  all_56_0 = e0 & op(e3, e3) = e0
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2, e0,
% 150.68/21.82  | | | | | | | | | |              e0, e0, simplifying with (45), (12225) gives:
% 150.68/21.82  | | | | | | | | | |   (12233)  all_10_2 = e0
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 150.68/21.82  | | | | | | | | | |              e3, e0, e3, simplifying with (167), (12230) gives:
% 150.68/21.82  | | | | | | | | | |   (12234)  all_52_12 = e3
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | REDUCE: (360), (12233) imply:
% 150.68/21.82  | | | | | | | | | |   (12235)   ~ (all_52_7 = e0)
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | REDUCE: (119), (12234) imply:
% 150.68/21.82  | | | | | | | | | |   (12236)   ~ (all_52_8 = e3)
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | REDUCE: (111), (12234) imply:
% 150.68/21.82  | | | | | | | | | |   (12237)   ~ (all_52_14 = e3)
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | SIMP: (12237) implies:
% 150.68/21.82  | | | | | | | | | |   (12238)   ~ (all_52_14 = e3)
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | REDUCE: (11866), (12233) imply:
% 150.68/21.82  | | | | | | | | | |   (12239)   ~ (e1 = e0)
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | BETA: splitting (233) gives:
% 150.68/21.82  | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | |   (12240)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 150.68/21.82  | | | | | | | | | | |              & op(e3, e2) = e2)
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | BETA: splitting (12240) gives:
% 150.68/21.82  | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | |   (12241)  all_56_0 = e2 & op(e3, e3) = e2
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | ALPHA: (12241) implies:
% 150.68/21.82  | | | | | | | | | | | |   (12242)  op(e3, e3) = e2
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | REF_CLOSE: (5), (12219), (12242), (function-axioms) are
% 150.68/21.82  | | | | | | | | | | | |            inconsistent by sub-proof #1073.
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | |   (12243)  all_56_1 = e2 & op(e3, e2) = e2
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | ALPHA: (12243) implies:
% 150.68/21.82  | | | | | | | | | | | |   (12244)  op(e3, e2) = e2
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | BETA: splitting (219) gives:
% 150.68/21.82  | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | |   (12245)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 150.68/21.82  | | | | | | | | | | | | |              & op(e2, e1) = e3)
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | REF_CLOSE: (164), (168), (11863), (12236), (12245),
% 150.68/21.82  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.82  | | | | | | | | | | | | |            #369.
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | |   (12246)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 150.68/21.82  | | | | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | BETA: splitting (12246) gives:
% 150.68/21.82  | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | |   (12247)  all_56_8 = e3 & op(e1, e1) = e3
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | ALPHA: (12247) implies:
% 150.68/21.82  | | | | | | | | | | | | | |   (12248)  op(e1, e1) = e3
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (45), (156), (158),
% 150.68/21.82  | | | | | | | | | | | | | |            (168), (169), (238), (367), (11860), (11865),
% 150.68/21.82  | | | | | | | | | | | | | |            (12216), (12219), (12225), (12226), (12227),
% 150.68/21.82  | | | | | | | | | | | | | |            (12228), (12236), (12248), (function-axioms) are
% 150.68/21.82  | | | | | | | | | | | | | |            inconsistent by sub-proof #61.
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | Case 2:
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | |   (12249)  all_56_14 = e3 & op(e0, e1) = e3
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | ALPHA: (12249) implies:
% 150.68/21.82  | | | | | | | | | | | | | |   (12250)  op(e0, e1) = e3
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 150.68/21.82  | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | |   (12251)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 150.68/21.82  | | | | | | | | | | | | | | |              & op(e1, e2) = e3)
% 150.68/21.82  | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | BETA: splitting (12251) gives:
% 150.68/21.82  | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | |   (12252)  all_56_6 = e3 & op(e1, e3) = e3
% 150.68/21.82  | | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | | ALPHA: (12252) implies:
% 150.68/21.82  | | | | | | | | | | | | | | | |   (12253)  op(e1, e3) = e3
% 150.68/21.82  | | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.68/21.82  | | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | | |   (12254)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.82  | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.82  | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.82  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.82  | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.82  | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.82  | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.82  | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.68/21.82  | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.68/21.82  | | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.68/21.82  | | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.82  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.82  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.68/21.82  | | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.68/21.82  | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.68/21.82  | | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.68/21.82  | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.68/21.82  | | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.68/21.82  | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.68/21.82  | | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.82  | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.82  | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.82  | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.82  | | | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | | | BETA: splitting (12254) gives:
% 150.68/21.82  | | | | | | | | | | | | | | | | | 
% 150.68/21.82  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.82  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | |   (12255)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.83  | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.83  | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | BETA: splitting (12255) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |   (12256)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | BETA: splitting (12256) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12257)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | ALPHA: (12257) implies:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12258)  op(e1, e1) = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (45), (156), (158),
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            (168), (169), (238), (367), (11860), (11865),
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            (12216), (12219), (12225), (12226), (12227),
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            (12228), (12236), (12258), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #61.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12259)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | ALPHA: (12259) implies:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12260)  op(e0, e0) = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12225), (12260), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |   (12261)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | BETA: splitting (12261) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12262)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | ALPHA: (12262) implies:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12263)  op(e1, e3) = e1
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (12253), (12263), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #119.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12264)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | ALPHA: (12264) implies:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12265)  op(e0, e0) = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12225), (12265), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1143.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | |   (12266)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.68/21.83  | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | BETA: splitting (12266) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |   (12267)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (12244), (12267), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #28.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |   (12268)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (11865), (12219), (12225), (12268),
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |            #88.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | |   (12269)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.83  | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.83  | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.83  | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.68/21.83  | | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.68/21.83  | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.68/21.83  | | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.68/21.83  | | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.68/21.83  | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.68/21.83  | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.83  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.83  | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.83  | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | BETA: splitting (12269) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | |   (12270)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | BETA: splitting (12270) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |   (12271)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (168), (9977), (12236), (12271),
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |            #1083.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |   (12272)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12219), (12225), (12226), (12272),
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |            #472.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | |   (12273)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.83  | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | BETA: splitting (12273) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |   (12274)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12228), (12274) are inconsistent by sub-proof
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |            #470.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |   (12275)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | BETA: splitting (12275) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12276)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | ALPHA: (12276) implies:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12277)   ~ (all_57_13 = e1)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12278)  op(e1, e1) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12226), (12277), (12278), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #959.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |   (12279)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | BETA: splitting (12279) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |   (12280)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12280) implies:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |   (12281)  all_57_12 = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |   (12282)   ~ (all_57_11 = e2)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12227), (12281), (12282) are inconsistent by
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |            sub-proof #890.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |   (12283)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | ALPHA: (12283) implies:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |   (12284)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12284) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |   (12285)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (12216), (12219), (12285),
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |            #538.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |   (12286)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12286) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |   (12287)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12287) implies:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |   (12288)  op(e0, e2) = e0
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (12235), (12288), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |   (12289)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_7))
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (11865), (12250), (12289),
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | |            #103.
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | |   (12290)  all_56_7 = e3 & op(e1, e2) = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | REF_CLOSE: (161), (11861), (12290), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #925.
% 150.68/21.83  | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | |   (12291)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 150.68/21.83  | | | | | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 150.68/21.83  | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | BETA: splitting (12291) gives:
% 150.68/21.83  | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | |   (12292)  all_56_8 = e3 & op(e1, e1) = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | ALPHA: (12292) implies:
% 150.68/21.83  | | | | | | | | | | | | | | | |   (12293)  op(e1, e1) = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (45), (156), (158),
% 150.68/21.83  | | | | | | | | | | | | | | | |            (168), (169), (238), (367), (11860), (11865),
% 150.68/21.83  | | | | | | | | | | | | | | | |            (12216), (12219), (12225), (12226), (12227),
% 150.68/21.83  | | | | | | | | | | | | | | | |            (12228), (12236), (12293), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #61.
% 150.68/21.83  | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | |   (12294)  all_56_11 = e3 & op(e1, e0) = e3
% 150.68/21.83  | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | | REF_CLOSE: (159), (12238), (12294), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #66.
% 150.68/21.83  | | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | |   (12295)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 150.68/21.83  | | | | | | | | | | |              & op(e3, e0) = e2)
% 150.68/21.83  | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | BETA: splitting (12295) gives:
% 150.68/21.83  | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | |   (12296)  all_56_4 = e2 & op(e3, e1) = e2
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | REF_CLOSE: (168), (9976), (12296), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | |            inconsistent by sub-proof #46.
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | |   (12297)  all_56_9 = e2 & op(e3, e0) = e2
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | ALPHA: (12297) implies:
% 150.68/21.83  | | | | | | | | | | | |   (12298)  op(e3, e0) = e2
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | REF_CLOSE: (9), (12230), (12298), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | |            inconsistent by sub-proof #41.
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | |   (12299)  all_56_2 = e0 & op(e2, e3) = e0
% 150.68/21.83  | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | REF_CLOSE: (166), (12215), (12299), (function-axioms) are
% 150.68/21.83  | | | | | | | | | |            inconsistent by sub-proof #840.
% 150.68/21.83  | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | End of split
% 150.68/21.83  | | | | | | | | | 
% 150.68/21.83  | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | 
% 150.68/21.83  | | | | | | | | |   (12300)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0
% 150.68/21.83  | | | | | | | | |              & op(e0, e3) = e0)
% 150.68/21.83  | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | BETA: splitting (12300) gives:
% 150.68/21.83  | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | |   (12301)  all_56_6 = e0 & op(e1, e3) = e0
% 150.68/21.83  | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | ALPHA: (12301) implies:
% 150.68/21.83  | | | | | | | | | |   (12302)  all_56_6 = e0
% 150.68/21.83  | | | | | | | | | |   (12303)  op(e1, e3) = e0
% 150.68/21.83  | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | BETA: splitting (215) gives:
% 150.68/21.83  | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | |   (12304)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 150.68/21.83  | | | | | | | | | | |              & op(e1, e2) = e3)
% 150.68/21.83  | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | REF_CLOSE: (7), (161), (11861), (12302), (12304),
% 150.68/21.83  | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.83  | | | | | | | | | | |            #112.
% 150.68/21.83  | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | |   (12305)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 150.68/21.83  | | | | | | | | | | |              e3 & op(e1, e0) = e3)
% 150.68/21.83  | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | BETA: splitting (12305) gives:
% 150.68/21.83  | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | |   (12306)  all_56_8 = e3 & op(e1, e1) = e3
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | ALPHA: (12306) implies:
% 150.68/21.83  | | | | | | | | | | | |   (12307)  op(e1, e1) = e3
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | REF_CLOSE: (9), (9980), (12307), (function-axioms) are
% 150.68/21.83  | | | | | | | | | | | |            inconsistent by sub-proof #834.
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | |   (12308)  all_56_11 = e3 & op(e1, e0) = e3
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | ALPHA: (12308) implies:
% 150.68/21.83  | | | | | | | | | | | |   (12309)  all_56_11 = e3
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | BETA: splitting (213) gives:
% 150.68/21.83  | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | |   (12310)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 150.68/21.83  | | | | | | | | | | | | |              & op(e1, e2) = e1)
% 150.68/21.83  | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | BETA: splitting (12310) gives:
% 150.68/21.83  | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | |   (12311)  all_56_6 = e1 & op(e1, e3) = e1
% 150.68/21.83  | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | ALPHA: (12311) implies:
% 150.68/21.83  | | | | | | | | | | | | | |   (12312)  op(e1, e3) = e1
% 150.68/21.83  | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | REF_CLOSE: (4), (162), (12303), (12312), (function-axioms)
% 150.68/21.83  | | | | | | | | | | | | | |            are inconsistent by sub-proof #1127.
% 150.68/21.83  | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | |   (12313)  all_56_7 = e1 & op(e1, e2) = e1
% 150.68/21.83  | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | ALPHA: (12313) implies:
% 150.68/21.83  | | | | | | | | | | | | | |   (12314)  all_56_7 = e1
% 150.68/21.83  | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 150.68/21.83  | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | Case 1:
% 150.68/21.83  | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | |   (12315)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 150.68/21.83  | | | | | | | | | | | | | | |              & op(e2, e2) = e0)
% 150.68/21.83  | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (11865), (12217), (12315),
% 150.68/21.83  | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.83  | | | | | | | | | | | | | | |            #89.
% 150.68/21.83  | | | | | | | | | | | | | | | 
% 150.68/21.83  | | | | | | | | | | | | | | Case 2:
% 150.68/21.83  | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | |   (12316)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 150.68/21.84  | | | | | | | | | | | | | | |              e0 & op(e0, e2) = e0)
% 150.68/21.84  | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | BETA: splitting (12316) gives:
% 150.68/21.84  | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | Case 1:
% 150.68/21.84  | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | |   (12317)  all_56_7 = e0 & op(e1, e2) = e0
% 150.68/21.84  | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | ALPHA: (12317) implies:
% 150.68/21.84  | | | | | | | | | | | | | | | |   (12318)  all_56_7 = e0
% 150.68/21.84  | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12314), (12318) are inconsistent by
% 150.68/21.84  | | | | | | | | | | | | | | | |            sub-proof #987.
% 150.68/21.84  | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | Case 2:
% 150.68/21.84  | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | |   (12319)  all_56_13 = e0 & op(e0, e2) = e0
% 150.68/21.84  | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | ALPHA: (12319) implies:
% 150.68/21.84  | | | | | | | | | | | | | | | |   (12320)  op(e0, e2) = e0
% 150.68/21.84  | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 150.68/21.84  | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.84  | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | |   (12321)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 150.68/21.84  | | | | | | | | | | | | | | | | |              e2 & op(e0, e2) = e2)
% 150.68/21.84  | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | BETA: splitting (12321) gives:
% 150.68/21.84  | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | |   (12322)  all_56_12 = e2 & op(e0, e3) = e2
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | | ALPHA: (12322) implies:
% 150.68/21.84  | | | | | | | | | | | | | | | | | |   (12323)  all_56_12 = e2
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (162), (230), (234),
% 150.68/21.84  | | | | | | | | | | | | | | | | | |            (12219), (12302), (12303), (12323),
% 150.68/21.84  | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.84  | | | | | | | | | | | | | | | | | |            #619.
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | |   (12324)  all_56_13 = e2 & op(e0, e2) = e2
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | | ALPHA: (12324) implies:
% 150.68/21.84  | | | | | | | | | | | | | | | | | |   (12325)  op(e0, e2) = e2
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12320), (12325), (function-axioms) are
% 150.68/21.84  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #31.
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.84  | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.84  | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | |   (12326)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 150.68/21.84  | | | | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 150.68/21.84  | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | BETA: splitting (12326) gives:
% 150.68/21.84  | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | Case 1:
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | |   (12327)  all_56_14 = e2 & op(e0, e1) = e2
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | | ALPHA: (12327) implies:
% 150.68/21.84  | | | | | | | | | | | | | | | | | |   (12328)  op(e0, e1) = e2
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (156), (9978), (12328), (function-axioms) are
% 150.68/21.84  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1092.
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | Case 2:
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | |   (12329)  all_56_15 = e2 & op(e0, e0) = e2
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | | ALPHA: (12329) implies:
% 150.68/21.84  | | | | | | | | | | | | | | | | | |   (12330)  op(e0, e0) = e2
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12225), (12330), (function-axioms) are
% 150.68/21.84  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1043.
% 150.68/21.84  | | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | | End of split
% 150.68/21.84  | | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | | End of split
% 150.68/21.84  | | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | | End of split
% 150.68/21.84  | | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | | End of split
% 150.68/21.84  | | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | End of split
% 150.68/21.84  | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | Case 2:
% 150.68/21.84  | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | |   (12331)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 150.68/21.84  | | | | | | | | | | | | |              e1 & op(e1, e0) = e1)
% 150.68/21.84  | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (9980), (12309), (12331),
% 150.68/21.84  | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.84  | | | | | | | | | | | | |            #33.
% 150.68/21.84  | | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | | End of split
% 150.68/21.84  | | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | | End of split
% 150.68/21.84  | | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | End of split
% 150.68/21.84  | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | Case 2:
% 150.68/21.84  | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | |   (12332)  all_56_12 = e0 & op(e0, e3) = e0
% 150.68/21.84  | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | ALPHA: (12332) implies:
% 150.68/21.84  | | | | | | | | | |   (12333)  op(e0, e3) = e0
% 150.68/21.84  | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | REF_CLOSE: (158), (12216), (12333), (function-axioms) are
% 150.68/21.84  | | | | | | | | | |            inconsistent by sub-proof #1142.
% 150.68/21.84  | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | End of split
% 150.68/21.84  | | | | | | | | | 
% 150.68/21.84  | | | | | | | | End of split
% 150.68/21.84  | | | | | | | | 
% 150.68/21.84  | | | | | | | Case 2:
% 150.68/21.84  | | | | | | | | 
% 150.68/21.84  | | | | | | | |   (12334)   ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.68/21.84  | | | | | | | |            $i(all_57_10)
% 150.68/21.84  | | | | | | | | 
% 150.68/21.84  | | | | | | | | ALPHA: (12334) implies:
% 150.68/21.84  | | | | | | | |   (12335)   ~ (all_57_10 = e0)
% 150.68/21.84  | | | | | | | |   (12336)  op(e3, e3) = all_57_10
% 150.68/21.84  | | | | | | | | 
% 150.68/21.84  | | | | | | | | REF_CLOSE: (12219), (12335), (12336), (function-axioms) are
% 150.68/21.84  | | | | | | | |            inconsistent by sub-proof #543.
% 150.68/21.84  | | | | | | | | 
% 150.68/21.84  | | | | | | | End of split
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | End of split
% 150.68/21.84  | | | | | | 
% 150.68/21.84  | | | | | End of split
% 150.68/21.84  | | | | | 
% 150.68/21.84  | | | | End of split
% 150.68/21.84  | | | | 
% 150.68/21.84  | | | Case 2:
% 150.68/21.84  | | | | 
% 150.68/21.84  | | | |   (12337)  all_10_2 = e1
% 150.68/21.84  | | | |   (12338)  ( ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 & op(e0,
% 150.68/21.84  | | | |                e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 150.68/21.84  | | | |              (all_10_1 = e2) & op(e0, e1) = all_10_1 & $i(all_10_1))
% 150.68/21.84  | | | | 
% 150.68/21.84  | | | | COMBINE_EQS: (308), (12337) imply:
% 150.68/21.84  | | | |   (12339)  all_30_2 = e1
% 150.68/21.84  | | | | 
% 150.68/21.84  | | | | REDUCE: (349), (12337) imply:
% 150.68/21.84  | | | |   (12340)   ~ (all_52_3 = e1)
% 150.68/21.84  | | | | 
% 150.68/21.84  | | | | REDUCE: (360), (12337) imply:
% 150.68/21.84  | | | |   (12341)   ~ (all_52_7 = e1)
% 150.68/21.84  | | | | 
% 150.68/21.84  | | | | REDUCE: (368), (12337) imply:
% 150.68/21.84  | | | |   (12342)   ~ (all_52_12 = e1)
% 150.68/21.84  | | | | 
% 150.68/21.84  | | | | REDUCE: (369), (12337) imply:
% 150.68/21.84  | | | |   (12343)   ~ (all_52_13 = e1)
% 150.68/21.84  | | | | 
% 150.68/21.84  | | | | REDUCE: (370), (12337) imply:
% 150.68/21.84  | | | |   (12344)   ~ (all_52_14 = e1)
% 150.68/21.84  | | | | 
% 150.68/21.84  | | | | REDUCE: (45), (12337) imply:
% 150.68/21.84  | | | |   (12345)  op(e0, e0) = e1
% 150.68/21.84  | | | | 
% 150.68/21.84  | | | | BETA: splitting (237) gives:
% 150.68/21.84  | | | | 
% 150.68/21.84  | | | | Case 1:
% 150.68/21.84  | | | | | 
% 150.68/21.84  | | | | |   (12346)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 &
% 150.68/21.84  | | | | |                  op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2)
% 150.68/21.84  | | | | |                  = all_57_12 & $i(all_57_12))) & ((all_57_1 = e1 &
% 150.68/21.84  | | | | |                  op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 150.68/21.84  | | | | |                  = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 &
% 150.68/21.84  | | | | |                  op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0)
% 150.68/21.84  | | | | |                  = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 150.68/21.84  | | | | |              op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | (
% 150.68/21.84  | | | | |                  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.68/21.84  | | | | |                  $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1)
% 150.68/21.84  | | | | |                | ( ~ (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 150.68/21.84  | | | | |                  $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 150.68/21.84  | | | | |                | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 150.68/21.84  | | | | |                  $i(all_57_15))))
% 150.68/21.84  | | | | | 
% 150.68/21.84  | | | | | BETA: splitting (12346) gives:
% 150.68/21.84  | | | | | 
% 150.68/21.84  | | | | | Case 1:
% 150.68/21.84  | | | | | | 
% 150.68/21.84  | | | | | |   (12347)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 &
% 150.68/21.84  | | | | | |                op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2)
% 150.68/21.84  | | | | | |                = all_57_12 & $i(all_57_12))) & ((all_57_1 = e1 &
% 150.68/21.84  | | | | | |                op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 150.68/21.84  | | | | | |                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 &
% 150.68/21.84  | | | | | |                op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0)
% 150.68/21.84  | | | | | |                = all_57_15 & $i(all_57_15)))
% 150.68/21.84  | | | | | | 
% 150.68/21.84  | | | | | | ALPHA: (12347) implies:
% 150.68/21.84  | | | | | |   (12348)  op(e3, e3) = e3
% 150.68/21.84  | | | | | |   (12349)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3)
% 150.68/21.84  | | | | | |              & op(e0, e0) = all_57_15 & $i(all_57_15))
% 150.68/21.84  | | | | | |   (12350)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3)
% 150.68/21.84  | | | | | |              & op(e1, e1) = all_57_14 & $i(all_57_14))
% 150.68/21.84  | | | | | |   (12351)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3)
% 150.68/21.84  | | | | | |              & op(e2, e2) = all_57_12 & $i(all_57_12))
% 150.68/21.84  | | | | | | 
% 150.68/21.84  | | | | | | BETA: splitting (12351) gives:
% 150.68/21.84  | | | | | | 
% 150.68/21.84  | | | | | | Case 1:
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | |   (12352)  all_57_0 = e2 & op(e2, e3) = e2
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | ALPHA: (12352) implies:
% 150.68/21.84  | | | | | | |   (12353)  op(e2, e3) = e2
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 150.68/21.84  | | | | | | |              e3, e2, simplifying with (166), (12353) gives:
% 150.68/21.84  | | | | | | |   (12354)  all_52_1 = e2
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e3,
% 150.68/21.84  | | | | | | |              e3, e3, simplifying with (51), (12348) gives:
% 150.68/21.84  | | | | | | |   (12355)  all_14_2 = e3
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | REDUCE: (148), (12354) imply:
% 150.68/21.84  | | | | | | |   (12356)   ~ (all_52_2 = e2)
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | REDUCE: (147), (12354) imply:
% 150.68/21.84  | | | | | | |   (12357)   ~ (all_52_3 = e2)
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | SIMP: (12357) implies:
% 150.68/21.84  | | | | | | |   (12358)   ~ (all_52_3 = e2)
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | REDUCE: (145), (12354) imply:
% 150.68/21.84  | | | | | | |   (12359)   ~ (all_52_9 = e2)
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | REDUCE: (144), (12354) imply:
% 150.68/21.84  | | | | | | |   (12360)   ~ (all_52_13 = e2)
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | SIMP: (12360) implies:
% 150.68/21.84  | | | | | | |   (12361)   ~ (all_52_13 = e2)
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | REDUCE: (11859), (12354) imply:
% 150.68/21.84  | | | | | | |   (12362)   ~ (e3 = e2)
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | REDUCE: (340), (12355) imply:
% 150.68/21.84  | | | | | | |   (12363)   ~ (all_52_3 = e3)
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | REDUCE: (344), (12355) imply:
% 150.68/21.84  | | | | | | |   (12364)   ~ (all_52_8 = e3)
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | REDUCE: (346), (12355) imply:
% 150.68/21.84  | | | | | | |   (12365)   ~ (all_52_12 = e3)
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | BETA: splitting (211) gives:
% 150.68/21.84  | | | | | | | 
% 150.68/21.84  | | | | | | | Case 1:
% 150.68/21.84  | | | | | | | | 
% 150.68/21.84  | | | | | | | |   (12366)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 &
% 150.68/21.84  | | | | | | | |              op(e2, e0) = e3)
% 150.68/21.84  | | | | | | | | 
% 150.68/21.84  | | | | | | | | REF_CLOSE: (163), (167), (11864), (12365), (12366),
% 150.68/21.84  | | | | | | | |            (function-axioms) are inconsistent by sub-proof #113.
% 150.68/21.84  | | | | | | | | 
% 150.68/21.84  | | | | | | | Case 2:
% 150.68/21.84  | | | | | | | | 
% 150.68/21.84  | | | | | | | |   (12367)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3
% 150.68/21.84  | | | | | | | |              & op(e0, e0) = e3)
% 150.68/21.84  | | | | | | | | 
% 150.68/21.84  | | | | | | | | BETA: splitting (12367) gives:
% 150.68/21.84  | | | | | | | | 
% 150.68/21.84  | | | | | | | | Case 1:
% 150.68/21.84  | | | | | | | | | 
% 150.68/21.84  | | | | | | | | |   (12368)  all_56_11 = e3 & op(e1, e0) = e3
% 150.68/21.84  | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | ALPHA: (12368) implies:
% 150.68/21.84  | | | | | | | | |   (12369)  all_56_11 = e3
% 150.68/21.84  | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | BETA: splitting (219) gives:
% 150.68/21.84  | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | Case 1:
% 150.68/21.84  | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | |   (12370)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 150.68/21.84  | | | | | | | | | |              & op(e2, e1) = e3)
% 150.68/21.84  | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | | REF_CLOSE: (164), (168), (11863), (12364), (12370),
% 150.68/21.84  | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.68/21.84  | | | | | | | | | |            #369.
% 150.68/21.84  | | | | | | | | | | 
% 150.68/21.84  | | | | | | | | | Case 2:
% 150.68/21.84  | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | |   (12371)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 150.84/21.84  | | | | | | | | | |              e3 & op(e0, e1) = e3)
% 150.84/21.84  | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | BETA: splitting (12371) gives:
% 150.84/21.84  | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | |   (12372)  all_56_8 = e3 & op(e1, e1) = e3
% 150.84/21.84  | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | ALPHA: (12372) implies:
% 150.84/21.84  | | | | | | | | | | |   (12373)  op(e1, e1) = e3
% 150.84/21.84  | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | REF_CLOSE: (9), (9980), (12373), (function-axioms) are
% 150.84/21.84  | | | | | | | | | | |            inconsistent by sub-proof #834.
% 150.84/21.84  | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | |   (12374)  all_56_14 = e3 & op(e0, e1) = e3
% 150.84/21.84  | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | ALPHA: (12374) implies:
% 150.84/21.84  | | | | | | | | | | |   (12375)  op(e0, e1) = e3
% 150.84/21.84  | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | BETA: splitting (205) gives:
% 150.84/21.84  | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | |   (12376)  all_56_15 = e0 & op(e0, e0) = e0
% 150.84/21.84  | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | ALPHA: (12376) implies:
% 150.84/21.84  | | | | | | | | | | | |   (12377)  op(e0, e0) = e0
% 150.84/21.84  | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | REF_CLOSE: (4), (12345), (12377), (function-axioms) are
% 150.84/21.84  | | | | | | | | | | | |            inconsistent by sub-proof #1040.
% 150.84/21.84  | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | |   (12378)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 150.84/21.84  | | | | | | | | | | | |                e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 150.84/21.84  | | | | | | | | | | | |                op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 150.84/21.84  | | | | | | | | | | | |                  e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 150.84/21.84  | | | | | | | | | | | |                e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 150.84/21.84  | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | ALPHA: (12378) implies:
% 150.84/21.84  | | | | | | | | | | | |   (12379)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 150.84/21.84  | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 150.84/21.84  | | | | | | | | | | | |                e0) = e0)
% 150.84/21.84  | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | BETA: splitting (196) gives:
% 150.84/21.84  | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | |   (12380)  all_54_7 = e3
% 150.84/21.84  | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | COMBINE_EQS: (259), (12380) imply:
% 150.84/21.84  | | | | | | | | | | | | |   (12381)  all_52_13 = e3
% 150.84/21.84  | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | REDUCE: (11864), (12381) imply:
% 150.84/21.84  | | | | | | | | | | | | |   (12382)  $false
% 150.84/21.84  | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | CLOSE: (12382) is inconsistent.
% 150.84/21.84  | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | |   (12383)   ~ (all_54_7 = e3)
% 150.84/21.84  | | | | | | | | | | | | |   (12384)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 150.84/21.84  | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | BETA: splitting (210) gives:
% 150.84/21.84  | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | |   (12385)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 150.84/21.84  | | | | | | | | | | | | | |              e2 & op(e2, e0) = e2)
% 150.84/21.84  | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | BETA: splitting (12385) gives:
% 150.84/21.84  | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | |   (12386)  all_56_9 = e2 & op(e3, e0) = e2
% 150.84/21.84  | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | ALPHA: (12386) implies:
% 150.84/21.84  | | | | | | | | | | | | | | |   (12387)  all_56_9 = e2
% 150.84/21.84  | | | | | | | | | | | | | | |   (12388)  op(e3, e0) = e2
% 150.84/21.84  | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | |   (12389)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 150.84/21.84  | | | | | | | | | | | | | | | |              & op(e2, e3) = e1)
% 150.84/21.84  | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (166), (12348), (12353), (12389),
% 150.84/21.84  | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.84/21.84  | | | | | | | | | | | | | | | |            #841.
% 150.84/21.84  | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | |   (12390)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 150.84/21.84  | | | | | | | | | | | | | | | |              e1 & op(e0, e3) = e1)
% 150.84/21.84  | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | BETA: splitting (12390) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | |   (12391)  all_56_6 = e1 & op(e1, e3) = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | ALPHA: (12391) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | |   (12392)  all_56_6 = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | |   (12393)  op(e1, e3) = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | |   (12394)  all_54_12 = e3
% 150.84/21.84  | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (12363), (12394) are inconsistent by
% 150.84/21.84  | | | | | | | | | | | | | | | | | |            sub-proof #1093.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | |   (12395)   ~ (all_54_12 = e3)
% 150.84/21.84  | | | | | | | | | | | | | | | | | |   (12396)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | BETA: splitting (12396) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | |   (12397)  all_54_12 = e2
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (12358), (12397) are inconsistent by
% 150.84/21.84  | | | | | | | | | | | | | | | | | | |            sub-proof #882.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | |   (12398)   ~ (all_54_12 = e2)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | |   (12399)  all_54_12 = e1 | all_54_12 = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | BETA: splitting (12399) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | |   (12400)  all_54_12 = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (248), (12340), (12400) are inconsistent by
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | |            sub-proof #1091.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | |   (12401)  all_54_12 = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (12401) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | |   (12402)  all_52_3 = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | SIMP: (12402) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | |   (12403)  all_52_3 = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (12403) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | |   (12404)   ~ (all_52_7 = e0)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | SIMP: (12404) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | |   (12405)   ~ (all_52_7 = e0)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | REDUCE: (12363), (12403) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | |   (12406)   ~ (e3 = e0)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | REDUCE: (12358), (12403) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | |   (12407)   ~ (e2 = e0)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | REDUCE: (12340), (12403) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | |   (12408)   ~ (e1 = e0)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | |   (12409)   ~ (all_30_2 = e1)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | REDUCE: (12339), (12409) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | |   (12410)  $false
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | CLOSE: (12410) is inconsistent.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | |   (12411)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | |              & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | |              $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | |              = all_30_1 & $i(all_30_1))
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12411) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | |   (12412)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = all_30_1 & $i(all_30_0) &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12412) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | |   (12413)   ~ (all_30_0 = e2)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | |   (12414)  op(e0, e1) = all_30_1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | |   (12415)  op(all_30_1, e0) = all_30_0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | |   (12416)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12416) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | |   (12417)  all_56_2 = e1 & op(e2, e3) = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12417) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | |   (12418)  op(e2, e3) = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (166), (12353), (12418), (function-axioms)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #842.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | |   (12419)  all_56_3 = e1 & op(e2, e2) = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12419) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | |   (12420)  op(e2, e2) = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11865), (12420), (function-axioms) are
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1136.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | |   (12421)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | |              e1 & op(e2, e0) = e1)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12421) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | |   (12422)  all_56_5 = e1 & op(e2, e1) = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12422) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | |   (12423)  all_56_5 = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | |   (12424)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e1) = e0)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12424) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12425)  all_56_4 = e0 & op(e3, e1) = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12425) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12426)  all_56_4 = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12427)  op(e3, e1) = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12428)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e2) = e1)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12428) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12429)  all_56_0 = e1 & op(e3, e3) = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12429) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12430)  op(e3, e3) = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (228), (232),
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (234), (12392), (12393), (12430),
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #547.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12431)  all_56_1 = e1 & op(e3, e2) = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12431) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12432)  all_56_1 = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12384) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12433)  all_54_7 = e2
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (12433) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12434)  all_52_13 = e2
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12361), (12434) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12435)  $false
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12435) is inconsistent.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12436)   ~ (all_54_7 = e2)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12437)  all_54_7 = e1 | all_54_7 = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12437) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12438)  all_54_7 = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (12438) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12439)  all_52_13 = e1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (12343), (12439) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12440)  $false
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (12440) is inconsistent.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12441)  all_54_7 = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (12441) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12442)  all_52_13 = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (12442) imply:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12443)   ~ (all_52_12 = e0)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12379) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12444)  all_56_9 = e0 & op(e3, e0) = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (12443), (12444), (function-axioms) are
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #986.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12445)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e1, e0) = e0)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12445) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12446)  all_56_10 = e0 & op(e2, e0) = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12446) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12447)  all_56_10 = e0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12338) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12448)   ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e1) = all_10_1 & $i(all_10_0) &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12448) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12449)  op(e0, e1) = all_10_1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12450)  op(all_10_1, e0) = all_10_0
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (112), (144), (166), (167), (196), (200), (259),
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (269), (11864), (12342), (12343), (12353),
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12365), (12375), (12413), (12414), (12415),
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12449), (12450), (function-axioms) are
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #84.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12451)   ~ (all_10_1 = e2) & op(e0, e1) = all_10_1 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_10_1)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12451) implies:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12452)  op(e0, e1) = all_10_1
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12453)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e1 & op(e1, e1) = all_57_14 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12453) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12454)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12454) gives:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12455)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12349), (12350), (12455), (function-axioms) are
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #814.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12456)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_2) & $i(all_57_14))
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12349), (12351), (12456), (function-axioms) are
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #831.
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.84  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12457)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12457) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12458)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_10))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (11860), (12458), (function-axioms) are
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #863.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12459)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_14 & $i(all_57_3) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12459) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12460)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12460) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12461)  op(e3, e3) = e2
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (36), (124), (127), (138), (139), (142),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (143), (156), (190), (191), (194), (195), (237),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (248), (257), (258), (348), (359), (9974),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11861), (11862), (11865), (12340), (12341),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12345), (12461), (function-axioms) are
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12462)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12462) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12463)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12463) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12464)  op(e0, e0) = e2
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (209), (211),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12379), (12387), (12447), (12464),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #489.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12465)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12465) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12466)  op(e2, e2) = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (226), (227),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11861), (11863), (12432), (12466),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #262.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12467)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = e2 & $i(all_57_9) & $i(all_57_12)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12467) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12468)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_13))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12468) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12469)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_12 & op(e2, e1) = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6) & $i(all_57_12))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12469) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12470)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12470) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12471)  op(e3, e1) = e3
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12427), (12471), (function-axioms) are
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #663.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12472)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12472) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12473)  op(e2, e1) = e2
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9977), (12473), (function-axioms) are
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1157.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12474)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (164), (9977), (12388), (12474),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #9.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12475)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12475) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12476)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_9) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12348), (12476), (function-axioms) are
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #975.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12477)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12477) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12478)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12478) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12479)  op(e2, e0) = e2
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (12361), (12479), (function-axioms) are
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12480)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e0) = e1 & $i(all_57_11) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                   ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                    = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  & $i(all_57_7))))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12480) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12481)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12481) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12482)  op(e1, e0) = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (12344), (12482), (function-axioms) are
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #961.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12483)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7)))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12483) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12484)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12484) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12485)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12485) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12486)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12486) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12487)  all_57_12 = e3
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12488)   ~ (all_57_0 = e2)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12351), (12487), (12488) are inconsistent by
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #832.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12489)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = e0 & $i(all_57_3))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12489) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12490)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_1)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12490) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12491)   ~ (all_57_1 = e1)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12492)  op(e1, e1) = e3
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12350), (12491), (12492), (function-axioms) are
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #815.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12493)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_3)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12493) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12494)  op(e3, e3) = e2
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (36), (124), (127), (138), (139), (142),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (143), (156), (190), (191), (194), (195), (237),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (247), (248), (257), (258), (348), (359), (9974),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11861), (11862), (11865), (12340), (12341),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12345), (12494), (function-axioms) are
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12495)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12495) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12496)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12496) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12497)  op(e0, e2) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (12405), (12497), (function-axioms) are
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1036.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12498)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = e0 & $i(all_57_7))
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12498) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12499)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12499) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12500)  op(e0, e1) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12375), (12414), (12452), (12500),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #82.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12501)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_7)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12501) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12502)  op(e2, e2) = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (161), (164), (166),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (220), (221), (222), (223), (224), (226), (227),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (11861), (11863), (12432), (12502),
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #262.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12503)  all_56_11 = e0 & op(e1, e0) = e0
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12369), (12503) are inconsistent by
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #199.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12504)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e3, e0) = e1)
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12504) gives:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12505)  all_56_4 = e1 & op(e3, e1) = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12505) implies:
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12506)  all_56_4 = e1
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12426), (12506) are inconsistent by
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #657.
% 150.84/21.85  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12507)  all_56_9 = e1 & op(e3, e0) = e1
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12507) implies:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (12508)  all_56_9 = e1
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (210), (12345), (12369),
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (12379), (12508), (function-axioms) are
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #498.
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12509)  all_56_5 = e0 & op(e2, e1) = e0
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12423), (12509) are inconsistent by
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #223.
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |   (12510)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & op(e0, e1) = e0)
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12510) gives:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12511)  all_56_8 = e0 & op(e1, e1) = e0
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12511) implies:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12512)  op(e1, e1) = e0
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9980), (12512), (function-axioms) are
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1006.
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12513)  all_56_14 = e0 & op(e0, e1) = e0
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12513) implies:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |   (12514)  op(e0, e1) = e0
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (12338), (12375), (12411), (12514),
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | |            #80.
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | |   (12515)  all_56_10 = e1 & op(e2, e0) = e1
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (12515) implies:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | |   (12516)  all_56_10 = e1
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (210), (12345), (12369),
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | |            (12379), (12516), (function-axioms) are
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #589.
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | |   (12517)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 &
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | |            $i(all_30_1)
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12338), (12375), (12517), (function-axioms) are
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #8.
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | Case 2:
% 150.84/21.86  | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | |   (12518)  all_56_12 = e1 & op(e0, e3) = e1
% 150.84/21.86  | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | ALPHA: (12518) implies:
% 150.84/21.86  | | | | | | | | | | | | | | | | |   (12519)  op(e0, e3) = e1
% 150.84/21.86  | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (12340), (12519), (function-axioms) are
% 150.84/21.86  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #405.
% 150.84/21.86  | | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | Case 2:
% 150.84/21.86  | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | |   (12520)  all_56_10 = e2 & op(e2, e0) = e2
% 150.84/21.86  | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | ALPHA: (12520) implies:
% 150.84/21.86  | | | | | | | | | | | | | | |   (12521)  op(e2, e0) = e2
% 150.84/21.86  | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | | REF_CLOSE: (163), (12361), (12521), (function-axioms) are
% 150.84/21.86  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1156.
% 150.84/21.86  | | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | Case 2:
% 150.84/21.86  | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | |   (12522)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 150.84/21.86  | | | | | | | | | | | | | |              e2 & op(e0, e0) = e2)
% 150.84/21.86  | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | | REF_CLOSE: (6), (159), (9979), (12345), (12522),
% 150.84/21.86  | | | | | | | | | | | | | |            (function-axioms) are inconsistent by sub-proof
% 150.84/21.86  | | | | | | | | | | | | | |            #5.
% 150.84/21.86  | | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | | 
% 150.84/21.86  | | | | | | | | Case 2:
% 150.84/21.86  | | | | | | | | | 
% 150.84/21.86  | | | | | | | | |   (12523)  all_56_15 = e3 & op(e0, e0) = e3
% 150.84/21.86  | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | ALPHA: (12523) implies:
% 150.84/21.86  | | | | | | | | |   (12524)  op(e0, e0) = e3
% 150.84/21.86  | | | | | | | | | 
% 150.84/21.86  | | | | | | | | | REF_CLOSE: (8), (12345), (12524), (function-axioms) are
% 150.84/21.86  | | | | | | | | |            inconsistent by sub-proof #1022.
% 150.84/21.86  | | | | | | | | | 
% 150.84/21.86  | | | | | | | | End of split
% 150.84/21.86  | | | | | | | | 
% 150.84/21.86  | | | | | | | End of split
% 150.84/21.86  | | | | | | | 
% 150.84/21.86  | | | | | | Case 2:
% 150.84/21.86  | | | | | | | 
% 150.84/21.86  | | | | | | |   (12525)   ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 150.84/21.86  | | | | | | |            $i(all_57_12)
% 150.84/21.86  | | | | | | | 
% 150.84/21.86  | | | | | | | ALPHA: (12525) implies:
% 150.84/21.86  | | | | | | |   (12526)   ~ (all_57_12 = e3)
% 150.84/21.86  | | | | | | |   (12527)  op(e2, e2) = all_57_12
% 150.84/21.86  | | | | | | | 
% 150.84/21.86  | | | | | | | REF_CLOSE: (11865), (12526), (12527), (function-axioms) are
% 150.84/21.86  | | | | | | |            inconsistent by sub-proof #126.
% 150.84/21.86  | | | | | | | 
% 150.84/21.86  | | | | | | End of split
% 150.84/21.86  | | | | | | 
% 150.84/21.86  | | | | | Case 2:
% 150.84/21.86  | | | | | | 
% 150.84/21.86  | | | | | |   (12528)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 &
% 150.84/21.86  | | | | | |                op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3, e3)
% 150.84/21.86  | | | | | |                = all_57_10 & $i(all_57_10))) & ((all_57_4 = e1 &
% 150.84/21.86  | | | | | |                op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 150.84/21.86  | | | | | |                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 &
% 150.84/21.86  | | | | | |                op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0)
% 150.84/21.86  | | | | | |                = all_57_15 & $i(all_57_15)))
% 150.84/21.86  | | | | | | 
% 150.84/21.86  | | | | | | ALPHA: (12528) implies:
% 150.84/21.86  | | | | | |   (12529)  op(e2, e2) = e2
% 150.84/21.86  | | | | | | 
% 150.84/21.86  | | | | | | REF_CLOSE: (9), (11865), (12529), (function-axioms) are inconsistent
% 150.84/21.86  | | | | | |            by sub-proof #1179.
% 150.84/21.86  | | | | | | 
% 150.84/21.86  | | | | | End of split
% 150.84/21.86  | | | | | 
% 150.84/21.86  | | | | Case 2:
% 150.84/21.86  | | | | | 
% 150.84/21.86  | | | | |   (12530)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 &
% 150.84/21.86  | | | | |                  op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3)
% 150.84/21.86  | | | | |                  = all_57_10 & $i(all_57_10))) & ((all_57_7 = e2 &
% 150.84/21.86  | | | | |                  op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 150.84/21.86  | | | | |                  = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 &
% 150.84/21.86  | | | | |                  op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0)
% 150.84/21.86  | | | | |                  = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 150.84/21.86  | | | | |              op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | (
% 150.84/21.86  | | | | |                  ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.84/21.86  | | | | |                  $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2)
% 150.84/21.86  | | | | |                | ( ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 150.84/21.86  | | | | |                  $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 150.84/21.86  | | | | |                | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.84/21.86  | | | | |                  $i(all_57_14))))
% 150.84/21.86  | | | | | 
% 150.84/21.86  | | | | | REF_CLOSE: (4), (36), (124), (127), (138), (139), (142), (143), (156),
% 150.84/21.86  | | | | |            (190), (191), (194), (195), (247), (248), (257), (258),
% 150.84/21.86  | | | | |            (348), (359), (9974), (11861), (11862), (12340), (12341),
% 150.84/21.86  | | | | |            (12345), (12530), (function-axioms) are inconsistent by
% 150.84/21.86  | | | | |            sub-proof #77.
% 150.84/21.86  | | | | | 
% 150.84/21.86  | | | | End of split
% 150.84/21.86  | | | | 
% 150.84/21.86  | | | End of split
% 150.84/21.86  | | | 
% 150.84/21.86  | | End of split
% 150.84/21.86  | | 
% 150.84/21.86  | End of split
% 150.84/21.86  | 
% 150.84/21.86  End of proof
% 150.84/21.86  
% 150.84/21.86  Sub-proof #1 shows that the following formulas are inconsistent:
% 150.84/21.86  ----------------------------------------------------------------
% 150.84/21.86    (1)  op(e0, e1) = all_52_11
% 150.84/21.86    (2)   ~ (all_52_7 = all_52_11)
% 150.84/21.86    (3)   ~ (all_52_2 = all_52_6)
% 150.84/21.86    (4)   ~ (all_52_3 = all_52_7)
% 150.84/21.86    (5)  all_54_9 = all_52_6
% 150.84/21.86    (6)  op(e1, e1) = all_4_2
% 150.84/21.86    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.86    (8)   ~ (all_52_2 = all_4_2)
% 150.84/21.86    (9)   ~ (all_52_7 = e1)
% 150.84/21.86    (10)   ~ (all_52_3 = all_52_11)
% 150.84/21.86    (11)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 150.84/21.86    (12)  op(e3, e3) = e2
% 150.84/21.86    (13)  op(e0, e0) = e1
% 150.84/21.86    (14)   ~ (all_52_7 = e3)
% 150.84/21.86    (15)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 150.84/21.86    (16)   ~ (all_52_2 = e2)
% 150.84/21.86    (17)   ~ (all_52_6 = e3)
% 150.84/21.86    (18)   ~ (all_52_3 = e1)
% 150.84/21.86    (19)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 150.84/21.86    (20)  all_54_12 = all_52_3
% 150.84/21.86    (21)   ~ (e1 = e0)
% 150.84/21.86    (22)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 150.84/21.86              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.84/21.86            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 150.84/21.86                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 150.84/21.86              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.84/21.86          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 150.84/21.86              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.84/21.86            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 150.84/21.86                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 150.84/21.86              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.84/21.86          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 150.84/21.86              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.84/21.86            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 150.84/21.86                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 150.84/21.86              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.84/21.86          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 150.84/21.86              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.84/21.86            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 150.84/21.86                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.84/21.86                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.84/21.86                $i(all_57_14))))
% 150.84/21.86    (23)  all_54_8 = all_52_2
% 150.84/21.86    (24)   ~ (e3 = e2)
% 150.84/21.86    (25)  all_54_13 = all_52_7
% 150.84/21.86    (26)   ~ (all_52_2 = all_52_3)
% 150.84/21.86    (27)   ~ (all_52_6 = all_52_7)
% 150.84/21.86    (28)  op(e2, e2) = e3
% 150.84/21.86    (29)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 150.84/21.86    (30)   ~ (all_52_6 = all_4_2)
% 150.84/21.86  
% 150.84/21.86  Begin of proof
% 150.84/21.86  | 
% 150.84/21.86  | BETA: splitting (22) gives:
% 150.84/21.86  | 
% 150.84/21.86  | Case 1:
% 150.84/21.86  | | 
% 150.84/21.86  | |   (31)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 150.84/21.86  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 150.84/21.86  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.84/21.86  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.84/21.86  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.84/21.86  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 150.84/21.86  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 150.84/21.86  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.84/21.86  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 150.84/21.86  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.84/21.86  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 150.84/21.86  | |               $i(all_57_15))))
% 150.84/21.86  | | 
% 150.84/21.86  | | REF_CLOSE: (7), (12), (24), (28), (31) are inconsistent by sub-proof #120.
% 150.84/21.86  | | 
% 150.84/21.86  | Case 2:
% 150.84/21.86  | | 
% 150.84/21.86  | |   (32)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 150.84/21.86  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.84/21.86  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.84/21.86  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.84/21.86  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 150.84/21.86  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 150.84/21.86  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 150.84/21.86  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.84/21.86  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 150.84/21.86  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 150.84/21.86  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 150.84/21.86  | |               all_57_14 & $i(all_57_14))))
% 150.84/21.86  | | 
% 150.84/21.86  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 150.84/21.86  | |            (14), (15), (16), (17), (18), (19), (20), (21), (23), (25), (26),
% 150.84/21.86  | |            (27), (29), (30), (32) are inconsistent by sub-proof #77.
% 150.84/21.86  | | 
% 150.84/21.86  | End of split
% 150.84/21.86  | 
% 150.84/21.86  End of proof
% 150.84/21.86  
% 150.84/21.86  Sub-proof #2 shows that the following formulas are inconsistent:
% 150.84/21.86  ----------------------------------------------------------------
% 150.84/21.86    (1)  op(e0, e1) = e3
% 150.84/21.86    (2)   ~ (e3 = e1)
% 150.84/21.86    (3)  all_56_10 = e3
% 150.84/21.86    (4)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 150.84/21.86         (all_56_14 = e0 & op(e0, e1) = e0)
% 150.84/21.86    (5)  op(e1, e3) = e3
% 150.84/21.86    (6)  op(e0, e2) = all_52_7
% 150.84/21.86    (7)  op(e1, e0) = e0
% 150.84/21.86    (8)   ~ (all_52_3 = all_52_7)
% 150.84/21.86    (9)  op(e3, e0) = e2
% 150.84/21.86    (10)   ~ (e2 = e0)
% 150.84/21.86    (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 150.84/21.86          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 150.84/21.86    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.86            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.86    (13)  op(e2, e3) = e1
% 150.84/21.86    (14)  op(e2, e0) = e3
% 150.84/21.86    (15)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 150.84/21.86            all_57_14 & $i(all_57_14))
% 150.84/21.86    (16)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 150.84/21.86          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 150.84/21.86    (17)  all_56_5 = e0
% 150.84/21.86    (18)  op(e0, e0) = e1
% 150.84/21.86    (19)   ~ (e3 = e0)
% 150.84/21.86    (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 150.84/21.86          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 150.84/21.86    (21)   ~ (all_52_9 = e2)
% 150.84/21.86    (22)  op(e0, e3) = all_52_3
% 150.84/21.86    (23)  all_56_14 = e3
% 150.84/21.86    (24)  op(e2, e2) = e2
% 150.84/21.86    (25)  op(e2, e1) = all_52_9
% 150.84/21.86    (26)   ~ (e1 = e0)
% 150.84/21.86    (27)   ~ (e3 = e2)
% 150.84/21.86    (28)   ~ (all_52_8 = e3)
% 150.84/21.86    (29)  all_56_9 = e2
% 150.84/21.86    (30)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 150.84/21.86          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 150.84/21.86    (31)  all_56_12 = e2
% 150.84/21.86    (32)  op(e3, e1) = all_52_8
% 150.84/21.86    (33)   ~ (e2 = e1)
% 150.84/21.86    (34)  all_56_1 = e3
% 150.84/21.86    (35)  op(e3, e0) = all_14_1
% 150.84/21.86    (36)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 150.84/21.86              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 150.84/21.86            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 150.84/21.86            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 150.84/21.86            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.84/21.86            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 150.84/21.86            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 150.84/21.86            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.84/21.86            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 150.84/21.86            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.84/21.86            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.84/21.86            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 150.84/21.86            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.84/21.86            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.84/21.86            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 150.84/21.86            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.84/21.86            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.84/21.86            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 150.84/21.86            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.84/21.86            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 150.84/21.86            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 150.84/21.86            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.84/21.86            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.84/21.86            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 150.84/21.86            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.84/21.86            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.84/21.86            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 150.84/21.86            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.84/21.86            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.86            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 150.84/21.86            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 150.84/21.86            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 150.84/21.86            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 150.84/21.86            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.84/21.86            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.86            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 150.84/21.86            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.86            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.84/21.86            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 150.84/21.86            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.86            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.84/21.86            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 150.84/21.86            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.84/21.86            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.84/21.86            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 150.84/21.86            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.84/21.86            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 150.84/21.86            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.84/21.86              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 150.84/21.86            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.84/21.86            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.84/21.86              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 150.84/21.86            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.84/21.86            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 150.84/21.86                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.84/21.86                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.86                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.84/21.86                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.84/21.86                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 150.84/21.86                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 150.84/21.86                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.84/21.86              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 150.84/21.86                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 150.84/21.86                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.84/21.86                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.84/21.86                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 150.84/21.86                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.84/21.86                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.84/21.86                $i(all_57_7))))
% 150.84/21.86    (37)  op(e0, e2) = e0
% 150.84/21.86    (38)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 150.84/21.86          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 150.84/21.86            e1)
% 150.84/21.86    (39)  op(e2, e3) = all_52_1
% 150.84/21.86  
% 150.84/21.86  Begin of proof
% 150.84/21.86  | 
% 150.84/21.86  | BETA: splitting (36) gives:
% 150.84/21.86  | 
% 150.84/21.86  | Case 1:
% 150.84/21.86  | | 
% 150.84/21.86  | |   (40)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 150.84/21.86  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 150.84/21.86  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 150.84/21.86  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 150.84/21.86  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 150.84/21.86  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 150.84/21.86  | |         (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 150.84/21.86  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 150.84/21.86  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 150.84/21.86  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 150.84/21.86  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 150.84/21.86  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) |
% 150.84/21.86  | |         (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 150.84/21.86  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.84/21.86  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.84/21.86  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 150.84/21.86  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.84/21.86  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 150.84/21.86  | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 150.84/21.86  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 150.84/21.86  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.84/21.86  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 150.84/21.86  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 150.84/21.86  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 150.84/21.86  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 150.84/21.86  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 150.84/21.86  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.84/21.86  | | 
% 150.84/21.86  | | BETA: splitting (40) gives:
% 150.84/21.86  | | 
% 150.84/21.86  | | Case 1:
% 150.84/21.86  | | | 
% 150.84/21.86  | | |   (41)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.84/21.86  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.84/21.86  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 150.84/21.86  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 150.84/21.86  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 150.84/21.86  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.84/21.86  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 150.84/21.86  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.84/21.86  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.84/21.86  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 150.84/21.86  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.84/21.86  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 150.84/21.86  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 150.84/21.86  | | | 
% 150.84/21.86  | | | BETA: splitting (41) gives:
% 150.84/21.86  | | | 
% 150.84/21.86  | | | Case 1:
% 150.84/21.86  | | | | 
% 150.84/21.86  | | | |   (42)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.84/21.86  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.84/21.86  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 150.84/21.86  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 150.84/21.86  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.84/21.86  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 150.84/21.86  | | | |           e3 & $i(all_57_2) & $i(all_57_12))
% 150.84/21.86  | | | | 
% 150.84/21.86  | | | | BETA: splitting (42) gives:
% 150.84/21.86  | | | | 
% 150.84/21.86  | | | | Case 1:
% 150.84/21.86  | | | | | 
% 150.84/21.86  | | | | |   (43)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.84/21.86  | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.84/21.86  | | | | |         op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 150.84/21.86  | | | | |         $i(all_57_12)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | ALPHA: (43) implies:
% 150.84/21.87  | | | | |   (44)  op(e2, e3) = e2
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | REF_CLOSE: (2), (3), (12), (17), (24), (26), (30), (33), (39), (44)
% 150.84/21.87  | | | | |            are inconsistent by sub-proof #333.
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | Case 2:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (45)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 150.84/21.87  | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.84/21.87  | | | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 150.84/21.87  | | | | |         $i(all_57_12)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | ALPHA: (45) implies:
% 150.84/21.87  | | | | |   (46)  op(e2, e3) = e2
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | REF_CLOSE: (2), (3), (12), (17), (24), (26), (30), (33), (39), (46)
% 150.84/21.87  | | | | |            are inconsistent by sub-proof #333.
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | End of split
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | Case 2:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | |   (47)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.87  | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.84/21.87  | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.84/21.87  | | | |           $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 150.84/21.87  | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.84/21.87  | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 150.84/21.87  | | | |           e3 & $i(all_57_2) & $i(all_57_14))
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | BETA: splitting (47) gives:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | Case 1:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (48)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.87  | | | | |         (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.84/21.87  | | | | |         op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.84/21.87  | | | | |         $i(all_57_14)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | ALPHA: (48) implies:
% 150.84/21.87  | | | | |   (49)  op(e1, e3) = e1
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | REF_CLOSE: (2), (5), (12), (49) are inconsistent by sub-proof #119.
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | Case 2:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (50)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 150.84/21.87  | | | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.84/21.87  | | | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 150.84/21.87  | | | | |         $i(all_57_14)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | ALPHA: (50) implies:
% 150.84/21.87  | | | | |   (51)  op(e0, e0) = e3
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | REF_CLOSE: (2), (12), (18), (51) are inconsistent by sub-proof #1022.
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | End of split
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | End of split
% 150.84/21.87  | | | 
% 150.84/21.87  | | Case 2:
% 150.84/21.87  | | | 
% 150.84/21.87  | | |   (52)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.87  | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.84/21.87  | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.84/21.87  | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5
% 150.84/21.87  | | |             = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 150.84/21.87  | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.84/21.87  | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.84/21.87  | | |           &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.84/21.87  | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 150.84/21.87  | | |           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 =
% 150.84/21.87  | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 150.84/21.87  | | |           & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 150.84/21.87  | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 150.84/21.87  | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.84/21.87  | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.87  | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.84/21.87  | | | 
% 150.84/21.87  | | | BETA: splitting (52) gives:
% 150.84/21.87  | | | 
% 150.84/21.87  | | | Case 1:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | |   (53)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.87  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.84/21.87  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.84/21.87  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 150.84/21.87  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 150.84/21.87  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.84/21.87  | | | |           $i(all_57_5) & $i(all_57_10))
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | BETA: splitting (53) gives:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | Case 1:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (54)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.87  | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.84/21.87  | | | | |         op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.84/21.87  | | | | |         $i(all_57_10)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | ALPHA: (54) implies:
% 150.84/21.87  | | | | |   (55)  all_57_14 = e2
% 150.84/21.87  | | | | |   (56)   ~ (all_57_4 = e1)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | REF_CLOSE: (15), (55), (56) are inconsistent by sub-proof #1005.
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | Case 2:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (57)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.84/21.87  | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.84/21.87  | | | | |         op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.84/21.87  | | | | |         $i(all_57_10)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | ALPHA: (57) implies:
% 150.84/21.87  | | | | |   (58)  op(e0, e0) = e2
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | REF_CLOSE: (2), (4), (10), (12), (19), (23), (26), (31), (33), (38),
% 150.84/21.87  | | | | |            (58) are inconsistent by sub-proof #107.
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | End of split
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | Case 2:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | |   (59)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.84/21.87  | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 150.84/21.87  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 150.84/21.87  | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 150.84/21.87  | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.84/21.87  | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 150.84/21.87  | | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.84/21.87  | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 150.84/21.87  | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.84/21.87  | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | BETA: splitting (59) gives:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | Case 1:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (60)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.84/21.87  | | | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 150.84/21.87  | | | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 150.84/21.87  | | | | |         $i(all_57_14)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | ALPHA: (60) implies:
% 150.84/21.87  | | | | |   (61)  op(e3, e3) = e2
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | REF_CLOSE: (2), (10), (12), (16), (19), (20), (26), (29), (33), (34),
% 150.84/21.87  | | | | |            (61) are inconsistent by sub-proof #654.
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | Case 2:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (62)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.84/21.87  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 150.84/21.87  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.84/21.87  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 150.84/21.87  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.84/21.87  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.87  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | BETA: splitting (62) gives:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | Case 1:
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | |   (63)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.84/21.87  | | | | | |         (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 150.84/21.87  | | | | | |         & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.84/21.87  | | | | | |         $i(all_57_14)
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | ALPHA: (63) implies:
% 150.84/21.87  | | | | | |   (64)  op(e0, e0) = e2
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | REF_CLOSE: (2), (4), (10), (12), (19), (23), (26), (31), (33), (38),
% 150.84/21.87  | | | | | |            (64) are inconsistent by sub-proof #107.
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | Case 2:
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | |   (65)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.84/21.87  | | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 150.84/21.87  | | | | | |         & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.84/21.87  | | | | | |         $i(all_57_10)
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | ALPHA: (65) implies:
% 150.84/21.87  | | | | | |   (66)  op(e2, e2) = e1
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | REF_CLOSE: (3), (10), (11), (12), (13), (17), (27), (33), (39), (66)
% 150.84/21.87  | | | | | |            are inconsistent by sub-proof #388.
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | End of split
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | End of split
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | End of split
% 150.84/21.87  | | | 
% 150.84/21.87  | | End of split
% 150.84/21.87  | | 
% 150.84/21.87  | Case 2:
% 150.84/21.87  | | 
% 150.84/21.87  | |   (67)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 150.84/21.87  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.84/21.87  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 150.84/21.87  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 150.84/21.87  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 150.84/21.87  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 150.84/21.87  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 150.84/21.87  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.84/21.87  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.84/21.87  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.84/21.87  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.87  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.84/21.87  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 150.84/21.87  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 150.84/21.87  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.84/21.87  | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.84/21.87  | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.84/21.87  | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 150.84/21.87  | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.84/21.87  | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.84/21.87  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 150.84/21.87  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 150.84/21.87  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 150.84/21.87  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.84/21.87  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 150.84/21.87  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.84/21.87  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 150.84/21.87  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.84/21.87  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.84/21.87  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 150.84/21.87  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 150.84/21.87  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.84/21.87  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.84/21.87  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.84/21.87  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.84/21.87  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 150.84/21.87  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 150.84/21.87  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.84/21.87  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.84/21.87  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.84/21.87  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.84/21.87  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.84/21.87  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.84/21.87  | |               $i(all_57_7))))
% 150.84/21.87  | | 
% 150.84/21.87  | | BETA: splitting (67) gives:
% 150.84/21.87  | | 
% 150.84/21.87  | | Case 1:
% 150.84/21.87  | | | 
% 150.84/21.87  | | |   (68)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.84/21.87  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.84/21.87  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.87  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 150.84/21.87  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.84/21.87  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.84/21.87  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 150.84/21.87  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.84/21.87  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 150.84/21.87  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 150.84/21.87  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.84/21.87  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.84/21.87  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 150.84/21.87  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.84/21.87  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.87  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.84/21.87  | | |           $i(all_57_13))
% 150.84/21.87  | | | 
% 150.84/21.87  | | | BETA: splitting (68) gives:
% 150.84/21.87  | | | 
% 150.84/21.87  | | | Case 1:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | |   (69)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.84/21.87  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.84/21.87  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.87  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 150.84/21.87  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 150.84/21.87  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 150.84/21.87  | | | |           e2 & $i(all_57_6) & $i(all_57_12))
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | REF_CLOSE: (12), (21), (25), (28), (32), (69) are inconsistent by
% 150.84/21.87  | | | |            sub-proof #1083.
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | Case 2:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | |   (70)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.84/21.87  | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.84/21.87  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.87  | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 150.84/21.87  | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.84/21.87  | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 150.84/21.87  | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 150.84/21.87  | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.84/21.87  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 150.84/21.87  | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | BETA: splitting (70) gives:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | Case 1:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (71)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.84/21.87  | | | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.84/21.87  | | | | |         op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.87  | | | | |         $i(all_57_12)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | ALPHA: (71) implies:
% 150.84/21.87  | | | | |   (72)  op(e2, e1) = e2
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | REF_CLOSE: (12), (21), (25), (72) are inconsistent by sub-proof #1157.
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | Case 2:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (73)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.84/21.87  | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.84/21.87  | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.84/21.87  | | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 150.84/21.87  | | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 150.84/21.87  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.84/21.87  | | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | BETA: splitting (73) gives:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | Case 1:
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | |   (74)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.84/21.87  | | | | | |         (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.84/21.87  | | | | | |         & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.84/21.87  | | | | | |         $i(all_57_11)
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | ALPHA: (74) implies:
% 150.84/21.87  | | | | | |   (75)  op(e3, e0) = e3
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | REF_CLOSE: (9), (12), (27), (35), (75) are inconsistent by sub-proof
% 150.84/21.87  | | | | | |            #14.
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | Case 2:
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | |   (76)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.84/21.87  | | | | | |         (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 150.84/21.87  | | | | | |         & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.84/21.87  | | | | | |         $i(all_57_13)
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | ALPHA: (76) implies:
% 150.84/21.87  | | | | | |   (77)  op(e3, e0) = e3
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | REF_CLOSE: (9), (12), (27), (35), (77) are inconsistent by sub-proof
% 150.84/21.87  | | | | | |            #14.
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | End of split
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | End of split
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | End of split
% 150.84/21.87  | | | 
% 150.84/21.87  | | Case 2:
% 150.84/21.87  | | | 
% 150.84/21.87  | | |   (78)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.84/21.87  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.84/21.87  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.84/21.87  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.84/21.87  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.84/21.87  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.84/21.87  | | |           $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0
% 150.84/21.87  | | |           &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.84/21.87  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 150.84/21.87  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 150.84/21.87  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.84/21.87  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 150.84/21.87  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.84/21.87  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.84/21.87  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.84/21.87  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.87  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 150.84/21.87  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.84/21.87  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 150.84/21.87  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.84/21.87  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 150.84/21.87  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.84/21.87  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 150.84/21.87  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.84/21.87  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.84/21.87  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.84/21.87  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.84/21.87  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.84/21.87  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.84/21.87  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 150.84/21.87  | | | 
% 150.84/21.87  | | | BETA: splitting (78) gives:
% 150.84/21.87  | | | 
% 150.84/21.87  | | | Case 1:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | |   (79)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.84/21.87  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.84/21.87  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.84/21.87  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 150.84/21.87  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.84/21.87  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.84/21.87  | | | |           e1 & $i(all_57_9) & $i(all_57_14))
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | BETA: splitting (79) gives:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | Case 1:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (80)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.84/21.87  | | | | |         (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.84/21.87  | | | | |         op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.84/21.87  | | | | |         $i(all_57_12)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | ALPHA: (80) implies:
% 150.84/21.87  | | | | |   (81)  op(e2, e0) = e2
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | REF_CLOSE: (12), (14), (27), (81) are inconsistent by sub-proof #854.
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | Case 2:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (82)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 150.84/21.87  | | | | |         (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.84/21.87  | | | | |         op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 150.84/21.87  | | | | |         $i(all_57_14)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | ALPHA: (82) implies:
% 150.84/21.87  | | | | |   (83)  op(e1, e0) = e1
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | REF_CLOSE: (7), (12), (26), (83) are inconsistent by sub-proof #467.
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | End of split
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | Case 2:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | |   (84)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 150.84/21.87  | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.84/21.87  | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.84/21.87  | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 150.84/21.87  | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.84/21.87  | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.84/21.87  | | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 150.84/21.87  | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 150.84/21.87  | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.84/21.87  | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.87  | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 150.84/21.87  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.84/21.87  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.84/21.87  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.84/21.87  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.84/21.87  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.84/21.87  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.87  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 150.84/21.87  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.84/21.87  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 150.84/21.87  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 150.84/21.87  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.84/21.87  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.84/21.87  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | BETA: splitting (84) gives:
% 150.84/21.87  | | | | 
% 150.84/21.87  | | | | Case 1:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (85)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 150.84/21.87  | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.84/21.87  | | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.84/21.87  | | | | |         $i(all_57_13)
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | ALPHA: (85) implies:
% 150.84/21.87  | | | | |   (86)  op(e2, e0) = e2
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | REF_CLOSE: (12), (14), (27), (86) are inconsistent by sub-proof #854.
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | Case 2:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | |   (87)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.84/21.87  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 150.84/21.87  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.84/21.87  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.84/21.87  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.87  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 150.84/21.87  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 150.84/21.87  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.84/21.87  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.84/21.87  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 150.84/21.87  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 150.84/21.87  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.84/21.87  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 150.84/21.87  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.84/21.87  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.84/21.87  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.84/21.87  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 150.84/21.87  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.84/21.87  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.84/21.87  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 150.84/21.87  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.84/21.87  | | | | |               $i(all_57_7))))
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | BETA: splitting (87) gives:
% 150.84/21.87  | | | | | 
% 150.84/21.87  | | | | | Case 1:
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | |   (88)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.84/21.87  | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 150.84/21.87  | | | | | |         & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.84/21.87  | | | | | |         $i(all_57_14)
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | ALPHA: (88) implies:
% 150.84/21.87  | | | | | |   (89)  op(e1, e0) = e1
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | REF_CLOSE: (7), (12), (26), (89) are inconsistent by sub-proof #467.
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | Case 2:
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | |   (90)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.84/21.87  | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 150.84/21.87  | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 150.84/21.87  | | | | | |               e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.84/21.87  | | | | | |             = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1,
% 150.84/21.87  | | | | | |               e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.84/21.87  | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.84/21.87  | | | | | |             (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 150.84/21.87  | | | | | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.84/21.87  | | | | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 150.84/21.87  | | | | | |             (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.84/21.87  | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.84/21.87  | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.84/21.87  | | | | | |             (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 150.84/21.87  | | | | | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.84/21.87  | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.84/21.87  | | | | | |             (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 150.84/21.87  | | | | | |             & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.84/21.87  | | | | | |             $i(all_57_7)))
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | ALPHA: (90) implies:
% 150.84/21.87  | | | | | |   (91)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.87  | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 150.84/21.87  | | | | | |           & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 150.84/21.87  | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.84/21.87  | | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 150.84/21.87  | | | | | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.84/21.87  | | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.84/21.87  | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.84/21.87  | | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.87  | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 150.84/21.87  | | | | | |           & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.84/21.87  | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 150.84/21.87  | | | | | |           & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 150.84/21.87  | | | | | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.84/21.87  | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.84/21.87  | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | BETA: splitting (91) gives:
% 150.84/21.87  | | | | | | 
% 150.84/21.87  | | | | | | Case 1:
% 150.84/21.87  | | | | | | | 
% 150.84/21.87  | | | | | | |   (92)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.87  | | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 150.84/21.87  | | | | | | |           e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 150.84/21.87  | | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.84/21.87  | | | | | | |             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.84/21.87  | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 150.84/21.87  | | | | | | |           = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 150.84/21.87  | | | | | | |             e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.84/21.87  | | | | | | |           $i(all_57_3))
% 150.84/21.87  | | | | | | | 
% 150.84/21.87  | | | | | | | BETA: splitting (92) gives:
% 150.84/21.87  | | | | | | | 
% 150.84/21.87  | | | | | | | Case 1:
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | |   (93)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.87  | | | | | | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 150.84/21.87  | | | | | | | |         e3 & op(e0, e3) = e0 & $i(all_57_0)
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | | ALPHA: (93) implies:
% 150.84/21.87  | | | | | | | |   (94)  op(e0, e3) = e0
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | | REF_CLOSE: (6), (8), (12), (22), (37), (94) are inconsistent by
% 150.84/21.87  | | | | | | | |            sub-proof #1123.
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | Case 2:
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | |   (95)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 150.84/21.87  | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 150.84/21.87  | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.84/21.87  | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 150.84/21.87  | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.84/21.87  | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | | BETA: splitting (95) gives:
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | | Case 1:
% 150.84/21.87  | | | | | | | | | 
% 150.84/21.87  | | | | | | | | |   (96)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 150.84/21.87  | | | | | | | | |         ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 150.84/21.87  | | | | | | | | |           e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)
% 150.84/21.87  | | | | | | | | | 
% 150.84/21.87  | | | | | | | | | ALPHA: (96) implies:
% 150.84/21.87  | | | | | | | | |   (97)  op(e0, e3) = e0
% 150.84/21.87  | | | | | | | | | 
% 150.84/21.87  | | | | | | | | | REF_CLOSE: (6), (8), (12), (22), (37), (97) are inconsistent
% 150.84/21.87  | | | | | | | | |            by sub-proof #1123.
% 150.84/21.87  | | | | | | | | | 
% 150.84/21.87  | | | | | | | | Case 2:
% 150.84/21.87  | | | | | | | | | 
% 150.84/21.87  | | | | | | | | |   (98)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 150.84/21.87  | | | | | | | | |         ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.84/21.87  | | | | | | | | |         all_57_3 & op(e0, e2) = e0 & $i(all_57_3)
% 150.84/21.87  | | | | | | | | | 
% 150.84/21.87  | | | | | | | | | ALPHA: (98) implies:
% 150.84/21.87  | | | | | | | | |   (99)  op(e3, e3) = e2
% 150.84/21.87  | | | | | | | | | 
% 150.84/21.87  | | | | | | | | | REF_CLOSE: (2), (10), (12), (16), (19), (20), (26), (29),
% 150.84/21.87  | | | | | | | | |            (33), (34), (99) are inconsistent by sub-proof
% 150.84/21.87  | | | | | | | | |            #654.
% 150.84/21.87  | | | | | | | | | 
% 150.84/21.87  | | | | | | | | End of split
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | End of split
% 150.84/21.87  | | | | | | | 
% 150.84/21.87  | | | | | | Case 2:
% 150.84/21.87  | | | | | | | 
% 150.84/21.87  | | | | | | |   (100)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.87  | | | | | | |            (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.84/21.87  | | | | | | |            e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.84/21.87  | | | | | | |            all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.84/21.87  | | | | | | |              e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 150.84/21.87  | | | | | | |            op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.84/21.87  | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.84/21.87  | | | | | | |              e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.84/21.87  | | | | | | |            op(e0, e1) = e0 & $i(all_57_7))
% 150.84/21.87  | | | | | | | 
% 150.84/21.87  | | | | | | | BETA: splitting (100) gives:
% 150.84/21.87  | | | | | | | 
% 150.84/21.87  | | | | | | | Case 1:
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | |   (101)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) & 
% 150.84/21.87  | | | | | | | |          ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1)
% 150.84/21.87  | | | | | | | |          = e2 & op(e0, e2) = e0 & $i(all_57_4)
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | | ALPHA: (101) implies:
% 150.84/21.87  | | | | | | | |   (102)  all_57_14 = e2
% 150.84/21.87  | | | | | | | |   (103)   ~ (all_57_4 = e1)
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | | REF_CLOSE: (15), (102), (103) are inconsistent by sub-proof
% 150.84/21.87  | | | | | | | |            #1005.
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | Case 2:
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | |   (104)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 150.84/21.87  | | | | | | | |            ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.84/21.87  | | | | | | | |            all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.84/21.87  | | | | | | | |          (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 150.84/21.87  | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.87  | | | | | | | |            all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.84/21.87  | | | | | | | | 
% 150.84/21.87  | | | | | | | | BETA: splitting (104) gives:
% 150.84/21.88  | | | | | | | | 
% 150.84/21.88  | | | | | | | | Case 1:
% 150.84/21.88  | | | | | | | | | 
% 150.84/21.88  | | | | | | | | |   (105)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &
% 150.84/21.88  | | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.84/21.88  | | | | | | | | |          all_57_6 & op(e0, e1) = e0 & $i(all_57_6)
% 150.84/21.88  | | | | | | | | | 
% 150.84/21.88  | | | | | | | | | ALPHA: (105) implies:
% 150.84/21.88  | | | | | | | | |   (106)  op(e0, e1) = e0
% 150.84/21.88  | | | | | | | | | 
% 150.84/21.88  | | | | | | | | | REF_CLOSE: (1), (12), (19), (106) are inconsistent by
% 150.84/21.88  | | | | | | | | |            sub-proof #104.
% 150.84/21.88  | | | | | | | | | 
% 150.84/21.88  | | | | | | | | Case 2:
% 150.84/21.88  | | | | | | | | | 
% 150.84/21.88  | | | | | | | | |   (107)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 150.84/21.88  | | | | | | | | |           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.88  | | | | | | | | |          all_57_7 & op(e0, e1) = e0 & $i(all_57_7)
% 150.84/21.88  | | | | | | | | | 
% 150.84/21.88  | | | | | | | | | ALPHA: (107) implies:
% 150.84/21.88  | | | | | | | | |   (108)  op(e2, e2) = e1
% 150.84/21.88  | | | | | | | | | 
% 150.84/21.88  | | | | | | | | | REF_CLOSE: (3), (10), (11), (12), (13), (17), (27), (33),
% 150.84/21.88  | | | | | | | | |            (39), (108) are inconsistent by sub-proof #388.
% 150.84/21.88  | | | | | | | | | 
% 150.84/21.88  | | | | | | | | End of split
% 150.84/21.88  | | | | | | | | 
% 150.84/21.88  | | | | | | | End of split
% 150.84/21.88  | | | | | | | 
% 150.84/21.88  | | | | | | End of split
% 150.84/21.88  | | | | | | 
% 150.84/21.88  | | | | | End of split
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | End of split
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | End of split
% 150.84/21.88  | | | 
% 150.84/21.88  | | End of split
% 150.84/21.88  | | 
% 150.84/21.88  | End of split
% 150.84/21.88  | 
% 150.84/21.88  End of proof
% 150.84/21.88  
% 150.84/21.88  Sub-proof #3 shows that the following formulas are inconsistent:
% 150.84/21.88  ----------------------------------------------------------------
% 150.84/21.88    (1)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 150.84/21.88         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 150.84/21.88    (2)   ~ (e3 = e1)
% 150.84/21.88    (3)  op(e1, e1) = e2
% 150.84/21.88    (4)  op(e0, e2) = all_52_7
% 150.84/21.88    (5)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 150.84/21.88         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 150.84/21.88    (6)   ~ (e2 = e0)
% 150.84/21.88    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.88    (8)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 150.84/21.88         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 150.84/21.88    (9)   ~ (all_52_7 = e1)
% 150.84/21.88    (10)   ~ (e3 = e0)
% 150.84/21.88    (11)  all_56_4 = e1
% 150.84/21.88    (12)  op(e3, e1) = e1
% 150.84/21.88    (13)   ~ (all_52_3 = e1)
% 150.84/21.88    (14)  op(e0, e3) = all_52_3
% 150.84/21.88    (15)   ~ (e1 = e0)
% 150.84/21.88    (16)   ~ (e3 = e2)
% 150.84/21.88    (17)  op(e3, e1) = all_52_8
% 150.84/21.88    (18)   ~ (e2 = e1)
% 150.84/21.88    (19)  op(e0, e0) = e0
% 150.84/21.88    (20)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 150.84/21.88          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 150.84/21.88            e1)
% 150.84/21.88  
% 150.84/21.88  Begin of proof
% 150.84/21.88  | 
% 150.84/21.88  | BETA: splitting (20) gives:
% 150.84/21.88  | 
% 150.84/21.88  | Case 1:
% 150.84/21.88  | | 
% 150.84/21.88  | |   (21)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 150.84/21.88  | |           e1)
% 150.84/21.88  | | 
% 150.84/21.88  | | REF_CLOSE: (4), (7), (9), (13), (14), (21) are inconsistent by sub-proof
% 150.84/21.88  | |            #23.
% 150.84/21.88  | | 
% 150.84/21.88  | Case 2:
% 150.84/21.88  | | 
% 150.84/21.88  | |   (22)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 150.84/21.88  | |           e1)
% 150.84/21.88  | | 
% 150.84/21.88  | | BETA: splitting (22) gives:
% 150.84/21.88  | | 
% 150.84/21.88  | | Case 1:
% 150.84/21.88  | | | 
% 150.84/21.88  | | |   (23)  all_56_14 = e1 & op(e0, e1) = e1
% 150.84/21.88  | | | 
% 150.84/21.88  | | | ALPHA: (23) implies:
% 150.84/21.88  | | |   (24)  all_56_14 = e1
% 150.84/21.88  | | |   (25)  op(e0, e1) = e1
% 150.84/21.88  | | | 
% 150.84/21.88  | | | BETA: splitting (1) gives:
% 150.84/21.88  | | | 
% 150.84/21.88  | | | Case 1:
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | |   (26)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1)
% 150.84/21.88  | | | |           = e3)
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | | BETA: splitting (26) gives:
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | | Case 1:
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | |   (27)  all_56_4 = e3 & op(e3, e1) = e3
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | ALPHA: (27) implies:
% 150.84/21.88  | | | | |   (28)  op(e3, e1) = e3
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | REF_CLOSE: (2), (7), (12), (17), (28) are inconsistent by sub-proof
% 150.84/21.88  | | | | |            #439.
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | Case 2:
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | |   (29)  all_56_5 = e3 & op(e2, e1) = e3
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | ALPHA: (29) implies:
% 150.84/21.88  | | | | |   (30)  all_56_5 = e3
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | BETA: splitting (5) gives:
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | Case 1:
% 150.84/21.88  | | | | | | 
% 150.84/21.88  | | | | | |   (31)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2,
% 150.84/21.88  | | | | | |             e1) = e0)
% 150.84/21.88  | | | | | | 
% 150.84/21.88  | | | | | | BETA: splitting (31) gives:
% 150.84/21.88  | | | | | | 
% 150.84/21.88  | | | | | | Case 1:
% 150.84/21.88  | | | | | | | 
% 150.84/21.88  | | | | | | |   (32)  all_56_4 = e0 & op(e3, e1) = e0
% 150.84/21.88  | | | | | | | 
% 150.84/21.88  | | | | | | | REF_CLOSE: (11), (15), (32) are inconsistent by sub-proof #347.
% 150.84/21.88  | | | | | | | 
% 150.84/21.88  | | | | | | Case 2:
% 150.84/21.88  | | | | | | | 
% 150.84/21.88  | | | | | | |   (33)  all_56_5 = e0 & op(e2, e1) = e0
% 150.84/21.88  | | | | | | | 
% 150.84/21.88  | | | | | | | REF_CLOSE: (10), (30), (33) are inconsistent by sub-proof #885.
% 150.84/21.88  | | | | | | | 
% 150.84/21.88  | | | | | | End of split
% 150.84/21.88  | | | | | | 
% 150.84/21.88  | | | | | Case 2:
% 150.84/21.88  | | | | | | 
% 150.84/21.88  | | | | | |   (34)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0,
% 150.84/21.88  | | | | | |             e1) = e0)
% 150.84/21.88  | | | | | | 
% 150.84/21.88  | | | | | | REF_CLOSE: (3), (6), (7), (15), (25), (34) are inconsistent by
% 150.84/21.88  | | | | | |            sub-proof #15.
% 150.84/21.88  | | | | | | 
% 150.84/21.88  | | | | | End of split
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | End of split
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | Case 2:
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | |   (35)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1)
% 150.84/21.88  | | | |           = e3)
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | | BETA: splitting (35) gives:
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | | Case 1:
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | |   (36)  all_56_8 = e3 & op(e1, e1) = e3
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | ALPHA: (36) implies:
% 150.84/21.88  | | | | |   (37)  op(e1, e1) = e3
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | REF_CLOSE: (5), (6), (7), (8), (10), (11), (15), (16), (18), (24),
% 150.84/21.88  | | | | |            (37) are inconsistent by sub-proof #254.
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | Case 2:
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | |   (38)  all_56_14 = e3 & op(e0, e1) = e3
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | REF_CLOSE: (2), (24), (38) are inconsistent by sub-proof #639.
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | End of split
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | End of split
% 150.84/21.88  | | | 
% 150.84/21.88  | | Case 2:
% 150.84/21.88  | | | 
% 150.84/21.88  | | |   (39)  all_56_15 = e1 & op(e0, e0) = e1
% 150.84/21.88  | | | 
% 150.84/21.88  | | | ALPHA: (39) implies:
% 150.84/21.88  | | |   (40)  op(e0, e0) = e1
% 150.84/21.88  | | | 
% 150.84/21.88  | | | REF_CLOSE: (7), (15), (19), (40) are inconsistent by sub-proof #1040.
% 150.84/21.88  | | | 
% 150.84/21.88  | | End of split
% 150.84/21.88  | | 
% 150.84/21.88  | End of split
% 150.84/21.88  | 
% 150.84/21.88  End of proof
% 150.84/21.88  
% 150.84/21.88  Sub-proof #4 shows that the following formulas are inconsistent:
% 150.84/21.88  ----------------------------------------------------------------
% 150.84/21.88    (1)  op(e3, e3) = all_14_2
% 150.84/21.88    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.88    (3)   ~ (all_52_12 = all_14_2)
% 150.84/21.88    (4)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 150.84/21.88             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.84/21.88           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 150.84/21.88           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.84/21.88           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 150.84/21.88           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 150.84/21.88           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 150.84/21.88           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.84/21.88           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.84/21.88    (5)  op(e3, e0) = all_52_12
% 150.84/21.88    (6)   ~ (all_52_9 = e2)
% 150.84/21.88    (7)  op(e2, e1) = all_52_9
% 150.84/21.88    (8)  op(e3, e3) = e3
% 150.84/21.88  
% 150.84/21.88  Begin of proof
% 150.84/21.88  | 
% 150.84/21.88  | BETA: splitting (4) gives:
% 150.84/21.88  | 
% 150.84/21.88  | Case 1:
% 150.84/21.88  | | 
% 150.84/21.88  | |   (9)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 150.84/21.88  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.84/21.88  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 150.84/21.88  | | 
% 150.84/21.88  | | ALPHA: (9) implies:
% 150.84/21.88  | |   (10)  op(e2, e1) = e2
% 150.84/21.88  | | 
% 150.84/21.88  | | REF_CLOSE: (2), (6), (7), (10) are inconsistent by sub-proof #1157.
% 150.84/21.88  | | 
% 150.84/21.88  | Case 2:
% 150.84/21.88  | | 
% 150.84/21.88  | |   (11)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.84/21.88  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.88  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.84/21.88  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 150.84/21.88  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 150.84/21.88  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.84/21.88  | |           $i(all_57_13))
% 150.84/21.88  | | 
% 150.84/21.88  | | REF_CLOSE: (1), (2), (3), (5), (8), (11) are inconsistent by sub-proof #58.
% 150.84/21.88  | | 
% 150.84/21.88  | End of split
% 150.84/21.88  | 
% 150.84/21.88  End of proof
% 150.84/21.88  
% 150.84/21.88  Sub-proof #5 shows that the following formulas are inconsistent:
% 150.84/21.88  ----------------------------------------------------------------
% 150.84/21.88    (1)   ~ (all_52_14 = e2)
% 150.84/21.88    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.88    (3)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 150.84/21.88    (4)  op(e1, e0) = all_52_14
% 150.84/21.88    (5)  op(e0, e0) = e1
% 150.84/21.88    (6)   ~ (e2 = e1)
% 150.84/21.88  
% 150.84/21.88  Begin of proof
% 150.84/21.88  | 
% 150.84/21.88  | BETA: splitting (3) gives:
% 150.84/21.88  | 
% 150.84/21.88  | Case 1:
% 150.84/21.88  | | 
% 150.84/21.88  | |   (7)  all_56_11 = e2 & op(e1, e0) = e2
% 150.84/21.88  | | 
% 150.84/21.88  | | ALPHA: (7) implies:
% 150.84/21.88  | |   (8)  op(e1, e0) = e2
% 150.84/21.88  | | 
% 150.84/21.88  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #974.
% 150.84/21.88  | | 
% 150.84/21.88  | Case 2:
% 150.84/21.88  | | 
% 150.84/21.88  | |   (9)  all_56_15 = e2 & op(e0, e0) = e2
% 150.84/21.88  | | 
% 150.84/21.88  | | ALPHA: (9) implies:
% 150.84/21.88  | |   (10)  op(e0, e0) = e2
% 150.84/21.88  | | 
% 150.84/21.88  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #978.
% 150.84/21.88  | | 
% 150.84/21.88  | End of split
% 150.84/21.88  | 
% 150.84/21.88  End of proof
% 150.84/21.88  
% 150.84/21.88  Sub-proof #6 shows that the following formulas are inconsistent:
% 150.84/21.88  ----------------------------------------------------------------
% 150.84/21.88    (1)  op(e1, e1) = e2
% 150.84/21.88    (2)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 150.84/21.88             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.84/21.88           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 150.84/21.88               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 150.84/21.88             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.84/21.88         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 150.84/21.88             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.84/21.88           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 150.84/21.88               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 150.84/21.88             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 150.84/21.88    (3)  op(e1, e1) = all_4_2
% 150.84/21.88    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.88    (5)  op(e0, e0) = e1
% 150.84/21.88    (6)   ~ (e1 = e0)
% 150.84/21.88    (7)   ~ (e2 = e1)
% 150.84/21.88  
% 150.84/21.88  Begin of proof
% 150.84/21.88  | 
% 150.84/21.88  | BETA: splitting (2) gives:
% 150.84/21.88  | 
% 150.84/21.88  | Case 1:
% 150.84/21.88  | | 
% 150.84/21.88  | |   (8)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3)
% 150.84/21.88  | |          | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.84/21.88  | |        ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 150.84/21.88  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 150.84/21.88  | |              e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 150.84/21.88  | |            $i(all_57_15)))
% 150.84/21.88  | | 
% 150.84/21.88  | | ALPHA: (8) implies:
% 150.84/21.88  | |   (9)  op(e1, e1) = e1
% 150.84/21.88  | | 
% 150.84/21.88  | | REF_CLOSE: (1), (3), (4), (7), (9) are inconsistent by sub-proof #1044.
% 150.84/21.88  | | 
% 150.84/21.88  | Case 2:
% 150.84/21.88  | | 
% 150.84/21.88  | |   (10)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 150.84/21.88  | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.84/21.88  | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.84/21.88  | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.84/21.88  | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 150.84/21.88  | |               e1) = all_57_14 & $i(all_57_14)))
% 150.84/21.88  | | 
% 150.84/21.88  | | ALPHA: (10) implies:
% 150.84/21.88  | |   (11)  op(e0, e0) = e0
% 150.84/21.88  | | 
% 150.84/21.88  | | REF_CLOSE: (4), (5), (6), (11) are inconsistent by sub-proof #1040.
% 150.84/21.88  | | 
% 150.84/21.88  | End of split
% 150.84/21.88  | 
% 150.84/21.88  End of proof
% 150.84/21.88  
% 150.84/21.88  Sub-proof #7 shows that the following formulas are inconsistent:
% 150.84/21.88  ----------------------------------------------------------------
% 150.84/21.88    (1)   ~ (e3 = e1)
% 150.84/21.88    (2)   ~ (all_52_2 = all_52_6)
% 150.84/21.88    (3)  op(e1, e1) = e2
% 150.84/21.88    (4)  op(e3, e0) = e2
% 150.84/21.88    (5)   ~ (e2 = e0)
% 150.84/21.88    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.88    (7)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 150.84/21.88           all_57_14 & $i(all_57_14))
% 150.84/21.88    (8)   ~ (all_52_14 = e1)
% 150.84/21.88    (9)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 150.84/21.88             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 150.84/21.88               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 150.84/21.88               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 150.84/21.88    (10)  op(e1, e0) = all_52_14
% 150.84/21.88    (11)   ~ (all_52_13 = e2)
% 150.84/21.88    (12)  op(e0, e0) = e1
% 150.84/21.88    (13)   ~ (e3 = e0)
% 150.84/21.88    (14)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 150.84/21.88          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 150.84/21.88    (15)  op(e3, e3) = e1
% 150.84/21.88    (16)  op(e1, e2) = all_52_6
% 150.84/21.88    (17)  op(e2, e0) = all_52_13
% 150.84/21.88    (18)   ~ (all_52_9 = e2)
% 150.84/21.88    (19)  op(e2, e2) = e2
% 150.84/21.88    (20)  op(e2, e1) = all_52_9
% 150.84/21.88    (21)   ~ (e1 = e0)
% 150.84/21.88    (22)   ~ (e3 = e2)
% 150.84/21.88    (23)  all_56_9 = e2
% 150.84/21.88    (24)  op(e1, e2) = e1
% 150.84/21.88    (25)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 150.84/21.88          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 150.84/21.88    (26)   ~ (e2 = e1)
% 150.84/21.88    (27)  op(e1, e3) = all_52_2
% 150.84/21.88    (28)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 150.84/21.88              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 150.84/21.88            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 150.84/21.88            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 150.84/21.88            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.84/21.88            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 150.84/21.88            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 150.84/21.88            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.84/21.88            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 150.84/21.88            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.84/21.88            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.84/21.88            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 150.84/21.88            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.84/21.88            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.84/21.88            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 150.84/21.88            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.84/21.88            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.84/21.88            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 150.84/21.88            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.84/21.88            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 150.84/21.88            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 150.84/21.88            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.84/21.88            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.84/21.88            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 150.84/21.88            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.84/21.88            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.84/21.88            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 150.84/21.88            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.84/21.88            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.88            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 150.84/21.88            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 150.84/21.88            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 150.84/21.88            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 150.84/21.88            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.84/21.88            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.88            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 150.84/21.88            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.88            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.84/21.88            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 150.84/21.88            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.88            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.84/21.88            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 150.84/21.88            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.84/21.88            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.84/21.88            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 150.84/21.88            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.84/21.88            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 150.84/21.88            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.84/21.88              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 150.84/21.88            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.84/21.88            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.84/21.88              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 150.84/21.88            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.84/21.88            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 150.84/21.88                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.84/21.88                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.88                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.84/21.88                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.84/21.88                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 150.84/21.88                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 150.84/21.88                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.84/21.88              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 150.84/21.88                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 150.84/21.88                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.84/21.88                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.84/21.88                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 150.84/21.88                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.84/21.88                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.84/21.88                $i(all_57_7))))
% 150.84/21.88    (29)  op(e2, e3) = all_52_1
% 150.84/21.88    (30)   ~ (all_52_1 = e2)
% 150.84/21.88  
% 150.84/21.88  Begin of proof
% 150.84/21.88  | 
% 150.84/21.88  | BETA: splitting (28) gives:
% 150.84/21.88  | 
% 150.84/21.88  | Case 1:
% 150.84/21.88  | | 
% 150.84/21.88  | |   (31)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 150.84/21.88  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 150.84/21.88  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 150.84/21.88  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 150.84/21.88  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 150.84/21.88  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 150.84/21.88  | |         (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 150.84/21.88  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 150.84/21.88  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 150.84/21.88  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 150.84/21.88  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 150.84/21.88  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) |
% 150.84/21.88  | |         (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 150.84/21.88  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.84/21.88  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.84/21.88  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 150.84/21.88  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.84/21.88  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 150.84/21.88  | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 150.84/21.88  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 150.84/21.88  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.84/21.88  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 150.84/21.88  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 150.84/21.88  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 150.84/21.88  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 150.84/21.88  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 150.84/21.88  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.84/21.88  | | 
% 150.84/21.88  | | BETA: splitting (31) gives:
% 150.84/21.88  | | 
% 150.84/21.88  | | Case 1:
% 150.84/21.88  | | | 
% 150.84/21.88  | | |   (32)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.84/21.88  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.84/21.88  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 150.84/21.88  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 150.84/21.88  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 150.84/21.88  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.84/21.88  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 150.84/21.88  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.84/21.88  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.84/21.88  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 150.84/21.88  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.84/21.88  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 150.84/21.88  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 150.84/21.88  | | | 
% 150.84/21.88  | | | REF_CLOSE: (1), (2), (6), (12), (16), (24), (27), (29), (30), (32) are
% 150.84/21.88  | | |            inconsistent by sub-proof #419.
% 150.84/21.88  | | | 
% 150.84/21.88  | | Case 2:
% 150.84/21.88  | | | 
% 150.84/21.88  | | |   (33)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.88  | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.84/21.88  | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.84/21.88  | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5
% 150.84/21.88  | | |             = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 150.84/21.88  | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.84/21.88  | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.84/21.88  | | |           &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.84/21.88  | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 150.84/21.88  | | |           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 =
% 150.84/21.88  | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 150.84/21.88  | | |           & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 150.84/21.88  | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 150.84/21.88  | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.84/21.88  | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.88  | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.84/21.88  | | | 
% 150.84/21.88  | | | BETA: splitting (33) gives:
% 150.84/21.88  | | | 
% 150.84/21.88  | | | Case 1:
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | |   (34)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.88  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.84/21.88  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.84/21.88  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 150.84/21.88  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 150.84/21.88  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.84/21.88  | | | |           $i(all_57_5) & $i(all_57_10))
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | | BETA: splitting (34) gives:
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | | Case 1:
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | |   (35)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.88  | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.84/21.88  | | | | |         op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.84/21.88  | | | | |         $i(all_57_10)
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | ALPHA: (35) implies:
% 150.84/21.88  | | | | |   (36)  all_57_14 = e2
% 150.84/21.88  | | | | |   (37)   ~ (all_57_4 = e1)
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | REF_CLOSE: (7), (36), (37) are inconsistent by sub-proof #1005.
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | Case 2:
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | |   (38)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.84/21.88  | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.84/21.88  | | | | |         op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.84/21.88  | | | | |         $i(all_57_10)
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | ALPHA: (38) implies:
% 150.84/21.88  | | | | |   (39)  op(e0, e0) = e2
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | REF_CLOSE: (1), (5), (6), (9), (13), (14), (21), (22), (23), (25),
% 150.84/21.88  | | | | |            (26), (39) are inconsistent by sub-proof #486.
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | End of split
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | Case 2:
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | |   (40)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.84/21.88  | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 150.84/21.88  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 150.84/21.88  | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 150.84/21.88  | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.84/21.88  | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 150.84/21.88  | | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.84/21.88  | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 150.84/21.88  | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.84/21.88  | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | | BETA: splitting (40) gives:
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | | Case 1:
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | |   (41)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.84/21.88  | | | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 150.84/21.88  | | | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 150.84/21.88  | | | | |         $i(all_57_14)
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | ALPHA: (41) implies:
% 150.84/21.88  | | | | |   (42)  op(e3, e3) = e2
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | REF_CLOSE: (6), (15), (26), (42) are inconsistent by sub-proof #1074.
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | Case 2:
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | |   (43)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.84/21.88  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 150.84/21.88  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.84/21.88  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 150.84/21.88  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.84/21.88  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.88  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | | REF_CLOSE: (1), (5), (6), (9), (13), (14), (19), (21), (22), (23),
% 150.84/21.88  | | | | |            (25), (26), (43) are inconsistent by sub-proof #59.
% 150.84/21.88  | | | | | 
% 150.84/21.88  | | | | End of split
% 150.84/21.88  | | | | 
% 150.84/21.88  | | | End of split
% 150.84/21.88  | | | 
% 150.84/21.88  | | End of split
% 150.84/21.88  | | 
% 150.84/21.88  | Case 2:
% 150.84/21.88  | | 
% 150.84/21.89  | |   (44)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 150.84/21.89  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.84/21.89  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 150.84/21.89  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 150.84/21.89  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 150.84/21.89  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 150.84/21.89  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 150.84/21.89  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.84/21.89  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.84/21.89  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.84/21.89  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.89  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.84/21.89  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 150.84/21.89  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 150.84/21.89  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.84/21.89  | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.84/21.89  | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.84/21.89  | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 150.84/21.89  | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.84/21.89  | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.84/21.89  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 150.84/21.89  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 150.84/21.89  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 150.84/21.89  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.84/21.89  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 150.84/21.89  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.84/21.89  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 150.84/21.89  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.84/21.89  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.84/21.89  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 150.84/21.89  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 150.84/21.89  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.84/21.89  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.84/21.89  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.84/21.89  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.84/21.89  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 150.84/21.89  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 150.84/21.89  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.84/21.89  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.84/21.89  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.84/21.89  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.84/21.89  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.84/21.89  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.84/21.89  | |               $i(all_57_7))))
% 150.84/21.89  | | 
% 150.84/21.89  | | BETA: splitting (44) gives:
% 150.84/21.89  | | 
% 150.84/21.89  | | Case 1:
% 150.84/21.89  | | | 
% 150.84/21.89  | | |   (45)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.84/21.89  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.84/21.89  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.89  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 150.84/21.89  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.84/21.89  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.84/21.89  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 150.84/21.89  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.84/21.89  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 150.84/21.89  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 150.84/21.89  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.84/21.89  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.84/21.89  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 150.84/21.89  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.84/21.89  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.84/21.89  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.84/21.89  | | |           $i(all_57_13))
% 150.84/21.89  | | | 
% 150.84/21.89  | | | BETA: splitting (45) gives:
% 150.84/21.89  | | | 
% 150.84/21.89  | | | Case 1:
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | |   (46)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.84/21.89  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.84/21.89  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.89  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 150.84/21.89  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 150.84/21.89  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 150.84/21.89  | | | |           e2 & $i(all_57_6) & $i(all_57_12))
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | | REF_CLOSE: (6), (15), (18), (20), (46) are inconsistent by sub-proof
% 150.84/21.89  | | | |            #417.
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | Case 2:
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | |   (47)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.84/21.89  | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.84/21.89  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.84/21.89  | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 150.84/21.89  | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.84/21.89  | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 150.84/21.89  | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 150.84/21.89  | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.84/21.89  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 150.84/21.89  | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | | REF_CLOSE: (4), (6), (18), (20), (22), (47) are inconsistent by
% 150.84/21.89  | | | |            sub-proof #9.
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | End of split
% 150.84/21.89  | | | 
% 150.84/21.89  | | Case 2:
% 150.84/21.89  | | | 
% 150.84/21.89  | | |   (48)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.84/21.89  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.84/21.89  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.84/21.89  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.84/21.89  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.84/21.89  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.84/21.89  | | |           $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0
% 150.84/21.89  | | |           &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.84/21.89  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 150.84/21.89  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 150.84/21.89  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.84/21.89  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 150.84/21.89  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.84/21.89  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.84/21.89  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.84/21.89  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.89  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 150.84/21.89  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.84/21.89  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 150.84/21.89  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.84/21.89  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 150.84/21.89  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.84/21.89  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 150.84/21.89  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.84/21.89  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.84/21.89  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.84/21.89  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.84/21.89  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.84/21.89  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.84/21.89  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 150.84/21.89  | | | 
% 150.84/21.89  | | | BETA: splitting (48) gives:
% 150.84/21.89  | | | 
% 150.84/21.89  | | | Case 1:
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | |   (49)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.84/21.89  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.84/21.89  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.84/21.89  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 150.84/21.89  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.84/21.89  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.84/21.89  | | | |           e1 & $i(all_57_9) & $i(all_57_14))
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | | REF_CLOSE: (6), (15), (21), (49) are inconsistent by sub-proof #956.
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | Case 2:
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | |   (50)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 150.84/21.89  | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.84/21.89  | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.84/21.89  | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 150.84/21.89  | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.84/21.89  | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.84/21.89  | | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 150.84/21.89  | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 150.84/21.89  | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.84/21.89  | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.84/21.89  | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 150.84/21.89  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.84/21.89  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.84/21.89  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.84/21.89  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.84/21.89  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.84/21.89  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.89  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 150.84/21.89  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.84/21.89  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 150.84/21.89  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 150.84/21.89  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.84/21.89  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.84/21.89  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | | BETA: splitting (50) gives:
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | | Case 1:
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | |   (51)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 150.84/21.89  | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.84/21.89  | | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.84/21.89  | | | | |         $i(all_57_13)
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | | ALPHA: (51) implies:
% 150.84/21.89  | | | | |   (52)  op(e2, e0) = e2
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | | REF_CLOSE: (6), (11), (17), (52) are inconsistent by sub-proof #1156.
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | Case 2:
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | |   (53)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.84/21.89  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 150.84/21.89  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.84/21.89  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.84/21.89  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.89  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 150.84/21.89  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 150.84/21.89  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.84/21.89  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.84/21.89  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 150.84/21.89  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 150.84/21.89  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.84/21.89  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 150.84/21.89  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.84/21.89  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.84/21.89  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.84/21.89  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 150.84/21.89  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.84/21.89  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.84/21.89  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 150.84/21.89  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.84/21.89  | | | | |               $i(all_57_7))))
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | | BETA: splitting (53) gives:
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | | Case 1:
% 150.84/21.89  | | | | | | 
% 150.84/21.89  | | | | | |   (54)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.84/21.89  | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 150.84/21.89  | | | | | |         & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.84/21.89  | | | | | |         $i(all_57_14)
% 150.84/21.89  | | | | | | 
% 150.84/21.89  | | | | | | ALPHA: (54) implies:
% 150.84/21.89  | | | | | |   (55)  op(e1, e0) = e1
% 150.84/21.89  | | | | | | 
% 150.84/21.89  | | | | | | REF_CLOSE: (6), (8), (10), (55) are inconsistent by sub-proof #961.
% 150.84/21.89  | | | | | | 
% 150.84/21.89  | | | | | Case 2:
% 150.84/21.89  | | | | | | 
% 150.84/21.89  | | | | | |   (56)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.84/21.89  | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 150.84/21.89  | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 150.84/21.89  | | | | | |               e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.84/21.89  | | | | | |             = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1,
% 150.84/21.89  | | | | | |               e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.84/21.89  | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.84/21.89  | | | | | |             (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 150.84/21.89  | | | | | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.84/21.89  | | | | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 150.84/21.89  | | | | | |             (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.84/21.89  | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.84/21.89  | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.84/21.89  | | | | | |             (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 150.84/21.89  | | | | | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.84/21.89  | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.84/21.89  | | | | | |             (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 150.84/21.89  | | | | | |             & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.84/21.89  | | | | | |             $i(all_57_7)))
% 150.84/21.89  | | | | | | 
% 150.84/21.89  | | | | | | ALPHA: (56) implies:
% 150.84/21.89  | | | | | |   (57)  op(e0, e0) = all_57_15
% 150.84/21.89  | | | | | |   (58)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.89  | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 150.84/21.89  | | | | | |           & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 150.84/21.89  | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.84/21.89  | | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 150.84/21.89  | | | | | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.84/21.89  | | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.84/21.89  | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.84/21.89  | | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.89  | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 150.84/21.89  | | | | | |           & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.84/21.89  | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 150.84/21.89  | | | | | |           & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 150.84/21.89  | | | | | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.84/21.89  | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.84/21.89  | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.84/21.89  | | | | | | 
% 150.84/21.89  | | | | | | BETA: splitting (58) gives:
% 150.84/21.89  | | | | | | 
% 150.84/21.89  | | | | | | Case 1:
% 150.84/21.89  | | | | | | | 
% 150.84/21.89  | | | | | | |   (59)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.89  | | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 150.84/21.89  | | | | | | |           e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 150.84/21.89  | | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.84/21.89  | | | | | | |             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.84/21.89  | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 150.84/21.89  | | | | | | |           = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 150.84/21.89  | | | | | | |             e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.84/21.89  | | | | | | |           $i(all_57_3))
% 150.84/21.89  | | | | | | | 
% 150.84/21.89  | | | | | | | BETA: splitting (59) gives:
% 150.84/21.89  | | | | | | | 
% 150.84/21.89  | | | | | | | Case 1:
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | |   (60)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.84/21.89  | | | | | | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 150.84/21.89  | | | | | | | |         e3 & op(e0, e3) = e0 & $i(all_57_0)
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | | ALPHA: (60) implies:
% 150.84/21.89  | | | | | | | |   (61)  op(e2, e2) = e3
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | | REF_CLOSE: (6), (19), (22), (61) are inconsistent by sub-proof
% 150.84/21.89  | | | | | | | |            #1179.
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | Case 2:
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | |   (62)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 150.84/21.89  | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 150.84/21.89  | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 150.84/21.89  | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 150.84/21.89  | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.84/21.89  | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | | BETA: splitting (62) gives:
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | | Case 1:
% 150.84/21.89  | | | | | | | | | 
% 150.84/21.89  | | | | | | | | |   (63)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 150.84/21.89  | | | | | | | | |         ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 150.84/21.89  | | | | | | | | |           e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)
% 150.84/21.89  | | | | | | | | | 
% 150.84/21.89  | | | | | | | | | ALPHA: (63) implies:
% 150.84/21.89  | | | | | | | | |   (64)  op(e1, e1) = e3
% 150.84/21.89  | | | | | | | | | 
% 150.84/21.89  | | | | | | | | | REF_CLOSE: (3), (6), (22), (64) are inconsistent by sub-proof
% 150.84/21.89  | | | | | | | | |            #834.
% 150.84/21.89  | | | | | | | | | 
% 150.84/21.89  | | | | | | | | Case 2:
% 150.84/21.89  | | | | | | | | | 
% 150.84/21.89  | | | | | | | | |   (65)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 150.84/21.89  | | | | | | | | |         ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.84/21.89  | | | | | | | | |         all_57_3 & op(e0, e2) = e0 & $i(all_57_3)
% 150.84/21.89  | | | | | | | | | 
% 150.84/21.89  | | | | | | | | | ALPHA: (65) implies:
% 150.84/21.89  | | | | | | | | |   (66)  op(e3, e3) = e2
% 150.84/21.89  | | | | | | | | | 
% 150.84/21.89  | | | | | | | | | REF_CLOSE: (6), (15), (26), (66) are inconsistent by sub-proof
% 150.84/21.89  | | | | | | | | |            #1074.
% 150.84/21.89  | | | | | | | | | 
% 150.84/21.89  | | | | | | | | End of split
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | End of split
% 150.84/21.89  | | | | | | | 
% 150.84/21.89  | | | | | | Case 2:
% 150.84/21.89  | | | | | | | 
% 150.84/21.89  | | | | | | |   (67)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.89  | | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.84/21.89  | | | | | | |           e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.84/21.89  | | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 150.84/21.89  | | | | | | |             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 150.84/21.89  | | | | | | |             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.84/21.89  | | | | | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 150.84/21.89  | | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.84/21.89  | | | | | | |           $i(all_57_7))
% 150.84/21.89  | | | | | | | 
% 150.84/21.89  | | | | | | | BETA: splitting (67) gives:
% 150.84/21.89  | | | | | | | 
% 150.84/21.89  | | | | | | | Case 1:
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | |   (68)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.84/21.89  | | | | | | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 150.84/21.89  | | | | | | | |         e2 & op(e0, e2) = e0 & $i(all_57_4)
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | | ALPHA: (68) implies:
% 150.84/21.89  | | | | | | | |   (69)  all_57_14 = e2
% 150.84/21.89  | | | | | | | |   (70)   ~ (all_57_4 = e1)
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | | REF_CLOSE: (7), (69), (70) are inconsistent by sub-proof #1005.
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | Case 2:
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | |   (71)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 150.84/21.89  | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.84/21.89  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 150.84/21.89  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.84/21.89  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 150.84/21.89  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | | REF_CLOSE: (6), (12), (19), (26), (57), (71) are inconsistent by
% 150.84/21.89  | | | | | | | |            sub-proof #415.
% 150.84/21.89  | | | | | | | | 
% 150.84/21.89  | | | | | | | End of split
% 150.84/21.89  | | | | | | | 
% 150.84/21.89  | | | | | | End of split
% 150.84/21.89  | | | | | | 
% 150.84/21.89  | | | | | End of split
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | End of split
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | End of split
% 150.84/21.89  | | | 
% 150.84/21.89  | | End of split
% 150.84/21.89  | | 
% 150.84/21.89  | End of split
% 150.84/21.89  | 
% 150.84/21.89  End of proof
% 150.84/21.89  
% 150.84/21.89  Sub-proof #8 shows that the following formulas are inconsistent:
% 150.84/21.89  ----------------------------------------------------------------
% 150.84/21.89    (1)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 & $i(all_30_1)
% 150.84/21.89    (2)  op(e0, e1) = e3
% 150.84/21.89    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.89    (4)  ( ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 & op(e0, e1) = all_10_1
% 150.84/21.89           & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e0, e1) =
% 150.84/21.89           all_10_1 & $i(all_10_1))
% 150.84/21.89  
% 150.84/21.89  Begin of proof
% 150.84/21.89  | 
% 150.84/21.89  | ALPHA: (1) implies:
% 150.84/21.89  |   (5)   ~ (all_30_1 = e3)
% 150.84/21.89  |   (6)  op(e0, e1) = all_30_1
% 150.84/21.89  | 
% 150.84/21.89  | BETA: splitting (4) gives:
% 150.84/21.89  | 
% 150.84/21.89  | Case 1:
% 150.84/21.89  | | 
% 150.84/21.89  | |   (7)   ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 & op(e0, e1) =
% 150.84/21.89  | |        all_10_1 & $i(all_10_0) & $i(all_10_1)
% 150.84/21.89  | | 
% 150.84/21.89  | | ALPHA: (7) implies:
% 150.84/21.89  | |   (8)  op(e0, e1) = all_10_1
% 150.84/21.89  | | 
% 150.84/21.89  | | REF_CLOSE: (2), (3), (5), (6), (8) are inconsistent by sub-proof #391.
% 150.84/21.89  | | 
% 150.84/21.89  | Case 2:
% 150.84/21.89  | | 
% 150.84/21.89  | |   (9)   ~ (all_10_1 = e2) & op(e0, e1) = all_10_1 & $i(all_10_1)
% 150.84/21.89  | | 
% 150.84/21.89  | | ALPHA: (9) implies:
% 150.84/21.89  | |   (10)  op(e0, e1) = all_10_1
% 150.84/21.89  | | 
% 150.84/21.89  | | REF_CLOSE: (2), (3), (5), (6), (10) are inconsistent by sub-proof #391.
% 150.84/21.89  | | 
% 150.84/21.89  | End of split
% 150.84/21.89  | 
% 150.84/21.89  End of proof
% 150.84/21.89  
% 150.84/21.89  Sub-proof #9 shows that the following formulas are inconsistent:
% 150.84/21.89  ----------------------------------------------------------------
% 150.84/21.89    (1)  op(e3, e0) = e2
% 150.84/21.89    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.89    (3)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 150.84/21.89             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.84/21.89           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 150.84/21.89           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.84/21.89           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 150.84/21.89           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 150.84/21.89           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 150.84/21.89           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.84/21.89           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.84/21.89    (4)   ~ (all_52_9 = e2)
% 150.84/21.89    (5)  op(e2, e1) = all_52_9
% 150.84/21.89    (6)   ~ (e3 = e2)
% 150.84/21.89  
% 150.84/21.89  Begin of proof
% 150.84/21.89  | 
% 150.84/21.89  | BETA: splitting (3) gives:
% 150.84/21.89  | 
% 150.84/21.89  | Case 1:
% 150.84/21.89  | | 
% 150.84/21.89  | |   (7)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 150.84/21.89  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.84/21.89  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 150.84/21.89  | | 
% 150.84/21.89  | | ALPHA: (7) implies:
% 150.84/21.89  | |   (8)  op(e2, e1) = e2
% 150.84/21.89  | | 
% 150.84/21.89  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #1157.
% 150.84/21.89  | | 
% 150.84/21.89  | Case 2:
% 150.84/21.89  | | 
% 150.84/21.89  | |   (9)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 150.84/21.89  | |            = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) =
% 150.84/21.89  | |          e0 & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 150.84/21.89  | |        (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 150.84/21.89  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 150.84/21.89  | |          e0 & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.84/21.89  | | 
% 150.84/21.89  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #40.
% 150.84/21.89  | | 
% 150.84/21.89  | End of split
% 150.84/21.89  | 
% 150.84/21.89  End of proof
% 150.84/21.89  
% 150.84/21.89  Sub-proof #10 shows that the following formulas are inconsistent:
% 150.84/21.89  ----------------------------------------------------------------
% 150.84/21.89    (1)  op(e0, e1) = all_52_11
% 150.84/21.89    (2)  op(e3, e3) = e0
% 150.84/21.89    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 150.84/21.89         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 150.84/21.89    (4)  op(e0, e2) = all_52_7
% 150.84/21.89    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.89    (6)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 150.84/21.89             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 150.84/21.89               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 150.84/21.89               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 150.84/21.89    (7)  op(e1, e0) = all_52_14
% 150.84/21.89    (8)   ~ (e3 = e0)
% 150.84/21.89    (9)   ~ (all_52_11 = e0)
% 150.84/21.89    (10)  op(e2, e0) = all_52_13
% 150.84/21.89    (11)   ~ (all_52_7 = e0)
% 150.84/21.89    (12)   ~ (e1 = e0)
% 150.84/21.89    (13)   ~ (all_52_1 = e1)
% 150.84/21.89    (14)   ~ (e3 = e2)
% 150.84/21.89    (15)   ~ (all_52_14 = e3)
% 150.84/21.89    (16)  all_56_9 = e2
% 150.84/21.89    (17)   ~ (all_52_13 = e3)
% 150.84/21.89    (18)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 150.84/21.89          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 150.84/21.89    (19)   ~ (all_52_2 = e1)
% 150.84/21.89    (20)  op(e1, e3) = all_52_2
% 150.84/21.89    (21)  op(e2, e3) = all_52_1
% 150.84/21.89  
% 150.84/21.89  Begin of proof
% 150.84/21.89  | 
% 150.84/21.89  | BETA: splitting (3) gives:
% 150.84/21.89  | 
% 150.84/21.89  | Case 1:
% 150.84/21.89  | | 
% 150.84/21.89  | |   (22)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 150.84/21.89  | |           e1)
% 150.84/21.89  | | 
% 150.84/21.89  | | REF_CLOSE: (2), (5), (12), (13), (21), (22) are inconsistent by sub-proof
% 150.84/21.89  | |            #12.
% 150.84/21.89  | | 
% 150.84/21.89  | Case 2:
% 150.84/21.89  | | 
% 150.84/21.89  | |   (23)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 150.84/21.89  | |           e1)
% 150.84/21.89  | | 
% 150.84/21.89  | | BETA: splitting (23) gives:
% 150.84/21.89  | | 
% 150.84/21.89  | | Case 1:
% 150.84/21.89  | | | 
% 150.84/21.89  | | |   (24)  all_56_6 = e1 & op(e1, e3) = e1
% 150.84/21.89  | | | 
% 150.84/21.89  | | | ALPHA: (24) implies:
% 150.84/21.89  | | |   (25)  op(e1, e3) = e1
% 150.84/21.89  | | | 
% 150.84/21.89  | | | REF_CLOSE: (5), (19), (20), (25) are inconsistent by sub-proof #1046.
% 150.84/21.89  | | | 
% 150.84/21.89  | | Case 2:
% 150.84/21.89  | | | 
% 150.84/21.89  | | |   (26)  all_56_12 = e1 & op(e0, e3) = e1
% 150.84/21.89  | | | 
% 150.84/21.89  | | | ALPHA: (26) implies:
% 150.84/21.89  | | |   (27)  all_56_12 = e1
% 150.84/21.89  | | | 
% 150.84/21.89  | | | BETA: splitting (18) gives:
% 150.84/21.89  | | | 
% 150.84/21.89  | | | Case 1:
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | |   (28)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0)
% 150.84/21.89  | | | |           = e3)
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | | BETA: splitting (28) gives:
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | | Case 1:
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | |   (29)  all_56_9 = e3 & op(e3, e0) = e3
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | | ALPHA: (29) implies:
% 150.84/21.89  | | | | |   (30)  all_56_9 = e3
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | | REF_CLOSE: (14), (16), (30) are inconsistent by sub-proof #964.
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | Case 2:
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | |   (31)  all_56_10 = e3 & op(e2, e0) = e3
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | | REF_CLOSE: (5), (10), (17), (31) are inconsistent by sub-proof #114.
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | End of split
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | Case 2:
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | |   (32)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0,
% 150.84/21.89  | | | |             e0) = e3)
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | | BETA: splitting (32) gives:
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | | Case 1:
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | |   (33)  all_56_11 = e3 & op(e1, e0) = e3
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | | REF_CLOSE: (5), (7), (15), (33) are inconsistent by sub-proof #66.
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | Case 2:
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | |   (34)  all_56_15 = e3 & op(e0, e0) = e3
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | | ALPHA: (34) implies:
% 150.84/21.89  | | | | |   (35)  op(e0, e0) = e3
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (11), (12), (27), (35) are
% 150.84/21.89  | | | | |            inconsistent by sub-proof #797.
% 150.84/21.89  | | | | | 
% 150.84/21.89  | | | | End of split
% 150.84/21.89  | | | | 
% 150.84/21.89  | | | End of split
% 150.84/21.89  | | | 
% 150.84/21.89  | | End of split
% 150.84/21.89  | | 
% 150.84/21.89  | End of split
% 150.84/21.89  | 
% 150.84/21.89  End of proof
% 150.84/21.89  
% 150.84/21.89  Sub-proof #11 shows that the following formulas are inconsistent:
% 150.84/21.89  ----------------------------------------------------------------
% 150.84/21.89    (1)   ~ (all_52_1 = e0)
% 150.84/21.89    (2)  all_56_6 = e2
% 150.84/21.89    (3)   ~ (e2 = e0)
% 150.84/21.89    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.89    (5)  all_56_12 = e1
% 150.84/21.89    (6)   ~ (all_52_1 = e3)
% 150.84/21.89    (7)   ~ (e3 = e0)
% 150.84/21.89    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 150.84/21.89         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 150.84/21.89    (9)   ~ (e1 = e0)
% 150.84/21.89    (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 150.84/21.89    (11)  op(e2, e3) = all_52_1
% 150.84/21.89  
% 150.84/21.89  Begin of proof
% 150.84/21.89  | 
% 150.84/21.89  | BETA: splitting (10) gives:
% 150.84/21.89  | 
% 150.84/21.89  | Case 1:
% 150.84/21.89  | | 
% 150.84/21.89  | |   (12)  all_56_0 = e3 & op(e3, e3) = e3
% 150.84/21.89  | | 
% 150.84/21.89  | | ALPHA: (12) implies:
% 150.84/21.89  | |   (13)  op(e3, e3) = e3
% 150.84/21.89  | | 
% 150.84/21.89  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (13) are
% 150.84/21.89  | |            inconsistent by sub-proof #108.
% 150.84/21.89  | | 
% 150.84/21.89  | Case 2:
% 150.84/21.89  | | 
% 150.84/21.89  | |   (14)  all_56_2 = e3 & op(e2, e3) = e3
% 150.84/21.89  | | 
% 150.84/21.89  | | REF_CLOSE: (4), (6), (11), (14) are inconsistent by sub-proof #917.
% 150.84/21.89  | | 
% 150.84/21.89  | End of split
% 150.84/21.89  | 
% 150.84/21.89  End of proof
% 150.84/21.89  
% 150.84/21.89  Sub-proof #12 shows that the following formulas are inconsistent:
% 150.84/21.89  ----------------------------------------------------------------
% 150.84/21.89    (1)  op(e3, e3) = e0
% 150.84/21.89    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.89           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.89    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 150.84/21.89    (4)   ~ (e1 = e0)
% 150.84/21.89    (5)   ~ (all_52_1 = e1)
% 150.84/21.89    (6)  op(e2, e3) = all_52_1
% 150.84/21.89  
% 150.84/21.89  Begin of proof
% 150.84/21.89  | 
% 150.84/21.89  | BETA: splitting (3) gives:
% 150.84/21.89  | 
% 150.84/21.89  | Case 1:
% 150.84/21.89  | | 
% 150.84/21.89  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 150.84/21.89  | | 
% 150.84/21.89  | | ALPHA: (7) implies:
% 150.84/21.89  | |   (8)  op(e3, e3) = e1
% 150.84/21.89  | | 
% 150.84/21.90  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #957.
% 150.84/21.90  | | 
% 150.84/21.90  | Case 2:
% 150.84/21.90  | | 
% 150.84/21.90  | |   (9)  all_56_2 = e1 & op(e2, e3) = e1
% 150.84/21.90  | | 
% 150.84/21.90  | | ALPHA: (9) implies:
% 150.84/21.90  | |   (10)  op(e2, e3) = e1
% 150.84/21.90  | | 
% 150.84/21.90  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1177.
% 150.84/21.90  | | 
% 150.84/21.90  | End of split
% 150.84/21.90  | 
% 150.84/21.90  End of proof
% 150.84/21.90  
% 150.84/21.90  Sub-proof #13 shows that the following formulas are inconsistent:
% 150.84/21.90  ----------------------------------------------------------------
% 150.84/21.90    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 150.84/21.90         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 150.84/21.90    (2)  op(e3, e3) = e0
% 150.84/21.90    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 150.84/21.90         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 150.84/21.90    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 150.84/21.90         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 150.84/21.90    (5)   ~ (all_52_2 = all_52_6)
% 150.84/21.90    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 150.84/21.90         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 150.84/21.90    (7)  op(e0, e0) = all_10_2
% 150.84/21.90    (8)  op(e3, e2) = all_52_4
% 150.84/21.90    (9)  op(e1, e1) = e2
% 150.84/21.90    (10)  op(e0, e2) = all_52_7
% 150.84/21.90    (11)  op(e3, e0) = e2
% 150.84/21.90    (12)   ~ (all_52_4 = e2)
% 150.84/21.90    (13)  op(e1, e1) = all_4_2
% 150.84/21.90    (14)   ~ (all_10_2 = e1)
% 150.84/21.90    (15)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 150.84/21.90          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 150.84/21.90    (16)   ~ (e2 = e0)
% 150.84/21.90    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.84/21.90            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.84/21.90    (18)  all_54_1 = all_52_4
% 150.84/21.90    (19)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 150.84/21.90          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 150.84/21.90    (20)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 150.84/21.90          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 150.84/21.90    (21)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 150.84/21.90    (22)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 150.84/21.90              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 150.84/21.90                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 150.84/21.90                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 150.84/21.90    (23)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 150.84/21.90          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 150.84/21.90    (24)  op(e1, e0) = all_52_14
% 150.84/21.90    (25)   ~ (all_52_13 = e2)
% 150.84/21.90    (26)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 150.84/21.90          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 150.84/21.90            e3)
% 150.84/21.90    (27)   ~ (e3 = e0)
% 150.84/21.90    (28)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 150.84/21.90          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 150.84/21.90    (29)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 150.84/21.90          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 150.84/21.90    (30)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 150.84/21.90    (31)   ~ (all_52_2 = e2)
% 150.84/21.90    (32)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 150.84/21.90          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 150.84/21.90    (33)  op(e1, e2) = all_52_6
% 150.84/21.90    (34)  op(e2, e0) = all_52_13
% 150.84/21.90    (35)   ~ (all_52_8 = e0)
% 150.84/21.90    (36)   ~ (all_52_4 = all_52_8)
% 150.84/21.90    (37)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 150.84/21.90          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 150.84/21.90    (38)   ~ (all_52_4 = all_52_6)
% 150.84/21.90    (39)   ~ (all_52_2 = e0)
% 150.84/21.90    (40)   ~ (e1 = e0)
% 150.98/21.90    (41)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 150.98/21.90              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.98/21.90            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 150.98/21.90                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 150.98/21.90              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.98/21.90          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 150.98/21.90              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.98/21.90            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 150.98/21.90                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 150.98/21.90              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.98/21.90          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 150.98/21.90              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.98/21.90            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 150.98/21.90                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 150.98/21.90              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.98/21.90          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 150.98/21.90              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.98/21.90            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 150.98/21.90                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.98/21.90                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.98/21.90                $i(all_57_14))))
% 150.98/21.90    (42)  all_54_8 = all_52_2
% 150.98/21.90    (43)   ~ (e3 = e2)
% 150.98/21.90    (44)  all_56_9 = e2
% 150.98/21.90    (45)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 150.98/21.90          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 150.98/21.90    (46)  all_56_12 = e2
% 150.98/21.90    (47)   ~ (all_52_6 = all_52_14)
% 150.98/21.90    (48)   ~ (all_10_2 = e2)
% 150.98/21.90    (49)  op(e3, e1) = all_52_8
% 150.98/21.90    (50)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 150.98/21.90          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 150.98/21.90    (51)   ~ (all_52_6 = all_52_7)
% 150.98/21.90    (52)   ~ (e2 = e1)
% 150.98/21.90    (53)   ~ (all_52_4 = e0)
% 150.98/21.90    (54)  op(e3, e0) = all_14_1
% 150.98/21.90    (55)  op(e1, e3) = all_52_2
% 150.98/21.90    (56)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 150.98/21.90          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 150.98/21.90            e1)
% 150.98/21.90    (57)  op(e2, e3) = all_52_1
% 150.98/21.90    (58)   ~ (all_52_6 = e2)
% 150.98/21.90  
% 150.98/21.90  Begin of proof
% 150.98/21.90  | 
% 150.98/21.90  | BETA: splitting (41) gives:
% 150.98/21.90  | 
% 150.98/21.90  | Case 1:
% 150.98/21.90  | | 
% 150.98/21.90  | |   (59)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 150.98/21.90  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 150.98/21.90  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.98/21.90  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.98/21.90  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.98/21.90  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 150.98/21.90  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 150.98/21.90  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.98/21.90  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 150.98/21.90  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.98/21.90  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 150.98/21.90  | |               $i(all_57_15))))
% 150.98/21.90  | | 
% 150.98/21.90  | | BETA: splitting (59) gives:
% 150.98/21.90  | | 
% 150.98/21.90  | | Case 1:
% 150.98/21.90  | | | 
% 150.98/21.90  | | |   (60)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 150.98/21.90  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 150.98/21.90  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.98/21.90  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.98/21.90  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.98/21.90  | | |               e0) = all_57_15 & $i(all_57_15)))
% 150.98/21.90  | | | 
% 150.98/21.90  | | | ALPHA: (60) implies:
% 150.98/21.90  | | |   (61)  op(e3, e3) = e3
% 150.98/21.90  | | | 
% 150.98/21.90  | | | REF_CLOSE: (2), (17), (27), (61) are inconsistent by sub-proof #1141.
% 150.98/21.90  | | | 
% 150.98/21.90  | | Case 2:
% 150.98/21.90  | | | 
% 150.98/21.90  | | |   (62)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 150.98/21.90  | | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.98/21.90  | | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.98/21.90  | | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.98/21.90  | | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.98/21.90  | | |               e0) = all_57_15 & $i(all_57_15)))
% 150.98/21.90  | | | 
% 150.98/21.90  | | | ALPHA: (62) implies:
% 150.98/21.90  | | |   (63)  op(e2, e2) = e2
% 150.98/21.90  | | |   (64)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 150.98/21.90  | | |             e1) = all_57_14 & $i(all_57_14))
% 150.98/21.90  | | | 
% 150.98/21.90  | | | BETA: splitting (64) gives:
% 150.98/21.90  | | | 
% 150.98/21.90  | | | Case 1:
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | |   (65)  all_57_4 = e1 & op(e1, e2) = e1
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | | ALPHA: (65) implies:
% 150.98/21.90  | | | |   (66)  op(e1, e2) = e1
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | | GROUND_INST: instantiating (17) with all_52_6, e1, e2, e1, simplifying
% 150.98/21.90  | | | |              with (33), (66) gives:
% 150.98/21.90  | | | |   (67)  all_52_6 = e1
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | | REDUCE: (5), (67) imply:
% 150.98/21.90  | | | |   (68)   ~ (all_52_2 = e1)
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | | REDUCE: (38), (67) imply:
% 150.98/21.90  | | | |   (69)   ~ (all_52_4 = e1)
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | | REDUCE: (51), (67) imply:
% 150.98/21.90  | | | |   (70)   ~ (all_52_7 = e1)
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | | SIMP: (70) implies:
% 150.98/21.90  | | | |   (71)   ~ (all_52_7 = e1)
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | | REDUCE: (47), (67) imply:
% 150.98/21.90  | | | |   (72)   ~ (all_52_14 = e1)
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | | SIMP: (72) implies:
% 150.98/21.90  | | | |   (73)   ~ (all_52_14 = e1)
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | | REDUCE: (58), (67) imply:
% 150.98/21.90  | | | |   (74)   ~ (e2 = e1)
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | | BETA: splitting (30) gives:
% 150.98/21.90  | | | | 
% 150.98/21.90  | | | | Case 1:
% 150.98/21.90  | | | | | 
% 150.98/21.90  | | | | |   (75)  all_54_8 = e3
% 150.98/21.90  | | | | | 
% 150.98/21.90  | | | | | COMBINE_EQS: (42), (75) imply:
% 150.98/21.90  | | | | |   (76)  all_52_2 = e3
% 150.98/21.90  | | | | | 
% 150.98/21.90  | | | | | SIMP: (76) implies:
% 150.98/21.90  | | | | |   (77)  all_52_2 = e3
% 150.98/21.90  | | | | | 
% 150.98/21.90  | | | | | REDUCE: (68), (77) imply:
% 150.98/21.90  | | | | |   (78)   ~ (e3 = e1)
% 150.98/21.90  | | | | | 
% 150.98/21.90  | | | | | REDUCE: (55), (77) imply:
% 150.98/21.90  | | | | |   (79)  op(e1, e3) = e3
% 150.98/21.90  | | | | | 
% 150.98/21.90  | | | | | BETA: splitting (6) gives:
% 150.98/21.90  | | | | | 
% 150.98/21.90  | | | | | Case 1:
% 150.98/21.90  | | | | | | 
% 150.98/21.90  | | | | | |   (80)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2,
% 150.98/21.90  | | | | | |             e3) = e3)
% 150.98/21.90  | | | | | | 
% 150.98/21.90  | | | | | | BETA: splitting (80) gives:
% 150.98/21.90  | | | | | | 
% 150.98/21.90  | | | | | | Case 1:
% 150.98/21.90  | | | | | | | 
% 150.98/21.90  | | | | | | |   (81)  all_56_0 = e3 & op(e3, e3) = e3
% 150.98/21.90  | | | | | | | 
% 150.98/21.90  | | | | | | | ALPHA: (81) implies:
% 150.98/21.90  | | | | | | |   (82)  op(e3, e3) = e3
% 150.98/21.90  | | | | | | | 
% 150.98/21.90  | | | | | | | REF_CLOSE: (2), (17), (27), (82) are inconsistent by sub-proof
% 150.98/21.90  | | | | | | |            #1141.
% 150.98/21.90  | | | | | | | 
% 150.98/21.90  | | | | | | Case 2:
% 150.98/21.90  | | | | | | | 
% 150.98/21.90  | | | | | | |   (83)  all_56_2 = e3 & op(e2, e3) = e3
% 150.98/21.90  | | | | | | | 
% 150.98/21.90  | | | | | | | REF_CLOSE: (2), (3), (17), (40), (46), (52), (78), (79), (83) are
% 150.98/21.90  | | | | | | |            inconsistent by sub-proof #18.
% 150.98/21.90  | | | | | | | 
% 150.98/21.90  | | | | | | End of split
% 150.98/21.90  | | | | | | 
% 150.98/21.90  | | | | | Case 2:
% 150.98/21.90  | | | | | | 
% 150.98/21.90  | | | | | |   (84)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0,
% 150.98/21.90  | | | | | |             e3) = e3)
% 150.98/21.90  | | | | | | 
% 150.98/21.90  | | | | | | BETA: splitting (84) gives:
% 150.98/21.90  | | | | | | 
% 150.98/21.90  | | | | | | Case 1:
% 150.98/21.90  | | | | | | | 
% 150.98/21.90  | | | | | | |   (85)  all_56_6 = e3 & op(e1, e3) = e3
% 150.98/21.90  | | | | | | | 
% 150.98/21.90  | | | | | | | ALPHA: (85) implies:
% 150.98/21.90  | | | | | | |   (86)  all_56_6 = e3
% 150.98/21.90  | | | | | | | 
% 150.98/21.90  | | | | | | | BETA: splitting (45) gives:
% 150.98/21.90  | | | | | | | 
% 150.98/21.90  | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | 
% 150.98/21.90  | | | | | | | |   (87)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 &
% 150.98/21.90  | | | | | | | |           op(e2, e2) = e0)
% 150.98/21.90  | | | | | | | | 
% 150.98/21.90  | | | | | | | | REF_CLOSE: (8), (16), (17), (53), (63), (87) are inconsistent by
% 150.98/21.90  | | | | | | | |            sub-proof #1012.
% 150.98/21.90  | | | | | | | | 
% 150.98/21.90  | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | 
% 150.98/21.90  | | | | | | | |   (88)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 &
% 150.98/21.90  | | | | | | | |           op(e0, e2) = e0)
% 150.98/21.90  | | | | | | | | 
% 150.98/21.90  | | | | | | | | BETA: splitting (88) gives:
% 150.98/21.90  | | | | | | | | 
% 150.98/21.90  | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | 
% 150.98/21.90  | | | | | | | | |   (89)  all_56_7 = e0 & op(e1, e2) = e0
% 150.98/21.90  | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | REF_CLOSE: (9), (13), (17), (20), (24), (40), (52), (73),
% 150.98/21.90  | | | | | | | | |            (78), (79), (89) are inconsistent by sub-proof #16.
% 150.98/21.90  | | | | | | | | | 
% 150.98/21.90  | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | 
% 150.98/21.90  | | | | | | | | |   (90)  all_56_13 = e0 & op(e0, e2) = e0
% 150.98/21.90  | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | ALPHA: (90) implies:
% 150.98/21.90  | | | | | | | | |   (91)  all_56_13 = e0
% 150.98/21.90  | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | BETA: splitting (29) gives:
% 150.98/21.90  | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | |   (92)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1
% 150.98/21.90  | | | | | | | | | |           & op(e2, e0) = e1)
% 150.98/21.90  | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | BETA: splitting (92) gives:
% 150.98/21.90  | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | |   (93)  all_56_9 = e1 & op(e3, e0) = e1
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | ALPHA: (93) implies:
% 150.98/21.90  | | | | | | | | | | |   (94)  all_56_9 = e1
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | REF_CLOSE: (44), (52), (94) are inconsistent by sub-proof
% 150.98/21.90  | | | | | | | | | | |            #948.
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | |   (95)  all_56_10 = e1 & op(e2, e0) = e1
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | ALPHA: (95) implies:
% 150.98/21.90  | | | | | | | | | | |   (96)  all_56_10 = e1
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | BETA: splitting (56) gives:
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | |   (97)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 150.98/21.90  | | | | | | | | | | | |           e1 & op(e0, e2) = e1)
% 150.98/21.90  | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | BETA: splitting (97) gives:
% 150.98/21.90  | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | |   (98)  all_56_12 = e1 & op(e0, e3) = e1
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | REF_CLOSE: (46), (52), (98) are inconsistent by sub-proof
% 150.98/21.90  | | | | | | | | | | | | |            #789.
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | |   (99)  all_56_13 = e1 & op(e0, e2) = e1
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | REF_CLOSE: (10), (17), (71), (99) are inconsistent by
% 150.98/21.90  | | | | | | | | | | | | |            sub-proof #414.
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | |   (100)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 150.98/21.90  | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 150.98/21.90  | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | BETA: splitting (100) gives:
% 150.98/21.90  | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | |   (101)  all_56_14 = e1 & op(e0, e1) = e1
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | ALPHA: (101) implies:
% 150.98/21.90  | | | | | | | | | | | | |   (102)  all_56_14 = e1
% 150.98/21.90  | | | | | | | | | | | | |   (103)  op(e0, e1) = e1
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | BETA: splitting (26) gives:
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | |   (104)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 150.98/21.90  | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 150.98/21.90  | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 150.98/21.90  | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | |   (105)  all_56_12 = e3 & op(e0, e3) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 150.98/21.90  | | | | | | | | | | | | | | |   (106)  all_56_12 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | COMBINE_EQS: (46), (106) imply:
% 150.98/21.90  | | | | | | | | | | | | | | |   (107)  e3 = e2
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | SIMP: (107) implies:
% 150.98/21.90  | | | | | | | | | | | | | | |   (108)  e3 = e2
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | COMBINE_EQS: (86), (108) imply:
% 150.98/21.90  | | | | | | | | | | | | | | |   (109)  all_56_6 = e2
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (6), (16), (17), (27), (28), (40), (43),
% 150.98/21.90  | | | | | | | | | | | | | | |            (46), (52), (78), (109) are inconsistent by
% 150.98/21.90  | | | | | | | | | | | | | | |            sub-proof #517.
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | |   (110)  all_56_13 = e3 & op(e0, e2) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | REF_CLOSE: (27), (91), (110) are inconsistent by sub-proof
% 150.98/21.90  | | | | | | | | | | | | | | |            #408.
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | |   (111)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 150.98/21.90  | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 150.98/21.90  | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 150.98/21.90  | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | |   (112)  all_56_14 = e3 & op(e0, e1) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | REF_CLOSE: (78), (102), (112) are inconsistent by sub-proof
% 150.98/21.90  | | | | | | | | | | | | | | |            #639.
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | |   (113)  all_56_15 = e3 & op(e0, e0) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 150.98/21.90  | | | | | | | | | | | | | | |   (114)  op(e0, e0) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | |   (115)  all_54_1 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | COMBINE_EQS: (18), (115) imply:
% 150.98/21.90  | | | | | | | | | | | | | | | |   (116)  all_52_4 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | SIMP: (116) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | |   (117)  all_52_4 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | REDUCE: (36), (117) imply:
% 150.98/21.90  | | | | | | | | | | | | | | | |   (118)   ~ (all_52_8 = e3)
% 150.98/21.90  | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | SIMP: (118) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | |   (119)   ~ (all_52_8 = e3)
% 150.98/21.90  | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | |   (120)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 150.98/21.90  | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | |   (121)  all_56_0 = e1 & op(e3, e3) = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | |   (122)  op(e3, e3) = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (17), (40), (122) are inconsistent by
% 150.98/21.90  | | | | | | | | | | | | | | | | | |            sub-proof #957.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | |   (123)  all_56_2 = e1 & op(e2, e3) = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | |   (124)  all_56_2 = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | BETA: splitting (23) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | |   (125)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e1)
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | |   (126)  all_56_0 = e1 & op(e3, e3) = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | |   (127)  op(e3, e3) = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (17), (40), (127) are inconsistent by
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | |            sub-proof #957.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | |   (128)  all_56_1 = e1 & op(e3, e2) = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (17), (69), (128) are inconsistent by
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | |            sub-proof #420.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | |   (129)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e1)
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | |   (130)  all_56_4 = e1 & op(e3, e1) = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | |   (131)  op(e3, e1) = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | BETA: splitting (19) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | |   (132)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |   (133)  all_56_0 = e3 & op(e3, e3) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |   (134)  op(e3, e3) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (16), (17), (27), (28), (32), (40), (43),
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |            (52), (57), (78), (86), (124), (134) are
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #93.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |   (135)  all_56_1 = e3 & op(e3, e2) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (135) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |   (136)  all_56_1 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | |   (137)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | |   (138)  all_56_4 = e0 & op(e3, e1) = e0
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (35), (49), (138) are inconsistent by
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1130.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | |   (139)  all_56_5 = e0 & op(e2, e1) = e0
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | |   (140)  all_56_5 = e0
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (141)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e3)
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (43), (63), (78), (124), (141) are
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #163.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | |   (142)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (143)  all_56_5 = e3 & op(e2, e1) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (144)  all_56_5 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (140), (144) imply:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (145)  e3 = e0
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (145) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (146)  e3 = e0
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (136), (146) imply:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (147)  all_56_1 = e0
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (16), (17), (19), (23), (27), (40),
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            (43), (49), (52), (78), (119), (147) are
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #492.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (148)  all_56_10 = e3 & op(e2, e0) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (149)  all_56_10 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | |   (150)  op(e2, e0) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (92) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (151)  all_56_9 = e1 & op(e3, e0) = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (152)  all_56_9 = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (16), (17), (22), (25), (27), (34),
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (40), (48), (52), (114), (149), (152) are
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #747.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (78), (96), (149) are inconsistent by sub-proof
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #677.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (153)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (7), (16), (17), (22), (27), (40), (43),
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (48), (52), (78), (114), (149), (150), (153) are
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #742.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | |   (154)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (16), (17), (40), (103), (154) are
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #15.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | |   (155)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |   (156)  all_56_4 = e3 & op(e3, e1) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |   (157)  op(e3, e1) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (49), (78), (131), (157) are inconsistent by
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #439.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |   (158)  all_56_9 = e3 & op(e3, e0) = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |   (159)  all_56_9 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (159) imply:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |   (160)  e3 = e2
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | SIMP: (160) implies:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |   (161)  e3 = e2
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (161) imply:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | |   (162)  all_56_6 = e2
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | |   (163)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (17), (27), (78), (124), (163) are
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #620.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (46), (84), (162) are inconsistent by
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #868.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | |   (164)  all_56_9 = e1 & op(e3, e0) = e1
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (44), (52), (164) are inconsistent by sub-proof
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | |            #656.
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | |   (165)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 150.98/21.90  | | | | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 150.98/21.90  | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (46), (52), (78), (79), (165) are
% 150.98/21.90  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #19.
% 150.98/21.90  | | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | |   (166)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 150.98/21.90  | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | | REF_CLOSE: (12), (18), (53), (69), (166) are inconsistent by
% 150.98/21.90  | | | | | | | | | | | | | | | |            sub-proof #875.
% 150.98/21.90  | | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | |   (167)  all_56_15 = e1 & op(e0, e0) = e1
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | ALPHA: (167) implies:
% 150.98/21.90  | | | | | | | | | | | | |   (168)  op(e0, e0) = e1
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | | REF_CLOSE: (1), (16), (17), (22), (27), (40), (43), (50),
% 150.98/21.90  | | | | | | | | | | | | |            (52), (78), (96), (168) are inconsistent by
% 150.98/21.90  | | | | | | | | | | | | |            sub-proof #445.
% 150.98/21.90  | | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | End of split
% 150.98/21.90  | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | Case 2:
% 150.98/21.90  | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | |   (169)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 150.98/21.90  | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 150.98/21.90  | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | BETA: splitting (169) gives:
% 150.98/21.90  | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | Case 1:
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | |   (170)  all_56_11 = e1 & op(e1, e0) = e1
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.90  | | | | | | | | | | | ALPHA: (170) implies:
% 150.98/21.90  | | | | | | | | | | |   (171)  op(e1, e0) = e1
% 150.98/21.90  | | | | | | | | | | | 
% 150.98/21.91  | | | | | | | | | | | REF_CLOSE: (17), (24), (73), (171) are inconsistent by
% 150.98/21.91  | | | | | | | | | | |            sub-proof #961.
% 150.98/21.91  | | | | | | | | | | | 
% 150.98/21.91  | | | | | | | | | | Case 2:
% 150.98/21.91  | | | | | | | | | | | 
% 150.98/21.91  | | | | | | | | | | |   (172)  all_56_15 = e1 & op(e0, e0) = e1
% 150.98/21.91  | | | | | | | | | | | 
% 150.98/21.91  | | | | | | | | | | | ALPHA: (172) implies:
% 150.98/21.91  | | | | | | | | | | |   (173)  op(e0, e0) = e1
% 150.98/21.91  | | | | | | | | | | | 
% 150.98/21.91  | | | | | | | | | | | REF_CLOSE: (7), (14), (17), (173) are inconsistent by
% 150.98/21.91  | | | | | | | | | | |            sub-proof #1116.
% 150.98/21.91  | | | | | | | | | | | 
% 150.98/21.91  | | | | | | | | | | End of split
% 150.98/21.91  | | | | | | | | | | 
% 150.98/21.91  | | | | | | | | | End of split
% 150.98/21.91  | | | | | | | | | 
% 150.98/21.91  | | | | | | | | End of split
% 150.98/21.91  | | | | | | | | 
% 150.98/21.91  | | | | | | | End of split
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | Case 2:
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | |   (174)  all_56_12 = e3 & op(e0, e3) = e3
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | | REF_CLOSE: (43), (46), (174) are inconsistent by sub-proof #575.
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | End of split
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | End of split
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | Case 2:
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | |   (175)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | | REF_CLOSE: (31), (39), (42), (68), (175) are inconsistent by sub-proof
% 150.98/21.91  | | | | |            #460.
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | End of split
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | Case 2:
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | |   (176)   ~ (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14)
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | | ALPHA: (176) implies:
% 150.98/21.91  | | | |   (177)   ~ (all_57_14 = e2)
% 150.98/21.91  | | | |   (178)  op(e1, e1) = all_57_14
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | | REF_CLOSE: (9), (17), (177), (178) are inconsistent by sub-proof #52.
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | End of split
% 150.98/21.91  | | | 
% 150.98/21.91  | | End of split
% 150.98/21.91  | | 
% 150.98/21.91  | Case 2:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (179)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 150.98/21.91  | |                e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.98/21.91  | |                $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.98/21.91  | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.98/21.91  | |            ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) &
% 150.98/21.91  | |                op(e0, e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 150.98/21.91  | |            op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 150.98/21.91  | |                (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.98/21.91  | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 150.98/21.91  | |                op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 150.98/21.91  | |                op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 150.98/21.91  | |                all_57_14 & $i(all_57_14))))
% 150.98/21.91  | | 
% 150.98/21.91  | | BETA: splitting (179) gives:
% 150.98/21.91  | | 
% 150.98/21.91  | | Case 1:
% 150.98/21.91  | | | 
% 150.98/21.91  | | |   (180)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 150.98/21.91  | | |              e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 150.98/21.91  | | |              $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 150.98/21.91  | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.98/21.91  | | |          ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) &
% 150.98/21.91  | | |              op(e0, e0) = all_57_15 & $i(all_57_15)))
% 150.98/21.91  | | | 
% 150.98/21.91  | | | ALPHA: (180) implies:
% 150.98/21.91  | | |   (181)  op(e1, e1) = e1
% 150.98/21.91  | | | 
% 150.98/21.91  | | | REF_CLOSE: (9), (13), (17), (52), (181) are inconsistent by sub-proof
% 150.98/21.91  | | |            #1044.
% 150.98/21.91  | | | 
% 150.98/21.91  | | Case 2:
% 150.98/21.91  | | | 
% 150.98/21.91  | | |   (182)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 150.98/21.91  | | |              e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 150.98/21.91  | | |              $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 150.98/21.91  | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.98/21.91  | | |          ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 150.98/21.91  | | |              op(e1, e1) = all_57_14 & $i(all_57_14)))
% 150.98/21.91  | | | 
% 150.98/21.91  | | | ALPHA: (182) implies:
% 150.98/21.91  | | |   (183)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) & op(e3,
% 150.98/21.91  | | |              e3) = all_57_10 & $i(all_57_10))
% 150.98/21.91  | | | 
% 150.98/21.91  | | | BETA: splitting (183) gives:
% 150.98/21.91  | | | 
% 150.98/21.91  | | | Case 1:
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | |   (184)  all_57_9 = e3 & op(e3, e0) = e3
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | | ALPHA: (184) implies:
% 150.98/21.91  | | | |   (185)  op(e3, e0) = e3
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | | REF_CLOSE: (11), (17), (43), (54), (185) are inconsistent by sub-proof
% 150.98/21.91  | | | |            #14.
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | Case 2:
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | |   (186)   ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10)
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | | ALPHA: (186) implies:
% 150.98/21.91  | | | |   (187)   ~ (all_57_10 = e0)
% 150.98/21.91  | | | |   (188)  op(e3, e3) = all_57_10
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | | REF_CLOSE: (2), (17), (187), (188) are inconsistent by sub-proof #543.
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | End of split
% 150.98/21.91  | | | 
% 150.98/21.91  | | End of split
% 150.98/21.91  | | 
% 150.98/21.91  | End of split
% 150.98/21.91  | 
% 150.98/21.91  End of proof
% 150.98/21.91  
% 150.98/21.91  Sub-proof #14 shows that the following formulas are inconsistent:
% 150.98/21.91  ----------------------------------------------------------------
% 150.98/21.91    (1)  op(e3, e0) = e3
% 150.98/21.91    (2)  op(e3, e0) = e2
% 150.98/21.91    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.91    (4)   ~ (e3 = e2)
% 150.98/21.91    (5)  op(e3, e0) = all_14_1
% 150.98/21.91  
% 150.98/21.91  Begin of proof
% 150.98/21.91  | 
% 150.98/21.91  | GROUND_INST: instantiating (3) with e2, all_14_1, e0, e3, simplifying with
% 150.98/21.91  |              (2), (5) gives:
% 150.98/21.91  |   (6)  all_14_1 = e2
% 150.98/21.91  | 
% 150.98/21.91  | GROUND_INST: instantiating (3) with e3, all_14_1, e0, e3, simplifying with
% 150.98/21.91  |              (1), (5) gives:
% 150.98/21.91  |   (7)  all_14_1 = e3
% 150.98/21.91  | 
% 150.98/21.91  | COMBINE_EQS: (6), (7) imply:
% 150.98/21.91  |   (8)  e3 = e2
% 150.98/21.91  | 
% 150.98/21.91  | REDUCE: (4), (8) imply:
% 150.98/21.91  |   (9)  $false
% 150.98/21.91  | 
% 150.98/21.91  | CLOSE: (9) is inconsistent.
% 150.98/21.91  | 
% 150.98/21.91  End of proof
% 150.98/21.91  
% 150.98/21.91  Sub-proof #15 shows that the following formulas are inconsistent:
% 150.98/21.91  ----------------------------------------------------------------
% 150.98/21.91    (1)  op(e0, e1) = e1
% 150.98/21.91    (2)  op(e1, e1) = e2
% 150.98/21.91    (3)   ~ (e2 = e0)
% 150.98/21.91    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.91    (5)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 150.98/21.91    (6)   ~ (e1 = e0)
% 150.98/21.91  
% 150.98/21.91  Begin of proof
% 150.98/21.91  | 
% 150.98/21.91  | BETA: splitting (5) gives:
% 150.98/21.91  | 
% 150.98/21.91  | Case 1:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (7)  all_56_8 = e0 & op(e1, e1) = e0
% 150.98/21.91  | | 
% 150.98/21.91  | | ALPHA: (7) implies:
% 150.98/21.91  | |   (8)  op(e1, e1) = e0
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1006.
% 150.98/21.91  | | 
% 150.98/21.91  | Case 2:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (9)  all_56_14 = e0 & op(e0, e1) = e0
% 150.98/21.91  | | 
% 150.98/21.91  | | ALPHA: (9) implies:
% 150.98/21.91  | |   (10)  op(e0, e1) = e0
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #899.
% 150.98/21.91  | | 
% 150.98/21.91  | End of split
% 150.98/21.91  | 
% 150.98/21.91  End of proof
% 150.98/21.91  
% 150.98/21.91  Sub-proof #16 shows that the following formulas are inconsistent:
% 150.98/21.91  ----------------------------------------------------------------
% 150.98/21.91    (1)   ~ (e3 = e1)
% 150.98/21.91    (2)  op(e1, e3) = e3
% 150.98/21.91    (3)  op(e1, e1) = e2
% 150.98/21.91    (4)  op(e1, e1) = all_4_2
% 150.98/21.91    (5)  all_56_7 = e0 & op(e1, e2) = e0
% 150.98/21.91    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.91    (7)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 150.98/21.91         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 150.98/21.91    (8)   ~ (all_52_14 = e1)
% 150.98/21.91    (9)  op(e1, e0) = all_52_14
% 150.98/21.91    (10)   ~ (e1 = e0)
% 150.98/21.91    (11)   ~ (e2 = e1)
% 150.98/21.91  
% 150.98/21.91  Begin of proof
% 150.98/21.91  | 
% 150.98/21.91  | ALPHA: (5) implies:
% 150.98/21.91  |   (12)  all_56_7 = e0
% 150.98/21.91  | 
% 150.98/21.91  | BETA: splitting (7) gives:
% 150.98/21.91  | 
% 150.98/21.91  | Case 1:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (13)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 150.98/21.91  | |           e1)
% 150.98/21.91  | | 
% 150.98/21.91  | | BETA: splitting (13) gives:
% 150.98/21.91  | | 
% 150.98/21.91  | | Case 1:
% 150.98/21.91  | | | 
% 150.98/21.91  | | |   (14)  all_56_6 = e1 & op(e1, e3) = e1
% 150.98/21.91  | | | 
% 150.98/21.91  | | | ALPHA: (14) implies:
% 150.98/21.91  | | |   (15)  op(e1, e3) = e1
% 150.98/21.91  | | | 
% 150.98/21.91  | | | REF_CLOSE: (1), (2), (6), (15) are inconsistent by sub-proof #119.
% 150.98/21.91  | | | 
% 150.98/21.91  | | Case 2:
% 150.98/21.91  | | | 
% 150.98/21.91  | | |   (16)  all_56_7 = e1 & op(e1, e2) = e1
% 150.98/21.91  | | | 
% 150.98/21.91  | | | ALPHA: (16) implies:
% 150.98/21.91  | | |   (17)  all_56_7 = e1
% 150.98/21.91  | | | 
% 150.98/21.91  | | | REF_CLOSE: (10), (12), (17) are inconsistent by sub-proof #987.
% 150.98/21.91  | | | 
% 150.98/21.91  | | End of split
% 150.98/21.91  | | 
% 150.98/21.91  | Case 2:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (18)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 150.98/21.91  | |           e1)
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (3), (4), (6), (8), (9), (11), (18) are inconsistent by sub-proof
% 150.98/21.91  | |            #17.
% 150.98/21.91  | | 
% 150.98/21.91  | End of split
% 150.98/21.91  | 
% 150.98/21.91  End of proof
% 150.98/21.91  
% 150.98/21.91  Sub-proof #17 shows that the following formulas are inconsistent:
% 150.98/21.91  ----------------------------------------------------------------
% 150.98/21.91    (1)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 150.98/21.91    (2)  op(e1, e1) = e2
% 150.98/21.91    (3)  op(e1, e1) = all_4_2
% 150.98/21.91    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.91    (5)   ~ (all_52_14 = e1)
% 150.98/21.91    (6)  op(e1, e0) = all_52_14
% 150.98/21.91    (7)   ~ (e2 = e1)
% 150.98/21.91  
% 150.98/21.91  Begin of proof
% 150.98/21.91  | 
% 150.98/21.91  | BETA: splitting (1) gives:
% 150.98/21.91  | 
% 150.98/21.91  | Case 1:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (8)  all_56_8 = e1 & op(e1, e1) = e1
% 150.98/21.91  | | 
% 150.98/21.91  | | ALPHA: (8) implies:
% 150.98/21.91  | |   (9)  op(e1, e1) = e1
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (2), (3), (4), (7), (9) are inconsistent by sub-proof #1044.
% 150.98/21.91  | | 
% 150.98/21.91  | Case 2:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (10)  all_56_11 = e1 & op(e1, e0) = e1
% 150.98/21.91  | | 
% 150.98/21.91  | | ALPHA: (10) implies:
% 150.98/21.91  | |   (11)  op(e1, e0) = e1
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (4), (5), (6), (11) are inconsistent by sub-proof #961.
% 150.98/21.91  | | 
% 150.98/21.91  | End of split
% 150.98/21.91  | 
% 150.98/21.91  End of proof
% 150.98/21.91  
% 150.98/21.91  Sub-proof #18 shows that the following formulas are inconsistent:
% 150.98/21.91  ----------------------------------------------------------------
% 150.98/21.91    (1)  op(e3, e3) = e0
% 150.98/21.91    (2)   ~ (e3 = e1)
% 150.98/21.91    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 150.98/21.91         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 150.98/21.91    (4)  op(e1, e3) = e3
% 150.98/21.91    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.91    (6)  all_56_2 = e3 & op(e2, e3) = e3
% 150.98/21.91    (7)   ~ (e1 = e0)
% 150.98/21.91    (8)  all_56_12 = e2
% 150.98/21.91    (9)   ~ (e2 = e1)
% 150.98/21.91  
% 150.98/21.91  Begin of proof
% 150.98/21.91  | 
% 150.98/21.91  | ALPHA: (6) implies:
% 150.98/21.91  |   (10)  all_56_2 = e3
% 150.98/21.91  | 
% 150.98/21.91  | BETA: splitting (3) gives:
% 150.98/21.91  | 
% 150.98/21.91  | Case 1:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (11)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 150.98/21.91  | |           e1)
% 150.98/21.91  | | 
% 150.98/21.91  | | BETA: splitting (11) gives:
% 150.98/21.91  | | 
% 150.98/21.91  | | Case 1:
% 150.98/21.91  | | | 
% 150.98/21.91  | | |   (12)  all_56_0 = e1 & op(e3, e3) = e1
% 150.98/21.91  | | | 
% 150.98/21.91  | | | ALPHA: (12) implies:
% 150.98/21.91  | | |   (13)  op(e3, e3) = e1
% 150.98/21.91  | | | 
% 150.98/21.91  | | | REF_CLOSE: (1), (5), (7), (13) are inconsistent by sub-proof #957.
% 150.98/21.91  | | | 
% 150.98/21.91  | | Case 2:
% 150.98/21.91  | | | 
% 150.98/21.91  | | |   (14)  all_56_2 = e1 & op(e2, e3) = e1
% 150.98/21.91  | | | 
% 150.98/21.91  | | | REF_CLOSE: (2), (10), (14) are inconsistent by sub-proof #791.
% 150.98/21.91  | | | 
% 150.98/21.91  | | End of split
% 150.98/21.91  | | 
% 150.98/21.91  | Case 2:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (15)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 150.98/21.91  | |           e1)
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (2), (4), (5), (8), (9), (15) are inconsistent by sub-proof #19.
% 150.98/21.91  | | 
% 150.98/21.91  | End of split
% 150.98/21.91  | 
% 150.98/21.91  End of proof
% 150.98/21.91  
% 150.98/21.91  Sub-proof #19 shows that the following formulas are inconsistent:
% 150.98/21.91  ----------------------------------------------------------------
% 150.98/21.91    (1)   ~ (e3 = e1)
% 150.98/21.91    (2)  op(e1, e3) = e3
% 150.98/21.91    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.91    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 150.98/21.91    (5)  all_56_12 = e2
% 150.98/21.91    (6)   ~ (e2 = e1)
% 150.98/21.91  
% 150.98/21.91  Begin of proof
% 150.98/21.91  | 
% 150.98/21.91  | BETA: splitting (4) gives:
% 150.98/21.91  | 
% 150.98/21.91  | Case 1:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (7)  all_56_6 = e1 & op(e1, e3) = e1
% 150.98/21.91  | | 
% 150.98/21.91  | | ALPHA: (7) implies:
% 150.98/21.91  | |   (8)  op(e1, e3) = e1
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #119.
% 150.98/21.91  | | 
% 150.98/21.91  | Case 2:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (9)  all_56_12 = e1 & op(e0, e3) = e1
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #789.
% 150.98/21.91  | | 
% 150.98/21.91  | End of split
% 150.98/21.91  | 
% 150.98/21.91  End of proof
% 150.98/21.91  
% 150.98/21.91  Sub-proof #20 shows that the following formulas are inconsistent:
% 150.98/21.91  ----------------------------------------------------------------
% 150.98/21.91    (1)   ~ (all_52_6 = e1)
% 150.98/21.91    (2)  all_54_9 = all_52_6
% 150.98/21.91    (3)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 150.98/21.91    (4)   ~ (all_52_6 = e0)
% 150.98/21.91    (5)   ~ (all_52_6 = e2)
% 150.98/21.91  
% 150.98/21.91  Begin of proof
% 150.98/21.91  | 
% 150.98/21.91  | BETA: splitting (3) gives:
% 150.98/21.91  | 
% 150.98/21.91  | Case 1:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (6)  all_54_9 = e2
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (2), (5), (6) are inconsistent by sub-proof #185.
% 150.98/21.91  | | 
% 150.98/21.91  | Case 2:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (7)  all_54_9 = e1 | all_54_9 = e0
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #137.
% 150.98/21.91  | | 
% 150.98/21.91  | End of split
% 150.98/21.91  | 
% 150.98/21.91  End of proof
% 150.98/21.91  
% 150.98/21.91  Sub-proof #21 shows that the following formulas are inconsistent:
% 150.98/21.91  ----------------------------------------------------------------
% 150.98/21.91    (1)  all_54_6 = all_52_9
% 150.98/21.91    (2)   ~ (all_52_1 = e0)
% 150.98/21.91    (3)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 150.98/21.91    (4)  op(e2, e0) = all_16_1
% 150.98/21.91    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.91    (6)  op(e2, e0) = e3
% 150.98/21.91    (7)   ~ (all_52_1 = all_52_9)
% 150.98/21.91    (8)   ~ (all_52_1 = e3)
% 150.98/21.91    (9)   ~ (all_52_9 = e2)
% 150.98/21.91    (10)  op(e3, e2) = e1
% 150.98/21.91    (11)  all_54_4 = all_52_1
% 150.98/21.91    (12)  ( ~ (all_18_0 = e1) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 150.98/21.91            all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e2,
% 150.98/21.91              e0) = all_18_1 & $i(all_18_1))
% 150.98/21.91    (13)   ~ (all_52_9 = e0)
% 150.98/21.91    (14)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 150.98/21.91  
% 150.98/21.91  Begin of proof
% 150.98/21.91  | 
% 150.98/21.91  | BETA: splitting (14) gives:
% 150.98/21.91  | 
% 150.98/21.91  | Case 1:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (15)  all_54_6 = e2
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (1), (9), (15) are inconsistent by sub-proof #379.
% 150.98/21.91  | | 
% 150.98/21.91  | Case 2:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (16)  all_54_6 = e1 | all_54_6 = e0
% 150.98/21.91  | | 
% 150.98/21.91  | | BETA: splitting (16) gives:
% 150.98/21.91  | | 
% 150.98/21.91  | | Case 1:
% 150.98/21.91  | | | 
% 150.98/21.91  | | |   (17)  all_54_6 = e1
% 150.98/21.91  | | | 
% 150.98/21.91  | | | COMBINE_EQS: (1), (17) imply:
% 150.98/21.91  | | |   (18)  all_52_9 = e1
% 150.98/21.91  | | | 
% 150.98/21.91  | | | SIMP: (18) implies:
% 150.98/21.91  | | |   (19)  all_52_9 = e1
% 150.98/21.91  | | | 
% 150.98/21.91  | | | REDUCE: (7), (19) imply:
% 150.98/21.91  | | |   (20)   ~ (all_52_1 = e1)
% 150.98/21.91  | | | 
% 150.98/21.91  | | | BETA: splitting (3) gives:
% 150.98/21.91  | | | 
% 150.98/21.91  | | | Case 1:
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | |   (21)  all_54_4 = e3
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | | REF_CLOSE: (8), (11), (21) are inconsistent by sub-proof #843.
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | Case 2:
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | |   (22)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | | BETA: splitting (12) gives:
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | | Case 1:
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | |   (23)   ~ (all_18_0 = e1) & op(all_18_1, e2) = all_18_0 & op(e2, e0)
% 150.98/21.91  | | | | |         = all_18_1 & $i(all_18_0) & $i(all_18_1)
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | | ALPHA: (23) implies:
% 150.98/21.91  | | | | |   (24)   ~ (all_18_0 = e1)
% 150.98/21.91  | | | | |   (25)  op(e2, e0) = all_18_1
% 150.98/21.91  | | | | |   (26)  op(all_18_1, e2) = all_18_0
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | | BETA: splitting (22) gives:
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | | Case 1:
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | | GROUND_INST: instantiating (5) with all_16_1, all_18_1, e0, e2,
% 150.98/21.91  | | | | | |              simplifying with (4), (25) gives:
% 150.98/21.91  | | | | | |   (27)  all_18_1 = all_16_1
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | | GROUND_INST: instantiating (5) with e3, all_18_1, e0, e2,
% 150.98/21.91  | | | | | |              simplifying with (6), (25) gives:
% 150.98/21.91  | | | | | |   (28)  all_18_1 = e3
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | | GROUND_INST: instantiating (5) with e1, all_18_0, e2, e3,
% 150.98/21.91  | | | | | |              simplifying with (10) gives:
% 150.98/21.91  | | | | | |   (29)  all_18_0 = e1 |  ~ (op(e3, e2) = all_18_0)
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | | COMBINE_EQS: (27), (28) imply:
% 150.98/21.91  | | | | | |   (30)  all_16_1 = e3
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | | REDUCE: (26), (28) imply:
% 150.98/21.91  | | | | | |   (31)  op(e3, e2) = all_18_0
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | | BETA: splitting (29) gives:
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | | Case 1:
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | |   (32)   ~ (op(e3, e2) = all_18_0)
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | | PRED_UNIFY: (31), (32) imply:
% 150.98/21.91  | | | | | | |   (33)  $false
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | | CLOSE: (33) is inconsistent.
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | Case 2:
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | |   (34)  all_18_0 = e1
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | | REDUCE: (24), (34) imply:
% 150.98/21.91  | | | | | | |   (35)  $false
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | | CLOSE: (35) is inconsistent.
% 150.98/21.91  | | | | | | | 
% 150.98/21.91  | | | | | | End of split
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | Case 2:
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | |   (36)  all_54_4 = e1 | all_54_4 = e0
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | | REF_CLOSE: (2), (11), (20), (36) are inconsistent by sub-proof #795.
% 150.98/21.91  | | | | | | 
% 150.98/21.91  | | | | | End of split
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | Case 2:
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | |   (37)   ~ (all_18_1 = e3) & op(e2, e0) = all_18_1 & $i(all_18_1)
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | | ALPHA: (37) implies:
% 150.98/21.91  | | | | |   (38)   ~ (all_18_1 = e3)
% 150.98/21.91  | | | | |   (39)  op(e2, e0) = all_18_1
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | | GROUND_INST: instantiating (5) with e3, all_18_1, e0, e2, simplifying
% 150.98/21.91  | | | | |              with (6), (39) gives:
% 150.98/21.91  | | | | |   (40)  all_18_1 = e3
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | | REDUCE: (38), (40) imply:
% 150.98/21.91  | | | | |   (41)  $false
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | | CLOSE: (41) is inconsistent.
% 150.98/21.91  | | | | | 
% 150.98/21.91  | | | | End of split
% 150.98/21.91  | | | | 
% 150.98/21.91  | | | End of split
% 150.98/21.91  | | | 
% 150.98/21.91  | | Case 2:
% 150.98/21.91  | | | 
% 150.98/21.91  | | |   (42)  all_54_6 = e0
% 150.98/21.91  | | | 
% 150.98/21.91  | | | COMBINE_EQS: (1), (42) imply:
% 150.98/21.91  | | |   (43)  all_52_9 = e0
% 150.98/21.91  | | | 
% 150.98/21.91  | | | SIMP: (43) implies:
% 150.98/21.91  | | |   (44)  all_52_9 = e0
% 150.98/21.91  | | | 
% 150.98/21.91  | | | REDUCE: (13), (44) imply:
% 150.98/21.91  | | |   (45)  $false
% 150.98/21.91  | | | 
% 150.98/21.91  | | | CLOSE: (45) is inconsistent.
% 150.98/21.91  | | | 
% 150.98/21.91  | | End of split
% 150.98/21.91  | | 
% 150.98/21.91  | End of split
% 150.98/21.91  | 
% 150.98/21.91  End of proof
% 150.98/21.91  
% 150.98/21.91  Sub-proof #22 shows that the following formulas are inconsistent:
% 150.98/21.91  ----------------------------------------------------------------
% 150.98/21.91    (1)  op(e1, e1) = e2
% 150.98/21.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.91    (3)   ~ (e3 = e0)
% 150.98/21.91    (4)   ~ (e3 = e2)
% 150.98/21.91    (5)   ~ (all_52_2 = e1)
% 150.98/21.91    (6)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 150.98/21.91             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 150.98/21.91           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 150.98/21.91           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 150.98/21.91           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.98/21.91           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 150.98/21.91           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 150.98/21.91           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 150.98/21.91           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 150.98/21.91           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 150.98/21.91           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 150.98/21.91           $i(all_57_14))
% 150.98/21.91    (7)  op(e0, e0) = e0
% 150.98/21.91    (8)  op(e1, e3) = all_52_2
% 150.98/21.91  
% 150.98/21.91  Begin of proof
% 150.98/21.91  | 
% 150.98/21.91  | BETA: splitting (6) gives:
% 150.98/21.91  | 
% 150.98/21.91  | Case 1:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (9)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 150.98/21.91  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 150.98/21.91  | |          all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 150.98/21.91  | |        (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 150.98/21.91  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 150.98/21.91  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.98/21.91  | | 
% 150.98/21.91  | | BETA: splitting (9) gives:
% 150.98/21.91  | | 
% 150.98/21.91  | | Case 1:
% 150.98/21.91  | | | 
% 150.98/21.91  | | |   (10)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.98/21.91  | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.98/21.91  | | |         op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 150.98/21.91  | | |         $i(all_57_12)
% 150.98/21.91  | | | 
% 150.98/21.91  | | | ALPHA: (10) implies:
% 150.98/21.91  | | |   (11)  op(e1, e1) = e3
% 150.98/21.91  | | | 
% 150.98/21.91  | | | REF_CLOSE: (1), (2), (4), (11) are inconsistent by sub-proof #834.
% 150.98/21.91  | | | 
% 150.98/21.91  | | Case 2:
% 150.98/21.91  | | | 
% 150.98/21.91  | | |   (12)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 150.98/21.91  | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.98/21.91  | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 150.98/21.91  | | |         $i(all_57_12)
% 150.98/21.91  | | | 
% 150.98/21.91  | | | ALPHA: (12) implies:
% 150.98/21.91  | | |   (13)  op(e0, e0) = e3
% 150.98/21.91  | | | 
% 150.98/21.91  | | | REF_CLOSE: (2), (3), (7), (13) are inconsistent by sub-proof #1143.
% 150.98/21.91  | | | 
% 150.98/21.91  | | End of split
% 150.98/21.91  | | 
% 150.98/21.91  | Case 2:
% 150.98/21.91  | | 
% 150.98/21.91  | |   (14)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 150.98/21.91  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 150.98/21.91  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 150.98/21.91  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 150.98/21.91  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 150.98/21.91  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 150.98/21.91  | | 
% 150.98/21.91  | | REF_CLOSE: (2), (3), (5), (7), (8), (14) are inconsistent by sub-proof
% 150.98/21.91  | |            #1045.
% 150.98/21.91  | | 
% 150.98/21.91  | End of split
% 150.98/21.91  | 
% 150.98/21.91  End of proof
% 150.98/21.91  
% 150.98/21.91  Sub-proof #23 shows that the following formulas are inconsistent:
% 150.98/21.91  ----------------------------------------------------------------
% 150.98/21.91    (1)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 150.98/21.91    (2)  op(e0, e2) = all_52_7
% 150.98/21.91    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.91    (4)   ~ (all_52_7 = e1)
% 150.98/21.91    (5)   ~ (all_52_3 = e1)
% 150.98/21.91    (6)  op(e0, e3) = all_52_3
% 150.98/21.91  
% 150.98/21.91  Begin of proof
% 150.98/21.91  | 
% 150.98/21.91  | BETA: splitting (1) gives:
% 150.98/21.91  | 
% 150.98/21.91  | Case 1:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (7)  all_56_12 = e1 & op(e0, e3) = e1
% 150.98/21.92  | | 
% 150.98/21.92  | | ALPHA: (7) implies:
% 150.98/21.92  | |   (8)  op(e0, e3) = e1
% 150.98/21.92  | | 
% 150.98/21.92  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #405.
% 150.98/21.92  | | 
% 150.98/21.92  | Case 2:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (9)  all_56_13 = e1 & op(e0, e2) = e1
% 150.98/21.92  | | 
% 150.98/21.92  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #414.
% 150.98/21.92  | | 
% 150.98/21.92  | End of split
% 150.98/21.92  | 
% 150.98/21.92  End of proof
% 150.98/21.92  
% 150.98/21.92  Sub-proof #24 shows that the following formulas are inconsistent:
% 150.98/21.92  ----------------------------------------------------------------
% 150.98/21.92    (1)  op(e0, e2) = all_52_7
% 150.98/21.92    (2)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 150.98/21.92    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.92    (4)  op(e1, e2) = all_52_6
% 150.98/21.92    (5)   ~ (all_52_7 = e2)
% 150.98/21.92    (6)   ~ (all_52_6 = e2)
% 150.98/21.92  
% 150.98/21.92  Begin of proof
% 150.98/21.92  | 
% 150.98/21.92  | BETA: splitting (2) gives:
% 150.98/21.92  | 
% 150.98/21.92  | Case 1:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (7)  all_56_7 = e2 & op(e1, e2) = e2
% 150.98/21.92  | | 
% 150.98/21.92  | | ALPHA: (7) implies:
% 150.98/21.92  | |   (8)  op(e1, e2) = e2
% 150.98/21.92  | | 
% 150.98/21.92  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #1171.
% 150.98/21.92  | | 
% 150.98/21.92  | Case 2:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (9)  all_56_13 = e2 & op(e0, e2) = e2
% 150.98/21.92  | | 
% 150.98/21.92  | | ALPHA: (9) implies:
% 150.98/21.92  | |   (10)  op(e0, e2) = e2
% 150.98/21.92  | | 
% 150.98/21.92  | | GROUND_INST: instantiating (3) with all_52_7, e2, e2, e0, simplifying with
% 150.98/21.92  | |              (1), (10) gives:
% 150.98/21.92  | |   (11)  all_52_7 = e2
% 150.98/21.92  | | 
% 150.98/21.92  | | REDUCE: (5), (11) imply:
% 150.98/21.92  | |   (12)  $false
% 150.98/21.92  | | 
% 150.98/21.92  | | CLOSE: (12) is inconsistent.
% 150.98/21.92  | | 
% 150.98/21.92  | End of split
% 150.98/21.92  | 
% 150.98/21.92  End of proof
% 150.98/21.92  
% 150.98/21.92  Sub-proof #25 shows that the following formulas are inconsistent:
% 150.98/21.92  ----------------------------------------------------------------
% 150.98/21.92    (1)   ~ (all_52_2 = all_52_14)
% 150.98/21.92    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 150.98/21.92         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 150.98/21.92    (3)   ~ (all_52_2 = all_52_6)
% 150.98/21.92    (4)   ~ (all_52_14 = e2)
% 150.98/21.92    (5)   ~ (all_52_3 = all_52_7)
% 150.98/21.92    (6)  all_54_9 = all_52_6
% 150.98/21.92    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.92    (8)  op(e2, e3) = e2
% 150.98/21.92    (9)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 150.98/21.92    (10)  op(e1, e0) = all_52_14
% 150.98/21.92    (11)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 150.98/21.92    (12)   ~ (all_52_2 = e2)
% 150.98/21.92    (13)  op(e0, e3) = all_52_3
% 150.98/21.92    (14)   ~ (all_52_2 = e3)
% 150.98/21.92    (15)   ~ (all_52_7 = e2)
% 150.98/21.92    (16)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 150.98/21.92    (17)   ~ (all_52_7 = e0)
% 150.98/21.92    (18)  all_54_8 = all_52_2
% 150.98/21.92    (19)  op(e1, e0) = e1
% 150.98/21.92    (20)   ~ (all_52_6 = all_52_14)
% 150.98/21.92    (21)  all_54_13 = all_52_7
% 150.98/21.92    (22)  op(e3, e3) = e3
% 150.98/21.92    (23)   ~ (all_52_6 = all_52_7)
% 150.98/21.92    (24)  op(e1, e3) = all_52_2
% 150.98/21.92    (25)  op(e2, e3) = all_52_1
% 150.98/21.92    (26)   ~ (all_52_6 = e2)
% 150.98/21.92  
% 150.98/21.92  Begin of proof
% 150.98/21.92  | 
% 150.98/21.92  | GROUND_INST: instantiating (7) with all_52_14, e1, e0, e1, simplifying with
% 150.98/21.92  |              (10), (19) gives:
% 150.98/21.92  |   (27)  all_52_14 = e1
% 150.98/21.92  | 
% 150.98/21.92  | REDUCE: (1), (27) imply:
% 150.98/21.92  |   (28)   ~ (all_52_2 = e1)
% 150.98/21.92  | 
% 150.98/21.92  | REDUCE: (20), (27) imply:
% 150.98/21.92  |   (29)   ~ (all_52_6 = e1)
% 150.98/21.92  | 
% 150.98/21.92  | REDUCE: (4), (27) imply:
% 150.98/21.92  |   (30)   ~ (e2 = e1)
% 150.98/21.92  | 
% 150.98/21.92  | SIMP: (30) implies:
% 150.98/21.92  |   (31)   ~ (e2 = e1)
% 150.98/21.92  | 
% 150.98/21.92  | BETA: splitting (9) gives:
% 150.98/21.92  | 
% 150.98/21.92  | Case 1:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (32)  all_54_9 = e3
% 150.98/21.92  | | 
% 150.98/21.92  | | COMBINE_EQS: (6), (32) imply:
% 150.98/21.92  | |   (33)  all_52_6 = e3
% 150.98/21.92  | | 
% 150.98/21.92  | | SIMP: (33) implies:
% 150.98/21.92  | |   (34)  all_52_6 = e3
% 150.98/21.92  | | 
% 150.98/21.92  | | REDUCE: (23), (34) imply:
% 150.98/21.92  | |   (35)   ~ (all_52_7 = e3)
% 150.98/21.92  | | 
% 150.98/21.92  | | SIMP: (35) implies:
% 150.98/21.92  | |   (36)   ~ (all_52_7 = e3)
% 150.98/21.92  | | 
% 150.98/21.92  | | REDUCE: (29), (34) imply:
% 150.98/21.92  | |   (37)   ~ (e3 = e1)
% 150.98/21.92  | | 
% 150.98/21.92  | | BETA: splitting (2) gives:
% 150.98/21.92  | | 
% 150.98/21.92  | | Case 1:
% 150.98/21.92  | | | 
% 150.98/21.92  | | |   (38)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 150.98/21.92  | | |           e1)
% 150.98/21.92  | | | 
% 150.98/21.92  | | | REF_CLOSE: (7), (8), (22), (25), (31), (37), (38) are inconsistent by
% 150.98/21.92  | | |            sub-proof #841.
% 150.98/21.92  | | | 
% 150.98/21.92  | | Case 2:
% 150.98/21.92  | | | 
% 150.98/21.92  | | |   (39)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 150.98/21.92  | | |           e1)
% 150.98/21.92  | | | 
% 150.98/21.92  | | | BETA: splitting (39) gives:
% 150.98/21.92  | | | 
% 150.98/21.92  | | | Case 1:
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | |   (40)  all_56_6 = e1 & op(e1, e3) = e1
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | | ALPHA: (40) implies:
% 150.98/21.92  | | | |   (41)  op(e1, e3) = e1
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | | REF_CLOSE: (7), (24), (28), (41) are inconsistent by sub-proof #1046.
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | Case 2:
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | |   (42)  all_56_12 = e1 & op(e0, e3) = e1
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | | ALPHA: (42) implies:
% 150.98/21.92  | | | |   (43)  op(e0, e3) = e1
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | | BETA: splitting (16) gives:
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | | Case 1:
% 150.98/21.92  | | | | | 
% 150.98/21.92  | | | | |   (44)  all_54_13 = e3
% 150.98/21.92  | | | | | 
% 150.98/21.92  | | | | | REF_CLOSE: (21), (36), (44) are inconsistent by sub-proof #845.
% 150.98/21.92  | | | | | 
% 150.98/21.92  | | | | Case 2:
% 150.98/21.92  | | | | | 
% 150.98/21.92  | | | | |   (45)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 150.98/21.92  | | | | | 
% 150.98/21.92  | | | | | BETA: splitting (45) gives:
% 150.98/21.92  | | | | | 
% 150.98/21.92  | | | | | Case 1:
% 150.98/21.92  | | | | | | 
% 150.98/21.92  | | | | | |   (46)  all_54_13 = e2
% 150.98/21.92  | | | | | | 
% 150.98/21.92  | | | | | | COMBINE_EQS: (21), (46) imply:
% 150.98/21.92  | | | | | |   (47)  all_52_7 = e2
% 150.98/21.92  | | | | | | 
% 150.98/21.92  | | | | | | SIMP: (47) implies:
% 150.98/21.92  | | | | | |   (48)  all_52_7 = e2
% 150.98/21.92  | | | | | | 
% 150.98/21.92  | | | | | | REDUCE: (15), (48) imply:
% 150.98/21.92  | | | | | |   (49)  $false
% 150.98/21.92  | | | | | | 
% 150.98/21.92  | | | | | | CLOSE: (49) is inconsistent.
% 150.98/21.92  | | | | | | 
% 150.98/21.92  | | | | | Case 2:
% 150.98/21.92  | | | | | | 
% 150.98/21.92  | | | | | |   (50)  all_54_13 = e1 | all_54_13 = e0
% 150.98/21.92  | | | | | | 
% 150.98/21.92  | | | | | | BETA: splitting (50) gives:
% 150.98/21.92  | | | | | | 
% 150.98/21.92  | | | | | | Case 1:
% 150.98/21.92  | | | | | | | 
% 150.98/21.92  | | | | | | |   (51)  all_54_13 = e1
% 150.98/21.92  | | | | | | | 
% 150.98/21.92  | | | | | | | COMBINE_EQS: (21), (51) imply:
% 150.98/21.92  | | | | | | |   (52)  all_52_7 = e1
% 150.98/21.92  | | | | | | | 
% 150.98/21.92  | | | | | | | SIMP: (52) implies:
% 150.98/21.92  | | | | | | |   (53)  all_52_7 = e1
% 150.98/21.92  | | | | | | | 
% 150.98/21.92  | | | | | | | REDUCE: (5), (53) imply:
% 150.98/21.92  | | | | | | |   (54)   ~ (all_52_3 = e1)
% 150.98/21.92  | | | | | | | 
% 150.98/21.92  | | | | | | | REF_CLOSE: (7), (13), (43), (54) are inconsistent by sub-proof
% 150.98/21.92  | | | | | | |            #405.
% 150.98/21.92  | | | | | | | 
% 150.98/21.92  | | | | | | Case 2:
% 150.98/21.92  | | | | | | | 
% 150.98/21.92  | | | | | | |   (55)  all_54_13 = e0
% 150.98/21.92  | | | | | | | 
% 150.98/21.92  | | | | | | | REF_CLOSE: (17), (21), (55) are inconsistent by sub-proof #984.
% 150.98/21.92  | | | | | | | 
% 150.98/21.92  | | | | | | End of split
% 150.98/21.92  | | | | | | 
% 150.98/21.92  | | | | | End of split
% 150.98/21.92  | | | | | 
% 150.98/21.92  | | | | End of split
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | End of split
% 150.98/21.92  | | | 
% 150.98/21.92  | | End of split
% 150.98/21.92  | | 
% 150.98/21.92  | Case 2:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (56)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 150.98/21.92  | | 
% 150.98/21.92  | | REF_CLOSE: (3), (6), (11), (12), (14), (18), (26), (28), (29), (56) are
% 150.98/21.92  | |            inconsistent by sub-proof #79.
% 150.98/21.92  | | 
% 150.98/21.92  | End of split
% 150.98/21.92  | 
% 150.98/21.92  End of proof
% 150.98/21.92  
% 150.98/21.92  Sub-proof #26 shows that the following formulas are inconsistent:
% 150.98/21.92  ----------------------------------------------------------------
% 150.98/21.92    (1)   ~ (e2 = e0)
% 150.98/21.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.92    (3)  op(e1, e3) = e1
% 150.98/21.92    (4)   ~ (e3 = e0)
% 150.98/21.92    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 150.98/21.92         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 150.98/21.92    (6)  all_56_2 = e2
% 150.98/21.92    (7)  op(e0, e3) = all_52_3
% 150.98/21.92    (8)   ~ (e1 = e0)
% 150.98/21.92    (9)   ~ (all_52_3 = e0)
% 150.98/21.92    (10)  op(e3, e3) = e3
% 150.98/21.92    (11)  op(e1, e3) = all_52_2
% 150.98/21.92  
% 150.98/21.92  Begin of proof
% 150.98/21.92  | 
% 150.98/21.92  | BETA: splitting (5) gives:
% 150.98/21.92  | 
% 150.98/21.92  | Case 1:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 150.98/21.92  | |           e0)
% 150.98/21.92  | | 
% 150.98/21.92  | | REF_CLOSE: (1), (2), (4), (6), (10), (12) are inconsistent by sub-proof
% 150.98/21.92  | |            #725.
% 150.98/21.92  | | 
% 150.98/21.92  | Case 2:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (13)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 150.98/21.92  | |           e0)
% 150.98/21.92  | | 
% 150.98/21.92  | | REF_CLOSE: (2), (3), (7), (8), (9), (11), (13) are inconsistent by sub-proof
% 150.98/21.92  | |            #669.
% 150.98/21.92  | | 
% 150.98/21.92  | End of split
% 150.98/21.92  | 
% 150.98/21.92  End of proof
% 150.98/21.92  
% 150.98/21.92  Sub-proof #27 shows that the following formulas are inconsistent:
% 150.98/21.92  ----------------------------------------------------------------
% 150.98/21.92    (1)  op(e3, e3) = all_14_2
% 150.98/21.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.92    (3)   ~ (all_52_12 = all_14_2)
% 150.98/21.92    (4)  op(e0, e0) = e2
% 150.98/21.92    (5)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 150.98/21.92             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.98/21.92           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 150.98/21.92           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.98/21.92           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 150.98/21.92           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 150.98/21.92           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 150.98/21.92           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 150.98/21.92           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.98/21.92    (6)  op(e3, e0) = all_52_12
% 150.98/21.92    (7)  op(e3, e3) = e3
% 150.98/21.92    (8)   ~ (e2 = e1)
% 150.98/21.92  
% 150.98/21.92  Begin of proof
% 150.98/21.92  | 
% 150.98/21.92  | BETA: splitting (5) gives:
% 150.98/21.92  | 
% 150.98/21.92  | Case 1:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (9)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 150.98/21.92  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.98/21.92  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 150.98/21.92  | | 
% 150.98/21.92  | | ALPHA: (9) implies:
% 150.98/21.92  | |   (10)  op(e0, e0) = e1
% 150.98/21.92  | | 
% 150.98/21.92  | | REF_CLOSE: (2), (4), (8), (10) are inconsistent by sub-proof #978.
% 150.98/21.92  | | 
% 150.98/21.92  | Case 2:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (11)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.98/21.92  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.98/21.92  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.98/21.92  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 150.98/21.92  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 150.98/21.92  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.98/21.92  | |           $i(all_57_13))
% 150.98/21.92  | | 
% 150.98/21.92  | | REF_CLOSE: (1), (2), (3), (6), (7), (11) are inconsistent by sub-proof #58.
% 150.98/21.92  | | 
% 150.98/21.92  | End of split
% 150.98/21.92  | 
% 150.98/21.92  End of proof
% 150.98/21.92  
% 150.98/21.92  Sub-proof #28 shows that the following formulas are inconsistent:
% 150.98/21.92  ----------------------------------------------------------------
% 150.98/21.92    (1)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 150.98/21.92             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.98/21.92           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 150.98/21.92           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 150.98/21.92           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 150.98/21.92           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 150.98/21.92    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.92    (3)  op(e3, e2) = e2
% 150.98/21.92    (4)   ~ (e3 = e2)
% 150.98/21.92  
% 150.98/21.92  Begin of proof
% 150.98/21.92  | 
% 150.98/21.92  | BETA: splitting (1) gives:
% 150.98/21.92  | 
% 150.98/21.92  | Case 1:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (5)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 150.98/21.92  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.98/21.92  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 150.98/21.92  | | 
% 150.98/21.92  | | ALPHA: (5) implies:
% 150.98/21.92  | |   (6)  op(e3, e2) = e3
% 150.98/21.92  | | 
% 150.98/21.92  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #29.
% 150.98/21.92  | | 
% 150.98/21.92  | Case 2:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (7)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 150.98/21.92  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.98/21.92  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 150.98/21.92  | | 
% 150.98/21.92  | | ALPHA: (7) implies:
% 150.98/21.92  | |   (8)  op(e3, e2) = e3
% 150.98/21.92  | | 
% 150.98/21.92  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #29.
% 150.98/21.92  | | 
% 150.98/21.92  | End of split
% 150.98/21.92  | 
% 150.98/21.92  End of proof
% 150.98/21.92  
% 150.98/21.92  Sub-proof #29 shows that the following formulas are inconsistent:
% 150.98/21.92  ----------------------------------------------------------------
% 150.98/21.92    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.92    (2)  op(e3, e2) = e3
% 150.98/21.92    (3)  op(e3, e2) = e2
% 150.98/21.92    (4)   ~ (e3 = e2)
% 150.98/21.92  
% 150.98/21.92  Begin of proof
% 150.98/21.92  | 
% 150.98/21.92  | GROUND_INST: instantiating (1) with e2, e3, e2, e3, simplifying with (2), (3)
% 150.98/21.92  |              gives:
% 150.98/21.92  |   (5)  e3 = e2
% 150.98/21.92  | 
% 150.98/21.92  | REDUCE: (4), (5) imply:
% 150.98/21.92  |   (6)  $false
% 150.98/21.92  | 
% 150.98/21.92  | CLOSE: (6) is inconsistent.
% 150.98/21.92  | 
% 150.98/21.92  End of proof
% 150.98/21.92  
% 150.98/21.92  Sub-proof #30 shows that the following formulas are inconsistent:
% 150.98/21.92  ----------------------------------------------------------------
% 150.98/21.92    (1)  op(e0, e1) = all_52_11
% 150.98/21.92    (2)   ~ (all_52_9 = all_52_13)
% 150.98/21.92    (3)   ~ (e2 = e0)
% 150.98/21.92    (4)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 150.98/21.92           all_57_12 & $i(all_57_12))
% 150.98/21.92    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.92           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.92    (6)  op(e2, e0) = e2
% 150.98/21.92    (7)  op(e3, e3) = e2
% 150.98/21.92    (8)  all_57_15 = e0
% 150.98/21.92    (9)   ~ (all_52_11 = e0)
% 150.98/21.92    (10)  op(e2, e0) = all_52_13
% 150.98/21.92    (11)  op(e0, e2) = e2
% 150.98/21.92    (12)  op(e0, e3) = all_52_3
% 150.98/21.92    (13)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 150.98/21.92              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.98/21.92            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 150.98/21.92            = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.98/21.92            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 150.98/21.92            op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.98/21.92            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2)
% 150.98/21.92            = all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0) =
% 150.98/21.92            e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &
% 150.98/21.92             ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 150.98/21.92            op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.98/21.92            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 150.98/21.92            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.98/21.92            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.98/21.92            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~
% 150.98/21.92            (all_57_9 = e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.98/21.92            all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.98/21.92            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 150.98/21.92            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.98/21.92            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 150.98/21.92            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.98/21.92              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 150.98/21.92            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.98/21.92            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.98/21.92              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 150.98/21.92            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.98/21.92            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 150.98/21.92                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.98/21.92                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.98/21.92                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.98/21.92                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.98/21.92                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 150.98/21.92                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 150.98/21.92                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.98/21.92              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 150.98/21.92                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 150.98/21.92                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.98/21.92                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.98/21.92                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 150.98/21.92                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.98/21.92                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.98/21.92                $i(all_57_7))))
% 150.98/21.92    (14)  op(e2, e1) = all_52_9
% 150.98/21.92    (15)   ~ (e1 = e0)
% 150.98/21.92    (16)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 150.98/21.92            all_57_14 & $i(all_57_14))
% 150.98/21.92    (17)   ~ (all_52_3 = e0)
% 150.98/21.92    (18)  op(e0, e0) = e0
% 150.98/21.92  
% 150.98/21.92  Begin of proof
% 150.98/21.92  | 
% 150.98/21.92  | BETA: splitting (13) gives:
% 150.98/21.92  | 
% 150.98/21.92  | Case 1:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (19)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 150.98/21.92  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.98/21.92  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 150.98/21.92  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 150.98/21.92  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 150.98/21.92  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 150.98/21.92  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 150.98/21.92  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.98/21.92  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.98/21.92  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.98/21.92  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.98/21.92  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.98/21.92  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 150.98/21.92  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 150.98/21.92  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.98/21.92  | |           $i(all_57_13))
% 150.98/21.92  | | 
% 150.98/21.92  | | REF_CLOSE: (2), (4), (5), (6), (10), (14), (15), (16), (18), (19) are
% 150.98/21.92  | |            inconsistent by sub-proof #32.
% 150.98/21.92  | | 
% 150.98/21.92  | Case 2:
% 150.98/21.92  | | 
% 150.98/21.92  | |   (20)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.98/21.92  | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.98/21.92  | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.98/21.92  | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 150.98/21.92  | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.98/21.92  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 150.98/21.92  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 150.98/21.92  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 150.98/21.92  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.98/21.92  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 150.98/21.92  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.98/21.92  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 150.98/21.92  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.98/21.92  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.98/21.92  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 150.98/21.92  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 150.98/21.92  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.98/21.92  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.98/21.92  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.98/21.92  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.98/21.92  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 150.98/21.92  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 150.98/21.92  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.98/21.92  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.98/21.92  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.98/21.92  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.98/21.92  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.98/21.92  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.98/21.92  | |               $i(all_57_7))))
% 150.98/21.92  | | 
% 150.98/21.92  | | BETA: splitting (20) gives:
% 150.98/21.92  | | 
% 150.98/21.92  | | Case 1:
% 150.98/21.92  | | | 
% 150.98/21.92  | | |   (21)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.98/21.92  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.98/21.92  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.98/21.92  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.98/21.92  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.98/21.92  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.98/21.92  | | |           $i(all_57_9) & $i(all_57_14))
% 150.98/21.92  | | | 
% 150.98/21.92  | | | REF_CLOSE: (3), (5), (7), (21) are inconsistent by sub-proof #1037.
% 150.98/21.92  | | | 
% 150.98/21.92  | | Case 2:
% 150.98/21.92  | | | 
% 150.98/21.92  | | |   (22)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 150.98/21.92  | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.98/21.92  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.98/21.92  | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 150.98/21.92  | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.98/21.92  | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.98/21.92  | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.98/21.92  | | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 150.98/21.92  | | |                 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 150.98/21.92  | | |               op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 150.98/21.92  | | |             (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.98/21.92  | | |               (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.98/21.92  | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 150.98/21.92  | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3)
% 150.98/21.92  | | |               = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.98/21.92  | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 150.98/21.92  | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.98/21.92  | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4))
% 150.98/21.92  | | |             | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.98/21.92  | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 150.98/21.92  | | |               op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 150.98/21.92  | | |               = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2)
% 150.98/21.92  | | |               = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.98/21.92  | | |               $i(all_57_7))))
% 150.98/21.92  | | | 
% 150.98/21.92  | | | BETA: splitting (22) gives:
% 150.98/21.92  | | | 
% 150.98/21.92  | | | Case 1:
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | |   (23)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 150.98/21.92  | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.98/21.92  | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.98/21.92  | | | |         $i(all_57_13)
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | | ALPHA: (23) implies:
% 150.98/21.92  | | | |   (24)   ~ (all_57_13 = e1)
% 150.98/21.92  | | | |   (25)  op(e1, e1) = e0
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | | REF_CLOSE: (5), (16), (24), (25) are inconsistent by sub-proof #959.
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | Case 2:
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | |   (26)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.98/21.92  | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.98/21.92  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.98/21.92  | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.98/21.92  | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.98/21.92  | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 150.98/21.92  | | | |               & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 150.98/21.92  | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.98/21.92  | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 150.98/21.92  | | | |               e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.98/21.92  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.98/21.92  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.98/21.92  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.92  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 150.98/21.92  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.98/21.92  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 150.98/21.92  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 150.98/21.92  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.98/21.92  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.98/21.92  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | | BETA: splitting (26) gives:
% 150.98/21.92  | | | | 
% 150.98/21.92  | | | | Case 1:
% 150.98/21.92  | | | | | 
% 150.98/21.93  | | | | |   (27)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.98/21.93  | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.98/21.93  | | | | |         op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.98/21.93  | | | | |         $i(all_57_14)
% 150.98/21.93  | | | | | 
% 150.98/21.93  | | | | | ALPHA: (27) implies:
% 150.98/21.93  | | | | |   (28)  all_57_12 = e0
% 150.98/21.93  | | | | |   (29)   ~ (all_57_11 = e2)
% 150.98/21.93  | | | | | 
% 150.98/21.93  | | | | | REF_CLOSE: (4), (28), (29) are inconsistent by sub-proof #890.
% 150.98/21.93  | | | | | 
% 150.98/21.93  | | | | Case 2:
% 150.98/21.93  | | | | | 
% 150.98/21.93  | | | | |   (30)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.98/21.93  | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3)
% 150.98/21.93  | | | | |             & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 150.98/21.93  | | | | |             e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 150.98/21.93  | | | | |             (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.98/21.93  | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.98/21.93  | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.98/21.93  | | | | |             (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.98/21.93  | | | | |             op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.98/21.93  | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.93  | | | | |             (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 150.98/21.93  | | | | |             & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.98/21.93  | | | | |             all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 150.98/21.93  | | | | |             & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 150.98/21.93  | | | | |             e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.98/21.93  | | | | |             (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.98/21.93  | | | | |             op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7)))
% 150.98/21.93  | | | | | 
% 150.98/21.93  | | | | | ALPHA: (30) implies:
% 150.98/21.93  | | | | |   (31)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.98/21.93  | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.98/21.93  | | | | |           op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.98/21.93  | | | | |           = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3)
% 150.98/21.93  | | | | |           = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.98/21.93  | | | | |           $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.98/21.93  | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.98/21.93  | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.98/21.93  | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.93  | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.98/21.93  | | | | |           op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 150.98/21.93  | | | | |           = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 150.98/21.93  | | | | |           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.98/21.93  | | | | |           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.98/21.93  | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.98/21.93  | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.98/21.93  | | | | | 
% 150.98/21.93  | | | | | BETA: splitting (31) gives:
% 150.98/21.93  | | | | | 
% 150.98/21.93  | | | | | Case 1:
% 150.98/21.93  | | | | | | 
% 150.98/21.93  | | | | | |   (32)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.98/21.93  | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 150.98/21.93  | | | | | |           & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 150.98/21.93  | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.98/21.93  | | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 150.98/21.93  | | | | | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.98/21.93  | | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.98/21.93  | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 150.98/21.93  | | | | | | 
% 150.98/21.93  | | | | | | BETA: splitting (32) gives:
% 150.98/21.93  | | | | | | 
% 150.98/21.93  | | | | | | Case 1:
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | |   (33)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.98/21.93  | | | | | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 150.98/21.93  | | | | | | |         & op(e0, e3) = e0 & $i(all_57_0)
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | | ALPHA: (33) implies:
% 150.98/21.93  | | | | | | |   (34)  op(e0, e3) = e0
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | | REF_CLOSE: (5), (12), (17), (34) are inconsistent by sub-proof
% 150.98/21.93  | | | | | | |            #1142.
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | Case 2:
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | |   (35)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.98/21.93  | | | | | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.98/21.93  | | | | | | |           e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 150.98/21.93  | | | | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 150.98/21.93  | | | | | | |             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 150.98/21.93  | | | | | | |             e2) = e0 & $i(all_57_3))
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | | BETA: splitting (35) gives:
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | | Case 1:
% 150.98/21.93  | | | | | | | | 
% 150.98/21.93  | | | | | | | |   (36)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.98/21.93  | | | | | | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.98/21.93  | | | | | | | |         e3 & op(e0, e3) = e0 & $i(all_57_1)
% 150.98/21.93  | | | | | | | | 
% 150.98/21.93  | | | | | | | | ALPHA: (36) implies:
% 150.98/21.93  | | | | | | | |   (37)  op(e0, e3) = e0
% 150.98/21.93  | | | | | | | | 
% 150.98/21.93  | | | | | | | | REF_CLOSE: (5), (12), (17), (37) are inconsistent by sub-proof
% 150.98/21.93  | | | | | | | |            #1142.
% 150.98/21.93  | | | | | | | | 
% 150.98/21.93  | | | | | | | Case 2:
% 150.98/21.93  | | | | | | | | 
% 150.98/21.93  | | | | | | | |   (38)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.98/21.93  | | | | | | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.98/21.93  | | | | | | | |         all_57_3 & op(e0, e2) = e0 & $i(all_57_3)
% 150.98/21.93  | | | | | | | | 
% 150.98/21.93  | | | | | | | | ALPHA: (38) implies:
% 150.98/21.93  | | | | | | | |   (39)   ~ (all_57_15 = e2)
% 150.98/21.93  | | | | | | | |   (40)  op(e0, e2) = e0
% 150.98/21.93  | | | | | | | | 
% 150.98/21.93  | | | | | | | | REDUCE: (8), (39) imply:
% 150.98/21.93  | | | | | | | |   (41)   ~ (e2 = e0)
% 150.98/21.93  | | | | | | | | 
% 150.98/21.93  | | | | | | | | GROUND_INST: instantiating (5) with e2, e0, e2, e0, simplifying
% 150.98/21.93  | | | | | | | |              with (11), (40) gives:
% 150.98/21.93  | | | | | | | |   (42)  e2 = e0
% 150.98/21.93  | | | | | | | | 
% 150.98/21.93  | | | | | | | | REDUCE: (3), (42) imply:
% 150.98/21.93  | | | | | | | |   (43)  $false
% 150.98/21.93  | | | | | | | | 
% 150.98/21.93  | | | | | | | | CLOSE: (43) is inconsistent.
% 150.98/21.93  | | | | | | | | 
% 150.98/21.93  | | | | | | | End of split
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | End of split
% 150.98/21.93  | | | | | | 
% 150.98/21.93  | | | | | Case 2:
% 150.98/21.93  | | | | | | 
% 150.98/21.93  | | | | | |   (44)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.93  | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 150.98/21.93  | | | | | |           & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.98/21.93  | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 150.98/21.93  | | | | | |           & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 150.98/21.93  | | | | | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.98/21.93  | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.98/21.93  | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.98/21.93  | | | | | | 
% 150.98/21.93  | | | | | | BETA: splitting (44) gives:
% 150.98/21.93  | | | | | | 
% 150.98/21.93  | | | | | | Case 1:
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | |   (45)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.93  | | | | | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 150.98/21.93  | | | | | | |         & op(e0, e2) = e0 & $i(all_57_4)
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | | ALPHA: (45) implies:
% 150.98/21.93  | | | | | | |   (46)  op(e0, e2) = e0
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | | REF_CLOSE: (3), (5), (11), (46) are inconsistent by sub-proof #31.
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | Case 2:
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | |   (47)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.98/21.93  | | | | | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.98/21.93  | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 150.98/21.93  | | | | | | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15
% 150.98/21.93  | | | | | | |             = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.98/21.93  | | | | | | |           op(e0, e1) = e0 & $i(all_57_7))
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | | REF_CLOSE: (1), (5), (9), (47) are inconsistent by sub-proof #851.
% 150.98/21.93  | | | | | | | 
% 150.98/21.93  | | | | | | End of split
% 150.98/21.93  | | | | | | 
% 150.98/21.93  | | | | | End of split
% 150.98/21.93  | | | | | 
% 150.98/21.93  | | | | End of split
% 150.98/21.93  | | | | 
% 150.98/21.93  | | | End of split
% 150.98/21.93  | | | 
% 150.98/21.93  | | End of split
% 150.98/21.93  | | 
% 150.98/21.93  | End of split
% 150.98/21.93  | 
% 150.98/21.93  End of proof
% 150.98/21.93  
% 150.98/21.93  Sub-proof #31 shows that the following formulas are inconsistent:
% 150.98/21.93  ----------------------------------------------------------------
% 150.98/21.93    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.93    (2)  op(e0, e2) = e2
% 150.98/21.93    (3)  op(e0, e2) = e0
% 150.98/21.93    (4)   ~ (e2 = e0)
% 150.98/21.93  
% 150.98/21.93  Begin of proof
% 150.98/21.93  | 
% 150.98/21.93  | GROUND_INST: instantiating (1) with e2, e0, e2, e0, simplifying with (2), (3)
% 150.98/21.93  |              gives:
% 150.98/21.93  |   (5)  e2 = e0
% 150.98/21.93  | 
% 150.98/21.93  | REDUCE: (4), (5) imply:
% 150.98/21.93  |   (6)  $false
% 150.98/21.93  | 
% 150.98/21.93  | CLOSE: (6) is inconsistent.
% 150.98/21.93  | 
% 150.98/21.93  End of proof
% 150.98/21.93  
% 150.98/21.93  Sub-proof #32 shows that the following formulas are inconsistent:
% 150.98/21.93  ----------------------------------------------------------------
% 150.98/21.93    (1)   ~ (all_52_9 = all_52_13)
% 150.98/21.93    (2)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 150.98/21.93           all_57_12 & $i(all_57_12))
% 150.98/21.93    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.93    (4)  op(e2, e0) = e2
% 150.98/21.93    (5)  op(e2, e0) = all_52_13
% 150.98/21.93    (6)  op(e2, e1) = all_52_9
% 150.98/21.93    (7)   ~ (e1 = e0)
% 150.98/21.93    (8)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 150.98/21.93           all_57_14 & $i(all_57_14))
% 150.98/21.93    (9)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 150.98/21.93             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.98/21.93           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 150.98/21.93           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 150.98/21.93           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 150.98/21.93           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 150.98/21.93           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2)
% 150.98/21.93           = all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1
% 150.98/21.93           & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 150.98/21.93           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 150.98/21.93           op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 150.98/21.93           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 150.98/21.93           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 150.98/21.93           op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.98/21.93           $i(all_57_10) & $i(all_57_13))
% 150.98/21.93    (10)  op(e0, e0) = e0
% 150.98/21.93  
% 150.98/21.93  Begin of proof
% 150.98/21.93  | 
% 150.98/21.93  | BETA: splitting (9) gives:
% 150.98/21.93  | 
% 150.98/21.93  | Case 1:
% 150.98/21.93  | | 
% 150.98/21.93  | |   (11)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 150.98/21.93  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.98/21.93  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 150.98/21.93  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 150.98/21.93  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 150.98/21.93  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 150.98/21.93  | | 
% 150.98/21.93  | | BETA: splitting (11) gives:
% 150.98/21.93  | | 
% 150.98/21.93  | | Case 1:
% 150.98/21.93  | | | 
% 150.98/21.93  | | |   (12)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.98/21.93  | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.98/21.93  | | |         op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.98/21.93  | | |         $i(all_57_10)
% 150.98/21.93  | | | 
% 150.98/21.93  | | | ALPHA: (12) implies:
% 150.98/21.93  | | |   (13)  op(e0, e0) = e1
% 150.98/21.93  | | | 
% 150.98/21.93  | | | REF_CLOSE: (3), (7), (10), (13) are inconsistent by sub-proof #1040.
% 150.98/21.93  | | | 
% 150.98/21.93  | | Case 2:
% 150.98/21.93  | | | 
% 150.98/21.93  | | |   (14)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 150.98/21.93  | | |         (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 150.98/21.93  | | |         op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 150.98/21.93  | | |         $i(all_57_12)
% 150.98/21.93  | | | 
% 150.98/21.93  | | | ALPHA: (14) implies:
% 150.98/21.93  | | |   (15)  op(e2, e1) = e2
% 150.98/21.93  | | | 
% 150.98/21.93  | | | REF_CLOSE: (1), (3), (4), (5), (6), (15) are inconsistent by sub-proof
% 150.98/21.93  | | |            #400.
% 150.98/21.93  | | | 
% 150.98/21.93  | | End of split
% 150.98/21.93  | | 
% 150.98/21.93  | Case 2:
% 150.98/21.93  | | 
% 150.98/21.93  | |   (16)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 150.98/21.93  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.98/21.93  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.98/21.93  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.98/21.93  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.98/21.93  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.98/21.93  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 150.98/21.93  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 150.98/21.93  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.98/21.93  | |           $i(all_57_13))
% 150.98/21.93  | | 
% 150.98/21.93  | | REF_CLOSE: (2), (3), (7), (8), (10), (16) are inconsistent by sub-proof #69.
% 150.98/21.93  | | 
% 150.98/21.93  | End of split
% 150.98/21.93  | 
% 150.98/21.93  End of proof
% 150.98/21.93  
% 150.98/21.93  Sub-proof #33 shows that the following formulas are inconsistent:
% 150.98/21.93  ----------------------------------------------------------------
% 150.98/21.93    (1)   ~ (e3 = e1)
% 150.98/21.93    (2)  all_56_11 = e3
% 150.98/21.93    (3)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 150.98/21.93    (4)  op(e1, e1) = e2
% 150.98/21.93    (5)  op(e1, e1) = all_4_2
% 150.98/21.93    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.93    (7)   ~ (e2 = e1)
% 150.98/21.93  
% 150.98/21.93  Begin of proof
% 150.98/21.93  | 
% 150.98/21.93  | BETA: splitting (3) gives:
% 150.98/21.93  | 
% 150.98/21.93  | Case 1:
% 150.98/21.93  | | 
% 150.98/21.93  | |   (8)  all_56_8 = e1 & op(e1, e1) = e1
% 150.98/21.93  | | 
% 150.98/21.93  | | ALPHA: (8) implies:
% 150.98/21.93  | |   (9)  op(e1, e1) = e1
% 150.98/21.93  | | 
% 150.98/21.93  | | REF_CLOSE: (4), (5), (6), (7), (9) are inconsistent by sub-proof #1044.
% 150.98/21.93  | | 
% 150.98/21.93  | Case 2:
% 150.98/21.93  | | 
% 150.98/21.93  | |   (10)  all_56_11 = e1 & op(e1, e0) = e1
% 150.98/21.93  | | 
% 150.98/21.93  | | ALPHA: (10) implies:
% 150.98/21.93  | |   (11)  all_56_11 = e1
% 150.98/21.93  | | 
% 150.98/21.93  | | REF_CLOSE: (1), (2), (11) are inconsistent by sub-proof #490.
% 150.98/21.93  | | 
% 150.98/21.93  | End of split
% 150.98/21.93  | 
% 150.98/21.93  End of proof
% 150.98/21.93  
% 150.98/21.93  Sub-proof #34 shows that the following formulas are inconsistent:
% 150.98/21.93  ----------------------------------------------------------------
% 150.98/21.93    (1)  all_56_13 = e2
% 150.98/21.93    (2)   ~ (e3 = e1)
% 150.98/21.93    (3)   ~ (e2 = e0)
% 150.98/21.93    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.93    (5)  op(e3, e3) = e2
% 150.98/21.93    (6)   ~ (e3 = e0)
% 150.98/21.93    (7)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 150.98/21.93             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.98/21.93           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 150.98/21.93               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 150.98/21.93             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.98/21.93         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 150.98/21.93             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.98/21.93           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 150.98/21.93               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 150.98/21.93             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 150.98/21.93    (8)   ~ (e1 = e0)
% 150.98/21.93    (9)   ~ (e3 = e2)
% 150.98/21.93    (10)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 150.98/21.93          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 150.98/21.93    (11)   ~ (e2 = e1)
% 150.98/21.93    (12)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 150.98/21.93          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 150.98/21.93    (13)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 150.98/21.93          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 150.98/21.93  
% 150.98/21.93  Begin of proof
% 150.98/21.93  | 
% 150.98/21.93  | BETA: splitting (7) gives:
% 150.98/21.93  | 
% 150.98/21.93  | Case 1:
% 150.98/21.93  | | 
% 150.98/21.93  | |   (14)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 150.98/21.93  | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 150.98/21.93  | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.98/21.93  | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.98/21.93  | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.98/21.93  | |               e0) = all_57_15 & $i(all_57_15)))
% 150.98/21.93  | | 
% 150.98/21.93  | | ALPHA: (14) implies:
% 150.98/21.93  | |   (15)  op(e3, e3) = e3
% 150.98/21.93  | | 
% 150.98/21.93  | | REF_CLOSE: (4), (5), (9), (15) are inconsistent by sub-proof #1085.
% 150.98/21.93  | | 
% 150.98/21.93  | Case 2:
% 150.98/21.93  | | 
% 150.98/21.93  | |   (16)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 150.98/21.93  | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.98/21.93  | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.98/21.93  | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.98/21.93  | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.98/21.93  | |               e0) = all_57_15 & $i(all_57_15)))
% 150.98/21.93  | | 
% 150.98/21.93  | | ALPHA: (16) implies:
% 150.98/21.93  | |   (17)  op(e2, e2) = e2
% 150.98/21.93  | | 
% 150.98/21.93  | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (11), (12), (13), (17)
% 150.98/21.93  | |            are inconsistent by sub-proof #1104.
% 150.98/21.93  | | 
% 150.98/21.93  | End of split
% 150.98/21.93  | 
% 150.98/21.93  End of proof
% 150.98/21.93  
% 150.98/21.93  Sub-proof #35 shows that the following formulas are inconsistent:
% 150.98/21.93  ----------------------------------------------------------------
% 150.98/21.93    (1)  all_56_13 = e2
% 150.98/21.93    (2)   ~ (e3 = e1)
% 150.98/21.93    (3)   ~ (e2 = e0)
% 150.98/21.93    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.93    (5)   ~ (e3 = e0)
% 150.98/21.93    (6)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 150.98/21.93    (7)   ~ (e1 = e0)
% 150.98/21.93    (8)   ~ (e3 = e2)
% 150.98/21.93    (9)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 150.98/21.93         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 150.98/21.93    (10)   ~ (e2 = e1)
% 150.98/21.93    (11)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 150.98/21.93          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 150.98/21.93    (12)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 150.98/21.93          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 150.98/21.93    (13)  op(e2, e3) = all_52_1
% 150.98/21.93    (14)   ~ (all_52_1 = e2)
% 150.98/21.93  
% 150.98/21.93  Begin of proof
% 150.98/21.93  | 
% 150.98/21.93  | BETA: splitting (6) gives:
% 150.98/21.93  | 
% 150.98/21.93  | Case 1:
% 150.98/21.93  | | 
% 150.98/21.93  | |   (15)  all_56_2 = e2 & op(e2, e3) = e2
% 150.98/21.93  | | 
% 150.98/21.93  | | ALPHA: (15) implies:
% 150.98/21.93  | |   (16)  op(e2, e3) = e2
% 150.98/21.93  | | 
% 150.98/21.93  | | REF_CLOSE: (4), (13), (14), (16) are inconsistent by sub-proof #1181.
% 150.98/21.93  | | 
% 150.98/21.93  | Case 2:
% 150.98/21.93  | | 
% 150.98/21.93  | |   (17)  all_56_3 = e2 & op(e2, e2) = e2
% 150.98/21.93  | | 
% 150.98/21.93  | | ALPHA: (17) implies:
% 150.98/21.93  | |   (18)  op(e2, e2) = e2
% 150.98/21.93  | | 
% 150.98/21.93  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (18)
% 150.98/21.93  | |            are inconsistent by sub-proof #1104.
% 150.98/21.93  | | 
% 150.98/21.93  | End of split
% 150.98/21.93  | 
% 150.98/21.93  End of proof
% 150.98/21.93  
% 150.98/21.93  Sub-proof #36 shows that the following formulas are inconsistent:
% 150.98/21.93  ----------------------------------------------------------------
% 150.98/21.93    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 150.98/21.93         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 150.98/21.93    (2)   ~ (e3 = e1)
% 150.98/21.93    (3)  op(e0, e0) = all_10_2
% 150.98/21.93    (4)  op(e1, e1) = e2
% 150.98/21.93    (5)   ~ (e2 = e0)
% 150.98/21.93    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.93    (7)  op(e0, e0) = e3
% 150.98/21.93    (8)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 150.98/21.93             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 150.98/21.93               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 150.98/21.93               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 150.98/21.93    (9)   ~ (e3 = e0)
% 150.98/21.93    (10)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 150.98/21.93          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 150.98/21.93    (11)  op(e2, e0) = all_52_13
% 150.98/21.93    (12)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 150.98/21.93    (13)   ~ (e1 = e0)
% 150.98/21.93    (14)   ~ (e3 = e2)
% 150.98/21.93    (15)   ~ (all_10_2 = e2)
% 150.98/21.93    (16)   ~ (e2 = e1)
% 150.98/21.93  
% 150.98/21.93  Begin of proof
% 150.98/21.93  | 
% 150.98/21.93  | BETA: splitting (12) gives:
% 150.98/21.93  | 
% 150.98/21.93  | Case 1:
% 150.98/21.93  | | 
% 150.98/21.93  | |   (17)  all_56_8 = e3 & op(e1, e1) = e3
% 150.98/21.93  | | 
% 150.98/21.93  | | ALPHA: (17) implies:
% 150.98/21.93  | |   (18)  op(e1, e1) = e3
% 150.98/21.93  | | 
% 150.98/21.93  | | REF_CLOSE: (4), (6), (14), (18) are inconsistent by sub-proof #834.
% 150.98/21.93  | | 
% 150.98/21.93  | Case 2:
% 150.98/21.93  | | 
% 150.98/21.93  | |   (19)  all_56_11 = e3 & op(e1, e0) = e3
% 150.98/21.93  | | 
% 150.98/21.93  | | ALPHA: (19) implies:
% 150.98/21.93  | |   (20)  all_56_11 = e3
% 150.98/21.93  | | 
% 150.98/21.93  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 150.98/21.93  | |            (15), (16), (20) are inconsistent by sub-proof #771.
% 150.98/21.93  | | 
% 150.98/21.93  | End of split
% 150.98/21.93  | 
% 150.98/21.93  End of proof
% 150.98/21.93  
% 150.98/21.93  Sub-proof #37 shows that the following formulas are inconsistent:
% 150.98/21.93  ----------------------------------------------------------------
% 150.98/21.93    (1)  op(e0, e1) = all_52_11
% 150.98/21.93    (2)   ~ (e3 = e1)
% 150.98/21.93    (3)   ~ (all_52_11 = all_10_2)
% 150.98/21.93    (4)  op(e2, e2) = e1
% 150.98/21.93    (5)  op(e0, e0) = all_10_2
% 150.98/21.93    (6)  op(e3, e2) = all_52_4
% 150.98/21.93    (7)  op(e1, e1) = e2
% 150.98/21.93    (8)  op(e0, e2) = all_52_7
% 150.98/21.93    (9)   ~ (all_10_2 = e1)
% 150.98/21.93    (10)   ~ (e2 = e0)
% 150.98/21.93    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.93            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.93    (12)   ~ (all_52_4 = e3)
% 150.98/21.93    (13)   ~ (all_10_2 = e3)
% 150.98/21.93    (14)  op(e3, e0) = all_52_12
% 150.98/21.93    (15)   ~ (e3 = e0)
% 150.98/21.93    (16)   ~ (all_52_12 = e3)
% 150.98/21.93    (17)   ~ (all_52_9 = e2)
% 150.98/21.93    (18)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 150.98/21.93    (19)  op(e0, e3) = all_52_3
% 150.98/21.93    (20)  op(e2, e1) = all_52_9
% 150.98/21.93    (21)   ~ (e1 = e0)
% 150.98/21.93    (22)   ~ (e3 = e2)
% 150.98/21.93    (23)   ~ (all_52_8 = e3)
% 150.98/21.93    (24)   ~ (all_52_7 = all_10_2)
% 150.98/21.93    (25)   ~ (all_10_2 = e2)
% 150.98/21.93    (26)  op(e3, e1) = all_52_8
% 150.98/21.93    (27)   ~ (all_52_3 = all_10_2)
% 150.98/21.93    (28)  op(e3, e3) = e3
% 150.98/21.93    (29)  all_54_15 = all_10_2
% 150.98/21.94    (30)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 150.98/21.94              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 150.98/21.94            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 150.98/21.94            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 150.98/21.94            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.98/21.94            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 150.98/21.94            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 150.98/21.94            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.98/21.94            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 150.98/21.94            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.98/21.94            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.98/21.94            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 150.98/21.94            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.98/21.94            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.98/21.94            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 150.98/21.94            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.98/21.94            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.98/21.94            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 150.98/21.94            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.98/21.94            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 150.98/21.94            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 150.98/21.94            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.98/21.94            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.98/21.94            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 150.98/21.94            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.98/21.94            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.98/21.94            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 150.98/21.94            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.98/21.94            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.98/21.94            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 150.98/21.94            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 150.98/21.94            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 150.98/21.94            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 150.98/21.94            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.98/21.94            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.98/21.94            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 150.98/21.94            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.98/21.94            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.98/21.94            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 150.98/21.94            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.98/21.94            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.98/21.94            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 150.98/21.94            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.98/21.94            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.98/21.94            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 150.98/21.94            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.98/21.94            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 150.98/21.94            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.98/21.94              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 150.98/21.94            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.98/21.94            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.98/21.94              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 150.98/21.94            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.98/21.94            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 150.98/21.94                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.98/21.94                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.98/21.94                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.98/21.94                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.98/21.94                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 150.98/21.94                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 150.98/21.94                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.98/21.94              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 150.98/21.94                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 150.98/21.94                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.98/21.94                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.98/21.94                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 150.98/21.94                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.98/21.94                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.98/21.94                $i(all_57_7))))
% 150.98/21.94  
% 150.98/21.94  Begin of proof
% 150.98/21.94  | 
% 150.98/21.94  | BETA: splitting (30) gives:
% 150.98/21.94  | 
% 150.98/21.94  | Case 1:
% 150.98/21.94  | | 
% 150.98/21.94  | |   (31)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 150.98/21.94  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 150.98/21.94  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 150.98/21.94  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 150.98/21.94  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 150.98/21.94  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 150.98/21.94  | |         (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 150.98/21.94  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 150.98/21.94  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 150.98/21.94  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 150.98/21.94  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 150.98/21.94  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) |
% 150.98/21.94  | |         (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 150.98/21.94  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 150.98/21.94  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 150.98/21.94  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 150.98/21.94  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.98/21.94  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 150.98/21.94  | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 150.98/21.94  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 150.98/21.94  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 150.98/21.94  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 150.98/21.94  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 150.98/21.94  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 150.98/21.94  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 150.98/21.94  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 150.98/21.94  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.98/21.94  | | 
% 150.98/21.94  | | BETA: splitting (31) gives:
% 150.98/21.94  | | 
% 150.98/21.94  | | Case 1:
% 150.98/21.94  | | | 
% 150.98/21.94  | | |   (32)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.98/21.94  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.98/21.94  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 150.98/21.94  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 150.98/21.94  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 150.98/21.94  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.98/21.94  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 150.98/21.94  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 150.98/21.94  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.98/21.94  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 150.98/21.94  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 150.98/21.94  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 150.98/21.94  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 150.98/21.94  | | | 
% 150.98/21.94  | | | BETA: splitting (32) gives:
% 150.98/21.94  | | | 
% 150.98/21.94  | | | Case 1:
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | |   (33)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.98/21.94  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 150.98/21.94  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 150.98/21.94  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 150.98/21.94  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.98/21.94  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 150.98/21.94  | | | |           e3 & $i(all_57_2) & $i(all_57_12))
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | | REF_CLOSE: (5), (7), (9), (11), (13), (18), (22), (25), (29), (33) are
% 150.98/21.94  | | | |            inconsistent by sub-proof #39.
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | Case 2:
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | |   (34)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.98/21.94  | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.98/21.94  | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.98/21.94  | | | |           $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 150.98/21.94  | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.98/21.94  | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 150.98/21.94  | | | |           e3 & $i(all_57_2) & $i(all_57_14))
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | | BETA: splitting (34) gives:
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | | Case 1:
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | |   (35)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.98/21.94  | | | | |         (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 150.98/21.94  | | | | |         op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 150.98/21.94  | | | | |         $i(all_57_14)
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | | ALPHA: (35) implies:
% 150.98/21.94  | | | | |   (36)  op(e2, e2) = e3
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | | REF_CLOSE: (2), (4), (11), (36) are inconsistent by sub-proof #1136.
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | Case 2:
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | |   (37)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 150.98/21.94  | | | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 150.98/21.94  | | | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 150.98/21.94  | | | | |         $i(all_57_14)
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | | ALPHA: (37) implies:
% 150.98/21.94  | | | | |   (38)  op(e0, e0) = e3
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | | REF_CLOSE: (5), (9), (11), (13), (18), (25), (29), (38) are
% 150.98/21.94  | | | | |            inconsistent by sub-proof #702.
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | End of split
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | End of split
% 150.98/21.94  | | | 
% 150.98/21.94  | | Case 2:
% 150.98/21.94  | | | 
% 150.98/21.94  | | |   (39)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.94  | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.98/21.94  | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.98/21.94  | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5
% 150.98/21.94  | | |             = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 150.98/21.94  | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.98/21.94  | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 150.98/21.94  | | |           &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 150.98/21.94  | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 150.98/21.94  | | |           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 =
% 150.98/21.94  | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 150.98/21.94  | | |           & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 150.98/21.94  | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 150.98/21.94  | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.98/21.94  | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 150.98/21.94  | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.98/21.94  | | | 
% 150.98/21.94  | | | BETA: splitting (39) gives:
% 150.98/21.94  | | | 
% 150.98/21.94  | | | Case 1:
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | |   (40)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.94  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.98/21.94  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 150.98/21.94  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 150.98/21.94  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 150.98/21.94  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.98/21.94  | | | |           $i(all_57_5) & $i(all_57_10))
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | | REF_CLOSE: (6), (11), (12), (40) are inconsistent by sub-proof #863.
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | Case 2:
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | |   (41)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.98/21.94  | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 150.98/21.94  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 150.98/21.94  | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 150.98/21.94  | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.98/21.94  | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 150.98/21.94  | | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.98/21.94  | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 150.98/21.94  | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.98/21.94  | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | | REF_CLOSE: (5), (11), (22), (23), (25), (26), (28), (41) are
% 150.98/21.94  | | | |            inconsistent by sub-proof #861.
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | End of split
% 150.98/21.94  | | | 
% 150.98/21.94  | | End of split
% 150.98/21.94  | | 
% 150.98/21.94  | Case 2:
% 150.98/21.94  | | 
% 150.98/21.94  | |   (42)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 150.98/21.94  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 150.98/21.94  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 150.98/21.94  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 150.98/21.94  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 150.98/21.94  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 150.98/21.94  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 150.98/21.94  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 150.98/21.94  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 150.98/21.94  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.98/21.94  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.98/21.94  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.98/21.94  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 150.98/21.94  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 150.98/21.94  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.98/21.94  | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 150.98/21.94  | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.98/21.94  | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 150.98/21.94  | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.98/21.94  | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.98/21.94  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 150.98/21.94  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 150.98/21.94  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 150.98/21.94  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 150.98/21.94  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 150.98/21.94  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.98/21.94  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 150.98/21.94  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 150.98/21.94  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 150.98/21.94  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 150.98/21.94  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 150.98/21.94  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 150.98/21.94  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.98/21.94  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 150.98/21.94  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.98/21.94  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 150.98/21.94  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 150.98/21.94  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.98/21.94  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 150.98/21.94  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.98/21.94  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 150.98/21.94  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.98/21.94  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.98/21.94  | |               $i(all_57_7))))
% 150.98/21.94  | | 
% 150.98/21.94  | | BETA: splitting (42) gives:
% 150.98/21.94  | | 
% 150.98/21.94  | | Case 1:
% 150.98/21.94  | | | 
% 150.98/21.94  | | |   (43)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.98/21.94  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.98/21.94  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.98/21.94  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 150.98/21.94  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 150.98/21.94  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.98/21.94  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 150.98/21.94  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 150.98/21.94  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 150.98/21.94  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 150.98/21.94  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 150.98/21.94  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.98/21.94  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 150.98/21.94  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 150.98/21.94  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.98/21.94  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.98/21.94  | | |           $i(all_57_13))
% 150.98/21.94  | | | 
% 150.98/21.94  | | | BETA: splitting (43) gives:
% 150.98/21.94  | | | 
% 150.98/21.94  | | | Case 1:
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | |   (44)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.98/21.94  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.98/21.94  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.98/21.94  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 150.98/21.94  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 150.98/21.94  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 150.98/21.94  | | | |           e2 & $i(all_57_6) & $i(all_57_12))
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | | REF_CLOSE: (11), (17), (20), (23), (26), (44) are inconsistent by
% 150.98/21.94  | | | |            sub-proof #1083.
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | Case 2:
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | |   (45)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 150.98/21.94  | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.98/21.94  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.98/21.94  | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 150.98/21.94  | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 150.98/21.94  | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 150.98/21.94  | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 150.98/21.94  | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.98/21.94  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 150.98/21.94  | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | | REF_CLOSE: (5), (9), (11), (14), (16), (45) are inconsistent by
% 150.98/21.94  | | | |            sub-proof #1080.
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | End of split
% 150.98/21.94  | | | 
% 150.98/21.94  | | Case 2:
% 150.98/21.94  | | | 
% 150.98/21.94  | | |   (46)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.98/21.94  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.98/21.94  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.98/21.94  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 150.98/21.94  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 150.98/21.94  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 150.98/21.94  | | |           $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0
% 150.98/21.94  | | |           &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 150.98/21.94  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 150.98/21.94  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 150.98/21.94  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 150.98/21.94  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 150.98/21.94  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 150.98/21.94  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.98/21.94  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.98/21.94  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.98/21.94  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 150.98/21.94  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.98/21.94  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 150.98/21.94  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.98/21.94  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 150.98/21.94  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.98/21.94  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 150.98/21.94  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.98/21.94  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.98/21.94  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 150.98/21.94  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.98/21.94  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 150.98/21.94  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 150.98/21.94  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 150.98/21.94  | | | 
% 150.98/21.94  | | | BETA: splitting (46) gives:
% 150.98/21.94  | | | 
% 150.98/21.94  | | | Case 1:
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | |   (47)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 150.98/21.94  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.98/21.94  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.98/21.94  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 150.98/21.94  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 150.98/21.94  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.98/21.94  | | | |           e1 & $i(all_57_9) & $i(all_57_14))
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | | REF_CLOSE: (11), (15), (28), (47) are inconsistent by sub-proof #975.
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | Case 2:
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | |   (48)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 150.98/21.94  | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.98/21.94  | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.98/21.94  | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 150.98/21.94  | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 150.98/21.94  | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 150.98/21.94  | | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 150.98/21.94  | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 150.98/21.94  | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 150.98/21.94  | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.98/21.94  | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 150.98/21.94  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 150.98/21.94  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.98/21.94  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.98/21.94  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.98/21.94  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.98/21.94  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.94  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 150.98/21.94  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.98/21.94  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 150.98/21.94  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 150.98/21.94  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.98/21.94  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.98/21.94  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | | BETA: splitting (48) gives:
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | | Case 1:
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | |   (49)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 150.98/21.94  | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 150.98/21.94  | | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.98/21.94  | | | | |         $i(all_57_13)
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | | ALPHA: (49) implies:
% 150.98/21.94  | | | | |   (50)  op(e1, e1) = e0
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | | REF_CLOSE: (7), (10), (11), (50) are inconsistent by sub-proof #1006.
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | Case 2:
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | |   (51)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.98/21.94  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 150.98/21.94  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.98/21.94  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 150.98/21.94  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.98/21.94  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 150.98/21.94  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 150.98/21.94  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 150.98/21.94  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.98/21.94  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 150.98/21.94  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 150.98/21.94  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.98/21.94  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 150.98/21.94  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.98/21.94  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.98/21.94  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.98/21.94  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 150.98/21.94  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.98/21.94  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.98/21.94  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 150.98/21.94  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.98/21.94  | | | | |               $i(all_57_7))))
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | | BETA: splitting (51) gives:
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | | Case 1:
% 150.98/21.94  | | | | | | 
% 150.98/21.94  | | | | | |   (52)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 150.98/21.94  | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 150.98/21.94  | | | | | |         & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.98/21.94  | | | | | |         $i(all_57_14)
% 150.98/21.94  | | | | | | 
% 150.98/21.94  | | | | | | ALPHA: (52) implies:
% 150.98/21.94  | | | | | |   (53)  op(e2, e2) = e0
% 150.98/21.94  | | | | | | 
% 150.98/21.94  | | | | | | REF_CLOSE: (4), (11), (21), (53) are inconsistent by sub-proof #853.
% 150.98/21.94  | | | | | | 
% 150.98/21.94  | | | | | Case 2:
% 150.98/21.94  | | | | | | 
% 150.98/21.94  | | | | | |   (54)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 150.98/21.94  | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 150.98/21.94  | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 150.98/21.94  | | | | | |               e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 150.98/21.94  | | | | | |             = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1,
% 150.98/21.94  | | | | | |               e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 150.98/21.94  | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.98/21.94  | | | | | |             (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 150.98/21.94  | | | | | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 150.98/21.94  | | | | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 150.98/21.94  | | | | | |             (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 150.98/21.94  | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 150.98/21.94  | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.98/21.94  | | | | | |             (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 150.98/21.94  | | | | | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 150.98/21.94  | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.98/21.94  | | | | | |             (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 150.98/21.94  | | | | | |             & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.98/21.94  | | | | | |             $i(all_57_7)))
% 150.98/21.94  | | | | | | 
% 150.98/21.94  | | | | | | ALPHA: (54) implies:
% 150.98/21.94  | | | | | |   (55)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.98/21.94  | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 150.98/21.94  | | | | | |           & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 150.98/21.94  | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 150.98/21.94  | | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 150.98/21.94  | | | | | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.98/21.94  | | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 150.98/21.94  | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.98/21.94  | | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.94  | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 150.98/21.94  | | | | | |           & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.98/21.94  | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 150.98/21.94  | | | | | |           & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 150.98/21.94  | | | | | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 150.98/21.94  | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 150.98/21.94  | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 150.98/21.94  | | | | | | 
% 150.98/21.94  | | | | | | BETA: splitting (18) gives:
% 150.98/21.94  | | | | | | 
% 150.98/21.94  | | | | | | Case 1:
% 150.98/21.94  | | | | | | | 
% 150.98/21.94  | | | | | | |   (56)  all_54_15 = e2
% 150.98/21.94  | | | | | | | 
% 150.98/21.94  | | | | | | | REF_CLOSE: (25), (29), (56) are inconsistent by sub-proof #1048.
% 150.98/21.94  | | | | | | | 
% 150.98/21.94  | | | | | | Case 2:
% 150.98/21.94  | | | | | | | 
% 150.98/21.94  | | | | | | |   (57)  all_54_15 = e1 | all_54_15 = e0
% 150.98/21.94  | | | | | | | 
% 150.98/21.94  | | | | | | | REF_CLOSE: (1), (3), (8), (9), (11), (19), (22), (24), (27), (28),
% 150.98/21.94  | | | | | | |            (29), (55), (57) are inconsistent by sub-proof #38.
% 150.98/21.94  | | | | | | | 
% 150.98/21.94  | | | | | | End of split
% 150.98/21.94  | | | | | | 
% 150.98/21.94  | | | | | End of split
% 150.98/21.94  | | | | | 
% 150.98/21.94  | | | | End of split
% 150.98/21.94  | | | | 
% 150.98/21.94  | | | End of split
% 150.98/21.94  | | | 
% 150.98/21.94  | | End of split
% 150.98/21.94  | | 
% 150.98/21.94  | End of split
% 150.98/21.94  | 
% 150.98/21.94  End of proof
% 150.98/21.94  
% 150.98/21.94  Sub-proof #38 shows that the following formulas are inconsistent:
% 150.98/21.94  ----------------------------------------------------------------
% 150.98/21.94    (1)  op(e0, e1) = all_52_11
% 150.98/21.94    (2)   ~ (all_52_11 = all_10_2)
% 150.98/21.94    (3)  op(e0, e2) = all_52_7
% 150.98/21.94    (4)   ~ (all_10_2 = e1)
% 150.98/21.94    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.95    (6)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 150.98/21.95             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.98/21.95           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 150.98/21.95           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 150.98/21.95             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 150.98/21.95           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.98/21.95           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 150.98/21.95           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 150.98/21.95           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 150.98/21.95           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 150.98/21.95           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 150.98/21.95         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 150.98/21.95             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.98/21.95           $i(all_57_7))
% 150.98/21.95    (7)  op(e0, e3) = all_52_3
% 150.98/21.95    (8)   ~ (e3 = e2)
% 150.98/21.95    (9)  all_54_15 = e1 | all_54_15 = e0
% 150.98/21.95    (10)   ~ (all_52_7 = all_10_2)
% 150.98/21.95    (11)   ~ (all_52_3 = all_10_2)
% 150.98/21.95    (12)  op(e3, e3) = e3
% 150.98/21.95    (13)  all_54_15 = all_10_2
% 150.98/21.95  
% 150.98/21.95  Begin of proof
% 150.98/21.95  | 
% 150.98/21.95  | BETA: splitting (9) gives:
% 150.98/21.95  | 
% 150.98/21.95  | Case 1:
% 150.98/21.95  | | 
% 150.98/21.95  | |   (14)  all_54_15 = e1
% 150.98/21.95  | | 
% 150.98/21.95  | | REF_CLOSE: (4), (13), (14) are inconsistent by sub-proof #1047.
% 150.98/21.95  | | 
% 150.98/21.95  | Case 2:
% 150.98/21.95  | | 
% 150.98/21.95  | |   (15)  all_54_15 = e0
% 150.98/21.95  | | 
% 150.98/21.95  | | COMBINE_EQS: (13), (15) imply:
% 150.98/21.95  | |   (16)  all_10_2 = e0
% 150.98/21.95  | | 
% 150.98/21.95  | | SIMP: (16) implies:
% 150.98/21.95  | |   (17)  all_10_2 = e0
% 150.98/21.95  | | 
% 150.98/21.95  | | REDUCE: (11), (17) imply:
% 150.98/21.95  | |   (18)   ~ (all_52_3 = e0)
% 150.98/21.95  | | 
% 150.98/21.95  | | REDUCE: (10), (17) imply:
% 150.98/21.95  | |   (19)   ~ (all_52_7 = e0)
% 150.98/21.95  | | 
% 150.98/21.95  | | REDUCE: (2), (17) imply:
% 150.98/21.95  | |   (20)   ~ (all_52_11 = e0)
% 150.98/21.95  | | 
% 150.98/21.95  | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (12), (18), (19), (20) are
% 150.98/21.95  | |            inconsistent by sub-proof #850.
% 150.98/21.95  | | 
% 150.98/21.95  | End of split
% 150.98/21.95  | 
% 150.98/21.95  End of proof
% 150.98/21.95  
% 150.98/21.95  Sub-proof #39 shows that the following formulas are inconsistent:
% 150.98/21.95  ----------------------------------------------------------------
% 150.98/21.95    (1)  op(e0, e0) = all_10_2
% 150.98/21.95    (2)  op(e1, e1) = e2
% 150.98/21.95    (3)   ~ (all_10_2 = e1)
% 150.98/21.95    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.95    (5)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 150.98/21.95             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 150.98/21.95           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 150.98/21.95           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 150.98/21.95           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.98/21.95           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.98/21.95    (6)   ~ (all_10_2 = e3)
% 150.98/21.95    (7)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 150.98/21.95    (8)   ~ (e3 = e2)
% 150.98/21.95    (9)   ~ (all_10_2 = e2)
% 150.98/21.95    (10)  all_54_15 = all_10_2
% 150.98/21.95  
% 150.98/21.95  Begin of proof
% 150.98/21.95  | 
% 150.98/21.95  | BETA: splitting (5) gives:
% 150.98/21.95  | 
% 150.98/21.95  | Case 1:
% 150.98/21.95  | | 
% 150.98/21.95  | |   (11)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 150.98/21.95  | |           = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 150.98/21.95  | |         all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 150.98/21.95  | | 
% 150.98/21.95  | | ALPHA: (11) implies:
% 150.98/21.95  | |   (12)  op(e1, e1) = e3
% 150.98/21.95  | | 
% 150.98/21.95  | | REF_CLOSE: (2), (4), (8), (12) are inconsistent by sub-proof #834.
% 150.98/21.95  | | 
% 150.98/21.95  | Case 2:
% 150.98/21.95  | | 
% 150.98/21.95  | |   (13)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 150.98/21.95  | |           = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 150.98/21.95  | |         all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 150.98/21.95  | | 
% 150.98/21.95  | | ALPHA: (13) implies:
% 150.98/21.95  | |   (14)  op(e0, e0) = e3
% 150.98/21.95  | | 
% 150.98/21.95  | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (14) are inconsistent by
% 150.98/21.95  | |            sub-proof #702.
% 150.98/21.95  | | 
% 150.98/21.95  | End of split
% 150.98/21.95  | 
% 150.98/21.95  End of proof
% 150.98/21.95  
% 150.98/21.95  Sub-proof #40 shows that the following formulas are inconsistent:
% 150.98/21.95  ----------------------------------------------------------------
% 150.98/21.95    (1)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 150.98/21.95             e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 150.98/21.95           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 =
% 150.98/21.95           e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 150.98/21.95           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 150.98/21.95           = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 150.98/21.95    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.95    (3)  op(e3, e0) = e2
% 150.98/21.95    (4)   ~ (e3 = e2)
% 150.98/21.95  
% 150.98/21.95  Begin of proof
% 150.98/21.95  | 
% 150.98/21.95  | BETA: splitting (1) gives:
% 150.98/21.95  | 
% 150.98/21.95  | Case 1:
% 150.98/21.95  | | 
% 150.98/21.95  | |   (5)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 150.98/21.95  | |          = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0
% 150.98/21.95  | |        & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)
% 150.98/21.95  | | 
% 150.98/21.95  | | ALPHA: (5) implies:
% 150.98/21.95  | |   (6)  op(e3, e0) = e3
% 150.98/21.95  | | 
% 150.98/21.95  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #41.
% 150.98/21.95  | | 
% 150.98/21.95  | Case 2:
% 150.98/21.95  | | 
% 150.98/21.95  | |   (7)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 150.98/21.95  | |          = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 150.98/21.95  | |        & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)
% 150.98/21.95  | | 
% 150.98/21.95  | | ALPHA: (7) implies:
% 150.98/21.95  | |   (8)  op(e3, e0) = e3
% 150.98/21.95  | | 
% 150.98/21.95  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #41.
% 150.98/21.95  | | 
% 150.98/21.95  | End of split
% 150.98/21.95  | 
% 150.98/21.95  End of proof
% 150.98/21.95  
% 150.98/21.95  Sub-proof #41 shows that the following formulas are inconsistent:
% 150.98/21.95  ----------------------------------------------------------------
% 150.98/21.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.95    (2)  op(e3, e0) = e3
% 150.98/21.95    (3)  op(e3, e0) = e2
% 150.98/21.95    (4)   ~ (e3 = e2)
% 150.98/21.95  
% 150.98/21.95  Begin of proof
% 150.98/21.95  | 
% 150.98/21.95  | GROUND_INST: instantiating (1) with e2, e3, e0, e3, simplifying with (2), (3)
% 150.98/21.95  |              gives:
% 150.98/21.95  |   (5)  e3 = e2
% 150.98/21.95  | 
% 150.98/21.95  | REDUCE: (4), (5) imply:
% 150.98/21.95  |   (6)  $false
% 150.98/21.95  | 
% 150.98/21.95  | CLOSE: (6) is inconsistent.
% 150.98/21.95  | 
% 150.98/21.95  End of proof
% 150.98/21.95  
% 150.98/21.95  Sub-proof #42 shows that the following formulas are inconsistent:
% 150.98/21.95  ----------------------------------------------------------------
% 150.98/21.95    (1)  op(e0, e1) = all_52_11
% 150.98/21.95    (2)   ~ (all_52_7 = all_52_11)
% 150.98/21.95    (3)   ~ (e3 = e1)
% 150.98/21.95    (4)   ~ (all_52_2 = all_52_6)
% 150.98/21.95    (5)  op(e1, e1) = e2
% 150.98/21.95    (6)  op(e1, e1) = all_4_2
% 150.98/21.95    (7)   ~ (e2 = e0)
% 150.98/21.95    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 150.98/21.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 150.98/21.95    (9)  op(e0, e0) = e3
% 150.98/21.95    (10)   ~ (all_52_13 = e2)
% 150.98/21.95    (11)   ~ (all_52_7 = e3)
% 150.98/21.95    (12)   ~ (e3 = e0)
% 150.98/21.95    (13)  op(e3, e3) = e1
% 150.98/21.95    (14)  op(e1, e2) = all_52_6
% 150.98/21.95    (15)  op(e2, e0) = all_52_13
% 150.98/21.95    (16)   ~ (all_52_9 = e2)
% 150.98/21.95    (17)   ~ (all_52_7 = e2)
% 150.98/21.95    (18)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 150.98/21.95    (19)  op(e2, e1) = all_52_9
% 150.98/21.95    (20)   ~ (e1 = e0)
% 150.98/21.95    (21)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 150.98/21.95              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 150.98/21.95            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 150.98/21.95                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 150.98/21.95              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.98/21.95          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 150.98/21.95              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.98/21.95            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 150.98/21.95                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 150.98/21.95              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.98/21.95          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 150.98/21.95              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.98/21.95            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 150.98/21.95                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 150.98/21.95              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 150.98/21.95          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 150.98/21.95              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.98/21.95            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 150.98/21.95                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 150.98/21.95                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 150.98/21.95                $i(all_57_14))))
% 150.98/21.95    (22)   ~ (e3 = e2)
% 150.98/21.95    (23)  all_54_13 = all_52_7
% 150.98/21.95    (24)   ~ (all_52_6 = all_52_7)
% 150.98/21.95    (25)   ~ (e2 = e1)
% 150.98/21.95    (26)  op(e1, e3) = all_52_2
% 150.98/21.95    (27)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 150.98/21.95              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 150.98/21.95            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 150.98/21.95            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 150.98/21.95            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 150.98/21.95            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 150.98/21.95            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 150.98/21.95            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 150.98/21.95            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 150.98/21.95            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.98/21.95            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 150.98/21.95            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 150.98/21.95            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.98/21.95            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.98/21.95            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 150.98/21.95            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.98/21.95            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.98/21.95            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 150.98/21.95            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.98/21.95            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 150.98/21.95            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 150.98/21.95            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.98/21.95            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.98/21.95            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 150.98/21.95            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.98/21.95            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.98/21.95            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 150.98/21.95            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 150.98/21.95            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.98/21.95            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 150.98/21.95            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 150.98/21.95            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 150.98/21.95            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 150.98/21.95            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 150.98/21.95            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 150.98/21.95            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 150.98/21.95            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.98/21.95            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 150.98/21.95            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 150.98/21.95            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 150.98/21.95            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 150.98/21.95            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 150.98/21.95            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.98/21.95            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 150.98/21.95            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 150.98/21.95            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 150.98/21.95            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 150.98/21.95            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 150.98/21.95              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 150.98/21.95            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 150.98/21.95            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 150.98/21.95              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 150.98/21.95            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 150.98/21.95            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 150.98/21.95                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 150.98/21.95                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 150.98/21.95                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 150.98/21.95                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 150.98/21.95                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 150.98/21.95                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 150.98/21.95                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 150.98/21.95              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 150.98/21.95                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 150.98/21.95                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 150.98/21.95                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 150.98/21.95                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 150.98/21.95                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 150.98/21.95                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 150.98/21.95                $i(all_57_7))))
% 150.98/21.95    (28)  op(e2, e3) = all_52_1
% 150.98/21.95    (29)   ~ (all_52_1 = e2)
% 150.98/21.95  
% 150.98/21.95  Begin of proof
% 150.98/21.95  | 
% 150.98/21.95  | BETA: splitting (21) gives:
% 150.98/21.95  | 
% 150.98/21.95  | Case 1:
% 150.98/21.95  | | 
% 150.98/21.95  | |   (30)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 150.98/21.95  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 150.98/21.95  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.98/21.95  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.98/21.95  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.98/21.95  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 150.98/21.95  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 150.98/21.95  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 150.98/21.95  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 150.98/21.95  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 150.98/21.95  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 150.98/21.95  | |               $i(all_57_15))))
% 150.98/21.95  | | 
% 150.98/21.95  | | BETA: splitting (30) gives:
% 150.98/21.95  | | 
% 150.98/21.95  | | Case 1:
% 150.98/21.95  | | | 
% 150.98/21.95  | | |   (31)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 150.98/21.95  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 150.98/21.95  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 150.98/21.95  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.98/21.95  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 150.98/21.95  | | |               e0) = all_57_15 & $i(all_57_15)))
% 150.98/21.95  | | | 
% 150.98/21.95  | | | ALPHA: (31) implies:
% 150.98/21.95  | | |   (32)  op(e3, e3) = e3
% 150.98/21.95  | | | 
% 150.98/21.95  | | | REF_CLOSE: (3), (8), (13), (32) are inconsistent by sub-proof #1178.
% 150.98/21.95  | | | 
% 150.98/21.95  | | Case 2:
% 150.98/21.95  | | | 
% 150.98/21.95  | | |   (33)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 150.98/21.95  | | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 150.98/21.95  | | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 150.98/21.95  | | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 150.98/21.95  | | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 150.98/21.95  | | |               e0) = all_57_15 & $i(all_57_15)))
% 150.98/21.95  | | | 
% 150.98/21.95  | | | ALPHA: (33) implies:
% 150.98/21.95  | | |   (34)  op(e2, e2) = e2
% 150.98/21.95  | | |   (35)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 150.98/21.95  | | |             e1) = all_57_14 & $i(all_57_14))
% 150.98/21.95  | | | 
% 150.98/21.95  | | | BETA: splitting (35) gives:
% 150.98/21.95  | | | 
% 150.98/21.95  | | | Case 1:
% 150.98/21.95  | | | | 
% 150.98/21.95  | | | |   (36)  all_57_4 = e1 & op(e1, e2) = e1
% 150.98/21.95  | | | | 
% 150.98/21.95  | | | | ALPHA: (36) implies:
% 150.98/21.95  | | | |   (37)  op(e1, e2) = e1
% 150.98/21.95  | | | | 
% 150.98/21.95  | | | | BETA: splitting (27) gives:
% 150.98/21.95  | | | | 
% 150.98/21.95  | | | | Case 1:
% 150.98/21.95  | | | | | 
% 150.98/21.95  | | | | |   (38)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.98/21.95  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 150.98/21.95  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 150.98/21.95  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 150.98/21.95  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 150.98/21.95  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 150.98/21.95  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 150.98/21.95  | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 150.98/21.95  | | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 150.98/21.95  | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 150.98/21.95  | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 150.98/21.95  | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 150.98/21.95  | | | | |           & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 150.98/21.95  | | | | |           $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 150.98/21.95  | | | | |           (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 150.98/21.95  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 150.98/21.95  | | | | |             e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3
% 150.98/21.95  | | | | |           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2)
% 150.98/21.95  | | | | |           & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.98/21.95  | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 150.98/21.95  | | | | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.98/21.95  | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 150.98/21.95  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 150.98/21.95  | | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 150.98/21.95  | | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.98/21.95  | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 150.98/21.95  | | | | |           = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 150.98/21.95  | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 150.98/21.95  | | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 150.98/21.95  | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.98/21.95  | | | | | 
% 150.98/21.95  | | | | | BETA: splitting (38) gives:
% 150.98/21.95  | | | | | 
% 150.98/21.95  | | | | | Case 1:
% 150.98/21.95  | | | | | | 
% 150.98/21.95  | | | | | |   (39)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 150.98/21.95  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 150.98/21.95  | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 150.98/21.95  | | | | | |           $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 & all_57_15
% 150.98/21.95  | | | | | |           = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2,
% 150.98/21.95  | | | | | |             e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 150.98/21.95  | | | | | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 150.98/21.95  | | | | | |         | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 150.98/21.95  | | | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 150.98/21.95  | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0)
% 150.98/21.95  | | | | | |           & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 150.98/21.95  | | | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 150.98/21.95  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 150.98/21.95  | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 150.98/21.95  | | | | | | 
% 150.98/21.95  | | | | | | REF_CLOSE: (4), (8), (14), (26), (28), (29), (37), (39) are
% 150.98/21.95  | | | | | |            inconsistent by sub-proof #53.
% 150.98/21.95  | | | | | | 
% 150.98/21.95  | | | | | Case 2:
% 150.98/21.95  | | | | | | 
% 150.98/21.95  | | | | | |   (40)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.95  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 150.98/21.95  | | | | | |           e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.98/21.95  | | | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15
% 150.98/21.95  | | | | | |           = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3,
% 150.98/21.95  | | | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 150.98/21.95  | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 150.98/21.95  | | | | | |         | (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.98/21.95  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3
% 150.98/21.95  | | | | | |           & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3)
% 150.98/21.95  | | | | | |           & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 150.98/21.95  | | | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 150.98/21.95  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 150.98/21.95  | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 =
% 150.98/21.95  | | | | | |           e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 150.98/21.95  | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 150.98/21.95  | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 150.98/21.95  | | | | | |           $i(all_57_10))
% 150.98/21.95  | | | | | | 
% 150.98/21.95  | | | | | | BETA: splitting (40) gives:
% 150.98/21.95  | | | | | | 
% 150.98/21.95  | | | | | | Case 1:
% 150.98/21.95  | | | | | | | 
% 150.98/21.95  | | | | | | |   (41)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.95  | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 150.98/21.95  | | | | | | |           e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.98/21.95  | | | | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 &
% 150.98/21.95  | | | | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 150.98/21.95  | | | | | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 150.98/21.95  | | | | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.98/21.95  | | | | | | |           $i(all_57_10))
% 150.98/21.95  | | | | | | | 
% 150.98/21.95  | | | | | | | BETA: splitting (41) gives:
% 150.98/21.95  | | | | | | | 
% 150.98/21.95  | | | | | | | Case 1:
% 150.98/21.95  | | | | | | | | 
% 150.98/21.95  | | | | | | | |   (42)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 150.98/21.95  | | | | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 150.98/21.95  | | | | | | | |         e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 150.98/21.95  | | | | | | | |         $i(all_57_4) & $i(all_57_10)
% 150.98/21.95  | | | | | | | | 
% 150.98/21.95  | | | | | | | | ALPHA: (42) implies:
% 150.98/21.95  | | | | | | | |   (43)  all_57_14 = e2
% 150.98/21.95  | | | | | | | |   (44)   ~ (all_57_4 = e1)
% 150.98/21.95  | | | | | | | | 
% 150.98/21.95  | | | | | | | | REF_CLOSE: (35), (43), (44) are inconsistent by sub-proof #1005.
% 150.98/21.95  | | | | | | | | 
% 150.98/21.95  | | | | | | | Case 2:
% 150.98/21.95  | | | | | | | | 
% 150.98/21.95  | | | | | | | |   (45)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 150.98/21.95  | | | | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 150.98/21.95  | | | | | | | |         e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 150.98/21.95  | | | | | | | |         $i(all_57_5) & $i(all_57_10)
% 150.98/21.95  | | | | | | | | 
% 150.98/21.95  | | | | | | | | ALPHA: (45) implies:
% 150.98/21.95  | | | | | | | |   (46)  op(e0, e0) = e2
% 150.98/21.95  | | | | | | | | 
% 150.98/21.95  | | | | | | | | REF_CLOSE: (8), (9), (22), (46) are inconsistent by sub-proof
% 150.98/21.95  | | | | | | | |            #1087.
% 150.98/21.95  | | | | | | | | 
% 150.98/21.95  | | | | | | | End of split
% 150.98/21.95  | | | | | | | 
% 150.98/21.95  | | | | | | Case 2:
% 150.98/21.95  | | | | | | | 
% 150.98/21.95  | | | | | | |   (47)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 150.98/21.95  | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 150.98/21.95  | | | | | | |           all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.98/21.95  | | | | | | |           $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 150.98/21.95  | | | | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 150.98/21.95  | | | | | | |             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 150.98/21.95  | | | | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 150.98/21.95  | | | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 150.98/21.95  | | | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 150.98/21.95  | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2,
% 150.98/21.95  | | | | | | |             e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 150.98/21.95  | | | | | | | 
% 150.98/21.95  | | | | | | | REF_CLOSE: (8), (9), (13), (22), (25), (34), (47) are inconsistent
% 150.98/21.95  | | | | | | |            by sub-proof #953.
% 150.98/21.95  | | | | | | | 
% 150.98/21.95  | | | | | | End of split
% 150.98/21.95  | | | | | | 
% 150.98/21.95  | | | | | End of split
% 150.98/21.95  | | | | | 
% 150.98/21.95  | | | | Case 2:
% 150.98/21.95  | | | | | 
% 151.14/21.96  | | | | |   (48)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/21.96  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.14/21.96  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/21.96  | | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 151.14/21.96  | | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 151.14/21.96  | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 151.14/21.96  | | | | |           = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 151.14/21.96  | | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 151.14/21.96  | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 151.14/21.96  | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 151.14/21.96  | | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/21.96  | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.14/21.96  | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.14/21.96  | | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 151.14/21.96  | | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 151.14/21.96  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 151.14/21.96  | | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 151.14/21.96  | | | | |           & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 = e0)
% 151.14/21.96  | | | | |           & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 151.14/21.96  | | | | |           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 151.14/21.96  | | | | |         | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 151.14/21.96  | | | | |           (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.14/21.96  | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 151.14/21.96  | | | | |           $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 151.14/21.96  | | | | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 151.14/21.96  | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 151.14/21.96  | | | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 151.14/21.96  | | | | |           & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0)
% 151.14/21.96  | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 151.14/21.96  | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14))
% 151.14/21.96  | | | | |         | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 151.14/21.96  | | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 151.14/21.96  | | | | |                 e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 151.14/21.96  | | | | |                 e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 151.14/21.96  | | | | |               = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1,
% 151.14/21.96  | | | | |                 e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.14/21.96  | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/21.96  | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 151.14/21.96  | | | | |               & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/21.96  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 151.14/21.96  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.14/21.96  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/21.96  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/21.96  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 151.14/21.96  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/21.96  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/21.96  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 151.14/21.96  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/21.96  | | | | |               $i(all_57_7))))
% 151.14/21.96  | | | | | 
% 151.14/21.96  | | | | | BETA: splitting (48) gives:
% 151.14/21.96  | | | | | 
% 151.14/21.96  | | | | | Case 1:
% 151.14/21.96  | | | | | | 
% 151.14/21.96  | | | | | |   (49)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/21.96  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 151.14/21.96  | | | | | |           e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 151.14/21.96  | | | | | |           $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 & all_57_10
% 151.14/21.96  | | | | | |           = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3,
% 151.14/21.96  | | | | | |             e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 151.14/21.96  | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.14/21.96  | | | | | |           $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~
% 151.14/21.96  | | | | | |           (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 151.14/21.96  | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 &
% 151.14/21.96  | | | | | |           op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 151.14/21.96  | | | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/21.96  | | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 151.14/21.96  | | | | | |           e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 151.14/21.96  | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 151.14/21.96  | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1)
% 151.14/21.96  | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 151.14/21.96  | | | | | |           e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.14/21.96  | | | | | |           $i(all_57_13))
% 151.14/21.96  | | | | | | 
% 151.14/21.96  | | | | | | BETA: splitting (49) gives:
% 151.14/21.96  | | | | | | 
% 151.14/21.96  | | | | | | Case 1:
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | |   (50)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/21.96  | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 151.14/21.96  | | | | | | |           e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 151.14/21.96  | | | | | | |           $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 &
% 151.14/21.96  | | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 151.14/21.96  | | | | | | |             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 151.14/21.96  | | | | | | |             e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.14/21.96  | | | | | | |           $i(all_57_12))
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | | REF_CLOSE: (3), (8), (9), (16), (19), (50) are inconsistent by
% 151.14/21.96  | | | | | | |            sub-proof #1021.
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | Case 2:
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | |   (51)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/21.96  | | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 151.14/21.96  | | | | | | |           e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 151.14/21.96  | | | | | | |           $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 151.14/21.96  | | | | | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 151.14/21.96  | | | | | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/21.96  | | | | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10)
% 151.14/21.96  | | | | | | |           & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 151.14/21.96  | | | | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 151.14/21.96  | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1,
% 151.14/21.96  | | | | | | |             e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | | BETA: splitting (51) gives:
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | | Case 1:
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | |   (52)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/21.96  | | | | | | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 151.14/21.96  | | | | | | | |         e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 151.14/21.96  | | | | | | | |         $i(all_57_8) & $i(all_57_12)
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | | ALPHA: (52) implies:
% 151.14/21.96  | | | | | | | |   (53)  op(e0, e0) = e1
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | | REF_CLOSE: (3), (8), (9), (53) are inconsistent by sub-proof
% 151.14/21.96  | | | | | | | |            #1022.
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | Case 2:
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | |   (54)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) & 
% 151.14/21.96  | | | | | | | |           ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 151.14/21.96  | | | | | | | |             e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.14/21.96  | | | | | | | |           & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 151.14/21.96  | | | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 =
% 151.14/21.96  | | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/21.96  | | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.14/21.96  | | | | | | | |           $i(all_57_10) & $i(all_57_13))
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | | BETA: splitting (54) gives:
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | | Case 1:
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | |   (55)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &
% 151.14/21.96  | | | | | | | | |          ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 151.14/21.96  | | | | | | | | |           e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.14/21.96  | | | | | | | | |         & $i(all_57_10) & $i(all_57_11)
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | ALPHA: (55) implies:
% 151.14/21.96  | | | | | | | | |   (56)  op(e2, e2) = e0
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | REF_CLOSE: (7), (8), (34), (56) are inconsistent by sub-proof
% 151.14/21.96  | | | | | | | | |            #1145.
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | Case 2:
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | |   (57)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &
% 151.14/21.96  | | | | | | | | |          ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 151.14/21.96  | | | | | | | | |           e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13
% 151.14/21.96  | | | | | | | | |         & $i(all_57_10) & $i(all_57_13)
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | ALPHA: (57) implies:
% 151.14/21.96  | | | | | | | | |   (58)  op(e1, e1) = e0
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | REF_CLOSE: (5), (7), (8), (58) are inconsistent by sub-proof
% 151.14/21.96  | | | | | | | | |            #1006.
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | End of split
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | End of split
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | End of split
% 151.14/21.96  | | | | | | 
% 151.14/21.96  | | | | | Case 2:
% 151.14/21.96  | | | | | | 
% 151.14/21.96  | | | | | |   (59)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 151.14/21.96  | | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9
% 151.14/21.96  | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 151.14/21.96  | | | | | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 151.14/21.96  | | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 151.14/21.96  | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1,
% 151.14/21.96  | | | | | |             e0) = e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 =
% 151.14/21.96  | | | | | |           e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13
% 151.14/21.96  | | | | | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 151.14/21.96  | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.14/21.96  | | | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 151.14/21.96  | | | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 151.14/21.96  | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 151.14/21.96  | | | | | |             e0) = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0)
% 151.14/21.96  | | | | | |           = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12
% 151.14/21.96  | | | | | |               = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 151.14/21.96  | | | | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 151.14/21.96  | | | | | |               e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &
% 151.14/21.96  | | | | | |                ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3)
% 151.14/21.96  | | | | | |               = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.14/21.96  | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/21.96  | | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 151.14/21.96  | | | | | |               e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/21.96  | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 151.14/21.96  | | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.14/21.96  | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/21.96  | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/21.96  | | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 151.14/21.96  | | | | | |               e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/21.96  | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/21.96  | | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 151.14/21.96  | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/21.96  | | | | | |               $i(all_57_7))))
% 151.14/21.96  | | | | | | 
% 151.14/21.96  | | | | | | BETA: splitting (59) gives:
% 151.14/21.96  | | | | | | 
% 151.14/21.96  | | | | | | Case 1:
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | |   (60)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 151.14/21.96  | | | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 151.14/21.96  | | | | | | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 151.14/21.96  | | | | | | |           $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 &
% 151.14/21.96  | | | | | | |           all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 151.14/21.96  | | | | | | |             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1,
% 151.14/21.96  | | | | | | |             e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 151.14/21.96  | | | | | | |           $i(all_57_14))
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | | REF_CLOSE: (8), (13), (20), (60) are inconsistent by sub-proof
% 151.14/21.96  | | | | | | |            #956.
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | Case 2:
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | |   (61)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) & 
% 151.14/21.96  | | | | | | |           ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0)
% 151.14/21.96  | | | | | | |           = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.14/21.96  | | | | | | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 151.14/21.96  | | | | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 =
% 151.14/21.96  | | | | | | |             e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 151.14/21.96  | | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11)
% 151.14/21.96  | | | | | | |           & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 151.14/21.96  | | | | | | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 151.14/21.96  | | | | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 151.14/21.96  | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.14/21.96  | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 151.14/21.96  | | | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 151.14/21.96  | | | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.14/21.96  | | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/21.96  | | | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 151.14/21.96  | | | | | | |               e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/21.96  | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 151.14/21.96  | | | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.14/21.96  | | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/21.96  | | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/21.96  | | | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 151.14/21.96  | | | | | | |               e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/21.96  | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/21.96  | | | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 151.14/21.96  | | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/21.96  | | | | | | |               $i(all_57_7))))
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | | BETA: splitting (61) gives:
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | | Case 1:
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | |   (62)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) & 
% 151.14/21.96  | | | | | | | |         ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0)
% 151.14/21.96  | | | | | | | |         = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.14/21.96  | | | | | | | |         $i(all_57_12) & $i(all_57_13)
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | | ALPHA: (62) implies:
% 151.14/21.96  | | | | | | | |   (63)  op(e2, e0) = e2
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | | REF_CLOSE: (8), (10), (15), (63) are inconsistent by sub-proof
% 151.14/21.96  | | | | | | | |            #1156.
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | Case 2:
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | |   (64)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &
% 151.14/21.96  | | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 151.14/21.96  | | | | | | | |           all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.14/21.96  | | | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 151.14/21.96  | | | | | | | |           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 151.14/21.96  | | | | | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/21.96  | | | | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 151.14/21.96  | | | | | | | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 151.14/21.96  | | | | | | | |             (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 151.14/21.96  | | | | | | | |               &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 151.14/21.96  | | | | | | | |               op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 151.14/21.96  | | | | | | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 151.14/21.96  | | | | | | | |                 e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 151.14/21.96  | | | | | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/21.96  | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 & 
% 151.14/21.96  | | | | | | | |               ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1,
% 151.14/21.96  | | | | | | | |                 e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.14/21.96  | | | | | | | |               e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 =
% 151.14/21.96  | | | | | | | |               e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 151.14/21.96  | | | | | | | |               op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 151.14/21.96  | | | | | | | |                 e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 151.14/21.96  | | | | | | | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.14/21.96  | | | | | | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 151.14/21.96  | | | | | | | |               all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | | BETA: splitting (64) gives:
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | | Case 1:
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | |   (65)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2)
% 151.14/21.96  | | | | | | | | |         &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 151.14/21.96  | | | | | | | | |         all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.14/21.96  | | | | | | | | |         $i(all_57_11) & $i(all_57_14)
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | ALPHA: (65) implies:
% 151.14/21.96  | | | | | | | | |   (66)  op(e2, e2) = e0
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | REF_CLOSE: (7), (8), (34), (66) are inconsistent by sub-proof
% 151.14/21.96  | | | | | | | | |            #1145.
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | Case 2:
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | |   (67)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 =
% 151.14/21.96  | | | | | | | | |             e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/21.96  | | | | | | | | |             (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 151.14/21.96  | | | | | | | | |               e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 151.14/21.96  | | | | | | | | |           (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 151.14/21.96  | | | | | | | | |             &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 151.14/21.96  | | | | | | | | |             op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 151.14/21.96  | | | | | | | | |           | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 151.14/21.96  | | | | | | | | |               e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 151.14/21.96  | | | | | | | | |             op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/21.96  | | | | | | | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 & 
% 151.14/21.96  | | | | | | | | |             ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1,
% 151.14/21.96  | | | | | | | | |               e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.14/21.96  | | | | | | | | |             e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 =
% 151.14/21.96  | | | | | | | | |             e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 151.14/21.96  | | | | | | | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 151.14/21.96  | | | | | | | | |               e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 151.14/21.96  | | | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.14/21.96  | | | | | | | | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 151.14/21.96  | | | | | | | | |             all_57_7 & op(e0, e1) = e0 & $i(all_57_7)))
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | ALPHA: (67) implies:
% 151.14/21.96  | | | | | | | | |   (68)  op(e0, e0) = all_57_15
% 151.14/21.96  | | | | | | | | |   (69)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &
% 151.14/21.96  | | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 151.14/21.96  | | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 151.14/21.96  | | | | | | | | |         (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 151.14/21.96  | | | | | | | | |            ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 151.14/21.96  | | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 151.14/21.96  | | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &
% 151.14/21.96  | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/21.96  | | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.14/21.96  | | | | | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &
% 151.14/21.96  | | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 151.14/21.96  | | | | | | | | |             e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 151.14/21.96  | | | | | | | | |         (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &
% 151.14/21.96  | | | | | | | | |            ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 151.14/21.96  | | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 151.14/21.96  | | | | | | | | |         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 151.14/21.96  | | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 151.14/21.96  | | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | BETA: splitting (69) gives:
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | Case 1:
% 151.14/21.96  | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | |   (70)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2)
% 151.14/21.96  | | | | | | | | | |           &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 151.14/21.96  | | | | | | | | | |           op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0))
% 151.14/21.96  | | | | | | | | | |         | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.14/21.96  | | | | | | | | | |             e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 151.14/21.96  | | | | | | | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.14/21.96  | | | | | | | | | |           $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 & 
% 151.14/21.96  | | | | | | | | | |           ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 151.14/21.96  | | | | | | | | | |             e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) =
% 151.14/21.96  | | | | | | | | | |           e0 & $i(all_57_3))
% 151.14/21.96  | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | REF_CLOSE: (8), (9), (13), (25), (68), (70) are inconsistent
% 151.14/21.96  | | | | | | | | | |            by sub-proof #952.
% 151.14/21.96  | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | Case 2:
% 151.14/21.96  | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | |   (71)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1)
% 151.14/21.96  | | | | | | | | | |           &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 &
% 151.14/21.96  | | | | | | | | | |           op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4))
% 151.14/21.96  | | | | | | | | | |         | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 151.14/21.96  | | | | | | | | | |             e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 151.14/21.96  | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/21.96  | | | | | | | | | |           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 & 
% 151.14/21.96  | | | | | | | | | |           ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 151.14/21.96  | | | | | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) =
% 151.14/21.96  | | | | | | | | | |           e0 & $i(all_57_7))
% 151.14/21.96  | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | BETA: splitting (71) gives:
% 151.14/21.96  | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | Case 1:
% 151.14/21.96  | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | |   (72)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 151.14/21.96  | | | | | | | | | | |           e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.14/21.96  | | | | | | | | | | |         all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/21.96  | | | | | | | | | | |         $i(all_57_4)
% 151.14/21.96  | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | ALPHA: (72) implies:
% 151.14/21.96  | | | | | | | | | | |   (73)  all_57_14 = e2
% 151.14/21.96  | | | | | | | | | | |   (74)   ~ (all_57_4 = e1)
% 151.14/21.96  | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | REF_CLOSE: (35), (73), (74) are inconsistent by sub-proof
% 151.14/21.96  | | | | | | | | | | |            #1005.
% 151.14/21.96  | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | Case 2:
% 151.14/21.96  | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | |   (75)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 151.14/21.96  | | | | | | | | | | |             e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 151.14/21.96  | | | | | | | | | | |           op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/21.96  | | | | | | | | | | |           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 151.14/21.96  | | | | | | | | | | |           &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.14/21.96  | | | | | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 151.14/21.96  | | | | | | | | | | |             e1) = e0 & $i(all_57_7))
% 151.14/21.96  | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | BETA: splitting (75) gives:
% 151.14/21.96  | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | Case 1:
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | |   (76)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 151.14/21.96  | | | | | | | | | | | |           e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 151.14/21.96  | | | | | | | | | | | |         op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/21.96  | | | | | | | | | | | |         $i(all_57_6)
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | | ALPHA: (76) implies:
% 151.14/21.96  | | | | | | | | | | | |   (77)  op(e0, e1) = e0
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_11, e0, e1, e0,
% 151.14/21.96  | | | | | | | | | | | |              simplifying with (1), (77) gives:
% 151.14/21.96  | | | | | | | | | | | |   (78)  all_52_11 = e0
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_6, e1, e2, e1,
% 151.14/21.96  | | | | | | | | | | | |              simplifying with (14), (37) gives:
% 151.14/21.96  | | | | | | | | | | | |   (79)  all_52_6 = e1
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | | REDUCE: (24), (79) imply:
% 151.14/21.96  | | | | | | | | | | | |   (80)   ~ (all_52_7 = e1)
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | | SIMP: (80) implies:
% 151.14/21.96  | | | | | | | | | | | |   (81)   ~ (all_52_7 = e1)
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | | REDUCE: (2), (78) imply:
% 151.14/21.96  | | | | | | | | | | | |   (82)   ~ (all_52_7 = e0)
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | | REF_CLOSE: (11), (17), (18), (23), (81), (82) are
% 151.14/21.96  | | | | | | | | | | | |            inconsistent by sub-proof #432.
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | Case 2:
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | |   (83)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 151.14/21.96  | | | | | | | | | | | |           e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 151.14/21.96  | | | | | | | | | | | |         op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/21.96  | | | | | | | | | | | |         $i(all_57_7)
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | | ALPHA: (83) implies:
% 151.14/21.96  | | | | | | | | | | | |   (84)  op(e2, e2) = e1
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | | REF_CLOSE: (8), (25), (34), (84) are inconsistent by
% 151.14/21.96  | | | | | | | | | | | |            sub-proof #1158.
% 151.14/21.96  | | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | | End of split
% 151.14/21.96  | | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | | End of split
% 151.14/21.96  | | | | | | | | | | 
% 151.14/21.96  | | | | | | | | | End of split
% 151.14/21.96  | | | | | | | | | 
% 151.14/21.96  | | | | | | | | End of split
% 151.14/21.96  | | | | | | | | 
% 151.14/21.96  | | | | | | | End of split
% 151.14/21.96  | | | | | | | 
% 151.14/21.96  | | | | | | End of split
% 151.14/21.96  | | | | | | 
% 151.14/21.96  | | | | | End of split
% 151.14/21.96  | | | | | 
% 151.14/21.96  | | | | End of split
% 151.14/21.96  | | | | 
% 151.14/21.96  | | | Case 2:
% 151.14/21.96  | | | | 
% 151.14/21.96  | | | |   (85)   ~ (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14)
% 151.14/21.96  | | | | 
% 151.14/21.96  | | | | ALPHA: (85) implies:
% 151.14/21.96  | | | |   (86)   ~ (all_57_14 = e2)
% 151.14/21.96  | | | |   (87)  op(e1, e1) = all_57_14
% 151.14/21.96  | | | | 
% 151.14/21.96  | | | | REF_CLOSE: (5), (8), (86), (87) are inconsistent by sub-proof #52.
% 151.14/21.96  | | | | 
% 151.14/21.96  | | | End of split
% 151.14/21.96  | | | 
% 151.14/21.96  | | End of split
% 151.14/21.96  | | 
% 151.14/21.96  | Case 2:
% 151.14/21.96  | | 
% 151.14/21.96  | |   (88)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.14/21.96  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.14/21.96  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.14/21.96  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/21.96  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.14/21.96  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 151.14/21.96  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 151.14/21.96  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/21.96  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 151.14/21.96  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 151.14/21.96  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 151.14/21.96  | |               all_57_14 & $i(all_57_14))))
% 151.14/21.96  | | 
% 151.14/21.96  | | REF_CLOSE: (5), (6), (8), (9), (12), (25), (88) are inconsistent by
% 151.14/21.96  | |            sub-proof #51.
% 151.14/21.96  | | 
% 151.14/21.96  | End of split
% 151.14/21.96  | 
% 151.14/21.96  End of proof
% 151.14/21.96  
% 151.14/21.96  Sub-proof #43 shows that the following formulas are inconsistent:
% 151.14/21.96  ----------------------------------------------------------------
% 151.14/21.96    (1)  op(e0, e1) = e3
% 151.14/21.96    (2)  op(e1, e1) = e2
% 151.14/21.96    (3)   ~ (e2 = e0)
% 151.14/21.96    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.96    (5)   ~ (e3 = e0)
% 151.14/21.96    (6)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.14/21.96  
% 151.14/21.96  Begin of proof
% 151.14/21.96  | 
% 151.14/21.96  | BETA: splitting (6) gives:
% 151.14/21.96  | 
% 151.14/21.96  | Case 1:
% 151.14/21.96  | | 
% 151.14/21.96  | |   (7)  all_56_8 = e0 & op(e1, e1) = e0
% 151.14/21.96  | | 
% 151.14/21.96  | | ALPHA: (7) implies:
% 151.14/21.96  | |   (8)  op(e1, e1) = e0
% 151.14/21.96  | | 
% 151.14/21.96  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1006.
% 151.14/21.96  | | 
% 151.14/21.96  | Case 2:
% 151.14/21.96  | | 
% 151.14/21.96  | |   (9)  all_56_14 = e0 & op(e0, e1) = e0
% 151.14/21.96  | | 
% 151.14/21.96  | | ALPHA: (9) implies:
% 151.14/21.96  | |   (10)  op(e0, e1) = e0
% 151.14/21.96  | | 
% 151.14/21.96  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #104.
% 151.14/21.96  | | 
% 151.14/21.96  | End of split
% 151.14/21.96  | 
% 151.14/21.96  End of proof
% 151.14/21.96  
% 151.14/21.96  Sub-proof #44 shows that the following formulas are inconsistent:
% 151.14/21.96  ----------------------------------------------------------------
% 151.14/21.96    (1)  op(e3, e1) = all_34_1
% 151.14/21.96    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.96           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.96    (3)  op(e3, e1) = all_22_1
% 151.14/21.96    (4)   ~ (all_22_1 = e0)
% 151.14/21.96    (5)  op(e3, e1) = e0
% 151.14/21.96  
% 151.14/21.96  Begin of proof
% 151.14/21.96  | 
% 151.14/21.96  | GROUND_INST: instantiating (2) with all_22_1, all_34_1, e1, e3, simplifying
% 151.14/21.96  |              with (1), (3) gives:
% 151.14/21.96  |   (6)  all_34_1 = all_22_1
% 151.14/21.96  | 
% 151.14/21.96  | GROUND_INST: instantiating (2) with e0, all_34_1, e1, e3, simplifying with
% 151.14/21.96  |              (1), (5) gives:
% 151.14/21.96  |   (7)  all_34_1 = e0
% 151.14/21.96  | 
% 151.14/21.96  | COMBINE_EQS: (6), (7) imply:
% 151.14/21.96  |   (8)  all_22_1 = e0
% 151.14/21.96  | 
% 151.14/21.96  | REDUCE: (4), (8) imply:
% 151.14/21.96  |   (9)  $false
% 151.14/21.96  | 
% 151.14/21.96  | CLOSE: (9) is inconsistent.
% 151.14/21.96  | 
% 151.14/21.96  End of proof
% 151.14/21.96  
% 151.14/21.96  Sub-proof #45 shows that the following formulas are inconsistent:
% 151.14/21.96  ----------------------------------------------------------------
% 151.14/21.96    (1)   ~ (all_52_6 = e1)
% 151.14/21.96    (2)  op(e3, e1) = all_34_1
% 151.14/21.96    (3)  all_54_9 = all_52_6
% 151.14/21.96    (4)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 151.14/21.97    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.97    (6)  op(e3, e1) = all_22_1
% 151.14/21.97    (7)  op(e0, e3) = e2
% 151.14/21.97    (8)   ~ (all_22_0 = e2)
% 151.14/21.97    (9)  op(e3, e1) = e0
% 151.14/21.97    (10)  op(all_22_1, e3) = all_22_0
% 151.14/21.97    (11)   ~ (all_52_6 = e2)
% 151.14/21.97  
% 151.14/21.97  Begin of proof
% 151.14/21.97  | 
% 151.14/21.97  | BETA: splitting (4) gives:
% 151.14/21.97  | 
% 151.14/21.97  | Case 1:
% 151.14/21.97  | | 
% 151.14/21.97  | |   (12)  all_54_9 = e2
% 151.14/21.97  | | 
% 151.14/21.97  | | REF_CLOSE: (3), (11), (12) are inconsistent by sub-proof #185.
% 151.14/21.97  | | 
% 151.14/21.97  | Case 2:
% 151.14/21.97  | | 
% 151.14/21.97  | |   (13)  all_54_9 = e1 | all_54_9 = e0
% 151.14/21.97  | | 
% 151.14/21.97  | | BETA: splitting (13) gives:
% 151.14/21.97  | | 
% 151.14/21.97  | | Case 1:
% 151.14/21.97  | | | 
% 151.14/21.97  | | |   (14)  all_54_9 = e1
% 151.14/21.97  | | | 
% 151.14/21.97  | | | REF_CLOSE: (1), (3), (14) are inconsistent by sub-proof #179.
% 151.14/21.97  | | | 
% 151.14/21.97  | | Case 2:
% 151.14/21.97  | | | 
% 151.14/21.97  | | | 
% 151.14/21.97  | | | GROUND_INST: instantiating (5) with all_22_1, all_34_1, e1, e3,
% 151.14/21.97  | | |              simplifying with (2), (6) gives:
% 151.14/21.97  | | |   (15)  all_34_1 = all_22_1
% 151.14/21.97  | | | 
% 151.14/21.97  | | | GROUND_INST: instantiating (5) with e0, all_34_1, e1, e3, simplifying with
% 151.14/21.97  | | |              (2), (9) gives:
% 151.14/21.97  | | |   (16)  all_34_1 = e0
% 151.14/21.97  | | | 
% 151.14/21.97  | | | GROUND_INST: instantiating (5) with e2, all_22_0, e3, e0, simplifying with
% 151.14/21.97  | | |              (7) gives:
% 151.14/21.97  | | |   (17)  all_22_0 = e2 |  ~ (op(e0, e3) = all_22_0)
% 151.14/21.97  | | | 
% 151.14/21.97  | | | COMBINE_EQS: (15), (16) imply:
% 151.14/21.97  | | |   (18)  all_22_1 = e0
% 151.14/21.97  | | | 
% 151.14/21.97  | | | REDUCE: (10), (18) imply:
% 151.14/21.97  | | |   (19)  op(e0, e3) = all_22_0
% 151.14/21.97  | | | 
% 151.14/21.97  | | | BETA: splitting (17) gives:
% 151.14/21.97  | | | 
% 151.14/21.97  | | | Case 1:
% 151.14/21.97  | | | | 
% 151.14/21.97  | | | |   (20)   ~ (op(e0, e3) = all_22_0)
% 151.14/21.97  | | | | 
% 151.14/21.97  | | | | PRED_UNIFY: (19), (20) imply:
% 151.14/21.97  | | | |   (21)  $false
% 151.14/21.97  | | | | 
% 151.14/21.97  | | | | CLOSE: (21) is inconsistent.
% 151.14/21.97  | | | | 
% 151.14/21.97  | | | Case 2:
% 151.14/21.97  | | | | 
% 151.14/21.97  | | | |   (22)  all_22_0 = e2
% 151.14/21.97  | | | | 
% 151.14/21.97  | | | | REDUCE: (8), (22) imply:
% 151.14/21.97  | | | |   (23)  $false
% 151.14/21.97  | | | | 
% 151.14/21.97  | | | | CLOSE: (23) is inconsistent.
% 151.14/21.97  | | | | 
% 151.14/21.97  | | | End of split
% 151.14/21.97  | | | 
% 151.14/21.97  | | End of split
% 151.14/21.97  | | 
% 151.14/21.97  | End of split
% 151.14/21.97  | 
% 151.14/21.97  End of proof
% 151.14/21.97  
% 151.14/21.97  Sub-proof #46 shows that the following formulas are inconsistent:
% 151.14/21.97  ----------------------------------------------------------------
% 151.14/21.97    (1)  all_56_4 = e2 & op(e3, e1) = e2
% 151.14/21.97    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.97    (3)  op(e3, e1) = all_52_8
% 151.14/21.97    (4)   ~ (all_52_8 = e2)
% 151.14/21.97  
% 151.14/21.97  Begin of proof
% 151.14/21.97  | 
% 151.14/21.97  | ALPHA: (1) implies:
% 151.14/21.97  |   (5)  op(e3, e1) = e2
% 151.14/21.97  | 
% 151.14/21.97  | GROUND_INST: instantiating (2) with all_52_8, e2, e1, e3, simplifying with
% 151.14/21.97  |              (3), (5) gives:
% 151.14/21.97  |   (6)  all_52_8 = e2
% 151.14/21.97  | 
% 151.14/21.97  | REDUCE: (4), (6) imply:
% 151.14/21.97  |   (7)  $false
% 151.14/21.97  | 
% 151.14/21.97  | CLOSE: (7) is inconsistent.
% 151.14/21.97  | 
% 151.14/21.97  End of proof
% 151.14/21.97  
% 151.14/21.97  Sub-proof #47 shows that the following formulas are inconsistent:
% 151.14/21.97  ----------------------------------------------------------------
% 151.14/21.97    (1)  all_56_6 = e2 & op(e1, e3) = e2
% 151.14/21.97    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.97    (3)  op(e1, e3) = all_52_2
% 151.14/21.97    (4)   ~ (all_52_2 = e2)
% 151.14/21.97  
% 151.14/21.97  Begin of proof
% 151.14/21.97  | 
% 151.14/21.97  | ALPHA: (1) implies:
% 151.14/21.97  |   (5)  op(e1, e3) = e2
% 151.14/21.97  | 
% 151.14/21.97  | GROUND_INST: instantiating (2) with all_52_2, e2, e3, e1, simplifying with
% 151.14/21.97  |              (3), (5) gives:
% 151.14/21.97  |   (6)  all_52_2 = e2
% 151.14/21.97  | 
% 151.14/21.97  | REDUCE: (4), (6) imply:
% 151.14/21.97  |   (7)  $false
% 151.14/21.97  | 
% 151.14/21.97  | CLOSE: (7) is inconsistent.
% 151.14/21.97  | 
% 151.14/21.97  End of proof
% 151.14/21.97  
% 151.14/21.97  Sub-proof #48 shows that the following formulas are inconsistent:
% 151.14/21.97  ----------------------------------------------------------------
% 151.14/21.97    (1)  op(e0, e1) = all_52_11
% 151.14/21.97    (2)   ~ (all_14_2 = e0)
% 151.14/21.97    (3)   ~ (all_52_2 = all_52_6)
% 151.14/21.97    (4)  op(e3, e3) = all_14_2
% 151.14/21.97    (5)  op(e0, e0) = all_10_2
% 151.14/21.97    (6)  op(e3, e2) = all_52_4
% 151.14/21.97    (7)  op(e1, e1) = e2
% 151.14/21.97    (8)  op(e0, e2) = all_52_7
% 151.14/21.97    (9)   ~ (all_52_14 = e2)
% 151.14/21.97    (10)   ~ (all_52_3 = all_52_7)
% 151.14/21.97    (11)   ~ (all_52_8 = all_14_2)
% 151.14/21.97    (12)  op(e1, e1) = all_4_2
% 151.14/21.97    (13)   ~ (all_10_2 = e1)
% 151.14/21.97    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.97            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.97    (15)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.14/21.97          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.14/21.97    (16)   ~ (all_52_4 = all_14_2)
% 151.14/21.97    (17)  op(e3, e3) = e2
% 151.14/21.97    (18)  op(e0, e0) = e2
% 151.14/21.97    (19)  op(e1, e0) = all_52_14
% 151.14/21.97    (20)   ~ (all_52_13 = e2)
% 151.14/21.97    (21)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 151.14/21.97    (22)  op(e1, e2) = all_52_6
% 151.14/21.97    (23)  op(e2, e0) = all_52_13
% 151.14/21.97    (24)   ~ (all_52_9 = e2)
% 151.14/21.97    (25)  op(e0, e3) = all_52_3
% 151.14/21.97    (26)  all_54_0 = all_14_2
% 151.14/21.97    (27)  op(e2, e1) = all_52_9
% 151.14/21.97    (28)   ~ (all_52_1 = all_14_2)
% 151.14/21.97    (29)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.14/21.97          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.14/21.97    (30)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.14/21.97              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/21.97            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.14/21.97                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.14/21.97              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/21.97          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.14/21.97              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/21.97            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.14/21.97                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.14/21.97              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/21.97          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 151.14/21.97              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/21.97            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 151.14/21.97                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 151.14/21.97              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/21.97          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 151.14/21.97              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/21.97            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 151.14/21.97                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 151.14/21.97                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.14/21.97                $i(all_57_14))))
% 151.14/21.97    (31)   ~ (e3 = e2)
% 151.14/21.97    (32)   ~ (all_52_1 = all_52_2)
% 151.14/21.97    (33)   ~ (all_14_2 = e1)
% 151.14/21.97    (34)  op(e3, e1) = all_52_8
% 151.14/21.97    (35)   ~ (all_52_8 = all_52_9)
% 151.14/21.97    (36)  op(e1, e3) = all_52_2
% 151.14/21.97    (37)   ~ (all_52_11 = e2)
% 151.14/21.97    (38)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.14/21.97              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.14/21.97            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.14/21.97            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.14/21.97            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.14/21.97            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.14/21.97            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 151.14/21.97            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.14/21.97            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 151.14/21.97            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 151.14/21.97            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.14/21.97            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 151.14/21.97            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.14/21.97            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.14/21.97            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 151.14/21.97            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.14/21.97            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.14/21.97            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 151.14/21.97            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/21.97            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 151.14/21.97            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 151.14/21.97            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.14/21.97            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.14/21.97            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 151.14/21.97            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/21.97            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.14/21.97            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.14/21.97            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/21.97            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/21.97            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 151.14/21.97            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.14/21.97            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.14/21.97            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.14/21.97            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.14/21.97            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/21.97            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 151.14/21.97            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/21.97            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.14/21.97            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 151.14/21.97            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/21.97            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.14/21.97            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 151.14/21.97            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.14/21.97            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 151.14/21.97            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 151.14/21.97            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.14/21.97            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 151.14/21.97            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 151.14/21.97              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 151.14/21.97            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.14/21.97            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 151.14/21.97              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.14/21.97            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.14/21.97            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 151.14/21.97                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 151.14/21.97                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.14/21.97                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.14/21.97                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 151.14/21.97                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 151.14/21.97                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 151.14/21.97                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.14/21.97              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 151.14/21.97                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.14/21.97                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/21.97                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.14/21.97                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 151.14/21.97                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.14/21.97                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/21.97                $i(all_57_7))))
% 151.14/21.97    (39)  op(e2, e3) = all_52_1
% 151.14/21.97    (40)   ~ (all_52_6 = e2)
% 151.14/21.97  
% 151.14/21.97  Begin of proof
% 151.14/21.97  | 
% 151.14/21.97  | GROUND_INST: instantiating (14) with all_14_2, e2, e3, e3, simplifying with
% 151.14/21.97  |              (4), (17) gives:
% 151.14/21.97  |   (41)  all_14_2 = e2
% 151.14/21.97  | 
% 151.14/21.97  | REDUCE: (28), (41) imply:
% 151.14/21.97  |   (42)   ~ (all_52_1 = e2)
% 151.14/21.97  | 
% 151.14/21.97  | REDUCE: (33), (41) imply:
% 151.14/21.97  |   (43)   ~ (e2 = e1)
% 151.14/21.97  | 
% 151.14/21.97  | REDUCE: (2), (41) imply:
% 151.14/21.97  |   (44)   ~ (e2 = e0)
% 151.14/21.97  | 
% 151.14/21.97  | BETA: splitting (30) gives:
% 151.14/21.97  | 
% 151.14/21.97  | Case 1:
% 151.14/21.97  | | 
% 151.14/21.97  | |   (45)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 151.14/21.97  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 151.14/21.97  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 151.14/21.97  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.14/21.97  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 151.14/21.97  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 151.14/21.97  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 151.14/21.97  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/21.97  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 151.14/21.97  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 151.14/21.97  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 151.14/21.97  | |               $i(all_57_15))))
% 151.14/21.97  | | 
% 151.14/21.97  | | BETA: splitting (45) gives:
% 151.14/21.97  | | 
% 151.14/21.97  | | Case 1:
% 151.14/21.97  | | | 
% 151.14/21.97  | | |   (46)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 151.14/21.97  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 151.14/21.97  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 151.14/21.97  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.14/21.97  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 151.14/21.97  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.14/21.97  | | | 
% 151.14/21.97  | | | ALPHA: (46) implies:
% 151.14/21.97  | | |   (47)  op(e3, e3) = e3
% 151.14/21.97  | | | 
% 151.14/21.97  | | | REF_CLOSE: (14), (17), (31), (47) are inconsistent by sub-proof #1085.
% 151.14/21.97  | | | 
% 151.14/21.97  | | Case 2:
% 151.14/21.97  | | | 
% 151.14/21.97  | | |   (48)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 151.14/21.97  | | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.14/21.97  | | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 151.14/21.97  | | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.14/21.97  | | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 151.14/21.97  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.14/21.97  | | | 
% 151.14/21.97  | | | ALPHA: (48) implies:
% 151.14/21.97  | | |   (49)  op(e2, e2) = e2
% 151.14/21.97  | | |   (50)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 151.14/21.97  | | |             e0) = all_57_15 & $i(all_57_15))
% 151.14/21.97  | | |   (51)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3,
% 151.14/21.97  | | |             e3) = all_57_10 & $i(all_57_10))
% 151.14/21.97  | | | 
% 151.14/21.97  | | | BETA: splitting (38) gives:
% 151.14/21.97  | | | 
% 151.14/21.97  | | | Case 1:
% 151.14/21.97  | | | | 
% 151.14/21.97  | | | |   (52)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.14/21.97  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.14/21.97  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 151.14/21.97  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 151.14/21.97  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 151.14/21.97  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 151.14/21.97  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.14/21.97  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 151.14/21.97  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 151.14/21.97  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 151.14/21.97  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 151.14/21.97  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 151.14/21.97  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 151.14/21.97  | | | |           $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 151.14/21.97  | | | |           (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 151.14/21.97  | | | |           & op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.14/21.97  | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 =
% 151.14/21.97  | | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 151.14/21.97  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 151.14/21.97  | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 151.14/21.97  | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 151.14/21.97  | | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 151.14/21.97  | | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 151.14/21.97  | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 151.14/21.97  | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.14/21.97  | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.14/21.97  | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 151.14/21.97  | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 151.14/21.97  | | | |           & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.14/21.97  | | | |           $i(all_57_7) & $i(all_57_10))
% 151.14/21.97  | | | | 
% 151.14/21.97  | | | | BETA: splitting (52) gives:
% 151.14/21.97  | | | | 
% 151.14/21.97  | | | | Case 1:
% 151.14/21.97  | | | | | 
% 151.14/21.97  | | | | |   (53)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.14/21.97  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 151.14/21.97  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 151.14/21.97  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 151.14/21.97  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 151.14/21.97  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 151.14/21.97  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.14/21.97  | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 151.14/21.97  | | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 151.14/21.97  | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 151.14/21.97  | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 151.14/21.97  | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 151.14/21.97  | | | | |           & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 151.14/21.97  | | | | |           $i(all_57_14))
% 151.14/21.97  | | | | | 
% 151.14/21.97  | | | | | REF_CLOSE: (14), (18), (31), (39), (42), (49), (53) are inconsistent
% 151.14/21.97  | | | | |            by sub-proof #1000.
% 151.14/21.97  | | | | | 
% 151.14/21.97  | | | | Case 2:
% 151.14/21.97  | | | | | 
% 151.14/21.97  | | | | |   (54)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/21.97  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 151.14/21.97  | | | | |           & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 151.14/21.97  | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 151.14/21.97  | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 151.14/21.97  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 151.14/21.97  | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1
% 151.14/21.97  | | | | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2)
% 151.14/21.97  | | | | |           & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1
% 151.14/21.97  | | | | |           & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 151.14/21.97  | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 151.14/21.97  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 151.14/21.97  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.14/21.97  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 151.14/21.97  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.14/21.97  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 151.14/21.97  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.14/21.97  | | | | | 
% 151.14/21.97  | | | | | BETA: splitting (54) gives:
% 151.14/21.97  | | | | | 
% 151.14/21.97  | | | | | Case 1:
% 151.14/21.97  | | | | | | 
% 151.14/21.97  | | | | | |   (55)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/21.97  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 151.14/21.97  | | | | | |           e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.14/21.97  | | | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15
% 151.14/21.97  | | | | | |           = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3,
% 151.14/21.97  | | | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 151.14/21.97  | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 151.14/21.97  | | | | | | 
% 151.14/21.97  | | | | | | BETA: splitting (55) gives:
% 151.14/21.97  | | | | | | 
% 151.14/21.97  | | | | | | Case 1:
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | |   (56)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/21.97  | | | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 151.14/21.97  | | | | | | |         e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.14/21.97  | | | | | | |         $i(all_57_4) & $i(all_57_10)
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | | ALPHA: (56) implies:
% 151.14/21.97  | | | | | | |   (57)   ~ (all_57_10 = e2)
% 151.14/21.97  | | | | | | |   (58)  op(e3, e3) = all_57_10
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | | REF_CLOSE: (14), (17), (57), (58) are inconsistent by sub-proof
% 151.14/21.97  | | | | | | |            #1031.
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | Case 2:
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | |   (59)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 151.14/21.97  | | | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 151.14/21.97  | | | | | | |         e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.14/21.97  | | | | | | |         $i(all_57_5) & $i(all_57_10)
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | | ALPHA: (59) implies:
% 151.14/21.97  | | | | | | |   (60)   ~ (all_57_5 = e0)
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | | REF_CLOSE: (14), (18), (50), (60) are inconsistent by sub-proof
% 151.14/21.97  | | | | | | |            #525.
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | End of split
% 151.14/21.97  | | | | | | 
% 151.14/21.97  | | | | | Case 2:
% 151.14/21.97  | | | | | | 
% 151.14/21.97  | | | | | |   (61)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.14/21.97  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3
% 151.14/21.97  | | | | | |           & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3)
% 151.14/21.97  | | | | | |           & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 151.14/21.97  | | | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 151.14/21.97  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 151.14/21.97  | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 =
% 151.14/21.97  | | | | | |           e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 151.14/21.97  | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 151.14/21.97  | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.14/21.97  | | | | | |           $i(all_57_10))
% 151.14/21.97  | | | | | | 
% 151.14/21.97  | | | | | | BETA: splitting (61) gives:
% 151.14/21.97  | | | | | | 
% 151.14/21.97  | | | | | | Case 1:
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | |   (62)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.14/21.97  | | | | | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3
% 151.14/21.97  | | | | | | |         & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3)
% 151.14/21.97  | | | | | | |         & $i(all_57_14)
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | | ALPHA: (62) implies:
% 151.14/21.97  | | | | | | |   (63)  all_57_10 = e2
% 151.14/21.97  | | | | | | |   (64)   ~ (all_57_3 = e3)
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | | REF_CLOSE: (51), (63), (64) are inconsistent by sub-proof #1018.
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | Case 2:
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | |   (65)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 151.14/21.97  | | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 151.14/21.97  | | | | | | |           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.14/21.97  | | | | | | |           $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 151.14/21.97  | | | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 151.14/21.97  | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/21.97  | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.14/21.97  | | | | | | |           $i(all_57_10))
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | | BETA: splitting (65) gives:
% 151.14/21.97  | | | | | | | 
% 151.14/21.97  | | | | | | | Case 1:
% 151.14/21.97  | | | | | | | | 
% 151.14/21.97  | | | | | | | |   (66)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 151.14/21.97  | | | | | | | |         (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 151.14/21.97  | | | | | | | |         all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.14/21.97  | | | | | | | |         $i(all_57_5) & $i(all_57_14)
% 151.14/21.97  | | | | | | | | 
% 151.14/21.97  | | | | | | | | ALPHA: (66) implies:
% 151.14/21.97  | | | | | | | |   (67)   ~ (all_57_5 = e0)
% 151.14/21.97  | | | | | | | | 
% 151.14/21.97  | | | | | | | | REF_CLOSE: (14), (18), (50), (67) are inconsistent by sub-proof
% 151.14/21.97  | | | | | | | |            #525.
% 151.14/21.97  | | | | | | | | 
% 151.14/21.97  | | | | | | | Case 2:
% 151.14/21.97  | | | | | | | | 
% 151.14/21.97  | | | | | | | |   (68)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.14/21.98  | | | | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 151.14/21.98  | | | | | | | |         e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.14/21.98  | | | | | | | |         $i(all_57_7) & $i(all_57_10)
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | | ALPHA: (68) implies:
% 151.14/21.98  | | | | | | | |   (69)  op(e2, e2) = e1
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | | REF_CLOSE: (7), (12), (14), (17), (18), (30), (31), (43), (44),
% 151.14/21.98  | | | | | | | |            (69) are inconsistent by sub-proof #706.
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | End of split
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | End of split
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | End of split
% 151.14/21.98  | | | | | 
% 151.14/21.98  | | | | End of split
% 151.14/21.98  | | | | 
% 151.14/21.98  | | | Case 2:
% 151.14/21.98  | | | | 
% 151.14/21.98  | | | |   (70)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/21.98  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/21.98  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/21.98  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 151.14/21.98  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 151.14/21.98  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 151.14/21.98  | | | |           e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 151.14/21.98  | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 151.14/21.98  | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 151.14/21.98  | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 151.14/21.98  | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/21.98  | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/21.98  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.14/21.98  | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 151.14/21.98  | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 151.14/21.98  | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 151.14/21.98  | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0 &
% 151.14/21.98  | | | |           all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 = e0) &
% 151.14/21.98  | | | |           op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 151.14/21.98  | | | |           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 151.14/21.98  | | | |         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 151.14/21.98  | | | |           (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.14/21.98  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 151.14/21.98  | | | |           $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 151.14/21.98  | | | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 151.14/21.98  | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 151.14/21.98  | | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 151.14/21.98  | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 151.14/21.98  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 151.14/21.98  | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 151.14/21.98  | | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 151.14/21.98  | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3)
% 151.14/21.98  | | | |               & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 151.14/21.98  | | | |               e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 151.14/21.98  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 151.14/21.98  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.14/21.98  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/21.98  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 151.14/21.98  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.14/21.98  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/21.98  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 151.14/21.98  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 151.14/21.98  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 151.14/21.98  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 151.14/21.98  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/21.98  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 151.14/21.98  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 151.14/21.98  | | | | 
% 151.14/21.98  | | | | BETA: splitting (70) gives:
% 151.14/21.98  | | | | 
% 151.14/21.98  | | | | Case 1:
% 151.14/21.98  | | | | | 
% 151.14/21.98  | | | | |   (71)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/21.98  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 151.14/21.98  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/21.98  | | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 151.14/21.98  | | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 151.14/21.98  | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 151.14/21.98  | | | | |           = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 151.14/21.98  | | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 151.14/21.98  | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 151.14/21.98  | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 151.14/21.98  | | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/21.98  | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 151.14/21.98  | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.14/21.98  | | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 151.14/21.98  | | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 151.14/21.98  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 151.14/21.98  | | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 151.14/21.98  | | | | | 
% 151.14/21.98  | | | | | BETA: splitting (71) gives:
% 151.14/21.98  | | | | | 
% 151.14/21.98  | | | | | Case 1:
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | |   (72)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/21.98  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 151.14/21.98  | | | | | |           e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 151.14/21.98  | | | | | |           $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 & all_57_10
% 151.14/21.98  | | | | | |           = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3,
% 151.14/21.98  | | | | | |             e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 151.14/21.98  | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.14/21.98  | | | | | |           $i(all_57_12))
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | | REF_CLOSE: (14), (18), (24), (27), (43), (72) are inconsistent by
% 151.14/21.98  | | | | | |            sub-proof #977.
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | Case 2:
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | |   (73)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/21.98  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 151.14/21.98  | | | | | |           e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 151.14/21.98  | | | | | |           $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12
% 151.14/21.98  | | | | | |           = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3,
% 151.14/21.98  | | | | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 151.14/21.98  | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 151.14/21.98  | | | | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/21.98  | | | | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 151.14/21.98  | | | | | |           e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.14/21.98  | | | | | |           $i(all_57_10) & $i(all_57_13))
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | | BETA: splitting (73) gives:
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | | Case 1:
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | |   (74)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/21.98  | | | | | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 151.14/21.98  | | | | | | |         e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 151.14/21.98  | | | | | | |         $i(all_57_8) & $i(all_57_12)
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | | ALPHA: (74) implies:
% 151.14/21.98  | | | | | | |   (75)  op(e0, e0) = e1
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | | REF_CLOSE: (14), (18), (43), (75) are inconsistent by sub-proof
% 151.14/21.98  | | | | | | |            #978.
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | Case 2:
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | |   (76)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/21.98  | | | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 151.14/21.98  | | | | | | |           e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 151.14/21.98  | | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 151.14/21.98  | | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 =
% 151.14/21.98  | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/21.98  | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10)
% 151.14/21.98  | | | | | | |           & $i(all_57_13))
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | | BETA: splitting (76) gives:
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | | Case 1:
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | |   (77)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) & 
% 151.14/21.98  | | | | | | | |         ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0)
% 151.14/21.98  | | | | | | | |         = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 151.14/21.98  | | | | | | | |         $i(all_57_10) & $i(all_57_11)
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | | ALPHA: (77) implies:
% 151.14/21.98  | | | | | | | |   (78)  op(e2, e2) = e0
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | | REF_CLOSE: (7), (12), (14), (17), (18), (30), (31), (43), (44),
% 151.14/21.98  | | | | | | | |            (78) are inconsistent by sub-proof #629.
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | Case 2:
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | |   (79)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) & 
% 151.14/21.98  | | | | | | | |         ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 151.14/21.98  | | | | | | | |         = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.14/21.98  | | | | | | | |         $i(all_57_10) & $i(all_57_13)
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | | ALPHA: (79) implies:
% 151.14/21.98  | | | | | | | |   (80)  op(e1, e1) = e0
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | | REF_CLOSE: (7), (14), (44), (80) are inconsistent by sub-proof
% 151.14/21.98  | | | | | | | |            #1006.
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | End of split
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | End of split
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | End of split
% 151.14/21.98  | | | | | 
% 151.14/21.98  | | | | Case 2:
% 151.14/21.98  | | | | | 
% 151.14/21.98  | | | | |   (81)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 151.14/21.98  | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.14/21.98  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 151.14/21.98  | | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 151.14/21.98  | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 151.14/21.98  | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 151.14/21.98  | | | | |           = e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 151.14/21.98  | | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 151.14/21.98  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 151.14/21.98  | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 151.14/21.98  | | | | |         (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 151.14/21.98  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.14/21.98  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.14/21.98  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 151.14/21.98  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/21.98  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 151.14/21.98  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 151.14/21.98  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 151.14/21.98  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.14/21.98  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 151.14/21.98  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 151.14/21.98  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/21.98  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 151.14/21.98  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.14/21.98  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/21.98  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/21.98  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 151.14/21.98  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/21.98  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/21.98  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 151.14/21.98  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/21.98  | | | | |               $i(all_57_7))))
% 151.14/21.98  | | | | | 
% 151.14/21.98  | | | | | BETA: splitting (81) gives:
% 151.14/21.98  | | | | | 
% 151.14/21.98  | | | | | Case 1:
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | |   (82)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 151.14/21.98  | | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9
% 151.14/21.98  | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 151.14/21.98  | | | | | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 151.14/21.98  | | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 151.14/21.98  | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1,
% 151.14/21.98  | | | | | |             e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | | REF_CLOSE: (14), (17), (44), (82) are inconsistent by sub-proof
% 151.14/21.98  | | | | | |            #1037.
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | Case 2:
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | |   (83)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 151.14/21.98  | | | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.14/21.98  | | | | | |           e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.14/21.98  | | | | | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 151.14/21.98  | | | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0)
% 151.14/21.98  | | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 151.14/21.98  | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.14/21.98  | | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 151.14/21.98  | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/21.98  | | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2)
% 151.14/21.98  | | | | | |               = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 =
% 151.14/21.98  | | | | | |               e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.14/21.98  | | | | | |               (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1)
% 151.14/21.98  | | | | | |               = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 151.14/21.98  | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.14/21.98  | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/21.98  | | | | | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5
% 151.14/21.98  | | | | | |               = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/21.98  | | | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1)
% 151.14/21.98  | | | | | |               = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 151.14/21.98  | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.14/21.98  | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 151.14/21.98  | | | | | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 151.14/21.98  | | | | | |               = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.14/21.98  | | | | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 151.14/21.98  | | | | | |               all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | | BETA: splitting (83) gives:
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | | Case 1:
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | |   (84)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 151.14/21.98  | | | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 151.14/21.98  | | | | | | |         e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.14/21.98  | | | | | | |         $i(all_57_12) & $i(all_57_13)
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | | ALPHA: (84) implies:
% 151.14/21.98  | | | | | | |   (85)  op(e2, e0) = e2
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | | REF_CLOSE: (14), (20), (23), (85) are inconsistent by sub-proof
% 151.14/21.98  | | | | | | |            #1156.
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | Case 2:
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | |   (86)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 151.14/21.98  | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 151.14/21.98  | | | | | | |           all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.14/21.98  | | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 151.14/21.98  | | | | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 151.14/21.98  | | | | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 151.14/21.98  | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.14/21.98  | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 151.14/21.98  | | | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 151.14/21.98  | | | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.14/21.98  | | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/21.98  | | | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 151.14/21.98  | | | | | | |               e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/21.98  | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 151.14/21.98  | | | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.14/21.98  | | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/21.98  | | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/21.98  | | | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 151.14/21.98  | | | | | | |               e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/21.98  | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/21.98  | | | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 151.14/21.98  | | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/21.98  | | | | | | |               $i(all_57_7))))
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | | BETA: splitting (86) gives:
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | | Case 1:
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | |   (87)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 151.14/21.98  | | | | | | | |         ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 151.14/21.98  | | | | | | | |         all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.14/21.98  | | | | | | | |         $i(all_57_11) & $i(all_57_14)
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | | ALPHA: (87) implies:
% 151.14/21.98  | | | | | | | |   (88)  op(e2, e2) = e0
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | | REF_CLOSE: (7), (12), (14), (17), (18), (30), (31), (43), (44),
% 151.14/21.98  | | | | | | | |            (88) are inconsistent by sub-proof #629.
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | Case 2:
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | |   (89)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0
% 151.14/21.98  | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/21.98  | | | | | | | |             (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 151.14/21.98  | | | | | | | |               e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 151.14/21.98  | | | | | | | |           (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 151.14/21.98  | | | | | | | |              ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 151.14/21.98  | | | | | | | |               e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 151.14/21.98  | | | | | | | |           (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &
% 151.14/21.98  | | | | | | | |              ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/21.98  | | | | | | | |             all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.14/21.98  | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &
% 151.14/21.98  | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 151.14/21.98  | | | | | | | |               e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 151.14/21.98  | | | | | | | |           (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &
% 151.14/21.98  | | | | | | | |              ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 151.14/21.98  | | | | | | | |             all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 151.14/21.98  | | | | | | | |           (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 151.14/21.98  | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 151.14/21.98  | | | | | | | |             all_57_7 & op(e0, e1) = e0 & $i(all_57_7)))
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | | ALPHA: (89) implies:
% 151.14/21.98  | | | | | | | |   (90)  op(e0, e0) = all_57_15
% 151.14/21.98  | | | | | | | |   (91)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 151.14/21.98  | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 151.14/21.98  | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 151.14/21.98  | | | | | | | |         (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 151.14/21.98  | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 151.14/21.98  | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 151.14/21.98  | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 151.14/21.98  | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/21.98  | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5
% 151.14/21.98  | | | | | | | |           = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/21.98  | | | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1)
% 151.14/21.98  | | | | | | | |           = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 151.14/21.98  | | | | | | | |           e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.14/21.98  | | | | | | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 151.14/21.98  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 151.14/21.98  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.14/21.98  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 151.14/21.98  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | | BETA: splitting (91) gives:
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | | Case 1:
% 151.14/21.98  | | | | | | | | | 
% 151.14/21.98  | | | | | | | | |   (92)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &
% 151.14/21.98  | | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 151.14/21.98  | | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 151.14/21.98  | | | | | | | | |         (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 151.14/21.98  | | | | | | | | |            ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 151.14/21.98  | | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 151.14/21.98  | | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &
% 151.14/21.98  | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/21.98  | | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 151.14/21.98  | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | BETA: splitting (92) gives:
% 151.14/21.98  | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | Case 1:
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | |   (93)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2)
% 151.14/21.98  | | | | | | | | | |         &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 151.14/21.98  | | | | | | | | | |         op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | ALPHA: (93) implies:
% 151.14/21.98  | | | | | | | | | |   (94)  op(e2, e2) = e3
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | REF_CLOSE: (14), (31), (49), (94) are inconsistent by
% 151.14/21.98  | | | | | | | | | |            sub-proof #1179.
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | Case 2:
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | |   (95)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 151.14/21.98  | | | | | | | | | |           &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 151.14/21.98  | | | | | | | | | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 151.14/21.98  | | | | | | | | | |         | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 151.14/21.98  | | | | | | | | | |             e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 151.14/21.98  | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/21.98  | | | | | | | | | |           $i(all_57_3))
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | BETA: splitting (95) gives:
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | Case 1:
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | |   (96)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.14/21.98  | | | | | | | | | | |           e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 151.14/21.98  | | | | | | | | | | |         all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.14/21.98  | | | | | | | | | | |         $i(all_57_1)
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | | ALPHA: (96) implies:
% 151.14/21.98  | | | | | | | | | | |   (97)  op(e1, e1) = e3
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10),
% 151.14/21.98  | | | | | | | | | | |            (11), (13), (14), (15), (16), (18), (19), (20),
% 151.14/21.98  | | | | | | | | | | |            (21), (22), (23), (24), (25), (26), (27), (29),
% 151.14/21.98  | | | | | | | | | | |            (30), (31), (32), (33), (34), (35), (36), (37),
% 151.14/21.98  | | | | | | | | | | |            (38), (39), (40), (43), (44), (49), (97) are
% 151.14/21.98  | | | | | | | | | | |            inconsistent by sub-proof #288.
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | Case 2:
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | |   (98)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 151.14/21.98  | | | | | | | | | | |           e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 151.14/21.98  | | | | | | | | | | |         op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/21.98  | | | | | | | | | | |         $i(all_57_3)
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | | ALPHA: (98) implies:
% 151.14/21.98  | | | | | | | | | | |   (99)   ~ (all_57_15 = e2)
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | | REF_CLOSE: (14), (18), (90), (99) are inconsistent by
% 151.14/21.98  | | | | | | | | | | |            sub-proof #901.
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | End of split
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | End of split
% 151.14/21.98  | | | | | | | | | 
% 151.14/21.98  | | | | | | | | Case 2:
% 151.14/21.98  | | | | | | | | | 
% 151.14/21.98  | | | | | | | | |   (100)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1)
% 151.14/21.98  | | | | | | | | |            &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 &
% 151.14/21.98  | | | | | | | | |            op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 151.14/21.98  | | | | | | | | |          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 151.14/21.98  | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.14/21.98  | | | | | | | | |              e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6))
% 151.14/21.98  | | | | | | | | |          | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 151.14/21.98  | | | | | | | | |              e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 151.14/21.98  | | | | | | | | |            op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/21.98  | | | | | | | | |            $i(all_57_7))
% 151.14/21.98  | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | BETA: splitting (100) gives:
% 151.14/21.98  | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | Case 1:
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | |   (101)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1)
% 151.14/21.98  | | | | | | | | | |          &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 &
% 151.14/21.98  | | | | | | | | | |          op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | ALPHA: (101) implies:
% 151.14/21.98  | | | | | | | | | |   (102)   ~ (all_57_15 = e2)
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | REF_CLOSE: (14), (18), (90), (102) are inconsistent by
% 151.14/21.98  | | | | | | | | | |            sub-proof #901.
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | Case 2:
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | |   (103)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 151.14/21.98  | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 151.14/21.98  | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/21.98  | | | | | | | | | |            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &
% 151.14/21.98  | | | | | | | | | |             ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 151.14/21.98  | | | | | | | | | |              e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) =
% 151.14/21.98  | | | | | | | | | |            e0 & $i(all_57_7))
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | BETA: splitting (103) gives:
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | Case 1:
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | |   (104)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 151.14/21.98  | | | | | | | | | | |            e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 151.14/21.98  | | | | | | | | | | |          op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/21.98  | | | | | | | | | | |          $i(all_57_6)
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | | ALPHA: (104) implies:
% 151.14/21.98  | | | | | | | | | | |   (105)  op(e3, e3) = e1
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | | REF_CLOSE: (14), (17), (43), (105) are inconsistent by
% 151.14/21.98  | | | | | | | | | | |            sub-proof #1074.
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | Case 2:
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | |   (106)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 151.14/21.98  | | | | | | | | | | |            e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 151.14/21.98  | | | | | | | | | | |          op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/21.98  | | | | | | | | | | |          $i(all_57_7)
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | | ALPHA: (106) implies:
% 151.14/21.98  | | | | | | | | | | |   (107)  op(e2, e2) = e1
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | | REF_CLOSE: (7), (12), (14), (17), (18), (30), (31), (43),
% 151.14/21.98  | | | | | | | | | | |            (44), (107) are inconsistent by sub-proof #706.
% 151.14/21.98  | | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | | End of split
% 151.14/21.98  | | | | | | | | | | 
% 151.14/21.98  | | | | | | | | | End of split
% 151.14/21.98  | | | | | | | | | 
% 151.14/21.98  | | | | | | | | End of split
% 151.14/21.98  | | | | | | | | 
% 151.14/21.98  | | | | | | | End of split
% 151.14/21.98  | | | | | | | 
% 151.14/21.98  | | | | | | End of split
% 151.14/21.98  | | | | | | 
% 151.14/21.98  | | | | | End of split
% 151.14/21.98  | | | | | 
% 151.14/21.98  | | | | End of split
% 151.14/21.98  | | | | 
% 151.14/21.98  | | | End of split
% 151.14/21.98  | | | 
% 151.14/21.98  | | End of split
% 151.14/21.98  | | 
% 151.14/21.98  | Case 2:
% 151.14/21.98  | | 
% 151.14/21.98  | |   (108)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.14/21.98  | |                e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.14/21.98  | |                $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.14/21.98  | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/21.98  | |            ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) &
% 151.14/21.98  | |                op(e0, e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 151.14/21.98  | |            op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 151.14/21.98  | |                (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/21.98  | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 151.14/21.98  | |                op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 151.14/21.98  | |                op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 151.14/21.98  | |                all_57_14 & $i(all_57_14))))
% 151.14/21.98  | | 
% 151.14/21.98  | | REF_CLOSE: (7), (12), (14), (18), (43), (44), (108) are inconsistent by
% 151.14/21.98  | |            sub-proof #707.
% 151.14/21.98  | | 
% 151.14/21.98  | End of split
% 151.14/21.98  | 
% 151.14/21.98  End of proof
% 151.14/21.98  
% 151.14/21.98  Sub-proof #49 shows that the following formulas are inconsistent:
% 151.14/21.98  ----------------------------------------------------------------
% 151.14/21.98    (1)  op(e0, e1) = all_52_11
% 151.14/21.98    (2)  op(e0, e0) = all_10_2
% 151.14/21.98    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.98    (4)   ~ (all_10_2 = e2)
% 151.14/21.98    (5)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 151.14/21.98    (6)   ~ (all_52_11 = e2)
% 151.14/21.98  
% 151.14/21.98  Begin of proof
% 151.14/21.98  | 
% 151.14/21.98  | BETA: splitting (5) gives:
% 151.14/21.98  | 
% 151.14/21.98  | Case 1:
% 151.14/21.98  | | 
% 151.14/21.98  | |   (7)  all_56_14 = e2 & op(e0, e1) = e2
% 151.14/21.98  | | 
% 151.14/21.98  | | ALPHA: (7) implies:
% 151.14/21.98  | |   (8)  op(e0, e1) = e2
% 151.14/21.98  | | 
% 151.14/21.98  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #1092.
% 151.14/21.98  | | 
% 151.14/21.98  | Case 2:
% 151.14/21.98  | | 
% 151.14/21.98  | |   (9)  all_56_15 = e2 & op(e0, e0) = e2
% 151.14/21.98  | | 
% 151.14/21.98  | | ALPHA: (9) implies:
% 151.14/21.98  | |   (10)  op(e0, e0) = e2
% 151.14/21.98  | | 
% 151.14/21.98  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #1097.
% 151.14/21.98  | | 
% 151.14/21.98  | End of split
% 151.14/21.98  | 
% 151.14/21.98  End of proof
% 151.14/21.98  
% 151.14/21.98  Sub-proof #50 shows that the following formulas are inconsistent:
% 151.14/21.98  ----------------------------------------------------------------
% 151.14/21.98    (1)   ~ (e3 = e1)
% 151.14/21.98    (2)  op(e0, e0) = all_10_2
% 151.14/21.98    (3)  op(e0, e2) = all_52_7
% 151.14/21.98    (4)   ~ (all_52_3 = all_52_7)
% 151.14/21.98    (5)   ~ (all_10_2 = e1)
% 151.14/21.98    (6)   ~ (e2 = e0)
% 151.14/21.98    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.98    (8)  op(e0, e0) = e2
% 151.14/21.98    (9)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.14/21.98             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 151.14/21.98               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.14/21.98               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.14/21.99    (10)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.14/21.99          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 151.14/21.99            e3)
% 151.14/21.99    (11)   ~ (e3 = e0)
% 151.14/21.99    (12)  op(e0, e3) = all_52_3
% 151.14/21.99    (13)   ~ (e1 = e0)
% 151.14/21.99    (14)   ~ (e3 = e2)
% 151.14/21.99    (15)  all_56_12 = e2
% 151.14/21.99    (16)   ~ (e2 = e1)
% 151.14/21.99    (17)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.14/21.99          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 151.14/21.99            e1)
% 151.14/21.99  
% 151.14/21.99  Begin of proof
% 151.14/21.99  | 
% 151.14/21.99  | BETA: splitting (10) gives:
% 151.14/21.99  | 
% 151.14/21.99  | Case 1:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (18)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 151.14/21.99  | |           e3)
% 151.14/21.99  | | 
% 151.14/21.99  | | BETA: splitting (18) gives:
% 151.14/21.99  | | 
% 151.14/21.99  | | Case 1:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (19)  all_56_12 = e3 & op(e0, e3) = e3
% 151.14/21.99  | | | 
% 151.14/21.99  | | | ALPHA: (19) implies:
% 151.14/21.99  | | |   (20)  all_56_12 = e3
% 151.14/21.99  | | | 
% 151.14/21.99  | | | REF_CLOSE: (14), (15), (20) are inconsistent by sub-proof #869.
% 151.14/21.99  | | | 
% 151.14/21.99  | | Case 2:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (21)  all_56_13 = e3 & op(e0, e2) = e3
% 151.14/21.99  | | | 
% 151.14/21.99  | | | ALPHA: (21) implies:
% 151.14/21.99  | | |   (22)  all_56_13 = e3
% 151.14/21.99  | | | 
% 151.14/21.99  | | | BETA: splitting (9) gives:
% 151.14/21.99  | | | 
% 151.14/21.99  | | | Case 1:
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | |   (23)  all_56_15 = e0 & op(e0, e0) = e0
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | | ALPHA: (23) implies:
% 151.14/21.99  | | | |   (24)  op(e0, e0) = e0
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | | REF_CLOSE: (6), (7), (8), (24) are inconsistent by sub-proof #1043.
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | Case 2:
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | |   (25)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 151.14/21.99  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 151.14/21.99  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 151.14/21.99  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | | ALPHA: (25) implies:
% 151.14/21.99  | | | |   (26)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 151.14/21.99  | | | |             e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | | BETA: splitting (26) gives:
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | | Case 1:
% 151.14/21.99  | | | | | 
% 151.14/21.99  | | | | |   (27)  all_56_12 = e0 & op(e0, e3) = e0
% 151.14/21.99  | | | | | 
% 151.14/21.99  | | | | | ALPHA: (27) implies:
% 151.14/21.99  | | | | |   (28)  op(e0, e3) = e0
% 151.14/21.99  | | | | | 
% 151.14/21.99  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (12), (13), (15), (16),
% 151.14/21.99  | | | | |            (17), (22), (26), (28) are inconsistent by sub-proof #1115.
% 151.14/21.99  | | | | | 
% 151.14/21.99  | | | | Case 2:
% 151.14/21.99  | | | | | 
% 151.14/21.99  | | | | |   (29)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 151.14/21.99  | | | | |             e1) = e0)
% 151.14/21.99  | | | | | 
% 151.14/21.99  | | | | | BETA: splitting (29) gives:
% 151.14/21.99  | | | | | 
% 151.14/21.99  | | | | | Case 1:
% 151.14/21.99  | | | | | | 
% 151.14/21.99  | | | | | |   (30)  all_56_13 = e0 & op(e0, e2) = e0
% 151.14/21.99  | | | | | | 
% 151.14/21.99  | | | | | | REF_CLOSE: (11), (22), (30) are inconsistent by sub-proof #1102.
% 151.14/21.99  | | | | | | 
% 151.14/21.99  | | | | | Case 2:
% 151.14/21.99  | | | | | | 
% 151.14/21.99  | | | | | |   (31)  all_56_14 = e0 & op(e0, e1) = e0
% 151.14/21.99  | | | | | | 
% 151.14/21.99  | | | | | | ALPHA: (31) implies:
% 151.14/21.99  | | | | | |   (32)  op(e0, e1) = e0
% 151.14/21.99  | | | | | | 
% 151.14/21.99  | | | | | | BETA: splitting (17) gives:
% 151.14/21.99  | | | | | | 
% 151.14/21.99  | | | | | | Case 1:
% 151.14/21.99  | | | | | | | 
% 151.14/21.99  | | | | | | |   (33)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 &
% 151.14/21.99  | | | | | | |           op(e0, e2) = e1)
% 151.14/21.99  | | | | | | | 
% 151.14/21.99  | | | | | | | REF_CLOSE: (1), (15), (16), (22), (33) are inconsistent by
% 151.14/21.99  | | | | | | |            sub-proof #1120.
% 151.14/21.99  | | | | | | | 
% 151.14/21.99  | | | | | | Case 2:
% 151.14/21.99  | | | | | | | 
% 151.14/21.99  | | | | | | |   (34)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 &
% 151.14/21.99  | | | | | | |           op(e0, e0) = e1)
% 151.14/21.99  | | | | | | | 
% 151.14/21.99  | | | | | | | REF_CLOSE: (7), (8), (13), (16), (32), (34) are inconsistent by
% 151.14/21.99  | | | | | | |            sub-proof #75.
% 151.14/21.99  | | | | | | | 
% 151.14/21.99  | | | | | | End of split
% 151.14/21.99  | | | | | | 
% 151.14/21.99  | | | | | End of split
% 151.14/21.99  | | | | | 
% 151.14/21.99  | | | | End of split
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | End of split
% 151.14/21.99  | | | 
% 151.14/21.99  | | End of split
% 151.14/21.99  | | 
% 151.14/21.99  | Case 2:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (35)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 151.14/21.99  | |           e3)
% 151.14/21.99  | | 
% 151.14/21.99  | | BETA: splitting (35) gives:
% 151.14/21.99  | | 
% 151.14/21.99  | | Case 1:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (36)  all_56_14 = e3 & op(e0, e1) = e3
% 151.14/21.99  | | | 
% 151.14/21.99  | | | ALPHA: (36) implies:
% 151.14/21.99  | | |   (37)  all_56_14 = e3
% 151.14/21.99  | | | 
% 151.14/21.99  | | | REF_CLOSE: (1), (6), (7), (8), (9), (11), (13), (15), (16), (17), (37) are
% 151.14/21.99  | | |            inconsistent by sub-proof #106.
% 151.14/21.99  | | | 
% 151.14/21.99  | | Case 2:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (38)  all_56_15 = e3 & op(e0, e0) = e3
% 151.14/21.99  | | | 
% 151.14/21.99  | | | ALPHA: (38) implies:
% 151.14/21.99  | | |   (39)  op(e0, e0) = e3
% 151.14/21.99  | | | 
% 151.14/21.99  | | | REF_CLOSE: (7), (8), (14), (39) are inconsistent by sub-proof #1087.
% 151.14/21.99  | | | 
% 151.14/21.99  | | End of split
% 151.14/21.99  | | 
% 151.14/21.99  | End of split
% 151.14/21.99  | 
% 151.14/21.99  End of proof
% 151.14/21.99  
% 151.14/21.99  Sub-proof #51 shows that the following formulas are inconsistent:
% 151.14/21.99  ----------------------------------------------------------------
% 151.14/21.99    (1)  op(e1, e1) = e2
% 151.14/21.99    (2)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 151.14/21.99             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/21.99           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 151.14/21.99               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 151.14/21.99             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/21.99         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 151.14/21.99             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/21.99           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 151.14/21.99               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 151.14/21.99             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 151.14/21.99    (3)  op(e1, e1) = all_4_2
% 151.14/21.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.99    (5)  op(e0, e0) = e3
% 151.14/21.99    (6)   ~ (e3 = e0)
% 151.14/21.99    (7)   ~ (e2 = e1)
% 151.14/21.99  
% 151.14/21.99  Begin of proof
% 151.14/21.99  | 
% 151.14/21.99  | BETA: splitting (2) gives:
% 151.14/21.99  | 
% 151.14/21.99  | Case 1:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (8)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3)
% 151.14/21.99  | |          | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/21.99  | |        ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 151.14/21.99  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 151.14/21.99  | |              e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 151.14/21.99  | |            $i(all_57_15)))
% 151.14/21.99  | | 
% 151.14/21.99  | | ALPHA: (8) implies:
% 151.14/21.99  | |   (9)  op(e1, e1) = e1
% 151.14/21.99  | | 
% 151.14/21.99  | | REF_CLOSE: (1), (3), (4), (7), (9) are inconsistent by sub-proof #1044.
% 151.14/21.99  | | 
% 151.14/21.99  | Case 2:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (10)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 151.14/21.99  | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.14/21.99  | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 151.14/21.99  | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/21.99  | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 151.14/21.99  | |               e1) = all_57_14 & $i(all_57_14)))
% 151.14/21.99  | | 
% 151.14/21.99  | | ALPHA: (10) implies:
% 151.14/21.99  | |   (11)  op(e0, e0) = e0
% 151.14/21.99  | | 
% 151.14/21.99  | | REF_CLOSE: (4), (5), (6), (11) are inconsistent by sub-proof #1143.
% 151.14/21.99  | | 
% 151.14/21.99  | End of split
% 151.14/21.99  | 
% 151.14/21.99  End of proof
% 151.14/21.99  
% 151.14/21.99  Sub-proof #52 shows that the following formulas are inconsistent:
% 151.14/21.99  ----------------------------------------------------------------
% 151.14/21.99    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.99    (2)  op(e1, e1) = all_57_14
% 151.14/21.99    (3)  op(e1, e1) = e2
% 151.14/21.99    (4)   ~ (all_57_14 = e2)
% 151.14/21.99  
% 151.14/21.99  Begin of proof
% 151.14/21.99  | 
% 151.14/21.99  | GROUND_INST: instantiating (1) with e2, all_57_14, e1, e1, simplifying with
% 151.14/21.99  |              (2), (3) gives:
% 151.14/21.99  |   (5)  all_57_14 = e2
% 151.14/21.99  | 
% 151.14/21.99  | REDUCE: (4), (5) imply:
% 151.14/21.99  |   (6)  $false
% 151.14/21.99  | 
% 151.14/21.99  | CLOSE: (6) is inconsistent.
% 151.14/21.99  | 
% 151.14/21.99  End of proof
% 151.14/21.99  
% 151.14/21.99  Sub-proof #53 shows that the following formulas are inconsistent:
% 151.14/21.99  ----------------------------------------------------------------
% 151.14/21.99    (1)   ~ (all_52_2 = all_52_6)
% 151.14/21.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.99    (3)  op(e1, e2) = all_52_6
% 151.14/21.99    (4)  op(e1, e2) = e1
% 151.14/21.99    (5)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.14/21.99             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.14/21.99           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.14/21.99           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.14/21.99           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.14/21.99           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.14/21.99           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 151.14/21.99           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 151.14/21.99           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 151.14/21.99           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 151.14/21.99           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 151.14/21.99           $i(all_57_14))
% 151.14/21.99    (6)  op(e1, e3) = all_52_2
% 151.14/21.99    (7)  op(e2, e3) = all_52_1
% 151.14/21.99    (8)   ~ (all_52_1 = e2)
% 151.14/21.99  
% 151.14/21.99  Begin of proof
% 151.14/21.99  | 
% 151.14/21.99  | BETA: splitting (5) gives:
% 151.14/21.99  | 
% 151.14/21.99  | Case 1:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (9)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 151.14/21.99  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.14/21.99  | |          all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 151.14/21.99  | |        (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 151.14/21.99  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 151.14/21.99  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 151.14/21.99  | | 
% 151.14/21.99  | | REF_CLOSE: (2), (7), (8), (9) are inconsistent by sub-proof #1180.
% 151.14/21.99  | | 
% 151.14/21.99  | Case 2:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (10)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 151.14/21.99  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 151.14/21.99  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 151.14/21.99  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 151.14/21.99  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 151.14/21.99  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 151.14/21.99  | | 
% 151.14/21.99  | | BETA: splitting (10) gives:
% 151.14/21.99  | | 
% 151.14/21.99  | | Case 1:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (11)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/21.99  | | |         (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 151.14/21.99  | | |         op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 151.14/21.99  | | |         $i(all_57_14)
% 151.14/21.99  | | | 
% 151.14/21.99  | | | ALPHA: (11) implies:
% 151.14/21.99  | | |   (12)  op(e1, e3) = e1
% 151.14/21.99  | | | 
% 151.14/21.99  | | | REF_CLOSE: (1), (2), (3), (4), (6), (12) are inconsistent by sub-proof
% 151.14/21.99  | | |            #911.
% 151.14/21.99  | | | 
% 151.14/21.99  | | Case 2:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (13)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 151.14/21.99  | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 151.14/21.99  | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 151.14/21.99  | | |         $i(all_57_14)
% 151.14/21.99  | | | 
% 151.14/21.99  | | | ALPHA: (13) implies:
% 151.14/21.99  | | |   (14)  op(e1, e3) = e1
% 151.14/21.99  | | | 
% 151.14/21.99  | | | REF_CLOSE: (1), (2), (3), (4), (6), (14) are inconsistent by sub-proof
% 151.14/21.99  | | |            #911.
% 151.14/21.99  | | | 
% 151.14/21.99  | | End of split
% 151.14/21.99  | | 
% 151.14/21.99  | End of split
% 151.14/21.99  | 
% 151.14/21.99  End of proof
% 151.14/21.99  
% 151.14/21.99  Sub-proof #54 shows that the following formulas are inconsistent:
% 151.14/21.99  ----------------------------------------------------------------
% 151.14/21.99    (1)   ~ (e3 = e1)
% 151.14/21.99    (2)  op(e0, e2) = all_52_7
% 151.14/21.99    (3)   ~ (all_52_3 = all_52_7)
% 151.14/21.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.99    (5)  op(e0, e0) = e3
% 151.14/21.99    (6)  op(e0, e3) = e0
% 151.14/21.99    (7)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 151.14/21.99             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.14/21.99           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 151.14/21.99           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.14/21.99             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/21.99           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/21.99           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 151.14/21.99           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 151.14/21.99           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 151.14/21.99           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 151.14/21.99           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 151.14/21.99         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 151.14/21.99             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/21.99           $i(all_57_7))
% 151.14/21.99    (8)  op(e0, e3) = all_52_3
% 151.14/21.99    (9)  op(e2, e2) = e2
% 151.14/21.99    (10)  op(e0, e0) = all_57_15
% 151.14/21.99    (11)   ~ (e3 = e2)
% 151.14/21.99    (12)  op(e3, e3) = e3
% 151.14/21.99    (13)   ~ (e2 = e1)
% 151.14/21.99  
% 151.14/21.99  Begin of proof
% 151.14/21.99  | 
% 151.14/21.99  | BETA: splitting (7) gives:
% 151.14/21.99  | 
% 151.14/21.99  | Case 1:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (14)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 151.14/21.99  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 151.14/21.99  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 151.14/21.99  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 151.14/21.99  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 151.14/21.99  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 151.14/21.99  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/21.99  | |           $i(all_57_3))
% 151.14/21.99  | | 
% 151.14/21.99  | | BETA: splitting (14) gives:
% 151.14/21.99  | | 
% 151.14/21.99  | | Case 1:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (15)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/21.99  | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 151.14/21.99  | | |         op(e0, e3) = e0 & $i(all_57_0)
% 151.14/21.99  | | | 
% 151.14/21.99  | | | ALPHA: (15) implies:
% 151.14/21.99  | | |   (16)   ~ (all_57_15 = e3)
% 151.14/21.99  | | | 
% 151.14/21.99  | | | REF_CLOSE: (4), (5), (10), (16) are inconsistent by sub-proof #1019.
% 151.14/21.99  | | | 
% 151.14/21.99  | | Case 2:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (17)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.14/21.99  | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 151.14/21.99  | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 151.14/21.99  | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 151.14/21.99  | | |           & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 151.14/21.99  | | | 
% 151.14/21.99  | | | BETA: splitting (17) gives:
% 151.14/21.99  | | | 
% 151.14/21.99  | | | Case 1:
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | |   (18)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.14/21.99  | | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 151.14/21.99  | | | |         op(e0, e3) = e0 & $i(all_57_1)
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | | ALPHA: (18) implies:
% 151.14/21.99  | | | |   (19)   ~ (all_57_15 = e3)
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | | REF_CLOSE: (4), (5), (10), (19) are inconsistent by sub-proof #1019.
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | Case 2:
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | |   (20)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.14/21.99  | | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 151.14/21.99  | | | |         op(e0, e2) = e0 & $i(all_57_3)
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | | ALPHA: (20) implies:
% 151.14/21.99  | | | |   (21)  op(e3, e3) = e2
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | | REF_CLOSE: (4), (11), (12), (21) are inconsistent by sub-proof #1085.
% 151.14/21.99  | | | | 
% 151.14/21.99  | | | End of split
% 151.14/21.99  | | | 
% 151.14/21.99  | | End of split
% 151.14/21.99  | | 
% 151.14/21.99  | Case 2:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (22)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 151.14/21.99  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.14/21.99  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/21.99  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.14/21.99  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 151.14/21.99  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.14/21.99  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/21.99  | |           $i(all_57_7))
% 151.14/21.99  | | 
% 151.14/21.99  | | BETA: splitting (22) gives:
% 151.14/21.99  | | 
% 151.14/21.99  | | Case 1:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (23)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/21.99  | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.14/21.99  | | |         op(e0, e2) = e0 & $i(all_57_4)
% 151.14/21.99  | | | 
% 151.14/21.99  | | | ALPHA: (23) implies:
% 151.14/21.99  | | |   (24)  op(e0, e2) = e0
% 151.14/21.99  | | | 
% 151.14/21.99  | | | REF_CLOSE: (2), (3), (4), (6), (8), (24) are inconsistent by sub-proof
% 151.14/21.99  | | |            #1123.
% 151.14/21.99  | | | 
% 151.14/21.99  | | Case 2:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (25)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.14/21.99  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.14/21.99  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 151.14/21.99  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 151.14/21.99  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.14/21.99  | | | 
% 151.14/21.99  | | | REF_CLOSE: (1), (4), (9), (12), (13), (25) are inconsistent by sub-proof
% 151.14/21.99  | | |            #1076.
% 151.14/21.99  | | | 
% 151.14/21.99  | | End of split
% 151.14/21.99  | | 
% 151.14/21.99  | End of split
% 151.14/21.99  | 
% 151.14/21.99  End of proof
% 151.14/21.99  
% 151.14/21.99  Sub-proof #55 shows that the following formulas are inconsistent:
% 151.14/21.99  ----------------------------------------------------------------
% 151.14/21.99    (1)   ~ (e3 = e1)
% 151.14/21.99    (2)  op(e3, e3) = all_14_2
% 151.14/21.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.99    (4)  op(e0, e0) = e3
% 151.14/21.99    (5)   ~ (all_52_12 = all_14_2)
% 151.14/21.99    (6)  op(e3, e0) = all_52_12
% 151.14/21.99    (7)   ~ (all_52_9 = e2)
% 151.14/21.99    (8)  op(e2, e1) = all_52_9
% 151.14/21.99    (9)   ~ (all_52_8 = e3)
% 151.14/21.99    (10)  op(e3, e1) = all_52_8
% 151.14/21.99    (11)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 151.14/21.99              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 151.14/21.99            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 151.14/21.99            = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 151.14/21.99            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 151.14/21.99            op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 151.14/21.99            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2)
% 151.14/21.99            = all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0) =
% 151.14/21.99            e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &
% 151.14/21.99             ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 151.14/21.99            op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 151.14/21.99            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 151.14/21.99            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 151.14/21.99            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.14/21.99            $i(all_57_10) & $i(all_57_13))
% 151.14/21.99    (12)  op(e3, e3) = e3
% 151.14/21.99  
% 151.14/21.99  Begin of proof
% 151.14/21.99  | 
% 151.14/21.99  | BETA: splitting (11) gives:
% 151.14/21.99  | 
% 151.14/21.99  | Case 1:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (13)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 151.14/21.99  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 151.14/21.99  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 151.14/21.99  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 151.14/21.99  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 151.14/21.99  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 151.14/21.99  | | 
% 151.14/21.99  | | REF_CLOSE: (3), (7), (8), (9), (10), (13) are inconsistent by sub-proof
% 151.14/21.99  | |            #1083.
% 151.14/21.99  | | 
% 151.14/21.99  | Case 2:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (14)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 151.14/21.99  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 151.14/21.99  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 151.14/21.99  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/21.99  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/21.99  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.14/21.99  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 151.14/21.99  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 151.14/21.99  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.14/21.99  | |           $i(all_57_13))
% 151.14/21.99  | | 
% 151.14/21.99  | | BETA: splitting (14) gives:
% 151.14/21.99  | | 
% 151.14/21.99  | | Case 1:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (15)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/21.99  | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.14/21.99  | | |         op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/21.99  | | |         $i(all_57_12)
% 151.14/21.99  | | | 
% 151.14/21.99  | | | ALPHA: (15) implies:
% 151.14/21.99  | | |   (16)  op(e0, e0) = e1
% 151.14/21.99  | | | 
% 151.14/21.99  | | | REF_CLOSE: (1), (3), (4), (16) are inconsistent by sub-proof #1022.
% 151.14/21.99  | | | 
% 151.14/21.99  | | Case 2:
% 151.14/21.99  | | | 
% 151.14/21.99  | | |   (17)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/21.99  | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/21.99  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.14/21.99  | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10
% 151.14/21.99  | | |             = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 151.14/21.99  | | |             e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.14/21.99  | | |           $i(all_57_10) & $i(all_57_13))
% 151.14/21.99  | | | 
% 151.14/21.99  | | | REF_CLOSE: (2), (3), (5), (6), (12), (17) are inconsistent by sub-proof
% 151.14/21.99  | | |            #58.
% 151.14/21.99  | | | 
% 151.14/21.99  | | End of split
% 151.14/21.99  | | 
% 151.14/21.99  | End of split
% 151.14/21.99  | 
% 151.14/21.99  End of proof
% 151.14/21.99  
% 151.14/21.99  Sub-proof #56 shows that the following formulas are inconsistent:
% 151.14/21.99  ----------------------------------------------------------------
% 151.14/21.99    (1)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 151.14/21.99             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 151.14/21.99           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 151.14/21.99           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 151.14/21.99           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 151.14/21.99           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 151.14/21.99           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3)
% 151.14/21.99           = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 151.14/21.99           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 151.14/21.99           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 151.14/21.99           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.14/21.99           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 151.14/21.99            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 151.14/21.99             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.14/21.99    (2)  op(e3, e3) = all_14_2
% 151.14/21.99    (3)  op(e3, e2) = all_52_4
% 151.14/21.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/21.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/21.99    (5)   ~ (all_52_12 = all_14_2)
% 151.14/21.99    (6)  op(e1, e0) = all_52_14
% 151.14/21.99    (7)   ~ (all_52_4 = e3)
% 151.14/21.99    (8)  op(e3, e0) = all_52_12
% 151.14/21.99    (9)  op(e2, e0) = all_52_13
% 151.14/21.99    (10)  op(e2, e2) = e2
% 151.14/21.99    (11)   ~ (e3 = e2)
% 151.14/21.99    (12)   ~ (all_52_14 = e3)
% 151.14/21.99    (13)   ~ (all_52_13 = e3)
% 151.14/21.99    (14)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 151.14/21.99          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.14/21.99    (15)  op(e3, e3) = e3
% 151.14/21.99    (16)   ~ (e2 = e1)
% 151.14/21.99  
% 151.14/21.99  Begin of proof
% 151.14/21.99  | 
% 151.14/21.99  | BETA: splitting (1) gives:
% 151.14/21.99  | 
% 151.14/21.99  | Case 1:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (17)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 151.14/21.99  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 151.14/21.99  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 151.14/21.99  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 151.14/21.99  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 151.14/21.99  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 151.14/21.99  | | 
% 151.14/21.99  | | REF_CLOSE: (3), (4), (7), (17) are inconsistent by sub-proof #863.
% 151.14/21.99  | | 
% 151.14/21.99  | Case 2:
% 151.14/21.99  | | 
% 151.14/21.99  | |   (18)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 151.14/21.99  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 151.14/21.99  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 151.14/21.99  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 151.14/21.99  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 151.14/21.99  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 151.14/21.99  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 151.14/21.99  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 151.14/21.99  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.14/21.99  | | 
% 151.14/21.99  | | BETA: splitting (18) gives:
% 151.14/21.99  | | 
% 151.14/21.99  | | Case 1:
% 151.14/21.99  | | | 
% 151.14/22.00  | | |   (19)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.14/22.00  | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 151.14/22.00  | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 151.14/22.00  | | |         $i(all_57_14)
% 151.14/22.00  | | | 
% 151.14/22.00  | | | ALPHA: (19) implies:
% 151.14/22.00  | | |   (20)  op(e3, e3) = e2
% 151.14/22.00  | | | 
% 151.14/22.00  | | | REF_CLOSE: (4), (11), (15), (20) are inconsistent by sub-proof #1085.
% 151.14/22.00  | | | 
% 151.14/22.00  | | Case 2:
% 151.14/22.00  | | | 
% 151.14/22.00  | | |   (21)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 151.14/22.00  | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.14/22.00  | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.14/22.00  | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7
% 151.14/22.00  | | |             = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 151.14/22.00  | | |             e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.14/22.00  | | |           $i(all_57_7) & $i(all_57_10))
% 151.14/22.00  | | | 
% 151.14/22.00  | | | BETA: splitting (21) gives:
% 151.14/22.00  | | | 
% 151.14/22.00  | | | Case 1:
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | |   (22)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 151.14/22.00  | | | |         (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.14/22.00  | | | |         op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.14/22.00  | | | |         $i(all_57_14)
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | | ALPHA: (22) implies:
% 151.14/22.00  | | | |   (23)  op(e0, e0) = e2
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (11), (12), (13), (14), (15),
% 151.14/22.00  | | | |            (23) are inconsistent by sub-proof #65.
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | Case 2:
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | |   (24)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.14/22.00  | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/22.00  | | | |         op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.14/22.00  | | | |         $i(all_57_10)
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | | ALPHA: (24) implies:
% 151.14/22.00  | | | |   (25)  op(e2, e2) = e1
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | | REF_CLOSE: (4), (10), (16), (25) are inconsistent by sub-proof #1158.
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | End of split
% 151.14/22.00  | | | 
% 151.14/22.00  | | End of split
% 151.14/22.00  | | 
% 151.14/22.00  | End of split
% 151.14/22.00  | 
% 151.14/22.00  End of proof
% 151.14/22.00  
% 151.14/22.00  Sub-proof #57 shows that the following formulas are inconsistent:
% 151.14/22.00  ----------------------------------------------------------------
% 151.14/22.00    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 151.14/22.00             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/22.00           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 151.14/22.00           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 151.14/22.00             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/22.00           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 151.14/22.00           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.14/22.00    (2)  op(e0, e1) = all_52_11
% 151.14/22.00    (3)  op(e0, e2) = all_52_7
% 151.14/22.00    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.00    (5)   ~ (all_52_11 = e0)
% 151.14/22.00    (6)  op(e2, e2) = e2
% 151.14/22.00    (7)   ~ (all_52_7 = e0)
% 151.14/22.00    (8)   ~ (e2 = e1)
% 151.14/22.00  
% 151.14/22.00  Begin of proof
% 151.14/22.00  | 
% 151.14/22.00  | BETA: splitting (1) gives:
% 151.14/22.00  | 
% 151.14/22.00  | Case 1:
% 151.14/22.00  | | 
% 151.14/22.00  | |   (9)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 151.14/22.00  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/22.00  | |        $i(all_57_4)
% 151.14/22.00  | | 
% 151.14/22.00  | | ALPHA: (9) implies:
% 151.14/22.00  | |   (10)  op(e0, e2) = e0
% 151.14/22.00  | | 
% 151.14/22.00  | | REF_CLOSE: (3), (4), (7), (10) are inconsistent by sub-proof #1036.
% 151.14/22.00  | | 
% 151.14/22.00  | Case 2:
% 151.14/22.00  | | 
% 151.14/22.00  | |   (11)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 151.14/22.00  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 151.14/22.00  | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/22.00  | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2,
% 151.14/22.00  | |             e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.14/22.00  | | 
% 151.14/22.00  | | REF_CLOSE: (2), (4), (5), (6), (8), (11) are inconsistent by sub-proof #954.
% 151.14/22.00  | | 
% 151.14/22.00  | End of split
% 151.14/22.00  | 
% 151.14/22.00  End of proof
% 151.14/22.00  
% 151.14/22.00  Sub-proof #58 shows that the following formulas are inconsistent:
% 151.14/22.00  ----------------------------------------------------------------
% 151.14/22.00    (1)  op(e3, e3) = all_14_2
% 151.14/22.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.00    (3)   ~ (all_52_12 = all_14_2)
% 151.14/22.00    (4)  op(e3, e0) = all_52_12
% 151.14/22.00    (5)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 151.14/22.00             e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 151.14/22.00           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 =
% 151.14/22.00           e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 151.14/22.00           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 151.14/22.00           = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 151.14/22.00    (6)  op(e3, e3) = e3
% 151.14/22.00  
% 151.14/22.00  Begin of proof
% 151.14/22.00  | 
% 151.14/22.00  | BETA: splitting (5) gives:
% 151.14/22.00  | 
% 151.14/22.00  | Case 1:
% 151.14/22.00  | | 
% 151.14/22.00  | |   (7)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 151.14/22.00  | |          = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0
% 151.14/22.00  | |        & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)
% 151.14/22.00  | | 
% 151.14/22.00  | | ALPHA: (7) implies:
% 151.14/22.00  | |   (8)  op(e3, e0) = e3
% 151.14/22.00  | | 
% 151.14/22.00  | | REF_CLOSE: (1), (2), (3), (4), (6), (8) are inconsistent by sub-proof #71.
% 151.14/22.00  | | 
% 151.14/22.00  | Case 2:
% 151.14/22.00  | | 
% 151.14/22.00  | |   (9)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 151.14/22.00  | |          = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 151.14/22.00  | |        & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)
% 151.14/22.00  | | 
% 151.14/22.00  | | ALPHA: (9) implies:
% 151.14/22.00  | |   (10)  op(e3, e0) = e3
% 151.14/22.00  | | 
% 151.14/22.00  | | REF_CLOSE: (1), (2), (3), (4), (6), (10) are inconsistent by sub-proof #71.
% 151.14/22.00  | | 
% 151.14/22.00  | End of split
% 151.14/22.00  | 
% 151.14/22.00  End of proof
% 151.14/22.00  
% 151.14/22.00  Sub-proof #59 shows that the following formulas are inconsistent:
% 151.14/22.00  ----------------------------------------------------------------
% 151.14/22.00    (1)   ~ (e3 = e1)
% 151.14/22.00    (2)   ~ (e2 = e0)
% 151.14/22.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.00    (4)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.14/22.00             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 151.14/22.00               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.14/22.00               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.14/22.00    (5)   ~ (e3 = e0)
% 151.14/22.00    (6)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 151.14/22.00         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 151.14/22.00    (7)  op(e2, e2) = e2
% 151.14/22.00    (8)   ~ (e1 = e0)
% 151.14/22.00    (9)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 151.14/22.00             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 151.14/22.00           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 151.14/22.00           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 151.14/22.00           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 151.14/22.00           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.14/22.00    (10)   ~ (e3 = e2)
% 151.14/22.00    (11)  all_56_9 = e2
% 151.14/22.00    (12)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 151.14/22.00          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.14/22.00    (13)   ~ (e2 = e1)
% 151.14/22.00  
% 151.14/22.00  Begin of proof
% 151.14/22.00  | 
% 151.14/22.00  | BETA: splitting (9) gives:
% 151.14/22.00  | 
% 151.14/22.00  | Case 1:
% 151.14/22.00  | | 
% 151.14/22.00  | |   (14)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 151.14/22.00  | |           = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 151.14/22.00  | |         all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 151.14/22.00  | | 
% 151.14/22.00  | | ALPHA: (14) implies:
% 151.14/22.00  | |   (15)  op(e0, e0) = e2
% 151.14/22.00  | | 
% 151.14/22.00  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12), (13), (15)
% 151.14/22.00  | |            are inconsistent by sub-proof #486.
% 151.14/22.00  | | 
% 151.14/22.00  | Case 2:
% 151.14/22.00  | | 
% 151.14/22.00  | |   (16)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 151.14/22.00  | |           = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1
% 151.14/22.00  | |         & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 151.14/22.00  | | 
% 151.14/22.00  | | ALPHA: (16) implies:
% 151.14/22.00  | |   (17)  op(e2, e2) = e1
% 151.14/22.00  | | 
% 151.14/22.00  | | REF_CLOSE: (3), (7), (13), (17) are inconsistent by sub-proof #1158.
% 151.14/22.00  | | 
% 151.14/22.00  | End of split
% 151.14/22.00  | 
% 151.14/22.00  End of proof
% 151.14/22.00  
% 151.14/22.00  Sub-proof #60 shows that the following formulas are inconsistent:
% 151.14/22.00  ----------------------------------------------------------------
% 151.14/22.00    (1)   ~ (e3 = e1)
% 151.14/22.00    (2)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.14/22.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.00    (4)  op(e1, e0) = all_52_14
% 151.14/22.00    (5)  op(e0, e0) = e1
% 151.14/22.00    (6)   ~ (all_52_14 = e3)
% 151.14/22.00  
% 151.14/22.00  Begin of proof
% 151.14/22.00  | 
% 151.14/22.00  | BETA: splitting (2) gives:
% 151.14/22.00  | 
% 151.14/22.00  | Case 1:
% 151.14/22.00  | | 
% 151.14/22.00  | |   (7)  all_56_11 = e3 & op(e1, e0) = e3
% 151.14/22.00  | | 
% 151.14/22.00  | | REF_CLOSE: (3), (4), (6), (7) are inconsistent by sub-proof #66.
% 151.14/22.00  | | 
% 151.14/22.00  | Case 2:
% 151.14/22.00  | | 
% 151.14/22.00  | |   (8)  all_56_15 = e3 & op(e0, e0) = e3
% 151.14/22.00  | | 
% 151.14/22.00  | | ALPHA: (8) implies:
% 151.14/22.00  | |   (9)  op(e0, e0) = e3
% 151.14/22.00  | | 
% 151.14/22.00  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1022.
% 151.14/22.00  | | 
% 151.14/22.00  | End of split
% 151.14/22.00  | 
% 151.14/22.00  End of proof
% 151.14/22.00  
% 151.14/22.00  Sub-proof #61 shows that the following formulas are inconsistent:
% 151.14/22.00  ----------------------------------------------------------------
% 151.14/22.00    (1)  op(e0, e1) = all_52_11
% 151.14/22.00    (2)  op(e3, e3) = e0
% 151.14/22.00    (3)   ~ (e3 = e1)
% 151.14/22.00    (4)   ~ (all_52_11 = all_10_2)
% 151.14/22.00    (5)  op(e0, e0) = all_10_2
% 151.14/22.00    (6)  op(e3, e2) = all_52_4
% 151.14/22.00    (7)   ~ (e2 = e0)
% 151.14/22.00    (8)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 151.14/22.00           all_57_12 & $i(all_57_12))
% 151.14/22.00    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.00    (10)   ~ (all_52_4 = e3)
% 151.14/22.00    (11)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) & op(e3, e3) =
% 151.14/22.00            all_57_10 & $i(all_57_10))
% 151.14/22.00    (12)   ~ (e3 = e0)
% 151.14/22.00    (13)  op(e0, e3) = all_52_3
% 151.14/22.00    (14)   ~ (e1 = e0)
% 151.14/22.00    (15)  op(e1, e1) = e3
% 151.14/22.00    (16)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 151.14/22.00            all_57_14 & $i(all_57_14))
% 151.14/22.00    (17)   ~ (e3 = e2)
% 151.14/22.00    (18)   ~ (all_52_8 = e3)
% 151.14/22.00    (19)   ~ (all_52_3 = e0)
% 151.14/22.00    (20)  op(e3, e1) = all_52_8
% 151.14/22.00    (21)  op(e0, e0) = e0
% 151.14/22.00    (22)  op(e2, e2) = e3
% 151.14/22.00    (23)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.14/22.00              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.14/22.00            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.14/22.00            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.14/22.00            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.14/22.00            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.14/22.00            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 151.14/22.00            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.14/22.00            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 151.14/22.00            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 151.14/22.00            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.14/22.00            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 151.14/22.00            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.14/22.00            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.14/22.00            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 151.14/22.00            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.14/22.00            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.14/22.00            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 151.14/22.00            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/22.00            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 151.14/22.00            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 151.14/22.00            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.14/22.00            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.14/22.00            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 151.14/22.00            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/22.00            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.14/22.00            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.14/22.00            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/22.00            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/22.00            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 151.14/22.00            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.14/22.00            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.14/22.00            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.14/22.00            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.14/22.00            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/22.00            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 151.14/22.00            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/22.00            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.14/22.00            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 151.14/22.00            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/22.00            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.14/22.00            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 151.14/22.00            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.14/22.00            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 151.14/22.00            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 151.14/22.00            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.14/22.00            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 151.14/22.00            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 151.14/22.00              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 151.14/22.00            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.14/22.00            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 151.14/22.00              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.14/22.00            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.14/22.00            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 151.14/22.00                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 151.14/22.00                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.14/22.00                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.14/22.00                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 151.14/22.00                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 151.14/22.00                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 151.14/22.00                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.14/22.00              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 151.14/22.00                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.14/22.00                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/22.00                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.14/22.00                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 151.14/22.00                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.14/22.00                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.00                $i(all_57_7))))
% 151.14/22.00  
% 151.14/22.00  Begin of proof
% 151.14/22.00  | 
% 151.14/22.00  | BETA: splitting (23) gives:
% 151.14/22.00  | 
% 151.14/22.00  | Case 1:
% 151.14/22.00  | | 
% 151.14/22.00  | |   (24)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 151.14/22.00  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.14/22.00  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 151.14/22.00  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 151.14/22.00  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 151.14/22.00  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 151.14/22.00  | |         (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 151.14/22.00  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 151.14/22.00  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 151.14/22.00  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 151.14/22.00  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 151.14/22.00  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) |
% 151.14/22.00  | |         (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 151.14/22.00  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 151.14/22.00  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 151.14/22.00  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 151.14/22.00  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 151.14/22.00  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 151.14/22.00  | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 151.14/22.00  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 151.14/22.00  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 151.14/22.00  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 151.14/22.00  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 151.14/22.00  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 151.14/22.00  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 151.14/22.00  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 151.14/22.00  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.14/22.00  | | 
% 151.14/22.00  | | BETA: splitting (24) gives:
% 151.14/22.00  | | 
% 151.14/22.00  | | Case 1:
% 151.14/22.00  | | | 
% 151.14/22.00  | | |   (25)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.14/22.00  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.14/22.00  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 151.14/22.00  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 151.14/22.00  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 151.14/22.00  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.14/22.00  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 151.14/22.00  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 151.14/22.00  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.14/22.00  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 151.14/22.00  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 151.14/22.00  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 151.14/22.00  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 151.14/22.00  | | | 
% 151.14/22.00  | | | BETA: splitting (25) gives:
% 151.14/22.00  | | | 
% 151.14/22.00  | | | Case 1:
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | |   (26)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.14/22.00  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.14/22.00  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 151.14/22.00  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 151.14/22.00  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 151.14/22.00  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 151.14/22.00  | | | |           e3 & $i(all_57_2) & $i(all_57_12))
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | | REF_CLOSE: (9), (12), (21), (22), (26) are inconsistent by sub-proof
% 151.14/22.00  | | | |            #64.
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | Case 2:
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | |   (27)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/22.00  | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 151.14/22.00  | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 151.14/22.00  | | | |           $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 151.14/22.00  | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 151.14/22.00  | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 151.14/22.00  | | | |           e3 & $i(all_57_2) & $i(all_57_14))
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | | REF_CLOSE: (9), (12), (15), (21), (27) are inconsistent by sub-proof
% 151.14/22.00  | | | |            #352.
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | End of split
% 151.14/22.00  | | | 
% 151.14/22.00  | | Case 2:
% 151.14/22.00  | | | 
% 151.14/22.00  | | |   (28)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/22.00  | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 151.14/22.00  | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 151.14/22.00  | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5
% 151.14/22.00  | | |             = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 151.14/22.00  | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.14/22.00  | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 151.14/22.00  | | |           &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 151.14/22.00  | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 151.14/22.00  | | |           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 =
% 151.14/22.00  | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 151.14/22.00  | | |           & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 151.14/22.00  | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 151.14/22.00  | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.14/22.00  | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 151.14/22.00  | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.14/22.00  | | | 
% 151.14/22.00  | | | BETA: splitting (28) gives:
% 151.14/22.00  | | | 
% 151.14/22.00  | | | Case 1:
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | |   (29)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/22.00  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 151.14/22.00  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 151.14/22.00  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 151.14/22.00  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 151.14/22.00  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.14/22.00  | | | |           $i(all_57_5) & $i(all_57_10))
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | | REF_CLOSE: (6), (9), (10), (15), (17), (29) are inconsistent by
% 151.14/22.00  | | | |            sub-proof #294.
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | Case 2:
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | |   (30)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.14/22.00  | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 151.14/22.00  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 151.14/22.00  | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 151.14/22.00  | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 151.14/22.00  | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 151.14/22.00  | | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 151.14/22.00  | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 151.14/22.00  | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 151.14/22.00  | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | | REF_CLOSE: (2), (3), (7), (9), (21), (22), (30) are inconsistent by
% 151.14/22.00  | | | |            sub-proof #88.
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | End of split
% 151.14/22.00  | | | 
% 151.14/22.00  | | End of split
% 151.14/22.00  | | 
% 151.14/22.00  | Case 2:
% 151.14/22.00  | | 
% 151.14/22.00  | |   (31)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 151.14/22.00  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 151.14/22.00  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 151.14/22.00  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 151.14/22.00  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 151.14/22.00  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 151.14/22.00  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 151.14/22.00  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 151.14/22.00  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 151.14/22.00  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/22.00  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/22.00  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.14/22.00  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 151.14/22.00  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 151.14/22.00  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.14/22.00  | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 151.14/22.00  | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 151.14/22.00  | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 151.14/22.00  | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 151.14/22.00  | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 151.14/22.00  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 151.14/22.00  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 151.14/22.00  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 151.14/22.00  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.14/22.00  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 151.14/22.00  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 151.14/22.00  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 151.14/22.00  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 151.14/22.00  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 151.14/22.00  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 151.14/22.00  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 151.14/22.00  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 151.14/22.00  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.14/22.00  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 151.14/22.00  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/22.00  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 151.14/22.00  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 151.14/22.00  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/22.00  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 151.14/22.00  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 151.14/22.00  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 151.14/22.00  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.14/22.00  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.00  | |               $i(all_57_7))))
% 151.14/22.00  | | 
% 151.14/22.00  | | BETA: splitting (31) gives:
% 151.14/22.00  | | 
% 151.14/22.00  | | Case 1:
% 151.14/22.00  | | | 
% 151.14/22.00  | | |   (32)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/22.00  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/22.00  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/22.00  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 151.14/22.00  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 151.14/22.00  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.14/22.00  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 151.14/22.00  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 151.14/22.00  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 151.14/22.00  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 151.14/22.00  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 151.14/22.00  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 151.14/22.00  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 151.14/22.00  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/22.00  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/22.00  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.14/22.00  | | |           $i(all_57_13))
% 151.14/22.00  | | | 
% 151.14/22.00  | | | BETA: splitting (32) gives:
% 151.14/22.00  | | | 
% 151.14/22.00  | | | Case 1:
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | |   (33)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/22.00  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/22.00  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/22.00  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 151.14/22.00  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 151.14/22.00  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 151.14/22.00  | | | |           e2 & $i(all_57_6) & $i(all_57_12))
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | | BETA: splitting (33) gives:
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | | Case 1:
% 151.14/22.00  | | | | | 
% 151.14/22.00  | | | | |   (34)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/22.00  | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/22.00  | | | | |         op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/22.00  | | | | |         $i(all_57_10)
% 151.14/22.00  | | | | | 
% 151.14/22.00  | | | | | ALPHA: (34) implies:
% 151.14/22.00  | | | | |   (35)  op(e3, e1) = e3
% 151.14/22.00  | | | | | 
% 151.14/22.00  | | | | | REF_CLOSE: (9), (18), (20), (35) are inconsistent by sub-proof #1164.
% 151.14/22.00  | | | | | 
% 151.14/22.00  | | | | Case 2:
% 151.14/22.00  | | | | | 
% 151.14/22.00  | | | | |   (36)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.14/22.00  | | | | |         (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.14/22.00  | | | | |         op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.14/22.00  | | | | |         $i(all_57_12)
% 151.14/22.00  | | | | | 
% 151.14/22.00  | | | | | ALPHA: (36) implies:
% 151.14/22.00  | | | | |   (37)  op(e3, e3) = e1
% 151.14/22.00  | | | | | 
% 151.14/22.00  | | | | | REF_CLOSE: (2), (9), (14), (37) are inconsistent by sub-proof #957.
% 151.14/22.00  | | | | | 
% 151.14/22.00  | | | | End of split
% 151.14/22.00  | | | | 
% 151.14/22.00  | | | Case 2:
% 151.14/22.00  | | | | 
% 151.14/22.01  | | | |   (38)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.14/22.01  | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.14/22.01  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/22.01  | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 151.14/22.01  | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 151.14/22.01  | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 151.14/22.01  | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 151.14/22.01  | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 151.14/22.01  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 151.14/22.01  | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | | REF_CLOSE: (2), (9), (14), (16), (21), (38) are inconsistent by
% 151.14/22.01  | | | |            sub-proof #472.
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | End of split
% 151.14/22.01  | | | 
% 151.14/22.01  | | Case 2:
% 151.14/22.01  | | | 
% 151.14/22.01  | | |   (39)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 151.14/22.01  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.14/22.01  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 151.14/22.01  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 151.14/22.01  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 151.14/22.01  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.14/22.01  | | |           $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0
% 151.14/22.01  | | |           &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 151.14/22.01  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 151.14/22.01  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 151.14/22.01  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 151.14/22.01  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 151.14/22.01  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 151.14/22.01  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 151.14/22.01  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 151.14/22.01  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.14/22.01  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 151.14/22.01  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 151.14/22.01  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 151.14/22.01  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.14/22.01  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 151.14/22.01  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 151.14/22.01  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 151.14/22.01  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/22.01  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/22.01  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 151.14/22.01  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 151.14/22.01  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.14/22.01  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.14/22.01  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 151.14/22.01  | | | 
% 151.14/22.01  | | | BETA: splitting (39) gives:
% 151.14/22.01  | | | 
% 151.14/22.01  | | | Case 1:
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | |   (40)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 151.14/22.01  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.14/22.01  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 151.14/22.01  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 151.14/22.01  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 151.14/22.01  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 151.14/22.01  | | | |           e1 & $i(all_57_9) & $i(all_57_14))
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | | REF_CLOSE: (11), (40) are inconsistent by sub-proof #470.
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | Case 2:
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | |   (41)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 151.14/22.01  | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 151.14/22.01  | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.14/22.01  | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 151.14/22.01  | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 151.14/22.01  | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 151.14/22.01  | | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 151.14/22.01  | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 151.14/22.01  | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 151.14/22.01  | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.14/22.01  | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 151.14/22.01  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 151.14/22.01  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.14/22.01  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/22.01  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 151.14/22.01  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.14/22.01  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/22.01  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 151.14/22.01  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 151.14/22.01  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 151.14/22.01  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 151.14/22.01  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/22.01  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 151.14/22.01  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | | BETA: splitting (41) gives:
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | | Case 1:
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | |   (42)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 151.14/22.01  | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 151.14/22.01  | | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.14/22.01  | | | | |         $i(all_57_13)
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | | ALPHA: (42) implies:
% 151.14/22.01  | | | | |   (43)   ~ (all_57_13 = e1)
% 151.14/22.01  | | | | |   (44)  op(e1, e1) = e0
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | | REF_CLOSE: (9), (16), (43), (44) are inconsistent by sub-proof #959.
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | Case 2:
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | |   (45)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 151.14/22.01  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.14/22.01  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.14/22.01  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 151.14/22.01  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/22.01  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 151.14/22.01  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 151.14/22.01  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 151.14/22.01  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.14/22.01  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 151.14/22.01  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 151.14/22.01  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/22.01  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 151.14/22.01  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.14/22.01  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/22.01  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/22.01  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 151.14/22.01  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/22.01  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/22.01  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 151.14/22.01  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.01  | | | | |               $i(all_57_7))))
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | | BETA: splitting (45) gives:
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | | Case 1:
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | |   (46)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 151.14/22.01  | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.14/22.01  | | | | | |         & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.14/22.01  | | | | | |         $i(all_57_14)
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | | ALPHA: (46) implies:
% 151.14/22.01  | | | | | |   (47)  all_57_12 = e0
% 151.14/22.01  | | | | | |   (48)   ~ (all_57_11 = e2)
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | | REF_CLOSE: (8), (47), (48) are inconsistent by sub-proof #890.
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | Case 2:
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | |   (49)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 151.14/22.01  | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 151.14/22.01  | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 151.14/22.01  | | | | | |               e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 151.14/22.01  | | | | | |             = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1,
% 151.14/22.01  | | | | | |               e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.14/22.01  | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/22.01  | | | | | |             (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 151.14/22.01  | | | | | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/22.01  | | | | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 151.14/22.01  | | | | | |             (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.14/22.01  | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/22.01  | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/22.01  | | | | | |             (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 151.14/22.01  | | | | | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/22.01  | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/22.01  | | | | | |             (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 151.14/22.01  | | | | | |             & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.01  | | | | | |             $i(all_57_7)))
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | | ALPHA: (49) implies:
% 151.14/22.01  | | | | | |   (50)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/22.01  | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 151.14/22.01  | | | | | |           & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 151.14/22.01  | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 151.14/22.01  | | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 151.14/22.01  | | | | | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/22.01  | | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 151.14/22.01  | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.14/22.01  | | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/22.01  | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 151.14/22.01  | | | | | |           & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 151.14/22.01  | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 151.14/22.01  | | | | | |           & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 151.14/22.01  | | | | | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/22.01  | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 151.14/22.01  | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | | BETA: splitting (50) gives:
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | | Case 1:
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | |   (51)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/22.01  | | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 151.14/22.01  | | | | | | |           e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 151.14/22.01  | | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 151.14/22.01  | | | | | | |             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.14/22.01  | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 151.14/22.01  | | | | | | |           = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 151.14/22.01  | | | | | | |             e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/22.01  | | | | | | |           $i(all_57_3))
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | REF_CLOSE: (2), (7), (9), (13), (19), (51) are inconsistent by
% 151.14/22.01  | | | | | | |            sub-proof #538.
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | Case 2:
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | |   (52)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/22.01  | | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 151.14/22.01  | | | | | | |           e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 151.14/22.01  | | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.14/22.01  | | | | | | |             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 151.14/22.01  | | | | | | |             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 151.14/22.01  | | | | | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 151.14/22.01  | | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.01  | | | | | | |           $i(all_57_7))
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | BETA: splitting (52) gives:
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | |   (53)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/22.01  | | | | | | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 151.14/22.01  | | | | | | | |         e2 & op(e0, e2) = e0 & $i(all_57_4)
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | | ALPHA: (53) implies:
% 151.14/22.01  | | | | | | | |   (54)  op(e1, e1) = e2
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | | REF_CLOSE: (9), (15), (17), (54) are inconsistent by sub-proof
% 151.14/22.01  | | | | | | | |            #834.
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | |   (55)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 151.14/22.01  | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 151.14/22.01  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 151.14/22.01  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.14/22.01  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 151.14/22.01  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (9), (21), (22), (55) are
% 151.14/22.01  | | | | | | | |            inconsistent by sub-proof #129.
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | End of split
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | End of split
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | End of split
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | End of split
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | End of split
% 151.14/22.01  | | | 
% 151.14/22.01  | | End of split
% 151.14/22.01  | | 
% 151.14/22.01  | End of split
% 151.14/22.01  | 
% 151.14/22.01  End of proof
% 151.14/22.01  
% 151.14/22.01  Sub-proof #62 shows that the following formulas are inconsistent:
% 151.14/22.01  ----------------------------------------------------------------
% 151.14/22.01    (1)  op(e0, e1) = all_52_11
% 151.14/22.01    (2)  all_56_8 = e3
% 151.14/22.01    (3)  op(e1, e3) = e2
% 151.14/22.01    (4)   ~ (e3 = e1)
% 151.14/22.01    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.14/22.01         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.14/22.01    (6)  all_56_6 = e2
% 151.14/22.01    (7)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.14/22.01         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.14/22.01    (8)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 151.14/22.01         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 151.14/22.01    (9)  ( ~ (all_12_0 = e0) & op(all_12_1, e1) = all_12_0 & op(e1, e3) = all_12_1
% 151.14/22.01           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e1, e3) =
% 151.14/22.01           all_12_1 & $i(all_12_1))
% 151.14/22.01    (10)  op(e3, e2) = all_52_4
% 151.14/22.01    (11)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.14/22.01          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.14/22.01    (12)   ~ (e2 = e0)
% 151.14/22.01    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.01            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.01    (14)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.14/22.01          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.14/22.01    (15)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.14/22.01          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.14/22.01    (16)  ( ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0 & op(e3, e1) =
% 151.14/22.01            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 151.14/22.01              e1) = all_22_1 & $i(all_22_1))
% 151.14/22.01    (17)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.14/22.01          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.14/22.01    (18)  all_56_13 = e1
% 151.14/22.01    (19)   ~ (all_52_4 = e3)
% 151.14/22.01    (20)   ~ (e3 = e0)
% 151.14/22.01    (21)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.14/22.01          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.14/22.01    (22)   ~ (all_52_11 = e0)
% 151.14/22.01    (23)   ~ (all_52_6 = e3)
% 151.14/22.01    (24)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.14/22.01          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.14/22.01    (25)  op(e3, e3) = e1
% 151.14/22.01    (26)  op(e1, e2) = all_52_6
% 151.14/22.01    (27)  ( ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0 & op(e3, e1) =
% 151.14/22.01            all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e3,
% 151.14/22.01              e1) = all_34_1 & $i(all_34_1))
% 151.14/22.01    (28)   ~ (e1 = e0)
% 151.14/22.01    (29)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.14/22.01          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.14/22.01    (30)  all_56_2 = e0
% 151.14/22.01    (31)  op(e1, e1) = e3
% 151.14/22.01    (32)   ~ (e3 = e2)
% 151.14/22.01    (33)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.14/22.01          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 151.14/22.01            e2)
% 151.14/22.01    (34)  ( ~ (all_8_0 = e2) & op(all_8_1, e1) = all_8_0 & op(e1, e3) = all_8_1 &
% 151.14/22.01            $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e1, e3) = all_8_1
% 151.14/22.01            & $i(all_8_1))
% 151.14/22.01    (35)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.14/22.01          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.14/22.01    (36)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.14/22.01          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.14/22.01    (37)  op(e2, e3) = e0
% 151.14/22.01    (38)  all_56_7 = e0
% 151.14/22.01    (39)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.14/22.01          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.14/22.01    (40)   ~ (e2 = e1)
% 151.14/22.01    (41)  op(e0, e0) = e0
% 151.14/22.01    (42)  op(e2, e2) = e3
% 151.14/22.01    (43)  all_56_12 = e3
% 151.14/22.01    (44)   ~ (all_52_4 = e0)
% 151.14/22.01    (45)   ~ (all_52_11 = e2)
% 151.14/22.01    (46)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.14/22.01          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.14/22.01  
% 151.14/22.01  Begin of proof
% 151.14/22.01  | 
% 151.14/22.01  | BETA: splitting (11) gives:
% 151.14/22.01  | 
% 151.14/22.01  | Case 1:
% 151.14/22.01  | | 
% 151.14/22.01  | |   (47)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 151.14/22.01  | |           e0)
% 151.14/22.01  | | 
% 151.14/22.01  | | BETA: splitting (47) gives:
% 151.14/22.01  | | 
% 151.14/22.01  | | Case 1:
% 151.14/22.01  | | | 
% 151.14/22.01  | | |   (48)  all_56_4 = e0 & op(e3, e1) = e0
% 151.14/22.01  | | | 
% 151.14/22.01  | | | ALPHA: (48) implies:
% 151.14/22.01  | | |   (49)  all_56_4 = e0
% 151.14/22.01  | | | 
% 151.14/22.01  | | | BETA: splitting (17) gives:
% 151.14/22.01  | | | 
% 151.14/22.01  | | | Case 1:
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | |   (50)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1)
% 151.14/22.01  | | | |           = e2)
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | | BETA: splitting (50) gives:
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | | Case 1:
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | |   (51)  all_56_4 = e2 & op(e3, e1) = e2
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | | ALPHA: (51) implies:
% 151.14/22.01  | | | | |   (52)  op(e3, e1) = e2
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | | REF_CLOSE: (13), (16), (27), (37), (52) are inconsistent by sub-proof
% 151.14/22.01  | | | | |            #965.
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | Case 2:
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | |   (53)  all_56_5 = e2 & op(e2, e1) = e2
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | | ALPHA: (53) implies:
% 151.14/22.01  | | | | |   (54)  all_56_5 = e2
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | | BETA: splitting (7) gives:
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | | Case 1:
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | |   (55)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2,
% 151.14/22.01  | | | | | |             e2) = e2)
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | | BETA: splitting (55) gives:
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | | Case 1:
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | |   (56)  all_56_1 = e2 & op(e3, e2) = e2
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | ALPHA: (56) implies:
% 151.14/22.01  | | | | | | |   (57)  all_56_1 = e2
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | BETA: splitting (15) gives:
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | |   (58)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 &
% 151.14/22.01  | | | | | | | |           op(e1, e2) = e1)
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | | BETA: splitting (58) gives:
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | |   (59)  all_56_6 = e1 & op(e1, e3) = e1
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | ALPHA: (59) implies:
% 151.14/22.01  | | | | | | | | |   (60)  all_56_6 = e1
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | REF_CLOSE: (12), (13), (24), (25), (30), (32), (40), (43),
% 151.14/22.01  | | | | | | | | |            (60) are inconsistent by sub-proof #548.
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | |   (61)  all_56_7 = e1 & op(e1, e2) = e1
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | REF_CLOSE: (28), (38), (61) are inconsistent by sub-proof
% 151.14/22.01  | | | | | | | | |            #1111.
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | End of split
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | |   (62)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 &
% 151.14/22.01  | | | | | | | |           op(e1, e0) = e1)
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | | BETA: splitting (62) gives:
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | |   (63)  all_56_8 = e1 & op(e1, e1) = e1
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | ALPHA: (63) implies:
% 151.14/22.01  | | | | | | | | |   (64)  op(e1, e1) = e1
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | REF_CLOSE: (4), (13), (31), (64) are inconsistent by sub-proof
% 151.14/22.01  | | | | | | | | |            #734.
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | |   (65)  all_56_11 = e1 & op(e1, e0) = e1
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | ALPHA: (65) implies:
% 151.14/22.01  | | | | | | | | |   (66)  all_56_11 = e1
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | BETA: splitting (36) gives:
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | |   (67)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 &
% 151.14/22.01  | | | | | | | | | |           op(e2, e1) = e1)
% 151.14/22.01  | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | BETA: splitting (67) gives:
% 151.14/22.01  | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | |   (68)  all_56_4 = e1 & op(e3, e1) = e1
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | ALPHA: (68) implies:
% 151.14/22.01  | | | | | | | | | | |   (69)  all_56_4 = e1
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | COMBINE_EQS: (49), (69) imply:
% 151.14/22.01  | | | | | | | | | | |   (70)  e1 = e0
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | SIMP: (70) implies:
% 151.14/22.01  | | | | | | | | | | |   (71)  e1 = e0
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | COMBINE_EQS: (66), (71) imply:
% 151.14/22.01  | | | | | | | | | | |   (72)  all_56_11 = e0
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | REF_CLOSE: (4), (12), (13), (15), (28), (29), (31), (32),
% 151.14/22.01  | | | | | | | | | | |            (38), (40), (72) are inconsistent by sub-proof
% 151.14/22.01  | | | | | | | | | | |            #145.
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | |   (73)  all_56_5 = e1 & op(e2, e1) = e1
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | ALPHA: (73) implies:
% 151.14/22.01  | | | | | | | | | | |   (74)  all_56_5 = e1
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | COMBINE_EQS: (54), (74) imply:
% 151.14/22.01  | | | | | | | | | | |   (75)  e2 = e1
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | COMBINE_EQS: (57), (75) imply:
% 151.14/22.01  | | | | | | | | | | |   (76)  all_56_1 = e1
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | BETA: splitting (5) gives:
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | |   (77)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 151.14/22.01  | | | | | | | | | | | |           & op(e3, e2) = e2)
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | BETA: splitting (77) gives:
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | |   (78)  all_56_0 = e2 & op(e3, e3) = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | ALPHA: (78) implies:
% 151.14/22.01  | | | | | | | | | | | | |   (79)  op(e3, e3) = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | REF_CLOSE: (13), (25), (40), (79) are inconsistent by
% 151.14/22.01  | | | | | | | | | | | | |            sub-proof #1074.
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | REDUCE: (40), (75) imply:
% 151.14/22.01  | | | | | | | | | | | | |   (80)  $false
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | CLOSE: (80) is inconsistent.
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | End of split
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | |   (81)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 151.14/22.01  | | | | | | | | | | | |           & op(e3, e0) = e2)
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | BETA: splitting (81) gives:
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | |   (82)  all_56_4 = e2 & op(e3, e1) = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | REF_CLOSE: (12), (49), (82) are inconsistent by sub-proof
% 151.14/22.01  | | | | | | | | | | | | |            #949.
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | |   (83)  all_56_9 = e2 & op(e3, e0) = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | ALPHA: (83) implies:
% 151.14/22.01  | | | | | | | | | | | | |   (84)  all_56_9 = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | REF_CLOSE: (4), (13), (14), (20), (25), (32), (49), (76),
% 151.14/22.01  | | | | | | | | | | | | |            (84) are inconsistent by sub-proof #593.
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | End of split
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | End of split
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | End of split
% 151.14/22.01  | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | |   (85)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1
% 151.14/22.01  | | | | | | | | | |           & op(e0, e1) = e1)
% 151.14/22.01  | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | BETA: splitting (85) gives:
% 151.14/22.01  | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | |   (86)  all_56_8 = e1 & op(e1, e1) = e1
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | ALPHA: (86) implies:
% 151.14/22.01  | | | | | | | | | | |   (87)  op(e1, e1) = e1
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | REF_CLOSE: (4), (13), (31), (87) are inconsistent by
% 151.14/22.01  | | | | | | | | | | |            sub-proof #734.
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | |   (88)  all_56_14 = e1 & op(e0, e1) = e1
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | ALPHA: (88) implies:
% 151.14/22.01  | | | | | | | | | | |   (89)  all_56_14 = e1
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | BETA: splitting (33) gives:
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | |   (90)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 151.14/22.01  | | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | BETA: splitting (90) gives:
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | |   (91)  all_56_12 = e2 & op(e0, e3) = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | ALPHA: (91) implies:
% 151.14/22.01  | | | | | | | | | | | | |   (92)  all_56_12 = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | REF_CLOSE: (2), (4), (6), (8), (12), (13), (15), (20), (21),
% 151.14/22.01  | | | | | | | | | | | | |            (25), (28), (29), (31), (32), (39), (40), (92) are
% 151.14/22.01  | | | | | | | | | | | | |            inconsistent by sub-proof #155.
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | |   (93)  all_56_13 = e2 & op(e0, e2) = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | ALPHA: (93) implies:
% 151.14/22.01  | | | | | | | | | | | | |   (94)  all_56_13 = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | COMBINE_EQS: (18), (94) imply:
% 151.14/22.01  | | | | | | | | | | | | |   (95)  e2 = e1
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | COMBINE_EQS: (54), (95) imply:
% 151.14/22.01  | | | | | | | | | | | | |   (96)  all_56_5 = e1
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | REF_CLOSE: (11), (12), (13), (17), (20), (28), (31), (32),
% 151.14/22.01  | | | | | | | | | | | | |            (40), (89), (96) are inconsistent by sub-proof
% 151.14/22.01  | | | | | | | | | | | | |            #247.
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | End of split
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | |   (97)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 151.14/22.01  | | | | | | | | | | | |           e2 & op(e0, e0) = e2)
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | BETA: splitting (97) gives:
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | Case 1:
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | |   (98)  all_56_14 = e2 & op(e0, e1) = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | ALPHA: (98) implies:
% 151.14/22.01  | | | | | | | | | | | | |   (99)  all_56_14 = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | COMBINE_EQS: (89), (99) imply:
% 151.14/22.01  | | | | | | | | | | | | |   (100)  e2 = e1
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | SIMP: (100) implies:
% 151.14/22.01  | | | | | | | | | | | | |   (101)  e2 = e1
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | COMBINE_EQS: (54), (101) imply:
% 151.14/22.01  | | | | | | | | | | | | |   (102)  all_56_5 = e1
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | REF_CLOSE: (11), (12), (13), (17), (20), (28), (31), (32),
% 151.14/22.01  | | | | | | | | | | | | |            (40), (89), (102) are inconsistent by sub-proof
% 151.14/22.01  | | | | | | | | | | | | |            #247.
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | Case 2:
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | |   (103)  all_56_15 = e2 & op(e0, e0) = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | ALPHA: (103) implies:
% 151.14/22.01  | | | | | | | | | | | | |   (104)  op(e0, e0) = e2
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | | REF_CLOSE: (12), (13), (41), (104) are inconsistent by
% 151.14/22.01  | | | | | | | | | | | | |            sub-proof #1043.
% 151.14/22.01  | | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | | End of split
% 151.14/22.01  | | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | | End of split
% 151.14/22.01  | | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | | End of split
% 151.14/22.01  | | | | | | | | | | 
% 151.14/22.01  | | | | | | | | | End of split
% 151.14/22.01  | | | | | | | | | 
% 151.14/22.01  | | | | | | | | End of split
% 151.14/22.01  | | | | | | | | 
% 151.14/22.01  | | | | | | | End of split
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | Case 2:
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | |   (105)  all_56_3 = e2 & op(e2, e2) = e2
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | ALPHA: (105) implies:
% 151.14/22.01  | | | | | | |   (106)  op(e2, e2) = e2
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | REF_CLOSE: (13), (32), (42), (106) are inconsistent by sub-proof
% 151.14/22.01  | | | | | | |            #1179.
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | End of split
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | Case 2:
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | |   (107)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 &
% 151.14/22.01  | | | | | |            op(e0, e2) = e2)
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | | BETA: splitting (107) gives:
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | | Case 1:
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | |   (108)  all_56_7 = e2 & op(e1, e2) = e2
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | ALPHA: (108) implies:
% 151.14/22.01  | | | | | | |   (109)  all_56_7 = e2
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | REF_CLOSE: (4), (10), (12), (13), (18), (19), (20), (23), (26),
% 151.14/22.01  | | | | | | |            (28), (35), (44), (46), (109) are inconsistent by
% 151.14/22.01  | | | | | | |            sub-proof #117.
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | Case 2:
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | |   (110)  all_56_13 = e2 & op(e0, e2) = e2
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | ALPHA: (110) implies:
% 151.14/22.01  | | | | | | |   (111)  all_56_13 = e2
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | COMBINE_EQS: (18), (111) imply:
% 151.14/22.01  | | | | | | |   (112)  e2 = e1
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | SIMP: (112) implies:
% 151.14/22.01  | | | | | | |   (113)  e2 = e1
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | COMBINE_EQS: (6), (113) imply:
% 151.14/22.01  | | | | | | |   (114)  all_56_6 = e1
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | | REF_CLOSE: (12), (13), (24), (25), (30), (32), (40), (43), (114)
% 151.14/22.01  | | | | | | |            are inconsistent by sub-proof #548.
% 151.14/22.01  | | | | | | | 
% 151.14/22.01  | | | | | | End of split
% 151.14/22.01  | | | | | | 
% 151.14/22.01  | | | | | End of split
% 151.14/22.01  | | | | | 
% 151.14/22.01  | | | | End of split
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | Case 2:
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | |   (115)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0,
% 151.14/22.01  | | | |              e1) = e2)
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | | REF_CLOSE: (1), (13), (31), (32), (45), (115) are inconsistent by
% 151.14/22.01  | | | |            sub-proof #275.
% 151.14/22.01  | | | | 
% 151.14/22.01  | | | End of split
% 151.14/22.01  | | | 
% 151.14/22.01  | | Case 2:
% 151.14/22.01  | | | 
% 151.14/22.01  | | |   (116)  all_56_5 = e0 & op(e2, e1) = e0
% 151.14/22.01  | | | 
% 151.14/22.02  | | | ALPHA: (116) implies:
% 151.14/22.02  | | |   (117)  op(e2, e1) = e0
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (3), (9), (13), (34), (117) are inconsistent by sub-proof #164.
% 151.14/22.02  | | | 
% 151.14/22.02  | | End of split
% 151.14/22.02  | | 
% 151.14/22.02  | Case 2:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (118)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 151.14/22.02  | |            e0)
% 151.14/22.02  | | 
% 151.14/22.02  | | REF_CLOSE: (1), (13), (20), (22), (31), (118) are inconsistent by sub-proof
% 151.14/22.02  | |            #198.
% 151.14/22.02  | | 
% 151.14/22.02  | End of split
% 151.14/22.02  | 
% 151.14/22.02  End of proof
% 151.14/22.02  
% 151.14/22.02  Sub-proof #63 shows that the following formulas are inconsistent:
% 151.14/22.02  ----------------------------------------------------------------
% 151.14/22.02    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 151.14/22.02    (2)   ~ (e2 = e0)
% 151.14/22.02    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.02    (4)  op(e3, e3) = e1
% 151.14/22.02    (5)  op(e2, e3) = e0
% 151.14/22.02    (6)   ~ (e2 = e1)
% 151.14/22.02    (7)  op(e2, e3) = all_52_1
% 151.14/22.02  
% 151.14/22.02  Begin of proof
% 151.14/22.02  | 
% 151.14/22.02  | BETA: splitting (1) gives:
% 151.14/22.02  | 
% 151.14/22.02  | Case 1:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (8)  all_56_0 = e2 & op(e3, e3) = e2
% 151.14/22.02  | | 
% 151.14/22.02  | | ALPHA: (8) implies:
% 151.14/22.02  | |   (9)  op(e3, e3) = e2
% 151.14/22.02  | | 
% 151.14/22.02  | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #1074.
% 151.14/22.02  | | 
% 151.14/22.02  | Case 2:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (10)  all_56_2 = e2 & op(e2, e3) = e2
% 151.14/22.02  | | 
% 151.14/22.02  | | ALPHA: (10) implies:
% 151.14/22.02  | |   (11)  op(e2, e3) = e2
% 151.14/22.02  | | 
% 151.14/22.02  | | REF_CLOSE: (2), (3), (5), (7), (11) are inconsistent by sub-proof #128.
% 151.14/22.02  | | 
% 151.14/22.02  | End of split
% 151.14/22.02  | 
% 151.14/22.02  End of proof
% 151.14/22.02  
% 151.14/22.02  Sub-proof #64 shows that the following formulas are inconsistent:
% 151.14/22.02  ----------------------------------------------------------------
% 151.14/22.02    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.02    (2)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.14/22.02             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.14/22.02           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.14/22.02           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.14/22.02           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.14/22.02           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 151.14/22.02    (3)   ~ (e3 = e0)
% 151.14/22.02    (4)  op(e0, e0) = e0
% 151.14/22.02    (5)  op(e2, e2) = e3
% 151.14/22.02  
% 151.14/22.02  Begin of proof
% 151.14/22.02  | 
% 151.14/22.02  | BETA: splitting (2) gives:
% 151.14/22.02  | 
% 151.14/22.02  | Case 1:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (6)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.14/22.02  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.14/22.02  | |        all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 151.14/22.02  | | 
% 151.14/22.02  | | ALPHA: (6) implies:
% 151.14/22.02  | |   (7)   ~ (all_57_12 = e3)
% 151.14/22.02  | |   (8)  op(e2, e2) = all_57_12
% 151.14/22.02  | | 
% 151.14/22.02  | | REF_CLOSE: (1), (5), (7), (8) are inconsistent by sub-proof #126.
% 151.14/22.02  | | 
% 151.14/22.02  | Case 2:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (9)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 151.14/22.02  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 151.14/22.02  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 151.14/22.02  | | 
% 151.14/22.02  | | ALPHA: (9) implies:
% 151.14/22.02  | |   (10)  op(e0, e0) = e3
% 151.14/22.02  | | 
% 151.14/22.02  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1143.
% 151.14/22.02  | | 
% 151.14/22.02  | End of split
% 151.14/22.02  | 
% 151.14/22.02  End of proof
% 151.14/22.02  
% 151.14/22.02  Sub-proof #65 shows that the following formulas are inconsistent:
% 151.14/22.02  ----------------------------------------------------------------
% 151.14/22.02    (1)  op(e3, e3) = all_14_2
% 151.14/22.02    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.02    (3)   ~ (all_52_12 = all_14_2)
% 151.14/22.02    (4)  op(e0, e0) = e2
% 151.14/22.02    (5)  op(e1, e0) = all_52_14
% 151.14/22.02    (6)  op(e3, e0) = all_52_12
% 151.14/22.02    (7)  op(e2, e0) = all_52_13
% 151.14/22.02    (8)   ~ (e3 = e2)
% 151.14/22.02    (9)   ~ (all_52_14 = e3)
% 151.14/22.02    (10)   ~ (all_52_13 = e3)
% 151.14/22.02    (11)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 151.14/22.02          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.14/22.02    (12)  op(e3, e3) = e3
% 151.14/22.02  
% 151.14/22.02  Begin of proof
% 151.14/22.02  | 
% 151.14/22.02  | BETA: splitting (11) gives:
% 151.14/22.02  | 
% 151.14/22.02  | Case 1:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (13)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 151.14/22.02  | |           e3)
% 151.14/22.02  | | 
% 151.14/22.02  | | BETA: splitting (13) gives:
% 151.14/22.02  | | 
% 151.14/22.02  | | Case 1:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (14)  all_56_9 = e3 & op(e3, e0) = e3
% 151.14/22.02  | | | 
% 151.14/22.02  | | | ALPHA: (14) implies:
% 151.14/22.02  | | |   (15)  op(e3, e0) = e3
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (1), (2), (3), (6), (12), (15) are inconsistent by sub-proof
% 151.14/22.02  | | |            #71.
% 151.14/22.02  | | | 
% 151.14/22.02  | | Case 2:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (16)  all_56_10 = e3 & op(e2, e0) = e3
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (2), (7), (10), (16) are inconsistent by sub-proof #114.
% 151.14/22.02  | | | 
% 151.14/22.02  | | End of split
% 151.14/22.02  | | 
% 151.14/22.02  | Case 2:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (17)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 151.14/22.02  | |           e3)
% 151.14/22.02  | | 
% 151.14/22.02  | | BETA: splitting (17) gives:
% 151.14/22.02  | | 
% 151.14/22.02  | | Case 1:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (18)  all_56_11 = e3 & op(e1, e0) = e3
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (2), (5), (9), (18) are inconsistent by sub-proof #66.
% 151.14/22.02  | | | 
% 151.14/22.02  | | Case 2:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (19)  all_56_15 = e3 & op(e0, e0) = e3
% 151.14/22.02  | | | 
% 151.14/22.02  | | | ALPHA: (19) implies:
% 151.14/22.02  | | |   (20)  op(e0, e0) = e3
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (2), (4), (8), (20) are inconsistent by sub-proof #1087.
% 151.14/22.02  | | | 
% 151.14/22.02  | | End of split
% 151.14/22.02  | | 
% 151.14/22.02  | End of split
% 151.14/22.02  | 
% 151.14/22.02  End of proof
% 151.14/22.02  
% 151.14/22.02  Sub-proof #66 shows that the following formulas are inconsistent:
% 151.14/22.02  ----------------------------------------------------------------
% 151.14/22.02    (1)  all_56_11 = e3 & op(e1, e0) = e3
% 151.14/22.02    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.02    (3)  op(e1, e0) = all_52_14
% 151.14/22.02    (4)   ~ (all_52_14 = e3)
% 151.14/22.02  
% 151.14/22.02  Begin of proof
% 151.14/22.02  | 
% 151.14/22.02  | ALPHA: (1) implies:
% 151.14/22.02  |   (5)  op(e1, e0) = e3
% 151.14/22.02  | 
% 151.14/22.02  | GROUND_INST: instantiating (2) with all_52_14, e3, e0, e1, simplifying with
% 151.14/22.02  |              (3), (5) gives:
% 151.14/22.02  |   (6)  all_52_14 = e3
% 151.14/22.02  | 
% 151.14/22.02  | REDUCE: (4), (6) imply:
% 151.14/22.02  |   (7)  $false
% 151.14/22.02  | 
% 151.14/22.02  | CLOSE: (7) is inconsistent.
% 151.14/22.02  | 
% 151.14/22.02  End of proof
% 151.14/22.02  
% 151.14/22.02  Sub-proof #67 shows that the following formulas are inconsistent:
% 151.14/22.02  ----------------------------------------------------------------
% 151.14/22.02    (1)  op(e0, e1) = all_52_11
% 151.14/22.02    (2)   ~ (e3 = e1)
% 151.14/22.02    (3)  op(e0, e2) = all_52_7
% 151.14/22.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.02    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 151.14/22.02             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.14/22.02           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 151.14/22.02           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.14/22.02             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/22.02           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/22.02           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 151.14/22.02           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 151.14/22.02           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 151.14/22.02           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 151.14/22.02           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 151.14/22.02         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 151.14/22.02             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.02           $i(all_57_7))
% 151.14/22.02    (6)   ~ (e3 = e0)
% 151.14/22.02    (7)  all_57_15 = e0
% 151.14/22.02    (8)   ~ (all_52_11 = e0)
% 151.14/22.02    (9)   ~ (all_52_7 = e0)
% 151.14/22.02    (10)  op(e1, e1) = e3
% 151.14/22.02    (11)   ~ (e3 = e2)
% 151.14/22.02    (12)  op(e0, e3) = e3
% 151.14/22.02    (13)  op(e2, e2) = e3
% 151.14/22.02  
% 151.14/22.02  Begin of proof
% 151.14/22.02  | 
% 151.14/22.02  | BETA: splitting (5) gives:
% 151.14/22.02  | 
% 151.14/22.02  | Case 1:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (14)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 151.14/22.02  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 151.14/22.02  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 151.14/22.02  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 151.14/22.02  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 151.14/22.02  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 151.14/22.02  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/22.02  | |           $i(all_57_3))
% 151.14/22.02  | | 
% 151.14/22.02  | | BETA: splitting (14) gives:
% 151.14/22.02  | | 
% 151.14/22.02  | | Case 1:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (15)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.14/22.02  | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 151.14/22.02  | | |         op(e0, e3) = e0 & $i(all_57_0)
% 151.14/22.02  | | | 
% 151.14/22.02  | | | ALPHA: (15) implies:
% 151.14/22.02  | | |   (16)  op(e0, e3) = e0
% 151.14/22.02  | | | 
% 151.14/22.02  | | | GROUND_INST: instantiating (4) with e3, e0, e3, e0, simplifying with (12),
% 151.14/22.02  | | |              (16) gives:
% 151.14/22.02  | | |   (17)  e3 = e0
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REDUCE: (6), (17) imply:
% 151.14/22.02  | | |   (18)  $false
% 151.14/22.02  | | | 
% 151.14/22.02  | | | CLOSE: (18) is inconsistent.
% 151.14/22.02  | | | 
% 151.14/22.02  | | Case 2:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (19)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.14/22.02  | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 151.14/22.02  | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 151.14/22.02  | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 151.14/22.02  | | |           & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 151.14/22.02  | | | 
% 151.14/22.02  | | | BETA: splitting (19) gives:
% 151.14/22.02  | | | 
% 151.14/22.02  | | | Case 1:
% 151.14/22.02  | | | | 
% 151.14/22.02  | | | |   (20)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.14/22.02  | | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 151.14/22.02  | | | |         op(e0, e3) = e0 & $i(all_57_1)
% 151.14/22.02  | | | | 
% 151.14/22.02  | | | | ALPHA: (20) implies:
% 151.14/22.02  | | | |   (21)   ~ (all_57_15 = e3)
% 151.14/22.02  | | | |   (22)  op(e0, e3) = e0
% 151.14/22.02  | | | | 
% 151.14/22.02  | | | | REDUCE: (7), (21) imply:
% 151.14/22.02  | | | |   (23)   ~ (e3 = e0)
% 151.14/22.02  | | | | 
% 151.14/22.02  | | | | GROUND_INST: instantiating (4) with e3, e0, e3, e0, simplifying with
% 151.14/22.02  | | | |              (12), (22) gives:
% 151.14/22.02  | | | |   (24)  e3 = e0
% 151.14/22.02  | | | | 
% 151.14/22.02  | | | | REDUCE: (6), (24) imply:
% 151.14/22.02  | | | |   (25)  $false
% 151.14/22.02  | | | | 
% 151.14/22.02  | | | | CLOSE: (25) is inconsistent.
% 151.14/22.02  | | | | 
% 151.14/22.02  | | | Case 2:
% 151.14/22.02  | | | | 
% 151.14/22.02  | | | |   (26)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.14/22.02  | | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 151.14/22.02  | | | |         op(e0, e2) = e0 & $i(all_57_3)
% 151.14/22.02  | | | | 
% 151.14/22.02  | | | | ALPHA: (26) implies:
% 151.14/22.02  | | | |   (27)  op(e0, e2) = e0
% 151.14/22.02  | | | | 
% 151.14/22.02  | | | | REF_CLOSE: (3), (4), (9), (27) are inconsistent by sub-proof #1036.
% 151.14/22.02  | | | | 
% 151.14/22.02  | | | End of split
% 151.14/22.02  | | | 
% 151.14/22.02  | | End of split
% 151.14/22.02  | | 
% 151.14/22.02  | Case 2:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (28)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 151.14/22.02  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.14/22.02  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/22.02  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.14/22.02  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 151.14/22.02  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.14/22.02  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.02  | |           $i(all_57_7))
% 151.14/22.02  | | 
% 151.14/22.02  | | BETA: splitting (28) gives:
% 151.14/22.02  | | 
% 151.14/22.02  | | Case 1:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (29)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/22.02  | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.14/22.02  | | |         op(e0, e2) = e0 & $i(all_57_4)
% 151.14/22.02  | | | 
% 151.14/22.02  | | | ALPHA: (29) implies:
% 151.14/22.02  | | |   (30)  op(e1, e1) = e2
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (4), (10), (11), (30) are inconsistent by sub-proof #834.
% 151.14/22.02  | | | 
% 151.14/22.02  | | Case 2:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (31)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.14/22.02  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.14/22.02  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 151.14/22.02  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 151.14/22.02  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (1), (2), (4), (8), (13), (31) are inconsistent by sub-proof
% 151.14/22.02  | | |            #68.
% 151.14/22.02  | | | 
% 151.14/22.02  | | End of split
% 151.14/22.02  | | 
% 151.14/22.02  | End of split
% 151.14/22.02  | 
% 151.14/22.02  End of proof
% 151.14/22.02  
% 151.14/22.02  Sub-proof #68 shows that the following formulas are inconsistent:
% 151.14/22.02  ----------------------------------------------------------------
% 151.14/22.02    (1)  op(e0, e1) = all_52_11
% 151.14/22.02    (2)   ~ (e3 = e1)
% 151.14/22.02    (3)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.14/22.02             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/22.02           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 151.14/22.02           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 151.14/22.02             e1) = e0 & $i(all_57_7))
% 151.14/22.02    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.02    (5)   ~ (all_52_11 = e0)
% 151.14/22.02    (6)  op(e2, e2) = e3
% 151.14/22.02  
% 151.14/22.02  Begin of proof
% 151.14/22.02  | 
% 151.14/22.02  | BETA: splitting (3) gives:
% 151.14/22.02  | 
% 151.14/22.02  | Case 1:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (7)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.14/22.02  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.14/22.02  | |        $i(all_57_6)
% 151.14/22.02  | | 
% 151.14/22.02  | | ALPHA: (7) implies:
% 151.14/22.02  | |   (8)  op(e0, e1) = e0
% 151.14/22.02  | | 
% 151.14/22.02  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1124.
% 151.14/22.02  | | 
% 151.14/22.02  | Case 2:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (9)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 151.14/22.02  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.02  | |        $i(all_57_7)
% 151.14/22.02  | | 
% 151.14/22.02  | | ALPHA: (9) implies:
% 151.14/22.02  | |   (10)  op(e2, e2) = e1
% 151.14/22.02  | | 
% 151.14/22.02  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #1136.
% 151.14/22.02  | | 
% 151.14/22.02  | End of split
% 151.14/22.02  | 
% 151.14/22.02  End of proof
% 151.14/22.02  
% 151.14/22.02  Sub-proof #69 shows that the following formulas are inconsistent:
% 151.14/22.02  ----------------------------------------------------------------
% 151.14/22.02    (1)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 151.14/22.02           all_57_12 & $i(all_57_12))
% 151.14/22.02    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.02    (3)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 151.14/22.02             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 151.14/22.02           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 151.14/22.02           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 151.14/22.02           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 151.14/22.02           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 151.14/22.02           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 151.14/22.02           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 151.14/22.02           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 151.14/22.02    (4)   ~ (e1 = e0)
% 151.14/22.02    (5)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 151.14/22.02           all_57_14 & $i(all_57_14))
% 151.14/22.02    (6)  op(e0, e0) = e0
% 151.14/22.02  
% 151.14/22.02  Begin of proof
% 151.14/22.02  | 
% 151.14/22.02  | BETA: splitting (3) gives:
% 151.14/22.02  | 
% 151.14/22.02  | Case 1:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (7)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 151.14/22.02  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 151.14/22.02  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 151.14/22.02  | | 
% 151.14/22.02  | | ALPHA: (7) implies:
% 151.14/22.02  | |   (8)  op(e0, e0) = e1
% 151.14/22.02  | | 
% 151.14/22.02  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1040.
% 151.14/22.02  | | 
% 151.14/22.02  | Case 2:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (9)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 151.14/22.02  | |            = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) =
% 151.14/22.02  | |          e0 & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 151.14/22.02  | |        (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 151.14/22.02  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 151.14/22.02  | |          e0 & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 151.14/22.02  | | 
% 151.14/22.02  | | BETA: splitting (9) gives:
% 151.14/22.02  | | 
% 151.14/22.02  | | Case 1:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (10)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/22.02  | | |         (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/22.02  | | |         op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.14/22.02  | | |         $i(all_57_11)
% 151.14/22.02  | | | 
% 151.14/22.02  | | | ALPHA: (10) implies:
% 151.14/22.02  | | |   (11)  all_57_12 = e0
% 151.14/22.02  | | |   (12)   ~ (all_57_11 = e2)
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (1), (11), (12) are inconsistent by sub-proof #890.
% 151.14/22.02  | | | 
% 151.14/22.02  | | Case 2:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (13)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.14/22.02  | | |         (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/22.02  | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.14/22.02  | | |         $i(all_57_13)
% 151.14/22.02  | | | 
% 151.14/22.02  | | | ALPHA: (13) implies:
% 151.14/22.02  | | |   (14)   ~ (all_57_13 = e1)
% 151.14/22.02  | | |   (15)  op(e1, e1) = e0
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (2), (5), (14), (15) are inconsistent by sub-proof #959.
% 151.14/22.02  | | | 
% 151.14/22.02  | | End of split
% 151.14/22.02  | | 
% 151.14/22.02  | End of split
% 151.14/22.02  | 
% 151.14/22.02  End of proof
% 151.14/22.02  
% 151.14/22.02  Sub-proof #70 shows that the following formulas are inconsistent:
% 151.14/22.02  ----------------------------------------------------------------
% 151.14/22.02    (1)   ~ (all_52_13 = e1)
% 151.14/22.02    (2)   ~ (e3 = e1)
% 151.14/22.02    (3)  op(e3, e0) = e3
% 151.14/22.02    (4)  op(e3, e3) = all_14_2
% 151.14/22.02    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.02    (6)   ~ (all_52_12 = all_14_2)
% 151.14/22.02    (7)   ~ (all_52_14 = e1)
% 151.14/22.02    (8)  op(e1, e0) = all_52_14
% 151.14/22.02    (9)  op(e3, e0) = all_52_12
% 151.14/22.02    (10)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 151.14/22.02          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 151.14/22.02    (11)  op(e2, e0) = all_52_13
% 151.14/22.02    (12)   ~ (e1 = e0)
% 151.14/22.02    (13)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.14/22.02              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.02            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.14/22.02                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.14/22.02              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/22.02          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.14/22.02              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.02            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.14/22.02                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.14/22.02              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/22.02          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 151.14/22.02              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.02            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 151.14/22.02                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 151.14/22.02              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/22.02          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 151.14/22.02              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.02            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 151.14/22.02                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 151.14/22.02                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.14/22.02                $i(all_57_14))))
% 151.14/22.02    (14)  op(e1, e1) = e3
% 151.14/22.02    (15)   ~ (e3 = e2)
% 151.14/22.02    (16)  op(e2, e2) = e3
% 151.14/22.02  
% 151.14/22.02  Begin of proof
% 151.14/22.02  | 
% 151.14/22.02  | BETA: splitting (13) gives:
% 151.14/22.02  | 
% 151.14/22.02  | Case 1:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (17)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 151.14/22.02  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 151.14/22.02  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 151.14/22.02  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.14/22.02  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 151.14/22.02  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 151.14/22.02  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 151.14/22.02  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.02  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 151.14/22.02  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 151.14/22.02  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 151.14/22.02  | |               $i(all_57_15))))
% 151.14/22.02  | | 
% 151.14/22.02  | | BETA: splitting (17) gives:
% 151.14/22.02  | | 
% 151.14/22.02  | | Case 1:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (18)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 151.14/22.02  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 151.14/22.02  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 151.14/22.02  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.14/22.02  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 151.14/22.02  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.14/22.02  | | | 
% 151.14/22.02  | | | ALPHA: (18) implies:
% 151.14/22.02  | | |   (19)  op(e3, e3) = e3
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (3), (4), (5), (6), (9), (19) are inconsistent by sub-proof
% 151.14/22.02  | | |            #71.
% 151.14/22.02  | | | 
% 151.14/22.02  | | Case 2:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (20)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 151.14/22.02  | | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.14/22.02  | | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 151.14/22.02  | | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.14/22.02  | | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 151.14/22.02  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.14/22.02  | | | 
% 151.14/22.02  | | | ALPHA: (20) implies:
% 151.14/22.02  | | |   (21)  op(e2, e2) = e2
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (5), (15), (16), (21) are inconsistent by sub-proof #1179.
% 151.14/22.02  | | | 
% 151.14/22.02  | | End of split
% 151.14/22.02  | | 
% 151.14/22.02  | Case 2:
% 151.14/22.02  | | 
% 151.14/22.02  | |   (22)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.14/22.02  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.14/22.02  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.14/22.02  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.02  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.14/22.02  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 151.14/22.02  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 151.14/22.02  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.02  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 151.14/22.02  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 151.14/22.02  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 151.14/22.02  | |               all_57_14 & $i(all_57_14))))
% 151.14/22.02  | | 
% 151.14/22.02  | | BETA: splitting (22) gives:
% 151.14/22.02  | | 
% 151.14/22.02  | | Case 1:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (23)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.14/22.02  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.14/22.02  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.14/22.02  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.02  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.14/22.02  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.14/22.02  | | | 
% 151.14/22.02  | | | ALPHA: (23) implies:
% 151.14/22.02  | | |   (24)  op(e1, e1) = e1
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (2), (5), (14), (24) are inconsistent by sub-proof #734.
% 151.14/22.02  | | | 
% 151.14/22.02  | | Case 2:
% 151.14/22.02  | | | 
% 151.14/22.02  | | |   (25)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 151.14/22.02  | | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.14/22.02  | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 151.14/22.02  | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.02  | | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 151.14/22.02  | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 151.14/22.02  | | | 
% 151.14/22.02  | | | ALPHA: (25) implies:
% 151.14/22.02  | | |   (26)  op(e0, e0) = e0
% 151.14/22.02  | | | 
% 151.14/22.02  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (26) are
% 151.14/22.02  | | |            inconsistent by sub-proof #510.
% 151.14/22.02  | | | 
% 151.14/22.02  | | End of split
% 151.14/22.02  | | 
% 151.14/22.02  | End of split
% 151.14/22.02  | 
% 151.14/22.02  End of proof
% 151.14/22.02  
% 151.14/22.02  Sub-proof #71 shows that the following formulas are inconsistent:
% 151.14/22.02  ----------------------------------------------------------------
% 151.14/22.02    (1)  op(e3, e0) = e3
% 151.14/22.02    (2)  op(e3, e3) = all_14_2
% 151.14/22.02    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.02    (4)   ~ (all_52_12 = all_14_2)
% 151.14/22.02    (5)  op(e3, e0) = all_52_12
% 151.14/22.02    (6)  op(e3, e3) = e3
% 151.14/22.02  
% 151.14/22.02  Begin of proof
% 151.14/22.02  | 
% 151.14/22.02  | GROUND_INST: instantiating (3) with all_52_12, e3, e0, e3, simplifying with
% 151.14/22.02  |              (1), (5) gives:
% 151.14/22.02  |   (7)  all_52_12 = e3
% 151.14/22.02  | 
% 151.14/22.02  | GROUND_INST: instantiating (3) with all_14_2, e3, e3, e3, simplifying with
% 151.14/22.02  |              (2), (6) gives:
% 151.14/22.02  |   (8)  all_14_2 = e3
% 151.14/22.02  | 
% 151.14/22.02  | REDUCE: (4), (7), (8) imply:
% 151.14/22.02  |   (9)  $false
% 151.14/22.02  | 
% 151.14/22.02  | CLOSE: (9) is inconsistent.
% 151.14/22.02  | 
% 151.14/22.02  End of proof
% 151.14/22.02  
% 151.14/22.02  Sub-proof #72 shows that the following formulas are inconsistent:
% 151.14/22.02  ----------------------------------------------------------------
% 151.14/22.02    (1)   ~ (e3 = e1)
% 151.14/22.02    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.02    (3)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 151.14/22.02           all_57_14 & $i(all_57_14))
% 151.14/22.03    (4)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 151.14/22.03             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.14/22.03           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 151.14/22.03           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.14/22.03             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/22.03           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/22.03           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 151.14/22.03           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 151.14/22.03           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 151.14/22.03           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 151.14/22.03           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 151.14/22.03         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 151.14/22.03             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.03           $i(all_57_7))
% 151.14/22.03    (5)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 151.14/22.03           all_57_12 & $i(all_57_12))
% 151.14/22.03    (6)  op(e1, e1) = e3
% 151.14/22.03    (7)   ~ (e3 = e2)
% 151.14/22.03    (8)  op(e3, e3) = e3
% 151.14/22.03    (9)  op(e2, e2) = e3
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | BETA: splitting (4) gives:
% 151.14/22.03  | 
% 151.14/22.03  | Case 1:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (10)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 151.14/22.03  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 151.14/22.03  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 151.14/22.03  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 151.14/22.03  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 151.14/22.03  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 151.14/22.03  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.14/22.03  | |           $i(all_57_3))
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (2), (3), (5), (7), (8), (10) are inconsistent by sub-proof #406.
% 151.14/22.03  | | 
% 151.14/22.03  | Case 2:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (11)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 151.14/22.03  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.14/22.03  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/22.03  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.14/22.03  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 151.14/22.03  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.14/22.03  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.03  | |           $i(all_57_7))
% 151.14/22.03  | | 
% 151.14/22.03  | | BETA: splitting (11) gives:
% 151.14/22.03  | | 
% 151.14/22.03  | | Case 1:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (12)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.14/22.03  | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.14/22.03  | | |         op(e0, e2) = e0 & $i(all_57_4)
% 151.14/22.03  | | | 
% 151.14/22.03  | | | ALPHA: (12) implies:
% 151.14/22.03  | | |   (13)  op(e1, e1) = e2
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REF_CLOSE: (2), (6), (7), (13) are inconsistent by sub-proof #834.
% 151.14/22.03  | | | 
% 151.14/22.03  | | Case 2:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (14)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.14/22.03  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.14/22.03  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 151.14/22.03  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 151.14/22.03  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.14/22.03  | | | 
% 151.14/22.03  | | | BETA: splitting (14) gives:
% 151.14/22.03  | | | 
% 151.14/22.03  | | | Case 1:
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | |   (15)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.14/22.03  | | | |         (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.14/22.03  | | | |         op(e0, e1) = e0 & $i(all_57_6)
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | | ALPHA: (15) implies:
% 151.14/22.03  | | | |   (16)  op(e3, e3) = e1
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | | REF_CLOSE: (1), (2), (8), (16) are inconsistent by sub-proof #1178.
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | Case 2:
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | |   (17)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.14/22.03  | | | |         (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.14/22.03  | | | |         op(e0, e1) = e0 & $i(all_57_7)
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | | ALPHA: (17) implies:
% 151.14/22.03  | | | |   (18)  op(e2, e2) = e1
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | | REF_CLOSE: (1), (2), (9), (18) are inconsistent by sub-proof #1136.
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | End of split
% 151.14/22.03  | | | 
% 151.14/22.03  | | End of split
% 151.14/22.03  | | 
% 151.14/22.03  | End of split
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #73 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)  all_56_12 = e3 & op(e0, e3) = e3
% 151.14/22.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.03    (3)  op(e0, e3) = all_52_3
% 151.14/22.03    (4)   ~ (all_52_3 = e3)
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | ALPHA: (1) implies:
% 151.14/22.03  |   (5)  op(e0, e3) = e3
% 151.14/22.03  | 
% 151.14/22.03  | GROUND_INST: instantiating (2) with all_52_3, e3, e3, e0, simplifying with
% 151.14/22.03  |              (3), (5) gives:
% 151.14/22.03  |   (6)  all_52_3 = e3
% 151.14/22.03  | 
% 151.14/22.03  | REDUCE: (4), (6) imply:
% 151.14/22.03  |   (7)  $false
% 151.14/22.03  | 
% 151.14/22.03  | CLOSE: (7) is inconsistent.
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #74 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)   ~ (all_52_6 = e1)
% 151.14/22.03    (2)  op(e0, e2) = all_52_7
% 151.14/22.03    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.03    (4)   ~ (all_52_7 = e1)
% 151.14/22.03    (5)  op(e1, e2) = all_52_6
% 151.14/22.03    (6)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | BETA: splitting (6) gives:
% 151.14/22.03  | 
% 151.14/22.03  | Case 1:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (7)  all_56_7 = e1 & op(e1, e2) = e1
% 151.14/22.03  | | 
% 151.14/22.03  | | ALPHA: (7) implies:
% 151.14/22.03  | |   (8)  op(e1, e2) = e1
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1042.
% 151.14/22.03  | | 
% 151.14/22.03  | Case 2:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (9)  all_56_13 = e1 & op(e0, e2) = e1
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #414.
% 151.14/22.03  | | 
% 151.14/22.03  | End of split
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #75 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 151.14/22.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.03    (3)  op(e0, e0) = e2
% 151.14/22.03    (4)  op(e0, e1) = e0
% 151.14/22.03    (5)   ~ (e1 = e0)
% 151.14/22.03    (6)   ~ (e2 = e1)
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | BETA: splitting (1) gives:
% 151.14/22.03  | 
% 151.14/22.03  | Case 1:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (7)  all_56_14 = e1 & op(e0, e1) = e1
% 151.14/22.03  | | 
% 151.14/22.03  | | ALPHA: (7) implies:
% 151.14/22.03  | |   (8)  op(e0, e1) = e1
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #899.
% 151.14/22.03  | | 
% 151.14/22.03  | Case 2:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (9)  all_56_15 = e1 & op(e0, e0) = e1
% 151.14/22.03  | | 
% 151.14/22.03  | | ALPHA: (9) implies:
% 151.14/22.03  | |   (10)  op(e0, e0) = e1
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #978.
% 151.14/22.03  | | 
% 151.14/22.03  | End of split
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #76 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)  all_56_1 = e1
% 151.14/22.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.03    (3)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 151.14/22.03    (4)   ~ (e3 = e2)
% 151.14/22.03    (5)   ~ (e2 = e1)
% 151.14/22.03    (6)  op(e2, e2) = e3
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | BETA: splitting (3) gives:
% 151.14/22.03  | 
% 151.14/22.03  | Case 1:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (7)  all_56_1 = e2 & op(e3, e2) = e2
% 151.14/22.03  | | 
% 151.14/22.03  | | ALPHA: (7) implies:
% 151.14/22.03  | |   (8)  all_56_1 = e2
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #595.
% 151.14/22.03  | | 
% 151.14/22.03  | Case 2:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (9)  all_56_3 = e2 & op(e2, e2) = e2
% 151.14/22.03  | | 
% 151.14/22.03  | | ALPHA: (9) implies:
% 151.14/22.03  | |   (10)  op(e2, e2) = e2
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #1179.
% 151.14/22.03  | | 
% 151.14/22.03  | End of split
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #77 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)  op(e0, e1) = all_52_11
% 151.14/22.03    (2)   ~ (all_52_7 = all_52_11)
% 151.14/22.03    (3)   ~ (all_52_2 = all_52_6)
% 151.14/22.03    (4)   ~ (all_52_3 = all_52_7)
% 151.14/22.03    (5)  all_54_9 = all_52_6
% 151.14/22.03    (6)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 151.14/22.03             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.03           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 151.14/22.03               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 151.14/22.03             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/22.03         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 151.14/22.03             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.03           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 151.14/22.03               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 151.14/22.03             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 151.14/22.03    (7)  op(e1, e1) = all_4_2
% 151.14/22.03    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.03    (9)   ~ (all_52_2 = all_4_2)
% 151.14/22.03    (10)   ~ (all_52_7 = e1)
% 151.14/22.03    (11)   ~ (all_52_3 = all_52_11)
% 151.14/22.03    (12)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 151.14/22.03    (13)  op(e0, e0) = e1
% 151.14/22.03    (14)   ~ (all_52_7 = e3)
% 151.14/22.03    (15)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 151.14/22.03    (16)   ~ (all_52_2 = e2)
% 151.14/22.03    (17)   ~ (all_52_6 = e3)
% 151.14/22.03    (18)   ~ (all_52_3 = e1)
% 151.14/22.03    (19)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 151.14/22.03    (20)  all_54_12 = all_52_3
% 151.14/22.03    (21)   ~ (e1 = e0)
% 151.14/22.03    (22)  all_54_8 = all_52_2
% 151.14/22.03    (23)  all_54_13 = all_52_7
% 151.14/22.03    (24)   ~ (all_52_2 = all_52_3)
% 151.14/22.03    (25)   ~ (all_52_6 = all_52_7)
% 151.14/22.03    (26)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 151.14/22.03    (27)   ~ (all_52_6 = all_4_2)
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | BETA: splitting (6) gives:
% 151.14/22.03  | 
% 151.14/22.03  | Case 1:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (28)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.14/22.03  | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.14/22.03  | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.14/22.03  | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.03  | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.14/22.03  | |               e0) = all_57_15 & $i(all_57_15)))
% 151.14/22.03  | | 
% 151.14/22.03  | | ALPHA: (28) implies:
% 151.14/22.03  | |   (29)  op(e1, e1) = e1
% 151.14/22.03  | |   (30)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.14/22.03  | |             e0) = all_57_15 & $i(all_57_15))
% 151.14/22.03  | | 
% 151.14/22.03  | | BETA: splitting (30) gives:
% 151.14/22.03  | | 
% 151.14/22.03  | | Case 1:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (31)  all_57_8 = e0 & op(e0, e1) = e0
% 151.14/22.03  | | | 
% 151.14/22.03  | | | ALPHA: (31) implies:
% 151.14/22.03  | | |   (32)  op(e0, e1) = e0
% 151.14/22.03  | | | 
% 151.14/22.03  | | | GROUND_INST: instantiating (8) with all_52_11, e0, e1, e0, simplifying
% 151.14/22.03  | | |              with (1), (32) gives:
% 151.14/22.03  | | |   (33)  all_52_11 = e0
% 151.14/22.03  | | | 
% 151.14/22.03  | | | GROUND_INST: instantiating (8) with all_4_2, e1, e1, e1, simplifying with
% 151.14/22.03  | | |              (7), (29) gives:
% 151.14/22.03  | | |   (34)  all_4_2 = e1
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REDUCE: (9), (34) imply:
% 151.14/22.03  | | |   (35)   ~ (all_52_2 = e1)
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REDUCE: (11), (33) imply:
% 151.14/22.03  | | |   (36)   ~ (all_52_3 = e0)
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REDUCE: (27), (34) imply:
% 151.14/22.03  | | |   (37)   ~ (all_52_6 = e1)
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REDUCE: (2), (33) imply:
% 151.14/22.03  | | |   (38)   ~ (all_52_7 = e0)
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REF_CLOSE: (3), (4), (5), (10), (12), (14), (15), (16), (17), (18), (19),
% 151.14/22.03  | | |            (20), (22), (23), (24), (25), (26), (35), (36), (37), (38) are
% 151.14/22.03  | | |            inconsistent by sub-proof #78.
% 151.14/22.03  | | | 
% 151.14/22.03  | | Case 2:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (39)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)
% 151.14/22.03  | | | 
% 151.14/22.03  | | | ALPHA: (39) implies:
% 151.14/22.03  | | |   (40)   ~ (all_57_15 = e1)
% 151.14/22.03  | | |   (41)  op(e0, e0) = all_57_15
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REF_CLOSE: (8), (13), (40), (41) are inconsistent by sub-proof #940.
% 151.14/22.03  | | | 
% 151.14/22.03  | | End of split
% 151.14/22.03  | | 
% 151.14/22.03  | Case 2:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (42)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 151.14/22.03  | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.14/22.03  | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 151.14/22.03  | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.03  | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 151.14/22.03  | |               e1) = all_57_14 & $i(all_57_14)))
% 151.14/22.03  | | 
% 151.14/22.03  | | ALPHA: (42) implies:
% 151.14/22.03  | |   (43)  op(e0, e0) = e0
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (8), (13), (21), (43) are inconsistent by sub-proof #1040.
% 151.14/22.03  | | 
% 151.14/22.03  | End of split
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #78 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)   ~ (all_52_6 = e1)
% 151.14/22.03    (2)   ~ (all_52_2 = all_52_6)
% 151.14/22.03    (3)   ~ (all_52_3 = all_52_7)
% 151.14/22.03    (4)  all_54_9 = all_52_6
% 151.14/22.03    (5)   ~ (all_52_7 = e1)
% 151.14/22.03    (6)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 151.14/22.03    (7)   ~ (all_52_7 = e3)
% 151.14/22.03    (8)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 151.14/22.03    (9)   ~ (all_52_2 = e2)
% 151.14/22.03    (10)   ~ (all_52_6 = e3)
% 151.14/22.03    (11)   ~ (all_52_3 = e1)
% 151.14/22.03    (12)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 151.14/22.03    (13)  all_54_12 = all_52_3
% 151.14/22.03    (14)   ~ (all_52_7 = e0)
% 151.14/22.03    (15)  all_54_8 = all_52_2
% 151.14/22.03    (16)   ~ (all_52_3 = e0)
% 151.14/22.03    (17)  all_54_13 = all_52_7
% 151.14/22.03    (18)   ~ (all_52_2 = e1)
% 151.14/22.03    (19)   ~ (all_52_2 = all_52_3)
% 151.14/22.03    (20)   ~ (all_52_6 = all_52_7)
% 151.14/22.03    (21)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | BETA: splitting (12) gives:
% 151.14/22.03  | 
% 151.14/22.03  | Case 1:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (22)  all_54_13 = e3
% 151.14/22.03  | | 
% 151.14/22.03  | | COMBINE_EQS: (17), (22) imply:
% 151.14/22.03  | |   (23)  all_52_7 = e3
% 151.14/22.03  | | 
% 151.14/22.03  | | REDUCE: (7), (23) imply:
% 151.14/22.03  | |   (24)  $false
% 151.14/22.03  | | 
% 151.14/22.03  | | CLOSE: (24) is inconsistent.
% 151.14/22.03  | | 
% 151.14/22.03  | Case 2:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (25)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 151.14/22.03  | | 
% 151.14/22.03  | | BETA: splitting (25) gives:
% 151.14/22.03  | | 
% 151.14/22.03  | | Case 1:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (26)  all_54_13 = e2
% 151.14/22.03  | | | 
% 151.14/22.03  | | | COMBINE_EQS: (17), (26) imply:
% 151.14/22.03  | | |   (27)  all_52_7 = e2
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REDUCE: (3), (27) imply:
% 151.14/22.03  | | |   (28)   ~ (all_52_3 = e2)
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REDUCE: (20), (27) imply:
% 151.14/22.03  | | |   (29)   ~ (all_52_6 = e2)
% 151.14/22.03  | | | 
% 151.14/22.03  | | | BETA: splitting (21) gives:
% 151.14/22.03  | | | 
% 151.14/22.03  | | | Case 1:
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | |   (30)  all_54_12 = e3
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | | COMBINE_EQS: (13), (30) imply:
% 151.14/22.03  | | | |   (31)  all_52_3 = e3
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | | SIMP: (31) implies:
% 151.14/22.03  | | | |   (32)  all_52_3 = e3
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | | REDUCE: (19), (32) imply:
% 151.14/22.03  | | | |   (33)   ~ (all_52_2 = e3)
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | | BETA: splitting (6) gives:
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | | Case 1:
% 151.14/22.03  | | | | | 
% 151.14/22.03  | | | | |   (34)  all_54_9 = e3
% 151.14/22.03  | | | | | 
% 151.14/22.03  | | | | | REF_CLOSE: (4), (10), (34) are inconsistent by sub-proof #186.
% 151.14/22.03  | | | | | 
% 151.14/22.03  | | | | Case 2:
% 151.14/22.03  | | | | | 
% 151.14/22.03  | | | | |   (35)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 151.14/22.03  | | | | | 
% 151.14/22.03  | | | | | REF_CLOSE: (1), (2), (4), (8), (9), (15), (18), (29), (33), (35) are
% 151.14/22.03  | | | | |            inconsistent by sub-proof #79.
% 151.14/22.03  | | | | | 
% 151.14/22.03  | | | | End of split
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | Case 2:
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | |   (36)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | | REF_CLOSE: (11), (13), (16), (28), (36) are inconsistent by sub-proof
% 151.14/22.03  | | | |            #881.
% 151.14/22.03  | | | | 
% 151.14/22.03  | | | End of split
% 151.14/22.03  | | | 
% 151.14/22.03  | | Case 2:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (37)  all_54_13 = e1 | all_54_13 = e0
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REF_CLOSE: (5), (14), (17), (37) are inconsistent by sub-proof #983.
% 151.14/22.03  | | | 
% 151.14/22.03  | | End of split
% 151.14/22.03  | | 
% 151.14/22.03  | End of split
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #79 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)   ~ (all_52_6 = e1)
% 151.14/22.03    (2)   ~ (all_52_2 = all_52_6)
% 151.14/22.03    (3)  all_54_9 = all_52_6
% 151.14/22.03    (4)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 151.14/22.03    (5)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 151.14/22.03    (6)   ~ (all_52_2 = e2)
% 151.14/22.03    (7)   ~ (all_52_2 = e3)
% 151.14/22.03    (8)  all_54_8 = all_52_2
% 151.14/22.03    (9)   ~ (all_52_2 = e1)
% 151.14/22.03    (10)   ~ (all_52_6 = e2)
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | BETA: splitting (4) gives:
% 151.14/22.03  | 
% 151.14/22.03  | Case 1:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (11)  all_54_9 = e2
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (3), (10), (11) are inconsistent by sub-proof #185.
% 151.14/22.03  | | 
% 151.14/22.03  | Case 2:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (12)  all_54_9 = e1 | all_54_9 = e0
% 151.14/22.03  | | 
% 151.14/22.03  | | BETA: splitting (12) gives:
% 151.14/22.03  | | 
% 151.14/22.03  | | Case 1:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (13)  all_54_9 = e1
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REF_CLOSE: (1), (3), (13) are inconsistent by sub-proof #179.
% 151.14/22.03  | | | 
% 151.14/22.03  | | Case 2:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (14)  all_54_9 = e0
% 151.14/22.03  | | | 
% 151.14/22.03  | | | COMBINE_EQS: (3), (14) imply:
% 151.14/22.03  | | |   (15)  all_52_6 = e0
% 151.14/22.03  | | | 
% 151.14/22.03  | | | SIMP: (15) implies:
% 151.14/22.03  | | |   (16)  all_52_6 = e0
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REDUCE: (2), (16) imply:
% 151.14/22.03  | | |   (17)   ~ (all_52_2 = e0)
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REF_CLOSE: (5), (6), (7), (8), (9), (17) are inconsistent by sub-proof
% 151.14/22.03  | | |            #102.
% 151.14/22.03  | | | 
% 151.14/22.03  | | End of split
% 151.14/22.03  | | 
% 151.14/22.03  | End of split
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #80 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)  op(e0, e1) = e3
% 151.14/22.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.03    (3)  op(e0, e1) = e0
% 151.14/22.03    (4)   ~ (e3 = e0)
% 151.14/22.03    (5)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) = all_30_1
% 151.14/22.03           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1) =
% 151.14/22.03           all_30_1 & $i(all_30_1))
% 151.14/22.03    (6)  ( ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 & op(e0, e1) = all_10_1
% 151.14/22.03           & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e0, e1) =
% 151.14/22.03           all_10_1 & $i(all_10_1))
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | BETA: splitting (6) gives:
% 151.14/22.03  | 
% 151.14/22.03  | Case 1:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (7)   ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 & op(e0, e1) =
% 151.14/22.03  | |        all_10_1 & $i(all_10_0) & $i(all_10_1)
% 151.14/22.03  | | 
% 151.14/22.03  | | ALPHA: (7) implies:
% 151.14/22.03  | |   (8)  op(e0, e1) = all_10_1
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (1), (2), (3), (4), (5), (8) are inconsistent by sub-proof #81.
% 151.14/22.03  | | 
% 151.14/22.03  | Case 2:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (9)   ~ (all_10_1 = e2) & op(e0, e1) = all_10_1 & $i(all_10_1)
% 151.14/22.03  | | 
% 151.14/22.03  | | ALPHA: (9) implies:
% 151.14/22.03  | |   (10)  op(e0, e1) = all_10_1
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (1), (2), (3), (4), (5), (10) are inconsistent by sub-proof #81.
% 151.14/22.03  | | 
% 151.14/22.03  | End of split
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #81 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)  op(e0, e1) = e3
% 151.14/22.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.03    (3)  op(e0, e1) = all_10_1
% 151.14/22.03    (4)  op(e0, e1) = e0
% 151.14/22.03    (5)   ~ (e3 = e0)
% 151.14/22.03    (6)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) = all_30_1
% 151.14/22.03           & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0, e1) =
% 151.14/22.03           all_30_1 & $i(all_30_1))
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | BETA: splitting (6) gives:
% 151.14/22.03  | 
% 151.14/22.03  | Case 1:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (7)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 151.14/22.03  | |        all_30_1 & $i(all_30_0) & $i(all_30_1)
% 151.14/22.03  | | 
% 151.14/22.03  | | ALPHA: (7) implies:
% 151.14/22.03  | |   (8)  op(e0, e1) = all_30_1
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (1), (2), (3), (4), (5), (8) are inconsistent by sub-proof #82.
% 151.14/22.03  | | 
% 151.14/22.03  | Case 2:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (9)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 & $i(all_30_1)
% 151.14/22.03  | | 
% 151.14/22.03  | | ALPHA: (9) implies:
% 151.14/22.03  | |   (10)   ~ (all_30_1 = e3)
% 151.14/22.03  | |   (11)  op(e0, e1) = all_30_1
% 151.14/22.03  | | 
% 151.14/22.03  | | REF_CLOSE: (1), (2), (3), (10), (11) are inconsistent by sub-proof #391.
% 151.14/22.03  | | 
% 151.14/22.03  | End of split
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #82 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)  op(e0, e1) = e3
% 151.14/22.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.03    (3)  op(e0, e1) = all_10_1
% 151.14/22.03    (4)  op(e0, e1) = e0
% 151.14/22.03    (5)  op(e0, e1) = all_30_1
% 151.14/22.03    (6)   ~ (e3 = e0)
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | GROUND_INST: instantiating (2) with e3, all_10_1, e1, e0, simplifying with
% 151.14/22.03  |              (1), (3) gives:
% 151.14/22.03  |   (7)  all_10_1 = e3
% 151.14/22.03  | 
% 151.14/22.03  | GROUND_INST: instantiating (2) with all_10_1, all_30_1, e1, e0, simplifying
% 151.14/22.03  |              with (3), (5) gives:
% 151.14/22.03  |   (8)  all_30_1 = all_10_1
% 151.14/22.03  | 
% 151.14/22.03  | GROUND_INST: instantiating (2) with e0, all_30_1, e1, e0, simplifying with
% 151.14/22.03  |              (4), (5) gives:
% 151.14/22.03  |   (9)  all_30_1 = e0
% 151.14/22.03  | 
% 151.14/22.03  | COMBINE_EQS: (8), (9) imply:
% 151.14/22.03  |   (10)  all_10_1 = e0
% 151.14/22.03  | 
% 151.14/22.03  | SIMP: (10) implies:
% 151.14/22.03  |   (11)  all_10_1 = e0
% 151.14/22.03  | 
% 151.14/22.03  | COMBINE_EQS: (7), (11) imply:
% 151.14/22.03  |   (12)  e3 = e0
% 151.14/22.03  | 
% 151.14/22.03  | SIMP: (12) implies:
% 151.14/22.03  |   (13)  e3 = e0
% 151.14/22.03  | 
% 151.14/22.03  | REDUCE: (6), (13) imply:
% 151.14/22.03  |   (14)  $false
% 151.14/22.03  | 
% 151.14/22.03  | CLOSE: (14) is inconsistent.
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #83 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)  all_56_15 = e1
% 151.14/22.03    (2)   ~ (e3 = e1)
% 151.14/22.03    (3)   ~ (e2 = e0)
% 151.14/22.03    (4)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.14/22.03             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 151.14/22.03               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.14/22.03               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.14/22.03    (5)   ~ (e3 = e0)
% 151.14/22.03    (6)   ~ (e1 = e0)
% 151.14/22.03    (7)  all_56_11 = e2 & op(e1, e0) = e2
% 151.14/22.03    (8)   ~ (e3 = e2)
% 151.14/22.03    (9)  all_56_9 = e2
% 151.14/22.03    (10)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 151.14/22.03          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.14/22.03  
% 151.14/22.03  Begin of proof
% 151.14/22.03  | 
% 151.14/22.03  | ALPHA: (7) implies:
% 151.14/22.03  |   (11)  all_56_11 = e2
% 151.14/22.03  | 
% 151.14/22.03  | BETA: splitting (10) gives:
% 151.14/22.03  | 
% 151.14/22.03  | Case 1:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (12)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 151.14/22.03  | |           e3)
% 151.14/22.03  | | 
% 151.14/22.03  | | BETA: splitting (12) gives:
% 151.14/22.03  | | 
% 151.14/22.03  | | Case 1:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (13)  all_56_9 = e3 & op(e3, e0) = e3
% 151.14/22.03  | | | 
% 151.14/22.03  | | | ALPHA: (13) implies:
% 151.14/22.03  | | |   (14)  all_56_9 = e3
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REF_CLOSE: (8), (9), (14) are inconsistent by sub-proof #964.
% 151.14/22.03  | | | 
% 151.14/22.03  | | Case 2:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (15)  all_56_10 = e3 & op(e2, e0) = e3
% 151.14/22.03  | | | 
% 151.14/22.03  | | | ALPHA: (15) implies:
% 151.14/22.03  | | |   (16)  all_56_10 = e3
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (11), (16) are inconsistent by
% 151.14/22.03  | | |            sub-proof #153.
% 151.14/22.03  | | | 
% 151.14/22.03  | | End of split
% 151.14/22.03  | | 
% 151.14/22.03  | Case 2:
% 151.14/22.03  | | 
% 151.14/22.03  | |   (17)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 151.14/22.03  | |           e3)
% 151.14/22.03  | | 
% 151.14/22.03  | | BETA: splitting (17) gives:
% 151.14/22.03  | | 
% 151.14/22.03  | | Case 1:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (18)  all_56_11 = e3 & op(e1, e0) = e3
% 151.14/22.03  | | | 
% 151.14/22.03  | | | ALPHA: (18) implies:
% 151.14/22.03  | | |   (19)  all_56_11 = e3
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REF_CLOSE: (8), (11), (19) are inconsistent by sub-proof #591.
% 151.14/22.03  | | | 
% 151.14/22.03  | | Case 2:
% 151.14/22.03  | | | 
% 151.14/22.03  | | |   (20)  all_56_15 = e3 & op(e0, e0) = e3
% 151.14/22.03  | | | 
% 151.14/22.03  | | | REF_CLOSE: (1), (2), (20) are inconsistent by sub-proof #338.
% 151.14/22.03  | | | 
% 151.14/22.03  | | End of split
% 151.14/22.03  | | 
% 151.14/22.03  | End of split
% 151.14/22.03  | 
% 151.14/22.03  End of proof
% 151.14/22.03  
% 151.14/22.03  Sub-proof #84 shows that the following formulas are inconsistent:
% 151.14/22.03  ----------------------------------------------------------------
% 151.14/22.03    (1)  op(e0, e1) = e3
% 151.14/22.03    (2)   ~ (all_52_13 = e1)
% 151.14/22.03    (3)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 151.14/22.03    (4)   ~ (all_30_0 = e2)
% 151.14/22.04    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.04    (6)  op(e2, e3) = e2
% 151.14/22.04    (7)   ~ (all_52_1 = all_52_13)
% 151.14/22.04    (8)   ~ (all_52_12 = e1)
% 151.14/22.04    (9)  op(e0, e1) = all_10_1
% 151.14/22.04    (10)  op(e3, e0) = all_52_12
% 151.14/22.04    (11)  op(e0, e1) = all_30_1
% 151.14/22.04    (12)   ~ (all_52_12 = all_52_13)
% 151.14/22.04    (13)   ~ (all_52_12 = e3)
% 151.14/22.04    (14)  op(all_30_1, e0) = all_30_0
% 151.14/22.04    (15)  all_54_3 = all_52_12
% 151.14/22.04    (16)   ~ (all_52_13 = e3)
% 151.14/22.04    (17)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 151.14/22.04    (18)  op(all_10_1, e0) = all_10_0
% 151.14/22.04    (19)  all_54_7 = all_52_13
% 151.14/22.04    (20)  op(e2, e3) = all_52_1
% 151.14/22.04  
% 151.14/22.04  Begin of proof
% 151.14/22.04  | 
% 151.14/22.04  | GROUND_INST: instantiating (5) with e3, all_30_1, e1, e0, simplifying with
% 151.14/22.04  |              (1), (11) gives:
% 151.14/22.04  |   (21)  all_30_1 = e3
% 151.14/22.04  | 
% 151.14/22.04  | GROUND_INST: instantiating (5) with all_10_1, all_30_1, e1, e0, simplifying
% 151.14/22.04  |              with (9), (11) gives:
% 151.14/22.04  |   (22)  all_30_1 = all_10_1
% 151.14/22.04  | 
% 151.14/22.04  | GROUND_INST: instantiating (5) with all_52_1, e2, e3, e2, simplifying with
% 151.14/22.04  |              (6), (20) gives:
% 151.14/22.04  |   (23)  all_52_1 = e2
% 151.14/22.04  | 
% 151.14/22.04  | GROUND_INST: instantiating (5) with all_52_12, all_10_0, e0, e3, simplifying
% 151.14/22.04  |              with (10) gives:
% 151.14/22.04  |   (24)  all_52_12 = all_10_0 |  ~ (op(e3, e0) = all_10_0)
% 151.14/22.04  | 
% 151.14/22.04  | GROUND_INST: instantiating (5) with all_10_0, all_30_0, e0, all_10_1,
% 151.14/22.04  |              simplifying with (18) gives:
% 151.14/22.04  |   (25)  all_30_0 = all_10_0 |  ~ (op(all_10_1, e0) = all_30_0)
% 151.14/22.04  | 
% 151.14/22.04  | COMBINE_EQS: (21), (22) imply:
% 151.14/22.04  |   (26)  all_10_1 = e3
% 151.14/22.04  | 
% 151.14/22.04  | SIMP: (26) implies:
% 151.14/22.04  |   (27)  all_10_1 = e3
% 151.14/22.04  | 
% 151.14/22.04  | REDUCE: (14), (21) imply:
% 151.14/22.04  |   (28)  op(e3, e0) = all_30_0
% 151.14/22.04  | 
% 151.14/22.04  | BETA: splitting (25) gives:
% 151.14/22.04  | 
% 151.14/22.04  | Case 1:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (29)   ~ (op(all_10_1, e0) = all_30_0)
% 151.14/22.04  | | 
% 151.14/22.04  | | REDUCE: (27), (29) imply:
% 151.14/22.04  | |   (30)   ~ (op(e3, e0) = all_30_0)
% 151.14/22.04  | | 
% 151.14/22.04  | | PRED_UNIFY: (28), (30) imply:
% 151.14/22.04  | |   (31)  $false
% 151.14/22.04  | | 
% 151.14/22.04  | | CLOSE: (31) is inconsistent.
% 151.14/22.04  | | 
% 151.14/22.04  | Case 2:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (32)  all_30_0 = all_10_0
% 151.14/22.04  | | 
% 151.14/22.04  | | REDUCE: (4), (32) imply:
% 151.14/22.04  | |   (33)   ~ (all_10_0 = e2)
% 151.14/22.04  | | 
% 151.14/22.04  | | REDUCE: (28), (32) imply:
% 151.14/22.04  | |   (34)  op(e3, e0) = all_10_0
% 151.14/22.04  | | 
% 151.14/22.04  | | BETA: splitting (3) gives:
% 151.14/22.04  | | 
% 151.14/22.04  | | Case 1:
% 151.14/22.04  | | | 
% 151.14/22.04  | | |   (35)  all_54_7 = e3
% 151.14/22.04  | | | 
% 151.14/22.04  | | | REF_CLOSE: (16), (19), (35) are inconsistent by sub-proof #1163.
% 151.14/22.04  | | | 
% 151.14/22.04  | | Case 2:
% 151.14/22.04  | | | 
% 151.14/22.04  | | |   (36)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 151.14/22.04  | | | 
% 151.14/22.04  | | | BETA: splitting (24) gives:
% 151.14/22.04  | | | 
% 151.14/22.04  | | | Case 1:
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | |   (37)   ~ (op(e3, e0) = all_10_0)
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | PRED_UNIFY: (34), (37) imply:
% 151.14/22.04  | | | |   (38)  $false
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | CLOSE: (38) is inconsistent.
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | Case 2:
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | |   (39)  all_52_12 = all_10_0
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | COMBINE_EQS: (15), (39) imply:
% 151.14/22.04  | | | |   (40)  all_54_3 = all_10_0
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | REDUCE: (12), (39) imply:
% 151.14/22.04  | | | |   (41)   ~ (all_52_13 = all_10_0)
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | SIMP: (41) implies:
% 151.14/22.04  | | | |   (42)   ~ (all_52_13 = all_10_0)
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | REDUCE: (13), (39) imply:
% 151.14/22.04  | | | |   (43)   ~ (all_10_0 = e3)
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | REDUCE: (8), (39) imply:
% 151.14/22.04  | | | |   (44)   ~ (all_10_0 = e1)
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | BETA: splitting (17) gives:
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | Case 1:
% 151.14/22.04  | | | | | 
% 151.14/22.04  | | | | |   (45)  all_54_3 = e3
% 151.14/22.04  | | | | | 
% 151.14/22.04  | | | | | COMBINE_EQS: (40), (45) imply:
% 151.14/22.04  | | | | |   (46)  all_10_0 = e3
% 151.14/22.04  | | | | | 
% 151.14/22.04  | | | | | SIMP: (46) implies:
% 151.14/22.04  | | | | |   (47)  all_10_0 = e3
% 151.14/22.04  | | | | | 
% 151.14/22.04  | | | | | REDUCE: (43), (47) imply:
% 151.14/22.04  | | | | |   (48)  $false
% 151.14/22.04  | | | | | 
% 151.14/22.04  | | | | | CLOSE: (48) is inconsistent.
% 151.14/22.04  | | | | | 
% 151.14/22.04  | | | | Case 2:
% 151.14/22.04  | | | | | 
% 151.14/22.04  | | | | |   (49)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 151.14/22.04  | | | | | 
% 151.14/22.04  | | | | | BETA: splitting (49) gives:
% 151.14/22.04  | | | | | 
% 151.14/22.04  | | | | | Case 1:
% 151.14/22.04  | | | | | | 
% 151.14/22.04  | | | | | |   (50)  all_54_3 = e2
% 151.14/22.04  | | | | | | 
% 151.14/22.04  | | | | | | COMBINE_EQS: (40), (50) imply:
% 151.14/22.04  | | | | | |   (51)  all_10_0 = e2
% 151.14/22.04  | | | | | | 
% 151.14/22.04  | | | | | | REDUCE: (33), (51) imply:
% 151.14/22.04  | | | | | |   (52)  $false
% 151.14/22.04  | | | | | | 
% 151.14/22.04  | | | | | | CLOSE: (52) is inconsistent.
% 151.14/22.04  | | | | | | 
% 151.14/22.04  | | | | | Case 2:
% 151.14/22.04  | | | | | | 
% 151.14/22.04  | | | | | |   (53)  all_54_3 = e1 | all_54_3 = e0
% 151.14/22.04  | | | | | | 
% 151.14/22.04  | | | | | | BETA: splitting (53) gives:
% 151.14/22.04  | | | | | | 
% 151.14/22.04  | | | | | | Case 1:
% 151.14/22.04  | | | | | | | 
% 151.14/22.04  | | | | | | |   (54)  all_54_3 = e1
% 151.14/22.04  | | | | | | | 
% 151.14/22.04  | | | | | | | COMBINE_EQS: (40), (54) imply:
% 151.14/22.04  | | | | | | |   (55)  all_10_0 = e1
% 151.14/22.04  | | | | | | | 
% 151.14/22.04  | | | | | | | REDUCE: (44), (55) imply:
% 151.14/22.04  | | | | | | |   (56)  $false
% 151.14/22.04  | | | | | | | 
% 151.14/22.04  | | | | | | | CLOSE: (56) is inconsistent.
% 151.14/22.04  | | | | | | | 
% 151.14/22.04  | | | | | | Case 2:
% 151.14/22.04  | | | | | | | 
% 151.14/22.04  | | | | | | |   (57)  all_54_3 = e0
% 151.14/22.04  | | | | | | | 
% 151.14/22.04  | | | | | | | COMBINE_EQS: (40), (57) imply:
% 151.14/22.04  | | | | | | |   (58)  all_10_0 = e0
% 151.14/22.04  | | | | | | | 
% 151.14/22.04  | | | | | | | REDUCE: (42), (58) imply:
% 151.14/22.04  | | | | | | |   (59)   ~ (all_52_13 = e0)
% 151.14/22.04  | | | | | | | 
% 151.14/22.04  | | | | | | | REF_CLOSE: (2), (5), (6), (7), (19), (20), (36), (59) are
% 151.14/22.04  | | | | | | |            inconsistent by sub-proof #169.
% 151.14/22.04  | | | | | | | 
% 151.14/22.04  | | | | | | End of split
% 151.14/22.04  | | | | | | 
% 151.14/22.04  | | | | | End of split
% 151.14/22.04  | | | | | 
% 151.14/22.04  | | | | End of split
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | End of split
% 151.14/22.04  | | | 
% 151.14/22.04  | | End of split
% 151.14/22.04  | | 
% 151.14/22.04  | End of split
% 151.14/22.04  | 
% 151.14/22.04  End of proof
% 151.14/22.04  
% 151.14/22.04  Sub-proof #85 shows that the following formulas are inconsistent:
% 151.14/22.04  ----------------------------------------------------------------
% 151.14/22.04    (1)  op(e3, e0) = e1
% 151.14/22.04    (2)  op(e3, e0) = all_28_1
% 151.14/22.04    (3)   ~ (all_14_1 = e1)
% 151.14/22.04    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.04    (5)  op(e3, e0) = all_14_1
% 151.14/22.04  
% 151.14/22.04  Begin of proof
% 151.14/22.04  | 
% 151.14/22.04  | GROUND_INST: instantiating (4) with all_14_1, all_28_1, e0, e3, simplifying
% 151.14/22.04  |              with (2), (5) gives:
% 151.14/22.04  |   (6)  all_28_1 = all_14_1
% 151.14/22.04  | 
% 151.14/22.04  | GROUND_INST: instantiating (4) with e1, all_28_1, e0, e3, simplifying with
% 151.14/22.04  |              (1), (2) gives:
% 151.14/22.04  |   (7)  all_28_1 = e1
% 151.14/22.04  | 
% 151.14/22.04  | COMBINE_EQS: (6), (7) imply:
% 151.14/22.04  |   (8)  all_14_1 = e1
% 151.14/22.04  | 
% 151.14/22.04  | SIMP: (8) implies:
% 151.14/22.04  |   (9)  all_14_1 = e1
% 151.14/22.04  | 
% 151.14/22.04  | REDUCE: (3), (9) imply:
% 151.14/22.04  |   (10)  $false
% 151.14/22.04  | 
% 151.14/22.04  | CLOSE: (10) is inconsistent.
% 151.14/22.04  | 
% 151.14/22.04  End of proof
% 151.14/22.04  
% 151.14/22.04  Sub-proof #86 shows that the following formulas are inconsistent:
% 151.14/22.04  ----------------------------------------------------------------
% 151.14/22.04    (1)  op(e3, e0) = e1
% 151.14/22.04    (2)  op(all_14_1, e3) = all_14_0
% 151.14/22.04    (3)  op(e3, e0) = all_28_1
% 151.14/22.04    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.04    (5)   ~ (all_52_3 = e1)
% 151.14/22.04    (6)  all_54_12 = all_52_3
% 151.14/22.04    (7)   ~ (all_52_2 = e0)
% 151.14/22.04    (8)  all_54_8 = all_52_2
% 151.14/22.04    (9)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 151.14/22.04    (10)   ~ (all_52_3 = e0)
% 151.14/22.04    (11)   ~ (all_52_2 = e1)
% 151.14/22.04    (12)   ~ (all_52_2 = all_52_3)
% 151.14/22.04    (13)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 151.14/22.04    (14)   ~ (all_14_0 = e2)
% 151.14/22.04    (15)  op(e3, e0) = all_14_1
% 151.14/22.04    (16)  op(e1, e3) = all_52_2
% 151.14/22.04  
% 151.14/22.04  Begin of proof
% 151.14/22.04  | 
% 151.14/22.04  | BETA: splitting (9) gives:
% 151.14/22.04  | 
% 151.14/22.04  | Case 1:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (17)  all_54_8 = e2
% 151.14/22.04  | | 
% 151.14/22.04  | | COMBINE_EQS: (8), (17) imply:
% 151.14/22.04  | |   (18)  all_52_2 = e2
% 151.14/22.04  | | 
% 151.14/22.04  | | SIMP: (18) implies:
% 151.14/22.04  | |   (19)  all_52_2 = e2
% 151.14/22.04  | | 
% 151.14/22.04  | | REDUCE: (12), (19) imply:
% 151.14/22.04  | |   (20)   ~ (all_52_3 = e2)
% 151.14/22.04  | | 
% 151.14/22.04  | | SIMP: (20) implies:
% 151.14/22.04  | |   (21)   ~ (all_52_3 = e2)
% 151.14/22.04  | | 
% 151.14/22.04  | | REDUCE: (16), (19) imply:
% 151.14/22.04  | |   (22)  op(e1, e3) = e2
% 151.14/22.04  | | 
% 151.14/22.04  | | BETA: splitting (13) gives:
% 151.14/22.04  | | 
% 151.14/22.04  | | Case 1:
% 151.14/22.04  | | | 
% 151.14/22.04  | | | 
% 151.14/22.04  | | | GROUND_INST: instantiating (4) with all_14_1, all_28_1, e0, e3,
% 151.14/22.04  | | |              simplifying with (3), (15) gives:
% 151.14/22.04  | | |   (23)  all_28_1 = all_14_1
% 151.14/22.04  | | | 
% 151.14/22.04  | | | GROUND_INST: instantiating (4) with e1, all_28_1, e0, e3, simplifying with
% 151.14/22.04  | | |              (1), (3) gives:
% 151.14/22.04  | | |   (24)  all_28_1 = e1
% 151.14/22.04  | | | 
% 151.14/22.04  | | | GROUND_INST: instantiating (4) with e2, all_14_0, e3, e1, simplifying with
% 151.14/22.04  | | |              (22) gives:
% 151.14/22.04  | | |   (25)  all_14_0 = e2 |  ~ (op(e1, e3) = all_14_0)
% 151.14/22.04  | | | 
% 151.14/22.04  | | | COMBINE_EQS: (23), (24) imply:
% 151.14/22.04  | | |   (26)  all_14_1 = e1
% 151.14/22.04  | | | 
% 151.14/22.04  | | | SIMP: (26) implies:
% 151.14/22.04  | | |   (27)  all_14_1 = e1
% 151.14/22.04  | | | 
% 151.14/22.04  | | | REDUCE: (2), (27) imply:
% 151.14/22.04  | | |   (28)  op(e1, e3) = all_14_0
% 151.14/22.04  | | | 
% 151.14/22.04  | | | BETA: splitting (25) gives:
% 151.14/22.04  | | | 
% 151.14/22.04  | | | Case 1:
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | |   (29)   ~ (op(e1, e3) = all_14_0)
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | PRED_UNIFY: (28), (29) imply:
% 151.14/22.04  | | | |   (30)  $false
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | CLOSE: (30) is inconsistent.
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | Case 2:
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | |   (31)  all_14_0 = e2
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | REDUCE: (14), (31) imply:
% 151.14/22.04  | | | |   (32)  $false
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | | CLOSE: (32) is inconsistent.
% 151.14/22.04  | | | | 
% 151.14/22.04  | | | End of split
% 151.14/22.04  | | | 
% 151.14/22.04  | | Case 2:
% 151.14/22.04  | | | 
% 151.14/22.04  | | |   (33)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 151.14/22.04  | | | 
% 151.14/22.04  | | | REF_CLOSE: (5), (6), (10), (21), (33) are inconsistent by sub-proof #881.
% 151.14/22.04  | | | 
% 151.14/22.04  | | End of split
% 151.14/22.04  | | 
% 151.14/22.04  | Case 2:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (34)  all_54_8 = e1 | all_54_8 = e0
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (7), (8), (11), (34) are inconsistent by sub-proof #461.
% 151.14/22.04  | | 
% 151.14/22.04  | End of split
% 151.14/22.04  | 
% 151.14/22.04  End of proof
% 151.14/22.04  
% 151.14/22.04  Sub-proof #87 shows that the following formulas are inconsistent:
% 151.14/22.04  ----------------------------------------------------------------
% 151.14/22.04    (1)  op(e3, e3) = e0
% 151.14/22.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.04    (3)   ~ (e3 = e0)
% 151.14/22.04    (4)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.14/22.04             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.04           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.14/22.04               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.14/22.04             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/22.04         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.14/22.04             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.04           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.14/22.04               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.14/22.04             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 151.14/22.04    (5)   ~ (e3 = e2)
% 151.14/22.04    (6)  op(e2, e2) = e3
% 151.14/22.04  
% 151.14/22.04  Begin of proof
% 151.14/22.04  | 
% 151.14/22.04  | BETA: splitting (4) gives:
% 151.14/22.04  | 
% 151.14/22.04  | Case 1:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2)
% 151.14/22.04  | |          | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.04  | |        ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 151.14/22.04  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 151.14/22.04  | |              e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 151.14/22.04  | |            $i(all_57_15)))
% 151.14/22.04  | | 
% 151.14/22.04  | | ALPHA: (7) implies:
% 151.14/22.04  | |   (8)  op(e3, e3) = e3
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1141.
% 151.14/22.04  | | 
% 151.14/22.04  | Case 2:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3)
% 151.14/22.04  | |          | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.04  | |        ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 151.14/22.04  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 151.14/22.04  | |              e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 151.14/22.04  | |            $i(all_57_15)))
% 151.14/22.04  | | 
% 151.14/22.04  | | ALPHA: (9) implies:
% 151.14/22.04  | |   (10)  op(e2, e2) = e2
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1179.
% 151.14/22.04  | | 
% 151.14/22.04  | End of split
% 151.14/22.04  | 
% 151.14/22.04  End of proof
% 151.14/22.04  
% 151.14/22.04  Sub-proof #88 shows that the following formulas are inconsistent:
% 151.14/22.04  ----------------------------------------------------------------
% 151.14/22.04    (1)  op(e3, e3) = e0
% 151.14/22.04    (2)   ~ (e3 = e1)
% 151.14/22.04    (3)   ~ (e2 = e0)
% 151.14/22.04    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.04    (5)  op(e0, e0) = e0
% 151.14/22.04    (6)  op(e2, e2) = e3
% 151.14/22.04    (7)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 151.14/22.04             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 151.14/22.04           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 151.14/22.04           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 151.14/22.04             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 151.14/22.04             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 151.14/22.04           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.14/22.04           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.14/22.04           $i(all_57_7) & $i(all_57_10))
% 151.14/22.04  
% 151.14/22.04  Begin of proof
% 151.14/22.04  | 
% 151.14/22.04  | BETA: splitting (7) gives:
% 151.14/22.04  | 
% 151.14/22.04  | Case 1:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (8)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 151.14/22.04  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 151.14/22.04  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 151.14/22.04  | | 
% 151.14/22.04  | | ALPHA: (8) implies:
% 151.14/22.04  | |   (9)  op(e3, e3) = e2
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #1073.
% 151.14/22.04  | | 
% 151.14/22.04  | Case 2:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (10)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 151.14/22.04  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 151.14/22.04  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 151.14/22.04  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 151.14/22.04  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 151.14/22.04  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (2), (3), (4), (5), (6), (10) are inconsistent by sub-proof #130.
% 151.14/22.04  | | 
% 151.14/22.04  | End of split
% 151.14/22.04  | 
% 151.14/22.04  End of proof
% 151.14/22.04  
% 151.14/22.04  Sub-proof #89 shows that the following formulas are inconsistent:
% 151.14/22.04  ----------------------------------------------------------------
% 151.14/22.04    (1)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 151.14/22.04    (2)  op(e3, e2) = all_52_4
% 151.14/22.04    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.04    (4)   ~ (e3 = e0)
% 151.14/22.04    (5)  op(e2, e2) = e3
% 151.14/22.04    (6)   ~ (all_52_4 = e0)
% 151.14/22.04  
% 151.14/22.04  Begin of proof
% 151.14/22.04  | 
% 151.14/22.04  | BETA: splitting (1) gives:
% 151.14/22.04  | 
% 151.14/22.04  | Case 1:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (7)  all_56_1 = e0 & op(e3, e2) = e0
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #1013.
% 151.14/22.04  | | 
% 151.14/22.04  | Case 2:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (8)  all_56_3 = e0 & op(e2, e2) = e0
% 151.14/22.04  | | 
% 151.14/22.04  | | ALPHA: (8) implies:
% 151.14/22.04  | |   (9)  op(e2, e2) = e0
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #719.
% 151.14/22.04  | | 
% 151.14/22.04  | End of split
% 151.14/22.04  | 
% 151.14/22.04  End of proof
% 151.14/22.04  
% 151.14/22.04  Sub-proof #90 shows that the following formulas are inconsistent:
% 151.14/22.04  ----------------------------------------------------------------
% 151.14/22.04    (1)   ~ (e3 = e1)
% 151.14/22.04    (2)  all_56_4 = e0
% 151.14/22.04    (3)  op(e3, e2) = all_52_4
% 151.14/22.04    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.04    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.14/22.04         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.14/22.04    (6)   ~ (all_52_4 = e3)
% 151.14/22.04    (7)  op(e3, e0) = all_52_12
% 151.14/22.04    (8)   ~ (e3 = e0)
% 151.14/22.04    (9)  op(e3, e3) = e1
% 151.14/22.04    (10)   ~ (all_52_12 = e3)
% 151.14/22.04  
% 151.14/22.04  Begin of proof
% 151.14/22.04  | 
% 151.14/22.04  | BETA: splitting (5) gives:
% 151.14/22.04  | 
% 151.14/22.04  | Case 1:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 151.14/22.04  | |           e3)
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (1), (3), (4), (6), (9), (11) are inconsistent by sub-proof #999.
% 151.14/22.04  | | 
% 151.14/22.04  | Case 2:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (12)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 151.14/22.04  | |           e3)
% 151.14/22.04  | | 
% 151.14/22.04  | | BETA: splitting (12) gives:
% 151.14/22.04  | | 
% 151.14/22.04  | | Case 1:
% 151.14/22.04  | | | 
% 151.14/22.04  | | |   (13)  all_56_4 = e3 & op(e3, e1) = e3
% 151.14/22.04  | | | 
% 151.14/22.04  | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #915.
% 151.14/22.04  | | | 
% 151.14/22.04  | | Case 2:
% 151.14/22.04  | | | 
% 151.14/22.04  | | |   (14)  all_56_9 = e3 & op(e3, e0) = e3
% 151.14/22.04  | | | 
% 151.14/22.04  | | | ALPHA: (14) implies:
% 151.14/22.04  | | |   (15)  op(e3, e0) = e3
% 151.14/22.04  | | | 
% 151.14/22.04  | | | REF_CLOSE: (4), (7), (10), (15) are inconsistent by sub-proof #1082.
% 151.14/22.04  | | | 
% 151.14/22.04  | | End of split
% 151.14/22.04  | | 
% 151.14/22.04  | End of split
% 151.14/22.04  | 
% 151.14/22.04  End of proof
% 151.14/22.04  
% 151.14/22.04  Sub-proof #91 shows that the following formulas are inconsistent:
% 151.14/22.04  ----------------------------------------------------------------
% 151.14/22.04    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 151.14/22.04             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.14/22.04           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 151.14/22.04           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 151.14/22.04             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/22.04           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 151.14/22.04           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.14/22.04    (2)   ~ (e3 = e1)
% 151.14/22.04    (3)  op(e1, e1) = all_4_2
% 151.14/22.04    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.04    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 151.14/22.04             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.14/22.04           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 151.14/22.04           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.14/22.04             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.14/22.04           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/22.04           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 151.14/22.04           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 151.14/22.04           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 151.14/22.04           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 151.14/22.04           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 151.14/22.04         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 151.14/22.04             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.04           $i(all_57_7))
% 151.14/22.04    (6)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 151.14/22.04           all_57_10 & $i(all_57_10))
% 151.14/22.04    (7)  op(e3, e3) = e1
% 151.14/22.04    (8)  op(e1, e1) = e1
% 151.14/22.04    (9)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 151.14/22.04           all_57_12 & $i(all_57_12))
% 151.14/22.04    (10)   ~ (e2 = e1)
% 151.14/22.04  
% 151.14/22.04  Begin of proof
% 151.14/22.04  | 
% 151.14/22.04  | BETA: splitting (1) gives:
% 151.14/22.04  | 
% 151.14/22.04  | Case 1:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (11)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 151.14/22.04  | |           = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 151.14/22.04  | |         & $i(all_57_4)
% 151.14/22.04  | | 
% 151.14/22.04  | | ALPHA: (11) implies:
% 151.14/22.04  | |   (12)  op(e1, e1) = e2
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (3), (4), (8), (10), (12) are inconsistent by sub-proof #1044.
% 151.14/22.04  | | 
% 151.14/22.04  | Case 2:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (13)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 151.14/22.04  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 151.14/22.04  | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.14/22.04  | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2,
% 151.14/22.04  | |             e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.14/22.04  | | 
% 151.14/22.04  | | BETA: splitting (13) gives:
% 151.14/22.04  | | 
% 151.14/22.04  | | Case 1:
% 151.14/22.04  | | | 
% 151.14/22.04  | | |   (14)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.14/22.04  | | |         (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.14/22.04  | | |         op(e0, e1) = e0 & $i(all_57_6)
% 151.14/22.04  | | | 
% 151.14/22.04  | | | ALPHA: (14) implies:
% 151.14/22.04  | | |   (15)   ~ (all_57_6 = e3)
% 151.14/22.04  | | | 
% 151.14/22.04  | | | REF_CLOSE: (4), (6), (7), (15) are inconsistent by sub-proof #456.
% 151.14/22.04  | | | 
% 151.14/22.04  | | Case 2:
% 151.14/22.04  | | | 
% 151.14/22.04  | | |   (16)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.14/22.04  | | |         (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.14/22.04  | | |         op(e0, e1) = e0 & $i(all_57_7)
% 151.14/22.04  | | | 
% 151.14/22.04  | | | ALPHA: (16) implies:
% 151.14/22.04  | | |   (17)  op(e2, e2) = e1
% 151.14/22.04  | | | 
% 151.14/22.04  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (17) are
% 151.14/22.04  | | |            inconsistent by sub-proof #399.
% 151.14/22.04  | | | 
% 151.14/22.04  | | End of split
% 151.14/22.04  | | 
% 151.14/22.04  | End of split
% 151.14/22.04  | 
% 151.14/22.04  End of proof
% 151.14/22.04  
% 151.14/22.04  Sub-proof #92 shows that the following formulas are inconsistent:
% 151.14/22.04  ----------------------------------------------------------------
% 151.14/22.04    (1)   ~ (e3 = e1)
% 151.14/22.04    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.04    (3)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.14/22.04             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.14/22.04           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.14/22.04           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.14/22.04           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.14/22.04           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 151.14/22.04    (4)  op(e1, e1) = e1
% 151.14/22.04    (5)  op(e2, e2) = e3
% 151.14/22.04  
% 151.14/22.04  Begin of proof
% 151.14/22.04  | 
% 151.14/22.04  | BETA: splitting (3) gives:
% 151.14/22.04  | 
% 151.14/22.04  | Case 1:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (6)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.14/22.04  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.14/22.04  | |        all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 151.14/22.04  | | 
% 151.14/22.04  | | ALPHA: (6) implies:
% 151.14/22.04  | |   (7)  op(e1, e1) = e3
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #734.
% 151.14/22.04  | | 
% 151.14/22.04  | Case 2:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (8)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 151.14/22.04  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 151.14/22.04  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 151.14/22.04  | | 
% 151.14/22.04  | | ALPHA: (8) implies:
% 151.14/22.04  | |   (9)   ~ (all_57_12 = e3)
% 151.14/22.04  | |   (10)  op(e2, e2) = all_57_12
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (2), (5), (9), (10) are inconsistent by sub-proof #126.
% 151.14/22.04  | | 
% 151.14/22.04  | End of split
% 151.14/22.04  | 
% 151.14/22.04  End of proof
% 151.14/22.04  
% 151.14/22.04  Sub-proof #93 shows that the following formulas are inconsistent:
% 151.14/22.04  ----------------------------------------------------------------
% 151.14/22.04    (1)   ~ (e3 = e1)
% 151.14/22.04    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.14/22.04         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.14/22.04    (3)   ~ (e2 = e0)
% 151.14/22.04    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.04    (5)   ~ (e3 = e0)
% 151.14/22.04    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.14/22.04         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.14/22.04    (7)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.14/22.04         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.14/22.04    (8)  all_56_2 = e1
% 151.14/22.04    (9)   ~ (e1 = e0)
% 151.14/22.04    (10)   ~ (e3 = e2)
% 151.14/22.04    (11)  op(e3, e3) = e3
% 151.14/22.04    (12)   ~ (e2 = e1)
% 151.14/22.04    (13)  all_56_6 = e3
% 151.14/22.04    (14)  op(e2, e3) = all_52_1
% 151.14/22.04  
% 151.14/22.04  Begin of proof
% 151.14/22.04  | 
% 151.14/22.04  | BETA: splitting (6) gives:
% 151.14/22.04  | 
% 151.14/22.04  | Case 1:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (15)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 151.14/22.04  | |           e0)
% 151.14/22.04  | | 
% 151.14/22.04  | | REF_CLOSE: (4), (5), (8), (9), (11), (15) are inconsistent by sub-proof
% 151.14/22.04  | |            #995.
% 151.14/22.04  | | 
% 151.14/22.04  | Case 2:
% 151.14/22.04  | | 
% 151.14/22.04  | |   (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 151.14/22.04  | |           e0)
% 151.14/22.04  | | 
% 151.14/22.04  | | BETA: splitting (16) gives:
% 151.14/22.04  | | 
% 151.14/22.04  | | Case 1:
% 151.14/22.04  | | | 
% 151.14/22.04  | | |   (17)  all_56_6 = e0 & op(e1, e3) = e0
% 151.14/22.04  | | | 
% 151.14/22.04  | | | REF_CLOSE: (5), (13), (17) are inconsistent by sub-proof #778.
% 151.14/22.04  | | | 
% 151.14/22.04  | | Case 2:
% 151.14/22.04  | | | 
% 151.14/22.04  | | |   (18)  all_56_12 = e0 & op(e0, e3) = e0
% 151.14/22.04  | | | 
% 151.14/22.04  | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (12), (13), (14),
% 151.14/22.04  | | |            (18) are inconsistent by sub-proof #777.
% 151.14/22.04  | | | 
% 151.14/22.04  | | End of split
% 151.14/22.04  | | 
% 151.14/22.04  | End of split
% 151.14/22.04  | 
% 151.14/22.04  End of proof
% 151.14/22.04  
% 151.14/22.04  Sub-proof #94 shows that the following formulas are inconsistent:
% 151.14/22.04  ----------------------------------------------------------------
% 151.14/22.04    (1)   ~ (e3 = e1)
% 151.14/22.04    (2)   ~ (all_57_13 = e1)
% 151.14/22.04    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.04    (4)  op(e1, e1) = e0
% 151.14/22.04    (5)  op(e3, e3) = e1
% 151.14/22.05    (6)   ~ (e1 = e0)
% 151.14/22.05    (7)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.14/22.05             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.05           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.14/22.05               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.14/22.05             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/22.05         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.14/22.05             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.05           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.14/22.05               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.14/22.05             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/22.05         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 151.14/22.05             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.05           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 151.14/22.05               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 151.14/22.05             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/22.05         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 151.14/22.05             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.05           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 151.14/22.05               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 151.14/22.05             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 151.14/22.05    (8)   ~ (e3 = e2)
% 151.14/22.05    (9)  op(e2, e2) = e3
% 151.14/22.05  
% 151.14/22.05  Begin of proof
% 151.14/22.05  | 
% 151.14/22.05  | BETA: splitting (7) gives:
% 151.14/22.05  | 
% 151.14/22.05  | Case 1:
% 151.14/22.05  | | 
% 151.14/22.05  | |   (10)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 151.14/22.05  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 151.14/22.05  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 151.14/22.05  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.14/22.05  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 151.14/22.05  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 151.14/22.05  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 151.14/22.05  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.05  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 151.14/22.05  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 151.14/22.05  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 151.14/22.05  | |               $i(all_57_15))))
% 151.14/22.05  | | 
% 151.14/22.05  | | REF_CLOSE: (1), (3), (5), (8), (9), (10) are inconsistent by sub-proof #100.
% 151.14/22.05  | | 
% 151.14/22.05  | Case 2:
% 151.14/22.05  | | 
% 151.14/22.05  | |   (11)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.14/22.05  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.14/22.05  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.14/22.05  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.05  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.14/22.05  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 151.14/22.05  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 151.14/22.05  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.05  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 151.14/22.05  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 151.14/22.05  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 151.14/22.05  | |               all_57_14 & $i(all_57_14))))
% 151.14/22.05  | | 
% 151.14/22.05  | | REF_CLOSE: (2), (3), (4), (6), (11) are inconsistent by sub-proof #958.
% 151.14/22.05  | | 
% 151.14/22.05  | End of split
% 151.14/22.05  | 
% 151.14/22.05  End of proof
% 151.14/22.05  
% 151.14/22.05  Sub-proof #95 shows that the following formulas are inconsistent:
% 151.14/22.05  ----------------------------------------------------------------
% 151.14/22.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.05    (2)  ( ~ (all_26_0 = e0) & op(all_26_1, e2) = all_26_0 & op(e2, e3) = all_26_1
% 151.14/22.05           & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e1) & op(e2, e3) =
% 151.14/22.05           all_26_1 & $i(all_26_1))
% 151.14/22.05    (3)  ( ~ (all_6_0 = e1) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 151.14/22.05           $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e0) & op(e2, e3) = all_6_1
% 151.14/22.05           & $i(all_6_1))
% 151.14/22.05    (4)  op(e0, e2) = e1
% 151.14/22.05    (5)  all_56_2 = e0 & op(e2, e3) = e0
% 151.14/22.05  
% 151.14/22.05  Begin of proof
% 151.14/22.05  | 
% 151.14/22.05  | ALPHA: (5) implies:
% 151.14/22.05  |   (6)  op(e2, e3) = e0
% 151.14/22.05  | 
% 151.14/22.05  | BETA: splitting (3) gives:
% 151.14/22.05  | 
% 151.14/22.05  | Case 1:
% 151.14/22.05  | | 
% 151.14/22.05  | |   (7)   ~ (all_6_0 = e1) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1
% 151.14/22.05  | |        & $i(all_6_0) & $i(all_6_1)
% 151.14/22.05  | | 
% 151.14/22.05  | | ALPHA: (7) implies:
% 151.14/22.05  | |   (8)   ~ (all_6_0 = e1)
% 151.14/22.05  | |   (9)  op(e2, e3) = all_6_1
% 151.14/22.05  | |   (10)  op(all_6_1, e2) = all_6_0
% 151.14/22.05  | | 
% 151.14/22.05  | | BETA: splitting (2) gives:
% 151.14/22.05  | | 
% 151.14/22.05  | | Case 1:
% 151.14/22.05  | | | 
% 151.14/22.05  | | |   (11)   ~ (all_26_0 = e0) & op(all_26_1, e2) = all_26_0 & op(e2, e3) =
% 151.14/22.05  | | |         all_26_1 & $i(all_26_0) & $i(all_26_1)
% 151.14/22.05  | | | 
% 151.14/22.05  | | | ALPHA: (11) implies:
% 151.14/22.05  | | |   (12)  op(e2, e3) = all_26_1
% 151.14/22.05  | | | 
% 151.14/22.05  | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (12) are inconsistent by
% 151.14/22.05  | | |            sub-proof #97.
% 151.14/22.05  | | | 
% 151.14/22.05  | | Case 2:
% 151.14/22.05  | | | 
% 151.14/22.05  | | |   (13)   ~ (all_26_1 = e1) & op(e2, e3) = all_26_1 & $i(all_26_1)
% 151.14/22.05  | | | 
% 151.14/22.05  | | | ALPHA: (13) implies:
% 151.14/22.05  | | |   (14)  op(e2, e3) = all_26_1
% 151.14/22.05  | | | 
% 151.14/22.05  | | | REF_CLOSE: (1), (4), (6), (8), (9), (10), (14) are inconsistent by
% 151.14/22.05  | | |            sub-proof #97.
% 151.14/22.05  | | | 
% 151.14/22.05  | | End of split
% 151.14/22.05  | | 
% 151.14/22.05  | Case 2:
% 151.14/22.05  | | 
% 151.14/22.05  | |   (15)   ~ (all_6_1 = e0) & op(e2, e3) = all_6_1 & $i(all_6_1)
% 151.14/22.05  | | 
% 151.14/22.05  | | ALPHA: (15) implies:
% 151.14/22.05  | |   (16)   ~ (all_6_1 = e0)
% 151.14/22.05  | |   (17)  op(e2, e3) = all_6_1
% 151.14/22.05  | | 
% 151.14/22.05  | | BETA: splitting (2) gives:
% 151.14/22.05  | | 
% 151.14/22.05  | | Case 1:
% 151.14/22.05  | | | 
% 151.14/22.05  | | |   (18)   ~ (all_26_0 = e0) & op(all_26_1, e2) = all_26_0 & op(e2, e3) =
% 151.14/22.05  | | |         all_26_1 & $i(all_26_0) & $i(all_26_1)
% 151.14/22.05  | | | 
% 151.14/22.05  | | | ALPHA: (18) implies:
% 151.14/22.05  | | |   (19)  op(e2, e3) = all_26_1
% 151.14/22.05  | | | 
% 151.14/22.05  | | | REF_CLOSE: (1), (6), (16), (17), (19) are inconsistent by sub-proof #96.
% 151.14/22.05  | | | 
% 151.14/22.05  | | Case 2:
% 151.14/22.05  | | | 
% 151.14/22.05  | | |   (20)   ~ (all_26_1 = e1) & op(e2, e3) = all_26_1 & $i(all_26_1)
% 151.14/22.05  | | | 
% 151.14/22.05  | | | ALPHA: (20) implies:
% 151.14/22.05  | | |   (21)  op(e2, e3) = all_26_1
% 151.14/22.05  | | | 
% 151.14/22.05  | | | REF_CLOSE: (1), (6), (16), (17), (21) are inconsistent by sub-proof #96.
% 151.14/22.05  | | | 
% 151.14/22.05  | | End of split
% 151.14/22.05  | | 
% 151.14/22.05  | End of split
% 151.14/22.05  | 
% 151.14/22.05  End of proof
% 151.14/22.05  
% 151.14/22.05  Sub-proof #96 shows that the following formulas are inconsistent:
% 151.14/22.05  ----------------------------------------------------------------
% 151.14/22.05    (1)   ~ (all_6_1 = e0)
% 151.14/22.05    (2)  op(e2, e3) = all_6_1
% 151.14/22.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.05    (4)  op(e2, e3) = e0
% 151.14/22.05    (5)  op(e2, e3) = all_26_1
% 151.14/22.05  
% 151.14/22.05  Begin of proof
% 151.14/22.05  | 
% 151.14/22.05  | GROUND_INST: instantiating (3) with all_6_1, all_26_1, e3, e2, simplifying
% 151.14/22.05  |              with (2), (5) gives:
% 151.14/22.05  |   (6)  all_26_1 = all_6_1
% 151.14/22.05  | 
% 151.14/22.05  | GROUND_INST: instantiating (3) with e0, all_26_1, e3, e2, simplifying with
% 151.14/22.05  |              (4), (5) gives:
% 151.14/22.05  |   (7)  all_26_1 = e0
% 151.14/22.05  | 
% 151.14/22.05  | COMBINE_EQS: (6), (7) imply:
% 151.14/22.05  |   (8)  all_6_1 = e0
% 151.14/22.05  | 
% 151.14/22.05  | SIMP: (8) implies:
% 151.14/22.05  |   (9)  all_6_1 = e0
% 151.14/22.05  | 
% 151.14/22.05  | REDUCE: (1), (9) imply:
% 151.14/22.05  |   (10)  $false
% 151.14/22.05  | 
% 151.14/22.05  | CLOSE: (10) is inconsistent.
% 151.14/22.05  | 
% 151.14/22.05  End of proof
% 151.14/22.05  
% 151.14/22.05  Sub-proof #97 shows that the following formulas are inconsistent:
% 151.14/22.05  ----------------------------------------------------------------
% 151.14/22.05    (1)  op(all_6_1, e2) = all_6_0
% 151.14/22.05    (2)   ~ (all_6_0 = e1)
% 151.14/22.05    (3)  op(e2, e3) = all_6_1
% 151.14/22.05    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.05    (5)  op(e0, e2) = e1
% 151.14/22.05    (6)  op(e2, e3) = e0
% 151.14/22.05    (7)  op(e2, e3) = all_26_1
% 151.14/22.05  
% 151.14/22.05  Begin of proof
% 151.14/22.05  | 
% 151.14/22.05  | GROUND_INST: instantiating (4) with all_6_1, all_26_1, e3, e2, simplifying
% 151.14/22.05  |              with (3), (7) gives:
% 151.14/22.05  |   (8)  all_26_1 = all_6_1
% 151.14/22.05  | 
% 151.14/22.05  | GROUND_INST: instantiating (4) with e0, all_26_1, e3, e2, simplifying with
% 151.14/22.05  |              (6), (7) gives:
% 151.14/22.05  |   (9)  all_26_1 = e0
% 151.14/22.05  | 
% 151.14/22.05  | GROUND_INST: instantiating (4) with e1, all_6_0, e2, e0, simplifying with (5)
% 151.14/22.05  |              gives:
% 151.14/22.05  |   (10)  all_6_0 = e1 |  ~ (op(e0, e2) = all_6_0)
% 151.14/22.05  | 
% 151.14/22.05  | COMBINE_EQS: (8), (9) imply:
% 151.14/22.05  |   (11)  all_6_1 = e0
% 151.14/22.05  | 
% 151.14/22.05  | SIMP: (11) implies:
% 151.14/22.05  |   (12)  all_6_1 = e0
% 151.14/22.05  | 
% 151.14/22.05  | REDUCE: (1), (12) imply:
% 151.14/22.05  |   (13)  op(e0, e2) = all_6_0
% 151.14/22.05  | 
% 151.14/22.05  | BETA: splitting (10) gives:
% 151.14/22.05  | 
% 151.14/22.05  | Case 1:
% 151.14/22.05  | | 
% 151.14/22.05  | |   (14)   ~ (op(e0, e2) = all_6_0)
% 151.14/22.05  | | 
% 151.14/22.05  | | PRED_UNIFY: (13), (14) imply:
% 151.14/22.05  | |   (15)  $false
% 151.14/22.05  | | 
% 151.14/22.05  | | CLOSE: (15) is inconsistent.
% 151.14/22.05  | | 
% 151.14/22.05  | Case 2:
% 151.14/22.05  | | 
% 151.14/22.05  | |   (16)  all_6_0 = e1
% 151.14/22.05  | | 
% 151.14/22.05  | | REDUCE: (2), (16) imply:
% 151.14/22.05  | |   (17)  $false
% 151.14/22.05  | | 
% 151.14/22.05  | | CLOSE: (17) is inconsistent.
% 151.14/22.05  | | 
% 151.14/22.05  | End of split
% 151.14/22.05  | 
% 151.14/22.05  End of proof
% 151.14/22.05  
% 151.14/22.05  Sub-proof #98 shows that the following formulas are inconsistent:
% 151.14/22.05  ----------------------------------------------------------------
% 151.14/22.05    (1)   ~ (e3 = e1)
% 151.14/22.05    (2)  op(e3, e2) = all_52_4
% 151.14/22.05    (3)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.14/22.05         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.14/22.05    (4)   ~ (e2 = e0)
% 151.14/22.05    (5)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.14/22.05         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 151.14/22.05    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.05    (7)   ~ (all_52_9 = e3)
% 151.14/22.05    (8)  all_56_10 = e1
% 151.14/22.05    (9)   ~ (e3 = e0)
% 151.14/22.05    (10)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 151.14/22.05    (11)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.14/22.05          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.14/22.05    (12)  op(e2, e1) = all_52_9
% 151.14/22.05    (13)   ~ (e1 = e0)
% 151.14/22.05    (14)   ~ (all_52_4 = e1)
% 151.14/22.05    (15)   ~ (e3 = e2)
% 151.14/22.05    (16)   ~ (e2 = e1)
% 151.14/22.05  
% 151.14/22.05  Begin of proof
% 151.14/22.05  | 
% 151.14/22.05  | BETA: splitting (10) gives:
% 151.14/22.05  | 
% 151.14/22.05  | Case 1:
% 151.14/22.05  | | 
% 151.14/22.05  | |   (17)  all_56_1 = e1 & op(e3, e2) = e1
% 151.14/22.05  | | 
% 151.14/22.05  | | REF_CLOSE: (2), (6), (14), (17) are inconsistent by sub-proof #420.
% 151.14/22.05  | | 
% 151.14/22.05  | Case 2:
% 151.14/22.05  | | 
% 151.14/22.05  | |   (18)  all_56_3 = e1 & op(e2, e2) = e1
% 151.14/22.05  | | 
% 151.14/22.05  | | ALPHA: (18) implies:
% 151.14/22.05  | |   (19)  all_56_3 = e1
% 151.14/22.05  | |   (20)  op(e2, e2) = e1
% 151.14/22.05  | | 
% 151.14/22.05  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 151.14/22.05  | |            (16), (19), (20) are inconsistent by sub-proof #264.
% 151.14/22.05  | | 
% 151.14/22.05  | End of split
% 151.14/22.05  | 
% 151.14/22.05  End of proof
% 151.14/22.05  
% 151.14/22.05  Sub-proof #99 shows that the following formulas are inconsistent:
% 151.14/22.05  ----------------------------------------------------------------
% 151.14/22.05    (1)  op(e0, e1) = all_52_11
% 151.14/22.05    (2)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 151.14/22.05         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 151.14/22.05    (3)   ~ (e3 = e1)
% 151.14/22.05    (4)   ~ (all_52_2 = all_52_14)
% 151.14/22.05    (5)   ~ (all_52_11 = all_10_2)
% 151.14/22.05    (6)  op(e0, e0) = all_10_2
% 151.14/22.05    (7)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 151.14/22.05    (8)   ~ (all_52_9 = all_52_13)
% 151.14/22.05    (9)  op(e1, e1) = all_4_2
% 151.14/22.05    (10)   ~ (e2 = e0)
% 151.14/22.05    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.05            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.14/22.05    (12)  all_54_10 = all_4_2
% 151.14/22.05    (13)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.14/22.05              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 151.14/22.05                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.14/22.05                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.14/22.05    (14)  op(e1, e0) = all_52_14
% 151.14/22.05    (15)  op(e0, e0) = e1
% 151.14/22.05    (16)   ~ (e3 = e0)
% 151.14/22.05    (17)  op(e3, e3) = e1
% 151.14/22.05    (18)  op(e2, e0) = all_52_13
% 151.14/22.05    (19)   ~ (all_52_14 = all_4_2)
% 151.14/22.05    (20)   ~ (all_4_2 = e2)
% 151.14/22.05    (21)  op(e2, e1) = all_52_9
% 151.14/22.05    (22)   ~ (e1 = e0)
% 151.14/22.05    (23)   ~ (all_52_1 = e1)
% 151.14/22.05    (24)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.14/22.05              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.05            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.14/22.05                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.14/22.05              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/22.05          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.14/22.05              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.05            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.14/22.05                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.14/22.05              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/22.05          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 151.14/22.05              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.05            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 151.14/22.05                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 151.14/22.05              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.14/22.05          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 151.14/22.05              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.05            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 151.14/22.05                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 151.14/22.05                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.14/22.05                $i(all_57_14))))
% 151.14/22.05    (25)   ~ (all_4_2 = e3)
% 151.14/22.05    (26)   ~ (e3 = e2)
% 151.14/22.05    (27)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.14/22.05          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.14/22.05    (28)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 151.14/22.05          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.14/22.05    (29)   ~ (all_52_2 = e1)
% 151.14/22.05    (30)   ~ (all_52_9 = all_4_2)
% 151.14/22.05    (31)   ~ (e2 = e1)
% 151.14/22.05    (32)  op(e2, e2) = e3
% 151.14/22.05    (33)  op(e1, e3) = all_52_2
% 151.14/22.05    (34)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.14/22.05              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.14/22.05            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.14/22.05            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.14/22.05            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.14/22.05            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.14/22.05            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 151.14/22.05            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.14/22.05            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 151.14/22.05            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 151.14/22.05            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.14/22.05            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 151.14/22.05            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.14/22.05            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.14/22.05            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 151.14/22.05            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.14/22.05            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.14/22.05            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 151.14/22.05            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.14/22.05            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 151.14/22.05            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 151.14/22.05            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.14/22.05            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.14/22.05            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 151.14/22.05            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/22.05            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.14/22.05            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.14/22.05            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.14/22.05            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/22.05            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 151.14/22.05            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.14/22.05            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.14/22.05            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.14/22.05            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.14/22.05            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.14/22.05            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 151.14/22.05            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/22.05            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.14/22.05            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 151.14/22.05            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.14/22.05            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.14/22.05            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 151.14/22.05            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.14/22.05            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 151.14/22.05            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 151.14/22.05            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.14/22.05            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 151.14/22.05            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 151.14/22.05              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 151.14/22.05            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.14/22.05            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 151.14/22.05              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.14/22.05            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.14/22.05            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 151.14/22.05                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 151.14/22.05                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.14/22.05                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.14/22.05                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 151.14/22.05                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 151.14/22.05                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 151.14/22.05                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.14/22.05              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 151.14/22.05                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.14/22.05                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.14/22.05                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.14/22.05                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 151.14/22.05                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.14/22.05                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.14/22.05                $i(all_57_7))))
% 151.14/22.05    (35)  op(e2, e3) = all_52_1
% 151.14/22.05  
% 151.14/22.05  Begin of proof
% 151.14/22.05  | 
% 151.14/22.05  | BETA: splitting (24) gives:
% 151.14/22.05  | 
% 151.14/22.05  | Case 1:
% 151.14/22.05  | | 
% 151.14/22.05  | |   (36)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 151.14/22.05  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 151.14/22.05  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 151.14/22.05  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.14/22.05  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 151.14/22.05  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 151.14/22.05  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 151.14/22.05  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.05  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 151.14/22.05  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 151.14/22.05  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 151.14/22.05  | |               $i(all_57_15))))
% 151.14/22.05  | | 
% 151.14/22.05  | | REF_CLOSE: (3), (11), (17), (26), (32), (36) are inconsistent by sub-proof
% 151.14/22.05  | |            #100.
% 151.14/22.05  | | 
% 151.14/22.05  | Case 2:
% 151.14/22.05  | | 
% 151.14/22.05  | |   (37)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.14/22.05  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.14/22.05  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.14/22.05  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.05  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.14/22.05  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 151.14/22.05  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 151.14/22.05  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.14/22.05  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 151.14/22.05  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 151.14/22.05  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 151.14/22.05  | |               all_57_14 & $i(all_57_14))))
% 151.14/22.05  | | 
% 151.14/22.05  | | BETA: splitting (37) gives:
% 151.14/22.05  | | 
% 151.14/22.05  | | Case 1:
% 151.14/22.05  | | | 
% 151.14/22.05  | | |   (38)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.14/22.05  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.14/22.05  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.14/22.05  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.05  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.14/22.05  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.14/22.05  | | | 
% 151.14/22.05  | | | ALPHA: (38) implies:
% 151.14/22.05  | | |   (39)  op(e1, e1) = e1
% 151.14/22.05  | | |   (40)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 151.14/22.05  | | |             e2) = all_57_12 & $i(all_57_12))
% 151.14/22.05  | | |   (41)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3,
% 151.14/22.05  | | |             e3) = all_57_10 & $i(all_57_10))
% 151.14/22.05  | | | 
% 151.14/22.05  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 151.14/22.05  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 151.14/22.05  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (33),
% 151.14/22.05  | | |            (34), (35), (39), (40), (41) are inconsistent by sub-proof
% 151.14/22.05  | | |            #381.
% 151.14/22.05  | | | 
% 151.14/22.05  | | Case 2:
% 151.14/22.05  | | | 
% 151.14/22.05  | | |   (42)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 151.14/22.05  | | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.14/22.05  | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 151.14/22.05  | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.14/22.05  | | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 151.14/22.05  | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 151.14/22.05  | | | 
% 151.14/22.05  | | | ALPHA: (42) implies:
% 151.14/22.05  | | |   (43)  op(e0, e0) = e0
% 151.14/22.05  | | | 
% 151.14/22.05  | | | REF_CLOSE: (11), (15), (22), (43) are inconsistent by sub-proof #1040.
% 151.14/22.05  | | | 
% 151.14/22.05  | | End of split
% 151.14/22.05  | | 
% 151.14/22.05  | End of split
% 151.14/22.05  | 
% 151.14/22.05  End of proof
% 151.14/22.05  
% 151.14/22.05  Sub-proof #100 shows that the following formulas are inconsistent:
% 151.14/22.05  ----------------------------------------------------------------
% 151.14/22.05    (1)   ~ (e3 = e1)
% 151.14/22.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.14/22.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.05    (3)  op(e3, e3) = e1
% 151.42/22.05    (4)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.42/22.05             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.42/22.05           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.42/22.05               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.42/22.05             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.42/22.05         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.42/22.05             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.42/22.05           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.42/22.05               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.42/22.05             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 151.42/22.06    (5)   ~ (e3 = e2)
% 151.42/22.06    (6)  op(e2, e2) = e3
% 151.42/22.06  
% 151.42/22.06  Begin of proof
% 151.42/22.06  | 
% 151.42/22.06  | BETA: splitting (4) gives:
% 151.42/22.06  | 
% 151.42/22.06  | Case 1:
% 151.42/22.06  | | 
% 151.42/22.06  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2)
% 151.42/22.06  | |          | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.42/22.06  | |        ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 151.42/22.06  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 151.42/22.06  | |              e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 151.42/22.06  | |            $i(all_57_15)))
% 151.42/22.06  | | 
% 151.42/22.06  | | ALPHA: (7) implies:
% 151.42/22.06  | |   (8)  op(e3, e3) = e3
% 151.42/22.06  | | 
% 151.42/22.06  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1178.
% 151.42/22.06  | | 
% 151.42/22.06  | Case 2:
% 151.42/22.06  | | 
% 151.42/22.06  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3)
% 151.42/22.06  | |          | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.42/22.06  | |        ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 151.42/22.06  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 151.42/22.06  | |              e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 151.42/22.06  | |            $i(all_57_15)))
% 151.42/22.06  | | 
% 151.42/22.06  | | ALPHA: (9) implies:
% 151.42/22.06  | |   (10)  op(e2, e2) = e2
% 151.42/22.06  | | 
% 151.42/22.06  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1179.
% 151.42/22.06  | | 
% 151.42/22.06  | End of split
% 151.42/22.06  | 
% 151.42/22.06  End of proof
% 151.42/22.06  
% 151.42/22.06  Sub-proof #101 shows that the following formulas are inconsistent:
% 151.42/22.06  ----------------------------------------------------------------
% 151.42/22.06    (1)   ~ (e3 = e1)
% 151.42/22.06    (2)   ~ (e2 = e0)
% 151.42/22.06    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.06    (4)  op(e3, e3) = e1
% 151.42/22.06    (5)   ~ (e2 = e1)
% 151.42/22.06    (6)  op(e0, e0) = e0
% 151.42/22.06    (7)  op(e2, e2) = e3
% 151.42/22.06    (8)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 151.42/22.06             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 151.42/22.06           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 151.42/22.06           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 151.42/22.06             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 151.42/22.06             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 151.42/22.06           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.42/22.06           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.42/22.06           $i(all_57_7) & $i(all_57_10))
% 151.42/22.06  
% 151.42/22.06  Begin of proof
% 151.42/22.06  | 
% 151.42/22.06  | BETA: splitting (8) gives:
% 151.42/22.06  | 
% 151.42/22.06  | Case 1:
% 151.42/22.06  | | 
% 151.42/22.06  | |   (9)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 151.42/22.06  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 151.42/22.06  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 151.42/22.06  | | 
% 151.42/22.06  | | ALPHA: (9) implies:
% 151.42/22.06  | |   (10)  op(e3, e3) = e2
% 151.42/22.06  | | 
% 151.42/22.06  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #1074.
% 151.42/22.06  | | 
% 151.42/22.06  | Case 2:
% 151.42/22.06  | | 
% 151.42/22.06  | |   (11)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 151.42/22.06  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 151.42/22.06  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 151.42/22.06  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 151.42/22.06  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 151.42/22.06  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.42/22.06  | | 
% 151.42/22.06  | | REF_CLOSE: (1), (2), (3), (6), (7), (11) are inconsistent by sub-proof #130.
% 151.42/22.06  | | 
% 151.42/22.06  | End of split
% 151.42/22.06  | 
% 151.42/22.06  End of proof
% 151.42/22.06  
% 151.42/22.06  Sub-proof #102 shows that the following formulas are inconsistent:
% 151.42/22.06  ----------------------------------------------------------------
% 151.42/22.06    (1)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 151.42/22.06    (2)   ~ (all_52_2 = e2)
% 151.42/22.06    (3)   ~ (all_52_2 = e3)
% 151.42/22.06    (4)   ~ (all_52_2 = e0)
% 151.42/22.06    (5)  all_54_8 = all_52_2
% 151.42/22.06    (6)   ~ (all_52_2 = e1)
% 151.42/22.06  
% 151.42/22.06  Begin of proof
% 151.42/22.06  | 
% 151.42/22.06  | BETA: splitting (1) gives:
% 151.42/22.06  | 
% 151.42/22.06  | Case 1:
% 151.42/22.06  | | 
% 151.42/22.06  | |   (7)  all_54_8 = e3
% 151.42/22.06  | | 
% 151.42/22.06  | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #394.
% 151.42/22.06  | | 
% 151.42/22.06  | Case 2:
% 151.42/22.06  | | 
% 151.42/22.06  | |   (8)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 151.42/22.06  | | 
% 151.42/22.06  | | REF_CLOSE: (2), (4), (5), (6), (8) are inconsistent by sub-proof #460.
% 151.42/22.06  | | 
% 151.42/22.06  | End of split
% 151.42/22.06  | 
% 151.42/22.06  End of proof
% 151.42/22.06  
% 151.42/22.06  Sub-proof #103 shows that the following formulas are inconsistent:
% 151.42/22.06  ----------------------------------------------------------------
% 151.42/22.06    (1)  op(e0, e1) = e3
% 151.42/22.06    (2)   ~ (e3 = e1)
% 151.42/22.06    (3)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.42/22.06             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.42/22.06           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 151.42/22.06           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 151.42/22.06             e1) = e0 & $i(all_57_7))
% 151.42/22.06    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.06    (5)   ~ (e3 = e0)
% 151.42/22.06    (6)  op(e2, e2) = e3
% 151.42/22.06  
% 151.42/22.06  Begin of proof
% 151.42/22.06  | 
% 151.42/22.06  | BETA: splitting (3) gives:
% 151.42/22.06  | 
% 151.42/22.06  | Case 1:
% 151.42/22.06  | | 
% 151.42/22.06  | |   (7)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.42/22.06  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.42/22.06  | |        $i(all_57_6)
% 151.42/22.06  | | 
% 151.42/22.06  | | ALPHA: (7) implies:
% 151.42/22.06  | |   (8)  op(e0, e1) = e0
% 151.42/22.06  | | 
% 151.42/22.06  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #104.
% 151.42/22.06  | | 
% 151.42/22.06  | Case 2:
% 151.42/22.06  | | 
% 151.42/22.06  | |   (9)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 151.42/22.06  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.42/22.06  | |        $i(all_57_7)
% 151.42/22.06  | | 
% 151.42/22.06  | | ALPHA: (9) implies:
% 151.42/22.06  | |   (10)  op(e2, e2) = e1
% 151.42/22.06  | | 
% 151.42/22.06  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #1136.
% 151.42/22.06  | | 
% 151.42/22.06  | End of split
% 151.42/22.06  | 
% 151.42/22.06  End of proof
% 151.42/22.06  
% 151.42/22.06  Sub-proof #104 shows that the following formulas are inconsistent:
% 151.42/22.06  ----------------------------------------------------------------
% 151.42/22.06    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.06    (2)  op(e0, e1) = e3
% 151.42/22.06    (3)  op(e0, e1) = e0
% 151.42/22.06    (4)   ~ (e3 = e0)
% 151.42/22.06  
% 151.42/22.06  Begin of proof
% 151.42/22.06  | 
% 151.42/22.06  | GROUND_INST: instantiating (1) with e3, e0, e1, e0, simplifying with (2), (3)
% 151.42/22.06  |              gives:
% 151.42/22.06  |   (5)  e3 = e0
% 151.42/22.06  | 
% 151.42/22.06  | REDUCE: (4), (5) imply:
% 151.42/22.06  |   (6)  $false
% 151.42/22.06  | 
% 151.42/22.06  | CLOSE: (6) is inconsistent.
% 151.42/22.06  | 
% 151.42/22.06  End of proof
% 151.42/22.06  
% 151.42/22.06  Sub-proof #105 shows that the following formulas are inconsistent:
% 151.42/22.06  ----------------------------------------------------------------
% 151.42/22.06    (1)  op(e0, e1) = e3
% 151.42/22.06    (2)   ~ (all_57_0 = e2)
% 151.42/22.06    (3)  op(e0, e1) = all_52_11
% 151.42/22.06    (4)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 151.42/22.06         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 151.42/22.06    (5)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 151.42/22.06    (6)   ~ (e3 = e1)
% 151.42/22.06    (7)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.42/22.06         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.42/22.06    (8)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 151.42/22.06         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 151.42/22.06    (9)  op(e0, e0) = all_10_2
% 151.42/22.06    (10)  op(e3, e2) = all_52_4
% 151.42/22.06    (11)  op(e0, e2) = all_52_7
% 151.42/22.06    (12)   ~ (all_52_14 = e2)
% 151.42/22.06    (13)   ~ (all_52_9 = all_52_13)
% 151.42/22.06    (14)   ~ (all_52_3 = all_52_7)
% 151.42/22.06    (15)  all_54_14 = all_52_11
% 151.42/22.06    (16)  op(e1, e1) = all_4_2
% 151.42/22.06    (17)  op(e1, e0) = e3
% 151.42/22.06    (18)   ~ (e2 = e0)
% 151.42/22.06    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.06            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.06    (20)  all_40_2 = e2
% 151.42/22.06    (21)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.42/22.06          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.42/22.06    (22)   ~ (all_52_1 = all_52_13)
% 151.42/22.06    (23)   ~ (all_52_2 = all_4_2)
% 151.42/22.06    (24)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.42/22.06          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.42/22.06    (25)   ~ (all_52_3 = e2)
% 151.42/22.06    (26)   ~ (all_52_3 = all_52_11)
% 151.42/22.06    (27)  op(e0, e3) = e0
% 151.42/22.06    (28)   ~ (all_52_9 = all_52_11)
% 151.42/22.06    (29)   ~ (all_52_9 = e3)
% 151.42/22.06    (30)  op(e0, e0) = e2
% 151.42/22.06    (31)   ~ (all_52_1 = all_52_9)
% 151.42/22.06    (32)   ~ (all_52_1 = e3)
% 151.42/22.06    (33)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.42/22.06              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 151.42/22.06                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.42/22.06                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.42/22.06    (34)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0 &
% 151.42/22.06            op(e0, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 151.42/22.06              e3) & op(e0, e2) = all_40_1 & $i(all_40_1))
% 151.42/22.06    (35)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 151.42/22.06          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 151.42/22.06    (36)  op(e2, e3) = all_57_0
% 151.42/22.06    (37)  op(e1, e0) = all_52_14
% 151.42/22.06    (38)   ~ (all_52_4 = e3)
% 151.42/22.06    (39)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 151.42/22.06              e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.42/22.06            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 151.42/22.06             ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.42/22.06              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.42/22.06            (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.42/22.06            all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 151.42/22.06            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 151.42/22.06            = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 151.42/22.06          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.42/22.06              e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.42/22.06            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 151.42/22.06             ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 151.42/22.06              e1) = e0 & $i(all_57_7))
% 151.42/22.06    (40)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.42/22.06    (41)  op(e3, e0) = all_52_12
% 151.42/22.06    (42)   ~ (e3 = e0)
% 151.42/22.06    (43)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.42/22.06          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.42/22.06    (44)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 151.42/22.06          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 151.42/22.06    (45)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 151.42/22.06          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 151.42/22.06    (46)   ~ (all_52_6 = e3)
% 151.42/22.06    (47)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.42/22.06          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.42/22.06    (48)  ( ~ (all_24_0 = e3) & op(all_24_1, e0) = all_24_0 & op(e0, e2) =
% 151.42/22.06            all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0,
% 151.42/22.06              e2) = all_24_1 & $i(all_24_1))
% 151.42/22.06    (49)  op(e1, e2) = all_52_6
% 151.42/22.06    (50)  op(e2, e0) = all_52_13
% 151.42/22.06    (51)   ~ (all_52_3 = e3)
% 151.42/22.06    (52)   ~ (all_57_15 = e3)
% 151.42/22.06    (53)   ~ (all_52_1 = all_52_3)
% 151.42/22.06    (54)   ~ (all_52_14 = all_4_2)
% 151.42/22.06    (55)  op(e0, e3) = all_52_3
% 151.42/22.06    (56)   ~ (all_4_2 = e2)
% 151.42/22.06    (57)  all_56_14 = e3
% 151.42/22.06    (58)   ~ (all_52_8 = all_52_11)
% 151.42/22.06    (59)  op(e2, e1) = all_52_9
% 151.42/22.06    (60)   ~ (e1 = e0)
% 151.42/22.06    (61)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.42/22.06          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.42/22.06    (62)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.42/22.06              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.42/22.06            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.42/22.06                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.42/22.06              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.42/22.06          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.42/22.06              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.42/22.06            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.42/22.06                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.42/22.06              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.42/22.06          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 151.42/22.06              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.42/22.06            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 151.42/22.06                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 151.42/22.06              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.42/22.06          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 151.42/22.06              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.42/22.06            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 151.42/22.06                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 151.42/22.06                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.42/22.06                $i(all_57_14))))
% 151.42/22.06    (63)   ~ (all_4_2 = e3)
% 151.42/22.06    (64)  all_57_12 = e3
% 151.42/22.06    (65)   ~ (e3 = e2)
% 151.42/22.06    (66)  all_54_4 = all_52_1
% 151.42/22.06    (67)   ~ (all_52_8 = e3)
% 151.42/22.06    (68)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.42/22.06          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 151.42/22.06            e2)
% 151.42/22.06    (69)   ~ (all_52_14 = all_10_2)
% 151.42/22.06    (70)   ~ (all_52_13 = e3)
% 151.42/22.06    (71)  ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0 & op(e0, e2) =
% 151.42/22.06            all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e0,
% 151.42/22.06              e2) = all_40_1 & $i(all_40_1))
% 151.42/22.06    (72)  op(e3, e1) = all_52_8
% 151.42/22.06    (73)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 151.42/22.06          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.42/22.06    (74)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.42/22.06          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.42/22.06    (75)  op(e3, e3) = e3
% 151.42/22.06    (76)   ~ (e2 = e1)
% 151.42/22.06    (77)   ~ (all_52_11 = all_4_2)
% 151.42/22.06    (78)  op(e2, e2) = e3
% 151.42/22.06    (79)  op(e1, e3) = all_52_2
% 151.42/22.06    (80)   ~ (all_52_11 = e2)
% 151.42/22.06    (81)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.42/22.06              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.42/22.06            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.42/22.06            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.42/22.06            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.42/22.06            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.42/22.06            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 151.42/22.06            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.42/22.06            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 151.42/22.06            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 151.42/22.06            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.42/22.06            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 151.42/22.06            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.42/22.06            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.42/22.06            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 151.42/22.06            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.42/22.06            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.42/22.06            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 151.42/22.06            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.42/22.06            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 151.42/22.06            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 151.42/22.06            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.42/22.06            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.42/22.06            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 151.42/22.06            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.42/22.06            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.42/22.06            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.42/22.06            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.42/22.06            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.42/22.06            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 151.42/22.06            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.42/22.06            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.42/22.06            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.42/22.06            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.42/22.06            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.42/22.06            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 151.42/22.06            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.42/22.06            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.42/22.06            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 151.42/22.06            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.42/22.06            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.42/22.06            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 151.42/22.06            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.42/22.06            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 151.42/22.06            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 151.42/22.06            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.42/22.06            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 151.42/22.06            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 151.42/22.06              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 151.42/22.06            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.42/22.06            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 151.42/22.06              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.42/22.06            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.42/22.06            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 151.42/22.06                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 151.42/22.06                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.42/22.06                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.42/22.06                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 151.42/22.06                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 151.42/22.06                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 151.42/22.06                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.42/22.06              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 151.42/22.06                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.42/22.06                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.42/22.06                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.42/22.06                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 151.42/22.06                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.42/22.06                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.42/22.06                $i(all_57_7))))
% 151.42/22.06    (82)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.42/22.06          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 151.42/22.06            e1)
% 151.42/22.06    (83)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 151.42/22.06          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 151.42/22.06    (84)  op(e2, e3) = all_52_1
% 151.42/22.06  
% 151.42/22.06  Begin of proof
% 151.42/22.06  | 
% 151.42/22.06  | BETA: splitting (62) gives:
% 151.42/22.06  | 
% 151.42/22.06  | Case 1:
% 151.42/22.06  | | 
% 151.42/22.06  | |   (85)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 151.42/22.06  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 151.42/22.06  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 151.42/22.06  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.42/22.06  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 151.42/22.06  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 151.42/22.06  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 151.42/22.06  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.42/22.06  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 151.42/22.06  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 151.42/22.06  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 151.42/22.06  | |               $i(all_57_15))))
% 151.42/22.06  | | 
% 151.42/22.06  | | BETA: splitting (85) gives:
% 151.42/22.06  | | 
% 151.42/22.06  | | Case 1:
% 151.42/22.06  | | | 
% 151.42/22.06  | | |   (86)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 151.42/22.06  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 151.42/22.06  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 151.42/22.06  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.42/22.06  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 151.42/22.06  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.42/22.06  | | | 
% 151.42/22.06  | | | ALPHA: (86) implies:
% 151.42/22.06  | | |   (87)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2,
% 151.42/22.06  | | |             e2) = all_57_12 & $i(all_57_12))
% 151.42/22.06  | | | 
% 151.42/22.06  | | | REF_CLOSE: (2), (64), (87) are inconsistent by sub-proof #832.
% 151.42/22.06  | | | 
% 151.42/22.06  | | Case 2:
% 151.42/22.06  | | | 
% 151.42/22.06  | | |   (88)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 151.42/22.06  | | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.42/22.06  | | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 151.42/22.06  | | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.42/22.06  | | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 151.42/22.06  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.42/22.06  | | | 
% 151.42/22.06  | | | ALPHA: (88) implies:
% 151.42/22.06  | | |   (89)  op(e2, e2) = e2
% 151.42/22.06  | | | 
% 151.42/22.06  | | | REF_CLOSE: (6), (16), (19), (39), (56), (63), (65), (75), (76), (89) are
% 151.42/22.06  | | |            inconsistent by sub-proof #1075.
% 151.42/22.06  | | | 
% 151.42/22.06  | | End of split
% 151.42/22.06  | | 
% 151.42/22.06  | Case 2:
% 151.42/22.06  | | 
% 151.42/22.06  | |   (90)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.42/22.06  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.42/22.06  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.42/22.06  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.42/22.06  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.42/22.06  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 151.42/22.06  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 151.42/22.06  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.42/22.06  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 151.42/22.06  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 151.42/22.06  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 151.42/22.06  | |               all_57_14 & $i(all_57_14))))
% 151.42/22.06  | | 
% 151.42/22.06  | | BETA: splitting (90) gives:
% 151.42/22.06  | | 
% 151.42/22.06  | | Case 1:
% 151.42/22.06  | | | 
% 151.42/22.06  | | |   (91)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.42/22.06  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.42/22.06  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.42/22.06  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.42/22.06  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.42/22.06  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.42/22.06  | | | 
% 151.42/22.06  | | | ALPHA: (91) implies:
% 151.42/22.06  | | |   (92)  op(e1, e1) = e1
% 151.42/22.06  | | |   (93)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.42/22.06  | | |             e0) = all_57_15 & $i(all_57_15))
% 151.42/22.06  | | |   (94)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3,
% 151.42/22.06  | | |             e3) = all_57_10 & $i(all_57_10))
% 151.42/22.06  | | | 
% 151.42/22.06  | | | BETA: splitting (94) gives:
% 151.42/22.06  | | | 
% 151.42/22.06  | | | Case 1:
% 151.42/22.06  | | | | 
% 151.42/22.06  | | | |   (95)  all_57_6 = e3 & op(e3, e1) = e3
% 151.42/22.07  | | | | 
% 151.42/22.07  | | | | ALPHA: (95) implies:
% 151.42/22.07  | | | |   (96)  op(e3, e1) = e3
% 151.42/22.07  | | | | 
% 151.42/22.07  | | | | REF_CLOSE: (19), (67), (72), (96) are inconsistent by sub-proof #1164.
% 151.42/22.07  | | | | 
% 151.42/22.07  | | | Case 2:
% 151.42/22.07  | | | | 
% 151.42/22.07  | | | |   (97)   ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10)
% 151.42/22.07  | | | | 
% 151.42/22.07  | | | | ALPHA: (97) implies:
% 151.42/22.07  | | | |   (98)   ~ (all_57_10 = e1)
% 151.42/22.07  | | | |   (99)  op(e3, e3) = all_57_10
% 151.42/22.07  | | | | 
% 151.42/22.07  | | | | BETA: splitting (93) gives:
% 151.42/22.07  | | | | 
% 151.42/22.07  | | | | Case 1:
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | |   (100)  all_57_8 = e0 & op(e0, e1) = e0
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | ALPHA: (100) implies:
% 151.42/22.07  | | | | |   (101)  op(e0, e1) = e0
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | GROUND_INST: instantiating (19) with e3, e0, e1, e0, simplifying with
% 151.42/22.07  | | | | |              (1), (101) gives:
% 151.42/22.07  | | | | |   (102)  e3 = e0
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | REDUCE: (42), (102) imply:
% 151.42/22.07  | | | | |   (103)  $false
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | CLOSE: (103) is inconsistent.
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | Case 2:
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | |   (104)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | ALPHA: (104) implies:
% 151.42/22.07  | | | | |   (105)   ~ (all_57_15 = e1)
% 151.42/22.07  | | | | |   (106)  op(e0, e0) = all_57_15
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | GROUND_INST: instantiating (19) with e2, all_57_15, e0, e0,
% 151.42/22.07  | | | | |              simplifying with (30), (106) gives:
% 151.42/22.07  | | | | |   (107)  all_57_15 = e2
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | GROUND_INST: instantiating (19) with all_52_3, e0, e3, e0, simplifying
% 151.42/22.07  | | | | |              with (27), (55) gives:
% 151.42/22.07  | | | | |   (108)  all_52_3 = e0
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | GROUND_INST: instantiating (19) with all_52_1, all_57_0, e3, e2,
% 151.42/22.07  | | | | |              simplifying with (36), (84) gives:
% 151.42/22.07  | | | | |   (109)  all_57_0 = all_52_1
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | GROUND_INST: instantiating (19) with e3, all_57_10, e3, e3,
% 151.42/22.07  | | | | |              simplifying with (75), (99) gives:
% 151.42/22.07  | | | | |   (110)  all_57_10 = e3
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | REDUCE: (2), (109) imply:
% 151.42/22.07  | | | | |   (111)   ~ (all_52_1 = e2)
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | REDUCE: (52), (107) imply:
% 151.42/22.07  | | | | |   (112)   ~ (e3 = e2)
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | REDUCE: (53), (108) imply:
% 151.42/22.07  | | | | |   (113)   ~ (all_52_1 = e0)
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | REDUCE: (51), (108) imply:
% 151.42/22.07  | | | | |   (114)   ~ (e3 = e0)
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | REDUCE: (25), (108) imply:
% 151.42/22.07  | | | | |   (115)   ~ (e2 = e0)
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | BETA: splitting (82) gives:
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | | Case 1:
% 151.42/22.07  | | | | | | 
% 151.42/22.07  | | | | | |   (116)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 &
% 151.42/22.07  | | | | | |            op(e0, e2) = e1)
% 151.42/22.07  | | | | | | 
% 151.42/22.07  | | | | | | BETA: splitting (116) gives:
% 151.42/22.07  | | | | | | 
% 151.42/22.07  | | | | | | Case 1:
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | |   (117)  all_56_12 = e1 & op(e0, e3) = e1
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | | ALPHA: (117) implies:
% 151.42/22.07  | | | | | | |   (118)  all_56_12 = e1
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | | BETA: splitting (47) gives:
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | | Case 1:
% 151.42/22.07  | | | | | | | | 
% 151.42/22.07  | | | | | | | |   (119)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 &
% 151.42/22.07  | | | | | | | |            op(e2, e3) = e2)
% 151.42/22.07  | | | | | | | | 
% 151.42/22.07  | | | | | | | | BETA: splitting (119) gives:
% 151.42/22.07  | | | | | | | | 
% 151.42/22.07  | | | | | | | | Case 1:
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | |   (120)  all_56_0 = e2 & op(e3, e3) = e2
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | | ALPHA: (120) implies:
% 151.42/22.07  | | | | | | | | |   (121)  op(e3, e3) = e2
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 151.42/22.07  | | | | | | | | |            (12), (13), (14), (15), (16), (18), (19), (20),
% 151.42/22.07  | | | | | | | | |            (21), (22), (23), (24), (25), (26), (28), (29),
% 151.42/22.07  | | | | | | | | |            (30), (31), (32), (33), (34), (35), (37), (38),
% 151.42/22.07  | | | | | | | | |            (40), (41), (42), (43), (44), (45), (46), (47),
% 151.42/22.07  | | | | | | | | |            (48), (49), (50), (53), (54), (55), (56), (58),
% 151.42/22.07  | | | | | | | | |            (59), (60), (61), (62), (63), (65), (66), (68),
% 151.42/22.07  | | | | | | | | |            (69), (70), (72), (73), (74), (76), (77), (78),
% 151.42/22.07  | | | | | | | | |            (79), (80), (81), (82), (83), (84), (92), (94),
% 151.42/22.07  | | | | | | | | |            (111), (121) are inconsistent by sub-proof #109.
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | Case 2:
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | |   (122)  all_56_2 = e2 & op(e2, e3) = e2
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | | ALPHA: (122) implies:
% 151.42/22.07  | | | | | | | | |   (123)  op(e2, e3) = e2
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | | REF_CLOSE: (19), (84), (111), (123) are inconsistent by
% 151.42/22.07  | | | | | | | | |            sub-proof #1181.
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | End of split
% 151.42/22.07  | | | | | | | | 
% 151.42/22.07  | | | | | | | Case 2:
% 151.42/22.07  | | | | | | | | 
% 151.42/22.07  | | | | | | | |   (124)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 &
% 151.42/22.07  | | | | | | | |            op(e0, e3) = e2)
% 151.42/22.07  | | | | | | | | 
% 151.42/22.07  | | | | | | | | BETA: splitting (124) gives:
% 151.42/22.07  | | | | | | | | 
% 151.42/22.07  | | | | | | | | Case 1:
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | |   (125)  all_56_6 = e2 & op(e1, e3) = e2
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | | ALPHA: (125) implies:
% 151.42/22.07  | | | | | | | | |   (126)  all_56_6 = e2
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | | REF_CLOSE: (18), (19), (42), (43), (60), (75), (84), (113),
% 151.42/22.07  | | | | | | | | |            (118), (126) are inconsistent by sub-proof #108.
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | Case 2:
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | |   (127)  all_56_12 = e2 & op(e0, e3) = e2
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | | ALPHA: (127) implies:
% 151.42/22.07  | | | | | | | | |   (128)  all_56_12 = e2
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | | REF_CLOSE: (6), (18), (19), (30), (33), (42), (57), (60),
% 151.42/22.07  | | | | | | | | |            (76), (82), (128) are inconsistent by sub-proof
% 151.42/22.07  | | | | | | | | |            #106.
% 151.42/22.07  | | | | | | | | | 
% 151.42/22.07  | | | | | | | | End of split
% 151.42/22.07  | | | | | | | | 
% 151.42/22.07  | | | | | | | End of split
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | Case 2:
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | |   (129)  all_56_13 = e1 & op(e0, e2) = e1
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | | ALPHA: (129) implies:
% 151.42/22.07  | | | | | | |   (130)  op(e0, e2) = e1
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | | REF_CLOSE: (17), (19), (48), (71), (130) are inconsistent by
% 151.42/22.07  | | | | | | |            sub-proof #520.
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | End of split
% 151.42/22.07  | | | | | | 
% 151.42/22.07  | | | | | Case 2:
% 151.42/22.07  | | | | | | 
% 151.42/22.07  | | | | | |   (131)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 &
% 151.42/22.07  | | | | | |            op(e0, e0) = e1)
% 151.42/22.07  | | | | | | 
% 151.42/22.07  | | | | | | BETA: splitting (131) gives:
% 151.42/22.07  | | | | | | 
% 151.42/22.07  | | | | | | Case 1:
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | |   (132)  all_56_14 = e1 & op(e0, e1) = e1
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | | REF_CLOSE: (6), (57), (132) are inconsistent by sub-proof #481.
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | Case 2:
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | |   (133)  all_56_15 = e1 & op(e0, e0) = e1
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | | ALPHA: (133) implies:
% 151.42/22.07  | | | | | | |   (134)  op(e0, e0) = e1
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | | REF_CLOSE: (19), (105), (106), (134) are inconsistent by sub-proof
% 151.42/22.07  | | | | | | |            #940.
% 151.42/22.07  | | | | | | | 
% 151.42/22.07  | | | | | | End of split
% 151.42/22.07  | | | | | | 
% 151.42/22.07  | | | | | End of split
% 151.42/22.07  | | | | | 
% 151.42/22.07  | | | | End of split
% 151.42/22.07  | | | | 
% 151.42/22.07  | | | End of split
% 151.42/22.07  | | | 
% 151.42/22.07  | | Case 2:
% 151.42/22.07  | | | 
% 151.42/22.07  | | |   (135)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 151.42/22.07  | | |              e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.42/22.07  | | |              $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 151.42/22.07  | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.42/22.07  | | |          ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 151.42/22.07  | | |              op(e1, e1) = all_57_14 & $i(all_57_14)))
% 151.42/22.07  | | | 
% 151.42/22.07  | | | ALPHA: (135) implies:
% 151.42/22.07  | | |   (136)  op(e0, e0) = e0
% 151.42/22.07  | | | 
% 151.42/22.07  | | | REF_CLOSE: (18), (19), (30), (136) are inconsistent by sub-proof #1043.
% 151.42/22.07  | | | 
% 151.42/22.07  | | End of split
% 151.42/22.07  | | 
% 151.42/22.07  | End of split
% 151.42/22.07  | 
% 151.42/22.07  End of proof
% 151.42/22.07  
% 151.42/22.07  Sub-proof #106 shows that the following formulas are inconsistent:
% 151.42/22.07  ----------------------------------------------------------------
% 151.42/22.07    (1)   ~ (e3 = e1)
% 151.42/22.07    (2)   ~ (e2 = e0)
% 151.42/22.07    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.07    (4)  op(e0, e0) = e2
% 151.42/22.07    (5)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.42/22.07             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 151.42/22.07               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.42/22.07               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.42/22.07    (6)   ~ (e3 = e0)
% 151.42/22.07    (7)  all_56_14 = e3
% 151.42/22.07    (8)   ~ (e1 = e0)
% 151.42/22.07    (9)  all_56_12 = e2
% 151.42/22.07    (10)   ~ (e2 = e1)
% 151.42/22.07    (11)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.42/22.07          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 151.42/22.07            e1)
% 151.42/22.07  
% 151.42/22.07  Begin of proof
% 151.42/22.07  | 
% 151.42/22.07  | BETA: splitting (5) gives:
% 151.42/22.07  | 
% 151.42/22.07  | Case 1:
% 151.42/22.07  | | 
% 151.42/22.07  | |   (12)  all_56_15 = e0 & op(e0, e0) = e0
% 151.42/22.07  | | 
% 151.42/22.07  | | ALPHA: (12) implies:
% 151.42/22.07  | |   (13)  op(e0, e0) = e0
% 151.42/22.07  | | 
% 151.42/22.07  | | REF_CLOSE: (2), (3), (4), (13) are inconsistent by sub-proof #1043.
% 151.42/22.07  | | 
% 151.42/22.07  | Case 2:
% 151.42/22.07  | | 
% 151.42/22.07  | |   (14)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 151.42/22.07  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 151.42/22.07  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 151.42/22.07  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 151.42/22.07  | | 
% 151.42/22.07  | | ALPHA: (14) implies:
% 151.42/22.07  | |   (15)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 151.42/22.07  | |           e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.42/22.07  | | 
% 151.42/22.07  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (15) are
% 151.42/22.07  | |            inconsistent by sub-proof #107.
% 151.42/22.07  | | 
% 151.42/22.07  | End of split
% 151.42/22.07  | 
% 151.42/22.07  End of proof
% 151.42/22.07  
% 151.42/22.07  Sub-proof #107 shows that the following formulas are inconsistent:
% 151.42/22.07  ----------------------------------------------------------------
% 151.42/22.07    (1)   ~ (e3 = e1)
% 151.42/22.07    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 151.42/22.07         (all_56_14 = e0 & op(e0, e1) = e0)
% 151.42/22.07    (3)   ~ (e2 = e0)
% 151.42/22.07    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.07    (5)  op(e0, e0) = e2
% 151.42/22.07    (6)   ~ (e3 = e0)
% 151.42/22.07    (7)  all_56_14 = e3
% 151.42/22.07    (8)   ~ (e1 = e0)
% 151.42/22.07    (9)  all_56_12 = e2
% 151.42/22.07    (10)   ~ (e2 = e1)
% 151.42/22.07    (11)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.42/22.07          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 151.42/22.07            e1)
% 151.42/22.07  
% 151.42/22.07  Begin of proof
% 151.42/22.07  | 
% 151.42/22.07  | BETA: splitting (11) gives:
% 151.42/22.07  | 
% 151.42/22.07  | Case 1:
% 151.42/22.07  | | 
% 151.42/22.07  | |   (12)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 151.42/22.07  | |           e1)
% 151.42/22.07  | | 
% 151.42/22.07  | | BETA: splitting (12) gives:
% 151.42/22.07  | | 
% 151.42/22.07  | | Case 1:
% 151.42/22.07  | | | 
% 151.42/22.07  | | |   (13)  all_56_12 = e1 & op(e0, e3) = e1
% 151.42/22.07  | | | 
% 151.42/22.07  | | | REF_CLOSE: (9), (10), (13) are inconsistent by sub-proof #789.
% 151.42/22.07  | | | 
% 151.42/22.07  | | Case 2:
% 151.42/22.07  | | | 
% 151.42/22.07  | | |   (14)  all_56_13 = e1 & op(e0, e2) = e1
% 151.42/22.07  | | | 
% 151.42/22.07  | | | ALPHA: (14) implies:
% 151.42/22.07  | | |   (15)  all_56_13 = e1
% 151.42/22.07  | | | 
% 151.42/22.07  | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (15) are inconsistent by
% 151.42/22.07  | | |            sub-proof #580.
% 151.42/22.07  | | | 
% 151.42/22.07  | | End of split
% 151.42/22.07  | | 
% 151.42/22.07  | Case 2:
% 151.42/22.07  | | 
% 151.42/22.07  | |   (16)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 151.42/22.07  | |           e1)
% 151.42/22.07  | | 
% 151.42/22.07  | | BETA: splitting (16) gives:
% 151.42/22.07  | | 
% 151.42/22.07  | | Case 1:
% 151.42/22.07  | | | 
% 151.42/22.07  | | |   (17)  all_56_14 = e1 & op(e0, e1) = e1
% 151.42/22.07  | | | 
% 151.42/22.07  | | | REF_CLOSE: (1), (7), (17) are inconsistent by sub-proof #481.
% 151.42/22.07  | | | 
% 151.42/22.07  | | Case 2:
% 151.42/22.07  | | | 
% 151.42/22.07  | | |   (18)  all_56_15 = e1 & op(e0, e0) = e1
% 151.42/22.07  | | | 
% 151.42/22.07  | | | ALPHA: (18) implies:
% 151.42/22.07  | | |   (19)  op(e0, e0) = e1
% 151.42/22.07  | | | 
% 151.42/22.07  | | | REF_CLOSE: (4), (5), (10), (19) are inconsistent by sub-proof #978.
% 151.42/22.07  | | | 
% 151.42/22.07  | | End of split
% 151.42/22.07  | | 
% 151.42/22.07  | End of split
% 151.42/22.07  | 
% 151.42/22.07  End of proof
% 151.42/22.07  
% 151.42/22.07  Sub-proof #108 shows that the following formulas are inconsistent:
% 151.42/22.07  ----------------------------------------------------------------
% 151.42/22.07    (1)   ~ (all_52_1 = e0)
% 151.42/22.07    (2)  all_56_6 = e2
% 151.42/22.07    (3)   ~ (e2 = e0)
% 151.42/22.07    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.07    (5)  all_56_12 = e1
% 151.42/22.07    (6)   ~ (e3 = e0)
% 151.42/22.07    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.42/22.07         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.42/22.07    (8)   ~ (e1 = e0)
% 151.42/22.07    (9)  op(e3, e3) = e3
% 151.42/22.07    (10)  op(e2, e3) = all_52_1
% 151.42/22.07  
% 151.42/22.07  Begin of proof
% 151.42/22.07  | 
% 151.42/22.07  | BETA: splitting (7) gives:
% 151.42/22.07  | 
% 151.42/22.07  | Case 1:
% 151.42/22.07  | | 
% 151.42/22.07  | |   (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 151.42/22.07  | |           e0)
% 151.42/22.07  | | 
% 151.42/22.07  | | REF_CLOSE: (1), (4), (6), (9), (10), (11) are inconsistent by sub-proof
% 151.42/22.07  | |            #839.
% 151.42/22.07  | | 
% 151.42/22.07  | Case 2:
% 151.42/22.07  | | 
% 151.42/22.07  | |   (12)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 151.42/22.07  | |           e0)
% 151.42/22.07  | | 
% 151.42/22.07  | | BETA: splitting (12) gives:
% 151.42/22.07  | | 
% 151.42/22.07  | | Case 1:
% 151.42/22.07  | | | 
% 151.42/22.07  | | |   (13)  all_56_6 = e0 & op(e1, e3) = e0
% 151.42/22.07  | | | 
% 151.42/22.07  | | | ALPHA: (13) implies:
% 151.42/22.07  | | |   (14)  all_56_6 = e0
% 151.42/22.07  | | | 
% 151.42/22.07  | | | REF_CLOSE: (2), (3), (14) are inconsistent by sub-proof #724.
% 151.42/22.07  | | | 
% 151.42/22.07  | | Case 2:
% 151.42/22.07  | | | 
% 151.42/22.07  | | |   (15)  all_56_12 = e0 & op(e0, e3) = e0
% 151.42/22.07  | | | 
% 151.42/22.07  | | | REF_CLOSE: (5), (8), (15) are inconsistent by sub-proof #1103.
% 151.42/22.07  | | | 
% 151.42/22.07  | | End of split
% 151.42/22.07  | | 
% 151.42/22.07  | End of split
% 151.42/22.07  | 
% 151.42/22.07  End of proof
% 151.42/22.07  
% 151.42/22.07  Sub-proof #109 shows that the following formulas are inconsistent:
% 151.42/22.07  ----------------------------------------------------------------
% 151.42/22.07    (1)  op(e0, e1) = all_52_11
% 151.42/22.07    (2)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 151.42/22.07         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 151.42/22.07    (3)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 151.42/22.07    (4)   ~ (e3 = e1)
% 151.42/22.07    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.42/22.07         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.42/22.07    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 151.42/22.07         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 151.42/22.07    (7)  op(e0, e0) = all_10_2
% 151.42/22.07    (8)  op(e3, e2) = all_52_4
% 151.42/22.07    (9)  op(e0, e2) = all_52_7
% 151.42/22.07    (10)   ~ (all_52_14 = e2)
% 151.42/22.07    (11)   ~ (all_52_9 = all_52_13)
% 151.42/22.07    (12)   ~ (all_52_3 = all_52_7)
% 151.42/22.07    (13)  all_54_14 = all_52_11
% 151.42/22.07    (14)  op(e1, e1) = all_4_2
% 151.42/22.07    (15)   ~ (e2 = e0)
% 151.42/22.07    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.07            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.07    (17)  all_40_2 = e2
% 151.42/22.07    (18)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.42/22.07          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.42/22.07    (19)   ~ (all_52_1 = all_52_13)
% 151.42/22.07    (20)   ~ (all_52_2 = all_4_2)
% 151.42/22.07    (21)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.42/22.07          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.42/22.07    (22)   ~ (all_52_3 = e2)
% 151.42/22.07    (23)   ~ (all_52_3 = all_52_11)
% 151.42/22.07    (24)   ~ (all_52_9 = all_52_11)
% 151.42/22.07    (25)   ~ (all_52_9 = e3)
% 151.42/22.07    (26)  op(e3, e3) = e2
% 151.42/22.07    (27)  op(e0, e0) = e2
% 151.42/22.07    (28)   ~ (all_52_1 = all_52_9)
% 151.42/22.07    (29)   ~ (all_52_1 = e3)
% 151.42/22.07    (30)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.42/22.07              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 151.42/22.07                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.42/22.07                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.42/22.07    (31)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0 &
% 151.42/22.07            op(e0, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 151.42/22.07              e3) & op(e0, e2) = all_40_1 & $i(all_40_1))
% 151.42/22.07    (32)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 151.42/22.07          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 151.42/22.07    (33)  op(e1, e0) = all_52_14
% 151.42/22.07    (34)   ~ (all_52_4 = e3)
% 151.42/22.07    (35)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 151.42/22.07            all_57_10 & $i(all_57_10))
% 151.42/22.07    (36)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.42/22.07    (37)  op(e3, e0) = all_52_12
% 151.42/22.07    (38)   ~ (e3 = e0)
% 151.42/22.07    (39)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.42/22.07          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.42/22.07    (40)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 151.42/22.07          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 151.42/22.07    (41)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 151.42/22.07          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 151.42/22.07    (42)   ~ (all_52_6 = e3)
% 151.42/22.07    (43)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.42/22.07          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.42/22.07    (44)  ( ~ (all_24_0 = e3) & op(all_24_1, e0) = all_24_0 & op(e0, e2) =
% 151.42/22.07            all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0,
% 151.42/22.07              e2) = all_24_1 & $i(all_24_1))
% 151.42/22.07    (45)  op(e1, e2) = all_52_6
% 151.42/22.07    (46)  op(e2, e0) = all_52_13
% 151.42/22.07    (47)   ~ (all_52_1 = all_52_3)
% 151.42/22.07    (48)   ~ (all_52_14 = all_4_2)
% 151.42/22.07    (49)  op(e0, e3) = all_52_3
% 151.42/22.07    (50)   ~ (all_4_2 = e2)
% 151.42/22.07    (51)  op(e1, e1) = e1
% 151.42/22.07    (52)   ~ (all_52_8 = all_52_11)
% 151.42/22.07    (53)  op(e2, e1) = all_52_9
% 151.42/22.07    (54)   ~ (e1 = e0)
% 151.42/22.07    (55)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.42/22.07          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.42/22.07    (56)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.42/22.07              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.42/22.07            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.42/22.07                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.42/22.07              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.42/22.07          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.42/22.07              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.42/22.07            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.42/22.07                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.42/22.07              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.42/22.07          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 151.42/22.07              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.42/22.07            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 151.42/22.07                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 151.42/22.07              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.42/22.07          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 151.42/22.07              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.42/22.07            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 151.42/22.07                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 151.42/22.07                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.42/22.07                $i(all_57_14))))
% 151.42/22.07    (57)   ~ (all_4_2 = e3)
% 151.42/22.07    (58)   ~ (e3 = e2)
% 151.42/22.07    (59)  all_54_4 = all_52_1
% 151.42/22.07    (60)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.42/22.07          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 151.42/22.07            e2)
% 151.42/22.07    (61)   ~ (all_52_14 = all_10_2)
% 151.42/22.07    (62)   ~ (all_52_13 = e3)
% 151.42/22.07    (63)  op(e3, e1) = all_52_8
% 151.42/22.07    (64)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 151.42/22.07          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.42/22.07    (65)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.42/22.07          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.42/22.07    (66)   ~ (e2 = e1)
% 151.42/22.07    (67)   ~ (all_52_11 = all_4_2)
% 151.42/22.07    (68)  op(e2, e2) = e3
% 151.42/22.07    (69)  op(e1, e3) = all_52_2
% 151.42/22.07    (70)   ~ (all_52_11 = e2)
% 151.42/22.08    (71)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.42/22.08              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.42/22.08            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.42/22.08            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.42/22.08            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.42/22.08            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.42/22.08            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 151.42/22.08            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.42/22.08            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 151.42/22.08            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 151.42/22.08            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.42/22.08            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 151.42/22.08            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.42/22.08            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.42/22.08            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 151.42/22.08            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.42/22.08            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.42/22.08            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 151.42/22.08            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.42/22.08            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 151.42/22.08            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 151.42/22.08            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.42/22.08            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.42/22.08            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 151.42/22.08            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.42/22.08            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.42/22.08            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.42/22.08            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.42/22.08            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.42/22.08            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 151.42/22.08            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.42/22.08            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.42/22.08            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.42/22.08            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.42/22.08            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.42/22.08            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 151.42/22.08            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.42/22.08            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.42/22.08            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 151.42/22.08            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.42/22.08            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.42/22.08            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 151.42/22.08            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.42/22.08            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 151.42/22.08            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 151.42/22.08            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.42/22.08            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 151.42/22.08            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 151.42/22.08              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 151.42/22.08            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.42/22.08            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 151.42/22.08              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.42/22.08            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.42/22.08            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 151.42/22.08                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 151.42/22.08                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.42/22.08                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.42/22.08                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 151.42/22.08                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 151.42/22.08                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 151.42/22.08                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.42/22.08              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 151.42/22.08                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.42/22.08                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.42/22.08                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.42/22.08                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 151.42/22.08                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.42/22.08                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.42/22.08                $i(all_57_7))))
% 151.42/22.08    (72)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.42/22.08          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 151.42/22.08            e1)
% 151.42/22.08    (73)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 151.42/22.08          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 151.42/22.08    (74)  op(e2, e3) = all_52_1
% 151.42/22.08    (75)   ~ (all_52_1 = e2)
% 151.42/22.08  
% 151.42/22.08  Begin of proof
% 151.42/22.08  | 
% 151.42/22.08  | BETA: splitting (21) gives:
% 151.42/22.08  | 
% 151.42/22.08  | Case 1:
% 151.42/22.08  | | 
% 151.42/22.08  | |   (76)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) =
% 151.42/22.08  | |           e2)
% 151.42/22.08  | | 
% 151.42/22.08  | | BETA: splitting (76) gives:
% 151.42/22.08  | | 
% 151.42/22.08  | | Case 1:
% 151.42/22.08  | | | 
% 151.42/22.08  | | |   (77)  all_56_4 = e2 & op(e3, e1) = e2
% 151.42/22.08  | | | 
% 151.42/22.08  | | | ALPHA: (77) implies:
% 151.42/22.08  | | |   (78)  all_56_4 = e2
% 151.42/22.08  | | | 
% 151.42/22.08  | | | REF_CLOSE: (4), (15), (16), (18), (26), (32), (38), (41), (54), (58),
% 151.42/22.08  | | |            (66), (78) are inconsistent by sub-proof #1062.
% 151.42/22.08  | | | 
% 151.42/22.08  | | Case 2:
% 151.42/22.08  | | | 
% 151.42/22.08  | | |   (79)  all_56_5 = e2 & op(e2, e1) = e2
% 151.42/22.08  | | | 
% 151.42/22.08  | | | ALPHA: (79) implies:
% 151.42/22.08  | | |   (80)  op(e2, e1) = e2
% 151.42/22.08  | | | 
% 151.42/22.08  | | | BETA: splitting (55) gives:
% 151.42/22.08  | | | 
% 151.42/22.08  | | | Case 1:
% 151.42/22.08  | | | | 
% 151.42/22.08  | | | |   (81)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2)
% 151.42/22.08  | | | |           = e2)
% 151.42/22.08  | | | | 
% 151.42/22.08  | | | | BETA: splitting (81) gives:
% 151.42/22.08  | | | | 
% 151.42/22.08  | | | | Case 1:
% 151.42/22.08  | | | | | 
% 151.42/22.08  | | | | |   (82)  all_56_6 = e2 & op(e1, e3) = e2
% 151.42/22.08  | | | | | 
% 151.42/22.08  | | | | | ALPHA: (82) implies:
% 151.42/22.08  | | | | |   (83)  all_56_6 = e2
% 151.42/22.08  | | | | | 
% 151.42/22.08  | | | | | REF_CLOSE: (4), (5), (6), (15), (16), (26), (38), (39), (54), (58),
% 151.42/22.08  | | | | |            (66), (83) are inconsistent by sub-proof #1050.
% 151.42/22.08  | | | | | 
% 151.42/22.08  | | | | Case 2:
% 151.42/22.08  | | | | | 
% 151.42/22.08  | | | | |   (84)  all_56_7 = e2 & op(e1, e2) = e2
% 151.42/22.08  | | | | | 
% 151.42/22.08  | | | | | ALPHA: (84) implies:
% 151.42/22.08  | | | | |   (85)  all_56_7 = e2
% 151.42/22.08  | | | | |   (86)  op(e1, e2) = e2
% 151.42/22.08  | | | | | 
% 151.42/22.08  | | | | | BETA: splitting (43) gives:
% 151.42/22.08  | | | | | 
% 151.42/22.08  | | | | | Case 1:
% 151.42/22.08  | | | | | | 
% 151.42/22.08  | | | | | |   (87)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2,
% 151.42/22.08  | | | | | |             e3) = e2)
% 151.42/22.08  | | | | | | 
% 151.42/22.08  | | | | | | BETA: splitting (87) gives:
% 151.42/22.08  | | | | | | 
% 151.42/22.08  | | | | | | Case 1:
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | |   (88)  all_56_0 = e2 & op(e3, e3) = e2
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | GROUND_INST: instantiating (16) with all_4_2, e1, e1, e1,
% 151.42/22.08  | | | | | | |              simplifying with (14), (51) gives:
% 151.42/22.08  | | | | | | |   (89)  all_4_2 = e1
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | GROUND_INST: instantiating (16) with all_52_6, e2, e2, e1,
% 151.42/22.08  | | | | | | |              simplifying with (45), (86) gives:
% 151.42/22.08  | | | | | | |   (90)  all_52_6 = e2
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | GROUND_INST: instantiating (16) with all_52_9, e2, e1, e2,
% 151.42/22.08  | | | | | | |              simplifying with (53), (80) gives:
% 151.42/22.08  | | | | | | |   (91)  all_52_9 = e2
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | REDUCE: (20), (89) imply:
% 151.42/22.08  | | | | | | |   (92)   ~ (all_52_2 = e1)
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | REDUCE: (24), (91) imply:
% 151.42/22.08  | | | | | | |   (93)   ~ (all_52_11 = e2)
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | REDUCE: (11), (91) imply:
% 151.42/22.08  | | | | | | |   (94)   ~ (all_52_13 = e2)
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | SIMP: (94) implies:
% 151.42/22.08  | | | | | | |   (95)   ~ (all_52_13 = e2)
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | REDUCE: (25), (91) imply:
% 151.42/22.08  | | | | | | |   (96)   ~ (e3 = e2)
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | REDUCE: (67), (89) imply:
% 151.42/22.08  | | | | | | |   (97)   ~ (all_52_11 = e1)
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | REDUCE: (48), (89) imply:
% 151.42/22.08  | | | | | | |   (98)   ~ (all_52_14 = e1)
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | REDUCE: (57), (89) imply:
% 151.42/22.08  | | | | | | |   (99)   ~ (e3 = e1)
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | REDUCE: (50), (89) imply:
% 151.42/22.08  | | | | | | |   (100)   ~ (e2 = e1)
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | BETA: splitting (71) gives:
% 151.42/22.08  | | | | | | | 
% 151.42/22.08  | | | | | | | Case 1:
% 151.42/22.08  | | | | | | | | 
% 151.42/22.08  | | | | | | | |   (101)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 151.42/22.08  | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 151.42/22.08  | | | | | | | |            all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 151.42/22.08  | | | | | | | |            $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 &
% 151.42/22.08  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 151.42/22.08  | | | | | | | |              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.42/22.08  | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.42/22.08  | | | | | | | |            $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.42/22.08  | | | | | | | |            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 151.42/22.08  | | | | | | | |              e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 151.42/22.08  | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 151.42/22.08  | | | | | | | |            $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 151.42/22.08  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 151.42/22.08  | | | | | | | |              e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 151.42/22.08  | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.42/22.08  | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 151.42/22.08  | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 151.42/22.08  | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 151.42/22.08  | | | | | | | |            op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.42/22.08  | | | | | | | |            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 &
% 151.42/22.08  | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 151.42/22.08  | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 151.42/22.08  | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.42/22.08  | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 151.42/22.08  | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 151.42/22.08  | | | | | | | |              e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 151.42/22.08  | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.42/22.08  | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 151.42/22.08  | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 151.42/22.08  | | | | | | | |              e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.42/22.08  | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.42/22.08  | | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 151.42/22.08  | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 151.42/22.08  | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.42/22.08  | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.42/22.08  | | | | | | | |            $i(all_57_7) & $i(all_57_10))
% 151.42/22.08  | | | | | | | | 
% 151.42/22.08  | | | | | | | | BETA: splitting (101) gives:
% 151.42/22.08  | | | | | | | | 
% 151.42/22.08  | | | | | | | | Case 1:
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | |   (102)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 151.42/22.08  | | | | | | | | |              e2) = all_57_12 & op(e1, e3) = all_57_1 & op(e1,
% 151.42/22.08  | | | | | | | | |              e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 151.42/22.08  | | | | | | | | |          (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 151.42/22.08  | | | | | | | | |              e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0,
% 151.42/22.08  | | | | | | | | |              e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 151.42/22.08  | | | | | | | | |          (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_14 = e3) & op(e2, e3) = all_57_0 &
% 151.42/22.08  | | | | | | | | |            op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.42/22.08  | | | | | | | | |            all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 151.42/22.08  | | | | | | | | |          (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 151.42/22.08  | | | | | | | | |              e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 151.42/22.08  | | | | | | | | |              e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | BETA: splitting (102) gives:
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | Case 1:
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | |   (103)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.42/22.08  | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 151.42/22.08  | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 151.42/22.08  | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 151.42/22.08  | | | | | | | | | |          (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 151.42/22.08  | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 151.42/22.08  | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.42/22.08  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | REF_CLOSE: (16), (74), (75), (103) are inconsistent by
% 151.42/22.08  | | | | | | | | | |            sub-proof #1180.
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | Case 2:
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | |   (104)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 151.42/22.08  | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 151.42/22.08  | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 151.42/22.08  | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 151.42/22.08  | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 151.42/22.08  | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 151.42/22.08  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 151.42/22.08  | | | | | | | | | |              e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2)
% 151.42/22.08  | | | | | | | | | |            & $i(all_57_14))
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | REF_CLOSE: (16), (27), (58), (69), (92), (104) are
% 151.42/22.08  | | | | | | | | | |            inconsistent by sub-proof #723.
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | End of split
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | Case 2:
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | |   (105)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.42/22.08  | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 151.42/22.08  | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 151.42/22.08  | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.42/22.08  | | | | | | | | |            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 151.42/22.08  | | | | | | | | |              e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 151.42/22.08  | | | | | | | | |          (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3,
% 151.42/22.08  | | | | | | | | |              e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 151.42/22.08  | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 151.42/22.08  | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 151.42/22.08  | | | | | | | | |              e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 151.42/22.08  | | | | | | | | |              e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 151.42/22.08  | | | | | | | | |          (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.42/22.08  | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 151.42/22.08  | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | BETA: splitting (105) gives:
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | Case 1:
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | |   (106)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 151.42/22.08  | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 151.42/22.08  | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 151.42/22.08  | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 151.42/22.08  | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 151.42/22.08  | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 151.42/22.08  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 151.42/22.08  | | | | | | | | | |              e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5)
% 151.42/22.08  | | | | | | | | | |            & $i(all_57_10))
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | REF_CLOSE: (8), (14), (16), (34), (51), (66), (106) are
% 151.42/22.08  | | | | | | | | | |            inconsistent by sub-proof #721.
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | Case 2:
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | |   (107)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 151.42/22.08  | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 151.42/22.08  | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 151.42/22.08  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14))
% 151.42/22.08  | | | | | | | | | |          | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 151.42/22.08  | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 151.42/22.08  | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 151.42/22.08  | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 151.42/22.08  | | | | | | | | | |          (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 151.42/22.08  | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.42/22.08  | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 151.42/22.08  | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.42/22.08  | | | | | | | | | |            $i(all_57_10))
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | BETA: splitting (107) gives:
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | Case 1:
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | |   (108)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 151.42/22.08  | | | | | | | | | | |            e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 151.42/22.08  | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 151.42/22.08  | | | | | | | | | | |            e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | ALPHA: (108) implies:
% 151.42/22.08  | | | | | | | | | | |   (109)  op(e1, e2) = e1
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | REF_CLOSE: (16), (66), (86), (109) are inconsistent by
% 151.42/22.08  | | | | | | | | | | |            sub-proof #711.
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | Case 2:
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | |   (110)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 151.42/22.08  | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 151.42/22.08  | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 151.42/22.08  | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 151.42/22.08  | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 151.42/22.08  | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.42/22.08  | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 151.42/22.08  | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.42/22.08  | | | | | | | | | | |            $i(all_57_10))
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | BETA: splitting (110) gives:
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | Case 1:
% 151.42/22.08  | | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | |   (111)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 151.42/22.08  | | | | | | | | | | | |            e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 151.42/22.08  | | | | | | | | | | | |          op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 151.42/22.08  | | | | | | | | | | | |          op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 151.42/22.08  | | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | | ALPHA: (111) implies:
% 151.42/22.08  | | | | | | | | | | | |   (112)  op(e1, e2) = e1
% 151.42/22.08  | | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | | REF_CLOSE: (16), (66), (86), (112) are inconsistent by
% 151.42/22.08  | | | | | | | | | | | |            sub-proof #711.
% 151.42/22.08  | | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | Case 2:
% 151.42/22.08  | | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | |   (113)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 151.42/22.08  | | | | | | | | | | | |            e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.42/22.08  | | | | | | | | | | | |          all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 151.42/22.08  | | | | | | | | | | | |          op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.42/22.08  | | | | | | | | | | | |          $i(all_57_10)
% 151.42/22.08  | | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | | ALPHA: (113) implies:
% 151.42/22.08  | | | | | | | | | | | |   (114)  op(e2, e2) = e1
% 151.42/22.08  | | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | | REF_CLOSE: (4), (14), (15), (16), (26), (27), (46), (54),
% 151.42/22.08  | | | | | | | | | | | |            (56), (58), (66), (71), (74), (75), (86), (95),
% 151.42/22.08  | | | | | | | | | | | |            (114) are inconsistent by sub-proof #708.
% 151.42/22.08  | | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | End of split
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | End of split
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | End of split
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | End of split
% 151.42/22.08  | | | | | | | | 
% 151.42/22.08  | | | | | | | Case 2:
% 151.42/22.08  | | | | | | | | 
% 151.42/22.08  | | | | | | | |   (115)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) & 
% 151.42/22.08  | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 151.42/22.08  | | | | | | | |              e1) = e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1
% 151.42/22.08  | | | | | | | |            & $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 &
% 151.42/22.08  | | | | | | | |            all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 151.42/22.08  | | | | | | | |              e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.42/22.08  | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.42/22.08  | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 151.42/22.08  | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 151.42/22.08  | | | | | | | |              e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.42/22.08  | | | | | | | |            op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 151.42/22.08  | | | | | | | |            $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 151.42/22.08  | | | | | | | |            all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 151.42/22.08  | | | | | | | |              = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.42/22.08  | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 151.42/22.08  | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 151.42/22.08  | | | | | | | |            all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 151.42/22.08  | | | | | | | |              = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.42/22.08  | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.42/22.08  | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0 &
% 151.42/22.08  | | | | | | | |            all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 =
% 151.42/22.08  | | | | | | | |              e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.42/22.08  | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 151.42/22.08  | | | | | | | |            $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 &
% 151.42/22.08  | | | | | | | |            all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 151.42/22.08  | | | | | | | |              e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.42/22.08  | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.42/22.08  | | | | | | | |            $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 151.42/22.08  | | | | | | | |            all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13
% 151.42/22.08  | | | | | | | |              = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 151.42/22.08  | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.42/22.08  | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 151.42/22.08  | | | | | | | |            all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14
% 151.42/22.08  | | | | | | | |              = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 151.42/22.08  | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 151.42/22.08  | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 151.42/22.08  | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 151.42/22.08  | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.42/22.08  | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 151.42/22.08  | | | | | | | |                  e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 151.42/22.08  | | | | | | | |              (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.42/22.08  | | | | | | | |                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 151.42/22.08  | | | | | | | |                all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.42/22.08  | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &
% 151.42/22.08  | | | | | | | |                 ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 151.42/22.08  | | | | | | | |                  e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) =
% 151.42/22.08  | | | | | | | |                e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 151.42/22.08  | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 151.42/22.08  | | | | | | | |                op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0,
% 151.42/22.08  | | | | | | | |                  e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 151.42/22.08  | | | | | | | |                all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.42/22.08  | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 151.42/22.08  | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 151.42/22.08  | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 151.42/22.08  | | | | | | | |                  e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 151.42/22.08  | | | | | | | |                op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.42/22.08  | | | | | | | |                $i(all_57_7))))
% 151.42/22.08  | | | | | | | | 
% 151.42/22.08  | | | | | | | | BETA: splitting (115) gives:
% 151.42/22.08  | | | | | | | | 
% 151.42/22.08  | | | | | | | | Case 1:
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | |   (116)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.42/22.08  | | | | | | | | |            op(e3, e1) = e3 & op(e0, e1) = all_57_8 & op(e0,
% 151.42/22.08  | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 151.42/22.08  | | | | | | | | |          (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3,
% 151.42/22.08  | | | | | | | | |              e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2,
% 151.42/22.08  | | | | | | | | |              e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 151.42/22.08  | | | | | | | | |          (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 151.42/22.08  | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 151.42/22.08  | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 151.42/22.08  | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 151.42/22.08  | | | | | | | | |            op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 151.42/22.08  | | | | | | | | |            all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 151.42/22.08  | | | | | | | | |          (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 151.42/22.08  | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 151.42/22.08  | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | BETA: splitting (116) gives:
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | Case 1:
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | |   (117)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 151.42/22.08  | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.42/22.08  | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 151.42/22.08  | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.42/22.08  | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 151.42/22.08  | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 151.42/22.08  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 151.42/22.08  | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 151.42/22.08  | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | REF_CLOSE: (16), (27), (35), (66), (117) are inconsistent by
% 151.42/22.08  | | | | | | | | | |            sub-proof #447.
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | Case 2:
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | |   (118)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 151.42/22.08  | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 151.42/22.08  | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 151.42/22.08  | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.42/22.08  | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 151.42/22.08  | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 151.42/22.08  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 151.42/22.08  | | | | | | | | | |              e2) = e0 & op(e2, e0) = all_57_11 &
% 151.42/22.08  | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 151.42/22.08  | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.42/22.08  | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 151.42/22.08  | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 151.42/22.08  | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | BETA: splitting (118) gives:
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | Case 1:
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | |   (119)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 151.42/22.08  | | | | | | | | | | |            e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 151.42/22.08  | | | | | | | | | | |          all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 151.42/22.08  | | | | | | | | | | |          all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.42/22.08  | | | | | | | | | | |          $i(all_57_12)
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | ALPHA: (119) implies:
% 151.42/22.08  | | | | | | | | | | |   (120)  op(e0, e0) = e1
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | REF_CLOSE: (16), (27), (66), (120) are inconsistent by
% 151.42/22.08  | | | | | | | | | | |            sub-proof #978.
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | Case 2:
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | |   (121)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 151.42/22.08  | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 151.42/22.08  | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 151.42/22.08  | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.42/22.08  | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 151.42/22.08  | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 151.42/22.08  | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.42/22.08  | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.42/22.08  | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | REF_CLOSE: (16), (38), (51), (54), (68), (121) are
% 151.42/22.08  | | | | | | | | | | |            inconsistent by sub-proof #122.
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | End of split
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | End of split
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | Case 2:
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | |   (122)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3,
% 151.42/22.08  | | | | | | | | |              e0) = all_57_9 & op(e2, e2) = all_57_12 & op(e2,
% 151.42/22.08  | | | | | | | | |              e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 151.42/22.08  | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 151.42/22.08  | | | | | | | | |            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3,
% 151.42/22.08  | | | | | | | | |              e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1,
% 151.42/22.08  | | | | | | | | |              e0) = e1 & $i(all_57_9) & $i(all_57_14)) |
% 151.42/22.08  | | | | | | | | |          (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 151.42/22.08  | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 151.42/22.08  | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 151.42/22.08  | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.42/22.08  | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &
% 151.42/22.08  | | | | | | | | |             ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2,
% 151.42/22.08  | | | | | | | | |              e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 151.42/22.08  | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.42/22.08  | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 151.42/22.08  | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 & 
% 151.42/22.08  | | | | | | | | |                ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 151.42/22.08  | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 151.42/22.08  | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 =
% 151.42/22.08  | | | | | | | | |                e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.42/22.08  | | | | | | | | |                (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 151.42/22.08  | | | | | | | | |                op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.42/22.08  | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 151.42/22.08  | | | | | | | | |                &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 151.42/22.08  | | | | | | | | |                op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 151.42/22.08  | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 =
% 151.42/22.08  | | | | | | | | |                e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.42/22.08  | | | | | | | | |                (all_57_15 = e2) & op(e1, e2) = all_57_4 &
% 151.42/22.08  | | | | | | | | |                op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.42/22.08  | | | | | | | | |                $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 151.42/22.08  | | | | | | | | |                &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 151.42/22.08  | | | | | | | | |                op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.42/22.08  | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 151.42/22.08  | | | | | | | | |                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.42/22.08  | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 151.42/22.08  | | | | | | | | |                = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | BETA: splitting (122) gives:
% 151.42/22.08  | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | Case 1:
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | |   (123)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 151.42/22.08  | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 151.42/22.08  | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 151.42/22.08  | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 151.42/22.08  | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 151.42/22.08  | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 151.42/22.08  | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 151.42/22.08  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | REF_CLOSE: (15), (16), (26), (123) are inconsistent by
% 151.42/22.08  | | | | | | | | | |            sub-proof #1037.
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | Case 2:
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | |   (124)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 151.42/22.08  | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 151.42/22.08  | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 151.42/22.08  | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.42/22.08  | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 151.42/22.08  | | | | | | | | | |            &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 151.42/22.08  | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1,
% 151.42/22.08  | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 &
% 151.42/22.08  | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 151.42/22.08  | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 151.42/22.08  | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.42/22.08  | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 151.42/22.08  | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.42/22.08  | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 151.42/22.08  | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 151.42/22.08  | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 151.42/22.08  | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 151.42/22.08  | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.42/22.08  | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 151.42/22.08  | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 151.42/22.08  | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 151.42/22.08  | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 151.42/22.08  | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.42/22.08  | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 151.42/22.08  | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.42/22.08  | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.42/22.08  | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 151.42/22.08  | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 151.42/22.08  | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 151.42/22.08  | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.42/22.08  | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7))))
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | BETA: splitting (124) gives:
% 151.42/22.08  | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | Case 1:
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | |   (125)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 151.42/22.08  | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 151.42/22.08  | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 151.42/22.08  | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.42/22.08  | | | | | | | | | | |          $i(all_57_13)
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | ALPHA: (125) implies:
% 151.42/22.08  | | | | | | | | | | |   (126)  op(e2, e0) = e2
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | | REF_CLOSE: (11), (16), (46), (53), (80), (126) are
% 151.42/22.08  | | | | | | | | | | |            inconsistent by sub-proof #400.
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | Case 2:
% 151.42/22.08  | | | | | | | | | | | 
% 151.42/22.08  | | | | | | | | | | |   (127)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 151.42/22.08  | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 151.42/22.08  | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 151.42/22.08  | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 151.42/22.08  | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 151.42/22.08  | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 151.42/22.09  | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 151.42/22.09  | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 151.42/22.09  | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 151.42/22.09  | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 151.42/22.09  | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 151.42/22.09  | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.42/22.09  | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 151.42/22.09  | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 151.42/22.09  | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.42/22.09  | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.42/22.09  | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 151.42/22.09  | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.42/22.09  | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 151.42/22.09  | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 151.42/22.09  | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.42/22.09  | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 151.42/22.09  | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 151.42/22.09  | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 151.42/22.09  | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 151.42/22.09  | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 151.42/22.09  | | | | | | | | | | |                & $i(all_57_7))))
% 151.42/22.09  | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | BETA: splitting (127) gives:
% 151.42/22.09  | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | |   (128)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 151.42/22.09  | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 151.42/22.09  | | | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 151.42/22.09  | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 151.42/22.09  | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | ALPHA: (128) implies:
% 151.42/22.09  | | | | | | | | | | | |   (129)  op(e1, e0) = e1
% 151.42/22.09  | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | REF_CLOSE: (16), (33), (98), (129) are inconsistent by
% 151.42/22.09  | | | | | | | | | | | |            sub-proof #961.
% 151.42/22.09  | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | |   (130)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 151.42/22.09  | | | | | | | | | | | |          ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 151.42/22.09  | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 151.42/22.09  | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.42/22.09  | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 151.42/22.09  | | | | | | | | | | | |              e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 151.42/22.09  | | | | | | | | | | | |              & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 151.42/22.09  | | | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 151.42/22.09  | | | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.42/22.09  | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 151.42/22.09  | | | | | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 &
% 151.42/22.09  | | | | | | | | | | | |              $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 151.42/22.09  | | | | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 151.42/22.09  | | | | | | | | | | | |              & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.42/22.09  | | | | | | | | | | | |              op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 151.42/22.09  | | | | | | | | | | | |              e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.42/22.09  | | | | | | | | | | | |              (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.42/22.09  | | | | | | | | | | | |                e1) = all_57_6 & op(e0, e1) = e0 &
% 151.42/22.09  | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 151.42/22.09  | | | | | | | | | | | |              e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 151.42/22.09  | | | | | | | | | | | |              & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.42/22.09  | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_7)))
% 151.42/22.09  | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | ALPHA: (130) implies:
% 151.42/22.09  | | | | | | | | | | | |   (131)  op(e0, e0) = all_57_15
% 151.42/22.09  | | | | | | | | | | | |   (132)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 151.42/22.09  | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 151.42/22.09  | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.42/22.09  | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 151.42/22.09  | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 151.42/22.09  | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.42/22.09  | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 151.42/22.09  | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.42/22.09  | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 151.42/22.09  | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.42/22.09  | | | | | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 151.42/22.09  | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.42/22.09  | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.42/22.09  | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 151.42/22.09  | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 151.42/22.09  | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 151.42/22.09  | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 151.42/22.09  | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.42/22.09  | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 151.42/22.09  | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.42/22.09  | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | GROUND_INST: instantiating (16) with e2, all_57_15, e0, e0,
% 151.42/22.09  | | | | | | | | | | | |              simplifying with (27), (131) gives:
% 151.42/22.09  | | | | | | | | | | | |   (133)  all_57_15 = e2
% 151.42/22.09  | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | BETA: splitting (132) gives:
% 151.42/22.09  | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | |   (134)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 151.42/22.09  | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 151.42/22.09  | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.42/22.09  | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 151.42/22.09  | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 151.42/22.09  | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.42/22.09  | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 151.42/22.09  | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.42/22.09  | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 151.42/22.09  | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 151.42/22.09  | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | BETA: splitting (134) gives:
% 151.42/22.09  | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | |   (135)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 151.42/22.09  | | | | | | | | | | | | | |            e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 151.42/22.09  | | | | | | | | | | | | | |          all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.42/22.09  | | | | | | | | | | | | | |          $i(all_57_0)
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | ALPHA: (135) implies:
% 151.42/22.09  | | | | | | | | | | | | | |   (136)   ~ (all_57_15 = e3)
% 151.42/22.09  | | | | | | | | | | | | | |   (137)   ~ (all_57_0 = e2)
% 151.42/22.09  | | | | | | | | | | | | | |   (138)  op(e0, e3) = e0
% 151.42/22.09  | | | | | | | | | | | | | |   (139)  op(e2, e3) = all_57_0
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_52_3, e0, e3, e0,
% 151.42/22.09  | | | | | | | | | | | | | |              simplifying with (49), (138) gives:
% 151.42/22.09  | | | | | | | | | | | | | |   (140)  all_52_3 = e0
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | GROUND_INST: instantiating (16) with all_52_1, all_57_0, e3,
% 151.42/22.09  | | | | | | | | | | | | | |              e2, simplifying with (74), (139) gives:
% 151.42/22.09  | | | | | | | | | | | | | |   (141)  all_57_0 = all_52_1
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | REDUCE: (47), (140) imply:
% 151.42/22.09  | | | | | | | | | | | | | |   (142)   ~ (all_52_1 = e0)
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | REDUCE: (12), (140) imply:
% 151.42/22.09  | | | | | | | | | | | | | |   (143)   ~ (all_52_7 = e0)
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | SIMP: (143) implies:
% 151.42/22.09  | | | | | | | | | | | | | |   (144)   ~ (all_52_7 = e0)
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | REDUCE: (23), (140) imply:
% 151.42/22.09  | | | | | | | | | | | | | |   (145)   ~ (all_52_11 = e0)
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | SIMP: (145) implies:
% 151.42/22.09  | | | | | | | | | | | | | |   (146)   ~ (all_52_11 = e0)
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | REDUCE: (22), (140) imply:
% 151.42/22.09  | | | | | | | | | | | | | |   (147)   ~ (e2 = e0)
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | BETA: splitting (65) gives:
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | |   (148)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 151.42/22.09  | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | |   (149)  all_56_6 = e0 & op(e1, e3) = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | |   (150)  all_56_6 = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | |   (151)  all_56_15 = e0 & op(e0, e0) = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | |   (152)  op(e0, e0) = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (27), (152) are inconsistent by
% 151.42/22.09  | | | | | | | | | | | | | | | | |            sub-proof #1043.
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | |   (153)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 151.42/22.09  | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 151.42/22.09  | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 151.42/22.09  | | | | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 151.42/22.09  | | | | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | |   (154)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 151.42/22.09  | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 151.42/22.09  | | | | | | | | | | | | | | | | |              e1) = e0)
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | |   (155)  all_54_14 = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (155) imply:
% 151.42/22.09  | | | | | | | | | | | | | | | | | |   (156)  all_52_11 = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | SIMP: (156) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | |   (157)  all_52_11 = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | REDUCE: (52), (157) imply:
% 151.42/22.09  | | | | | | | | | | | | | | | | | |   (158)   ~ (all_52_8 = e3)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |   (159)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | |   (160)  all_56_12 = e1 & op(e0, e3) = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | |   (161)  all_56_12 = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (9), (16), (54), (144), (146), (154), (161)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #798.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | |   (162)  all_56_13 = e1 & op(e0, e2) = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | |   (163)  op(e0, e2) = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (164)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e3)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (38), (42), (45), (150), (164) are
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #112.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (165)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | |   (166)  all_56_8 = e3 & op(e1, e1) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | |   (167)  op(e1, e1) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (51), (167) are inconsistent by
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #734.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | |   (168)  all_56_11 = e3 & op(e1, e0) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | |   (169)  op(e1, e0) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |   (170)   ~ (all_40_2 = e2)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (170) imply:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |   (171)  $false
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (171) is inconsistent.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |   (172)  ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |            & op(e0, e2) = all_40_1 & $i(all_40_0) &
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e0, e2)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |            = all_40_1 & $i(all_40_1))
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (44), (163), (169), (172) are inconsistent
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #520.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |   (173)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (16), (27), (51), (58), (63), (66),
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |            (80), (158), (173) are inconsistent by sub-proof
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |            #111.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | |   (174)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (23), (49), (70), (97), (138), (174)
% 151.42/22.09  | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #110.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | |   (175)  all_56_7 = e0 & op(e1, e2) = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | REF_CLOSE: (15), (85), (175) are inconsistent by sub-proof
% 151.42/22.09  | | | | | | | | | | | | | | | |            #611.
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | |   (176)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 151.42/22.09  | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | |   (177)  all_56_8 = e0 & op(e1, e1) = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | |   (178)  op(e1, e1) = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | REF_CLOSE: (16), (51), (54), (178) are inconsistent by
% 151.42/22.09  | | | | | | | | | | | | | | | |            sub-proof #1038.
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | |   (179)  all_56_11 = e0 & op(e1, e0) = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | |   (180)  all_56_11 = e0
% 151.42/22.09  | | | | | | | | | | | | | | | |   (181)  op(e1, e0) = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | |   (182)  all_54_4 = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (182) imply:
% 151.42/22.09  | | | | | | | | | | | | | | | | |   (183)  all_52_1 = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | REDUCE: (29), (183) imply:
% 151.42/22.09  | | | | | | | | | | | | | | | | |   (184)  $false
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | |   (185)   ~ (all_54_4 = e3)
% 151.42/22.09  | | | | | | | | | | | | | | | | |   (186)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | |   (187)  all_54_4 = e2
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (187) imply:
% 151.42/22.09  | | | | | | | | | | | | | | | | | |   (188)  all_52_1 = e2
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | REDUCE: (75), (188) imply:
% 151.42/22.09  | | | | | | | | | | | | | | | | | |   (189)  $false
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | CLOSE: (189) is inconsistent.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | |   (190)   ~ (all_54_4 = e2)
% 151.42/22.09  | | | | | | | | | | | | | | | | | |   (191)  all_54_4 = e1 | all_54_4 = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |   (192)  all_56_15 = e0 & op(e0, e0) = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |   (193)  op(e0, e0) = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (16), (33), (61), (181), (193) are
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #453.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |   (194)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |   (195)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 151.42/22.09  | | | | | | | | | | | | | | | | | | |              e1) = e0)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | |   (196)  all_54_14 = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (196) imply:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | |   (197)  all_52_11 = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | SIMP: (197) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | |   (198)  all_52_11 = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | REDUCE: (52), (198) imply:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | |   (199)   ~ (all_52_8 = e3)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (200)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | |   (201)  all_56_12 = e1 & op(e0, e3) = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | |   (202)  all_56_12 = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (9), (16), (54), (144), (146), (195), (202)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #798.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | |   (203)  all_56_13 = e1 & op(e0, e2) = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | |   (204)  all_56_13 = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |   (205)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (58), (63), (80), (199), (205) are
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #623.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |   (206)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | |   (207)  all_56_8 = e3 & op(e1, e1) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | |   (208)  op(e1, e1) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (51), (208) are inconsistent by
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #734.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | |   (209)  all_56_14 = e3 & op(e0, e1) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | |   (210)  all_56_14 = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  all_56_9 = e3 & op(e3, e0) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  op(e3, e0) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  all_54_4 = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (59), (214) imply:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_52_1 = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (215) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  all_52_1 = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (19), (216) imply:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)   ~ (all_52_13 = e1)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (217) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (218)   ~ (all_52_13 = e1)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (219)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (37), (46), (213), (218), (219) are
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #511.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (220)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (221)  all_56_11 = e1 & op(e1, e0) = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (222)  op(e1, e0) = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (54), (181), (222) are inconsistent by
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #467.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (223)  all_56_15 = e1 & op(e0, e0) = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (224)  op(e0, e0) = e1
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (16), (38), (54), (58), (60), (66), (195),
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (204), (210), (224) are inconsistent by sub-proof
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #386.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  all_54_4 = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (59), (142), (225) are inconsistent by sub-proof
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #796.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  all_56_10 = e3 & op(e2, e0) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (46), (62), (226) are inconsistent by
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #114.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  all_56_11 = e3 & op(e1, e0) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (180), (228) are inconsistent by sub-proof
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            #561.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (229)  all_56_15 = e3 & op(e0, e0) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  op(e0, e0) = e3
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (131), (136), (230) are inconsistent by
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1019.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | |   (231)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (16), (27), (51), (58), (63), (66),
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | |            (80), (199), (231) are inconsistent by sub-proof
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | |            #111.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | |   (232)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (23), (49), (70), (97), (138), (232)
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #110.
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | |   (233)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.42/22.09  | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 151.42/22.09  | | | | | | | | | | | | | |            all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 151.42/22.09  | | | | | | | | | | | | | |            $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 151.42/22.09  | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 151.42/22.09  | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 151.42/22.09  | | | | | | | | | | | | | |              e2) = e0 & $i(all_57_3))
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | REF_CLOSE: (4), (16), (27), (51), (131), (233) are
% 151.42/22.09  | | | | | | | | | | | | | |            inconsistent by sub-proof #718.
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | |   (234)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 151.42/22.09  | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.42/22.09  | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.42/22.09  | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 151.42/22.09  | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 151.42/22.09  | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 151.42/22.09  | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 151.42/22.09  | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.42/22.09  | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 151.42/22.09  | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.42/22.09  | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | BETA: splitting (234) gives:
% 151.42/22.09  | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | |   (235)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 151.42/22.09  | | | | | | | | | | | | | |            e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 151.42/22.09  | | | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.42/22.09  | | | | | | | | | | | | | |          $i(all_57_4)
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | ALPHA: (235) implies:
% 151.42/22.09  | | | | | | | | | | | | | |   (236)  op(e1, e1) = e2
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | REF_CLOSE: (14), (16), (51), (66), (236) are inconsistent by
% 151.42/22.09  | | | | | | | | | | | | | |            sub-proof #1044.
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | |   (237)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 151.42/22.09  | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 151.42/22.09  | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.42/22.09  | | | | | | | | | | | | | |            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 151.42/22.09  | | | | | | | | | | | | | |            &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.42/22.09  | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 151.42/22.09  | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_7))
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | Case 1:
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | |   (238)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 151.42/22.09  | | | | | | | | | | | | | | |            e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 151.42/22.09  | | | | | | | | | | | | | | |          op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.42/22.09  | | | | | | | | | | | | | | |          $i(all_57_6)
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 151.42/22.09  | | | | | | | | | | | | | | |   (239)   ~ (all_57_6 = e3)
% 151.42/22.09  | | | | | | | | | | | | | | |   (240)  op(e3, e3) = e1
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | REF_CLOSE: (16), (35), (239), (240) are inconsistent by
% 151.42/22.09  | | | | | | | | | | | | | | |            sub-proof #456.
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | Case 2:
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | |   (241)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 151.42/22.09  | | | | | | | | | | | | | | |            e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 151.42/22.09  | | | | | | | | | | | | | | |          op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.42/22.09  | | | | | | | | | | | | | | |          $i(all_57_7)
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | ALPHA: (241) implies:
% 151.42/22.09  | | | | | | | | | | | | | | |   (242)  op(e2, e2) = e1
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (15), (16), (26), (27), (46), (54),
% 151.42/22.09  | | | | | | | | | | | | | | |            (56), (58), (66), (71), (74), (75), (86), (95),
% 151.42/22.09  | | | | | | | | | | | | | | |            (242) are inconsistent by sub-proof #708.
% 151.42/22.09  | | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | | 
% 151.42/22.09  | | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | | 
% 151.42/22.09  | | | | | | | | End of split
% 151.42/22.09  | | | | | | | | 
% 151.42/22.09  | | | | | | | End of split
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | Case 2:
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | |   (243)  all_56_2 = e2 & op(e2, e3) = e2
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | | ALPHA: (243) implies:
% 151.42/22.09  | | | | | | |   (244)  op(e2, e3) = e2
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | | REF_CLOSE: (16), (74), (75), (244) are inconsistent by sub-proof
% 151.42/22.09  | | | | | | |            #1181.
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | End of split
% 151.42/22.09  | | | | | | 
% 151.42/22.09  | | | | | Case 2:
% 151.42/22.09  | | | | | | 
% 151.42/22.09  | | | | | |   (245)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 &
% 151.42/22.09  | | | | | |            op(e0, e3) = e2)
% 151.42/22.09  | | | | | | 
% 151.42/22.09  | | | | | | BETA: splitting (245) gives:
% 151.42/22.09  | | | | | | 
% 151.42/22.09  | | | | | | Case 1:
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | |   (246)  all_56_6 = e2 & op(e1, e3) = e2
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | | ALPHA: (246) implies:
% 151.42/22.09  | | | | | | |   (247)  all_56_6 = e2
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | | REF_CLOSE: (4), (5), (6), (15), (16), (26), (38), (39), (54),
% 151.42/22.09  | | | | | | |            (58), (66), (247) are inconsistent by sub-proof #1050.
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | Case 2:
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | |   (248)  all_56_12 = e2 & op(e0, e3) = e2
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | | ALPHA: (248) implies:
% 151.42/22.09  | | | | | | |   (249)  all_56_12 = e2
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | | REF_CLOSE: (4), (5), (6), (15), (16), (26), (38), (39), (54),
% 151.42/22.09  | | | | | | |            (58), (66), (249) are inconsistent by sub-proof #781.
% 151.42/22.09  | | | | | | | 
% 151.42/22.09  | | | | | | End of split
% 151.42/22.09  | | | | | | 
% 151.42/22.09  | | | | | End of split
% 151.42/22.09  | | | | | 
% 151.42/22.09  | | | | End of split
% 151.42/22.09  | | | | 
% 151.42/22.09  | | | Case 2:
% 151.42/22.09  | | | | 
% 151.42/22.09  | | | |   (250)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1,
% 151.42/22.09  | | | |              e0) = e2)
% 151.42/22.09  | | | | 
% 151.42/22.09  | | | | REF_CLOSE: (10), (14), (16), (33), (51), (66), (250) are inconsistent by
% 151.42/22.09  | | | |            sub-proof #715.
% 151.42/22.09  | | | | 
% 151.42/22.09  | | | End of split
% 151.42/22.09  | | | 
% 151.42/22.09  | | End of split
% 151.42/22.09  | | 
% 151.42/22.09  | Case 2:
% 151.42/22.09  | | 
% 151.42/22.09  | |   (251)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) =
% 151.42/22.09  | |            e2)
% 151.42/22.09  | | 
% 151.42/22.09  | | BETA: splitting (251) gives:
% 151.42/22.09  | | 
% 151.42/22.09  | | Case 1:
% 151.42/22.09  | | | 
% 151.42/22.09  | | |   (252)  all_56_8 = e2 & op(e1, e1) = e2
% 151.42/22.09  | | | 
% 151.42/22.09  | | | ALPHA: (252) implies:
% 151.42/22.09  | | |   (253)  op(e1, e1) = e2
% 151.42/22.09  | | | 
% 151.42/22.09  | | | REF_CLOSE: (14), (16), (51), (66), (253) are inconsistent by sub-proof
% 151.42/22.09  | | |            #1044.
% 151.42/22.09  | | | 
% 151.42/22.09  | | Case 2:
% 151.42/22.09  | | | 
% 151.42/22.09  | | |   (254)  all_56_14 = e2 & op(e0, e1) = e2
% 151.42/22.09  | | | 
% 151.42/22.09  | | | ALPHA: (254) implies:
% 151.42/22.09  | | |   (255)  op(e0, e1) = e2
% 151.42/22.09  | | | 
% 151.42/22.09  | | | REF_CLOSE: (1), (16), (70), (255) are inconsistent by sub-proof #1092.
% 151.42/22.09  | | | 
% 151.42/22.09  | | End of split
% 151.42/22.09  | | 
% 151.42/22.09  | End of split
% 151.42/22.09  | 
% 151.42/22.09  End of proof
% 151.42/22.09  
% 151.42/22.09  Sub-proof #110 shows that the following formulas are inconsistent:
% 151.42/22.09  ----------------------------------------------------------------
% 151.42/22.09    (1)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.42/22.09    (2)  all_54_14 = all_52_11
% 151.42/22.09    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.09    (4)   ~ (all_52_3 = all_52_11)
% 151.42/22.09    (5)  op(e0, e3) = e0
% 151.42/22.09    (6)  op(e0, e3) = all_52_3
% 151.42/22.09    (7)   ~ (all_52_11 = e1)
% 151.42/22.09    (8)   ~ (all_52_11 = e2)
% 151.42/22.09  
% 151.42/22.09  Begin of proof
% 151.42/22.09  | 
% 151.42/22.09  | BETA: splitting (1) gives:
% 151.42/22.09  | 
% 151.42/22.09  | Case 1:
% 151.42/22.09  | | 
% 151.42/22.09  | |   (9)  all_54_14 = e2
% 151.42/22.09  | | 
% 151.42/22.09  | | REF_CLOSE: (2), (8), (9) are inconsistent by sub-proof #902.
% 151.42/22.09  | | 
% 151.42/22.09  | Case 2:
% 151.42/22.09  | | 
% 151.42/22.09  | |   (10)  all_54_14 = e1 | all_54_14 = e0
% 151.42/22.09  | | 
% 151.42/22.09  | | BETA: splitting (10) gives:
% 151.42/22.09  | | 
% 151.42/22.09  | | Case 1:
% 151.42/22.09  | | | 
% 151.42/22.09  | | |   (11)  all_54_14 = e1
% 151.42/22.09  | | | 
% 151.42/22.09  | | | REF_CLOSE: (2), (7), (11) are inconsistent by sub-proof #753.
% 151.42/22.09  | | | 
% 151.42/22.09  | | Case 2:
% 151.42/22.09  | | | 
% 151.42/22.09  | | |   (12)  all_54_14 = e0
% 151.42/22.09  | | | 
% 151.42/22.09  | | | COMBINE_EQS: (2), (12) imply:
% 151.42/22.09  | | |   (13)  all_52_11 = e0
% 151.42/22.09  | | | 
% 151.42/22.09  | | | SIMP: (13) implies:
% 151.42/22.09  | | |   (14)  all_52_11 = e0
% 151.42/22.09  | | | 
% 151.42/22.09  | | | REDUCE: (4), (14) imply:
% 151.42/22.09  | | |   (15)   ~ (all_52_3 = e0)
% 151.42/22.09  | | | 
% 151.42/22.09  | | | REF_CLOSE: (3), (5), (6), (15) are inconsistent by sub-proof #1142.
% 151.42/22.09  | | | 
% 151.42/22.09  | | End of split
% 151.42/22.09  | | 
% 151.42/22.09  | End of split
% 151.42/22.09  | 
% 151.42/22.09  End of proof
% 151.42/22.09  
% 151.42/22.09  Sub-proof #111 shows that the following formulas are inconsistent:
% 151.42/22.09  ----------------------------------------------------------------
% 151.42/22.09    (1)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 151.42/22.09         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 151.42/22.09    (2)   ~ (e3 = e1)
% 151.42/22.09    (3)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 151.42/22.09    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.09    (5)  op(e0, e0) = e2
% 151.42/22.09    (6)  op(e2, e1) = e2
% 151.42/22.10    (7)  op(e1, e1) = e1
% 151.42/22.10    (8)   ~ (e3 = e2)
% 151.42/22.10    (9)   ~ (all_52_8 = e3)
% 151.42/22.10    (10)  op(e3, e1) = all_52_8
% 151.42/22.10    (11)   ~ (e2 = e1)
% 151.42/22.10  
% 151.42/22.10  Begin of proof
% 151.42/22.10  | 
% 151.42/22.10  | BETA: splitting (3) gives:
% 151.42/22.10  | 
% 151.42/22.10  | Case 1:
% 151.42/22.10  | | 
% 151.42/22.10  | |   (12)  all_56_14 = e1 & op(e0, e1) = e1
% 151.42/22.10  | | 
% 151.42/22.10  | | ALPHA: (12) implies:
% 151.42/22.10  | |   (13)  all_56_14 = e1
% 151.42/22.10  | | 
% 151.42/22.10  | | BETA: splitting (1) gives:
% 151.42/22.10  | | 
% 151.42/22.10  | | Case 1:
% 151.42/22.10  | | | 
% 151.42/22.10  | | |   (14)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) =
% 151.42/22.10  | | |           e3)
% 151.42/22.10  | | | 
% 151.42/22.10  | | | REF_CLOSE: (4), (6), (8), (9), (10), (14) are inconsistent by sub-proof
% 151.42/22.10  | | |            #623.
% 151.42/22.10  | | | 
% 151.42/22.10  | | Case 2:
% 151.42/22.10  | | | 
% 151.42/22.10  | | |   (15)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 151.42/22.10  | | |           e3)
% 151.42/22.10  | | | 
% 151.42/22.10  | | | REF_CLOSE: (2), (4), (7), (13), (15) are inconsistent by sub-proof #638.
% 151.42/22.10  | | | 
% 151.42/22.10  | | End of split
% 151.42/22.10  | | 
% 151.42/22.10  | Case 2:
% 151.42/22.10  | | 
% 151.42/22.10  | |   (16)  all_56_15 = e1 & op(e0, e0) = e1
% 151.42/22.10  | | 
% 151.42/22.10  | | ALPHA: (16) implies:
% 151.42/22.10  | |   (17)  op(e0, e0) = e1
% 151.42/22.10  | | 
% 151.42/22.10  | | REF_CLOSE: (4), (5), (11), (17) are inconsistent by sub-proof #978.
% 151.42/22.10  | | 
% 151.42/22.10  | End of split
% 151.42/22.10  | 
% 151.42/22.10  End of proof
% 151.42/22.10  
% 151.42/22.10  Sub-proof #112 shows that the following formulas are inconsistent:
% 151.42/22.10  ----------------------------------------------------------------
% 151.42/22.10    (1)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3)
% 151.42/22.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.10    (3)  all_56_6 = e0
% 151.42/22.10    (4)   ~ (e3 = e0)
% 151.42/22.10    (5)   ~ (all_52_6 = e3)
% 151.42/22.10    (6)  op(e1, e2) = all_52_6
% 151.42/22.10  
% 151.42/22.10  Begin of proof
% 151.42/22.10  | 
% 151.42/22.10  | BETA: splitting (1) gives:
% 151.42/22.10  | 
% 151.42/22.10  | Case 1:
% 151.42/22.10  | | 
% 151.42/22.10  | |   (7)  all_56_6 = e3 & op(e1, e3) = e3
% 151.42/22.10  | | 
% 151.42/22.10  | | ALPHA: (7) implies:
% 151.42/22.10  | |   (8)  all_56_6 = e3
% 151.42/22.10  | | 
% 151.42/22.10  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #784.
% 151.42/22.10  | | 
% 151.42/22.10  | Case 2:
% 151.42/22.10  | | 
% 151.42/22.10  | |   (9)  all_56_7 = e3 & op(e1, e2) = e3
% 151.42/22.10  | | 
% 151.42/22.10  | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #925.
% 151.42/22.10  | | 
% 151.42/22.10  | End of split
% 151.42/22.10  | 
% 151.42/22.10  End of proof
% 151.42/22.10  
% 151.42/22.10  Sub-proof #113 shows that the following formulas are inconsistent:
% 151.42/22.10  ----------------------------------------------------------------
% 151.42/22.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.42/22.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.42/22.10    (2)  op(e3, e0) = all_52_12
% 151.42/22.10    (3)   ~ (all_52_12 = e3)
% 151.42/22.10    (4)  op(e2, e0) = all_52_13
% 151.42/22.10    (5)   ~ (all_52_13 = e3)
% 151.42/22.10    (6)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.42/22.10  
% 151.42/22.10  Begin of proof
% 151.42/22.10  | 
% 151.42/22.10  | BETA: splitting (6) gives:
% 151.42/22.10  | 
% 151.42/22.10  | Case 1:
% 151.42/22.10  | | 
% 151.42/22.10  | |   (7)  all_56_9 = e3 & op(e3, e0) = e3
% 151.42/22.10  | | 
% 151.42/22.10  | | ALPHA: (7) implies:
% 151.42/22.10  | |   (8)  op(e3, e0) = e3
% 151.42/22.10  | | 
% 151.42/22.10  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1082.
% 151.42/22.10  | | 
% 151.42/22.10  | Case 2:
% 151.42/22.10  | | 
% 151.42/22.10  | |   (9)  all_56_10 = e3 & op(e2, e0) = e3
% 151.42/22.10  | | 
% 151.42/22.10  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #114.
% 151.42/22.10  | | 
% 151.42/22.10  | End of split
% 151.42/22.10  | 
% 151.42/22.10  End of proof
% 151.42/22.10  
% 151.42/22.10  Sub-proof #114 shows that the following formulas are inconsistent:
% 151.42/22.10  ----------------------------------------------------------------
% 151.42/22.10    (1)  all_56_10 = e3 & op(e2, e0) = e3
% 151.42/22.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.10    (3)  op(e2, e0) = all_52_13
% 151.52/22.10    (4)   ~ (all_52_13 = e3)
% 151.52/22.10  
% 151.52/22.10  Begin of proof
% 151.52/22.10  | 
% 151.52/22.10  | ALPHA: (1) implies:
% 151.52/22.10  |   (5)  op(e2, e0) = e3
% 151.52/22.10  | 
% 151.52/22.10  | GROUND_INST: instantiating (2) with all_52_13, e3, e0, e2, simplifying with
% 151.52/22.10  |              (3), (5) gives:
% 151.52/22.10  |   (6)  all_52_13 = e3
% 151.52/22.10  | 
% 151.52/22.10  | REDUCE: (4), (6) imply:
% 151.52/22.10  |   (7)  $false
% 151.52/22.10  | 
% 151.52/22.10  | CLOSE: (7) is inconsistent.
% 151.52/22.10  | 
% 151.52/22.10  End of proof
% 151.52/22.10  
% 151.52/22.10  Sub-proof #115 shows that the following formulas are inconsistent:
% 151.52/22.10  ----------------------------------------------------------------
% 151.52/22.10    (1)  op(e1, e1) = all_4_2
% 151.52/22.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.10    (3)  op(e0, e0) = e2
% 151.52/22.10    (4)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 151.52/22.10             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.52/22.10           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 151.52/22.10           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.52/22.10             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.52/22.10           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.52/22.10           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 151.52/22.10           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 151.52/22.10           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 151.52/22.10           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 151.52/22.10           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 151.52/22.10         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 151.52/22.10             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.52/22.10           $i(all_57_7))
% 151.52/22.10    (5)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 151.52/22.10           all_57_10 & $i(all_57_10))
% 151.52/22.10    (6)  op(e0, e3) = all_52_3
% 151.52/22.10    (7)  op(e1, e1) = e1
% 151.52/22.10    (8)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 151.52/22.10           all_57_12 & $i(all_57_12))
% 151.52/22.10    (9)  op(e0, e0) = all_57_15
% 151.52/22.10    (10)   ~ (all_52_3 = e0)
% 151.52/22.10    (11)   ~ (e2 = e1)
% 151.52/22.10  
% 151.52/22.10  Begin of proof
% 151.52/22.10  | 
% 151.52/22.10  | BETA: splitting (4) gives:
% 151.52/22.10  | 
% 151.52/22.10  | Case 1:
% 151.52/22.10  | | 
% 151.52/22.10  | |   (12)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 151.52/22.10  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 151.52/22.10  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 151.52/22.10  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 151.52/22.10  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 151.52/22.10  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 151.52/22.10  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.52/22.10  | |           $i(all_57_3))
% 151.52/22.10  | | 
% 151.52/22.10  | | REF_CLOSE: (2), (3), (6), (9), (10), (12) are inconsistent by sub-proof
% 151.52/22.10  | |            #900.
% 151.52/22.10  | | 
% 151.52/22.10  | Case 2:
% 151.52/22.10  | | 
% 151.52/22.10  | |   (13)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 151.52/22.10  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.52/22.10  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.52/22.10  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.52/22.10  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 151.52/22.10  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.52/22.10  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.52/22.10  | |           $i(all_57_7))
% 151.52/22.10  | | 
% 151.52/22.10  | | REF_CLOSE: (1), (2), (5), (7), (8), (11), (13) are inconsistent by sub-proof
% 151.52/22.10  | |            #454.
% 151.52/22.10  | | 
% 151.52/22.10  | End of split
% 151.52/22.10  | 
% 151.52/22.10  End of proof
% 151.52/22.10  
% 151.52/22.10  Sub-proof #116 shows that the following formulas are inconsistent:
% 151.52/22.10  ----------------------------------------------------------------
% 151.52/22.10    (1)   ~ (all_52_6 = e1)
% 151.52/22.10    (2)  op(e3, e3) = e0
% 151.52/22.10    (3)   ~ (e3 = e1)
% 151.52/22.10    (4)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.52/22.10         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.52/22.10    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.52/22.10         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.52/22.10    (6)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.52/22.10         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.52/22.10    (7)  op(e1, e3) = e3
% 151.52/22.10    (8)  op(e3, e2) = all_52_4
% 151.52/22.10    (9)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.52/22.10         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.52/22.10    (10)   ~ (e2 = e0)
% 151.52/22.10    (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.52/22.10          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 151.52/22.10    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.10            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.10    (13)  op(e0, e0) = e3
% 151.52/22.10    (14)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.52/22.10          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.52/22.10    (15)  op(e2, e0) = e2
% 151.52/22.10    (16)   ~ (all_52_9 = e3)
% 151.52/22.10    (17)   ~ (all_52_14 = e1)
% 151.52/22.10    (18)  op(e3, e1) = e3
% 151.52/22.10    (19)  op(e1, e0) = all_52_14
% 151.52/22.10    (20)   ~ (all_52_4 = e3)
% 151.52/22.10    (21)   ~ (e3 = e0)
% 151.52/22.10    (22)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 151.52/22.10          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 151.52/22.10    (23)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 151.52/22.10          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 151.52/22.10    (24)   ~ (all_52_6 = e3)
% 151.52/22.10    (25)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.52/22.10          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.52/22.10    (26)  op(e1, e2) = all_52_6
% 151.52/22.10    (27)  op(e2, e0) = all_52_13
% 151.52/22.10    (28)  op(e1, e2) = e2
% 151.52/22.10    (29)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.52/22.10          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.52/22.10    (30)  op(e2, e1) = all_52_9
% 151.52/22.10    (31)   ~ (e1 = e0)
% 151.52/22.10    (32)  all_56_7 = e2
% 151.52/22.10    (33)   ~ (e3 = e2)
% 151.52/22.10    (34)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.52/22.10          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.52/22.10    (35)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.52/22.10          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.52/22.10    (36)   ~ (e2 = e1)
% 151.52/22.10    (37)   ~ (all_52_4 = e0)
% 151.52/22.10    (38)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.52/22.10          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.52/22.10    (39)  all_56_6 = e3
% 151.52/22.10    (40)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.52/22.10          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.52/22.10    (41)  op(e2, e3) = all_52_1
% 151.52/22.10    (42)   ~ (all_52_1 = e2)
% 151.52/22.10  
% 151.52/22.10  Begin of proof
% 151.52/22.10  | 
% 151.52/22.10  | BETA: splitting (22) gives:
% 151.52/22.10  | 
% 151.52/22.10  | Case 1:
% 151.52/22.10  | | 
% 151.52/22.10  | |   (43)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 151.52/22.10  | |           e1)
% 151.52/22.10  | | 
% 151.52/22.10  | | BETA: splitting (43) gives:
% 151.52/22.10  | | 
% 151.52/22.10  | | Case 1:
% 151.52/22.10  | | | 
% 151.52/22.10  | | |   (44)  all_56_9 = e1 & op(e3, e0) = e1
% 151.52/22.10  | | | 
% 151.52/22.10  | | | ALPHA: (44) implies:
% 151.52/22.10  | | |   (45)  all_56_9 = e1
% 151.52/22.10  | | | 
% 151.52/22.10  | | | BETA: splitting (25) gives:
% 151.52/22.10  | | | 
% 151.52/22.10  | | | Case 1:
% 151.52/22.10  | | | | 
% 151.52/22.10  | | | |   (46)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3)
% 151.52/22.10  | | | |           = e2)
% 151.52/22.10  | | | | 
% 151.52/22.10  | | | | REF_CLOSE: (2), (10), (12), (41), (42), (46) are inconsistent by
% 151.52/22.10  | | | |            sub-proof #526.
% 151.52/22.10  | | | | 
% 151.52/22.10  | | | Case 2:
% 151.52/22.10  | | | | 
% 151.52/22.10  | | | |   (47)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3)
% 151.52/22.10  | | | |           = e2)
% 151.52/22.10  | | | | 
% 151.52/22.10  | | | | BETA: splitting (47) gives:
% 151.52/22.10  | | | | 
% 151.52/22.10  | | | | Case 1:
% 151.52/22.10  | | | | | 
% 151.52/22.10  | | | | |   (48)  all_56_6 = e2 & op(e1, e3) = e2
% 151.52/22.10  | | | | | 
% 151.52/22.10  | | | | | REF_CLOSE: (33), (39), (48) are inconsistent by sub-proof #779.
% 151.52/22.10  | | | | | 
% 151.52/22.10  | | | | Case 2:
% 151.52/22.10  | | | | | 
% 151.52/22.10  | | | | |   (49)  all_56_12 = e2 & op(e0, e3) = e2
% 151.52/22.10  | | | | | 
% 151.52/22.10  | | | | | ALPHA: (49) implies:
% 151.52/22.10  | | | | |   (50)  all_56_12 = e2
% 151.52/22.10  | | | | | 
% 151.52/22.10  | | | | | BETA: splitting (5) gives:
% 151.52/22.10  | | | | | 
% 151.52/22.10  | | | | | Case 1:
% 151.52/22.10  | | | | | | 
% 151.52/22.10  | | | | | |   (51)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3,
% 151.52/22.10  | | | | | |             e2) = e2)
% 151.52/22.10  | | | | | | 
% 151.52/22.10  | | | | | | BETA: splitting (51) gives:
% 151.52/22.10  | | | | | | 
% 151.52/22.10  | | | | | | Case 1:
% 151.52/22.10  | | | | | | | 
% 151.52/22.10  | | | | | | |   (52)  all_56_0 = e2 & op(e3, e3) = e2
% 151.52/22.10  | | | | | | | 
% 151.52/22.10  | | | | | | | ALPHA: (52) implies:
% 151.52/22.10  | | | | | | |   (53)  op(e3, e3) = e2
% 151.52/22.10  | | | | | | | 
% 151.52/22.10  | | | | | | | REF_CLOSE: (2), (10), (12), (53) are inconsistent by sub-proof
% 151.52/22.10  | | | | | | |            #1073.
% 151.52/22.10  | | | | | | | 
% 151.52/22.10  | | | | | | Case 2:
% 151.52/22.10  | | | | | | | 
% 151.52/22.10  | | | | | | |   (54)  all_56_1 = e2 & op(e3, e2) = e2
% 151.52/22.10  | | | | | | | 
% 151.52/22.10  | | | | | | | ALPHA: (54) implies:
% 151.52/22.10  | | | | | | |   (55)  all_56_1 = e2
% 151.52/22.10  | | | | | | | 
% 151.52/22.10  | | | | | | | BETA: splitting (4) gives:
% 151.52/22.10  | | | | | | | 
% 151.52/22.10  | | | | | | | Case 1:
% 151.52/22.10  | | | | | | | | 
% 151.52/22.10  | | | | | | | |   (56)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 &
% 151.52/22.10  | | | | | | | |           op(e2, e3) = e1)
% 151.52/22.10  | | | | | | | | 
% 151.52/22.10  | | | | | | | | BETA: splitting (56) gives:
% 151.52/22.10  | | | | | | | | 
% 151.52/22.10  | | | | | | | | Case 1:
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | |   (57)  all_56_0 = e1 & op(e3, e3) = e1
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | ALPHA: (57) implies:
% 151.52/22.10  | | | | | | | | |   (58)  op(e3, e3) = e1
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | REF_CLOSE: (3), (5), (8), (10), (12), (14), (21), (23), (31),
% 151.52/22.10  | | | | | | | | |            (33), (36), (37), (45), (58) are inconsistent by
% 151.52/22.10  | | | | | | | | |            sub-proof #913.
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | Case 2:
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | |   (59)  all_56_2 = e1 & op(e2, e3) = e1
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | ALPHA: (59) implies:
% 151.52/22.10  | | | | | | | | |   (60)  all_56_2 = e1
% 151.52/22.10  | | | | | | | | |   (61)  op(e2, e3) = e1
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | BETA: splitting (38) gives:
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | Case 1:
% 151.52/22.10  | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | |   (62)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 &
% 151.52/22.10  | | | | | | | | | |           op(e2, e2) = e1)
% 151.52/22.10  | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | BETA: splitting (62) gives:
% 151.52/22.10  | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | Case 1:
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | |   (63)  all_56_1 = e1 & op(e3, e2) = e1
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | | ALPHA: (63) implies:
% 151.52/22.10  | | | | | | | | | | |   (64)  all_56_1 = e1
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | | REF_CLOSE: (36), (55), (64) are inconsistent by sub-proof
% 151.52/22.10  | | | | | | | | | | |            #595.
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | Case 2:
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | |   (65)  all_56_3 = e1 & op(e2, e2) = e1
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | | ALPHA: (65) implies:
% 151.52/22.10  | | | | | | | | | | |   (66)  op(e2, e2) = e1
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | | REF_CLOSE: (1), (3), (6), (9), (10), (11), (12), (16), (21),
% 151.52/22.10  | | | | | | | | | | |            (24), (26), (29), (30), (31), (33), (34), (35),
% 151.52/22.10  | | | | | | | | | | |            (36), (38), (40), (41), (60), (61), (66) are
% 151.52/22.10  | | | | | | | | | | |            inconsistent by sub-proof #172.
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | End of split
% 151.52/22.10  | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | Case 2:
% 151.52/22.10  | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | |   (67)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1
% 151.52/22.10  | | | | | | | | | |           & op(e0, e2) = e1)
% 151.52/22.10  | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | BETA: splitting (67) gives:
% 151.52/22.10  | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | Case 1:
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | |   (68)  all_56_7 = e1 & op(e1, e2) = e1
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | | ALPHA: (68) implies:
% 151.52/22.10  | | | | | | | | | | |   (69)  op(e1, e2) = e1
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | | REF_CLOSE: (12), (28), (36), (69) are inconsistent by
% 151.52/22.10  | | | | | | | | | | |            sub-proof #711.
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | Case 2:
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | |   (70)  all_56_13 = e1 & op(e0, e2) = e1
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | | ALPHA: (70) implies:
% 151.52/22.10  | | | | | | | | | | |   (71)  all_56_13 = e1
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | | REF_CLOSE: (3), (8), (10), (12), (20), (21), (24), (26),
% 151.52/22.10  | | | | | | | | | | |            (31), (32), (35), (37), (40), (71) are
% 151.52/22.10  | | | | | | | | | | |            inconsistent by sub-proof #117.
% 151.52/22.10  | | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | | End of split
% 151.52/22.10  | | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | End of split
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | End of split
% 151.52/22.10  | | | | | | | | 
% 151.52/22.10  | | | | | | | Case 2:
% 151.52/22.10  | | | | | | | | 
% 151.52/22.10  | | | | | | | |   (72)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 &
% 151.52/22.10  | | | | | | | |           op(e0, e3) = e1)
% 151.52/22.10  | | | | | | | | 
% 151.52/22.10  | | | | | | | | BETA: splitting (72) gives:
% 151.52/22.10  | | | | | | | | 
% 151.52/22.10  | | | | | | | | Case 1:
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | |   (73)  all_56_6 = e1 & op(e1, e3) = e1
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | ALPHA: (73) implies:
% 151.52/22.10  | | | | | | | | |   (74)  op(e1, e3) = e1
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | REF_CLOSE: (3), (7), (12), (74) are inconsistent by sub-proof
% 151.52/22.10  | | | | | | | | |            #119.
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | Case 2:
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | |   (75)  all_56_12 = e1 & op(e0, e3) = e1
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | ALPHA: (75) implies:
% 151.52/22.10  | | | | | | | | |   (76)  all_56_12 = e1
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | | REF_CLOSE: (36), (50), (76) are inconsistent by sub-proof
% 151.52/22.10  | | | | | | | | |            #1122.
% 151.52/22.10  | | | | | | | | | 
% 151.52/22.10  | | | | | | | | End of split
% 151.52/22.10  | | | | | | | | 
% 151.52/22.10  | | | | | | | End of split
% 151.52/22.10  | | | | | | | 
% 151.52/22.10  | | | | | | End of split
% 151.52/22.10  | | | | | | 
% 151.52/22.10  | | | | | Case 2:
% 151.52/22.10  | | | | | | 
% 151.52/22.10  | | | | | |   (77)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3,
% 151.52/22.10  | | | | | |             e0) = e2)
% 151.52/22.10  | | | | | | 
% 151.52/22.10  | | | | | | REF_CLOSE: (12), (18), (33), (36), (45), (77) are inconsistent by
% 151.52/22.10  | | | | | |            sub-proof #502.
% 151.52/22.10  | | | | | | 
% 151.52/22.10  | | | | | End of split
% 151.52/22.10  | | | | | 
% 151.52/22.10  | | | | End of split
% 151.52/22.10  | | | | 
% 151.52/22.10  | | | End of split
% 151.52/22.10  | | | 
% 151.52/22.10  | | Case 2:
% 151.52/22.10  | | | 
% 151.52/22.10  | | |   (78)  all_56_10 = e1 & op(e2, e0) = e1
% 151.52/22.10  | | | 
% 151.52/22.10  | | | ALPHA: (78) implies:
% 151.52/22.10  | | |   (79)  op(e2, e0) = e1
% 151.52/22.10  | | | 
% 151.52/22.10  | | | REF_CLOSE: (12), (15), (27), (36), (79) are inconsistent by sub-proof
% 151.52/22.10  | | |            #904.
% 151.52/22.10  | | | 
% 151.52/22.10  | | End of split
% 151.52/22.10  | | 
% 151.52/22.10  | Case 2:
% 151.52/22.10  | | 
% 151.52/22.10  | |   (80)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 151.52/22.10  | |           e1)
% 151.52/22.10  | | 
% 151.52/22.10  | | REF_CLOSE: (3), (12), (13), (17), (19), (80) are inconsistent by sub-proof
% 151.52/22.10  | |            #732.
% 151.52/22.10  | | 
% 151.52/22.10  | End of split
% 151.52/22.10  | 
% 151.52/22.10  End of proof
% 151.52/22.10  
% 151.52/22.10  Sub-proof #117 shows that the following formulas are inconsistent:
% 151.52/22.10  ----------------------------------------------------------------
% 151.52/22.10    (1)   ~ (e3 = e1)
% 151.52/22.10    (2)  op(e3, e2) = all_52_4
% 151.52/22.10    (3)   ~ (e2 = e0)
% 151.52/22.10    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.10    (5)  all_56_13 = e1
% 151.52/22.10    (6)   ~ (all_52_4 = e3)
% 151.52/22.10    (7)   ~ (e3 = e0)
% 151.52/22.10    (8)   ~ (all_52_6 = e3)
% 151.52/22.10    (9)  op(e1, e2) = all_52_6
% 151.52/22.10    (10)   ~ (e1 = e0)
% 151.52/22.10    (11)  all_56_7 = e2
% 151.52/22.10    (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.52/22.10          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.52/22.10    (13)   ~ (all_52_4 = e0)
% 151.52/22.10    (14)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.52/22.10          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.52/22.10  
% 151.52/22.10  Begin of proof
% 151.52/22.10  | 
% 151.52/22.10  | BETA: splitting (12) gives:
% 151.52/22.10  | 
% 151.52/22.10  | Case 1:
% 151.52/22.10  | | 
% 151.52/22.10  | |   (15)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 151.52/22.10  | |           e0)
% 151.52/22.10  | | 
% 151.52/22.10  | | BETA: splitting (15) gives:
% 151.52/22.10  | | 
% 151.52/22.10  | | Case 1:
% 151.52/22.10  | | | 
% 151.52/22.10  | | |   (16)  all_56_1 = e0 & op(e3, e2) = e0
% 151.52/22.10  | | | 
% 151.52/22.10  | | | REF_CLOSE: (2), (4), (13), (16) are inconsistent by sub-proof #1013.
% 151.52/22.10  | | | 
% 151.52/22.10  | | Case 2:
% 151.52/22.10  | | | 
% 151.52/22.10  | | |   (17)  all_56_3 = e0 & op(e2, e2) = e0
% 151.52/22.10  | | | 
% 151.52/22.10  | | | ALPHA: (17) implies:
% 151.52/22.10  | | |   (18)  op(e2, e2) = e0
% 151.52/22.10  | | | 
% 151.52/22.10  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (14), (18) are
% 151.52/22.10  | | |            inconsistent by sub-proof #210.
% 151.52/22.10  | | | 
% 151.52/22.10  | | End of split
% 151.52/22.10  | | 
% 151.52/22.10  | Case 2:
% 151.52/22.10  | | 
% 151.52/22.10  | |   (19)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 151.52/22.10  | |           e0)
% 151.52/22.10  | | 
% 151.52/22.10  | | BETA: splitting (19) gives:
% 151.52/22.10  | | 
% 151.52/22.10  | | Case 1:
% 151.52/22.10  | | | 
% 151.52/22.10  | | |   (20)  all_56_7 = e0 & op(e1, e2) = e0
% 151.52/22.10  | | | 
% 151.52/22.10  | | | ALPHA: (20) implies:
% 151.52/22.10  | | |   (21)  all_56_7 = e0
% 151.52/22.10  | | | 
% 151.52/22.10  | | | REF_CLOSE: (3), (11), (21) are inconsistent by sub-proof #483.
% 151.52/22.10  | | | 
% 151.52/22.10  | | Case 2:
% 151.52/22.10  | | | 
% 151.52/22.10  | | |   (22)  all_56_13 = e0 & op(e0, e2) = e0
% 151.52/22.10  | | | 
% 151.52/22.10  | | | REF_CLOSE: (5), (10), (22) are inconsistent by sub-proof #737.
% 151.52/22.10  | | | 
% 151.52/22.10  | | End of split
% 151.52/22.10  | | 
% 151.52/22.10  | End of split
% 151.52/22.10  | 
% 151.52/22.10  End of proof
% 151.52/22.10  
% 151.52/22.10  Sub-proof #118 shows that the following formulas are inconsistent:
% 151.52/22.10  ----------------------------------------------------------------
% 151.52/22.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.10    (2)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 151.52/22.10    (3)   ~ (e3 = e2)
% 151.52/22.10    (4)  op(e2, e2) = e3
% 151.52/22.10    (5)  op(e2, e3) = all_52_1
% 151.52/22.10    (6)   ~ (all_52_1 = e2)
% 151.52/22.10  
% 151.52/22.10  Begin of proof
% 151.52/22.10  | 
% 151.52/22.10  | BETA: splitting (2) gives:
% 151.52/22.10  | 
% 151.52/22.10  | Case 1:
% 151.52/22.10  | | 
% 151.52/22.10  | |   (7)  all_56_2 = e2 & op(e2, e3) = e2
% 151.52/22.10  | | 
% 151.52/22.10  | | ALPHA: (7) implies:
% 151.52/22.10  | |   (8)  op(e2, e3) = e2
% 151.52/22.10  | | 
% 151.52/22.10  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #1181.
% 151.52/22.10  | | 
% 151.52/22.10  | Case 2:
% 151.52/22.10  | | 
% 151.52/22.10  | |   (9)  all_56_3 = e2 & op(e2, e2) = e2
% 151.52/22.10  | | 
% 151.52/22.10  | | ALPHA: (9) implies:
% 151.52/22.10  | |   (10)  op(e2, e2) = e2
% 151.52/22.10  | | 
% 151.52/22.10  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1179.
% 151.52/22.10  | | 
% 151.52/22.10  | End of split
% 151.52/22.10  | 
% 151.52/22.10  End of proof
% 151.52/22.10  
% 151.52/22.10  Sub-proof #119 shows that the following formulas are inconsistent:
% 151.52/22.10  ----------------------------------------------------------------
% 151.52/22.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.10    (2)  op(e1, e3) = e3
% 151.52/22.10    (3)  op(e1, e3) = e1
% 151.52/22.10    (4)   ~ (e3 = e1)
% 151.52/22.10  
% 151.52/22.10  Begin of proof
% 151.52/22.10  | 
% 151.52/22.10  | GROUND_INST: instantiating (1) with e3, e1, e3, e1, simplifying with (2), (3)
% 151.52/22.10  |              gives:
% 151.52/22.10  |   (5)  e3 = e1
% 151.52/22.10  | 
% 151.52/22.10  | REDUCE: (4), (5) imply:
% 151.52/22.10  |   (6)  $false
% 151.52/22.10  | 
% 151.52/22.10  | CLOSE: (6) is inconsistent.
% 151.52/22.10  | 
% 151.52/22.10  End of proof
% 151.52/22.10  
% 151.52/22.10  Sub-proof #120 shows that the following formulas are inconsistent:
% 151.52/22.10  ----------------------------------------------------------------
% 151.52/22.10    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.10    (2)  op(e3, e3) = e2
% 151.52/22.11    (3)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.52/22.11             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.52/22.11           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.52/22.11               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.52/22.11             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.52/22.11         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.52/22.11             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.52/22.11           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.52/22.11               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.52/22.11             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 151.52/22.11    (4)   ~ (e3 = e2)
% 151.52/22.11    (5)  op(e2, e2) = e3
% 151.52/22.11  
% 151.52/22.11  Begin of proof
% 151.52/22.11  | 
% 151.52/22.11  | BETA: splitting (3) gives:
% 151.52/22.11  | 
% 151.52/22.11  | Case 1:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (6)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2)
% 151.52/22.11  | |          | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.52/22.11  | |        ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 151.52/22.11  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 151.52/22.11  | |              e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 151.52/22.11  | |            $i(all_57_15)))
% 151.52/22.11  | | 
% 151.52/22.11  | | ALPHA: (6) implies:
% 151.52/22.11  | |   (7)  op(e3, e3) = e3
% 151.52/22.11  | | 
% 151.52/22.11  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #1085.
% 151.52/22.11  | | 
% 151.52/22.11  | Case 2:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (8)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3)
% 151.52/22.11  | |          | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.52/22.11  | |        ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 151.52/22.11  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 151.52/22.11  | |              e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 151.52/22.11  | |            $i(all_57_15)))
% 151.52/22.11  | | 
% 151.52/22.11  | | ALPHA: (8) implies:
% 151.52/22.11  | |   (9)  op(e2, e2) = e2
% 151.52/22.11  | | 
% 151.52/22.11  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1179.
% 151.52/22.11  | | 
% 151.52/22.11  | End of split
% 151.52/22.11  | 
% 151.52/22.11  End of proof
% 151.52/22.11  
% 151.52/22.11  Sub-proof #121 shows that the following formulas are inconsistent:
% 151.52/22.11  ----------------------------------------------------------------
% 151.52/22.11    (1)   ~ (all_52_13 = e1)
% 151.52/22.11    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.52/22.11         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.52/22.11    (3)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 151.52/22.11    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.11    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.52/22.11         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.52/22.11    (6)   ~ (all_52_13 = e0)
% 151.52/22.11    (7)   ~ (all_52_12 = e1)
% 151.52/22.11    (8)  op(e3, e3) = e2
% 151.52/22.11    (9)   ~ (all_52_8 = all_52_12)
% 151.52/22.11    (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 151.52/22.11          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 151.52/22.11    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 151.52/22.11          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 151.52/22.11    (12)   ~ (all_52_12 = all_52_13)
% 151.52/22.11    (13)  ( ~ (all_36_0 = e1) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 151.52/22.11            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e3,
% 151.52/22.11              e2) = all_36_1 & $i(all_36_1))
% 151.52/22.11    (14)  op(e2, e0) = all_52_13
% 151.52/22.11    (15)  op(e1, e0) = all_50_1
% 151.52/22.11    (16)   ~ (e1 = e0)
% 151.52/22.11    (17)  all_56_2 = e0
% 151.52/22.11    (18)  op(e1, e0) = e1
% 151.52/22.11    (19)  all_56_1 = e0
% 151.52/22.11    (20)  all_54_3 = all_52_12
% 151.52/22.11    (21)   ~ (all_52_13 = e3)
% 151.52/22.11    (22)  op(e3, e1) = all_52_8
% 151.52/22.11    (23)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 151.52/22.11          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.52/22.11    (24)   ~ (all_52_2 = e1)
% 151.52/22.11    (25)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 151.52/22.11    (26)  op(e0, e0) = e0
% 151.52/22.11    (27)  all_54_7 = all_52_13
% 151.52/22.11    (28)  op(e1, e3) = all_52_2
% 151.52/22.11    (29)   ~ (all_52_12 = e0)
% 151.52/22.11  
% 151.52/22.11  Begin of proof
% 151.52/22.11  | 
% 151.52/22.11  | BETA: splitting (3) gives:
% 151.52/22.11  | 
% 151.52/22.11  | Case 1:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (30)  all_54_7 = e3
% 151.52/22.11  | | 
% 151.52/22.11  | | REF_CLOSE: (21), (27), (30) are inconsistent by sub-proof #1163.
% 151.52/22.11  | | 
% 151.52/22.11  | Case 2:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (31)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 151.52/22.11  | | 
% 151.52/22.11  | | BETA: splitting (31) gives:
% 151.52/22.11  | | 
% 151.52/22.11  | | Case 1:
% 151.52/22.11  | | | 
% 151.52/22.11  | | |   (32)  all_54_7 = e2
% 151.52/22.11  | | | 
% 151.52/22.11  | | | COMBINE_EQS: (27), (32) imply:
% 151.52/22.11  | | |   (33)  all_52_13 = e2
% 151.52/22.11  | | | 
% 151.52/22.11  | | | SIMP: (33) implies:
% 151.52/22.11  | | |   (34)  all_52_13 = e2
% 151.52/22.11  | | | 
% 151.52/22.11  | | | REDUCE: (12), (34) imply:
% 151.52/22.11  | | |   (35)   ~ (all_52_12 = e2)
% 151.52/22.11  | | | 
% 151.52/22.11  | | | REDUCE: (1), (34) imply:
% 151.52/22.11  | | |   (36)   ~ (e2 = e1)
% 151.52/22.11  | | | 
% 151.52/22.11  | | | REDUCE: (6), (34) imply:
% 151.52/22.11  | | |   (37)   ~ (e2 = e0)
% 151.52/22.11  | | | 
% 151.52/22.11  | | | REDUCE: (14), (34) imply:
% 151.52/22.11  | | |   (38)  op(e2, e0) = e2
% 151.52/22.11  | | | 
% 151.52/22.11  | | | BETA: splitting (25) gives:
% 151.52/22.11  | | | 
% 151.52/22.11  | | | Case 1:
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | |   (39)  all_54_3 = e3
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | COMBINE_EQS: (20), (39) imply:
% 151.52/22.11  | | | |   (40)  all_52_12 = e3
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | SIMP: (40) implies:
% 151.52/22.11  | | | |   (41)  all_52_12 = e3
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | REDUCE: (9), (41) imply:
% 151.52/22.11  | | | |   (42)   ~ (all_52_8 = e3)
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | REDUCE: (35), (41) imply:
% 151.52/22.11  | | | |   (43)   ~ (e3 = e2)
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | REDUCE: (7), (41) imply:
% 151.52/22.11  | | | |   (44)   ~ (e3 = e1)
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | REDUCE: (29), (41) imply:
% 151.52/22.11  | | | |   (45)   ~ (e3 = e0)
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | BETA: splitting (23) gives:
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | Case 1:
% 151.52/22.11  | | | | | 
% 151.52/22.11  | | | | |   (46)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2,
% 151.52/22.11  | | | | |             e0) = e3)
% 151.52/22.11  | | | | | 
% 151.52/22.11  | | | | | BETA: splitting (46) gives:
% 151.52/22.11  | | | | | 
% 151.52/22.11  | | | | | Case 1:
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | |   (47)  all_56_9 = e3 & op(e3, e0) = e3
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | | ALPHA: (47) implies:
% 151.52/22.11  | | | | | |   (48)  all_56_9 = e3
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | | BETA: splitting (10) gives:
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | | Case 1:
% 151.52/22.11  | | | | | | | 
% 151.52/22.11  | | | | | | |   (49)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 &
% 151.52/22.11  | | | | | | |           op(e3, e2) = e1)
% 151.52/22.11  | | | | | | | 
% 151.52/22.11  | | | | | | | BETA: splitting (49) gives:
% 151.52/22.11  | | | | | | | 
% 151.52/22.11  | | | | | | | Case 1:
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | |   (50)  all_56_0 = e1 & op(e3, e3) = e1
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | | ALPHA: (50) implies:
% 151.52/22.11  | | | | | | | |   (51)  op(e3, e3) = e1
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | | REF_CLOSE: (4), (8), (36), (51) are inconsistent by sub-proof
% 151.52/22.11  | | | | | | | |            #1074.
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | Case 2:
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | |   (52)  all_56_1 = e1 & op(e3, e2) = e1
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | | ALPHA: (52) implies:
% 151.52/22.11  | | | | | | | |   (53)  all_56_1 = e1
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | | REF_CLOSE: (16), (19), (53) are inconsistent by sub-proof #1107.
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | End of split
% 151.52/22.11  | | | | | | | 
% 151.52/22.11  | | | | | | Case 2:
% 151.52/22.11  | | | | | | | 
% 151.52/22.11  | | | | | | |   (54)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 &
% 151.52/22.11  | | | | | | |           op(e3, e0) = e1)
% 151.52/22.11  | | | | | | | 
% 151.52/22.11  | | | | | | | BETA: splitting (54) gives:
% 151.52/22.11  | | | | | | | 
% 151.52/22.11  | | | | | | | Case 1:
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | |   (55)  all_56_4 = e1 & op(e3, e1) = e1
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | | ALPHA: (55) implies:
% 151.52/22.11  | | | | | | | |   (56)  all_56_4 = e1
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | | BETA: splitting (2) gives:
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | | Case 1:
% 151.52/22.11  | | | | | | | | | 
% 151.52/22.11  | | | | | | | | |   (57)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 &
% 151.52/22.11  | | | | | | | | |           op(e2, e3) = e1)
% 151.52/22.11  | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | BETA: splitting (57) gives:
% 151.52/22.11  | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | Case 1:
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | |   (58)  all_56_0 = e1 & op(e3, e3) = e1
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | ALPHA: (58) implies:
% 151.52/22.11  | | | | | | | | | |   (59)  op(e3, e3) = e1
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | REF_CLOSE: (4), (8), (36), (59) are inconsistent by sub-proof
% 151.52/22.11  | | | | | | | | | |            #1074.
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | Case 2:
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | |   (60)  all_56_2 = e1 & op(e2, e3) = e1
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | ALPHA: (60) implies:
% 151.52/22.11  | | | | | | | | | |   (61)  all_56_2 = e1
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | COMBINE_EQS: (17), (61) imply:
% 151.52/22.11  | | | | | | | | | |   (62)  e1 = e0
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | REDUCE: (16), (62) imply:
% 151.52/22.11  | | | | | | | | | |   (63)  $false
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | CLOSE: (63) is inconsistent.
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | End of split
% 151.52/22.11  | | | | | | | | | 
% 151.52/22.11  | | | | | | | | Case 2:
% 151.52/22.11  | | | | | | | | | 
% 151.52/22.11  | | | | | | | | |   (64)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 &
% 151.52/22.11  | | | | | | | | |           op(e0, e3) = e1)
% 151.52/22.11  | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | BETA: splitting (64) gives:
% 151.52/22.11  | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | Case 1:
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | |   (65)  all_56_6 = e1 & op(e1, e3) = e1
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | ALPHA: (65) implies:
% 151.52/22.11  | | | | | | | | | |   (66)  op(e1, e3) = e1
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | REF_CLOSE: (4), (24), (28), (66) are inconsistent by
% 151.52/22.11  | | | | | | | | | |            sub-proof #1046.
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | Case 2:
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | |   (67)  all_56_12 = e1 & op(e0, e3) = e1
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | ALPHA: (67) implies:
% 151.52/22.11  | | | | | | | | | |   (68)  op(e0, e3) = e1
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | BETA: splitting (11) gives:
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | Case 1:
% 151.52/22.11  | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | |   (69)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 151.52/22.11  | | | | | | | | | | |           & op(e3, e2) = e0)
% 151.52/22.11  | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | | REF_CLOSE: (4), (8), (13), (37), (68), (69) are inconsistent
% 151.52/22.11  | | | | | | | | | | |            by sub-proof #735.
% 151.52/22.11  | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | Case 2:
% 151.52/22.11  | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | |   (70)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 151.52/22.11  | | | | | | | | | | |           & op(e3, e0) = e0)
% 151.52/22.11  | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | | BETA: splitting (70) gives:
% 151.52/22.11  | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | | Case 1:
% 151.52/22.11  | | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | | |   (71)  all_56_4 = e0 & op(e3, e1) = e0
% 151.52/22.11  | | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | | | ALPHA: (71) implies:
% 151.52/22.11  | | | | | | | | | | | |   (72)  all_56_4 = e0
% 151.52/22.11  | | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | | | REF_CLOSE: (16), (56), (72) are inconsistent by sub-proof
% 151.52/22.11  | | | | | | | | | | | |            #657.
% 151.52/22.11  | | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | | Case 2:
% 151.52/22.11  | | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | | |   (73)  all_56_9 = e0 & op(e3, e0) = e0
% 151.52/22.11  | | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | | | REF_CLOSE: (45), (48), (73) are inconsistent by sub-proof
% 151.52/22.11  | | | | | | | | | | | |            #446.
% 151.52/22.11  | | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | | End of split
% 151.52/22.11  | | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | | End of split
% 151.52/22.11  | | | | | | | | | | 
% 151.52/22.11  | | | | | | | | | End of split
% 151.52/22.11  | | | | | | | | | 
% 151.52/22.11  | | | | | | | | End of split
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | Case 2:
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | |   (74)  all_56_9 = e1 & op(e3, e0) = e1
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | | ALPHA: (74) implies:
% 151.52/22.11  | | | | | | | |   (75)  all_56_9 = e1
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | | REF_CLOSE: (4), (5), (8), (19), (22), (42), (43), (44), (45),
% 151.52/22.11  | | | | | | | |            (75) are inconsistent by sub-proof #808.
% 151.52/22.11  | | | | | | | | 
% 151.52/22.11  | | | | | | | End of split
% 151.52/22.11  | | | | | | | 
% 151.52/22.11  | | | | | | End of split
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | Case 2:
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | |   (76)  all_56_10 = e3 & op(e2, e0) = e3
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | | ALPHA: (76) implies:
% 151.52/22.11  | | | | | |   (77)  op(e2, e0) = e3
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | | REF_CLOSE: (4), (38), (43), (77) are inconsistent by sub-proof #854.
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | End of split
% 151.52/22.11  | | | | | 
% 151.52/22.11  | | | | Case 2:
% 151.52/22.11  | | | | | 
% 151.52/22.11  | | | | |   (78)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0,
% 151.52/22.11  | | | | |             e0) = e3)
% 151.52/22.11  | | | | | 
% 151.52/22.11  | | | | | BETA: splitting (78) gives:
% 151.52/22.11  | | | | | 
% 151.52/22.11  | | | | | Case 1:
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | |   (79)  all_56_11 = e3 & op(e1, e0) = e3
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | | ALPHA: (79) implies:
% 151.52/22.11  | | | | | |   (80)  op(e1, e0) = e3
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | | REF_CLOSE: (4), (15), (18), (44), (80) are inconsistent by sub-proof
% 151.52/22.11  | | | | | |            #123.
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | Case 2:
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | |   (81)  all_56_15 = e3 & op(e0, e0) = e3
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | | ALPHA: (81) implies:
% 151.52/22.11  | | | | | |   (82)  op(e0, e0) = e3
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | | REF_CLOSE: (4), (26), (45), (82) are inconsistent by sub-proof
% 151.52/22.11  | | | | | |            #1143.
% 151.52/22.11  | | | | | | 
% 151.52/22.11  | | | | | End of split
% 151.52/22.11  | | | | | 
% 151.52/22.11  | | | | End of split
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | Case 2:
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | |   (83)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | REF_CLOSE: (7), (20), (29), (35), (83) are inconsistent by sub-proof
% 151.52/22.11  | | | |            #758.
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | End of split
% 151.52/22.11  | | | 
% 151.52/22.11  | | Case 2:
% 151.52/22.11  | | | 
% 151.52/22.11  | | |   (84)  all_54_7 = e1 | all_54_7 = e0
% 151.52/22.11  | | | 
% 151.52/22.11  | | | REF_CLOSE: (1), (6), (27), (84) are inconsistent by sub-proof #170.
% 151.52/22.11  | | | 
% 151.52/22.11  | | End of split
% 151.52/22.11  | | 
% 151.52/22.11  | End of split
% 151.52/22.11  | 
% 151.52/22.11  End of proof
% 151.52/22.11  
% 151.52/22.11  Sub-proof #122 shows that the following formulas are inconsistent:
% 151.52/22.11  ----------------------------------------------------------------
% 151.52/22.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.11    (2)   ~ (e3 = e0)
% 151.52/22.11    (3)  op(e1, e1) = e1
% 151.52/22.11    (4)   ~ (e1 = e0)
% 151.52/22.11    (5)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 151.52/22.11             e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 151.52/22.11           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 =
% 151.52/22.11           e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 151.52/22.11           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 151.52/22.11           = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 151.52/22.11    (6)  op(e2, e2) = e3
% 151.52/22.11  
% 151.52/22.11  Begin of proof
% 151.52/22.11  | 
% 151.52/22.11  | BETA: splitting (5) gives:
% 151.52/22.11  | 
% 151.52/22.11  | Case 1:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (7)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 151.52/22.11  | |          = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0
% 151.52/22.11  | |        & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)
% 151.52/22.11  | | 
% 151.52/22.11  | | ALPHA: (7) implies:
% 151.52/22.11  | |   (8)  op(e2, e2) = e0
% 151.52/22.11  | | 
% 151.52/22.11  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #719.
% 151.52/22.11  | | 
% 151.52/22.11  | Case 2:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (9)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 151.52/22.11  | |          = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 151.52/22.11  | |        & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)
% 151.52/22.11  | | 
% 151.52/22.11  | | ALPHA: (9) implies:
% 151.52/22.11  | |   (10)  op(e1, e1) = e0
% 151.52/22.11  | | 
% 151.52/22.11  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1038.
% 151.52/22.11  | | 
% 151.52/22.11  | End of split
% 151.52/22.11  | 
% 151.52/22.11  End of proof
% 151.52/22.11  
% 151.52/22.11  Sub-proof #123 shows that the following formulas are inconsistent:
% 151.52/22.11  ----------------------------------------------------------------
% 151.52/22.11    (1)   ~ (e3 = e1)
% 151.52/22.11    (2)  op(e1, e0) = e3
% 151.52/22.11    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.11    (4)  op(e1, e0) = all_50_1
% 151.52/22.11    (5)  op(e1, e0) = e1
% 151.52/22.11  
% 151.52/22.11  Begin of proof
% 151.52/22.11  | 
% 151.52/22.11  | GROUND_INST: instantiating (3) with e3, all_50_1, e0, e1, simplifying with
% 151.52/22.11  |              (2), (4) gives:
% 151.52/22.11  |   (6)  all_50_1 = e3
% 151.52/22.11  | 
% 151.52/22.11  | GROUND_INST: instantiating (3) with e1, all_50_1, e0, e1, simplifying with
% 151.52/22.11  |              (4), (5) gives:
% 151.52/22.11  |   (7)  all_50_1 = e1
% 151.52/22.11  | 
% 151.52/22.11  | COMBINE_EQS: (6), (7) imply:
% 151.52/22.11  |   (8)  e3 = e1
% 151.52/22.11  | 
% 151.52/22.11  | SIMP: (8) implies:
% 151.52/22.11  |   (9)  e3 = e1
% 151.52/22.11  | 
% 151.52/22.11  | REDUCE: (1), (9) imply:
% 151.52/22.11  |   (10)  $false
% 151.52/22.11  | 
% 151.52/22.11  | CLOSE: (10) is inconsistent.
% 151.52/22.11  | 
% 151.52/22.11  End of proof
% 151.52/22.11  
% 151.52/22.11  Sub-proof #124 shows that the following formulas are inconsistent:
% 151.52/22.11  ----------------------------------------------------------------
% 151.52/22.11    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.52/22.11         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.52/22.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.11    (3)   ~ (e3 = e0)
% 151.52/22.11    (4)   ~ (all_52_8 = e0)
% 151.52/22.11    (5)  op(e1, e1) = e1
% 151.52/22.11    (6)  all_56_14 = e3
% 151.52/22.11    (7)  op(e2, e1) = all_52_9
% 151.52/22.11    (8)   ~ (e1 = e0)
% 151.52/22.11    (9)  op(e3, e1) = all_52_8
% 151.52/22.11    (10)   ~ (all_52_9 = e0)
% 151.52/22.11  
% 151.52/22.11  Begin of proof
% 151.52/22.11  | 
% 151.52/22.11  | BETA: splitting (1) gives:
% 151.52/22.11  | 
% 151.52/22.11  | Case 1:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (11)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 151.52/22.11  | |           e0)
% 151.52/22.11  | | 
% 151.52/22.11  | | BETA: splitting (11) gives:
% 151.52/22.11  | | 
% 151.52/22.11  | | Case 1:
% 151.52/22.11  | | | 
% 151.52/22.11  | | |   (12)  all_56_4 = e0 & op(e3, e1) = e0
% 151.52/22.11  | | | 
% 151.52/22.11  | | | REF_CLOSE: (2), (4), (9), (12) are inconsistent by sub-proof #1130.
% 151.52/22.11  | | | 
% 151.52/22.11  | | Case 2:
% 151.52/22.11  | | | 
% 151.52/22.11  | | |   (13)  all_56_5 = e0 & op(e2, e1) = e0
% 151.52/22.11  | | | 
% 151.52/22.11  | | | REF_CLOSE: (2), (7), (10), (13) are inconsistent by sub-proof #1144.
% 151.52/22.11  | | | 
% 151.52/22.11  | | End of split
% 151.52/22.11  | | 
% 151.52/22.11  | Case 2:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (14)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 151.52/22.11  | |           e0)
% 151.52/22.11  | | 
% 151.52/22.11  | | BETA: splitting (14) gives:
% 151.52/22.11  | | 
% 151.52/22.11  | | Case 1:
% 151.52/22.11  | | | 
% 151.52/22.11  | | |   (15)  all_56_8 = e0 & op(e1, e1) = e0
% 151.52/22.11  | | | 
% 151.52/22.11  | | | ALPHA: (15) implies:
% 151.52/22.11  | | |   (16)  op(e1, e1) = e0
% 151.52/22.11  | | | 
% 151.52/22.11  | | | REF_CLOSE: (2), (5), (8), (16) are inconsistent by sub-proof #1038.
% 151.52/22.11  | | | 
% 151.52/22.11  | | Case 2:
% 151.52/22.11  | | | 
% 151.52/22.11  | | |   (17)  all_56_14 = e0 & op(e0, e1) = e0
% 151.52/22.11  | | | 
% 151.52/22.11  | | | REF_CLOSE: (3), (6), (17) are inconsistent by sub-proof #622.
% 151.52/22.11  | | | 
% 151.52/22.11  | | End of split
% 151.52/22.11  | | 
% 151.52/22.11  | End of split
% 151.52/22.11  | 
% 151.52/22.11  End of proof
% 151.52/22.11  
% 151.52/22.11  Sub-proof #125 shows that the following formulas are inconsistent:
% 151.52/22.11  ----------------------------------------------------------------
% 151.52/22.11    (1)   ~ (e3 = e1)
% 151.52/22.11    (2)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.52/22.11         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.52/22.11    (3)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.52/22.11         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.52/22.11    (4)   ~ (e2 = e0)
% 151.52/22.11    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.11    (6)   ~ (all_52_13 = e0)
% 151.52/22.11    (7)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 151.52/22.11           all_57_12 & $i(all_57_12))
% 151.52/22.11    (8)   ~ (e3 = e0)
% 151.52/22.11    (9)   ~ (all_52_6 = e3)
% 151.52/22.11    (10)  op(e1, e2) = all_52_6
% 151.52/22.11    (11)  op(e2, e0) = all_52_13
% 151.52/22.11    (12)  op(e2, e1) = all_52_9
% 151.52/22.11    (13)   ~ (e1 = e0)
% 151.52/22.11    (14)   ~ (e3 = e2)
% 151.52/22.11    (15)  all_56_1 = e0
% 151.52/22.11    (16)   ~ (all_52_9 = e0)
% 151.52/22.11    (17)   ~ (e2 = e1)
% 151.52/22.11    (18)  op(e2, e2) = e3
% 151.52/22.11    (19)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.52/22.11          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.52/22.11    (20)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.52/22.11          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.52/22.11    (21)  op(e2, e3) = all_52_1
% 151.52/22.11  
% 151.52/22.11  Begin of proof
% 151.52/22.11  | 
% 151.52/22.11  | BETA: splitting (7) gives:
% 151.52/22.11  | 
% 151.52/22.11  | Case 1:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (22)  all_57_0 = e2 & op(e2, e3) = e2
% 151.52/22.11  | | 
% 151.52/22.11  | | ALPHA: (22) implies:
% 151.52/22.11  | |   (23)  op(e2, e3) = e2
% 151.52/22.11  | | 
% 151.52/22.11  | | BETA: splitting (3) gives:
% 151.52/22.11  | | 
% 151.52/22.11  | | Case 1:
% 151.52/22.11  | | | 
% 151.52/22.11  | | |   (24)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 151.52/22.11  | | |           e0)
% 151.52/22.11  | | | 
% 151.52/22.11  | | | BETA: splitting (24) gives:
% 151.52/22.11  | | | 
% 151.52/22.11  | | | Case 1:
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | |   (25)  all_56_2 = e0 & op(e2, e3) = e0
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | ALPHA: (25) implies:
% 151.52/22.11  | | | |   (26)  op(e2, e3) = e0
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | REF_CLOSE: (4), (5), (21), (23), (26) are inconsistent by sub-proof
% 151.52/22.11  | | | |            #128.
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | Case 2:
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | |   (27)  all_56_3 = e0 & op(e2, e2) = e0
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (13), (14), (15), (17),
% 151.52/22.11  | | | |            (19), (20), (27) are inconsistent by sub-proof #127.
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | End of split
% 151.52/22.11  | | | 
% 151.52/22.11  | | Case 2:
% 151.52/22.11  | | | 
% 151.52/22.11  | | |   (28)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 151.52/22.11  | | |           e0)
% 151.52/22.11  | | | 
% 151.52/22.11  | | | BETA: splitting (28) gives:
% 151.52/22.11  | | | 
% 151.52/22.11  | | | Case 1:
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | |   (29)  all_56_5 = e0 & op(e2, e1) = e0
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | REF_CLOSE: (5), (12), (16), (29) are inconsistent by sub-proof #1144.
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | Case 2:
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | |   (30)  all_56_10 = e0 & op(e2, e0) = e0
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | | REF_CLOSE: (5), (6), (11), (30) are inconsistent by sub-proof #540.
% 151.52/22.11  | | | | 
% 151.52/22.11  | | | End of split
% 151.52/22.11  | | | 
% 151.52/22.11  | | End of split
% 151.52/22.11  | | 
% 151.52/22.11  | Case 2:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (31)   ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12)
% 151.52/22.11  | | 
% 151.52/22.11  | | ALPHA: (31) implies:
% 151.52/22.11  | |   (32)   ~ (all_57_12 = e3)
% 151.52/22.11  | |   (33)  op(e2, e2) = all_57_12
% 151.52/22.11  | | 
% 151.52/22.11  | | REF_CLOSE: (5), (18), (32), (33) are inconsistent by sub-proof #126.
% 151.52/22.11  | | 
% 151.52/22.11  | End of split
% 151.52/22.11  | 
% 151.52/22.11  End of proof
% 151.52/22.11  
% 151.52/22.11  Sub-proof #126 shows that the following formulas are inconsistent:
% 151.52/22.11  ----------------------------------------------------------------
% 151.52/22.11    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.11    (2)  op(e2, e2) = all_57_12
% 151.52/22.11    (3)  op(e2, e2) = e3
% 151.52/22.11    (4)   ~ (all_57_12 = e3)
% 151.52/22.11  
% 151.52/22.11  Begin of proof
% 151.52/22.11  | 
% 151.52/22.11  | GROUND_INST: instantiating (1) with e3, all_57_12, e2, e2, simplifying with
% 151.52/22.11  |              (2), (3) gives:
% 151.52/22.11  |   (5)  all_57_12 = e3
% 151.52/22.11  | 
% 151.52/22.11  | REDUCE: (4), (5) imply:
% 151.52/22.11  |   (6)  $false
% 151.52/22.11  | 
% 151.52/22.11  | CLOSE: (6) is inconsistent.
% 151.52/22.11  | 
% 151.52/22.11  End of proof
% 151.52/22.11  
% 151.52/22.11  Sub-proof #127 shows that the following formulas are inconsistent:
% 151.52/22.11  ----------------------------------------------------------------
% 151.52/22.11    (1)   ~ (e3 = e1)
% 151.52/22.11    (2)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.52/22.11         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.52/22.11    (3)   ~ (e2 = e0)
% 151.52/22.11    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.11    (5)   ~ (e3 = e0)
% 151.52/22.11    (6)   ~ (all_52_6 = e3)
% 151.52/22.11    (7)  all_56_3 = e0 & op(e2, e2) = e0
% 151.52/22.11    (8)  op(e1, e2) = all_52_6
% 151.52/22.11    (9)   ~ (e1 = e0)
% 151.52/22.11    (10)   ~ (e3 = e2)
% 151.52/22.11    (11)  all_56_1 = e0
% 151.52/22.11    (12)   ~ (e2 = e1)
% 151.52/22.11    (13)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.52/22.11          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.52/22.11    (14)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.52/22.11          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.52/22.11  
% 151.52/22.11  Begin of proof
% 151.52/22.11  | 
% 151.52/22.11  | ALPHA: (7) implies:
% 151.52/22.11  |   (15)  op(e2, e2) = e0
% 151.52/22.11  | 
% 151.52/22.11  | BETA: splitting (14) gives:
% 151.52/22.11  | 
% 151.52/22.11  | Case 1:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 151.52/22.11  | |           e3)
% 151.52/22.11  | | 
% 151.52/22.11  | | REF_CLOSE: (4), (5), (11), (15), (16) are inconsistent by sub-proof #196.
% 151.52/22.11  | | 
% 151.52/22.11  | Case 2:
% 151.52/22.11  | | 
% 151.52/22.11  | |   (17)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 151.52/22.11  | |           e3)
% 151.52/22.11  | | 
% 151.52/22.11  | | BETA: splitting (17) gives:
% 151.52/22.11  | | 
% 151.52/22.11  | | Case 1:
% 151.52/22.11  | | | 
% 151.52/22.11  | | |   (18)  all_56_7 = e3 & op(e1, e2) = e3
% 151.52/22.11  | | | 
% 151.52/22.11  | | | REF_CLOSE: (4), (6), (8), (18) are inconsistent by sub-proof #925.
% 151.52/22.11  | | | 
% 151.52/22.11  | | Case 2:
% 151.52/22.11  | | | 
% 151.52/22.11  | | |   (19)  all_56_13 = e3 & op(e0, e2) = e3
% 151.52/22.11  | | | 
% 151.52/22.11  | | | ALPHA: (19) implies:
% 151.52/22.11  | | |   (20)  all_56_13 = e3
% 151.52/22.11  | | | 
% 151.52/22.11  | | | REF_CLOSE: (1), (2), (3), (4), (9), (10), (11), (12), (13), (15), (20) are
% 151.52/22.11  | | |            inconsistent by sub-proof #136.
% 151.52/22.11  | | | 
% 151.52/22.11  | | End of split
% 151.52/22.11  | | 
% 151.52/22.11  | End of split
% 151.52/22.11  | 
% 151.52/22.11  End of proof
% 151.52/22.11  
% 151.52/22.11  Sub-proof #128 shows that the following formulas are inconsistent:
% 151.52/22.11  ----------------------------------------------------------------
% 151.52/22.11    (1)   ~ (e2 = e0)
% 151.52/22.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.11    (3)  op(e2, e3) = e2
% 151.52/22.11    (4)  op(e2, e3) = e0
% 151.52/22.11    (5)  op(e2, e3) = all_52_1
% 151.52/22.11  
% 151.52/22.11  Begin of proof
% 151.52/22.11  | 
% 151.52/22.12  | GROUND_INST: instantiating (2) with all_52_1, e0, e3, e2, simplifying with
% 151.52/22.12  |              (4), (5) gives:
% 151.52/22.12  |   (6)  all_52_1 = e0
% 151.52/22.12  | 
% 151.52/22.12  | GROUND_INST: instantiating (2) with all_52_1, e2, e3, e2, simplifying with
% 151.52/22.12  |              (3), (5) gives:
% 151.52/22.12  |   (7)  all_52_1 = e2
% 151.52/22.12  | 
% 151.52/22.12  | COMBINE_EQS: (6), (7) imply:
% 151.52/22.12  |   (8)  e2 = e0
% 151.52/22.12  | 
% 151.52/22.12  | SIMP: (8) implies:
% 151.52/22.12  |   (9)  e2 = e0
% 151.52/22.12  | 
% 151.52/22.12  | REDUCE: (1), (9) imply:
% 151.52/22.12  |   (10)  $false
% 151.52/22.12  | 
% 151.52/22.12  | CLOSE: (10) is inconsistent.
% 151.52/22.12  | 
% 151.52/22.12  End of proof
% 151.52/22.12  
% 151.52/22.12  Sub-proof #129 shows that the following formulas are inconsistent:
% 151.52/22.12  ----------------------------------------------------------------
% 151.52/22.12    (1)  op(e0, e1) = all_52_11
% 151.52/22.12    (2)   ~ (e3 = e1)
% 151.52/22.12    (3)   ~ (all_52_11 = all_10_2)
% 151.52/22.12    (4)  op(e0, e0) = all_10_2
% 151.52/22.12    (5)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.52/22.12             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.52/22.12           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 151.52/22.12           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 151.52/22.12             e1) = e0 & $i(all_57_7))
% 151.52/22.12    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.12    (7)  op(e0, e0) = e0
% 151.52/22.12    (8)  op(e2, e2) = e3
% 151.52/22.12  
% 151.52/22.12  Begin of proof
% 151.52/22.12  | 
% 151.52/22.12  | BETA: splitting (5) gives:
% 151.52/22.12  | 
% 151.52/22.12  | Case 1:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (9)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.52/22.12  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.52/22.12  | |        $i(all_57_6)
% 151.52/22.12  | | 
% 151.52/22.12  | | ALPHA: (9) implies:
% 151.52/22.12  | |   (10)  op(e0, e1) = e0
% 151.52/22.12  | | 
% 151.52/22.12  | | REF_CLOSE: (1), (3), (4), (6), (7), (10) are inconsistent by sub-proof
% 151.52/22.12  | |            #1034.
% 151.52/22.12  | | 
% 151.52/22.12  | Case 2:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (11)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15
% 151.52/22.12  | |           = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 151.52/22.12  | |         & $i(all_57_7)
% 151.52/22.12  | | 
% 151.52/22.12  | | ALPHA: (11) implies:
% 151.52/22.12  | |   (12)  op(e2, e2) = e1
% 151.52/22.12  | | 
% 151.52/22.12  | | REF_CLOSE: (2), (6), (8), (12) are inconsistent by sub-proof #1136.
% 151.52/22.12  | | 
% 151.52/22.12  | End of split
% 151.52/22.12  | 
% 151.52/22.12  End of proof
% 151.52/22.12  
% 151.52/22.12  Sub-proof #130 shows that the following formulas are inconsistent:
% 151.52/22.12  ----------------------------------------------------------------
% 151.52/22.12    (1)   ~ (e3 = e1)
% 151.52/22.12    (2)   ~ (e2 = e0)
% 151.52/22.12    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.12    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 151.52/22.12             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 151.52/22.12           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 151.52/22.12           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 151.52/22.12           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 151.52/22.12           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.52/22.12    (5)  op(e0, e0) = e0
% 151.52/22.12    (6)  op(e2, e2) = e3
% 151.52/22.12  
% 151.52/22.12  Begin of proof
% 151.52/22.12  | 
% 151.52/22.12  | BETA: splitting (4) gives:
% 151.52/22.12  | 
% 151.52/22.12  | Case 1:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 151.52/22.12  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 151.52/22.12  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 151.52/22.12  | | 
% 151.52/22.12  | | ALPHA: (7) implies:
% 151.52/22.12  | |   (8)  op(e0, e0) = e2
% 151.52/22.12  | | 
% 151.52/22.12  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1043.
% 151.52/22.12  | | 
% 151.52/22.12  | Case 2:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 151.52/22.12  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 151.52/22.12  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 151.52/22.12  | | 
% 151.52/22.12  | | ALPHA: (9) implies:
% 151.52/22.12  | |   (10)  op(e2, e2) = e1
% 151.52/22.12  | | 
% 151.52/22.12  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #1136.
% 151.52/22.12  | | 
% 151.52/22.12  | End of split
% 151.52/22.12  | 
% 151.52/22.12  End of proof
% 151.52/22.12  
% 151.52/22.12  Sub-proof #131 shows that the following formulas are inconsistent:
% 151.52/22.12  ----------------------------------------------------------------
% 151.52/22.12    (1)   ~ (e3 = e1)
% 151.52/22.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.12    (3)   ~ (e3 = e0)
% 151.52/22.12    (4)  op(e1, e1) = e1
% 151.52/22.12    (5)   ~ (all_52_2 = e1)
% 151.52/22.12    (6)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.52/22.12             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.52/22.12           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.52/22.12           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.52/22.12           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.52/22.12           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.52/22.12           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 151.52/22.12           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 151.52/22.12           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 151.52/22.12           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 151.52/22.12           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 151.52/22.12           $i(all_57_14))
% 151.52/22.12    (7)  op(e0, e0) = e0
% 151.52/22.12    (8)  op(e1, e3) = all_52_2
% 151.52/22.12  
% 151.52/22.12  Begin of proof
% 151.52/22.12  | 
% 151.52/22.12  | BETA: splitting (6) gives:
% 151.52/22.12  | 
% 151.52/22.12  | Case 1:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (9)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 151.52/22.12  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.52/22.12  | |          all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 151.52/22.12  | |        (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 151.52/22.12  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 151.52/22.12  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 151.52/22.12  | | 
% 151.52/22.12  | | BETA: splitting (9) gives:
% 151.52/22.12  | | 
% 151.52/22.12  | | Case 1:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (10)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.52/22.12  | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.52/22.12  | | |         op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 151.52/22.12  | | |         $i(all_57_12)
% 151.52/22.12  | | | 
% 151.52/22.12  | | | ALPHA: (10) implies:
% 151.52/22.12  | | |   (11)  op(e1, e1) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | REF_CLOSE: (1), (2), (4), (11) are inconsistent by sub-proof #734.
% 151.52/22.12  | | | 
% 151.52/22.12  | | Case 2:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (12)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 151.52/22.12  | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.52/22.12  | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 151.52/22.12  | | |         $i(all_57_12)
% 151.52/22.12  | | | 
% 151.52/22.12  | | | ALPHA: (12) implies:
% 151.52/22.12  | | |   (13)  op(e0, e0) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | REF_CLOSE: (2), (3), (7), (13) are inconsistent by sub-proof #1143.
% 151.52/22.12  | | | 
% 151.52/22.12  | | End of split
% 151.52/22.12  | | 
% 151.52/22.12  | Case 2:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (14)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 151.52/22.12  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 151.52/22.12  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 151.52/22.12  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 151.52/22.12  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 151.52/22.12  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 151.52/22.12  | | 
% 151.52/22.12  | | REF_CLOSE: (2), (3), (5), (7), (8), (14) are inconsistent by sub-proof
% 151.52/22.12  | |            #1045.
% 151.52/22.12  | | 
% 151.52/22.12  | End of split
% 151.52/22.12  | 
% 151.52/22.12  End of proof
% 151.52/22.12  
% 151.52/22.12  Sub-proof #132 shows that the following formulas are inconsistent:
% 151.52/22.12  ----------------------------------------------------------------
% 151.52/22.12    (1)  all_56_6 = e3 & op(e1, e3) = e3
% 151.52/22.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.12    (3)  op(e1, e3) = all_52_2
% 151.52/22.12    (4)   ~ (all_52_2 = e3)
% 151.52/22.12  
% 151.52/22.12  Begin of proof
% 151.52/22.12  | 
% 151.52/22.12  | ALPHA: (1) implies:
% 151.52/22.12  |   (5)  op(e1, e3) = e3
% 151.52/22.12  | 
% 151.52/22.12  | GROUND_INST: instantiating (2) with all_52_2, e3, e3, e1, simplifying with
% 151.52/22.12  |              (3), (5) gives:
% 151.52/22.12  |   (6)  all_52_2 = e3
% 151.52/22.12  | 
% 151.52/22.12  | REDUCE: (4), (6) imply:
% 151.52/22.12  |   (7)  $false
% 151.52/22.12  | 
% 151.52/22.12  | CLOSE: (7) is inconsistent.
% 151.52/22.12  | 
% 151.52/22.12  End of proof
% 151.52/22.12  
% 151.52/22.12  Sub-proof #133 shows that the following formulas are inconsistent:
% 151.52/22.12  ----------------------------------------------------------------
% 151.52/22.12    (1)  all_56_8 = e3
% 151.52/22.12    (2)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 151.52/22.12    (3)   ~ (e3 = e1)
% 151.52/22.12    (4)  all_56_11 = e2
% 151.52/22.12    (5)   ~ (e2 = e0)
% 151.52/22.12    (6)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.52/22.12         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.52/22.12    (7)  all_56_12 = e1
% 151.52/22.12    (8)   ~ (e3 = e0)
% 151.52/22.12    (9)   ~ (e1 = e0)
% 151.52/22.12    (10)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.52/22.12          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.52/22.12    (11)   ~ (e2 = e1)
% 151.52/22.12  
% 151.52/22.12  Begin of proof
% 151.52/22.12  | 
% 151.52/22.12  | BETA: splitting (2) gives:
% 151.52/22.12  | 
% 151.52/22.12  | Case 1:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (12)  all_56_6 = e3 & op(e1, e3) = e3
% 151.52/22.12  | | 
% 151.52/22.12  | | ALPHA: (12) implies:
% 151.52/22.12  | |   (13)  all_56_6 = e3
% 151.52/22.12  | | 
% 151.52/22.12  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (13) are
% 151.52/22.12  | |            inconsistent by sub-proof #608.
% 151.52/22.12  | | 
% 151.52/22.12  | Case 2:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (14)  all_56_12 = e3 & op(e0, e3) = e3
% 151.52/22.12  | | 
% 151.52/22.12  | | REF_CLOSE: (3), (7), (14) are inconsistent by sub-proof #919.
% 151.52/22.12  | | 
% 151.52/22.12  | End of split
% 151.52/22.12  | 
% 151.52/22.12  End of proof
% 151.52/22.12  
% 151.52/22.12  Sub-proof #134 shows that the following formulas are inconsistent:
% 151.52/22.12  ----------------------------------------------------------------
% 151.52/22.12    (1)  op(e3, e3) = e0
% 151.52/22.12    (2)   ~ (e3 = e1)
% 151.52/22.12    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.52/22.12         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.52/22.12    (4)  all_56_11 = e2
% 151.52/22.12    (5)   ~ (e2 = e0)
% 151.52/22.12    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.12    (7)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.52/22.12         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.52/22.12    (8)   ~ (all_52_9 = e3)
% 151.52/22.12    (9)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.52/22.12             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 151.52/22.12               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.52/22.12               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.52/22.12    (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 151.52/22.12          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 151.52/22.12    (11)  op(e0, e0) = e1
% 151.52/22.12    (12)   ~ (e3 = e0)
% 151.52/22.12    (13)  all_56_2 = e1
% 151.52/22.12    (14)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.52/22.12          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.52/22.12    (15)  op(e2, e2) = e2
% 151.52/22.12    (16)  op(e2, e1) = all_52_9
% 151.52/22.12    (17)   ~ (e1 = e0)
% 151.52/22.12    (18)   ~ (e3 = e2)
% 151.52/22.12    (19)   ~ (all_52_8 = e3)
% 151.52/22.12    (20)  op(e3, e1) = all_52_8
% 151.52/22.12    (21)   ~ (e2 = e1)
% 151.52/22.12  
% 151.52/22.12  Begin of proof
% 151.52/22.12  | 
% 151.52/22.12  | BETA: splitting (14) gives:
% 151.52/22.12  | 
% 151.52/22.12  | Case 1:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (22)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 151.52/22.12  | |           e3)
% 151.52/22.12  | | 
% 151.52/22.12  | | BETA: splitting (22) gives:
% 151.52/22.12  | | 
% 151.52/22.12  | | Case 1:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (23)  all_56_2 = e3 & op(e2, e3) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | ALPHA: (23) implies:
% 151.52/22.12  | | |   (24)  all_56_2 = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | COMBINE_EQS: (13), (24) imply:
% 151.52/22.12  | | |   (25)  e3 = e1
% 151.52/22.12  | | | 
% 151.52/22.12  | | | REDUCE: (2), (25) imply:
% 151.52/22.12  | | |   (26)  $false
% 151.52/22.12  | | | 
% 151.52/22.12  | | | CLOSE: (26) is inconsistent.
% 151.52/22.12  | | | 
% 151.52/22.12  | | Case 2:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (27)  all_56_3 = e3 & op(e2, e2) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | ALPHA: (27) implies:
% 151.52/22.12  | | |   (28)  op(e2, e2) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | REF_CLOSE: (6), (15), (18), (28) are inconsistent by sub-proof #1179.
% 151.52/22.12  | | | 
% 151.52/22.12  | | End of split
% 151.52/22.12  | | 
% 151.52/22.12  | Case 2:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (29)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 151.52/22.12  | |           e3)
% 151.52/22.12  | | 
% 151.52/22.12  | | BETA: splitting (29) gives:
% 151.52/22.12  | | 
% 151.52/22.12  | | Case 1:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (30)  all_56_5 = e3 & op(e2, e1) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | REF_CLOSE: (6), (8), (16), (30) are inconsistent by sub-proof #647.
% 151.52/22.12  | | | 
% 151.52/22.12  | | Case 2:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (31)  all_56_10 = e3 & op(e2, e0) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | ALPHA: (31) implies:
% 151.52/22.12  | | |   (32)  all_56_10 = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | BETA: splitting (9) gives:
% 151.52/22.12  | | | 
% 151.52/22.12  | | | Case 1:
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | |   (33)  all_56_15 = e0 & op(e0, e0) = e0
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | ALPHA: (33) implies:
% 151.52/22.12  | | | |   (34)  op(e0, e0) = e0
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | REF_CLOSE: (6), (11), (17), (34) are inconsistent by sub-proof #1040.
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | Case 2:
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | |   (35)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 151.52/22.12  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 151.52/22.12  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 151.52/22.12  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | ALPHA: (35) implies:
% 151.52/22.12  | | | |   (36)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0)
% 151.52/22.12  | | | |           = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | BETA: splitting (36) gives:
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | Case 1:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | |   (37)  all_56_9 = e0 & op(e3, e0) = e0
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | ALPHA: (37) implies:
% 151.52/22.12  | | | | |   (38)  all_56_9 = e0
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (10), (12), (17), (18), (19),
% 151.52/22.12  | | | | |            (20), (21), (38) are inconsistent by sub-proof #687.
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | Case 2:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | |   (39)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 151.52/22.12  | | | | |             e0) = e0)
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | BETA: splitting (39) gives:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | Case 1:
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | |   (40)  all_56_10 = e0 & op(e2, e0) = e0
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | | ALPHA: (40) implies:
% 151.52/22.12  | | | | | |   (41)  all_56_10 = e0
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | | REF_CLOSE: (12), (32), (41) are inconsistent by sub-proof #1134.
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | Case 2:
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | |   (42)  all_56_11 = e0 & op(e1, e0) = e0
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | | REF_CLOSE: (4), (5), (42) are inconsistent by sub-proof #1149.
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | End of split
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | End of split
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | End of split
% 151.52/22.12  | | | 
% 151.52/22.12  | | End of split
% 151.52/22.12  | | 
% 151.52/22.12  | End of split
% 151.52/22.12  | 
% 151.52/22.12  End of proof
% 151.52/22.12  
% 151.52/22.12  Sub-proof #135 shows that the following formulas are inconsistent:
% 151.52/22.12  ----------------------------------------------------------------
% 151.52/22.12    (1)  all_56_8 = e3
% 151.52/22.12    (2)  op(e3, e3) = e0
% 151.52/22.12    (3)   ~ (e3 = e1)
% 151.52/22.12    (4)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.52/22.12         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.52/22.12    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 151.52/22.12         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 151.52/22.12    (6)   ~ (e2 = e0)
% 151.52/22.12    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.12    (8)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.52/22.12         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.52/22.12    (9)   ~ (e3 = e0)
% 151.52/22.12    (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.52/22.12          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.52/22.12    (11)   ~ (e1 = e0)
% 151.52/22.12    (12)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.52/22.12          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.52/22.12    (13)  all_56_2 = e0
% 151.52/22.12    (14)  op(e1, e1) = e3
% 151.52/22.12    (15)   ~ (e3 = e2)
% 151.52/22.12    (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.52/22.12          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.52/22.12    (17)   ~ (e2 = e1)
% 151.52/22.12  
% 151.52/22.12  Begin of proof
% 151.52/22.12  | 
% 151.52/22.12  | BETA: splitting (5) gives:
% 151.52/22.12  | 
% 151.52/22.12  | Case 1:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (18)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 151.52/22.12  | |           e3)
% 151.52/22.12  | | 
% 151.52/22.12  | | BETA: splitting (18) gives:
% 151.52/22.12  | | 
% 151.52/22.12  | | Case 1:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (19)  all_56_0 = e3 & op(e3, e3) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | ALPHA: (19) implies:
% 151.52/22.12  | | |   (20)  op(e3, e3) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | REF_CLOSE: (2), (7), (9), (20) are inconsistent by sub-proof #1141.
% 151.52/22.12  | | | 
% 151.52/22.12  | | Case 2:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (21)  all_56_2 = e3 & op(e2, e3) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | ALPHA: (21) implies:
% 151.52/22.12  | | |   (22)  all_56_2 = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | REF_CLOSE: (9), (13), (22) are inconsistent by sub-proof #1137.
% 151.52/22.12  | | | 
% 151.52/22.12  | | End of split
% 151.52/22.12  | | 
% 151.52/22.12  | Case 2:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (23)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 151.52/22.12  | |           e3)
% 151.52/22.12  | | 
% 151.52/22.12  | | BETA: splitting (23) gives:
% 151.52/22.12  | | 
% 151.52/22.12  | | Case 1:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (24)  all_56_6 = e3 & op(e1, e3) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | ALPHA: (24) implies:
% 151.52/22.12  | | |   (25)  all_56_6 = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (11), (12), (14), (15), (16),
% 151.52/22.12  | | |            (17), (25) are inconsistent by sub-proof #607.
% 151.52/22.12  | | | 
% 151.52/22.12  | | Case 2:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (26)  all_56_12 = e3 & op(e0, e3) = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | ALPHA: (26) implies:
% 151.52/22.12  | | |   (27)  all_56_12 = e3
% 151.52/22.12  | | | 
% 151.52/22.12  | | | BETA: splitting (10) gives:
% 151.52/22.12  | | | 
% 151.52/22.12  | | | Case 1:
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | |   (28)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3)
% 151.52/22.12  | | | |           = e2)
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | BETA: splitting (28) gives:
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | Case 1:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | |   (29)  all_56_0 = e2 & op(e3, e3) = e2
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | ALPHA: (29) implies:
% 151.52/22.12  | | | | |   (30)  op(e3, e3) = e2
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | REF_CLOSE: (2), (6), (7), (30) are inconsistent by sub-proof #1073.
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | Case 2:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | |   (31)  all_56_2 = e2 & op(e2, e3) = e2
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | REF_CLOSE: (6), (13), (31) are inconsistent by sub-proof #994.
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | End of split
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | Case 2:
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | |   (32)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3)
% 151.52/22.12  | | | |           = e2)
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | BETA: splitting (32) gives:
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | Case 1:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | |   (33)  all_56_6 = e2 & op(e1, e3) = e2
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | ALPHA: (33) implies:
% 151.52/22.12  | | | | |   (34)  all_56_6 = e2
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | BETA: splitting (4) gives:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | Case 1:
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | |   (35)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2,
% 151.52/22.12  | | | | | |             e3) = e1)
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | | BETA: splitting (35) gives:
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | | Case 1:
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | |   (36)  all_56_0 = e1 & op(e3, e3) = e1
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | | ALPHA: (36) implies:
% 151.52/22.12  | | | | | | |   (37)  op(e3, e3) = e1
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | | REF_CLOSE: (2), (7), (11), (37) are inconsistent by sub-proof
% 151.52/22.12  | | | | | | |            #957.
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | Case 2:
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | |   (38)  all_56_2 = e1 & op(e2, e3) = e1
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | | ALPHA: (38) implies:
% 151.52/22.12  | | | | | | |   (39)  all_56_2 = e1
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | | REF_CLOSE: (11), (13), (39) are inconsistent by sub-proof #1060.
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | End of split
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | Case 2:
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | |   (40)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0,
% 151.52/22.12  | | | | | |             e3) = e1)
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | | BETA: splitting (40) gives:
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | | Case 1:
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | |   (41)  all_56_6 = e1 & op(e1, e3) = e1
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | | REF_CLOSE: (17), (34), (41) are inconsistent by sub-proof #1058.
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | Case 2:
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | |   (42)  all_56_12 = e1 & op(e0, e3) = e1
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | | ALPHA: (42) implies:
% 151.52/22.12  | | | | | | |   (43)  all_56_12 = e1
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | | REF_CLOSE: (3), (27), (43) are inconsistent by sub-proof #1056.
% 151.52/22.12  | | | | | | | 
% 151.52/22.12  | | | | | | End of split
% 151.52/22.12  | | | | | | 
% 151.52/22.12  | | | | | End of split
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | Case 2:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | |   (44)  all_56_12 = e2 & op(e0, e3) = e2
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | ALPHA: (44) implies:
% 151.52/22.12  | | | | |   (45)  all_56_12 = e2
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | REF_CLOSE: (15), (27), (45) are inconsistent by sub-proof #869.
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | End of split
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | End of split
% 151.52/22.12  | | | 
% 151.52/22.12  | | End of split
% 151.52/22.12  | | 
% 151.52/22.12  | End of split
% 151.52/22.12  | 
% 151.52/22.12  End of proof
% 151.52/22.12  
% 151.52/22.12  Sub-proof #136 shows that the following formulas are inconsistent:
% 151.52/22.12  ----------------------------------------------------------------
% 151.52/22.12    (1)   ~ (e3 = e1)
% 151.52/22.12    (2)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.52/22.12         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.52/22.12    (3)   ~ (e2 = e0)
% 151.52/22.12    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.12    (5)   ~ (e1 = e0)
% 151.52/22.12    (6)  all_56_13 = e3
% 151.52/22.12    (7)   ~ (e3 = e2)
% 151.52/22.12    (8)  all_56_1 = e0
% 151.52/22.12    (9)   ~ (e2 = e1)
% 151.52/22.12    (10)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.52/22.12          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.52/22.12    (11)  op(e2, e2) = e0
% 151.52/22.12  
% 151.52/22.12  Begin of proof
% 151.52/22.12  | 
% 151.52/22.12  | BETA: splitting (2) gives:
% 151.52/22.12  | 
% 151.52/22.12  | Case 1:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (12)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 151.52/22.12  | |           e2)
% 151.52/22.12  | | 
% 151.52/22.12  | | BETA: splitting (12) gives:
% 151.52/22.12  | | 
% 151.52/22.12  | | Case 1:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (13)  all_56_1 = e2 & op(e3, e2) = e2
% 151.52/22.12  | | | 
% 151.52/22.12  | | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #848.
% 151.52/22.12  | | | 
% 151.52/22.12  | | Case 2:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (14)  all_56_3 = e2 & op(e2, e2) = e2
% 151.52/22.12  | | | 
% 151.52/22.12  | | | ALPHA: (14) implies:
% 151.52/22.12  | | |   (15)  op(e2, e2) = e2
% 151.52/22.12  | | | 
% 151.52/22.12  | | | REF_CLOSE: (3), (4), (11), (15) are inconsistent by sub-proof #1145.
% 151.52/22.12  | | | 
% 151.52/22.12  | | End of split
% 151.52/22.12  | | 
% 151.52/22.12  | Case 2:
% 151.52/22.12  | | 
% 151.52/22.12  | |   (16)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 151.52/22.12  | |           e2)
% 151.52/22.12  | | 
% 151.52/22.12  | | BETA: splitting (16) gives:
% 151.52/22.12  | | 
% 151.52/22.12  | | Case 1:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (17)  all_56_7 = e2 & op(e1, e2) = e2
% 151.52/22.12  | | | 
% 151.52/22.12  | | | ALPHA: (17) implies:
% 151.52/22.12  | | |   (18)  all_56_7 = e2
% 151.52/22.12  | | | 
% 151.52/22.12  | | | BETA: splitting (10) gives:
% 151.52/22.12  | | | 
% 151.52/22.12  | | | Case 1:
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | |   (19)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2)
% 151.52/22.12  | | | |           = e1)
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | BETA: splitting (19) gives:
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | Case 1:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | |   (20)  all_56_1 = e1 & op(e3, e2) = e1
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | ALPHA: (20) implies:
% 151.52/22.12  | | | | |   (21)  all_56_1 = e1
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | REF_CLOSE: (5), (8), (21) are inconsistent by sub-proof #1107.
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | Case 2:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | |   (22)  all_56_3 = e1 & op(e2, e2) = e1
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | ALPHA: (22) implies:
% 151.52/22.12  | | | | |   (23)  op(e2, e2) = e1
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | REF_CLOSE: (4), (5), (11), (23) are inconsistent by sub-proof #853.
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | End of split
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | Case 2:
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | |   (24)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2)
% 151.52/22.12  | | | |           = e1)
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | BETA: splitting (24) gives:
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | | Case 1:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | |   (25)  all_56_7 = e1 & op(e1, e2) = e1
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | REF_CLOSE: (9), (18), (25) are inconsistent by sub-proof #612.
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | Case 2:
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | |   (26)  all_56_13 = e1 & op(e0, e2) = e1
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | ALPHA: (26) implies:
% 151.52/22.12  | | | | |   (27)  all_56_13 = e1
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | | REF_CLOSE: (1), (6), (27) are inconsistent by sub-proof #1121.
% 151.52/22.12  | | | | | 
% 151.52/22.12  | | | | End of split
% 151.52/22.12  | | | | 
% 151.52/22.12  | | | End of split
% 151.52/22.12  | | | 
% 151.52/22.12  | | Case 2:
% 151.52/22.12  | | | 
% 151.52/22.12  | | |   (28)  all_56_13 = e2 & op(e0, e2) = e2
% 151.52/22.12  | | | 
% 151.52/22.12  | | | REF_CLOSE: (6), (7), (28) are inconsistent by sub-proof #847.
% 151.52/22.12  | | | 
% 151.52/22.12  | | End of split
% 151.52/22.12  | | 
% 151.52/22.12  | End of split
% 151.52/22.12  | 
% 151.52/22.12  End of proof
% 151.52/22.12  
% 151.52/22.12  Sub-proof #137 shows that the following formulas are inconsistent:
% 151.52/22.12  ----------------------------------------------------------------
% 151.52/22.12    (1)  all_54_9 = e1 | all_54_9 = e0
% 151.52/22.12    (2)  all_54_9 = all_52_6
% 151.52/22.12    (3)   ~ (all_52_6 = e1)
% 151.52/22.12    (4)   ~ (all_52_6 = e0)
% 151.52/22.12  
% 151.52/22.12  Begin of proof
% 151.52/22.12  | 
% 151.52/22.12  | BETA: splitting (1) gives:
% 151.52/22.12  | 
% 151.52/22.12  | Case 1:
% 151.52/22.12  | | 
% 151.52/22.13  | |   (5)  all_54_9 = e1
% 151.52/22.13  | | 
% 151.52/22.13  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #179.
% 151.52/22.13  | | 
% 151.52/22.13  | Case 2:
% 151.52/22.13  | | 
% 151.52/22.13  | |   (6)  all_54_9 = e0
% 151.52/22.13  | | 
% 151.52/22.13  | | COMBINE_EQS: (2), (6) imply:
% 151.52/22.13  | |   (7)  all_52_6 = e0
% 151.52/22.13  | | 
% 151.52/22.13  | | SIMP: (7) implies:
% 151.52/22.13  | |   (8)  all_52_6 = e0
% 151.52/22.13  | | 
% 151.52/22.13  | | REDUCE: (4), (8) imply:
% 151.52/22.13  | |   (9)  $false
% 151.52/22.13  | | 
% 151.52/22.13  | | CLOSE: (9) is inconsistent.
% 151.52/22.13  | | 
% 151.52/22.13  | End of split
% 151.52/22.13  | 
% 151.52/22.13  End of proof
% 151.52/22.13  
% 151.52/22.13  Sub-proof #138 shows that the following formulas are inconsistent:
% 151.52/22.13  ----------------------------------------------------------------
% 151.52/22.13    (1)  all_56_8 = e3
% 151.52/22.13    (2)   ~ (e3 = e1)
% 151.52/22.13    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.52/22.13         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.52/22.13    (4)  op(e2, e2) = e1
% 151.52/22.13    (5)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.52/22.13         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.52/22.13    (6)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.52/22.13         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.52/22.13    (7)   ~ (e2 = e0)
% 151.52/22.13    (8)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.52/22.13         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 151.52/22.13    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.13    (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.52/22.13          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.52/22.13    (11)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.52/22.13          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.52/22.13    (12)  all_56_6 = e1
% 151.52/22.13    (13)   ~ (all_52_9 = e3)
% 151.52/22.13    (14)  op(e1, e3) = e1
% 151.52/22.13    (15)   ~ (e3 = e0)
% 151.52/22.13    (16)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.52/22.13          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.52/22.13    (17)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 151.52/22.13          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 151.52/22.13    (18)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 151.52/22.13          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 151.52/22.13    (19)   ~ (all_52_6 = e3)
% 151.52/22.13    (20)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.52/22.13          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.52/22.13    (21)  op(e1, e2) = all_52_6
% 151.52/22.13    (22)  all_56_3 = e1
% 151.52/22.13    (23)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.52/22.13          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.52/22.13    (24)  op(e2, e1) = all_52_9
% 151.52/22.13    (25)   ~ (e1 = e0)
% 151.52/22.13    (26)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.52/22.13          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.52/22.13    (27)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.52/22.13              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.52/22.13            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.52/22.13                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.52/22.13              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.52/22.13          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.52/22.13              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.52/22.13            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.52/22.13                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.52/22.13              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.52/22.13          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 151.52/22.13              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.52/22.13            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 151.52/22.13                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 151.52/22.13              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.52/22.13          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 151.52/22.13              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.52/22.13            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 151.52/22.13                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 151.52/22.13                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.52/22.13                $i(all_57_14))))
% 151.52/22.13    (28)  op(e1, e1) = e3
% 151.52/22.13    (29)   ~ (e3 = e2)
% 151.52/22.13    (30)   ~ (all_52_8 = e3)
% 151.52/22.13    (31)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.52/22.13          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.52/22.13    (32)  op(e3, e1) = all_52_8
% 151.52/22.13    (33)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 151.52/22.13              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 151.52/22.13            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 151.52/22.13            = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 151.52/22.13            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 151.52/22.13            op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 151.52/22.13            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2)
% 151.52/22.13            = all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0) =
% 151.52/22.13            e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &
% 151.52/22.13             ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 151.52/22.13            op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 151.52/22.13            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 151.52/22.13            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 151.52/22.13            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.52/22.13            $i(all_57_10) & $i(all_57_13))
% 151.52/22.13    (34)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.52/22.13          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.52/22.13    (35)   ~ (e2 = e1)
% 151.52/22.13    (36)  op(e1, e3) = all_52_2
% 151.52/22.13    (37)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.52/22.13          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.52/22.13    (38)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.52/22.13          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 151.52/22.13            e1)
% 151.52/22.13  
% 151.52/22.13  Begin of proof
% 151.52/22.13  | 
% 151.52/22.13  | BETA: splitting (33) gives:
% 151.52/22.13  | 
% 151.52/22.13  | Case 1:
% 151.52/22.13  | | 
% 151.52/22.13  | |   (39)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 151.52/22.13  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 151.52/22.13  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 151.52/22.13  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 151.52/22.13  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 151.52/22.13  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 151.52/22.13  | | 
% 151.52/22.13  | | BETA: splitting (39) gives:
% 151.52/22.13  | | 
% 151.52/22.13  | | Case 1:
% 151.52/22.13  | | | 
% 151.52/22.13  | | |   (40)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.52/22.13  | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.52/22.13  | | |         op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.52/22.13  | | |         $i(all_57_10)
% 151.52/22.13  | | | 
% 151.52/22.13  | | | ALPHA: (40) implies:
% 151.52/22.13  | | |   (41)  op(e3, e1) = e3
% 151.52/22.13  | | | 
% 151.52/22.13  | | | REF_CLOSE: (9), (30), (32), (41) are inconsistent by sub-proof #1164.
% 151.52/22.13  | | | 
% 151.52/22.13  | | Case 2:
% 151.52/22.13  | | | 
% 151.52/22.13  | | |   (42)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.52/22.13  | | |         (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.52/22.13  | | |         op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.52/22.13  | | |         $i(all_57_12)
% 151.52/22.13  | | | 
% 151.52/22.13  | | | ALPHA: (42) implies:
% 151.52/22.13  | | |   (43)  op(e3, e3) = e1
% 151.52/22.13  | | | 
% 151.52/22.13  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 151.52/22.13  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 151.52/22.13  | | |            (23), (24), (25), (26), (27), (28), (29), (31), (34), (35),
% 151.52/22.13  | | |            (36), (37), (38), (43) are inconsistent by sub-proof #139.
% 151.52/22.13  | | | 
% 151.52/22.13  | | End of split
% 151.52/22.13  | | 
% 151.52/22.13  | Case 2:
% 151.52/22.13  | | 
% 151.52/22.13  | |   (44)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 151.52/22.13  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 151.52/22.13  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 151.52/22.13  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.52/22.13  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.52/22.13  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.52/22.13  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 151.52/22.13  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 151.52/22.13  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.52/22.13  | |           $i(all_57_13))
% 151.52/22.13  | | 
% 151.52/22.13  | | BETA: splitting (44) gives:
% 151.52/22.13  | | 
% 151.52/22.13  | | Case 1:
% 151.52/22.13  | | | 
% 151.52/22.13  | | |   (45)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 151.52/22.13  | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.52/22.13  | | |         op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.52/22.13  | | |         $i(all_57_12)
% 151.52/22.13  | | | 
% 151.52/22.13  | | | ALPHA: (45) implies:
% 151.52/22.13  | | |   (46)   ~ (all_57_12 = e1)
% 151.52/22.13  | | |   (47)  op(e2, e2) = all_57_12
% 151.52/22.13  | | | 
% 151.52/22.13  | | | REF_CLOSE: (4), (9), (46), (47) are inconsistent by sub-proof #1014.
% 151.52/22.13  | | | 
% 151.52/22.13  | | Case 2:
% 151.52/22.13  | | | 
% 151.52/22.13  | | |   (48)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.52/22.13  | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.52/22.13  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.52/22.13  | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10
% 151.52/22.13  | | |             = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 151.52/22.13  | | |             e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 151.52/22.13  | | |           $i(all_57_10) & $i(all_57_13))
% 151.52/22.13  | | | 
% 151.52/22.13  | | | BETA: splitting (48) gives:
% 151.52/22.13  | | | 
% 151.52/22.13  | | | Case 1:
% 151.52/22.13  | | | | 
% 151.52/22.13  | | | |   (49)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.52/22.13  | | | |         (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.52/22.13  | | | |         op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.52/22.13  | | | |         $i(all_57_11)
% 151.52/22.13  | | | | 
% 151.52/22.13  | | | | ALPHA: (49) implies:
% 151.52/22.13  | | | |   (50)  op(e2, e2) = e0
% 151.52/22.13  | | | | 
% 151.52/22.13  | | | | REF_CLOSE: (4), (9), (25), (50) are inconsistent by sub-proof #853.
% 151.52/22.13  | | | | 
% 151.52/22.13  | | | Case 2:
% 151.52/22.13  | | | | 
% 151.52/22.13  | | | |   (51)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 151.52/22.13  | | | |         (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.52/22.13  | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.52/22.13  | | | |         $i(all_57_13)
% 151.52/22.13  | | | | 
% 151.52/22.13  | | | | ALPHA: (51) implies:
% 151.52/22.13  | | | |   (52)  op(e1, e1) = e0
% 151.52/22.13  | | | | 
% 151.52/22.13  | | | | REF_CLOSE: (9), (15), (28), (52) are inconsistent by sub-proof #896.
% 151.52/22.13  | | | | 
% 151.52/22.13  | | | End of split
% 151.52/22.13  | | | 
% 151.52/22.13  | | End of split
% 151.52/22.13  | | 
% 151.52/22.13  | End of split
% 151.52/22.13  | 
% 151.52/22.13  End of proof
% 151.52/22.13  
% 151.52/22.13  Sub-proof #139 shows that the following formulas are inconsistent:
% 151.52/22.13  ----------------------------------------------------------------
% 151.52/22.13    (1)  all_56_8 = e3
% 151.52/22.13    (2)   ~ (e3 = e1)
% 151.52/22.13    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.52/22.13         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.52/22.13    (4)  op(e2, e2) = e1
% 151.52/22.13    (5)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.52/22.13         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.52/22.13    (6)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.52/22.13         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.52/22.13    (7)   ~ (e2 = e0)
% 151.52/22.13    (8)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.52/22.13         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 151.52/22.13    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.13    (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.52/22.13          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.52/22.13    (11)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.52/22.13          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.52/22.13    (12)  all_56_6 = e1
% 151.52/22.13    (13)   ~ (all_52_9 = e3)
% 151.52/22.13    (14)  op(e1, e3) = e1
% 151.52/22.13    (15)   ~ (e3 = e0)
% 151.52/22.13    (16)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.52/22.13          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.52/22.13    (17)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 151.52/22.13          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 151.52/22.13    (18)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 151.52/22.13          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 151.52/22.13    (19)   ~ (all_52_6 = e3)
% 151.52/22.13    (20)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.52/22.13          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.52/22.13    (21)  op(e3, e3) = e1
% 151.52/22.13    (22)  op(e1, e2) = all_52_6
% 151.52/22.13    (23)  all_56_3 = e1
% 151.52/22.13    (24)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.52/22.13          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.52/22.13    (25)  op(e2, e1) = all_52_9
% 151.52/22.13    (26)   ~ (e1 = e0)
% 151.52/22.13    (27)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.52/22.13          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.52/22.13    (28)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.52/22.13              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.52/22.13            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.52/22.13                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.52/22.13              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.52/22.13          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.52/22.13              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.52/22.13            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.52/22.13                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.52/22.13              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.52/22.13          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 151.52/22.13              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.52/22.13            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 151.52/22.13                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 151.52/22.13              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.52/22.13          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 151.52/22.13              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.52/22.13            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 151.52/22.13                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 151.52/22.13                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.52/22.13                $i(all_57_14))))
% 151.52/22.13    (29)  op(e1, e1) = e3
% 151.52/22.13    (30)   ~ (e3 = e2)
% 151.52/22.13    (31)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.52/22.13          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.52/22.13    (32)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.52/22.13          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.52/22.13    (33)   ~ (e2 = e1)
% 151.52/22.13    (34)  op(e1, e3) = all_52_2
% 151.52/22.13    (35)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.52/22.13          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.52/22.13    (36)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.52/22.13          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 151.52/22.13            e1)
% 151.52/22.13  
% 151.52/22.13  Begin of proof
% 151.52/22.13  | 
% 151.52/22.13  | BETA: splitting (28) gives:
% 151.52/22.13  | 
% 151.52/22.13  | Case 1:
% 151.52/22.13  | | 
% 151.52/22.13  | |   (37)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 151.52/22.13  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 151.52/22.13  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 151.52/22.13  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.52/22.13  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 151.52/22.13  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 151.52/22.13  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 151.52/22.13  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.52/22.13  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 151.52/22.13  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 151.52/22.13  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 151.52/22.13  | |               $i(all_57_15))))
% 151.52/22.13  | | 
% 151.52/22.13  | | REF_CLOSE: (2), (4), (9), (21), (33), (37) are inconsistent by sub-proof
% 151.52/22.13  | |            #898.
% 151.52/22.13  | | 
% 151.52/22.13  | Case 2:
% 151.52/22.13  | | 
% 151.52/22.13  | |   (38)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.52/22.13  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.52/22.13  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.52/22.13  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.52/22.13  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.52/22.13  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 151.52/22.13  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 151.52/22.13  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.52/22.13  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 151.52/22.13  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 151.52/22.13  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 151.52/22.13  | |               all_57_14 & $i(all_57_14))))
% 151.52/22.13  | | 
% 151.52/22.13  | | BETA: splitting (38) gives:
% 151.52/22.13  | | 
% 151.52/22.13  | | Case 1:
% 151.52/22.13  | | | 
% 151.52/22.13  | | |   (39)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.52/22.13  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.52/22.13  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.52/22.13  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.52/22.13  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 151.52/22.13  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.52/22.13  | | | 
% 151.52/22.13  | | | ALPHA: (39) implies:
% 151.52/22.13  | | |   (40)  op(e1, e1) = e1
% 151.52/22.13  | | | 
% 151.52/22.13  | | | REF_CLOSE: (2), (9), (29), (40) are inconsistent by sub-proof #734.
% 151.52/22.13  | | | 
% 151.52/22.13  | | Case 2:
% 151.52/22.13  | | | 
% 151.52/22.13  | | |   (41)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 151.52/22.13  | | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 151.52/22.13  | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 151.52/22.13  | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.52/22.13  | | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 151.52/22.13  | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 151.52/22.13  | | | 
% 151.52/22.13  | | | ALPHA: (41) implies:
% 151.52/22.13  | | |   (42)  op(e0, e0) = e0
% 151.52/22.13  | | | 
% 151.52/22.13  | | | BETA: splitting (17) gives:
% 151.52/22.13  | | | 
% 151.52/22.13  | | | Case 1:
% 151.52/22.13  | | | | 
% 151.52/22.13  | | | |   (43)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0)
% 151.52/22.13  | | | |           = e1)
% 151.52/22.13  | | | | 
% 151.52/22.13  | | | | BETA: splitting (43) gives:
% 151.52/22.13  | | | | 
% 151.52/22.13  | | | | Case 1:
% 151.52/22.13  | | | | | 
% 151.52/22.13  | | | | |   (44)  all_56_9 = e1 & op(e3, e0) = e1
% 151.52/22.13  | | | | | 
% 151.52/22.13  | | | | | ALPHA: (44) implies:
% 151.52/22.13  | | | | |   (45)  all_56_9 = e1
% 151.52/22.13  | | | | | 
% 151.52/22.13  | | | | | BETA: splitting (36) gives:
% 151.52/22.13  | | | | | 
% 151.52/22.13  | | | | | Case 1:
% 151.52/22.13  | | | | | | 
% 151.52/22.13  | | | | | |   (46)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 &
% 151.52/22.13  | | | | | |           op(e0, e2) = e1)
% 151.52/22.13  | | | | | | 
% 151.52/22.13  | | | | | | BETA: splitting (46) gives:
% 151.52/22.13  | | | | | | 
% 151.52/22.13  | | | | | | Case 1:
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | |   (47)  all_56_12 = e1 & op(e0, e3) = e1
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | | ALPHA: (47) implies:
% 151.52/22.13  | | | | | | |   (48)  all_56_12 = e1
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | | BETA: splitting (20) gives:
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | | Case 1:
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | |   (49)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 &
% 151.52/22.13  | | | | | | | |           op(e2, e3) = e2)
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | | BETA: splitting (49) gives:
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | | Case 1:
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | |   (50)  all_56_0 = e2 & op(e3, e3) = e2
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | ALPHA: (50) implies:
% 151.52/22.13  | | | | | | | | |   (51)  op(e3, e3) = e2
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | REF_CLOSE: (9), (21), (33), (51) are inconsistent by sub-proof
% 151.52/22.13  | | | | | | | | |            #1074.
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | Case 2:
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | |   (52)  all_56_2 = e2 & op(e2, e3) = e2
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | ALPHA: (52) implies:
% 151.52/22.13  | | | | | | | | |   (53)  all_56_2 = e2
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | BETA: splitting (16) gives:
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | Case 1:
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | |   (54)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 &
% 151.52/22.13  | | | | | | | | | |           op(e2, e3) = e0)
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | REF_CLOSE: (7), (9), (21), (26), (53), (54) are inconsistent
% 151.52/22.13  | | | | | | | | | |            by sub-proof #574.
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | Case 2:
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | |   (55)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0
% 151.52/22.13  | | | | | | | | | |           & op(e0, e3) = e0)
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | REF_CLOSE: (9), (14), (26), (34), (48), (55) are inconsistent
% 151.52/22.13  | | | | | | | | | |            by sub-proof #838.
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | End of split
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | End of split
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | Case 2:
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | |   (56)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 &
% 151.52/22.13  | | | | | | | |           op(e0, e3) = e2)
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | | BETA: splitting (56) gives:
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | | Case 1:
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | |   (57)  all_56_6 = e2 & op(e1, e3) = e2
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | REF_CLOSE: (12), (33), (57) are inconsistent by sub-proof
% 151.52/22.13  | | | | | | | | |            #837.
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | Case 2:
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | |   (58)  all_56_12 = e2 & op(e0, e3) = e2
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | REF_CLOSE: (33), (48), (58) are inconsistent by sub-proof
% 151.52/22.13  | | | | | | | | |            #929.
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | End of split
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | End of split
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | Case 2:
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | |   (59)  all_56_13 = e1 & op(e0, e2) = e1
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | | REF_CLOSE: (2), (3), (7), (9), (15), (18), (19), (21), (22), (23),
% 151.52/22.13  | | | | | | |            (26), (30), (33), (35), (45), (59) are inconsistent by
% 151.52/22.13  | | | | | | |            sub-proof #252.
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | End of split
% 151.52/22.13  | | | | | | 
% 151.52/22.13  | | | | | Case 2:
% 151.52/22.13  | | | | | | 
% 151.52/22.13  | | | | | |   (60)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 &
% 151.52/22.13  | | | | | |           op(e0, e0) = e1)
% 151.52/22.13  | | | | | | 
% 151.52/22.13  | | | | | | BETA: splitting (60) gives:
% 151.52/22.13  | | | | | | 
% 151.52/22.13  | | | | | | Case 1:
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | |   (61)  all_56_14 = e1 & op(e0, e1) = e1
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (10), (11), (15), (18),
% 151.52/22.13  | | | | | | |            (21), (26), (29), (30), (31), (33), (45), (61) are
% 151.52/22.13  | | | | | | |            inconsistent by sub-proof #250.
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | Case 2:
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | |   (62)  all_56_15 = e1 & op(e0, e0) = e1
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | | ALPHA: (62) implies:
% 151.52/22.13  | | | | | | |   (63)  op(e0, e0) = e1
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | | REF_CLOSE: (9), (26), (42), (63) are inconsistent by sub-proof
% 151.52/22.13  | | | | | | |            #1040.
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | End of split
% 151.52/22.13  | | | | | | 
% 151.52/22.13  | | | | | End of split
% 151.52/22.13  | | | | | 
% 151.52/22.13  | | | | Case 2:
% 151.52/22.13  | | | | | 
% 151.52/22.13  | | | | |   (64)  all_56_10 = e1 & op(e2, e0) = e1
% 151.52/22.13  | | | | | 
% 151.52/22.13  | | | | | ALPHA: (64) implies:
% 151.52/22.13  | | | | |   (65)  all_56_10 = e1
% 151.52/22.13  | | | | | 
% 151.52/22.13  | | | | | BETA: splitting (24) gives:
% 151.52/22.13  | | | | | 
% 151.52/22.13  | | | | | Case 1:
% 151.52/22.13  | | | | | | 
% 151.52/22.13  | | | | | |   (66)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2,
% 151.52/22.13  | | | | | |             e2) = e3)
% 151.52/22.13  | | | | | | 
% 151.52/22.13  | | | | | | BETA: splitting (66) gives:
% 151.52/22.13  | | | | | | 
% 151.52/22.13  | | | | | | Case 1:
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | |   (67)  all_56_2 = e3 & op(e2, e3) = e3
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | | ALPHA: (67) implies:
% 151.52/22.13  | | | | | | |   (68)  all_56_2 = e3
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | | BETA: splitting (8) gives:
% 151.52/22.13  | | | | | | | 
% 151.52/22.13  | | | | | | | Case 1:
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | |   (69)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 &
% 151.52/22.13  | | | | | | | |           op(e2, e2) = e2)
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | | REF_CLOSE: (4), (9), (30), (33), (68), (69) are inconsistent by
% 151.52/22.13  | | | | | | | |            sub-proof #267.
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | Case 2:
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | |   (70)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 &
% 151.52/22.13  | | | | | | | |           op(e2, e0) = e2)
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | | BETA: splitting (70) gives:
% 151.52/22.13  | | | | | | | | 
% 151.52/22.13  | | | | | | | | Case 1:
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | |   (71)  all_56_5 = e2 & op(e2, e1) = e2
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | ALPHA: (71) implies:
% 151.52/22.13  | | | | | | | | |   (72)  all_56_5 = e2
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | BETA: splitting (20) gives:
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | Case 1:
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | |   (73)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 &
% 151.52/22.13  | | | | | | | | | |           op(e2, e3) = e2)
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | BETA: splitting (73) gives:
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | Case 1:
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | |   (74)  all_56_0 = e2 & op(e3, e3) = e2
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | | ALPHA: (74) implies:
% 151.52/22.13  | | | | | | | | | | |   (75)  op(e3, e3) = e2
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | | REF_CLOSE: (9), (21), (33), (75) are inconsistent by
% 151.52/22.13  | | | | | | | | | | |            sub-proof #1074.
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | Case 2:
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | |   (76)  all_56_2 = e2 & op(e2, e3) = e2
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | | ALPHA: (76) implies:
% 151.52/22.13  | | | | | | | | | | |   (77)  all_56_2 = e2
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | | REF_CLOSE: (30), (68), (77) are inconsistent by sub-proof
% 151.52/22.13  | | | | | | | | | | |            #685.
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | End of split
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | Case 2:
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | |   (78)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2
% 151.52/22.13  | | | | | | | | | |           & op(e0, e3) = e2)
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | BETA: splitting (78) gives:
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | Case 1:
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | |   (79)  all_56_6 = e2 & op(e1, e3) = e2
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | | ALPHA: (79) implies:
% 151.52/22.13  | | | | | | | | | | |   (80)  all_56_6 = e2
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | | COMBINE_EQS: (12), (80) imply:
% 151.52/22.13  | | | | | | | | | | |   (81)  e2 = e1
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | | COMBINE_EQS: (72), (81) imply:
% 151.52/22.13  | | | | | | | | | | |   (82)  all_56_5 = e1
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (15), (24), (26), (30),
% 151.52/22.13  | | | | | | | | | | |            (33), (65), (68), (82) are inconsistent by
% 151.52/22.13  | | | | | | | | | | |            sub-proof #678.
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | Case 2:
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | |   (83)  all_56_12 = e2 & op(e0, e3) = e2
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | | ALPHA: (83) implies:
% 151.52/22.13  | | | | | | | | | | |   (84)  all_56_12 = e2
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | | REF_CLOSE: (7), (9), (14), (15), (16), (21), (26), (34),
% 151.52/22.13  | | | | | | | | | | |            (68), (84) are inconsistent by sub-proof #551.
% 151.52/22.13  | | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | | End of split
% 151.52/22.13  | | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | End of split
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | Case 2:
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | |   (85)  all_56_10 = e2 & op(e2, e0) = e2
% 151.52/22.13  | | | | | | | | | 
% 151.52/22.13  | | | | | | | | | REF_CLOSE: (33), (65), (85) are inconsistent by sub-proof
% 151.52/22.14  | | | | | | | | |            #266.
% 151.52/22.14  | | | | | | | | | 
% 151.52/22.14  | | | | | | | | End of split
% 151.52/22.14  | | | | | | | | 
% 151.52/22.14  | | | | | | | End of split
% 151.52/22.14  | | | | | | | 
% 151.52/22.14  | | | | | | Case 2:
% 151.52/22.14  | | | | | | | 
% 151.52/22.14  | | | | | | |   (86)  all_56_3 = e3 & op(e2, e2) = e3
% 151.52/22.14  | | | | | | | 
% 151.52/22.14  | | | | | | | REF_CLOSE: (2), (23), (86) are inconsistent by sub-proof #274.
% 151.52/22.14  | | | | | | | 
% 151.52/22.14  | | | | | | End of split
% 151.52/22.14  | | | | | | 
% 151.52/22.14  | | | | | Case 2:
% 151.52/22.14  | | | | | | 
% 151.52/22.14  | | | | | |   (87)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2,
% 151.52/22.14  | | | | | |             e0) = e3)
% 151.52/22.14  | | | | | | 
% 151.52/22.14  | | | | | | REF_CLOSE: (2), (9), (13), (25), (65), (87) are inconsistent by
% 151.52/22.14  | | | | | |            sub-proof #265.
% 151.52/22.14  | | | | | | 
% 151.52/22.14  | | | | | End of split
% 151.52/22.14  | | | | | 
% 151.52/22.14  | | | | End of split
% 151.52/22.14  | | | | 
% 151.52/22.14  | | | Case 2:
% 151.52/22.14  | | | | 
% 151.52/22.14  | | | |   (88)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0,
% 151.52/22.14  | | | |             e0) = e1)
% 151.52/22.14  | | | | 
% 151.52/22.14  | | | | BETA: splitting (88) gives:
% 151.52/22.14  | | | | 
% 151.52/22.14  | | | | Case 1:
% 151.52/22.14  | | | | | 
% 151.52/22.14  | | | | |   (89)  all_56_11 = e1 & op(e1, e0) = e1
% 151.52/22.14  | | | | | 
% 151.52/22.14  | | | | | ALPHA: (89) implies:
% 151.52/22.14  | | | | |   (90)  all_56_11 = e1
% 151.52/22.14  | | | | |   (91)  op(e1, e0) = e1
% 151.52/22.14  | | | | | 
% 151.52/22.14  | | | | | REF_CLOSE: (7), (9), (12), (14), (15), (26), (27), (29), (30), (32),
% 151.52/22.14  | | | | |            (33), (34), (90), (91) are inconsistent by sub-proof #232.
% 151.52/22.14  | | | | | 
% 151.52/22.14  | | | | Case 2:
% 151.52/22.14  | | | | | 
% 151.52/22.14  | | | | |   (92)  all_56_15 = e1 & op(e0, e0) = e1
% 151.52/22.14  | | | | | 
% 151.52/22.14  | | | | | ALPHA: (92) implies:
% 151.52/22.14  | | | | |   (93)  op(e0, e0) = e1
% 151.52/22.14  | | | | | 
% 151.52/22.14  | | | | | REF_CLOSE: (9), (26), (42), (93) are inconsistent by sub-proof #1040.
% 151.52/22.14  | | | | | 
% 151.52/22.14  | | | | End of split
% 151.52/22.14  | | | | 
% 151.52/22.14  | | | End of split
% 151.52/22.14  | | | 
% 151.52/22.14  | | End of split
% 151.52/22.14  | | 
% 151.52/22.14  | End of split
% 151.52/22.14  | 
% 151.52/22.14  End of proof
% 151.52/22.14  
% 151.52/22.14  Sub-proof #140 shows that the following formulas are inconsistent:
% 151.52/22.14  ----------------------------------------------------------------
% 151.52/22.14    (1)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.52/22.14             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.52/22.14           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.52/22.14           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.52/22.14           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.52/22.14           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.52/22.14           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 151.52/22.14           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 151.52/22.14           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 151.52/22.14           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 151.52/22.14           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 151.52/22.14           $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &
% 151.52/22.14            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 151.52/22.14             e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 151.52/22.14         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 151.52/22.14             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 151.52/22.14           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4
% 151.52/22.14           = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 151.52/22.14           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1)
% 151.52/22.14           = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 151.52/22.14           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2)
% 151.52/22.14           = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2
% 151.52/22.14           & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 151.52/22.14           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 151.52/22.14             e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.52/22.14           $i(all_57_10))
% 151.52/22.14    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.52/22.14           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.52/22.14    (3)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 151.52/22.14           all_57_14 & $i(all_57_14))
% 151.52/22.14    (4)  op(e0, e0) = e1
% 151.52/22.14    (5)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 151.52/22.14           all_57_12 & $i(all_57_12))
% 151.52/22.14    (6)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 151.52/22.14           all_57_15 & $i(all_57_15))
% 151.52/22.14    (7)  op(e1, e1) = e3
% 151.52/22.14    (8)   ~ (e3 = e2)
% 151.52/22.14    (9)   ~ (all_52_8 = e3)
% 151.52/22.14    (10)  op(e3, e1) = all_52_8
% 151.52/22.14    (11)  op(e3, e3) = e3
% 151.52/22.14    (12)   ~ (e2 = e1)
% 151.52/22.14  
% 151.52/22.14  Begin of proof
% 151.52/22.14  | 
% 151.52/22.14  | BETA: splitting (1) gives:
% 151.52/22.14  | 
% 151.52/22.14  | Case 1:
% 151.52/22.14  | | 
% 151.52/22.14  | |   (13)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 151.52/22.14  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.52/22.14  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 151.52/22.14  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 151.52/22.14  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 151.52/22.14  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 151.52/22.14  | |         (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 151.52/22.14  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 151.52/22.14  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 151.52/22.14  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 151.52/22.14  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 151.52/22.14  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 151.52/22.14  | | 
% 151.52/22.14  | | BETA: splitting (13) gives:
% 151.52/22.14  | | 
% 151.52/22.14  | | Case 1:
% 151.52/22.14  | | | 
% 151.52/22.14  | | |   (14)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.52/22.14  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 151.52/22.14  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 151.52/22.14  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 151.52/22.14  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 151.52/22.14  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.52/22.14  | | |           $i(all_57_2) & $i(all_57_12))
% 151.52/22.14  | | | 
% 151.52/22.14  | | | REF_CLOSE: (2), (3), (6), (14) are inconsistent by sub-proof #814.
% 151.52/22.14  | | | 
% 151.52/22.14  | | Case 2:
% 151.52/22.14  | | | 
% 151.52/22.14  | | |   (15)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.52/22.14  | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 151.52/22.14  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 151.52/22.14  | | |           $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2
% 151.52/22.14  | | |             = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 151.52/22.14  | | |           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.52/22.14  | | |           $i(all_57_2) & $i(all_57_14))
% 151.52/22.14  | | | 
% 151.52/22.14  | | | REF_CLOSE: (2), (5), (6), (15) are inconsistent by sub-proof #831.
% 151.52/22.14  | | | 
% 151.52/22.14  | | End of split
% 151.52/22.14  | | 
% 151.52/22.14  | Case 2:
% 151.52/22.14  | | 
% 151.52/22.14  | |   (16)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 151.52/22.14  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 151.52/22.14  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 151.52/22.14  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 151.52/22.14  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 151.52/22.14  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 151.52/22.14  | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 151.52/22.14  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 151.52/22.14  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 151.52/22.14  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 151.52/22.14  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 151.52/22.14  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 151.52/22.14  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 151.52/22.14  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 151.52/22.14  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.52/22.14  | | 
% 151.52/22.14  | | BETA: splitting (16) gives:
% 151.52/22.14  | | 
% 151.52/22.14  | | Case 1:
% 151.52/22.14  | | | 
% 151.52/22.14  | | |   (17)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.52/22.14  | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 151.52/22.14  | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 151.52/22.14  | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5
% 151.52/22.14  | | |             = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 151.52/22.14  | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.52/22.14  | | |           $i(all_57_5) & $i(all_57_10))
% 151.52/22.14  | | | 
% 151.52/22.14  | | | REF_CLOSE: (2), (4), (7), (8), (12), (17) are inconsistent by sub-proof
% 151.52/22.14  | | |            #435.
% 151.52/22.14  | | | 
% 151.52/22.14  | | Case 2:
% 151.52/22.14  | | | 
% 151.52/22.14  | | |   (18)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.52/22.14  | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 151.52/22.14  | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 151.52/22.14  | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5
% 151.52/22.14  | | |             = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 151.52/22.14  | | |           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.52/22.14  | | |           $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1
% 151.52/22.14  | | |           &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 151.52/22.14  | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 151.52/22.14  | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 151.52/22.14  | | | 
% 151.52/22.14  | | | BETA: splitting (18) gives:
% 151.52/22.14  | | | 
% 151.52/22.14  | | | Case 1:
% 151.52/22.14  | | | | 
% 151.52/22.14  | | | |   (19)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.52/22.14  | | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 151.52/22.14  | | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 151.52/22.14  | | | |         $i(all_57_14)
% 151.52/22.14  | | | | 
% 151.52/22.14  | | | | ALPHA: (19) implies:
% 151.52/22.14  | | | |   (20)  op(e3, e3) = e2
% 151.52/22.14  | | | | 
% 151.52/22.14  | | | | REF_CLOSE: (2), (8), (11), (20) are inconsistent by sub-proof #1085.
% 151.52/22.14  | | | | 
% 151.52/22.14  | | | Case 2:
% 151.52/22.14  | | | | 
% 151.67/22.14  | | | |   (21)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 151.67/22.14  | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.67/22.14  | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.67/22.14  | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 151.67/22.14  | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 151.67/22.14  | | | |           & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.67/22.14  | | | |           $i(all_57_7) & $i(all_57_10))
% 151.67/22.14  | | | | 
% 151.67/22.14  | | | | BETA: splitting (21) gives:
% 151.67/22.14  | | | | 
% 151.67/22.14  | | | | Case 1:
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | |   (22)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 151.67/22.14  | | | | |         (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.67/22.14  | | | | |         op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.67/22.14  | | | | |         $i(all_57_14)
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | ALPHA: (22) implies:
% 151.67/22.14  | | | | |   (23)  op(e0, e0) = e2
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | REF_CLOSE: (2), (4), (12), (23) are inconsistent by sub-proof #978.
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | Case 2:
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | |   (24)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.67/22.14  | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.67/22.14  | | | | |         op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.67/22.14  | | | | |         $i(all_57_10)
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | ALPHA: (24) implies:
% 151.67/22.14  | | | | |   (25)  op(e3, e1) = e3
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | REF_CLOSE: (2), (9), (10), (25) are inconsistent by sub-proof #1164.
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | End of split
% 151.67/22.14  | | | | 
% 151.67/22.14  | | | End of split
% 151.67/22.14  | | | 
% 151.67/22.14  | | End of split
% 151.67/22.14  | | 
% 151.67/22.14  | End of split
% 151.67/22.14  | 
% 151.67/22.14  End of proof
% 151.67/22.14  
% 151.67/22.14  Sub-proof #141 shows that the following formulas are inconsistent:
% 151.67/22.14  ----------------------------------------------------------------
% 151.67/22.14    (1)  all_56_8 = e3
% 151.67/22.14    (2)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 151.67/22.14         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 151.67/22.14    (3)  all_56_15 = e1
% 151.67/22.14    (4)   ~ (e3 = e1)
% 151.67/22.14    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 151.67/22.14         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 151.67/22.14    (6)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.14         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.67/22.14    (7)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.14         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.14    (8)   ~ (e2 = e0)
% 151.67/22.14    (9)  all_56_14 = e1
% 151.67/22.14    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.14    (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.67/22.14          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.67/22.14    (12)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.67/22.14          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.67/22.14    (13)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.67/22.14          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.67/22.14    (14)   ~ (all_52_9 = e3)
% 151.67/22.14    (15)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.14              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 151.67/22.14                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.67/22.14                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.67/22.14    (16)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.14          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 151.67/22.14            e3)
% 151.67/22.14    (17)  op(e0, e0) = e1
% 151.67/22.14    (18)   ~ (e3 = e0)
% 151.67/22.14    (19)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.14          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.14    (20)  op(e3, e3) = e1
% 151.67/22.14    (21)  op(e1, e2) = all_52_6
% 151.67/22.14    (22)   ~ (all_52_9 = e2)
% 151.67/22.14    (23)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.14          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.14    (24)  op(e2, e2) = e2
% 151.67/22.14    (25)  op(e2, e1) = all_52_9
% 151.67/22.14    (26)   ~ (e1 = e0)
% 151.67/22.14    (27)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.67/22.14          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.67/22.14    (28)  op(e1, e1) = e3
% 151.67/22.14    (29)   ~ (e3 = e2)
% 151.67/22.14    (30)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.67/22.14          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 151.67/22.14            e2)
% 151.67/22.14    (31)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.14          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.67/22.14    (32)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.14          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.14    (33)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.67/22.14          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.67/22.14    (34)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 151.67/22.14          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.67/22.14    (35)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.67/22.14          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.67/22.14    (36)   ~ (e2 = e1)
% 151.67/22.14    (37)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.14          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.14    (38)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.14          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.14    (39)   ~ (all_52_6 = e2)
% 151.67/22.14  
% 151.67/22.14  Begin of proof
% 151.67/22.14  | 
% 151.67/22.14  | BETA: splitting (13) gives:
% 151.67/22.14  | 
% 151.67/22.14  | Case 1:
% 151.67/22.14  | | 
% 151.67/22.14  | |   (40)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) =
% 151.67/22.14  | |           e2)
% 151.67/22.14  | | 
% 151.67/22.14  | | BETA: splitting (40) gives:
% 151.67/22.14  | | 
% 151.67/22.14  | | Case 1:
% 151.67/22.14  | | | 
% 151.67/22.14  | | |   (41)  all_56_4 = e2 & op(e3, e1) = e2
% 151.67/22.14  | | | 
% 151.67/22.14  | | | ALPHA: (41) implies:
% 151.67/22.14  | | |   (42)  all_56_4 = e2
% 151.67/22.14  | | | 
% 151.67/22.14  | | | BETA: splitting (31) gives:
% 151.67/22.14  | | | 
% 151.67/22.14  | | | Case 1:
% 151.67/22.14  | | | | 
% 151.67/22.14  | | | |   (43)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2)
% 151.67/22.14  | | | |           = e1)
% 151.67/22.14  | | | | 
% 151.67/22.14  | | | | BETA: splitting (43) gives:
% 151.67/22.14  | | | | 
% 151.67/22.14  | | | | Case 1:
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | |   (44)  all_56_2 = e1 & op(e2, e3) = e1
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | ALPHA: (44) implies:
% 151.67/22.14  | | | | |   (45)  all_56_2 = e1
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 151.67/22.14  | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 151.67/22.14  | | | | |            (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 151.67/22.14  | | | | |            (35), (36), (37), (38), (39), (42), (45) are inconsistent
% 151.67/22.14  | | | | |            by sub-proof #152.
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | Case 2:
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | |   (46)  all_56_3 = e1 & op(e2, e2) = e1
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | ALPHA: (46) implies:
% 151.67/22.14  | | | | |   (47)  op(e2, e2) = e1
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | REF_CLOSE: (10), (24), (36), (47) are inconsistent by sub-proof #1158.
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | End of split
% 151.67/22.14  | | | | 
% 151.67/22.14  | | | Case 2:
% 151.67/22.14  | | | | 
% 151.67/22.14  | | | |   (48)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0)
% 151.67/22.14  | | | |           = e1)
% 151.67/22.14  | | | | 
% 151.67/22.14  | | | | BETA: splitting (48) gives:
% 151.67/22.14  | | | | 
% 151.67/22.14  | | | | Case 1:
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | |   (49)  all_56_5 = e1 & op(e2, e1) = e1
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | ALPHA: (49) implies:
% 151.67/22.14  | | | | |   (50)  all_56_5 = e1
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | REF_CLOSE: (7), (8), (9), (10), (18), (26), (28), (42), (50) are
% 151.67/22.14  | | | | |            inconsistent by sub-proof #249.
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | Case 2:
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | |   (51)  all_56_10 = e1 & op(e2, e0) = e1
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | ALPHA: (51) implies:
% 151.67/22.14  | | | | |   (52)  all_56_10 = e1
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | | REF_CLOSE: (2), (4), (8), (10), (15), (17), (18), (26), (29), (34),
% 151.67/22.14  | | | | |            (36), (52) are inconsistent by sub-proof #445.
% 151.67/22.14  | | | | | 
% 151.67/22.14  | | | | End of split
% 151.67/22.14  | | | | 
% 151.67/22.14  | | | End of split
% 151.67/22.14  | | | 
% 151.67/22.14  | | Case 2:
% 151.67/22.14  | | | 
% 151.67/22.14  | | |   (53)  all_56_5 = e2 & op(e2, e1) = e2
% 151.67/22.14  | | | 
% 151.67/22.14  | | | ALPHA: (53) implies:
% 151.67/22.14  | | |   (54)  op(e2, e1) = e2
% 151.67/22.14  | | | 
% 151.67/22.14  | | | REF_CLOSE: (10), (22), (25), (54) are inconsistent by sub-proof #1157.
% 151.67/22.14  | | | 
% 151.67/22.14  | | End of split
% 151.67/22.14  | | 
% 151.67/22.14  | Case 2:
% 151.67/22.14  | | 
% 151.67/22.14  | |   (55)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) =
% 151.67/22.14  | |           e2)
% 151.67/22.14  | | 
% 151.67/22.14  | | REF_CLOSE: (9), (10), (28), (29), (36), (55) are inconsistent by sub-proof
% 151.67/22.14  | |            #255.
% 151.67/22.14  | | 
% 151.67/22.14  | End of split
% 151.67/22.14  | 
% 151.67/22.14  End of proof
% 151.67/22.14  
% 151.67/22.14  Sub-proof #142 shows that the following formulas are inconsistent:
% 151.67/22.14  ----------------------------------------------------------------
% 151.67/22.14    (1)  op(e2, e1) = e1
% 151.67/22.14    (2)  op(e0, e1) = all_52_11
% 151.67/22.14    (3)  all_56_8 = e3
% 151.67/22.14    (4)   ~ (all_52_7 = all_52_11)
% 151.67/22.14    (5)   ~ (e3 = e1)
% 151.67/22.14    (6)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.67/22.14         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.67/22.14    (7)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.67/22.14         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.67/22.14    (8)  op(e0, e0) = all_10_2
% 151.67/22.14    (9)  op(e3, e2) = all_52_4
% 151.67/22.14    (10)   ~ (all_52_4 = all_52_7)
% 151.67/22.14    (11)  all_56_7 = e1
% 151.67/22.14    (12)  op(e0, e2) = all_52_7
% 151.67/22.14    (13)   ~ (all_52_3 = all_52_7)
% 151.67/22.14    (14)  all_54_14 = all_52_11
% 151.67/22.14    (15)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.14          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.67/22.14    (16)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.14          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.14    (17)  all_56_5 = e1
% 151.67/22.14    (18)   ~ (e2 = e0)
% 151.67/22.14    (19)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.67/22.14          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 151.67/22.14    (20)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.14    (21)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.67/22.14          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.67/22.14    (22)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.67/22.14          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.67/22.14    (23)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.67/22.14          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.67/22.14    (24)   ~ (all_52_3 = all_52_11)
% 151.67/22.14    (25)   ~ (all_52_9 = all_52_11)
% 151.67/22.14    (26)   ~ (all_52_9 = e3)
% 151.67/22.14    (27)   ~ (all_52_11 = e3)
% 151.67/22.14    (28)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.14              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 151.67/22.14                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.67/22.14                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.67/22.14    (29)  op(e1, e0) = all_52_14
% 151.67/22.14    (30)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.14          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 151.67/22.14            e3)
% 151.67/22.14    (31)  op(e0, e0) = e1
% 151.67/22.14    (32)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 151.67/22.14              e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.67/22.14            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 151.67/22.14             ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.67/22.14              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.67/22.14            (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.67/22.14            all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 151.67/22.14            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 151.67/22.14            = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 151.67/22.14          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.67/22.14              e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.67/22.14            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 151.67/22.14             ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 151.67/22.14              e1) = e0 & $i(all_57_7))
% 151.67/22.14    (33)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.67/22.14    (34)   ~ (e3 = e0)
% 151.67/22.14    (35)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.14          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.14    (36)   ~ (all_52_6 = e3)
% 151.67/22.14    (37)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.67/22.14          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.67/22.14    (38)  op(e3, e3) = e1
% 151.67/22.14    (39)  op(e1, e2) = all_52_6
% 151.67/22.14    (40)   ~ (all_52_9 = e2)
% 151.67/22.14    (41)   ~ (all_52_3 = e1)
% 151.67/22.14    (42)  op(e0, e3) = all_52_3
% 151.67/22.14    (43)   ~ (all_52_7 = e2)
% 151.67/22.14    (44)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 151.67/22.14    (45)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.14          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.14    (46)  op(e2, e1) = all_52_9
% 151.67/22.14    (47)   ~ (e1 = e0)
% 151.67/22.14    (48)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.67/22.14          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.67/22.15    (49)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 151.67/22.15              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.67/22.15            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 151.67/22.15                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 151.67/22.15              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.67/22.15          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 151.67/22.15              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.67/22.15            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 151.67/22.15                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 151.67/22.15              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.67/22.15          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 151.67/22.15              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.67/22.15            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 151.67/22.15                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 151.67/22.15              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 151.67/22.15          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 151.67/22.15              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.67/22.15            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 151.67/22.15                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 151.67/22.15                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 151.67/22.15                $i(all_57_14))))
% 151.67/22.15    (50)  op(e1, e1) = e3
% 151.67/22.15    (51)  op(e0, e0) = all_57_15
% 151.67/22.15    (52)   ~ (e3 = e2)
% 151.67/22.15    (53)   ~ (all_52_8 = e3)
% 151.67/22.15    (54)  op(e1, e2) = e1
% 151.67/22.15    (55)   ~ (all_52_14 = all_10_2)
% 151.67/22.15    (56)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.15          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.67/22.15    (57)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.15          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.15    (58)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.67/22.15          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.67/22.15    (59)  all_54_13 = all_52_7
% 151.67/22.15    (60)  op(e3, e1) = all_52_8
% 151.67/22.15    (61)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.67/22.15          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.67/22.15    (62)   ~ (all_52_6 = all_52_7)
% 151.67/22.15    (63)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.15          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.15    (64)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.15          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.15    (65)  op(e2, e3) = all_52_1
% 151.67/22.15    (66)   ~ (all_52_1 = e2)
% 151.67/22.15  
% 151.67/22.15  Begin of proof
% 151.67/22.15  | 
% 151.67/22.15  | BETA: splitting (49) gives:
% 151.67/22.15  | 
% 151.67/22.15  | Case 1:
% 151.67/22.15  | | 
% 151.67/22.15  | |   (67)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 151.67/22.15  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 151.67/22.15  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 151.67/22.15  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.67/22.15  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 151.67/22.15  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 151.67/22.15  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 151.67/22.15  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.67/22.15  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 151.67/22.15  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 151.67/22.15  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 151.67/22.15  | |               $i(all_57_15))))
% 151.67/22.15  | | 
% 151.67/22.15  | | BETA: splitting (67) gives:
% 151.67/22.15  | | 
% 151.67/22.15  | | Case 1:
% 151.67/22.15  | | | 
% 151.67/22.15  | | |   (68)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 151.67/22.15  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 151.67/22.15  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 151.67/22.15  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.67/22.15  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 151.67/22.15  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.67/22.15  | | | 
% 151.67/22.15  | | | ALPHA: (68) implies:
% 151.67/22.15  | | |   (69)  op(e3, e3) = e3
% 151.67/22.15  | | | 
% 151.67/22.15  | | | REF_CLOSE: (5), (20), (38), (69) are inconsistent by sub-proof #1178.
% 151.67/22.15  | | | 
% 151.67/22.15  | | Case 2:
% 151.67/22.15  | | | 
% 151.67/22.15  | | |   (70)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 151.67/22.15  | | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.67/22.15  | | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 151.67/22.15  | | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 151.67/22.15  | | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 151.67/22.15  | | |               e0) = all_57_15 & $i(all_57_15)))
% 151.67/22.15  | | | 
% 151.67/22.15  | | | ALPHA: (70) implies:
% 151.67/22.15  | | |   (71)  op(e2, e2) = e2
% 151.67/22.15  | | |   (72)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 151.67/22.15  | | |             e1) = all_57_14 & $i(all_57_14))
% 151.67/22.15  | | | 
% 151.67/22.15  | | | GROUND_INST: instantiating (20) with e1, all_57_15, e0, e0, simplifying
% 151.67/22.15  | | |              with (31), (51) gives:
% 151.67/22.15  | | |   (73)  all_57_15 = e1
% 151.67/22.15  | | | 
% 151.67/22.15  | | | GROUND_INST: instantiating (20) with all_52_6, e1, e2, e1, simplifying
% 151.67/22.15  | | |              with (39), (54) gives:
% 151.67/22.15  | | |   (74)  all_52_6 = e1
% 151.67/22.15  | | | 
% 151.67/22.15  | | | GROUND_INST: instantiating (20) with all_52_9, e1, e1, e2, simplifying
% 151.67/22.15  | | |              with (1), (46) gives:
% 151.67/22.15  | | |   (75)  all_52_9 = e1
% 151.67/22.15  | | | 
% 151.67/22.15  | | | REDUCE: (62), (74) imply:
% 151.67/22.15  | | |   (76)   ~ (all_52_7 = e1)
% 151.67/22.15  | | | 
% 151.67/22.15  | | | SIMP: (76) implies:
% 151.67/22.15  | | |   (77)   ~ (all_52_7 = e1)
% 151.67/22.15  | | | 
% 151.67/22.15  | | | REDUCE: (25), (75) imply:
% 151.67/22.15  | | |   (78)   ~ (all_52_11 = e1)
% 151.67/22.15  | | | 
% 151.67/22.15  | | | SIMP: (78) implies:
% 151.67/22.15  | | |   (79)   ~ (all_52_11 = e1)
% 151.67/22.15  | | | 
% 151.67/22.15  | | | REDUCE: (26), (75) imply:
% 151.67/22.15  | | |   (80)   ~ (e3 = e1)
% 151.67/22.15  | | | 
% 151.67/22.15  | | | REDUCE: (40), (75) imply:
% 151.67/22.15  | | |   (81)   ~ (e2 = e1)
% 151.67/22.15  | | | 
% 151.67/22.15  | | | SIMP: (81) implies:
% 151.67/22.15  | | |   (82)   ~ (e2 = e1)
% 151.67/22.15  | | | 
% 151.67/22.15  | | | BETA: splitting (32) gives:
% 151.67/22.15  | | | 
% 151.67/22.15  | | | Case 1:
% 151.67/22.15  | | | | 
% 151.67/22.15  | | | |   (83)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.67/22.15  | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 151.67/22.15  | | | |           op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 151.67/22.15  | | | |           e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 151.67/22.15  | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 151.67/22.15  | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.67/22.15  | | | |           (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 151.67/22.15  | | | |           op(e0, e2) = e0 & $i(all_57_3))
% 151.67/22.15  | | | | 
% 151.67/22.15  | | | | BETA: splitting (83) gives:
% 151.67/22.15  | | | | 
% 151.67/22.15  | | | | Case 1:
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | |   (84)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 151.67/22.15  | | | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 151.67/22.15  | | | | |         op(e0, e3) = e0 & $i(all_57_0)
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | | ALPHA: (84) implies:
% 151.67/22.15  | | | | |   (85)  op(e0, e3) = e0
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 151.67/22.15  | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 151.67/22.15  | | | | |            (23), (24), (26), (27), (28), (29), (30), (31), (32), (33),
% 151.67/22.15  | | | | |            (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 151.67/22.15  | | | | |            (44), (45), (46), (48), (50), (51), (53), (55), (56), (57),
% 151.67/22.15  | | | | |            (58), (59), (60), (61), (62), (63), (64), (65), (66), (71),
% 151.67/22.15  | | | | |            (72), (77), (79), (82), (85) are inconsistent by sub-proof
% 151.67/22.15  | | | | |            #143.
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | Case 2:
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | |   (86)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.67/22.15  | | | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 151.67/22.15  | | | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 151.67/22.15  | | | | |           = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3)
% 151.67/22.15  | | | | |           = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 151.67/22.15  | | | | |           $i(all_57_3))
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | | BETA: splitting (86) gives:
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | | Case 1:
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | |   (87)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 151.67/22.15  | | | | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 151.67/22.15  | | | | | |         op(e0, e3) = e0 & $i(all_57_1)
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | | ALPHA: (87) implies:
% 151.67/22.15  | | | | | |   (88)   ~ (all_57_15 = e3)
% 151.67/22.15  | | | | | |   (89)  op(e0, e3) = e0
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 151.67/22.15  | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 151.67/22.15  | | | | | |            (22), (23), (24), (26), (27), (28), (29), (30), (31),
% 151.67/22.15  | | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40),
% 151.67/22.15  | | | | | |            (41), (42), (43), (44), (45), (46), (48), (50), (51),
% 151.67/22.15  | | | | | |            (53), (55), (56), (57), (58), (59), (60), (61), (62),
% 151.67/22.15  | | | | | |            (63), (64), (65), (66), (71), (72), (77), (79), (82),
% 151.67/22.15  | | | | | |            (89) are inconsistent by sub-proof #143.
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | Case 2:
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | |   (90)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 151.67/22.15  | | | | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 151.67/22.15  | | | | | |         op(e0, e2) = e0 & $i(all_57_3)
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | | ALPHA: (90) implies:
% 151.67/22.15  | | | | | |   (91)  op(e3, e3) = e2
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | | REF_CLOSE: (20), (38), (82), (91) are inconsistent by sub-proof
% 151.67/22.15  | | | | | |            #1074.
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | End of split
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | End of split
% 151.67/22.15  | | | | 
% 151.67/22.15  | | | Case 2:
% 151.67/22.15  | | | | 
% 151.67/22.15  | | | |   (92)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.67/22.15  | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.67/22.15  | | | |           op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 =
% 151.67/22.15  | | | |           e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 151.67/22.15  | | | |           e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 151.67/22.15  | | | |         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.67/22.15  | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.67/22.15  | | | |           op(e0, e1) = e0 & $i(all_57_7))
% 151.67/22.15  | | | | 
% 151.67/22.15  | | | | BETA: splitting (92) gives:
% 151.67/22.15  | | | | 
% 151.67/22.15  | | | | Case 1:
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | |   (93)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 151.67/22.15  | | | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.67/22.15  | | | | |         op(e0, e2) = e0 & $i(all_57_4)
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | | ALPHA: (93) implies:
% 151.67/22.15  | | | | |   (94)  op(e1, e1) = e2
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | | REF_CLOSE: (20), (50), (52), (94) are inconsistent by sub-proof #834.
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | Case 2:
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | |   (95)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.67/22.15  | | | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.67/22.15  | | | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 151.67/22.15  | | | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2)
% 151.67/22.15  | | | | |           = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.67/22.15  | | | | |           $i(all_57_7))
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | | BETA: splitting (95) gives:
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | | Case 1:
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | |   (96)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 151.67/22.15  | | | | | |         (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.67/22.15  | | | | | |         op(e0, e1) = e0 & $i(all_57_6)
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | | ALPHA: (96) implies:
% 151.67/22.15  | | | | | |   (97)   ~ (all_57_15 = e1)
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | | REDUCE: (73), (97) imply:
% 151.67/22.15  | | | | | |   (98)  $false
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | | CLOSE: (98) is inconsistent.
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | Case 2:
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | |   (99)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 151.67/22.15  | | | | | |         (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 151.67/22.15  | | | | | |         op(e0, e1) = e0 & $i(all_57_7)
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | | ALPHA: (99) implies:
% 151.67/22.15  | | | | | |   (100)  op(e2, e2) = e1
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | | REF_CLOSE: (20), (71), (82), (100) are inconsistent by sub-proof
% 151.67/22.15  | | | | | |            #1158.
% 151.67/22.15  | | | | | | 
% 151.67/22.15  | | | | | End of split
% 151.67/22.15  | | | | | 
% 151.67/22.15  | | | | End of split
% 151.67/22.15  | | | | 
% 151.67/22.15  | | | End of split
% 151.67/22.15  | | | 
% 151.67/22.15  | | End of split
% 151.67/22.15  | | 
% 151.67/22.15  | Case 2:
% 151.67/22.15  | | 
% 151.67/22.15  | |   (101)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 151.67/22.15  | |                e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 151.67/22.15  | |                $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 151.67/22.15  | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 151.67/22.15  | |            ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) &
% 151.67/22.15  | |                op(e0, e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 151.67/22.15  | |            op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 151.67/22.15  | |                (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 151.67/22.15  | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 151.67/22.15  | |                op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 151.67/22.15  | |                op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 151.67/22.15  | |                all_57_14 & $i(all_57_14))))
% 151.67/22.15  | | 
% 151.67/22.15  | | REF_CLOSE: (5), (20), (31), (47), (50), (101) are inconsistent by sub-proof
% 151.67/22.15  | |            #429.
% 151.67/22.15  | | 
% 151.67/22.15  | End of split
% 151.67/22.15  | 
% 151.67/22.15  End of proof
% 151.67/22.15  
% 151.67/22.15  Sub-proof #143 shows that the following formulas are inconsistent:
% 151.67/22.15  ----------------------------------------------------------------
% 151.67/22.15    (1)  op(e0, e1) = all_52_11
% 151.67/22.15    (2)  all_56_8 = e3
% 151.67/22.15    (3)   ~ (all_52_7 = all_52_11)
% 151.67/22.15    (4)   ~ (e3 = e1)
% 151.67/22.15    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.67/22.15         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.67/22.15    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.67/22.15         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.67/22.15    (7)  op(e0, e0) = all_10_2
% 151.67/22.15    (8)  op(e3, e2) = all_52_4
% 151.67/22.15    (9)   ~ (all_52_4 = all_52_7)
% 151.67/22.15    (10)  all_56_7 = e1
% 151.67/22.15    (11)  op(e0, e2) = all_52_7
% 151.67/22.15    (12)   ~ (all_52_3 = all_52_7)
% 151.67/22.15    (13)  all_54_14 = all_52_11
% 151.67/22.15    (14)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.15          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.67/22.15    (15)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.15          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.15    (16)  all_56_5 = e1
% 151.67/22.15    (17)   ~ (e2 = e0)
% 151.67/22.15    (18)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.67/22.15          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 151.67/22.15    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.15            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.15    (20)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.67/22.15          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.67/22.15    (21)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.67/22.15          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.67/22.15    (22)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.67/22.15          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.67/22.15    (23)   ~ (all_52_7 = e1)
% 151.67/22.15    (24)   ~ (all_52_3 = all_52_11)
% 151.67/22.15    (25)  op(e0, e3) = e0
% 151.67/22.15    (26)   ~ (all_52_9 = e3)
% 151.67/22.15    (27)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 151.67/22.15            all_57_14 & $i(all_57_14))
% 151.67/22.15    (28)   ~ (all_52_11 = e3)
% 151.67/22.15    (29)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.15              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 151.67/22.15                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.67/22.15                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.67/22.15    (30)  op(e1, e0) = all_52_14
% 151.67/22.15    (31)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.15          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 151.67/22.15            e3)
% 151.67/22.15    (32)  op(e0, e0) = e1
% 151.67/22.15    (33)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 151.67/22.15              e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.67/22.15            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 151.67/22.15             ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.67/22.15              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.67/22.15            (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.67/22.15            all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 151.67/22.15            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 151.67/22.15            = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 151.67/22.15          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.67/22.15              e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.67/22.15            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 151.67/22.15             ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 151.67/22.15              e1) = e0 & $i(all_57_7))
% 151.67/22.15    (34)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.67/22.15    (35)   ~ (e3 = e0)
% 151.67/22.15    (36)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.15          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.15    (37)   ~ (all_52_6 = e3)
% 151.67/22.15    (38)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.67/22.15          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.67/22.15    (39)  op(e3, e3) = e1
% 151.67/22.15    (40)  op(e1, e2) = all_52_6
% 151.67/22.15    (41)   ~ (all_52_9 = e2)
% 151.67/22.15    (42)   ~ (all_52_3 = e1)
% 151.67/22.15    (43)  op(e0, e3) = all_52_3
% 151.67/22.15    (44)   ~ (all_52_7 = e2)
% 151.67/22.15    (45)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 151.67/22.15    (46)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.15          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.16    (47)  op(e2, e2) = e2
% 151.67/22.16    (48)  op(e2, e1) = all_52_9
% 151.67/22.16    (49)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.67/22.16          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.67/22.16    (50)  op(e1, e1) = e3
% 151.67/22.16    (51)  op(e0, e0) = all_57_15
% 151.67/22.16    (52)   ~ (all_52_8 = e3)
% 151.67/22.16    (53)   ~ (all_52_14 = all_10_2)
% 151.67/22.16    (54)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.16          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.67/22.16    (55)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.16          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.16    (56)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.67/22.16          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.67/22.16    (57)  all_54_13 = all_52_7
% 151.67/22.16    (58)  op(e3, e1) = all_52_8
% 151.67/22.16    (59)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.67/22.16          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.67/22.16    (60)   ~ (all_52_6 = all_52_7)
% 151.67/22.16    (61)   ~ (e2 = e1)
% 151.67/22.16    (62)   ~ (all_52_11 = e1)
% 151.67/22.16    (63)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.16          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.16    (64)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.16          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.16    (65)  op(e2, e3) = all_52_1
% 151.67/22.16    (66)   ~ (all_52_1 = e2)
% 151.67/22.16  
% 151.67/22.16  Begin of proof
% 151.67/22.16  | 
% 151.67/22.16  | GROUND_INST: instantiating (19) with all_52_3, e0, e3, e0, simplifying with
% 151.67/22.16  |              (25), (43) gives:
% 151.67/22.16  |   (67)  all_52_3 = e0
% 151.67/22.16  | 
% 151.67/22.16  | REDUCE: (12), (67) imply:
% 151.67/22.16  |   (68)   ~ (all_52_7 = e0)
% 151.67/22.16  | 
% 151.67/22.16  | SIMP: (68) implies:
% 151.67/22.16  |   (69)   ~ (all_52_7 = e0)
% 151.67/22.16  | 
% 151.67/22.16  | REDUCE: (24), (67) imply:
% 151.67/22.16  |   (70)   ~ (all_52_11 = e0)
% 151.67/22.16  | 
% 151.67/22.16  | SIMP: (70) implies:
% 151.67/22.16  |   (71)   ~ (all_52_11 = e0)
% 151.67/22.16  | 
% 151.67/22.16  | REDUCE: (42), (67) imply:
% 151.67/22.16  |   (72)   ~ (e1 = e0)
% 151.67/22.16  | 
% 151.67/22.16  | SIMP: (72) implies:
% 151.67/22.16  |   (73)   ~ (e1 = e0)
% 151.67/22.16  | 
% 151.67/22.16  | BETA: splitting (45) gives:
% 151.67/22.16  | 
% 151.67/22.16  | Case 1:
% 151.67/22.16  | | 
% 151.67/22.16  | |   (74)  all_54_13 = e3
% 151.67/22.16  | | 
% 151.67/22.16  | | COMBINE_EQS: (57), (74) imply:
% 151.67/22.16  | |   (75)  all_52_7 = e3
% 151.67/22.16  | | 
% 151.67/22.16  | | SIMP: (75) implies:
% 151.67/22.16  | |   (76)  all_52_7 = e3
% 151.67/22.16  | | 
% 151.67/22.16  | | REDUCE: (9), (76) imply:
% 151.67/22.16  | |   (77)   ~ (all_52_4 = e3)
% 151.67/22.16  | | 
% 151.67/22.16  | | REDUCE: (3), (76) imply:
% 151.67/22.16  | |   (78)   ~ (all_52_11 = e3)
% 151.67/22.16  | | 
% 151.67/22.16  | | REDUCE: (44), (76) imply:
% 151.67/22.16  | |   (79)   ~ (e3 = e2)
% 151.67/22.16  | | 
% 151.67/22.16  | | BETA: splitting (20) gives:
% 151.67/22.16  | | 
% 151.67/22.16  | | Case 1:
% 151.67/22.16  | | | 
% 151.67/22.16  | | |   (80)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 151.67/22.16  | | |           e3)
% 151.67/22.16  | | | 
% 151.67/22.16  | | | REF_CLOSE: (4), (8), (19), (39), (77), (80) are inconsistent by sub-proof
% 151.67/22.16  | | |            #999.
% 151.67/22.16  | | | 
% 151.67/22.16  | | Case 2:
% 151.67/22.16  | | | 
% 151.67/22.16  | | |   (81)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 151.67/22.16  | | |           e3)
% 151.67/22.16  | | | 
% 151.67/22.16  | | | BETA: splitting (81) gives:
% 151.67/22.16  | | | 
% 151.67/22.16  | | | Case 1:
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | |   (82)  all_56_4 = e3 & op(e3, e1) = e3
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | | ALPHA: (82) implies:
% 151.67/22.16  | | | |   (83)  op(e3, e1) = e3
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | | REF_CLOSE: (19), (52), (58), (83) are inconsistent by sub-proof #1164.
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | Case 2:
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | |   (84)  all_56_9 = e3 & op(e3, e0) = e3
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | | ALPHA: (84) implies:
% 151.67/22.16  | | | |   (85)  all_56_9 = e3
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | | BETA: splitting (34) gives:
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | | Case 1:
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | |   (86)  all_54_14 = e3
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | REF_CLOSE: (13), (28), (86) are inconsistent by sub-proof #903.
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | Case 2:
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | |   (87)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | REF_CLOSE: (1), (4), (6), (13), (15), (16), (17), (19), (35), (37),
% 151.67/22.16  | | | | |            (39), (40), (47), (50), (55), (61), (62), (63), (64), (71),
% 151.67/22.16  | | | | |            (73), (79), (85), (87) are inconsistent by sub-proof #150.
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | End of split
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | End of split
% 151.67/22.16  | | | 
% 151.67/22.16  | | End of split
% 151.67/22.16  | | 
% 151.67/22.16  | Case 2:
% 151.67/22.16  | | 
% 151.67/22.16  | |   (88)   ~ (all_54_13 = e3)
% 151.67/22.16  | | 
% 151.67/22.16  | | REDUCE: (57), (88) imply:
% 151.67/22.16  | |   (89)   ~ (all_52_7 = e3)
% 151.67/22.16  | | 
% 151.67/22.16  | | BETA: splitting (34) gives:
% 151.67/22.16  | | 
% 151.67/22.16  | | Case 1:
% 151.67/22.16  | | | 
% 151.67/22.16  | | |   (90)  all_54_14 = e3
% 151.67/22.16  | | | 
% 151.67/22.16  | | | REF_CLOSE: (13), (28), (90) are inconsistent by sub-proof #903.
% 151.67/22.16  | | | 
% 151.67/22.16  | | Case 2:
% 151.67/22.16  | | | 
% 151.67/22.16  | | |   (91)   ~ (all_54_14 = e3)
% 151.67/22.16  | | |   (92)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.67/22.16  | | | 
% 151.67/22.16  | | | BETA: splitting (59) gives:
% 151.67/22.16  | | | 
% 151.67/22.16  | | | Case 1:
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | |   (93)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2)
% 151.67/22.16  | | | |           = e0)
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | | BETA: splitting (93) gives:
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | | Case 1:
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | |   (94)  all_56_6 = e0 & op(e1, e3) = e0
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | ALPHA: (94) implies:
% 151.67/22.16  | | | | |   (95)  all_56_6 = e0
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | BETA: splitting (92) gives:
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | Case 1:
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | |   (96)  all_54_14 = e2
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | COMBINE_EQS: (13), (96) imply:
% 151.67/22.16  | | | | | |   (97)  all_52_11 = e2
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | SIMP: (97) implies:
% 151.67/22.16  | | | | | |   (98)  all_52_11 = e2
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | REDUCE: (28), (98) imply:
% 151.67/22.16  | | | | | |   (99)   ~ (e3 = e2)
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | SIMP: (99) implies:
% 151.67/22.16  | | | | | |   (100)   ~ (e3 = e2)
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | REDUCE: (1), (98) imply:
% 151.67/22.16  | | | | | |   (101)  op(e0, e1) = e2
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | BETA: splitting (6) gives:
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | Case 1:
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | |   (102)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 &
% 151.67/22.16  | | | | | | |            op(e3, e2) = e2)
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | | REF_CLOSE: (4), (17), (19), (35), (37), (39), (40), (47), (55),
% 151.67/22.16  | | | | | | |            (61), (63), (64), (73), (100), (102) are inconsistent
% 151.67/22.16  | | | | | | |            by sub-proof #156.
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | Case 2:
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | |   (103)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 &
% 151.67/22.16  | | | | | | |            op(e3, e0) = e2)
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | | BETA: splitting (103) gives:
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | |   (104)  all_56_4 = e2 & op(e3, e1) = e2
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | | ALPHA: (104) implies:
% 151.67/22.16  | | | | | | | |   (105)  all_56_4 = e2
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | | REF_CLOSE: (15), (16), (17), (19), (35), (50), (73), (101),
% 151.67/22.16  | | | | | | | |            (105) are inconsistent by sub-proof #221.
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | Case 2:
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | |   (106)  all_56_9 = e2 & op(e3, e0) = e2
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | | ALPHA: (106) implies:
% 151.67/22.16  | | | | | | | |   (107)  all_56_9 = e2
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | | BETA: splitting (46) gives:
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | |   (108)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 &
% 151.67/22.16  | | | | | | | | |            op(e2, e2) = e3)
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (10), (11), (12), (13),
% 151.67/22.16  | | | | | | | | |            (14), (15), (16), (17), (19), (20), (22), (25),
% 151.67/22.16  | | | | | | | | |            (27), (31), (33), (35), (36), (37), (38), (39),
% 151.67/22.16  | | | | | | | | |            (40), (41), (43), (46), (47), (48), (50), (51),
% 151.67/22.16  | | | | | | | | |            (54), (55), (56), (61), (62), (63), (64), (65),
% 151.67/22.16  | | | | | | | | |            (66), (71), (73), (92), (100), (101), (108) are
% 151.67/22.16  | | | | | | | | |            inconsistent by sub-proof #148.
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | Case 2:
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | |   (109)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 &
% 151.67/22.16  | | | | | | | | |            op(e2, e0) = e3)
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | BETA: splitting (109) gives:
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | |   (110)  all_56_5 = e3 & op(e2, e1) = e3
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | REF_CLOSE: (19), (26), (48), (110) are inconsistent by
% 151.67/22.16  | | | | | | | | | |            sub-proof #647.
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | Case 2:
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | |   (111)  all_56_10 = e3 & op(e2, e0) = e3
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | ALPHA: (111) implies:
% 151.67/22.16  | | | | | | | | | |   (112)  all_56_10 = e3
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | BETA: splitting (29) gives:
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | |   (113)  all_56_15 = e0 & op(e0, e0) = e0
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | ALPHA: (113) implies:
% 151.67/22.16  | | | | | | | | | | |   (114)  op(e0, e0) = e0
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | REF_CLOSE: (19), (32), (73), (114) are inconsistent by
% 151.67/22.16  | | | | | | | | | | |            sub-proof #1040.
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | Case 2:
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | |   (115)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 151.67/22.16  | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 151.67/22.16  | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 151.67/22.16  | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 151.67/22.16  | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | ALPHA: (115) implies:
% 151.67/22.16  | | | | | | | | | | |   (116)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 151.67/22.16  | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 151.67/22.16  | | | | | | | | | | |              e0) = e0)
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | BETA: splitting (49) gives:
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | |   (117)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 151.67/22.16  | | | | | | | | | | | |            & op(e1, e2) = e2)
% 151.67/22.16  | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | BETA: splitting (117) gives:
% 151.67/22.16  | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | |   (118)  all_56_6 = e2 & op(e1, e3) = e2
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | ALPHA: (118) implies:
% 151.67/22.16  | | | | | | | | | | | | |   (119)  all_56_6 = e2
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | REF_CLOSE: (17), (95), (119) are inconsistent by sub-proof
% 151.67/22.16  | | | | | | | | | | | | |            #724.
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | Case 2:
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | |   (120)  all_56_7 = e2 & op(e1, e2) = e2
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | REF_CLOSE: (19), (23), (40), (45), (57), (60), (69), (89),
% 151.67/22.16  | | | | | | | | | | | | |            (120) are inconsistent by sub-proof #835.
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | End of split
% 151.67/22.16  | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | Case 2:
% 151.67/22.16  | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | |   (121)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 151.67/22.16  | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 151.67/22.16  | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | REF_CLOSE: (17), (19), (35), (50), (100), (107), (112),
% 151.67/22.16  | | | | | | | | | | | |            (116), (121) are inconsistent by sub-proof #147.
% 151.67/22.16  | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | End of split
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | End of split
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | End of split
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | End of split
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | End of split
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | End of split
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | Case 2:
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | |   (122)  all_54_14 = e1 | all_54_14 = e0
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | REF_CLOSE: (13), (62), (71), (122) are inconsistent by sub-proof
% 151.67/22.16  | | | | | |            #375.
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | End of split
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | Case 2:
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | |   (123)  all_56_7 = e0 & op(e1, e2) = e0
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | ALPHA: (123) implies:
% 151.67/22.16  | | | | |   (124)  all_56_7 = e0
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | REF_CLOSE: (10), (73), (124) are inconsistent by sub-proof #987.
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | End of split
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | Case 2:
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | |   (125)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1,
% 151.67/22.16  | | | |              e0) = e0)
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | | BETA: splitting (125) gives:
% 151.67/22.16  | | | | 
% 151.67/22.16  | | | | Case 1:
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | |   (126)  all_56_8 = e0 & op(e1, e1) = e0
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | ALPHA: (126) implies:
% 151.67/22.16  | | | | |   (127)  op(e1, e1) = e0
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | REF_CLOSE: (19), (35), (50), (127) are inconsistent by sub-proof #896.
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | Case 2:
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | |   (128)  all_56_11 = e0 & op(e1, e0) = e0
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | ALPHA: (128) implies:
% 151.67/22.16  | | | | |   (129)  all_56_11 = e0
% 151.67/22.16  | | | | |   (130)  op(e1, e0) = e0
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | BETA: splitting (92) gives:
% 151.67/22.16  | | | | | 
% 151.67/22.16  | | | | | Case 1:
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | |   (131)  all_54_14 = e2
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | COMBINE_EQS: (13), (131) imply:
% 151.67/22.16  | | | | | |   (132)  all_52_11 = e2
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | SIMP: (132) implies:
% 151.67/22.16  | | | | | |   (133)  all_52_11 = e2
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | REDUCE: (28), (133) imply:
% 151.67/22.16  | | | | | |   (134)   ~ (e3 = e2)
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | SIMP: (134) implies:
% 151.67/22.16  | | | | | |   (135)   ~ (e3 = e2)
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | REDUCE: (1), (133) imply:
% 151.67/22.16  | | | | | |   (136)  op(e0, e1) = e2
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | BETA: splitting (6) gives:
% 151.67/22.16  | | | | | | 
% 151.67/22.16  | | | | | | Case 1:
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | |   (137)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 &
% 151.67/22.16  | | | | | | |            op(e3, e2) = e2)
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | | REF_CLOSE: (4), (17), (19), (35), (37), (39), (40), (47), (55),
% 151.67/22.16  | | | | | | |            (61), (63), (64), (73), (135), (137) are inconsistent
% 151.67/22.16  | | | | | | |            by sub-proof #156.
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | Case 2:
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | |   (138)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 &
% 151.67/22.16  | | | | | | |            op(e3, e0) = e2)
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | | BETA: splitting (138) gives:
% 151.67/22.16  | | | | | | | 
% 151.67/22.16  | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | |   (139)  all_56_4 = e2 & op(e3, e1) = e2
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | | ALPHA: (139) implies:
% 151.67/22.16  | | | | | | | |   (140)  all_56_4 = e2
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | | REF_CLOSE: (15), (16), (17), (19), (35), (50), (73), (136),
% 151.67/22.16  | | | | | | | |            (140) are inconsistent by sub-proof #221.
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | Case 2:
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | |   (141)  all_56_9 = e2 & op(e3, e0) = e2
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | | ALPHA: (141) implies:
% 151.67/22.16  | | | | | | | |   (142)  all_56_9 = e2
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | | BETA: splitting (46) gives:
% 151.67/22.16  | | | | | | | | 
% 151.67/22.16  | | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | |   (143)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 &
% 151.67/22.16  | | | | | | | | |            op(e2, e2) = e3)
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (10), (11), (12), (13),
% 151.67/22.16  | | | | | | | | |            (14), (15), (16), (17), (19), (20), (22), (25),
% 151.67/22.16  | | | | | | | | |            (27), (31), (33), (35), (36), (37), (38), (39),
% 151.67/22.16  | | | | | | | | |            (40), (41), (43), (46), (47), (48), (50), (51),
% 151.67/22.16  | | | | | | | | |            (54), (55), (56), (61), (62), (63), (64), (65),
% 151.67/22.16  | | | | | | | | |            (66), (71), (73), (92), (135), (136), (143) are
% 151.67/22.16  | | | | | | | | |            inconsistent by sub-proof #148.
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | Case 2:
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | |   (144)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 &
% 151.67/22.16  | | | | | | | | |            op(e2, e0) = e3)
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | BETA: splitting (144) gives:
% 151.67/22.16  | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | |   (145)  all_56_5 = e3 & op(e2, e1) = e3
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | REF_CLOSE: (19), (26), (48), (145) are inconsistent by
% 151.67/22.16  | | | | | | | | | |            sub-proof #647.
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | Case 2:
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | |   (146)  all_56_10 = e3 & op(e2, e0) = e3
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | ALPHA: (146) implies:
% 151.67/22.16  | | | | | | | | | |   (147)  all_56_10 = e3
% 151.67/22.16  | | | | | | | | | |   (148)  op(e2, e0) = e3
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | BETA: splitting (64) gives:
% 151.67/22.16  | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | |   (149)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 151.67/22.16  | | | | | | | | | | |            & op(e2, e2) = e3)
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | BETA: splitting (149) gives:
% 151.67/22.16  | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | |   (150)  all_56_1 = e3 & op(e3, e2) = e3
% 151.67/22.16  | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | ALPHA: (150) implies:
% 151.67/22.16  | | | | | | | | | | | |   (151)  all_56_1 = e3
% 151.67/22.16  | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | BETA: splitting (22) gives:
% 151.67/22.16  | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | |   (152)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 151.67/22.16  | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (19), (35), (41), (48), (50),
% 151.67/22.16  | | | | | | | | | | | | |            (73), (136), (152) are inconsistent by sub-proof
% 151.67/22.16  | | | | | | | | | | | | |            #149.
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | Case 2:
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | |   (153)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 151.67/22.16  | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | BETA: splitting (153) gives:
% 151.67/22.16  | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | Case 1:
% 151.67/22.16  | | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | |   (154)  all_56_8 = e2 & op(e1, e1) = e2
% 151.67/22.16  | | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | | ALPHA: (154) implies:
% 151.67/22.16  | | | | | | | | | | | | | |   (155)  op(e1, e1) = e2
% 151.67/22.16  | | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | | REF_CLOSE: (19), (50), (135), (155) are inconsistent by
% 151.67/22.16  | | | | | | | | | | | | | |            sub-proof #834.
% 151.67/22.16  | | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | Case 2:
% 151.67/22.16  | | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | |   (156)  all_56_14 = e2 & op(e0, e1) = e2
% 151.67/22.16  | | | | | | | | | | | | | | 
% 151.67/22.16  | | | | | | | | | | | | | | ALPHA: (156) implies:
% 151.67/22.16  | | | | | | | | | | | | | |   (157)  all_56_14 = e2
% 151.67/22.17  | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 151.67/22.17  | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | |   (158)  all_56_15 = e0 & op(e0, e0) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 151.67/22.17  | | | | | | | | | | | | | | |   (159)  op(e0, e0) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | REF_CLOSE: (7), (19), (30), (53), (130), (159) are
% 151.67/22.17  | | | | | | | | | | | | | | |            inconsistent by sub-proof #453.
% 151.67/22.17  | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | |   (160)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 151.67/22.17  | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 151.67/22.17  | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 151.67/22.17  | | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 151.67/22.17  | | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 151.67/22.17  | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 151.67/22.17  | | | | | | | | | | | | | | |   (161)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 151.67/22.17  | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 151.67/22.17  | | | | | | | | | | | | | | |              e0) = e0)
% 151.67/22.17  | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 151.67/22.17  | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | |   (162)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 151.67/22.17  | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 151.67/22.17  | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | BETA: splitting (162) gives:
% 151.67/22.17  | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | |   (163)  all_56_6 = e2 & op(e1, e3) = e2
% 151.67/22.17  | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | |   (164)  all_56_6 = e2
% 151.67/22.17  | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 151.67/22.17  | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | |   (165)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 151.67/22.17  | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |   (166)  all_56_2 = e0 & op(e2, e3) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |   (167)  all_56_2 = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | |   (168)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |   (169)  all_56_12 = e3 & op(e0, e3) = e3
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |   (170)  all_56_12 = e3
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | |   (171)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |   (172)  all_56_1 = e0 & op(e3, e2) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |   (173)  all_56_1 = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (173) imply:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |   (174)  e3 = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (17), (19), (26), (35), (36), (46),
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |            (47), (48), (61), (73), (135), (147), (164),
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |            (170), (174) are inconsistent by sub-proof #161.
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |   (175)  all_56_3 = e0 & op(e2, e2) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |   (176)  op(e2, e2) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (18), (19), (61), (135), (148), (167),
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |            (176) are inconsistent by sub-proof #671.
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | |   (177)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |   (178)  all_56_7 = e0 & op(e1, e2) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |   (179)  all_56_7 = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17), (19), (21), (49), (50), (61), (73),
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |            (129), (135), (179) are inconsistent by sub-proof
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |            #145.
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |   (180)  all_56_13 = e0 & op(e0, e2) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |   (181)  op(e0, e2) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (19), (69), (181) are inconsistent by
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1036.
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |   (182)  all_56_13 = e3 & op(e0, e2) = e3
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |   (183)  all_56_13 = e3
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (13), (15), (16), (17), (19),
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |            (20), (35), (37), (39), (40), (47), (50), (55),
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |            (56), (61), (62), (63), (64), (71), (73), (92),
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |            (135), (136), (157), (183) are inconsistent by
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |            sub-proof #144.
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | |   (184)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |   (185)  all_56_14 = e3 & op(e0, e1) = e3
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |   (186)  all_56_14 = e3
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (157), (186) imply:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |   (187)  e3 = e2
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | SIMP: (187) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |   (188)  e3 = e2
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (151), (188) imply:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |   (189)  all_56_1 = e2
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17), (19), (35), (37), (40), (47), (55),
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |            (61), (63), (64), (73), (135), (189) are
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #921.
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |   (190)  all_56_15 = e3 & op(e0, e0) = e3
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |   (191)  op(e0, e0) = e3
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (12), (17), (19), (25), (27), (33), (43),
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |            (47), (51), (61), (136), (191) are inconsistent by
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | |            sub-proof #298.
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |   (192)  all_56_3 = e0 & op(e2, e2) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |   (193)  op(e2, e2) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (47), (193) are inconsistent by
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |            sub-proof #1145.
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | |   (194)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 151.67/22.17  | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 151.67/22.17  | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |   (195)  all_56_5 = e0 & op(e2, e1) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |   (196)  all_56_5 = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (16), (196) imply:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |   (197)  e1 = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (197) imply:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |   (198)  all_56_7 = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (17), (19), (21), (49), (50), (61), (73),
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |            (129), (135), (198) are inconsistent by sub-proof
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |            #145.
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |   (199)  all_56_10 = e0 & op(e2, e0) = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |   (200)  all_56_10 = e0
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (147), (200) are inconsistent by sub-proof
% 151.67/22.17  | | | | | | | | | | | | | | | | | | |            #1134.
% 151.67/22.17  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | |   (201)  all_56_7 = e2 & op(e1, e2) = e2
% 151.67/22.17  | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (23), (40), (45), (57), (60), (69), (89),
% 151.67/22.17  | | | | | | | | | | | | | | | | |            (201) are inconsistent by sub-proof #835.
% 151.67/22.17  | | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | |   (202)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 151.67/22.17  | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 151.67/22.17  | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | | REF_CLOSE: (17), (19), (35), (50), (135), (142), (147),
% 151.67/22.17  | | | | | | | | | | | | | | | |            (161), (202) are inconsistent by sub-proof #147.
% 151.67/22.17  | | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | |   (203)  all_56_3 = e3 & op(e2, e2) = e3
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | ALPHA: (203) implies:
% 151.67/22.17  | | | | | | | | | | | |   (204)  op(e2, e2) = e3
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | REF_CLOSE: (19), (47), (135), (204) are inconsistent by
% 151.67/22.17  | | | | | | | | | | | |            sub-proof #1179.
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | |   (205)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 151.67/22.17  | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 151.67/22.17  | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | BETA: splitting (205) gives:
% 151.67/22.17  | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | |   (206)  all_56_7 = e3 & op(e1, e2) = e3
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | REF_CLOSE: (19), (37), (40), (206) are inconsistent by
% 151.67/22.17  | | | | | | | | | | | |            sub-proof #925.
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | |   (207)  all_56_13 = e3 & op(e0, e2) = e3
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | ALPHA: (207) implies:
% 151.67/22.17  | | | | | | | | | | | |   (208)  all_56_13 = e3
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | BETA: splitting (22) gives:
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | |   (209)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 151.67/22.17  | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 151.67/22.17  | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | REF_CLOSE: (15), (16), (17), (19), (35), (41), (48), (50),
% 151.67/22.17  | | | | | | | | | | | | |            (73), (136), (209) are inconsistent by sub-proof
% 151.67/22.17  | | | | | | | | | | | | |            #149.
% 151.67/22.17  | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | |   (210)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 151.67/22.17  | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 151.67/22.17  | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | BETA: splitting (210) gives:
% 151.67/22.17  | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | Case 1:
% 151.67/22.17  | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | |   (211)  all_56_8 = e2 & op(e1, e1) = e2
% 151.67/22.17  | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | ALPHA: (211) implies:
% 151.67/22.17  | | | | | | | | | | | | | |   (212)  op(e1, e1) = e2
% 151.67/22.17  | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | REF_CLOSE: (19), (50), (135), (212) are inconsistent by
% 151.67/22.17  | | | | | | | | | | | | | |            sub-proof #834.
% 151.67/22.17  | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | Case 2:
% 151.67/22.17  | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | |   (213)  all_56_14 = e2 & op(e0, e1) = e2
% 151.67/22.17  | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | ALPHA: (213) implies:
% 151.67/22.17  | | | | | | | | | | | | | |   (214)  all_56_14 = e2
% 151.67/22.17  | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (6), (13), (15), (16), (17), (19),
% 151.67/22.17  | | | | | | | | | | | | | |            (20), (35), (37), (39), (40), (47), (50), (55),
% 151.67/22.17  | | | | | | | | | | | | | |            (56), (61), (62), (63), (64), (71), (73), (92),
% 151.67/22.17  | | | | | | | | | | | | | |            (135), (136), (208), (214) are inconsistent by
% 151.67/22.17  | | | | | | | | | | | | | |            sub-proof #144.
% 151.67/22.17  | | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | | 
% 151.67/22.17  | | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | | 
% 151.67/22.17  | | | | | | | | End of split
% 151.67/22.17  | | | | | | | | 
% 151.67/22.17  | | | | | | | End of split
% 151.67/22.17  | | | | | | | 
% 151.67/22.17  | | | | | | End of split
% 151.67/22.17  | | | | | | 
% 151.67/22.17  | | | | | Case 2:
% 151.67/22.17  | | | | | | 
% 151.67/22.17  | | | | | |   (215)  all_54_14 = e1 | all_54_14 = e0
% 151.67/22.17  | | | | | | 
% 151.67/22.17  | | | | | | REF_CLOSE: (13), (62), (71), (215) are inconsistent by sub-proof
% 151.67/22.17  | | | | | |            #375.
% 151.67/22.17  | | | | | | 
% 151.67/22.17  | | | | | End of split
% 151.67/22.17  | | | | | 
% 151.67/22.17  | | | | End of split
% 151.67/22.17  | | | | 
% 151.67/22.17  | | | End of split
% 151.67/22.17  | | | 
% 151.67/22.17  | | End of split
% 151.67/22.17  | | 
% 151.67/22.17  | End of split
% 151.67/22.17  | 
% 151.67/22.17  End of proof
% 151.67/22.17  
% 151.67/22.17  Sub-proof #144 shows that the following formulas are inconsistent:
% 151.67/22.17  ----------------------------------------------------------------
% 151.67/22.17    (1)  op(e0, e1) = all_52_11
% 151.67/22.17    (2)  all_56_8 = e3
% 151.67/22.17    (3)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.67/22.17    (4)   ~ (e3 = e1)
% 151.67/22.17    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.67/22.17         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.67/22.17    (6)  all_54_14 = all_52_11
% 151.67/22.17    (7)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.17         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.17    (8)  all_56_5 = e1
% 151.67/22.17    (9)   ~ (e2 = e0)
% 151.67/22.17    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.17            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.17    (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.67/22.17          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.67/22.17    (12)  all_56_14 = e2
% 151.67/22.17    (13)   ~ (e3 = e0)
% 151.67/22.17    (14)   ~ (all_52_11 = e0)
% 151.67/22.17    (15)   ~ (all_52_6 = e3)
% 151.67/22.17    (16)  op(e3, e3) = e1
% 151.67/22.17    (17)  op(e1, e2) = all_52_6
% 151.67/22.17    (18)  op(e0, e1) = e2
% 151.67/22.17    (19)  op(e2, e2) = e2
% 151.67/22.17    (20)   ~ (e1 = e0)
% 151.67/22.17    (21)  all_56_13 = e3
% 151.67/22.17    (22)  op(e1, e1) = e3
% 151.67/22.17    (23)   ~ (e3 = e2)
% 151.67/22.17    (24)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.17          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.17    (25)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.67/22.17          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.67/22.17    (26)   ~ (e2 = e1)
% 151.67/22.17    (27)   ~ (all_52_11 = e1)
% 151.67/22.17    (28)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.17          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.17    (29)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.17          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.17  
% 151.67/22.17  Begin of proof
% 151.67/22.17  | 
% 151.67/22.17  | BETA: splitting (11) gives:
% 151.67/22.17  | 
% 151.67/22.17  | Case 1:
% 151.67/22.17  | | 
% 151.67/22.17  | |   (30)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 151.67/22.17  | |           e3)
% 151.67/22.17  | | 
% 151.67/22.17  | | REF_CLOSE: (4), (9), (10), (13), (16), (19), (20), (21), (24), (26), (28),
% 151.67/22.17  | |            (30) are inconsistent by sub-proof #876.
% 151.67/22.17  | | 
% 151.67/22.17  | Case 2:
% 151.67/22.17  | | 
% 151.67/22.17  | |   (31)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 151.67/22.17  | |           e3)
% 151.67/22.17  | | 
% 151.67/22.17  | | BETA: splitting (31) gives:
% 151.67/22.17  | | 
% 151.67/22.17  | | Case 1:
% 151.67/22.17  | | | 
% 151.67/22.17  | | |   (32)  all_56_4 = e3 & op(e3, e1) = e3
% 151.67/22.17  | | | 
% 151.67/22.17  | | | ALPHA: (32) implies:
% 151.67/22.17  | | |   (33)  all_56_4 = e3
% 151.67/22.17  | | | 
% 151.67/22.17  | | | REF_CLOSE: (2), (4), (7), (9), (10), (12), (13), (18), (20), (22), (25),
% 151.67/22.17  | | |            (26), (33) are inconsistent by sub-proof #354.
% 151.67/22.17  | | | 
% 151.67/22.17  | | Case 2:
% 151.67/22.17  | | | 
% 151.67/22.17  | | |   (34)  all_56_9 = e3 & op(e3, e0) = e3
% 151.67/22.17  | | | 
% 151.67/22.17  | | | ALPHA: (34) implies:
% 151.67/22.17  | | |   (35)  all_56_9 = e3
% 151.67/22.17  | | | 
% 151.67/22.17  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14), (15),
% 151.67/22.17  | | |            (16), (17), (19), (20), (22), (23), (24), (26), (27), (28),
% 151.67/22.17  | | |            (29), (35) are inconsistent by sub-proof #150.
% 151.67/22.17  | | | 
% 151.67/22.17  | | End of split
% 151.67/22.17  | | 
% 151.67/22.17  | End of split
% 151.67/22.17  | 
% 151.67/22.17  End of proof
% 151.67/22.17  
% 151.67/22.17  Sub-proof #145 shows that the following formulas are inconsistent:
% 151.67/22.17  ----------------------------------------------------------------
% 151.67/22.17    (1)   ~ (e3 = e1)
% 151.67/22.17    (2)   ~ (e2 = e0)
% 151.67/22.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.17    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.67/22.17         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.67/22.17    (5)  all_56_11 = e0
% 151.67/22.17    (6)   ~ (e1 = e0)
% 151.67/22.17    (7)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.67/22.17         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.67/22.17    (8)  op(e1, e1) = e3
% 151.67/22.17    (9)   ~ (e3 = e2)
% 151.67/22.17    (10)  all_56_7 = e0
% 151.67/22.17    (11)   ~ (e2 = e1)
% 151.67/22.17  
% 151.67/22.17  Begin of proof
% 151.67/22.17  | 
% 151.67/22.17  | BETA: splitting (4) gives:
% 151.67/22.17  | 
% 151.67/22.17  | Case 1:
% 151.67/22.17  | | 
% 151.67/22.17  | |   (12)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 151.67/22.17  | |           e1)
% 151.67/22.17  | | 
% 151.67/22.17  | | BETA: splitting (12) gives:
% 151.67/22.17  | | 
% 151.67/22.17  | | Case 1:
% 151.67/22.17  | | | 
% 151.67/22.17  | | |   (13)  all_56_6 = e1 & op(e1, e3) = e1
% 151.67/22.17  | | | 
% 151.67/22.17  | | | ALPHA: (13) implies:
% 151.67/22.17  | | |   (14)  all_56_6 = e1
% 151.67/22.17  | | | 
% 151.67/22.17  | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (11), (14) are inconsistent
% 151.67/22.17  | | |            by sub-proof #146.
% 151.67/22.17  | | | 
% 151.67/22.17  | | Case 2:
% 151.67/22.17  | | | 
% 151.67/22.17  | | |   (15)  all_56_7 = e1 & op(e1, e2) = e1
% 151.67/22.17  | | | 
% 151.67/22.17  | | | REF_CLOSE: (6), (10), (15) are inconsistent by sub-proof #1111.
% 151.67/22.17  | | | 
% 151.67/22.17  | | End of split
% 151.67/22.17  | | 
% 151.67/22.17  | Case 2:
% 151.67/22.17  | | 
% 151.67/22.17  | |   (16)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 151.67/22.17  | |           e1)
% 151.67/22.17  | | 
% 151.67/22.17  | | BETA: splitting (16) gives:
% 151.67/22.17  | | 
% 151.67/22.17  | | Case 1:
% 151.67/22.17  | | | 
% 151.67/22.17  | | |   (17)  all_56_8 = e1 & op(e1, e1) = e1
% 151.67/22.17  | | | 
% 151.67/22.17  | | | ALPHA: (17) implies:
% 151.67/22.17  | | |   (18)  op(e1, e1) = e1
% 151.67/22.17  | | | 
% 151.67/22.17  | | | REF_CLOSE: (1), (3), (8), (18) are inconsistent by sub-proof #734.
% 151.67/22.17  | | | 
% 151.67/22.17  | | Case 2:
% 151.67/22.17  | | | 
% 151.67/22.17  | | |   (19)  all_56_11 = e1 & op(e1, e0) = e1
% 151.67/22.17  | | | 
% 151.67/22.17  | | | REF_CLOSE: (5), (6), (19) are inconsistent by sub-proof #805.
% 151.67/22.17  | | | 
% 151.67/22.17  | | End of split
% 151.67/22.17  | | 
% 151.67/22.17  | End of split
% 151.67/22.17  | 
% 151.67/22.17  End of proof
% 151.67/22.17  
% 151.67/22.17  Sub-proof #146 shows that the following formulas are inconsistent:
% 151.67/22.17  ----------------------------------------------------------------
% 151.67/22.17    (1)   ~ (e2 = e0)
% 151.67/22.17    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.17    (3)  all_56_6 = e1
% 151.67/22.17    (4)  all_56_11 = e0
% 151.67/22.17    (5)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.67/22.17         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.67/22.17    (6)  op(e1, e1) = e3
% 151.67/22.17    (7)   ~ (e3 = e2)
% 151.67/22.17    (8)  all_56_7 = e0
% 151.67/22.17    (9)   ~ (e2 = e1)
% 151.67/22.17  
% 151.67/22.17  Begin of proof
% 151.67/22.17  | 
% 151.67/22.17  | BETA: splitting (5) gives:
% 151.67/22.17  | 
% 151.67/22.17  | Case 1:
% 151.67/22.17  | | 
% 151.67/22.17  | |   (10)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 151.67/22.17  | |           e2)
% 151.67/22.17  | | 
% 151.67/22.17  | | BETA: splitting (10) gives:
% 151.67/22.17  | | 
% 151.67/22.17  | | Case 1:
% 151.67/22.17  | | | 
% 151.67/22.17  | | |   (11)  all_56_6 = e2 & op(e1, e3) = e2
% 151.67/22.17  | | | 
% 151.67/22.17  | | | REF_CLOSE: (3), (9), (11) are inconsistent by sub-proof #837.
% 151.67/22.17  | | | 
% 151.67/22.17  | | Case 2:
% 151.67/22.17  | | | 
% 151.67/22.17  | | |   (12)  all_56_7 = e2 & op(e1, e2) = e2
% 151.67/22.17  | | | 
% 151.67/22.17  | | | REF_CLOSE: (1), (8), (12) are inconsistent by sub-proof #740.
% 151.67/22.17  | | | 
% 151.67/22.17  | | End of split
% 151.67/22.17  | | 
% 151.67/22.17  | Case 2:
% 151.67/22.17  | | 
% 151.67/22.17  | |   (13)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 151.67/22.17  | |           e2)
% 151.67/22.17  | | 
% 151.67/22.17  | | BETA: splitting (13) gives:
% 151.67/22.17  | | 
% 151.67/22.17  | | Case 1:
% 151.67/22.17  | | | 
% 151.67/22.17  | | |   (14)  all_56_8 = e2 & op(e1, e1) = e2
% 151.67/22.17  | | | 
% 151.67/22.17  | | | ALPHA: (14) implies:
% 151.67/22.17  | | |   (15)  op(e1, e1) = e2
% 151.67/22.17  | | | 
% 151.67/22.17  | | | REF_CLOSE: (2), (6), (7), (15) are inconsistent by sub-proof #834.
% 151.67/22.17  | | | 
% 151.67/22.17  | | Case 2:
% 151.67/22.17  | | | 
% 151.67/22.17  | | |   (16)  all_56_11 = e2 & op(e1, e0) = e2
% 151.67/22.17  | | | 
% 151.67/22.17  | | | REF_CLOSE: (1), (4), (16) are inconsistent by sub-proof #459.
% 151.67/22.17  | | | 
% 151.67/22.17  | | End of split
% 151.67/22.17  | | 
% 151.67/22.17  | End of split
% 151.67/22.17  | 
% 151.67/22.17  End of proof
% 151.67/22.17  
% 151.67/22.17  Sub-proof #147 shows that the following formulas are inconsistent:
% 151.67/22.17  ----------------------------------------------------------------
% 151.67/22.17    (1)  all_56_10 = e3
% 151.67/22.17    (2)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 151.67/22.17         (all_56_11 = e0 & op(e1, e0) = e0)
% 151.67/22.17    (3)   ~ (e2 = e0)
% 151.67/22.17    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.17    (5)   ~ (e3 = e0)
% 151.67/22.17    (6)  op(e1, e1) = e3
% 151.67/22.17    (7)   ~ (e3 = e2)
% 151.67/22.17    (8)  all_56_9 = e2
% 151.67/22.17    (9)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.67/22.17  
% 151.67/22.17  Begin of proof
% 151.67/22.17  | 
% 151.67/22.17  | BETA: splitting (9) gives:
% 151.67/22.17  | 
% 151.67/22.17  | Case 1:
% 151.67/22.17  | | 
% 151.67/22.17  | |   (10)  all_56_8 = e2 & op(e1, e1) = e2
% 151.67/22.17  | | 
% 151.67/22.17  | | ALPHA: (10) implies:
% 151.67/22.17  | |   (11)  op(e1, e1) = e2
% 151.67/22.17  | | 
% 151.67/22.17  | | REF_CLOSE: (4), (6), (7), (11) are inconsistent by sub-proof #834.
% 151.67/22.17  | | 
% 151.67/22.17  | Case 2:
% 151.67/22.17  | | 
% 151.67/22.17  | |   (12)  all_56_11 = e2 & op(e1, e0) = e2
% 151.67/22.17  | | 
% 151.67/22.17  | | ALPHA: (12) implies:
% 151.67/22.17  | |   (13)  all_56_11 = e2
% 151.67/22.17  | | 
% 151.67/22.17  | | REF_CLOSE: (1), (2), (3), (5), (8), (13) are inconsistent by sub-proof #154.
% 151.67/22.17  | | 
% 151.67/22.17  | End of split
% 151.67/22.17  | 
% 151.67/22.17  End of proof
% 151.67/22.17  
% 151.67/22.17  Sub-proof #148 shows that the following formulas are inconsistent:
% 151.67/22.17  ----------------------------------------------------------------
% 151.67/22.17    (1)  op(e0, e1) = all_52_11
% 151.67/22.17    (2)  all_56_8 = e3
% 151.67/22.18    (3)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.67/22.18    (4)   ~ (e3 = e1)
% 151.67/22.18    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.67/22.18         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.67/22.18    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.67/22.18         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.67/22.18    (7)  all_56_7 = e1
% 151.67/22.18    (8)  op(e0, e2) = all_52_7
% 151.67/22.18    (9)   ~ (all_52_3 = all_52_7)
% 151.67/22.18    (10)  all_54_14 = all_52_11
% 151.67/22.18    (11)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.18          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.67/22.18    (12)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.18          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.18    (13)  all_56_5 = e1
% 151.67/22.18    (14)   ~ (e2 = e0)
% 151.67/22.18    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.18    (16)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.67/22.18          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.67/22.18    (17)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.67/22.18          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.67/22.18    (18)  op(e0, e3) = e0
% 151.67/22.18    (19)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 151.67/22.18            all_57_14 & $i(all_57_14))
% 151.67/22.18    (20)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.18          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 151.67/22.18            e3)
% 151.67/22.18    (21)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 151.67/22.18              e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.67/22.18            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 151.67/22.18             ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 151.67/22.18              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 151.67/22.18            (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.67/22.18            all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 151.67/22.18            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 151.67/22.18            = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 151.67/22.18          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 151.67/22.18              e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 151.67/22.18            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 151.67/22.18             ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 151.67/22.18              e1) = e0 & $i(all_57_7))
% 151.67/22.18    (22)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 151.67/22.18    (23)   ~ (e3 = e0)
% 151.67/22.18    (24)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.18          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.18    (25)   ~ (all_52_11 = e0)
% 151.67/22.18    (26)   ~ (all_52_6 = e3)
% 151.67/22.18    (27)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.67/22.18          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.67/22.18    (28)  op(e3, e3) = e1
% 151.67/22.18    (29)  op(e1, e2) = all_52_6
% 151.67/22.18    (30)   ~ (all_52_9 = e2)
% 151.67/22.18    (31)  op(e0, e1) = e2
% 151.67/22.18    (32)  op(e0, e3) = all_52_3
% 151.67/22.18    (33)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.18          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.18    (34)  op(e2, e2) = e2
% 151.67/22.18    (35)  op(e2, e1) = all_52_9
% 151.67/22.18    (36)   ~ (e1 = e0)
% 151.67/22.18    (37)  op(e1, e1) = e3
% 151.67/22.18    (38)  op(e0, e0) = all_57_15
% 151.67/22.18    (39)   ~ (e3 = e2)
% 151.67/22.18    (40)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.18          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.67/22.18    (41)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.18          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.18    (42)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.67/22.18          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.67/22.18    (43)   ~ (e2 = e1)
% 151.67/22.18    (44)   ~ (all_52_11 = e1)
% 151.67/22.18    (45)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.18          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.18    (46)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.18          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.18    (47)  op(e2, e3) = all_52_1
% 151.67/22.18    (48)   ~ (all_52_1 = e2)
% 151.67/22.18  
% 151.67/22.18  Begin of proof
% 151.67/22.18  | 
% 151.67/22.18  | BETA: splitting (22) gives:
% 151.67/22.18  | 
% 151.67/22.18  | Case 1:
% 151.67/22.18  | | 
% 151.67/22.18  | |   (49)  all_56_2 = e3 & op(e2, e3) = e3
% 151.67/22.18  | | 
% 151.67/22.18  | | ALPHA: (49) implies:
% 151.67/22.18  | |   (50)  all_56_2 = e3
% 151.67/22.18  | | 
% 151.67/22.18  | | BETA: splitting (17) gives:
% 151.67/22.18  | | 
% 151.67/22.18  | | Case 1:
% 151.67/22.18  | | | 
% 151.67/22.18  | | |   (51)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) =
% 151.67/22.18  | | |           e2)
% 151.67/22.18  | | | 
% 151.67/22.18  | | | REF_CLOSE: (12), (13), (14), (15), (23), (30), (31), (35), (36), (37),
% 151.67/22.18  | | |            (51) are inconsistent by sub-proof #149.
% 151.67/22.18  | | | 
% 151.67/22.18  | | Case 2:
% 151.67/22.18  | | | 
% 151.67/22.18  | | |   (52)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) =
% 151.67/22.18  | | |           e2)
% 151.67/22.18  | | | 
% 151.67/22.18  | | | BETA: splitting (52) gives:
% 151.67/22.18  | | | 
% 151.67/22.18  | | | Case 1:
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | |   (53)  all_56_8 = e2 & op(e1, e1) = e2
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | | ALPHA: (53) implies:
% 151.67/22.18  | | | |   (54)  op(e1, e1) = e2
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | | REF_CLOSE: (15), (37), (39), (54) are inconsistent by sub-proof #834.
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | Case 2:
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | |   (55)  all_56_14 = e2 & op(e0, e1) = e2
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | | ALPHA: (55) implies:
% 151.67/22.18  | | | |   (56)  all_56_14 = e2
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | | BETA: splitting (16) gives:
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | | Case 1:
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | |   (57)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3,
% 151.67/22.18  | | | | |             e2) = e3)
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | | BETA: splitting (57) gives:
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | | Case 1:
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | |   (58)  all_56_0 = e3 & op(e3, e3) = e3
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | | ALPHA: (58) implies:
% 151.67/22.18  | | | | | |   (59)  op(e3, e3) = e3
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | | REF_CLOSE: (4), (15), (28), (59) are inconsistent by sub-proof
% 151.67/22.18  | | | | | |            #1178.
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | Case 2:
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | |   (60)  all_56_1 = e3 & op(e3, e2) = e3
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | | ALPHA: (60) implies:
% 151.67/22.18  | | | | | |   (61)  all_56_1 = e3
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | | BETA: splitting (20) gives:
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | | Case 1:
% 151.67/22.18  | | | | | | | 
% 151.67/22.18  | | | | | | |   (62)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 &
% 151.67/22.18  | | | | | | |           op(e0, e2) = e3)
% 151.67/22.18  | | | | | | | 
% 151.67/22.18  | | | | | | | BETA: splitting (62) gives:
% 151.67/22.18  | | | | | | | 
% 151.67/22.18  | | | | | | | Case 1:
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | |   (63)  all_56_12 = e3 & op(e0, e3) = e3
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | | ALPHA: (63) implies:
% 151.67/22.18  | | | | | | | |   (64)  all_56_12 = e3
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | | BETA: splitting (27) gives:
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | | Case 1:
% 151.67/22.18  | | | | | | | | | 
% 151.67/22.18  | | | | | | | | |   (65)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 &
% 151.67/22.18  | | | | | | | | |           op(e2, e3) = e2)
% 151.67/22.18  | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | REF_CLOSE: (15), (28), (43), (47), (48), (65) are inconsistent
% 151.67/22.18  | | | | | | | | |            by sub-proof #938.
% 151.67/22.18  | | | | | | | | | 
% 151.67/22.18  | | | | | | | | Case 2:
% 151.67/22.18  | | | | | | | | | 
% 151.67/22.18  | | | | | | | | |   (66)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 &
% 151.67/22.18  | | | | | | | | |           op(e0, e3) = e2)
% 151.67/22.18  | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | BETA: splitting (66) gives:
% 151.67/22.18  | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | Case 1:
% 151.67/22.18  | | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | |   (67)  all_56_6 = e2 & op(e1, e3) = e2
% 151.67/22.18  | | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | | ALPHA: (67) implies:
% 151.67/22.18  | | | | | | | | | |   (68)  all_56_6 = e2
% 151.67/22.18  | | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | | REF_CLOSE: (4), (5), (14), (23), (24), (36), (43), (50),
% 151.67/22.18  | | | | | | | | | |            (64), (68) are inconsistent by sub-proof #162.
% 151.67/22.18  | | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | Case 2:
% 151.67/22.18  | | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | |   (69)  all_56_12 = e2 & op(e0, e3) = e2
% 151.67/22.18  | | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | | ALPHA: (69) implies:
% 151.67/22.18  | | | | | | | | | |   (70)  all_56_12 = e2
% 151.67/22.18  | | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | | COMBINE_EQS: (64), (70) imply:
% 151.67/22.18  | | | | | | | | | |   (71)  e3 = e2
% 151.67/22.18  | | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | | COMBINE_EQS: (61), (71) imply:
% 151.67/22.18  | | | | | | | | | |   (72)  all_56_1 = e2
% 151.67/22.18  | | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | | REF_CLOSE: (4), (14), (15), (23), (26), (29), (34), (36),
% 151.67/22.18  | | | | | | | | | |            (39), (41), (43), (45), (46), (72) are
% 151.67/22.18  | | | | | | | | | |            inconsistent by sub-proof #921.
% 151.67/22.18  | | | | | | | | | | 
% 151.67/22.18  | | | | | | | | | End of split
% 151.67/22.18  | | | | | | | | | 
% 151.67/22.18  | | | | | | | | End of split
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | Case 2:
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | |   (73)  all_56_13 = e3 & op(e0, e2) = e3
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | | ALPHA: (73) implies:
% 151.67/22.18  | | | | | | | |   (74)  all_56_13 = e3
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | | REF_CLOSE: (7), (14), (15), (23), (34), (36), (41), (61), (74)
% 151.67/22.18  | | | | | | | |            are inconsistent by sub-proof #879.
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | End of split
% 151.67/22.18  | | | | | | | 
% 151.67/22.18  | | | | | | Case 2:
% 151.67/22.18  | | | | | | | 
% 151.67/22.18  | | | | | | |   (75)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 &
% 151.67/22.18  | | | | | | |           op(e0, e0) = e3)
% 151.67/22.18  | | | | | | | 
% 151.67/22.18  | | | | | | | BETA: splitting (75) gives:
% 151.67/22.18  | | | | | | | 
% 151.67/22.18  | | | | | | | Case 1:
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | |   (76)  all_56_14 = e3 & op(e0, e1) = e3
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | | REF_CLOSE: (4), (14), (15), (23), (26), (29), (34), (36), (39),
% 151.67/22.18  | | | | | | | |            (41), (43), (45), (46), (56), (61), (76) are
% 151.67/22.18  | | | | | | | |            inconsistent by sub-proof #180.
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | Case 2:
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | |   (77)  all_56_15 = e3 & op(e0, e0) = e3
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | | ALPHA: (77) implies:
% 151.67/22.18  | | | | | | | |   (78)  op(e0, e0) = e3
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | | REF_CLOSE: (8), (9), (14), (15), (18), (19), (21), (31), (32),
% 151.67/22.18  | | | | | | | |            (34), (38), (43), (78) are inconsistent by sub-proof
% 151.67/22.18  | | | | | | | |            #298.
% 151.67/22.18  | | | | | | | | 
% 151.67/22.18  | | | | | | | End of split
% 151.67/22.18  | | | | | | | 
% 151.67/22.18  | | | | | | End of split
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | End of split
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | Case 2:
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | |   (79)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3,
% 151.67/22.18  | | | | |             e0) = e3)
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | | BETA: splitting (79) gives:
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | | Case 1:
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | |   (80)  all_56_4 = e3 & op(e3, e1) = e3
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | | ALPHA: (80) implies:
% 151.67/22.18  | | | | | |   (81)  all_56_4 = e3
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | | REF_CLOSE: (2), (4), (11), (12), (14), (15), (23), (33), (34), (36),
% 151.67/22.18  | | | | | |            (39), (40), (42), (43), (50), (56), (81) are inconsistent
% 151.67/22.18  | | | | | |            by sub-proof #312.
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | Case 2:
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | |   (82)  all_56_9 = e3 & op(e3, e0) = e3
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | | ALPHA: (82) implies:
% 151.67/22.18  | | | | | |   (83)  all_56_9 = e3
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | | REF_CLOSE: (1), (3), (4), (6), (10), (12), (13), (14), (15), (23),
% 151.67/22.18  | | | | | |            (25), (26), (28), (29), (34), (36), (37), (39), (41),
% 151.67/22.18  | | | | | |            (43), (44), (45), (46), (83) are inconsistent by
% 151.67/22.18  | | | | | |            sub-proof #150.
% 151.67/22.18  | | | | | | 
% 151.67/22.18  | | | | | End of split
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | End of split
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | End of split
% 151.67/22.18  | | | 
% 151.67/22.18  | | End of split
% 151.67/22.18  | | 
% 151.67/22.18  | Case 2:
% 151.67/22.18  | | 
% 151.67/22.18  | |   (84)  all_56_3 = e3 & op(e2, e2) = e3
% 151.67/22.18  | | 
% 151.67/22.18  | | ALPHA: (84) implies:
% 151.67/22.18  | |   (85)  op(e2, e2) = e3
% 151.67/22.18  | | 
% 151.67/22.18  | | REF_CLOSE: (15), (34), (39), (85) are inconsistent by sub-proof #1179.
% 151.67/22.18  | | 
% 151.67/22.18  | End of split
% 151.67/22.18  | 
% 151.67/22.18  End of proof
% 151.67/22.18  
% 151.67/22.18  Sub-proof #149 shows that the following formulas are inconsistent:
% 151.67/22.18  ----------------------------------------------------------------
% 151.67/22.18    (1)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2)
% 151.67/22.18    (2)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.18         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.18    (3)  all_56_5 = e1
% 151.67/22.18    (4)   ~ (e2 = e0)
% 151.67/22.18    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.18    (6)   ~ (e3 = e0)
% 151.67/22.18    (7)   ~ (all_52_9 = e2)
% 151.67/22.18    (8)  op(e0, e1) = e2
% 151.67/22.18    (9)  op(e2, e1) = all_52_9
% 151.67/22.18    (10)   ~ (e1 = e0)
% 151.67/22.18    (11)  op(e1, e1) = e3
% 151.67/22.18  
% 151.67/22.18  Begin of proof
% 151.67/22.18  | 
% 151.67/22.18  | BETA: splitting (1) gives:
% 151.67/22.18  | 
% 151.67/22.18  | Case 1:
% 151.67/22.18  | | 
% 151.67/22.18  | |   (12)  all_56_4 = e2 & op(e3, e1) = e2
% 151.67/22.18  | | 
% 151.67/22.18  | | ALPHA: (12) implies:
% 151.67/22.18  | |   (13)  all_56_4 = e2
% 151.67/22.18  | | 
% 151.67/22.18  | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (10), (11), (13) are inconsistent
% 151.67/22.18  | |            by sub-proof #221.
% 151.67/22.18  | | 
% 151.67/22.18  | Case 2:
% 151.67/22.18  | | 
% 151.67/22.18  | |   (14)  all_56_5 = e2 & op(e2, e1) = e2
% 151.67/22.18  | | 
% 151.67/22.18  | | ALPHA: (14) implies:
% 151.67/22.18  | |   (15)  op(e2, e1) = e2
% 151.67/22.18  | | 
% 151.67/22.18  | | REF_CLOSE: (5), (7), (9), (15) are inconsistent by sub-proof #1157.
% 151.67/22.18  | | 
% 151.67/22.18  | End of split
% 151.67/22.18  | 
% 151.67/22.18  End of proof
% 151.67/22.18  
% 151.67/22.18  Sub-proof #150 shows that the following formulas are inconsistent:
% 151.67/22.18  ----------------------------------------------------------------
% 151.67/22.18    (1)  op(e0, e1) = all_52_11
% 151.67/22.18    (2)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 151.67/22.18    (3)   ~ (e3 = e1)
% 151.67/22.18    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.67/22.18         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.67/22.18    (5)  all_56_9 = e3
% 151.67/22.18    (6)  all_54_14 = all_52_11
% 151.67/22.18    (7)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.18         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.18    (8)  all_56_5 = e1
% 151.67/22.18    (9)   ~ (e2 = e0)
% 151.67/22.18    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.18    (11)   ~ (e3 = e0)
% 151.67/22.18    (12)   ~ (all_52_11 = e0)
% 151.67/22.18    (13)   ~ (all_52_6 = e3)
% 151.67/22.18    (14)  op(e3, e3) = e1
% 151.67/22.18    (15)  op(e1, e2) = all_52_6
% 151.67/22.18    (16)  op(e2, e2) = e2
% 151.67/22.18    (17)   ~ (e1 = e0)
% 151.67/22.18    (18)  op(e1, e1) = e3
% 151.67/22.18    (19)   ~ (e3 = e2)
% 151.67/22.18    (20)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.18          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.18    (21)   ~ (e2 = e1)
% 151.67/22.18    (22)   ~ (all_52_11 = e1)
% 151.67/22.18    (23)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.18          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.18    (24)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.18          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.18  
% 151.67/22.18  Begin of proof
% 151.67/22.18  | 
% 151.67/22.18  | BETA: splitting (4) gives:
% 151.67/22.18  | 
% 151.67/22.18  | Case 1:
% 151.67/22.18  | | 
% 151.67/22.18  | |   (25)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) =
% 151.67/22.18  | |           e2)
% 151.67/22.18  | | 
% 151.67/22.18  | | REF_CLOSE: (3), (9), (10), (11), (13), (14), (15), (16), (17), (19), (20),
% 151.67/22.18  | |            (21), (23), (24), (25) are inconsistent by sub-proof #156.
% 151.67/22.18  | | 
% 151.67/22.18  | Case 2:
% 151.67/22.18  | | 
% 151.67/22.18  | |   (26)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 151.67/22.18  | |           e2)
% 151.67/22.18  | | 
% 151.67/22.18  | | BETA: splitting (26) gives:
% 151.67/22.18  | | 
% 151.67/22.18  | | Case 1:
% 151.67/22.18  | | | 
% 151.67/22.18  | | |   (27)  all_56_4 = e2 & op(e3, e1) = e2
% 151.67/22.18  | | | 
% 151.67/22.18  | | | ALPHA: (27) implies:
% 151.67/22.18  | | |   (28)  all_56_4 = e2
% 151.67/22.18  | | | 
% 151.67/22.18  | | | BETA: splitting (2) gives:
% 151.67/22.18  | | | 
% 151.67/22.18  | | | Case 1:
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | |   (29)  all_54_14 = e2
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | | COMBINE_EQS: (6), (29) imply:
% 151.67/22.18  | | | |   (30)  all_52_11 = e2
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | | SIMP: (30) implies:
% 151.67/22.18  | | | |   (31)  all_52_11 = e2
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | | REDUCE: (1), (31) imply:
% 151.67/22.18  | | | |   (32)  op(e0, e1) = e2
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | | REF_CLOSE: (7), (8), (9), (10), (11), (17), (18), (28), (32) are
% 151.67/22.18  | | | |            inconsistent by sub-proof #221.
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | Case 2:
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | |   (33)  all_54_14 = e1 | all_54_14 = e0
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | | BETA: splitting (33) gives:
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | | Case 1:
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | |   (34)  all_54_14 = e1
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | | REF_CLOSE: (6), (22), (34) are inconsistent by sub-proof #753.
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | Case 2:
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | |   (35)  all_54_14 = e0
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | | REF_CLOSE: (6), (12), (35) are inconsistent by sub-proof #886.
% 151.67/22.18  | | | | | 
% 151.67/22.18  | | | | End of split
% 151.67/22.18  | | | | 
% 151.67/22.18  | | | End of split
% 151.67/22.18  | | | 
% 151.67/22.18  | | Case 2:
% 151.67/22.18  | | | 
% 151.67/22.18  | | |   (36)  all_56_9 = e2 & op(e3, e0) = e2
% 151.67/22.18  | | | 
% 151.67/22.18  | | | ALPHA: (36) implies:
% 151.67/22.18  | | |   (37)  all_56_9 = e2
% 151.67/22.18  | | | 
% 151.67/22.18  | | | REF_CLOSE: (5), (19), (37) are inconsistent by sub-proof #964.
% 151.67/22.18  | | | 
% 151.67/22.18  | | End of split
% 151.67/22.18  | | 
% 151.67/22.18  | End of split
% 151.67/22.18  | 
% 151.67/22.18  End of proof
% 151.67/22.18  
% 151.67/22.18  Sub-proof #151 shows that the following formulas are inconsistent:
% 151.67/22.18  ----------------------------------------------------------------
% 151.67/22.18    (1)  all_56_8 = e3
% 151.67/22.18    (2)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 151.67/22.18         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 151.67/22.18    (3)  all_56_15 = e1
% 151.67/22.18    (4)   ~ (e3 = e1)
% 151.67/22.18    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.67/22.18         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.67/22.18    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 151.67/22.18         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 151.67/22.18    (7)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.18         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.67/22.18    (8)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.18         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.18    (9)   ~ (e2 = e0)
% 151.67/22.18    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.18    (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.67/22.18          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.67/22.18    (12)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.67/22.18          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.67/22.18    (13)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.67/22.18          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.67/22.18    (14)   ~ (all_52_9 = e3)
% 151.67/22.18    (15)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.18              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 151.67/22.18                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.67/22.18                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.67/22.18    (16)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.18          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 151.67/22.18            e3)
% 151.67/22.18    (17)  op(e0, e0) = e1
% 151.67/22.18    (18)   ~ (e3 = e0)
% 151.67/22.18    (19)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.18          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.18    (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 151.67/22.18          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.18    (21)   ~ (all_52_6 = e3)
% 151.67/22.18    (22)  op(e3, e3) = e1
% 151.67/22.18    (23)  all_56_4 = e1
% 151.67/22.18    (24)  op(e1, e2) = all_52_6
% 151.67/22.18    (25)   ~ (all_52_9 = e2)
% 151.67/22.18    (26)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.18          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.18    (27)  op(e2, e2) = e2
% 151.67/22.18    (28)  op(e2, e1) = all_52_9
% 151.67/22.18    (29)   ~ (e1 = e0)
% 151.67/22.18    (30)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.67/22.18          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.67/22.18    (31)  op(e1, e1) = e3
% 151.67/22.18    (32)   ~ (e3 = e2)
% 151.67/22.18    (33)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.67/22.18          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 151.67/22.18            e2)
% 151.67/22.18    (34)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.18          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.67/22.18    (35)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.18          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.18    (36)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.67/22.18          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.67/22.18    (37)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 151.67/22.18          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.67/22.19    (38)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.67/22.19          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.67/22.19    (39)   ~ (e2 = e1)
% 151.67/22.19    (40)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.19          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.19    (41)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.19          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.19    (42)   ~ (all_52_6 = e2)
% 151.67/22.19  
% 151.67/22.19  Begin of proof
% 151.67/22.19  | 
% 151.67/22.19  | BETA: splitting (13) gives:
% 151.67/22.19  | 
% 151.67/22.19  | Case 1:
% 151.67/22.19  | | 
% 151.67/22.19  | |   (43)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) =
% 151.67/22.19  | |           e2)
% 151.67/22.19  | | 
% 151.67/22.19  | | BETA: splitting (43) gives:
% 151.67/22.19  | | 
% 151.67/22.19  | | Case 1:
% 151.67/22.19  | | | 
% 151.67/22.19  | | |   (44)  all_56_4 = e2 & op(e3, e1) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | ALPHA: (44) implies:
% 151.67/22.19  | | |   (45)  all_56_4 = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | REF_CLOSE: (23), (39), (45) are inconsistent by sub-proof #980.
% 151.67/22.19  | | | 
% 151.67/22.19  | | Case 2:
% 151.67/22.19  | | | 
% 151.67/22.19  | | |   (46)  all_56_5 = e2 & op(e2, e1) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | ALPHA: (46) implies:
% 151.67/22.19  | | |   (47)  op(e2, e1) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | REF_CLOSE: (10), (25), (28), (47) are inconsistent by sub-proof #1157.
% 151.67/22.19  | | | 
% 151.67/22.19  | | End of split
% 151.67/22.19  | | 
% 151.67/22.19  | Case 2:
% 151.67/22.19  | | 
% 151.67/22.19  | |   (48)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) =
% 151.67/22.19  | |           e2)
% 151.67/22.19  | | 
% 151.67/22.19  | | BETA: splitting (48) gives:
% 151.67/22.19  | | 
% 151.67/22.19  | | Case 1:
% 151.67/22.19  | | | 
% 151.67/22.19  | | |   (49)  all_56_8 = e2 & op(e1, e1) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | ALPHA: (49) implies:
% 151.67/22.19  | | |   (50)  op(e1, e1) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | REF_CLOSE: (10), (31), (32), (50) are inconsistent by sub-proof #834.
% 151.67/22.19  | | | 
% 151.67/22.19  | | Case 2:
% 151.67/22.19  | | | 
% 151.67/22.19  | | |   (51)  all_56_14 = e2 & op(e0, e1) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | ALPHA: (51) implies:
% 151.67/22.19  | | |   (52)  all_56_14 = e2
% 151.67/22.19  | | |   (53)  op(e0, e1) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | BETA: splitting (34) gives:
% 151.67/22.19  | | | 
% 151.67/22.19  | | | Case 1:
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | |   (54)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2)
% 151.67/22.19  | | | |           = e1)
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | | BETA: splitting (54) gives:
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | | Case 1:
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | |   (55)  all_56_2 = e1 & op(e2, e3) = e1
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | ALPHA: (55) implies:
% 151.67/22.19  | | | | |   (56)  all_56_2 = e1
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | BETA: splitting (5) gives:
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | Case 1:
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | |   (57)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3,
% 151.67/22.19  | | | | | |             e2) = e2)
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | | REF_CLOSE: (4), (9), (10), (18), (21), (22), (24), (27), (29), (32),
% 151.67/22.19  | | | | | |            (35), (39), (40), (41), (57) are inconsistent by
% 151.67/22.19  | | | | | |            sub-proof #156.
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | Case 2:
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | |   (58)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3,
% 151.67/22.19  | | | | | |             e0) = e2)
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | | BETA: splitting (58) gives:
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | | Case 1:
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | |   (59)  all_56_4 = e2 & op(e3, e1) = e2
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | ALPHA: (59) implies:
% 151.67/22.19  | | | | | | |   (60)  all_56_4 = e2
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12),
% 151.67/22.19  | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (22), (24),
% 151.67/22.19  | | | | | | |            (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 151.67/22.19  | | | | | | |            (34), (35), (36), (38), (39), (40), (41), (42), (56),
% 151.67/22.19  | | | | | | |            (60) are inconsistent by sub-proof #152.
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | Case 2:
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | |   (61)  all_56_9 = e2 & op(e3, e0) = e2
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | ALPHA: (61) implies:
% 151.67/22.19  | | | | | | |   (62)  all_56_9 = e2
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | BETA: splitting (11) gives:
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | Case 1:
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | |   (63)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 &
% 151.67/22.19  | | | | | | | |           op(e3, e2) = e3)
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | | BETA: splitting (63) gives:
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | | Case 1:
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | |   (64)  all_56_0 = e3 & op(e3, e3) = e3
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | ALPHA: (64) implies:
% 151.67/22.19  | | | | | | | | |   (65)  op(e3, e3) = e3
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | REF_CLOSE: (4), (10), (22), (65) are inconsistent by sub-proof
% 151.67/22.19  | | | | | | | | |            #1178.
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | Case 2:
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | |   (66)  all_56_1 = e3 & op(e3, e2) = e3
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | ALPHA: (66) implies:
% 151.67/22.19  | | | | | | | | |   (67)  all_56_1 = e3
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | REF_CLOSE: (9), (10), (18), (20), (22), (23), (29), (62), (67)
% 151.67/22.19  | | | | | | | | |            are inconsistent by sub-proof #566.
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | End of split
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | Case 2:
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | |   (68)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 &
% 151.67/22.19  | | | | | | | |           op(e3, e0) = e3)
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | | REF_CLOSE: (1), (4), (8), (9), (10), (18), (29), (31), (32),
% 151.67/22.19  | | | | | | | |            (36), (39), (52), (53), (62), (68) are inconsistent
% 151.67/22.19  | | | | | | | |            by sub-proof #353.
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | End of split
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | End of split
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | End of split
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | Case 2:
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | |   (69)  all_56_3 = e1 & op(e2, e2) = e1
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | ALPHA: (69) implies:
% 151.67/22.19  | | | | |   (70)  op(e2, e2) = e1
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | REF_CLOSE: (10), (27), (39), (70) are inconsistent by sub-proof #1158.
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | End of split
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | Case 2:
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | |   (71)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0)
% 151.67/22.19  | | | |           = e1)
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | | BETA: splitting (71) gives:
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | | Case 1:
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | |   (72)  all_56_5 = e1 & op(e2, e1) = e1
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | ALPHA: (72) implies:
% 151.67/22.19  | | | | |   (73)  all_56_5 = e1
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | BETA: splitting (8) gives:
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | Case 1:
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | |   (74)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2,
% 151.67/22.19  | | | | | |             e1) = e0)
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | | BETA: splitting (74) gives:
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | | Case 1:
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | |   (75)  all_56_4 = e0 & op(e3, e1) = e0
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | ALPHA: (75) implies:
% 151.67/22.19  | | | | | | |   (76)  all_56_4 = e0
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | REF_CLOSE: (23), (29), (76) are inconsistent by sub-proof #657.
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | Case 2:
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | |   (77)  all_56_5 = e0 & op(e2, e1) = e0
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | ALPHA: (77) implies:
% 151.67/22.19  | | | | | | |   (78)  all_56_5 = e0
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | REF_CLOSE: (29), (73), (78) are inconsistent by sub-proof #682.
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | End of split
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | Case 2:
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | |   (79)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0,
% 151.67/22.19  | | | | | |             e1) = e0)
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | | REF_CLOSE: (9), (10), (18), (31), (53), (79) are inconsistent by
% 151.67/22.19  | | | | | |            sub-proof #222.
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | End of split
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | Case 2:
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | |   (80)  all_56_10 = e1 & op(e2, e0) = e1
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | ALPHA: (80) implies:
% 151.67/22.19  | | | | |   (81)  all_56_10 = e1
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | REF_CLOSE: (2), (4), (9), (10), (15), (17), (18), (29), (32), (37),
% 151.67/22.19  | | | | |            (39), (81) are inconsistent by sub-proof #445.
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | End of split
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | End of split
% 151.67/22.19  | | | 
% 151.67/22.19  | | End of split
% 151.67/22.19  | | 
% 151.67/22.19  | End of split
% 151.67/22.19  | 
% 151.67/22.19  End of proof
% 151.67/22.19  
% 151.67/22.19  Sub-proof #152 shows that the following formulas are inconsistent:
% 151.67/22.19  ----------------------------------------------------------------
% 151.67/22.19    (1)  all_56_8 = e3
% 151.67/22.19    (2)  all_56_15 = e1
% 151.67/22.19    (3)   ~ (e3 = e1)
% 151.67/22.19    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 151.67/22.19         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 151.67/22.19    (5)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.19         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.67/22.19    (6)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.19         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.19    (7)   ~ (e2 = e0)
% 151.67/22.19    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.19    (9)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.67/22.19         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.67/22.19    (10)  all_56_4 = e2
% 151.67/22.19    (11)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.67/22.19          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.67/22.19    (12)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.67/22.19          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.67/22.19    (13)   ~ (all_52_9 = e3)
% 151.67/22.19    (14)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.19              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 151.67/22.19                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.67/22.19                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.67/22.19    (15)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.19          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 151.67/22.19            e3)
% 151.67/22.19    (16)  op(e0, e0) = e1
% 151.67/22.19    (17)   ~ (e3 = e0)
% 151.67/22.19    (18)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.19          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.19    (19)  op(e3, e3) = e1
% 151.67/22.19    (20)  op(e1, e2) = all_52_6
% 151.67/22.19    (21)   ~ (all_52_9 = e2)
% 151.67/22.19    (22)  all_56_2 = e1
% 151.67/22.19    (23)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.19          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.19    (24)  op(e2, e2) = e2
% 151.67/22.19    (25)  op(e2, e1) = all_52_9
% 151.67/22.19    (26)   ~ (e1 = e0)
% 151.67/22.19    (27)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.67/22.19          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.67/22.19    (28)  op(e1, e1) = e3
% 151.67/22.19    (29)   ~ (e3 = e2)
% 151.67/22.19    (30)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.67/22.19          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 151.67/22.19            e2)
% 151.67/22.19    (31)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.19          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.67/22.19    (32)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.19          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.19    (33)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.67/22.19          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.67/22.19    (34)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.67/22.19          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.67/22.19    (35)   ~ (e2 = e1)
% 151.67/22.19    (36)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.19          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.19    (37)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.19          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.19    (38)   ~ (all_52_6 = e2)
% 151.67/22.19  
% 151.67/22.19  Begin of proof
% 151.67/22.19  | 
% 151.67/22.19  | BETA: splitting (30) gives:
% 151.67/22.19  | 
% 151.67/22.19  | Case 1:
% 151.67/22.19  | | 
% 151.67/22.19  | |   (39)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 151.67/22.19  | |           e2)
% 151.67/22.19  | | 
% 151.67/22.19  | | BETA: splitting (39) gives:
% 151.67/22.19  | | 
% 151.67/22.19  | | Case 1:
% 151.67/22.19  | | | 
% 151.67/22.19  | | |   (40)  all_56_12 = e2 & op(e0, e3) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | ALPHA: (40) implies:
% 151.67/22.19  | | |   (41)  all_56_12 = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | BETA: splitting (23) gives:
% 151.67/22.19  | | | 
% 151.67/22.19  | | | Case 1:
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | |   (42)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2)
% 151.67/22.19  | | | |           = e3)
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | | REF_CLOSE: (3), (8), (22), (24), (29), (42) are inconsistent by
% 151.67/22.19  | | | |            sub-proof #163.
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | Case 2:
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | |   (43)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0)
% 151.67/22.19  | | | |           = e3)
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | | BETA: splitting (43) gives:
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | | Case 1:
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | |   (44)  all_56_5 = e3 & op(e2, e1) = e3
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | REF_CLOSE: (8), (13), (25), (44) are inconsistent by sub-proof #647.
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | Case 2:
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | |   (45)  all_56_10 = e3 & op(e2, e0) = e3
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | ALPHA: (45) implies:
% 151.67/22.19  | | | | |   (46)  all_56_10 = e3
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | BETA: splitting (15) gives:
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | | Case 1:
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | |   (47)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 &
% 151.67/22.19  | | | | | |           op(e0, e2) = e3)
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | | BETA: splitting (47) gives:
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | | Case 1:
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | |   (48)  all_56_12 = e3 & op(e0, e3) = e3
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | ALPHA: (48) implies:
% 151.67/22.19  | | | | | | |   (49)  all_56_12 = e3
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | REF_CLOSE: (29), (41), (49) are inconsistent by sub-proof #869.
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | Case 2:
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | |   (50)  all_56_13 = e3 & op(e0, e2) = e3
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | ALPHA: (50) implies:
% 151.67/22.19  | | | | | | |   (51)  all_56_13 = e3
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | BETA: splitting (27) gives:
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | | Case 1:
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | |   (52)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 &
% 151.67/22.19  | | | | | | | |           op(e1, e2) = e2)
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | | BETA: splitting (52) gives:
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | | Case 1:
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | |   (53)  all_56_6 = e2 & op(e1, e3) = e2
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | ALPHA: (53) implies:
% 151.67/22.19  | | | | | | | | |   (54)  all_56_6 = e2
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (11), (17), (18), (19),
% 151.67/22.19  | | | | | | | | |            (26), (27), (28), (29), (34), (35), (41), (54) are
% 151.67/22.19  | | | | | | | | |            inconsistent by sub-proof #155.
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | Case 2:
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | |   (55)  all_56_7 = e2 & op(e1, e2) = e2
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | ALPHA: (55) implies:
% 151.67/22.19  | | | | | | | | |   (56)  op(e1, e2) = e2
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | REF_CLOSE: (8), (20), (38), (56) are inconsistent by sub-proof
% 151.67/22.19  | | | | | | | | |            #1171.
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | End of split
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | Case 2:
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | |   (57)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 &
% 151.67/22.19  | | | | | | | |           op(e1, e0) = e2)
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | | BETA: splitting (57) gives:
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | | Case 1:
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | |   (58)  all_56_8 = e2 & op(e1, e1) = e2
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | ALPHA: (58) implies:
% 151.67/22.19  | | | | | | | | |   (59)  op(e1, e1) = e2
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | REF_CLOSE: (8), (28), (29), (59) are inconsistent by sub-proof
% 151.67/22.19  | | | | | | | | |            #834.
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | Case 2:
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | |   (60)  all_56_11 = e2 & op(e1, e0) = e2
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | ALPHA: (60) implies:
% 151.67/22.19  | | | | | | | | |   (61)  all_56_11 = e2
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | BETA: splitting (9) gives:
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | Case 1:
% 151.67/22.19  | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | |   (62)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 &
% 151.67/22.19  | | | | | | | | | |           op(e3, e2) = e3)
% 151.67/22.19  | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | REF_CLOSE: (3), (7), (8), (17), (19), (24), (26), (32), (35),
% 151.67/22.19  | | | | | | | | | |            (36), (51), (62) are inconsistent by sub-proof
% 151.67/22.19  | | | | | | | | | |            #876.
% 151.67/22.19  | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | Case 2:
% 151.67/22.19  | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | |   (63)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 &
% 151.67/22.19  | | | | | | | | | |           op(e3, e0) = e3)
% 151.67/22.19  | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | BETA: splitting (63) gives:
% 151.67/22.19  | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | Case 1:
% 151.67/22.19  | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | |   (64)  all_56_4 = e3 & op(e3, e1) = e3
% 151.67/22.19  | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | ALPHA: (64) implies:
% 151.67/22.19  | | | | | | | | | | |   (65)  all_56_4 = e3
% 151.67/22.19  | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | REF_CLOSE: (3), (7), (8), (12), (14), (16), (17), (21), (24),
% 151.67/22.19  | | | | | | | | | | |            (25), (26), (28), (29), (32), (35), (36), (37),
% 151.67/22.19  | | | | | | | | | | |            (41), (51), (65) are inconsistent by sub-proof
% 151.67/22.19  | | | | | | | | | | |            #359.
% 151.67/22.19  | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | Case 2:
% 151.67/22.19  | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | |   (66)  all_56_9 = e3 & op(e3, e0) = e3
% 151.67/22.19  | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | ALPHA: (66) implies:
% 151.67/22.19  | | | | | | | | | | |   (67)  all_56_9 = e3
% 151.67/22.19  | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | BETA: splitting (4) gives:
% 151.67/22.19  | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | Case 1:
% 151.67/22.19  | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | |   (68)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 151.67/22.19  | | | | | | | | | | | |           & op(e2, e3) = e3)
% 151.67/22.19  | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | REF_CLOSE: (3), (5), (7), (8), (17), (19), (24), (26), (31),
% 151.67/22.19  | | | | | | | | | | | |            (35), (46), (68) are inconsistent by sub-proof
% 151.67/22.19  | | | | | | | | | | | |            #278.
% 151.67/22.19  | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | Case 2:
% 151.67/22.19  | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | |   (69)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 151.67/22.19  | | | | | | | | | | | |           e3 & op(e0, e3) = e3)
% 151.67/22.19  | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | BETA: splitting (69) gives:
% 151.67/22.19  | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | Case 1:
% 151.67/22.19  | | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | |   (70)  all_56_6 = e3 & op(e1, e3) = e3
% 151.67/22.19  | | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | | ALPHA: (70) implies:
% 151.67/22.19  | | | | | | | | | | | | |   (71)  all_56_6 = e3
% 151.67/22.19  | | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | | REF_CLOSE: (1), (3), (7), (11), (17), (26), (34), (35), (61),
% 151.67/22.19  | | | | | | | | | | | | |            (71) are inconsistent by sub-proof #608.
% 151.67/22.19  | | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | Case 2:
% 151.67/22.19  | | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | |   (72)  all_56_12 = e3 & op(e0, e3) = e3
% 151.67/22.19  | | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | | ALPHA: (72) implies:
% 151.67/22.19  | | | | | | | | | | | | |   (73)  all_56_12 = e3
% 151.67/22.19  | | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | | COMBINE_EQS: (41), (73) imply:
% 151.67/22.19  | | | | | | | | | | | | |   (74)  e3 = e2
% 151.67/22.19  | | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | | SIMP: (74) implies:
% 151.67/22.19  | | | | | | | | | | | | |   (75)  e3 = e2
% 151.67/22.19  | | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | | COMBINE_EQS: (67), (75) imply:
% 151.67/22.19  | | | | | | | | | | | | |   (76)  all_56_9 = e2
% 151.67/22.19  | | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | | REF_CLOSE: (2), (7), (14), (17), (26), (46), (61), (76) are
% 151.67/22.19  | | | | | | | | | | | | |            inconsistent by sub-proof #153.
% 151.67/22.19  | | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | | End of split
% 151.67/22.19  | | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | | End of split
% 151.67/22.19  | | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | | End of split
% 151.67/22.19  | | | | | | | | | | 
% 151.67/22.19  | | | | | | | | | End of split
% 151.67/22.19  | | | | | | | | | 
% 151.67/22.19  | | | | | | | | End of split
% 151.67/22.19  | | | | | | | | 
% 151.67/22.19  | | | | | | | End of split
% 151.67/22.19  | | | | | | | 
% 151.67/22.19  | | | | | | End of split
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | Case 2:
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | |   (77)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 &
% 151.67/22.19  | | | | | |           op(e0, e0) = e3)
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | | REF_CLOSE: (3), (6), (7), (8), (10), (16), (17), (26), (28), (33),
% 151.67/22.19  | | | | | |            (35), (77) are inconsistent by sub-proof #159.
% 151.67/22.19  | | | | | | 
% 151.67/22.19  | | | | | End of split
% 151.67/22.19  | | | | | 
% 151.67/22.19  | | | | End of split
% 151.67/22.19  | | | | 
% 151.67/22.19  | | | End of split
% 151.67/22.19  | | | 
% 151.67/22.19  | | Case 2:
% 151.67/22.19  | | | 
% 151.67/22.19  | | |   (78)  all_56_13 = e2 & op(e0, e2) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | ALPHA: (78) implies:
% 151.67/22.19  | | |   (79)  all_56_13 = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | REF_CLOSE: (3), (7), (8), (17), (24), (26), (29), (32), (35), (36), (37),
% 151.67/22.19  | | |            (79) are inconsistent by sub-proof #1104.
% 151.67/22.19  | | | 
% 151.67/22.19  | | End of split
% 151.67/22.19  | | 
% 151.67/22.19  | Case 2:
% 151.67/22.19  | | 
% 151.67/22.19  | |   (80)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 151.67/22.19  | |           e2)
% 151.67/22.19  | | 
% 151.67/22.19  | | BETA: splitting (80) gives:
% 151.67/22.19  | | 
% 151.67/22.19  | | Case 1:
% 151.67/22.19  | | | 
% 151.67/22.19  | | |   (81)  all_56_14 = e2 & op(e0, e1) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | REF_CLOSE: (3), (6), (7), (8), (10), (17), (26), (28), (33), (35), (81)
% 151.67/22.19  | | |            are inconsistent by sub-proof #217.
% 151.67/22.19  | | | 
% 151.67/22.19  | | Case 2:
% 151.67/22.19  | | | 
% 151.67/22.19  | | |   (82)  all_56_15 = e2 & op(e0, e0) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | ALPHA: (82) implies:
% 151.67/22.19  | | |   (83)  op(e0, e0) = e2
% 151.67/22.19  | | | 
% 151.67/22.19  | | | REF_CLOSE: (8), (16), (35), (83) are inconsistent by sub-proof #978.
% 151.67/22.19  | | | 
% 151.67/22.19  | | End of split
% 151.67/22.19  | | 
% 151.67/22.19  | End of split
% 151.67/22.19  | 
% 151.67/22.19  End of proof
% 151.67/22.19  
% 151.67/22.19  Sub-proof #153 shows that the following formulas are inconsistent:
% 151.67/22.19  ----------------------------------------------------------------
% 151.67/22.19    (1)  all_56_15 = e1
% 151.67/22.19    (2)  all_56_10 = e3
% 151.67/22.19    (3)  all_56_11 = e2
% 151.67/22.19    (4)   ~ (e2 = e0)
% 151.67/22.19    (5)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.19             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 151.67/22.19               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.67/22.19               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.67/22.19    (6)   ~ (e3 = e0)
% 151.67/22.19    (7)   ~ (e1 = e0)
% 151.67/22.19    (8)  all_56_9 = e2
% 151.67/22.19  
% 151.67/22.19  Begin of proof
% 151.67/22.19  | 
% 151.67/22.19  | BETA: splitting (5) gives:
% 151.67/22.19  | 
% 151.67/22.19  | Case 1:
% 151.67/22.19  | | 
% 151.67/22.19  | |   (9)  all_56_15 = e0 & op(e0, e0) = e0
% 151.67/22.19  | | 
% 151.67/22.19  | | REF_CLOSE: (1), (7), (9) are inconsistent by sub-proof #409.
% 151.67/22.19  | | 
% 151.67/22.19  | Case 2:
% 151.67/22.19  | | 
% 151.67/22.19  | |   (10)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 151.67/22.19  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 151.67/22.19  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 151.67/22.19  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 151.67/22.19  | | 
% 151.67/22.19  | | ALPHA: (10) implies:
% 151.67/22.19  | |   (11)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 151.67/22.19  | |           e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.67/22.19  | | 
% 151.67/22.19  | | REF_CLOSE: (2), (3), (4), (6), (8), (11) are inconsistent by sub-proof #154.
% 151.67/22.19  | | 
% 151.67/22.19  | End of split
% 151.67/22.19  | 
% 151.67/22.19  End of proof
% 151.67/22.19  
% 151.67/22.19  Sub-proof #154 shows that the following formulas are inconsistent:
% 151.67/22.19  ----------------------------------------------------------------
% 151.67/22.19    (1)  all_56_10 = e3
% 151.67/22.19    (2)  all_56_11 = e2
% 151.67/22.19    (3)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 151.67/22.19         (all_56_11 = e0 & op(e1, e0) = e0)
% 151.67/22.19    (4)   ~ (e2 = e0)
% 151.67/22.19    (5)   ~ (e3 = e0)
% 151.67/22.19    (6)  all_56_9 = e2
% 151.67/22.19  
% 151.67/22.19  Begin of proof
% 151.67/22.19  | 
% 151.67/22.19  | BETA: splitting (3) gives:
% 151.67/22.19  | 
% 151.67/22.19  | Case 1:
% 151.67/22.19  | | 
% 151.67/22.19  | |   (7)  all_56_9 = e0 & op(e3, e0) = e0
% 151.67/22.19  | | 
% 151.67/22.19  | | ALPHA: (7) implies:
% 151.67/22.19  | |   (8)  all_56_9 = e0
% 151.67/22.19  | | 
% 151.67/22.19  | | REF_CLOSE: (4), (6), (8) are inconsistent by sub-proof #776.
% 151.67/22.19  | | 
% 151.67/22.19  | Case 2:
% 151.67/22.19  | | 
% 151.67/22.19  | |   (9)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 151.67/22.19  | |          e0)
% 151.67/22.19  | | 
% 151.67/22.19  | | BETA: splitting (9) gives:
% 151.67/22.19  | | 
% 151.67/22.19  | | Case 1:
% 151.67/22.19  | | | 
% 151.67/22.19  | | |   (10)  all_56_10 = e0 & op(e2, e0) = e0
% 151.67/22.19  | | | 
% 151.67/22.19  | | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #749.
% 151.67/22.19  | | | 
% 151.67/22.19  | | Case 2:
% 151.67/22.19  | | | 
% 151.67/22.19  | | |   (11)  all_56_11 = e0 & op(e1, e0) = e0
% 151.67/22.19  | | | 
% 151.67/22.19  | | | REF_CLOSE: (2), (4), (11) are inconsistent by sub-proof #322.
% 151.67/22.19  | | | 
% 151.67/22.19  | | End of split
% 151.67/22.19  | | 
% 151.67/22.19  | End of split
% 151.67/22.19  | 
% 151.67/22.19  End of proof
% 151.67/22.19  
% 151.67/22.19  Sub-proof #155 shows that the following formulas are inconsistent:
% 151.67/22.19  ----------------------------------------------------------------
% 151.67/22.19    (1)  all_56_8 = e3
% 151.67/22.19    (2)   ~ (e3 = e1)
% 151.67/22.19    (3)  all_56_6 = e2
% 151.67/22.19    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 151.67/22.19         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 151.67/22.19    (5)   ~ (e2 = e0)
% 151.67/22.20    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.20    (7)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.67/22.20         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.67/22.20    (8)   ~ (e3 = e0)
% 151.67/22.20    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.20         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.20    (10)  op(e3, e3) = e1
% 151.67/22.20    (11)   ~ (e1 = e0)
% 151.67/22.20    (12)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.67/22.20          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.67/22.20    (13)  op(e1, e1) = e3
% 151.67/22.20    (14)   ~ (e3 = e2)
% 151.67/22.20    (15)  all_56_12 = e2
% 151.67/22.20    (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.67/22.20          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.67/22.20    (17)   ~ (e2 = e1)
% 151.67/22.20  
% 151.67/22.20  Begin of proof
% 151.67/22.20  | 
% 151.67/22.20  | BETA: splitting (4) gives:
% 151.67/22.20  | 
% 151.67/22.20  | Case 1:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (18)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 151.67/22.20  | |           e3)
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (15), (18) are
% 151.67/22.20  | |            inconsistent by sub-proof #870.
% 151.67/22.20  | | 
% 151.67/22.20  | Case 2:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (19)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 151.67/22.20  | |           e3)
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (11), (12), (13), (14), (15), (16),
% 151.67/22.20  | |            (17), (19) are inconsistent by sub-proof #427.
% 151.67/22.20  | | 
% 151.67/22.20  | End of split
% 151.67/22.20  | 
% 151.67/22.20  End of proof
% 151.67/22.20  
% 151.67/22.20  Sub-proof #156 shows that the following formulas are inconsistent:
% 151.67/22.20  ----------------------------------------------------------------
% 151.67/22.20    (1)   ~ (e3 = e1)
% 151.67/22.20    (2)   ~ (e2 = e0)
% 151.67/22.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.20    (4)   ~ (e3 = e0)
% 151.67/22.20    (5)   ~ (all_52_6 = e3)
% 151.67/22.20    (6)  op(e3, e3) = e1
% 151.67/22.20    (7)  op(e1, e2) = all_52_6
% 151.67/22.20    (8)  op(e2, e2) = e2
% 151.67/22.20    (9)   ~ (e1 = e0)
% 151.67/22.20    (10)   ~ (e3 = e2)
% 151.67/22.20    (11)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.20          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.20    (12)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2)
% 151.67/22.20    (13)   ~ (e2 = e1)
% 151.67/22.20    (14)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.20          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.20    (15)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.20          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.20  
% 151.67/22.20  Begin of proof
% 151.67/22.20  | 
% 151.67/22.20  | BETA: splitting (12) gives:
% 151.67/22.20  | 
% 151.67/22.20  | Case 1:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (16)  all_56_0 = e2 & op(e3, e3) = e2
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (16) implies:
% 151.67/22.20  | |   (17)  op(e3, e3) = e2
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (3), (6), (13), (17) are inconsistent by sub-proof #1074.
% 151.67/22.20  | | 
% 151.67/22.20  | Case 2:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (18)  all_56_1 = e2 & op(e3, e2) = e2
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (18) implies:
% 151.67/22.20  | |   (19)  all_56_1 = e2
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 151.67/22.20  | |            (15), (19) are inconsistent by sub-proof #921.
% 151.67/22.20  | | 
% 151.67/22.20  | End of split
% 151.67/22.20  | 
% 151.67/22.20  End of proof
% 151.67/22.20  
% 151.67/22.20  Sub-proof #157 shows that the following formulas are inconsistent:
% 151.67/22.20  ----------------------------------------------------------------
% 151.67/22.20    (1)   ~ (e3 = e1)
% 151.67/22.20    (2)   ~ (e2 = e0)
% 151.67/22.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.20    (4)  op(e1, e3) = e1
% 151.67/22.20    (5)   ~ (e3 = e0)
% 151.67/22.20    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.20         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.20    (7)  op(e3, e3) = e1
% 151.67/22.20    (8)   ~ (e1 = e0)
% 151.67/22.20    (9)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 151.67/22.20    (10)  all_56_12 = e2
% 151.67/22.20    (11)  op(e1, e3) = all_52_2
% 151.67/22.20  
% 151.67/22.20  Begin of proof
% 151.67/22.20  | 
% 151.67/22.20  | BETA: splitting (9) gives:
% 151.67/22.20  | 
% 151.67/22.20  | Case 1:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (12)  all_56_0 = e3 & op(e3, e3) = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (12) implies:
% 151.67/22.20  | |   (13)  op(e3, e3) = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (1), (3), (7), (13) are inconsistent by sub-proof #1178.
% 151.67/22.20  | | 
% 151.67/22.20  | Case 2:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (14)  all_56_2 = e3 & op(e2, e3) = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (14) implies:
% 151.67/22.20  | |   (15)  all_56_2 = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (15) are
% 151.67/22.20  | |            inconsistent by sub-proof #551.
% 151.67/22.20  | | 
% 151.67/22.20  | End of split
% 151.67/22.20  | 
% 151.67/22.20  End of proof
% 151.67/22.20  
% 151.67/22.20  Sub-proof #158 shows that the following formulas are inconsistent:
% 151.67/22.20  ----------------------------------------------------------------
% 151.67/22.20    (1)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 151.67/22.20    (2)   ~ (e3 = e1)
% 151.67/22.20    (3)   ~ (e2 = e0)
% 151.67/22.20    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.20    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.67/22.20         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.67/22.20    (6)  all_56_4 = e2
% 151.67/22.20    (7)  op(e3, e3) = e2
% 151.67/22.20    (8)   ~ (e3 = e0)
% 151.67/22.20    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 151.67/22.20         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.20    (10)   ~ (e1 = e0)
% 151.67/22.20    (11)   ~ (e3 = e2)
% 151.67/22.20    (12)   ~ (all_52_8 = e3)
% 151.67/22.20    (13)  op(e3, e1) = all_52_8
% 151.67/22.20    (14)   ~ (e2 = e1)
% 151.67/22.20  
% 151.67/22.20  Begin of proof
% 151.67/22.20  | 
% 151.67/22.20  | BETA: splitting (1) gives:
% 151.67/22.20  | 
% 151.67/22.20  | Case 1:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (15)  all_56_4 = e1 & op(e3, e1) = e1
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (6), (14), (15) are inconsistent by sub-proof #1066.
% 151.67/22.20  | | 
% 151.67/22.20  | Case 2:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (16)  all_56_9 = e1 & op(e3, e0) = e1
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (16) implies:
% 151.67/22.20  | |   (17)  all_56_9 = e1
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 151.67/22.20  | |            (17) are inconsistent by sub-proof #484.
% 151.67/22.20  | | 
% 151.67/22.20  | End of split
% 151.67/22.20  | 
% 151.67/22.20  End of proof
% 151.67/22.20  
% 151.67/22.20  Sub-proof #159 shows that the following formulas are inconsistent:
% 151.67/22.20  ----------------------------------------------------------------
% 151.67/22.20    (1)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 151.67/22.20    (2)   ~ (e3 = e1)
% 151.67/22.20    (3)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.20         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.20    (4)   ~ (e2 = e0)
% 151.67/22.20    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.20    (6)  all_56_4 = e2
% 151.67/22.20    (7)  op(e0, e0) = e1
% 151.67/22.20    (8)   ~ (e3 = e0)
% 151.67/22.20    (9)   ~ (e1 = e0)
% 151.67/22.20    (10)  op(e1, e1) = e3
% 151.67/22.20    (11)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.67/22.20          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.67/22.20    (12)   ~ (e2 = e1)
% 151.67/22.20  
% 151.67/22.20  Begin of proof
% 151.67/22.20  | 
% 151.67/22.20  | BETA: splitting (1) gives:
% 151.67/22.20  | 
% 151.67/22.20  | Case 1:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (13)  all_56_14 = e3 & op(e0, e1) = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (13) implies:
% 151.67/22.20  | |   (14)  all_56_14 = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | BETA: splitting (3) gives:
% 151.67/22.20  | | 
% 151.67/22.20  | | Case 1:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (15)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 151.67/22.20  | | |           e0)
% 151.67/22.20  | | | 
% 151.67/22.20  | | | BETA: splitting (15) gives:
% 151.67/22.20  | | | 
% 151.67/22.20  | | | Case 1:
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | |   (16)  all_56_4 = e0 & op(e3, e1) = e0
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | | REF_CLOSE: (4), (6), (16) are inconsistent by sub-proof #1070.
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | Case 2:
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | |   (17)  all_56_5 = e0 & op(e2, e1) = e0
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | | ALPHA: (17) implies:
% 151.67/22.20  | | | |   (18)  all_56_5 = e0
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | | BETA: splitting (11) gives:
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | | Case 1:
% 151.67/22.20  | | | | | 
% 151.67/22.20  | | | | |   (19)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2,
% 151.67/22.20  | | | | |             e1) = e1)
% 151.67/22.20  | | | | | 
% 151.67/22.20  | | | | | BETA: splitting (19) gives:
% 151.67/22.20  | | | | | 
% 151.67/22.20  | | | | | Case 1:
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | |   (20)  all_56_4 = e1 & op(e3, e1) = e1
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | | REF_CLOSE: (6), (12), (20) are inconsistent by sub-proof #1066.
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | Case 2:
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | |   (21)  all_56_5 = e1 & op(e2, e1) = e1
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | | REF_CLOSE: (9), (18), (21) are inconsistent by sub-proof #334.
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | End of split
% 151.67/22.20  | | | | | 
% 151.67/22.20  | | | | Case 2:
% 151.67/22.20  | | | | | 
% 151.67/22.20  | | | | |   (22)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0,
% 151.67/22.20  | | | | |             e1) = e1)
% 151.67/22.20  | | | | | 
% 151.67/22.20  | | | | | BETA: splitting (22) gives:
% 151.67/22.20  | | | | | 
% 151.67/22.20  | | | | | Case 1:
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | |   (23)  all_56_8 = e1 & op(e1, e1) = e1
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | | ALPHA: (23) implies:
% 151.67/22.20  | | | | | |   (24)  op(e1, e1) = e1
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | | REF_CLOSE: (2), (5), (10), (24) are inconsistent by sub-proof #734.
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | Case 2:
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | |   (25)  all_56_14 = e1 & op(e0, e1) = e1
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | | REF_CLOSE: (2), (14), (25) are inconsistent by sub-proof #188.
% 151.67/22.20  | | | | | | 
% 151.67/22.20  | | | | | End of split
% 151.67/22.20  | | | | | 
% 151.67/22.20  | | | | End of split
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | End of split
% 151.67/22.20  | | | 
% 151.67/22.20  | | Case 2:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (26)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 151.67/22.20  | | |           e0)
% 151.67/22.20  | | | 
% 151.67/22.20  | | | BETA: splitting (26) gives:
% 151.67/22.20  | | | 
% 151.67/22.20  | | | Case 1:
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | |   (27)  all_56_8 = e0 & op(e1, e1) = e0
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | | ALPHA: (27) implies:
% 151.67/22.20  | | | |   (28)  op(e1, e1) = e0
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | | REF_CLOSE: (5), (8), (10), (28) are inconsistent by sub-proof #896.
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | Case 2:
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | |   (29)  all_56_14 = e0 & op(e0, e1) = e0
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | | REF_CLOSE: (8), (14), (29) are inconsistent by sub-proof #469.
% 151.67/22.20  | | | | 
% 151.67/22.20  | | | End of split
% 151.67/22.20  | | | 
% 151.67/22.20  | | End of split
% 151.67/22.20  | | 
% 151.67/22.20  | Case 2:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (30)  all_56_15 = e3 & op(e0, e0) = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (30) implies:
% 151.67/22.20  | |   (31)  op(e0, e0) = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (2), (5), (7), (31) are inconsistent by sub-proof #1022.
% 151.67/22.20  | | 
% 151.67/22.20  | End of split
% 151.67/22.20  | 
% 151.67/22.20  End of proof
% 151.67/22.20  
% 151.67/22.20  Sub-proof #160 shows that the following formulas are inconsistent:
% 151.67/22.20  ----------------------------------------------------------------
% 151.67/22.20    (1)  all_56_1 = e1
% 151.67/22.20    (2)  all_56_7 = e1
% 151.67/22.20    (3)   ~ (e2 = e0)
% 151.67/22.20    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.20    (5)   ~ (e3 = e0)
% 151.67/22.20    (6)  op(e2, e2) = e2
% 151.67/22.20    (7)   ~ (e1 = e0)
% 151.67/22.20    (8)  all_56_13 = e3
% 151.67/22.20    (9)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.20         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.20  
% 151.67/22.20  Begin of proof
% 151.67/22.20  | 
% 151.67/22.20  | BETA: splitting (9) gives:
% 151.67/22.20  | 
% 151.67/22.20  | Case 1:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (10)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 151.67/22.20  | |           e0)
% 151.67/22.20  | | 
% 151.67/22.20  | | BETA: splitting (10) gives:
% 151.67/22.20  | | 
% 151.67/22.20  | | Case 1:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (11)  all_56_1 = e0 & op(e3, e2) = e0
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (1), (7), (11) are inconsistent by sub-proof #1072.
% 151.67/22.20  | | | 
% 151.67/22.20  | | Case 2:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (12)  all_56_3 = e0 & op(e2, e2) = e0
% 151.67/22.20  | | | 
% 151.67/22.20  | | | ALPHA: (12) implies:
% 151.67/22.20  | | |   (13)  op(e2, e2) = e0
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (3), (4), (6), (13) are inconsistent by sub-proof #1145.
% 151.67/22.20  | | | 
% 151.67/22.20  | | End of split
% 151.67/22.20  | | 
% 151.67/22.20  | Case 2:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (14)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 151.67/22.20  | |           e0)
% 151.67/22.20  | | 
% 151.67/22.20  | | BETA: splitting (14) gives:
% 151.67/22.20  | | 
% 151.67/22.20  | | Case 1:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (15)  all_56_7 = e0 & op(e1, e2) = e0
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (2), (7), (15) are inconsistent by sub-proof #880.
% 151.67/22.20  | | | 
% 151.67/22.20  | | Case 2:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (16)  all_56_13 = e0 & op(e0, e2) = e0
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (5), (8), (16) are inconsistent by sub-proof #1102.
% 151.67/22.20  | | | 
% 151.67/22.20  | | End of split
% 151.67/22.20  | | 
% 151.67/22.20  | End of split
% 151.67/22.20  | 
% 151.67/22.20  End of proof
% 151.67/22.20  
% 151.67/22.20  Sub-proof #161 shows that the following formulas are inconsistent:
% 151.67/22.20  ----------------------------------------------------------------
% 151.67/22.20    (1)   ~ (e3 = e1)
% 151.67/22.20    (2)  all_56_10 = e3
% 151.67/22.20    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.67/22.20         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.67/22.20    (4)  all_56_6 = e2
% 151.67/22.20    (5)   ~ (e2 = e0)
% 151.67/22.20    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.20    (7)   ~ (all_52_9 = e3)
% 151.67/22.20    (8)   ~ (e3 = e0)
% 151.67/22.20    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.20         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.20    (10)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.20          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.20    (11)  op(e2, e2) = e2
% 151.67/22.20    (12)  op(e2, e1) = all_52_9
% 151.67/22.20    (13)   ~ (e1 = e0)
% 151.67/22.20    (14)   ~ (e3 = e2)
% 151.67/22.20    (15)   ~ (e2 = e1)
% 151.67/22.20    (16)  all_56_12 = e3
% 151.67/22.20    (17)  e3 = e0
% 151.67/22.20  
% 151.67/22.20  Begin of proof
% 151.67/22.20  | 
% 151.67/22.20  | SIMP: (17) implies:
% 151.67/22.20  |   (18)  e3 = e0
% 151.67/22.20  | 
% 151.67/22.20  | COMBINE_EQS: (2), (18) imply:
% 151.67/22.20  |   (19)  all_56_10 = e0
% 151.67/22.20  | 
% 151.67/22.20  | BETA: splitting (10) gives:
% 151.67/22.20  | 
% 151.67/22.20  | Case 1:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (20)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 151.67/22.20  | |           e3)
% 151.67/22.20  | | 
% 151.67/22.20  | | BETA: splitting (20) gives:
% 151.67/22.20  | | 
% 151.67/22.20  | | Case 1:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (21)  all_56_2 = e3 & op(e2, e3) = e3
% 151.67/22.20  | | | 
% 151.67/22.20  | | | ALPHA: (21) implies:
% 151.67/22.20  | | |   (22)  all_56_2 = e3
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (13), (15), (16), (22) are
% 151.67/22.20  | | |            inconsistent by sub-proof #162.
% 151.67/22.20  | | | 
% 151.67/22.20  | | Case 2:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (23)  all_56_3 = e3 & op(e2, e2) = e3
% 151.67/22.20  | | | 
% 151.67/22.20  | | | ALPHA: (23) implies:
% 151.67/22.20  | | |   (24)  op(e2, e2) = e3
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (6), (11), (14), (24) are inconsistent by sub-proof #1179.
% 151.67/22.20  | | | 
% 151.67/22.20  | | End of split
% 151.67/22.20  | | 
% 151.67/22.20  | Case 2:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (25)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 151.67/22.20  | |           e3)
% 151.67/22.20  | | 
% 151.67/22.20  | | BETA: splitting (25) gives:
% 151.67/22.20  | | 
% 151.67/22.20  | | Case 1:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (26)  all_56_5 = e3 & op(e2, e1) = e3
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (6), (7), (12), (26) are inconsistent by sub-proof #647.
% 151.67/22.20  | | | 
% 151.67/22.20  | | Case 2:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (27)  all_56_10 = e3 & op(e2, e0) = e3
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (8), (19), (27) are inconsistent by sub-proof #813.
% 151.67/22.20  | | | 
% 151.67/22.20  | | End of split
% 151.67/22.20  | | 
% 151.67/22.20  | End of split
% 151.67/22.20  | 
% 151.67/22.20  End of proof
% 151.67/22.20  
% 151.67/22.20  Sub-proof #162 shows that the following formulas are inconsistent:
% 151.67/22.20  ----------------------------------------------------------------
% 151.67/22.20    (1)   ~ (e3 = e1)
% 151.67/22.20    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.67/22.20         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.67/22.20    (3)  all_56_6 = e2
% 151.67/22.20    (4)   ~ (e2 = e0)
% 151.67/22.20    (5)   ~ (e3 = e0)
% 151.67/22.20    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.20         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.20    (7)   ~ (e1 = e0)
% 151.67/22.20    (8)   ~ (e2 = e1)
% 151.67/22.20    (9)  all_56_2 = e3
% 151.67/22.20    (10)  all_56_12 = e3
% 151.67/22.20  
% 151.67/22.20  Begin of proof
% 151.67/22.20  | 
% 151.67/22.20  | BETA: splitting (6) gives:
% 151.67/22.20  | 
% 151.67/22.20  | Case 1:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 151.67/22.20  | |           e0)
% 151.67/22.20  | | 
% 151.67/22.20  | | BETA: splitting (11) gives:
% 151.67/22.20  | | 
% 151.67/22.20  | | Case 1:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (12)  all_56_0 = e0 & op(e3, e3) = e0
% 151.67/22.20  | | | 
% 151.67/22.20  | | | ALPHA: (12) implies:
% 151.67/22.20  | | |   (13)  all_56_0 = e0
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (1), (2), (3), (7), (8), (9), (10), (13) are inconsistent by
% 151.67/22.20  | | |            sub-proof #181.
% 151.67/22.20  | | | 
% 151.67/22.20  | | Case 2:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (14)  all_56_2 = e0 & op(e2, e3) = e0
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (5), (9), (14) are inconsistent by sub-proof #932.
% 151.67/22.20  | | | 
% 151.67/22.20  | | End of split
% 151.67/22.20  | | 
% 151.67/22.20  | Case 2:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (15)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 151.67/22.20  | |           e0)
% 151.67/22.20  | | 
% 151.67/22.20  | | BETA: splitting (15) gives:
% 151.67/22.20  | | 
% 151.67/22.20  | | Case 1:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (16)  all_56_6 = e0 & op(e1, e3) = e0
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (3), (4), (16) are inconsistent by sub-proof #1054.
% 151.67/22.20  | | | 
% 151.67/22.20  | | Case 2:
% 151.67/22.20  | | | 
% 151.67/22.20  | | |   (17)  all_56_12 = e0 & op(e0, e3) = e0
% 151.67/22.20  | | | 
% 151.67/22.20  | | | REF_CLOSE: (5), (10), (17) are inconsistent by sub-proof #635.
% 151.67/22.20  | | | 
% 151.67/22.20  | | End of split
% 151.67/22.20  | | 
% 151.67/22.20  | End of split
% 151.67/22.20  | 
% 151.67/22.20  End of proof
% 151.67/22.20  
% 151.67/22.20  Sub-proof #163 shows that the following formulas are inconsistent:
% 151.67/22.20  ----------------------------------------------------------------
% 151.67/22.20    (1)   ~ (e3 = e1)
% 151.67/22.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.20    (3)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 151.67/22.20    (4)  all_56_2 = e1
% 151.67/22.20    (5)  op(e2, e2) = e2
% 151.67/22.20    (6)   ~ (e3 = e2)
% 151.67/22.20  
% 151.67/22.20  Begin of proof
% 151.67/22.20  | 
% 151.67/22.20  | BETA: splitting (3) gives:
% 151.67/22.20  | 
% 151.67/22.20  | Case 1:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (7)  all_56_2 = e3 & op(e2, e3) = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (7) implies:
% 151.67/22.20  | |   (8)  all_56_2 = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #1053.
% 151.67/22.20  | | 
% 151.67/22.20  | Case 2:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (9)  all_56_3 = e3 & op(e2, e2) = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (9) implies:
% 151.67/22.20  | |   (10)  op(e2, e2) = e3
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1179.
% 151.67/22.20  | | 
% 151.67/22.20  | End of split
% 151.67/22.20  | 
% 151.67/22.20  End of proof
% 151.67/22.20  
% 151.67/22.20  Sub-proof #164 shows that the following formulas are inconsistent:
% 151.67/22.20  ----------------------------------------------------------------
% 151.67/22.20    (1)  op(e1, e3) = e2
% 151.67/22.20    (2)  ( ~ (all_12_0 = e0) & op(all_12_1, e1) = all_12_0 & op(e1, e3) = all_12_1
% 151.67/22.20           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e1, e3) =
% 151.67/22.20           all_12_1 & $i(all_12_1))
% 151.67/22.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.20    (4)  op(e2, e1) = e0
% 151.67/22.20    (5)  ( ~ (all_8_0 = e2) & op(all_8_1, e1) = all_8_0 & op(e1, e3) = all_8_1 &
% 151.67/22.20           $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e0) & op(e1, e3) = all_8_1
% 151.67/22.20           & $i(all_8_1))
% 151.67/22.20  
% 151.67/22.20  Begin of proof
% 151.67/22.20  | 
% 151.67/22.20  | BETA: splitting (5) gives:
% 151.67/22.20  | 
% 151.67/22.20  | Case 1:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (6)   ~ (all_8_0 = e2) & op(all_8_1, e1) = all_8_0 & op(e1, e3) = all_8_1
% 151.67/22.20  | |        & $i(all_8_0) & $i(all_8_1)
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (6) implies:
% 151.67/22.20  | |   (7)  op(e1, e3) = all_8_1
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (1), (2), (3), (4), (7) are inconsistent by sub-proof #165.
% 151.67/22.20  | | 
% 151.67/22.20  | Case 2:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (8)   ~ (all_8_1 = e0) & op(e1, e3) = all_8_1 & $i(all_8_1)
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (8) implies:
% 151.67/22.20  | |   (9)  op(e1, e3) = all_8_1
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (1), (2), (3), (4), (9) are inconsistent by sub-proof #165.
% 151.67/22.20  | | 
% 151.67/22.20  | End of split
% 151.67/22.20  | 
% 151.67/22.20  End of proof
% 151.67/22.20  
% 151.67/22.20  Sub-proof #165 shows that the following formulas are inconsistent:
% 151.67/22.20  ----------------------------------------------------------------
% 151.67/22.20    (1)  op(e1, e3) = e2
% 151.67/22.20    (2)  ( ~ (all_12_0 = e0) & op(all_12_1, e1) = all_12_0 & op(e1, e3) = all_12_1
% 151.67/22.20           & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e1, e3) =
% 151.67/22.20           all_12_1 & $i(all_12_1))
% 151.67/22.20    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.20    (4)  op(e2, e1) = e0
% 151.67/22.20    (5)  op(e1, e3) = all_8_1
% 151.67/22.20  
% 151.67/22.20  Begin of proof
% 151.67/22.20  | 
% 151.67/22.20  | BETA: splitting (2) gives:
% 151.67/22.20  | 
% 151.67/22.20  | Case 1:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (6)   ~ (all_12_0 = e0) & op(all_12_1, e1) = all_12_0 & op(e1, e3) =
% 151.67/22.20  | |        all_12_1 & $i(all_12_0) & $i(all_12_1)
% 151.67/22.20  | | 
% 151.67/22.20  | | ALPHA: (6) implies:
% 151.67/22.20  | |   (7)   ~ (all_12_0 = e0)
% 151.67/22.20  | |   (8)  op(e1, e3) = all_12_1
% 151.67/22.20  | |   (9)  op(all_12_1, e1) = all_12_0
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (1), (3), (4), (7), (8), (9) are inconsistent by sub-proof #177.
% 151.67/22.20  | | 
% 151.67/22.20  | Case 2:
% 151.67/22.20  | | 
% 151.67/22.20  | |   (10)   ~ (all_12_1 = e2) & op(e1, e3) = all_12_1 & $i(all_12_1)
% 151.67/22.20  | | 
% 151.67/22.20  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #176.
% 151.67/22.20  | | 
% 151.67/22.20  | End of split
% 151.67/22.21  | 
% 151.67/22.21  End of proof
% 151.67/22.21  
% 151.67/22.21  Sub-proof #166 shows that the following formulas are inconsistent:
% 151.67/22.21  ----------------------------------------------------------------
% 151.67/22.21    (1)   ~ (all_52_6 = e1)
% 151.67/22.21    (2)   ~ (e3 = e1)
% 151.67/22.21    (3)  op(e2, e2) = e1
% 151.67/22.21    (4)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.67/22.21         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.67/22.21    (5)  all_56_10 = e1 & op(e2, e0) = e1
% 151.67/22.21    (6)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.21         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.67/22.21    (7)   ~ (e2 = e0)
% 151.67/22.21    (8)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.67/22.21         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 151.67/22.21    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.21    (10)   ~ (all_52_9 = e3)
% 151.67/22.21    (11)   ~ (e3 = e0)
% 151.67/22.21    (12)   ~ (all_52_6 = e3)
% 151.67/22.21    (13)  op(e1, e2) = all_52_6
% 151.67/22.21    (14)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.21          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.21    (15)  op(e2, e1) = all_52_9
% 151.67/22.21    (16)   ~ (e1 = e0)
% 151.67/22.21    (17)   ~ (e3 = e2)
% 151.67/22.21    (18)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.21          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.67/22.21    (19)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.21          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.21    (20)   ~ (e2 = e1)
% 151.67/22.21    (21)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.21          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.21    (22)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.21          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.21    (23)  op(e2, e3) = all_52_1
% 151.67/22.21  
% 151.67/22.21  Begin of proof
% 151.67/22.21  | 
% 151.67/22.21  | ALPHA: (5) implies:
% 151.67/22.21  |   (24)  all_56_10 = e1
% 151.67/22.21  | 
% 151.67/22.21  | BETA: splitting (21) gives:
% 151.67/22.21  | 
% 151.67/22.21  | Case 1:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (25)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 151.67/22.21  | |           e1)
% 151.67/22.21  | | 
% 151.67/22.21  | | BETA: splitting (25) gives:
% 151.67/22.21  | | 
% 151.67/22.21  | | Case 1:
% 151.67/22.21  | | | 
% 151.67/22.21  | | |   (26)  all_56_1 = e1 & op(e3, e2) = e1
% 151.67/22.21  | | | 
% 151.67/22.21  | | | ALPHA: (26) implies:
% 151.67/22.21  | | |   (27)  all_56_1 = e1
% 151.67/22.21  | | | 
% 151.67/22.21  | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 151.67/22.21  | | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (27) are
% 151.67/22.21  | | |            inconsistent by sub-proof #262.
% 151.67/22.21  | | | 
% 151.67/22.21  | | Case 2:
% 151.67/22.21  | | | 
% 151.67/22.21  | | |   (28)  all_56_3 = e1 & op(e2, e2) = e1
% 151.67/22.21  | | | 
% 151.67/22.21  | | | ALPHA: (28) implies:
% 151.67/22.21  | | |   (29)  all_56_3 = e1
% 151.67/22.21  | | | 
% 151.67/22.21  | | | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (11), (14), (15), (16),
% 151.67/22.21  | | |            (17), (20), (24), (29) are inconsistent by sub-proof #264.
% 151.67/22.21  | | | 
% 151.67/22.21  | | End of split
% 151.67/22.21  | | 
% 151.67/22.21  | Case 2:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (30)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 151.67/22.21  | |           e1)
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 151.67/22.21  | |            (14), (15), (16), (17), (18), (19), (20), (22), (23), (30) are
% 151.67/22.21  | |            inconsistent by sub-proof #173.
% 151.67/22.21  | | 
% 151.67/22.21  | End of split
% 151.67/22.21  | 
% 151.67/22.21  End of proof
% 151.67/22.21  
% 151.67/22.21  Sub-proof #167 shows that the following formulas are inconsistent:
% 151.67/22.21  ----------------------------------------------------------------
% 151.67/22.21    (1)  op(e3, e3) = e0
% 151.67/22.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.21    (3)   ~ (e3 = e0)
% 151.67/22.21    (4)  op(e1, e1) = e3
% 151.67/22.21    (5)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 151.67/22.21             e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 151.67/22.21           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 =
% 151.67/22.21           e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 151.67/22.21           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 151.67/22.21           = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 151.67/22.21  
% 151.67/22.21  Begin of proof
% 151.67/22.21  | 
% 151.67/22.21  | BETA: splitting (5) gives:
% 151.67/22.21  | 
% 151.67/22.21  | Case 1:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (6)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 151.67/22.21  | |          = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0
% 151.67/22.21  | |        & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)
% 151.67/22.21  | | 
% 151.67/22.21  | | ALPHA: (6) implies:
% 151.67/22.21  | |   (7)   ~ (all_57_10 = e0)
% 151.67/22.21  | |   (8)  op(e3, e3) = all_57_10
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (1), (2), (7), (8) are inconsistent by sub-proof #543.
% 151.67/22.21  | | 
% 151.67/22.21  | Case 2:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (9)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 151.67/22.21  | |          = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 151.67/22.21  | |        & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)
% 151.67/22.21  | | 
% 151.67/22.21  | | ALPHA: (9) implies:
% 151.67/22.21  | |   (10)  op(e1, e1) = e0
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #896.
% 151.67/22.21  | | 
% 151.67/22.21  | End of split
% 151.67/22.21  | 
% 151.67/22.21  End of proof
% 151.67/22.21  
% 151.67/22.21  Sub-proof #168 shows that the following formulas are inconsistent:
% 151.67/22.21  ----------------------------------------------------------------
% 151.67/22.21    (1)   ~ (all_52_13 = e1)
% 151.67/22.21    (2)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 151.67/22.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.21    (4)  op(e2, e3) = e2
% 151.67/22.21    (5)   ~ (all_52_13 = e0)
% 151.67/22.21    (6)   ~ (all_52_1 = all_52_13)
% 151.67/22.21    (7)   ~ (all_52_13 = e3)
% 151.67/22.21    (8)  all_54_7 = all_52_13
% 151.67/22.21    (9)  op(e2, e3) = all_52_1
% 151.67/22.21  
% 151.67/22.21  Begin of proof
% 151.67/22.21  | 
% 151.67/22.21  | BETA: splitting (2) gives:
% 151.67/22.21  | 
% 151.67/22.21  | Case 1:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (10)  all_54_7 = e3
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (7), (8), (10) are inconsistent by sub-proof #1163.
% 151.67/22.21  | | 
% 151.67/22.21  | Case 2:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (11)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (11) are inconsistent by
% 151.67/22.21  | |            sub-proof #169.
% 151.67/22.21  | | 
% 151.67/22.21  | End of split
% 151.67/22.21  | 
% 151.67/22.21  End of proof
% 151.67/22.21  
% 151.67/22.21  Sub-proof #169 shows that the following formulas are inconsistent:
% 151.67/22.21  ----------------------------------------------------------------
% 151.67/22.21    (1)   ~ (all_52_13 = e1)
% 151.67/22.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.21    (3)  op(e2, e3) = e2
% 151.67/22.21    (4)   ~ (all_52_13 = e0)
% 151.67/22.21    (5)   ~ (all_52_1 = all_52_13)
% 151.67/22.21    (6)  all_54_7 = all_52_13
% 151.67/22.21    (7)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 151.67/22.21    (8)  op(e2, e3) = all_52_1
% 151.67/22.21  
% 151.67/22.21  Begin of proof
% 151.67/22.21  | 
% 151.67/22.21  | BETA: splitting (7) gives:
% 151.67/22.21  | 
% 151.67/22.21  | Case 1:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (9)  all_54_7 = e2
% 151.67/22.21  | | 
% 151.67/22.21  | | COMBINE_EQS: (6), (9) imply:
% 151.67/22.21  | |   (10)  all_52_13 = e2
% 151.67/22.21  | | 
% 151.67/22.21  | | SIMP: (10) implies:
% 151.67/22.21  | |   (11)  all_52_13 = e2
% 151.67/22.21  | | 
% 151.67/22.21  | | REDUCE: (5), (11) imply:
% 151.67/22.21  | |   (12)   ~ (all_52_1 = e2)
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (2), (3), (8), (12) are inconsistent by sub-proof #1181.
% 151.67/22.21  | | 
% 151.67/22.21  | Case 2:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (13)  all_54_7 = e1 | all_54_7 = e0
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (1), (4), (6), (13) are inconsistent by sub-proof #170.
% 151.67/22.21  | | 
% 151.67/22.21  | End of split
% 151.67/22.21  | 
% 151.67/22.21  End of proof
% 151.67/22.21  
% 151.67/22.21  Sub-proof #170 shows that the following formulas are inconsistent:
% 151.67/22.21  ----------------------------------------------------------------
% 151.67/22.21    (1)  all_54_7 = e1 | all_54_7 = e0
% 151.67/22.21    (2)  all_54_7 = all_52_13
% 151.67/22.21    (3)   ~ (all_52_13 = e1)
% 151.67/22.21    (4)   ~ (all_52_13 = e0)
% 151.67/22.21  
% 151.67/22.21  Begin of proof
% 151.67/22.21  | 
% 151.67/22.21  | BETA: splitting (1) gives:
% 151.67/22.21  | 
% 151.67/22.21  | Case 1:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (5)  all_54_7 = e1
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #495.
% 151.67/22.21  | | 
% 151.67/22.21  | Case 2:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (6)  all_54_7 = e0
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1161.
% 151.67/22.21  | | 
% 151.67/22.21  | End of split
% 151.67/22.21  | 
% 151.67/22.21  End of proof
% 151.67/22.21  
% 151.67/22.21  Sub-proof #171 shows that the following formulas are inconsistent:
% 151.67/22.21  ----------------------------------------------------------------
% 151.67/22.21    (1)  op(e3, e3) = e0
% 151.67/22.21    (2)  op(e3, e2) = all_52_4
% 151.67/22.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.21    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3)
% 151.67/22.21    (5)   ~ (all_52_4 = e3)
% 151.67/22.21    (6)   ~ (e3 = e0)
% 151.67/22.21  
% 151.67/22.21  Begin of proof
% 151.67/22.21  | 
% 151.67/22.21  | BETA: splitting (4) gives:
% 151.67/22.21  | 
% 151.67/22.21  | Case 1:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (7)  all_56_0 = e3 & op(e3, e3) = e3
% 151.67/22.21  | | 
% 151.67/22.21  | | ALPHA: (7) implies:
% 151.67/22.21  | |   (8)  op(e3, e3) = e3
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #1141.
% 151.67/22.21  | | 
% 151.67/22.21  | Case 2:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (9)  all_56_1 = e3 & op(e3, e2) = e3
% 151.67/22.21  | | 
% 151.67/22.21  | | ALPHA: (9) implies:
% 151.67/22.21  | |   (10)  op(e3, e2) = e3
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #1166.
% 151.67/22.21  | | 
% 151.67/22.21  | End of split
% 151.67/22.21  | 
% 151.67/22.21  End of proof
% 151.67/22.21  
% 151.67/22.21  Sub-proof #172 shows that the following formulas are inconsistent:
% 151.67/22.21  ----------------------------------------------------------------
% 151.67/22.21    (1)   ~ (all_52_6 = e1)
% 151.67/22.21    (2)   ~ (e3 = e1)
% 151.67/22.21    (3)  op(e2, e2) = e1
% 151.67/22.21    (4)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.67/22.21         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.67/22.21    (5)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.21         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.67/22.21    (6)   ~ (e2 = e0)
% 151.67/22.21    (7)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.67/22.21         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 151.67/22.21    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.21    (9)  op(e2, e3) = e1
% 151.67/22.21    (10)   ~ (all_52_9 = e3)
% 151.67/22.21    (11)   ~ (e3 = e0)
% 151.67/22.21    (12)   ~ (all_52_6 = e3)
% 151.67/22.21    (13)  op(e1, e2) = all_52_6
% 151.67/22.21    (14)  all_56_2 = e1
% 151.67/22.21    (15)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.21          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.21    (16)  op(e2, e1) = all_52_9
% 151.67/22.21    (17)   ~ (e1 = e0)
% 151.67/22.21    (18)   ~ (e3 = e2)
% 151.67/22.21    (19)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.21          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.67/22.21    (20)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.21          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.21    (21)   ~ (e2 = e1)
% 151.67/22.21    (22)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.21          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.21    (23)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.21          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.21    (24)  op(e2, e3) = all_52_1
% 151.67/22.21  
% 151.67/22.21  Begin of proof
% 151.67/22.21  | 
% 151.67/22.21  | BETA: splitting (22) gives:
% 151.67/22.21  | 
% 151.67/22.21  | Case 1:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (25)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 151.67/22.21  | |           e1)
% 151.67/22.21  | | 
% 151.67/22.21  | | BETA: splitting (25) gives:
% 151.67/22.21  | | 
% 151.67/22.21  | | Case 1:
% 151.67/22.21  | | | 
% 151.67/22.21  | | |   (26)  all_56_1 = e1 & op(e3, e2) = e1
% 151.67/22.21  | | | 
% 151.67/22.21  | | | ALPHA: (26) implies:
% 151.67/22.21  | | |   (27)  all_56_1 = e1
% 151.67/22.21  | | | 
% 151.67/22.21  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 151.67/22.21  | | |            (15), (16), (17), (18), (19), (20), (21), (23), (24), (27) are
% 151.67/22.21  | | |            inconsistent by sub-proof #262.
% 151.67/22.21  | | | 
% 151.67/22.21  | | Case 2:
% 151.67/22.21  | | | 
% 151.67/22.21  | | |   (28)  all_56_3 = e1 & op(e2, e2) = e1
% 151.67/22.21  | | | 
% 151.67/22.21  | | | ALPHA: (28) implies:
% 151.67/22.21  | | |   (29)  all_56_3 = e1
% 151.67/22.21  | | | 
% 151.67/22.21  | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (11), (14), (15),
% 151.67/22.21  | | |            (16), (17), (18), (21), (24), (29) are inconsistent by
% 151.67/22.21  | | |            sub-proof #273.
% 151.67/22.21  | | | 
% 151.67/22.21  | | End of split
% 151.67/22.21  | | 
% 151.67/22.21  | Case 2:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (30)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 151.67/22.21  | |           e1)
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 151.67/22.21  | |            (15), (16), (17), (18), (19), (20), (21), (23), (24), (30) are
% 151.67/22.21  | |            inconsistent by sub-proof #173.
% 151.67/22.21  | | 
% 151.67/22.21  | End of split
% 151.67/22.21  | 
% 151.67/22.21  End of proof
% 151.67/22.21  
% 151.67/22.21  Sub-proof #173 shows that the following formulas are inconsistent:
% 151.67/22.21  ----------------------------------------------------------------
% 151.67/22.21    (1)   ~ (all_52_6 = e1)
% 151.67/22.21    (2)   ~ (e3 = e1)
% 151.67/22.21    (3)  op(e2, e2) = e1
% 151.67/22.21    (4)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.67/22.21         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.67/22.21    (5)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.21         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.67/22.21    (6)   ~ (e2 = e0)
% 151.67/22.21    (7)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 151.67/22.21         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 151.67/22.21    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.21    (9)   ~ (all_52_9 = e3)
% 151.67/22.21    (10)   ~ (e3 = e0)
% 151.67/22.21    (11)   ~ (all_52_6 = e3)
% 151.67/22.21    (12)  op(e1, e2) = all_52_6
% 151.67/22.21    (13)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.21          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.21    (14)  op(e2, e1) = all_52_9
% 151.67/22.21    (15)   ~ (e1 = e0)
% 151.67/22.21    (16)   ~ (e3 = e2)
% 151.67/22.21    (17)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.21          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.67/22.21    (18)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.21          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.21    (19)   ~ (e2 = e1)
% 151.67/22.21    (20)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.21          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.21    (21)  op(e2, e3) = all_52_1
% 151.67/22.21    (22)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.21  
% 151.67/22.21  Begin of proof
% 151.67/22.21  | 
% 151.67/22.21  | BETA: splitting (22) gives:
% 151.67/22.21  | 
% 151.67/22.21  | Case 1:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (23)  all_56_7 = e1 & op(e1, e2) = e1
% 151.67/22.21  | | 
% 151.67/22.21  | | ALPHA: (23) implies:
% 151.67/22.21  | |   (24)  op(e1, e2) = e1
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (1), (8), (12), (24) are inconsistent by sub-proof #1042.
% 151.67/22.21  | | 
% 151.67/22.21  | Case 2:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (25)  all_56_13 = e1 & op(e0, e2) = e1
% 151.67/22.21  | | 
% 151.67/22.21  | | ALPHA: (25) implies:
% 151.67/22.21  | |   (26)  all_56_13 = e1
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 151.67/22.21  | |            (14), (15), (16), (17), (18), (19), (20), (21), (26) are
% 151.67/22.21  | |            inconsistent by sub-proof #226.
% 151.67/22.21  | | 
% 151.67/22.21  | End of split
% 151.67/22.21  | 
% 151.67/22.21  End of proof
% 151.67/22.21  
% 151.67/22.21  Sub-proof #174 shows that the following formulas are inconsistent:
% 151.67/22.21  ----------------------------------------------------------------
% 151.67/22.21    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 151.67/22.21             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.67/22.21           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 151.67/22.21           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 151.67/22.21             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.67/22.21           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 151.67/22.21           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.67/22.21    (2)  op(e3, e3) = e0
% 151.67/22.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.21    (4)  op(e2, e2) = e2
% 151.67/22.21    (5)   ~ (e1 = e0)
% 151.67/22.21    (6)  op(e1, e1) = e3
% 151.67/22.21    (7)   ~ (e3 = e2)
% 151.67/22.21    (8)   ~ (e2 = e1)
% 151.67/22.21  
% 151.67/22.21  Begin of proof
% 151.67/22.21  | 
% 151.67/22.21  | BETA: splitting (1) gives:
% 151.67/22.21  | 
% 151.67/22.21  | Case 1:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (9)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 151.67/22.21  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 151.67/22.21  | |        $i(all_57_4)
% 151.67/22.21  | | 
% 151.67/22.21  | | ALPHA: (9) implies:
% 151.67/22.21  | |   (10)  op(e1, e1) = e2
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (3), (6), (7), (10) are inconsistent by sub-proof #834.
% 151.67/22.21  | | 
% 151.67/22.21  | Case 2:
% 151.67/22.21  | | 
% 151.67/22.21  | |   (11)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 151.67/22.21  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 151.67/22.21  | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 151.67/22.21  | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2,
% 151.67/22.21  | |             e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 151.67/22.21  | | 
% 151.67/22.21  | | REF_CLOSE: (2), (3), (4), (5), (8), (11) are inconsistent by sub-proof #537.
% 151.67/22.21  | | 
% 151.67/22.21  | End of split
% 151.67/22.21  | 
% 151.67/22.21  End of proof
% 151.67/22.21  
% 151.67/22.21  Sub-proof #175 shows that the following formulas are inconsistent:
% 151.67/22.21  ----------------------------------------------------------------
% 151.67/22.21    (1)  all_54_6 = all_52_9
% 151.67/22.21    (2)  op(e0, e1) = all_52_11
% 151.67/22.21    (3)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 151.67/22.21    (4)  all_56_8 = e3
% 151.67/22.21    (5)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 151.67/22.21         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 151.67/22.21    (6)   ~ (all_52_7 = all_52_11)
% 151.67/22.21    (7)   ~ (all_52_6 = e1)
% 151.67/22.21    (8)  op(e3, e3) = e0
% 151.67/22.21    (9)  all_54_2 = all_52_8
% 151.67/22.21    (10)   ~ (e3 = e1)
% 151.67/22.21    (11)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.67/22.21          (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.67/22.21    (12)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.67/22.21          (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.67/22.21    (13)   ~ (all_52_11 = all_10_2)
% 151.67/22.21    (14)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 151.67/22.21          (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 151.67/22.21    (15)  op(e0, e0) = all_10_2
% 151.67/22.21    (16)  ( ~ (all_12_0 = e0) & op(all_12_1, e1) = all_12_0 & op(e1, e3) =
% 151.67/22.21            all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e2) & op(e1,
% 151.67/22.21              e3) = all_12_1 & $i(all_12_1))
% 151.67/22.21    (17)  op(e3, e2) = all_52_4
% 151.67/22.21    (18)  op(e0, e2) = all_52_7
% 151.67/22.21    (19)   ~ (all_52_3 = all_52_7)
% 151.67/22.21    (20)  all_54_9 = all_52_6
% 151.67/22.21    (21)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.21          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.67/22.21    (22)   ~ (all_10_2 = e1)
% 151.67/22.21    (23)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.21          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.21    (24)  all_42_2 = all_10_2
% 151.67/22.21    (25)   ~ (all_52_4 = all_52_12)
% 151.67/22.21    (26)   ~ (e2 = e0)
% 151.67/22.21    (27)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.21            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.21    (28)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.67/22.21          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.67/22.21    (29)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.67/22.21          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.67/22.22    (30)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.67/22.22          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.67/22.22    (31)   ~ (all_52_12 = e1)
% 151.67/22.22    (32)   ~ (all_52_3 = all_52_11)
% 151.67/22.22    (33)   ~ (all_52_9 = all_52_11)
% 151.67/22.22    (34)   ~ (all_52_9 = e3)
% 151.67/22.22    (35)  all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 151.67/22.22    (36)  all_56_0 = e0
% 151.67/22.22    (37)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.22              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 151.67/22.22                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.67/22.22                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.67/22.22    (38)   ~ (all_52_8 = all_52_12)
% 151.67/22.22    (39)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 151.67/22.22          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 151.67/22.22    (40)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.22          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 151.67/22.22            e3)
% 151.67/22.22    (41)  op(e3, e0) = all_52_12
% 151.67/22.22    (42)   ~ (e3 = e0)
% 151.67/22.22    (43)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.22          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.22    (44)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 151.67/22.22          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 151.67/22.22    (45)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 151.67/22.22          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.22    (46)   ~ (all_52_6 = e3)
% 151.67/22.22    (47)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.67/22.22          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.67/22.22    (48)   ~ (all_52_12 = all_52_13)
% 151.67/22.22    (49)  op(e1, e2) = all_52_6
% 151.67/22.22    (50)   ~ (all_52_12 = e3)
% 151.67/22.22    (51)  op(e2, e0) = all_52_13
% 151.67/22.22    (52)   ~ (all_52_9 = e2)
% 151.67/22.22    (53)   ~ (all_52_8 = e0)
% 151.67/22.22    (54)   ~ (all_52_4 = all_52_8)
% 151.67/22.22    (55)  op(e0, e3) = all_52_3
% 151.67/22.22    (56)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.22          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.22    (57)  op(e2, e2) = e2
% 151.67/22.22    (58)  op(e2, e1) = all_52_9
% 151.67/22.22    (59)   ~ (e1 = e0)
% 151.67/22.22    (60)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.67/22.22          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.67/22.22    (61)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 151.67/22.22    (62)  op(e1, e1) = e3
% 151.67/22.22    (63)   ~ (e3 = e2)
% 151.67/22.22    (64)  op(e1, e0) = e1
% 151.67/22.22    (65)   ~ (all_52_8 = e3)
% 151.67/22.22    (66)  all_56_9 = e2
% 151.67/22.22    (67)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.67/22.22          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 151.67/22.22            e2)
% 151.67/22.22    (68)  all_54_3 = all_52_12
% 151.67/22.22    (69)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.22          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.67/22.22    (70)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.22          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.22    (71)   ~ (all_52_3 = e0)
% 151.67/22.22    (72)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 151.67/22.22    (73)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.67/22.22          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.67/22.22    (74)   ~ (all_10_2 = e2)
% 151.67/22.22    (75)   ~ (all_52_12 = all_10_2)
% 151.67/22.22    (76)  op(e3, e1) = all_52_8
% 151.67/22.22    (77)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 151.67/22.22    (78)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.67/22.22          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.67/22.22    (79)   ~ (all_52_3 = all_10_2)
% 151.67/22.22    (80)   ~ (all_52_6 = all_52_7)
% 151.67/22.22    (81)   ~ (e2 = e1)
% 151.67/22.22    (82)   ~ (all_52_8 = all_52_9)
% 151.67/22.22    (83)  op(e1, e3) = all_8_1
% 151.67/22.22    (84)  all_54_15 = all_10_2
% 151.67/22.22    (85)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.22          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.22    (86)  op(e1, e3) = all_52_2
% 151.67/22.22    (87)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.67/22.22              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.67/22.22            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.67/22.22            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.67/22.22            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.67/22.22            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.67/22.22            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 151.67/22.22            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.67/22.22            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 151.67/22.22            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 151.67/22.22            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.67/22.22            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 151.67/22.22            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.67/22.22            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.67/22.22            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 151.67/22.22            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.67/22.22            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.67/22.22            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 151.67/22.22            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.67/22.22            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 151.67/22.22            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 151.67/22.22            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.67/22.22            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.67/22.22            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 151.67/22.22            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.67/22.22            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.67/22.22            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.67/22.22            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.67/22.22            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.67/22.22            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 151.67/22.22            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.67/22.22            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.67/22.22            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.67/22.22            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.67/22.22            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.67/22.22            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 151.67/22.22            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.67/22.22            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.67/22.22            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 151.67/22.22            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.67/22.22            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.67/22.22            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 151.67/22.22            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.67/22.22            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 151.67/22.22            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 151.67/22.22            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.67/22.22            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 151.67/22.22            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 151.67/22.22              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 151.67/22.22            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.67/22.22            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 151.67/22.22              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.67/22.22            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.67/22.22            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 151.67/22.22                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 151.67/22.22                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.67/22.22                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.67/22.22                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 151.67/22.22                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 151.67/22.22                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 151.67/22.22                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 151.67/22.22              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 151.67/22.22                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 151.67/22.22                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 151.67/22.22                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 151.67/22.22                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 151.67/22.22                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 151.67/22.22                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 151.67/22.22                $i(all_57_7))))
% 151.67/22.22    (88)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.22          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.22    (89)   ~ (all_52_12 = e0)
% 151.67/22.22    (90)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.22          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 151.67/22.22            e1)
% 151.67/22.22    (91)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e2) & op(all_42_1, e0) = all_42_0 &
% 151.67/22.22            op(e0, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 151.67/22.22              e1) & op(e0, e3) = all_42_1 & $i(all_42_1))
% 151.67/22.22    (92)  op(e2, e3) = all_52_1
% 151.67/22.22    (93)   ~ (all_52_1 = e2)
% 151.67/22.22    (94)   ~ (all_52_6 = e2)
% 151.67/22.22  
% 151.67/22.22  Begin of proof
% 151.67/22.22  | 
% 151.67/22.22  | BETA: splitting (35) gives:
% 151.67/22.22  | 
% 151.67/22.22  | Case 1:
% 151.67/22.22  | | 
% 151.67/22.22  | |   (95)  all_54_9 = e3
% 151.67/22.22  | | 
% 151.67/22.22  | | REF_CLOSE: (20), (46), (95) are inconsistent by sub-proof #186.
% 151.67/22.22  | | 
% 151.67/22.22  | Case 2:
% 151.67/22.22  | | 
% 151.67/22.22  | |   (96)   ~ (all_54_9 = e3)
% 151.67/22.22  | |   (97)  all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 151.67/22.22  | | 
% 151.67/22.22  | | BETA: splitting (60) gives:
% 151.67/22.22  | | 
% 151.67/22.22  | | Case 1:
% 151.67/22.22  | | | 
% 151.67/22.22  | | |   (98)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 151.67/22.22  | | |           e2)
% 151.67/22.22  | | | 
% 151.67/22.22  | | | BETA: splitting (98) gives:
% 151.67/22.22  | | | 
% 151.67/22.22  | | | Case 1:
% 151.67/22.22  | | | | 
% 151.67/22.22  | | | |   (99)  all_56_6 = e2 & op(e1, e3) = e2
% 151.67/22.22  | | | | 
% 151.67/22.22  | | | | ALPHA: (99) implies:
% 151.67/22.22  | | | |   (100)  all_56_6 = e2
% 151.67/22.22  | | | |   (101)  op(e1, e3) = e2
% 151.67/22.22  | | | | 
% 151.67/22.22  | | | | BETA: splitting (28) gives:
% 151.67/22.22  | | | | 
% 151.67/22.22  | | | | Case 1:
% 151.67/22.22  | | | | | 
% 151.67/22.22  | | | | |   (102)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3,
% 151.67/22.22  | | | | |              e2) = e3)
% 151.67/22.22  | | | | | 
% 151.67/22.22  | | | | | BETA: splitting (102) gives:
% 151.67/22.22  | | | | | 
% 151.67/22.22  | | | | | Case 1:
% 151.67/22.22  | | | | | | 
% 151.67/22.22  | | | | | |   (103)  all_56_0 = e3 & op(e3, e3) = e3
% 151.67/22.22  | | | | | | 
% 151.67/22.22  | | | | | | ALPHA: (103) implies:
% 151.67/22.22  | | | | | |   (104)  op(e3, e3) = e3
% 151.67/22.22  | | | | | | 
% 151.67/22.22  | | | | | | REF_CLOSE: (8), (27), (42), (104) are inconsistent by sub-proof
% 151.67/22.22  | | | | | |            #1141.
% 151.67/22.22  | | | | | | 
% 151.67/22.22  | | | | | Case 2:
% 151.67/22.22  | | | | | | 
% 151.67/22.22  | | | | | |   (105)  all_56_1 = e3 & op(e3, e2) = e3
% 151.67/22.22  | | | | | | 
% 151.67/22.22  | | | | | | ALPHA: (105) implies:
% 151.67/22.22  | | | | | |   (106)  all_56_1 = e3
% 151.67/22.22  | | | | | | 
% 151.67/22.22  | | | | | | BETA: splitting (97) gives:
% 151.67/22.22  | | | | | | 
% 151.67/22.22  | | | | | | Case 1:
% 151.67/22.22  | | | | | | | 
% 151.67/22.22  | | | | | | |   (107)  all_54_9 = e2
% 151.67/22.22  | | | | | | | 
% 151.67/22.22  | | | | | | | REF_CLOSE: (20), (94), (107) are inconsistent by sub-proof #185.
% 151.67/22.22  | | | | | | | 
% 151.67/22.22  | | | | | | Case 2:
% 151.67/22.22  | | | | | | | 
% 151.67/22.22  | | | | | | |   (108)   ~ (all_54_9 = e2)
% 151.67/22.22  | | | | | | |   (109)  all_54_9 = e1 | all_54_9 = e0
% 151.67/22.22  | | | | | | | 
% 151.67/22.22  | | | | | | | BETA: splitting (44) gives:
% 151.67/22.22  | | | | | | | 
% 151.67/22.22  | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | 
% 151.67/22.22  | | | | | | | |   (110)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 &
% 151.67/22.22  | | | | | | | |            op(e2, e0) = e1)
% 151.67/22.22  | | | | | | | | 
% 151.67/22.22  | | | | | | | | BETA: splitting (110) gives:
% 151.67/22.22  | | | | | | | | 
% 151.67/22.22  | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | 
% 151.67/22.22  | | | | | | | | |   (111)  all_56_9 = e1 & op(e3, e0) = e1
% 151.67/22.22  | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | ALPHA: (111) implies:
% 151.67/22.22  | | | | | | | | |   (112)  all_56_9 = e1
% 151.67/22.22  | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | REF_CLOSE: (66), (81), (112) are inconsistent by sub-proof
% 151.67/22.22  | | | | | | | | |            #948.
% 151.67/22.22  | | | | | | | | | 
% 151.67/22.22  | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | 
% 151.67/22.22  | | | | | | | | |   (113)  all_56_10 = e1 & op(e2, e0) = e1
% 151.67/22.22  | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | ALPHA: (113) implies:
% 151.67/22.22  | | | | | | | | |   (114)  all_56_10 = e1
% 151.67/22.22  | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | BETA: splitting (67) gives:
% 151.67/22.22  | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | |   (115)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 151.67/22.22  | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 151.67/22.22  | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | BETA: splitting (115) gives:
% 151.67/22.22  | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | |   (116)  all_56_12 = e2 & op(e0, e3) = e2
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | ALPHA: (116) implies:
% 151.67/22.22  | | | | | | | | | | |   (117)  all_56_12 = e2
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | BETA: splitting (56) gives:
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | |   (118)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 151.67/22.22  | | | | | | | | | | | |            & op(e2, e2) = e3)
% 151.67/22.22  | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | BETA: splitting (118) gives:
% 151.67/22.22  | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | |   (119)  all_56_2 = e3 & op(e2, e3) = e3
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | ALPHA: (119) implies:
% 151.67/22.22  | | | | | | | | | | | | |   (120)  all_56_2 = e3
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | BETA: splitting (29) gives:
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | |   (121)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 151.67/22.22  | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | REF_CLOSE: (7), (27), (49), (81), (100), (121) are
% 151.67/22.22  | | | | | | | | | | | | | |            inconsistent by sub-proof #524.
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | |   (122)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 151.67/22.22  | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | |   (123)  all_56_8 = e1 & op(e1, e1) = e1
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 151.67/22.22  | | | | | | | | | | | | | | |   (124)  op(e1, e1) = e1
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | REF_CLOSE: (10), (27), (62), (124) are inconsistent by
% 151.67/22.22  | | | | | | | | | | | | | | |            sub-proof #734.
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | |   (125)  all_56_11 = e1 & op(e1, e0) = e1
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 151.67/22.22  | | | | | | | | | | | | | | |   (126)  all_56_11 = e1
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | |   (127)  all_54_3 = e3
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | REF_CLOSE: (50), (68), (127) are inconsistent by sub-proof
% 151.67/22.22  | | | | | | | | | | | | | | | |            #451.
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | |   (128)   ~ (all_54_3 = e3)
% 151.67/22.22  | | | | | | | | | | | | | | | |   (129)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (11), (12), (13),
% 151.67/22.22  | | | | | | | | | | | | | | | |            (14), (15), (17), (18), (19), (21), (22), (23),
% 151.67/22.22  | | | | | | | | | | | | | | | |            (24), (25), (27), (28), (29), (30), (31), (32),
% 151.67/22.22  | | | | | | | | | | | | | | | |            (34), (37), (38), (39), (42), (43), (44), (45),
% 151.67/22.22  | | | | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 151.67/22.22  | | | | | | | | | | | | | | | |            (54), (55), (56), (57), (58), (60), (62), (64),
% 151.67/22.22  | | | | | | | | | | | | | | | |            (65), (67), (68), (69), (70), (72), (73), (75),
% 151.67/22.22  | | | | | | | | | | | | | | | |            (78), (79), (84), (85), (86), (87), (88), (89),
% 151.67/22.22  | | | | | | | | | | | | | | | |            (90), (91), (92), (93), (94), (117), (120), (126),
% 151.67/22.22  | | | | | | | | | | | | | | | |            (129) are inconsistent by sub-proof #182.
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | End of split
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | End of split
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | End of split
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | |   (130)  all_56_3 = e3 & op(e2, e2) = e3
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | ALPHA: (130) implies:
% 151.67/22.22  | | | | | | | | | | | | |   (131)  op(e2, e2) = e3
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | REF_CLOSE: (27), (57), (63), (131) are inconsistent by
% 151.67/22.22  | | | | | | | | | | | | |            sub-proof #1179.
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | End of split
% 151.67/22.22  | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | |   (132)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 151.67/22.22  | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 151.67/22.22  | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | BETA: splitting (132) gives:
% 151.67/22.22  | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | |   (133)  all_56_5 = e3 & op(e2, e1) = e3
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | REF_CLOSE: (27), (34), (58), (133) are inconsistent by
% 151.67/22.22  | | | | | | | | | | | | |            sub-proof #647.
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | |   (134)  all_56_10 = e3 & op(e2, e0) = e3
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | REF_CLOSE: (10), (114), (134) are inconsistent by sub-proof
% 151.67/22.22  | | | | | | | | | | | | |            #683.
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | End of split
% 151.67/22.22  | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | End of split
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | |   (135)  all_56_13 = e2 & op(e0, e2) = e2
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | ALPHA: (135) implies:
% 151.67/22.22  | | | | | | | | | | |   (136)  all_56_13 = e2
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | REF_CLOSE: (10), (26), (27), (42), (57), (59), (70), (81),
% 151.67/22.22  | | | | | | | | | | |            (85), (106), (136) are inconsistent by sub-proof
% 151.67/22.22  | | | | | | | | | | |            #1108.
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | End of split
% 151.67/22.22  | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | |   (137)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 151.67/22.22  | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 151.67/22.22  | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | BETA: splitting (137) gives:
% 151.67/22.22  | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | |   (138)  all_56_14 = e2 & op(e0, e1) = e2
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | ALPHA: (138) implies:
% 151.67/22.22  | | | | | | | | | | |   (139)  all_56_14 = e2
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | BETA: splitting (56) gives:
% 151.67/22.22  | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | |   (140)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 151.67/22.22  | | | | | | | | | | | |            & op(e2, e2) = e3)
% 151.67/22.22  | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | BETA: splitting (140) gives:
% 151.67/22.22  | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | |   (141)  all_56_2 = e3 & op(e2, e3) = e3
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | ALPHA: (141) implies:
% 151.67/22.22  | | | | | | | | | | | | |   (142)  all_56_2 = e3
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | BETA: splitting (37) gives:
% 151.67/22.22  | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | |   (143)  all_56_15 = e0 & op(e0, e0) = e0
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | ALPHA: (143) implies:
% 151.67/22.22  | | | | | | | | | | | | | |   (144)  op(e0, e0) = e0
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | |   (145)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 151.67/22.22  | | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | |   (146)  all_56_12 = e3 & op(e0, e3) = e3
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 151.67/22.22  | | | | | | | | | | | | | | | |   (147)  all_56_12 = e3
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | REF_CLOSE: (10), (11), (36), (59), (81), (100), (142), (147)
% 151.67/22.22  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #181.
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | |   (148)  all_56_13 = e3 & op(e0, e2) = e3
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 151.67/22.22  | | | | | | | | | | | | | | | |   (149)  all_56_13 = e3
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | REF_CLOSE: (10), (26), (27), (42), (57), (59), (70), (81),
% 151.67/22.22  | | | | | | | | | | | | | | | |            (85), (106), (149) are inconsistent by sub-proof
% 151.67/22.22  | | | | | | | | | | | | | | | |            #877.
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | End of split
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | |   (150)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 151.67/22.22  | | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | BETA: splitting (150) gives:
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | |   (151)  all_56_14 = e3 & op(e0, e1) = e3
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | REF_CLOSE: (10), (26), (27), (42), (46), (49), (57), (59),
% 151.67/22.22  | | | | | | | | | | | | | | | |            (63), (70), (81), (85), (88), (106), (139), (151)
% 151.67/22.22  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #180.
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | |   (152)  all_56_15 = e3 & op(e0, e0) = e3
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 151.67/22.22  | | | | | | | | | | | | | | | |   (153)  op(e0, e0) = e3
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | REF_CLOSE: (27), (42), (144), (153) are inconsistent by
% 151.67/22.22  | | | | | | | | | | | | | | | |            sub-proof #1143.
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | End of split
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | End of split
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | |   (154)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 151.67/22.22  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 151.67/22.22  | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 151.67/22.22  | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 151.67/22.22  | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | ALPHA: (154) implies:
% 151.67/22.22  | | | | | | | | | | | | | |   (155)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 151.67/22.22  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 151.67/22.22  | | | | | | | | | | | | | |              e1) = e0)
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 151.67/22.22  | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | |   (156)  all_54_3 = e3
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | REF_CLOSE: (50), (68), (156) are inconsistent by sub-proof
% 151.67/22.22  | | | | | | | | | | | | | | |            #451.
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | |   (157)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 151.67/22.22  | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | |   (158)  all_54_3 = e2
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | COMBINE_EQS: (68), (158) imply:
% 151.67/22.22  | | | | | | | | | | | | | | | |   (159)  all_52_12 = e2
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | SIMP: (159) implies:
% 151.67/22.22  | | | | | | | | | | | | | | | |   (160)  all_52_12 = e2
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | REDUCE: (38), (160) imply:
% 151.67/22.22  | | | | | | | | | | | | | | | |   (161)   ~ (all_52_8 = e2)
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 151.67/22.22  | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | |   (162)  all_54_2 = e3
% 151.67/22.22  | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (65), (162) are inconsistent by sub-proof
% 151.67/22.22  | | | | | | | | | | | | | | | | |            #184.
% 151.67/22.22  | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | |   (163)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 151.67/22.22  | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 151.67/22.22  | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | |   (164)  all_54_2 = e2
% 151.67/22.22  | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (161), (164) are inconsistent by sub-proof
% 151.67/22.22  | | | | | | | | | | | | | | | | | |            #183.
% 151.67/22.22  | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | |   (165)  all_54_2 = e1 | all_54_2 = e0
% 151.67/22.22  | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | |   (166)  all_54_2 = e1
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (166) imply:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | |   (167)  all_52_8 = e1
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | SIMP: (167) implies:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | |   (168)  all_52_8 = e1
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | REDUCE: (82), (168) imply:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | |   (169)   ~ (all_52_9 = e1)
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | SIMP: (169) implies:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | |   (170)   ~ (all_52_9 = e1)
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | |   (171)  all_54_6 = e3
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (34), (171) are inconsistent by sub-proof
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | |            #650.
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | |   (172)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | |   (173)  all_54_6 = e2
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (52), (173) are inconsistent by sub-proof
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | |            #379.
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.22  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | |   (174)  all_54_6 = e1 | all_54_6 = e0
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | |   (175)  all_54_6 = e1
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (170), (175) are inconsistent by sub-proof
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | |            #378.
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | |   (176)  all_54_6 = e0
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1), (176) imply:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | |   (177)  all_52_9 = e0
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | SIMP: (177) implies:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | |   (178)  all_52_9 = e0
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | REDUCE: (33), (178) imply:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | |   (179)   ~ (all_52_11 = e0)
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | SIMP: (179) implies:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | |   (180)   ~ (all_52_11 = e0)
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (109) gives:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | |   (181)  all_54_9 = e1
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (20), (181) are inconsistent by sub-proof
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | |            #179.
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | |   (182)  all_54_9 = e0
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (20), (182) imply:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | |   (183)  all_52_6 = e0
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (183) implies:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | |   (184)  all_52_6 = e0
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (80), (184) imply:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | |   (185)   ~ (all_52_7 = e0)
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (185) implies:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | |   (186)   ~ (all_52_7 = e0)
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | |   (187)  all_56_12 = e0 & op(e0, e3) = e0
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | |   (188)  op(e0, e3) = e0
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (27), (55), (71), (188) are inconsistent by
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1142.
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | |   (189)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (18), (27), (180), (186), (189) are
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #799.
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | |   (190)  all_54_2 = e0
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (53), (190) are inconsistent by sub-proof
% 151.67/22.23  | | | | | | | | | | | | | | | | | | |            #383.
% 151.67/22.23  | | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | |   (191)  all_54_3 = e1 | all_54_3 = e0
% 151.67/22.23  | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | | REF_CLOSE: (31), (68), (89), (191) are inconsistent by
% 151.67/22.23  | | | | | | | | | | | | | | | |            sub-proof #759.
% 151.67/22.23  | | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | |   (192)  all_56_3 = e3 & op(e2, e2) = e3
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | ALPHA: (192) implies:
% 151.67/22.23  | | | | | | | | | | | | |   (193)  op(e2, e2) = e3
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | REF_CLOSE: (27), (57), (63), (193) are inconsistent by
% 151.67/22.23  | | | | | | | | | | | | |            sub-proof #1179.
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | |   (194)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 151.67/22.23  | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | BETA: splitting (194) gives:
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | |   (195)  all_56_5 = e3 & op(e2, e1) = e3
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | REF_CLOSE: (27), (34), (58), (195) are inconsistent by
% 151.67/22.23  | | | | | | | | | | | | |            sub-proof #647.
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | |   (196)  all_56_10 = e3 & op(e2, e0) = e3
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | REF_CLOSE: (10), (114), (196) are inconsistent by sub-proof
% 151.67/22.23  | | | | | | | | | | | | |            #683.
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | |   (197)  all_56_15 = e2 & op(e0, e0) = e2
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | ALPHA: (197) implies:
% 151.67/22.23  | | | | | | | | | | |   (198)  op(e0, e0) = e2
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | REF_CLOSE: (15), (27), (74), (198) are inconsistent by
% 151.67/22.23  | | | | | | | | | | |            sub-proof #1097.
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | 
% 151.67/22.23  | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | 
% 151.67/22.23  | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | 
% 151.67/22.23  | | | | | | | |   (199)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 &
% 151.67/22.23  | | | | | | | |            op(e0, e0) = e1)
% 151.67/22.23  | | | | | | | | 
% 151.67/22.23  | | | | | | | | BETA: splitting (199) gives:
% 151.67/22.23  | | | | | | | | 
% 151.67/22.23  | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | 
% 151.67/22.23  | | | | | | | | |   (200)  all_56_11 = e1 & op(e1, e0) = e1
% 151.67/22.23  | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | ALPHA: (200) implies:
% 151.67/22.23  | | | | | | | | |   (201)  all_56_11 = e1
% 151.67/22.23  | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | BETA: splitting (67) gives:
% 151.67/22.23  | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | |   (202)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 151.67/22.23  | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 151.67/22.23  | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | BETA: splitting (202) gives:
% 151.67/22.23  | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | |   (203)  all_56_12 = e2 & op(e0, e3) = e2
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | ALPHA: (203) implies:
% 151.67/22.23  | | | | | | | | | | |   (204)  all_56_12 = e2
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | BETA: splitting (77) gives:
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | |   (205)  all_54_3 = e3
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | REF_CLOSE: (50), (68), (205) are inconsistent by sub-proof
% 151.67/22.23  | | | | | | | | | | | |            #451.
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | |   (206)   ~ (all_54_3 = e3)
% 151.67/22.23  | | | | | | | | | | | |   (207)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | BETA: splitting (14) gives:
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | |   (208)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 151.67/22.23  | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | BETA: splitting (208) gives:
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | |   (209)  all_56_0 = e3 & op(e3, e3) = e3
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | ALPHA: (209) implies:
% 151.67/22.23  | | | | | | | | | | | | | |   (210)  op(e3, e3) = e3
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | REF_CLOSE: (8), (27), (42), (210) are inconsistent by
% 151.67/22.23  | | | | | | | | | | | | | |            sub-proof #1141.
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | |   (211)  all_56_2 = e3 & op(e2, e3) = e3
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | ALPHA: (211) implies:
% 151.67/22.23  | | | | | | | | | | | | | |   (212)  all_56_2 = e3
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (11), (12), (13),
% 151.67/22.23  | | | | | | | | | | | | | |            (14), (15), (17), (18), (19), (21), (22), (23),
% 151.67/22.23  | | | | | | | | | | | | | |            (24), (25), (27), (28), (29), (30), (31), (32),
% 151.67/22.23  | | | | | | | | | | | | | |            (34), (37), (38), (39), (42), (43), (44), (45),
% 151.67/22.23  | | | | | | | | | | | | | |            (46), (47), (48), (49), (50), (51), (52), (53),
% 151.67/22.23  | | | | | | | | | | | | | |            (54), (55), (56), (57), (58), (60), (62), (64),
% 151.67/22.23  | | | | | | | | | | | | | |            (65), (67), (68), (69), (70), (72), (73), (75),
% 151.67/22.23  | | | | | | | | | | | | | |            (78), (79), (84), (85), (86), (87), (88), (89),
% 151.67/22.23  | | | | | | | | | | | | | |            (90), (91), (92), (93), (94), (201), (204), (207),
% 151.67/22.23  | | | | | | | | | | | | | |            (212) are inconsistent by sub-proof #182.
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | |   (213)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 151.67/22.23  | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | BETA: splitting (213) gives:
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | |   (214)  all_56_6 = e3 & op(e1, e3) = e3
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | ALPHA: (214) implies:
% 151.67/22.23  | | | | | | | | | | | | | |   (215)  all_56_6 = e3
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | REF_CLOSE: (4), (10), (26), (27), (29), (42), (59), (60),
% 151.67/22.23  | | | | | | | | | | | | | |            (62), (63), (78), (81), (215) are inconsistent by
% 151.67/22.23  | | | | | | | | | | | | | |            sub-proof #607.
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | |   (216)  all_56_12 = e3 & op(e0, e3) = e3
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | REF_CLOSE: (10), (26), (27), (42), (46), (49), (57), (59),
% 151.67/22.23  | | | | | | | | | | | | | |            (63), (70), (81), (85), (88), (106), (204), (216)
% 151.67/22.23  | | | | | | | | | | | | | |            are inconsistent by sub-proof #178.
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | |   (217)  all_56_13 = e2 & op(e0, e2) = e2
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | ALPHA: (217) implies:
% 151.67/22.23  | | | | | | | | | | |   (218)  all_56_13 = e2
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | REF_CLOSE: (10), (26), (27), (42), (57), (59), (70), (81),
% 151.67/22.23  | | | | | | | | | | |            (85), (106), (218) are inconsistent by sub-proof
% 151.67/22.23  | | | | | | | | | | |            #1108.
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | |   (219)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 151.67/22.23  | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 151.67/22.23  | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | BETA: splitting (219) gives:
% 151.67/22.23  | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | |   (220)  all_56_14 = e2 & op(e0, e1) = e2
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | ALPHA: (220) implies:
% 151.67/22.23  | | | | | | | | | | |   (221)  op(e0, e1) = e2
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | BETA: splitting (16) gives:
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | |   (222)   ~ (all_12_0 = e0) & op(all_12_1, e1) = all_12_0 &
% 151.67/22.23  | | | | | | | | | | | |          op(e1, e3) = all_12_1 & $i(all_12_0) &
% 151.67/22.23  | | | | | | | | | | | |          $i(all_12_1)
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | ALPHA: (222) implies:
% 151.67/22.23  | | | | | | | | | | | |   (223)   ~ (all_12_0 = e0)
% 151.67/22.23  | | | | | | | | | | | |   (224)  op(e1, e3) = all_12_1
% 151.67/22.23  | | | | | | | | | | | |   (225)  op(all_12_1, e1) = all_12_0
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | BETA: splitting (23) gives:
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | |   (226)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 151.67/22.23  | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | BETA: splitting (226) gives:
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | Case 1:
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | |   (227)  all_56_4 = e0 & op(e3, e1) = e0
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | REF_CLOSE: (27), (53), (76), (227) are inconsistent by
% 151.67/22.23  | | | | | | | | | | | | | |            sub-proof #1130.
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | |   (228)  all_56_5 = e0 & op(e2, e1) = e0
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | ALPHA: (228) implies:
% 151.67/22.23  | | | | | | | | | | | | | |   (229)  op(e2, e1) = e0
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | | REF_CLOSE: (27), (101), (223), (224), (225), (229) are
% 151.67/22.23  | | | | | | | | | | | | | |            inconsistent by sub-proof #177.
% 151.67/22.23  | | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | |   (230)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 151.67/22.23  | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | | REF_CLOSE: (26), (27), (42), (62), (221), (230) are
% 151.67/22.23  | | | | | | | | | | | | |            inconsistent by sub-proof #222.
% 151.67/22.23  | | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | |   (231)   ~ (all_12_1 = e2) & op(e1, e3) = all_12_1 &
% 151.67/22.23  | | | | | | | | | | | |          $i(all_12_1)
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | | REF_CLOSE: (27), (83), (101), (231) are inconsistent by
% 151.67/22.23  | | | | | | | | | | | |            sub-proof #176.
% 151.67/22.23  | | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | |   (232)  all_56_15 = e2 & op(e0, e0) = e2
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | ALPHA: (232) implies:
% 151.67/22.23  | | | | | | | | | | |   (233)  op(e0, e0) = e2
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | | REF_CLOSE: (15), (27), (74), (233) are inconsistent by
% 151.67/22.23  | | | | | | | | | | |            sub-proof #1097.
% 151.67/22.23  | | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | | 
% 151.67/22.23  | | | | | | | | Case 2:
% 151.67/22.23  | | | | | | | | | 
% 151.67/22.23  | | | | | | | | |   (234)  all_56_15 = e1 & op(e0, e0) = e1
% 151.67/22.23  | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | ALPHA: (234) implies:
% 151.67/22.23  | | | | | | | | |   (235)  op(e0, e0) = e1
% 151.67/22.23  | | | | | | | | | 
% 151.67/22.23  | | | | | | | | | REF_CLOSE: (15), (22), (27), (235) are inconsistent by
% 151.67/22.23  | | | | | | | | |            sub-proof #1116.
% 151.67/22.23  | | | | | | | | | 
% 151.67/22.23  | | | | | | | | End of split
% 151.67/22.23  | | | | | | | | 
% 151.67/22.23  | | | | | | | End of split
% 151.67/22.23  | | | | | | | 
% 151.67/22.23  | | | | | | End of split
% 151.67/22.23  | | | | | | 
% 151.67/22.23  | | | | | End of split
% 151.67/22.23  | | | | | 
% 151.67/22.23  | | | | Case 2:
% 151.67/22.23  | | | | | 
% 151.67/22.23  | | | | |   (236)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3,
% 151.67/22.23  | | | | |              e0) = e3)
% 151.67/22.23  | | | | | 
% 151.67/22.23  | | | | | BETA: splitting (236) gives:
% 151.67/22.23  | | | | | 
% 151.67/22.23  | | | | | Case 1:
% 151.67/22.23  | | | | | | 
% 151.67/22.23  | | | | | |   (237)  all_56_4 = e3 & op(e3, e1) = e3
% 151.67/22.23  | | | | | | 
% 151.67/22.23  | | | | | | ALPHA: (237) implies:
% 151.67/22.23  | | | | | |   (238)  op(e3, e1) = e3
% 151.67/22.23  | | | | | | 
% 151.67/22.23  | | | | | | REF_CLOSE: (27), (65), (76), (238) are inconsistent by sub-proof
% 151.67/22.23  | | | | | |            #1164.
% 151.67/22.23  | | | | | | 
% 151.67/22.23  | | | | | Case 2:
% 151.67/22.23  | | | | | | 
% 151.67/22.23  | | | | | |   (239)  all_56_9 = e3 & op(e3, e0) = e3
% 151.67/22.23  | | | | | | 
% 151.67/22.23  | | | | | | ALPHA: (239) implies:
% 151.67/22.23  | | | | | |   (240)  op(e3, e0) = e3
% 151.67/22.23  | | | | | | 
% 151.67/22.23  | | | | | | REF_CLOSE: (27), (41), (50), (240) are inconsistent by sub-proof
% 151.67/22.23  | | | | | |            #1082.
% 151.67/22.23  | | | | | | 
% 151.67/22.23  | | | | | End of split
% 151.67/22.23  | | | | | 
% 151.67/22.23  | | | | End of split
% 151.67/22.23  | | | | 
% 151.67/22.23  | | | Case 2:
% 151.67/22.23  | | | | 
% 151.67/22.23  | | | |   (241)  all_56_7 = e2 & op(e1, e2) = e2
% 151.67/22.23  | | | | 
% 151.67/22.23  | | | | ALPHA: (241) implies:
% 151.67/22.23  | | | |   (242)  op(e1, e2) = e2
% 151.67/22.23  | | | | 
% 151.67/22.23  | | | | REF_CLOSE: (27), (49), (94), (242) are inconsistent by sub-proof #1171.
% 151.67/22.23  | | | | 
% 151.67/22.23  | | | End of split
% 151.67/22.23  | | | 
% 151.67/22.23  | | Case 2:
% 151.67/22.23  | | | 
% 151.67/22.23  | | |   (243)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0)
% 151.67/22.23  | | |            = e2)
% 151.67/22.23  | | | 
% 151.67/22.23  | | | REF_CLOSE: (27), (62), (63), (64), (81), (243) are inconsistent by
% 151.67/22.23  | | |            sub-proof #280.
% 151.67/22.23  | | | 
% 151.67/22.23  | | End of split
% 151.67/22.23  | | 
% 151.67/22.23  | End of split
% 151.67/22.23  | 
% 151.67/22.23  End of proof
% 151.67/22.23  
% 151.67/22.23  Sub-proof #176 shows that the following formulas are inconsistent:
% 151.67/22.23  ----------------------------------------------------------------
% 151.67/22.23    (1)   ~ (all_12_1 = e2) & op(e1, e3) = all_12_1 & $i(all_12_1)
% 151.67/22.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.23    (3)  op(e1, e3) = all_8_1
% 151.67/22.23    (4)  op(e1, e3) = e2
% 151.67/22.23  
% 151.67/22.23  Begin of proof
% 151.67/22.23  | 
% 151.67/22.23  | ALPHA: (1) implies:
% 151.67/22.23  |   (5)   ~ (all_12_1 = e2)
% 151.67/22.23  |   (6)  op(e1, e3) = all_12_1
% 151.67/22.23  | 
% 151.67/22.23  | GROUND_INST: instantiating (2) with all_8_1, all_12_1, e3, e1, simplifying
% 151.67/22.23  |              with (3), (6) gives:
% 151.67/22.23  |   (7)  all_12_1 = all_8_1
% 151.67/22.23  | 
% 151.67/22.23  | GROUND_INST: instantiating (2) with e2, all_12_1, e3, e1, simplifying with
% 151.67/22.23  |              (4), (6) gives:
% 151.67/22.23  |   (8)  all_12_1 = e2
% 151.67/22.23  | 
% 151.67/22.23  | COMBINE_EQS: (7), (8) imply:
% 151.67/22.23  |   (9)  all_8_1 = e2
% 151.67/22.23  | 
% 151.67/22.23  | REDUCE: (5), (8) imply:
% 151.67/22.23  |   (10)  $false
% 151.67/22.23  | 
% 151.67/22.23  | CLOSE: (10) is inconsistent.
% 151.67/22.23  | 
% 151.67/22.23  End of proof
% 151.67/22.23  
% 151.67/22.23  Sub-proof #177 shows that the following formulas are inconsistent:
% 151.67/22.23  ----------------------------------------------------------------
% 151.67/22.23    (1)  op(e1, e3) = e2
% 151.67/22.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.23    (3)  op(e2, e1) = e0
% 151.67/22.23    (4)   ~ (all_12_0 = e0)
% 151.67/22.23    (5)  op(all_12_1, e1) = all_12_0
% 151.67/22.23    (6)  op(e1, e3) = all_12_1
% 151.67/22.23  
% 151.67/22.23  Begin of proof
% 151.67/22.23  | 
% 151.67/22.23  | GROUND_INST: instantiating (2) with e2, all_12_1, e3, e1, simplifying with
% 151.67/22.23  |              (1), (6) gives:
% 151.67/22.23  |   (7)  all_12_1 = e2
% 151.67/22.23  | 
% 151.67/22.23  | GROUND_INST: instantiating (2) with e0, all_12_0, e1, e2, simplifying with (3)
% 151.67/22.23  |              gives:
% 151.67/22.23  |   (8)  all_12_0 = e0 |  ~ (op(e2, e1) = all_12_0)
% 151.67/22.23  | 
% 151.67/22.23  | REDUCE: (5), (7) imply:
% 151.67/22.23  |   (9)  op(e2, e1) = all_12_0
% 151.67/22.23  | 
% 151.67/22.23  | BETA: splitting (8) gives:
% 151.67/22.23  | 
% 151.67/22.23  | Case 1:
% 151.67/22.23  | | 
% 151.67/22.23  | |   (10)   ~ (op(e2, e1) = all_12_0)
% 151.67/22.23  | | 
% 151.67/22.23  | | PRED_UNIFY: (9), (10) imply:
% 151.67/22.23  | |   (11)  $false
% 151.67/22.23  | | 
% 151.67/22.23  | | CLOSE: (11) is inconsistent.
% 151.67/22.23  | | 
% 151.67/22.23  | Case 2:
% 151.67/22.23  | | 
% 151.67/22.23  | |   (12)  all_12_0 = e0
% 151.67/22.23  | | 
% 151.67/22.23  | | REDUCE: (4), (12) imply:
% 151.67/22.23  | |   (13)  $false
% 151.67/22.23  | | 
% 151.67/22.23  | | CLOSE: (13) is inconsistent.
% 151.67/22.23  | | 
% 151.67/22.23  | End of split
% 151.67/22.23  | 
% 151.67/22.23  End of proof
% 151.67/22.23  
% 151.67/22.23  Sub-proof #178 shows that the following formulas are inconsistent:
% 151.67/22.23  ----------------------------------------------------------------
% 151.67/22.23    (1)   ~ (e3 = e1)
% 151.67/22.23    (2)  all_56_12 = e3 & op(e0, e3) = e3
% 151.67/22.23    (3)   ~ (e2 = e0)
% 151.67/22.23    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.23    (5)   ~ (e3 = e0)
% 151.67/22.23    (6)   ~ (all_52_6 = e3)
% 151.67/22.23    (7)  op(e1, e2) = all_52_6
% 151.67/22.23    (8)  op(e2, e2) = e2
% 151.67/22.23    (9)   ~ (e1 = e0)
% 151.67/22.23    (10)   ~ (e3 = e2)
% 151.67/22.23    (11)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.23          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.23    (12)  all_56_12 = e2
% 151.67/22.23    (13)   ~ (e2 = e1)
% 151.67/22.23    (14)  all_56_1 = e3
% 151.67/22.23    (15)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.23          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.23    (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.23          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.23  
% 151.67/22.23  Begin of proof
% 151.67/22.23  | 
% 151.67/22.23  | ALPHA: (2) implies:
% 151.67/22.23  |   (17)  all_56_12 = e3
% 151.67/22.23  | 
% 151.67/22.23  | COMBINE_EQS: (12), (17) imply:
% 151.67/22.23  |   (18)  e3 = e2
% 151.67/22.23  | 
% 151.67/22.23  | COMBINE_EQS: (14), (18) imply:
% 151.67/22.23  |   (19)  all_56_1 = e2
% 151.67/22.23  | 
% 151.67/22.23  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (15),
% 151.67/22.23  |            (16), (19) are inconsistent by sub-proof #921.
% 151.67/22.23  | 
% 151.67/22.23  End of proof
% 151.67/22.23  
% 151.67/22.23  Sub-proof #179 shows that the following formulas are inconsistent:
% 151.67/22.23  ----------------------------------------------------------------
% 151.67/22.23    (1)  all_54_9 = all_52_6
% 151.67/22.23    (2)  all_54_9 = e1
% 151.67/22.23    (3)   ~ (all_52_6 = e1)
% 151.67/22.23  
% 151.67/22.23  Begin of proof
% 151.67/22.23  | 
% 151.67/22.23  | COMBINE_EQS: (1), (2) imply:
% 151.67/22.23  |   (4)  all_52_6 = e1
% 151.67/22.23  | 
% 151.67/22.23  | SIMP: (4) implies:
% 151.67/22.23  |   (5)  all_52_6 = e1
% 151.67/22.23  | 
% 151.67/22.23  | REDUCE: (3), (5) imply:
% 151.67/22.23  |   (6)  $false
% 151.67/22.23  | 
% 151.67/22.23  | CLOSE: (6) is inconsistent.
% 151.67/22.23  | 
% 151.67/22.23  End of proof
% 151.67/22.23  
% 151.67/22.23  Sub-proof #180 shows that the following formulas are inconsistent:
% 151.67/22.23  ----------------------------------------------------------------
% 151.67/22.23    (1)   ~ (e3 = e1)
% 151.67/22.23    (2)   ~ (e2 = e0)
% 151.67/22.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.23    (4)  all_56_14 = e2
% 151.67/22.23    (5)   ~ (e3 = e0)
% 151.67/22.23    (6)   ~ (all_52_6 = e3)
% 151.67/22.23    (7)  op(e1, e2) = all_52_6
% 151.67/22.23    (8)  op(e2, e2) = e2
% 151.67/22.23    (9)   ~ (e1 = e0)
% 151.67/22.23    (10)   ~ (e3 = e2)
% 151.67/22.23    (11)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.23          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.23    (12)   ~ (e2 = e1)
% 151.67/22.23    (13)  all_56_14 = e3 & op(e0, e1) = e3
% 151.67/22.23    (14)  all_56_1 = e3
% 151.67/22.23    (15)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.23          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.23    (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.23          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 151.67/22.23  
% 151.67/22.23  Begin of proof
% 151.67/22.23  | 
% 151.67/22.23  | ALPHA: (13) implies:
% 151.67/22.23  |   (17)  all_56_14 = e3
% 151.67/22.23  | 
% 151.67/22.23  | COMBINE_EQS: (4), (17) imply:
% 151.67/22.23  |   (18)  e3 = e2
% 151.67/22.23  | 
% 151.67/22.23  | COMBINE_EQS: (14), (18) imply:
% 151.67/22.23  |   (19)  all_56_1 = e2
% 151.67/22.23  | 
% 151.67/22.23  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (15),
% 151.67/22.23  |            (16), (19) are inconsistent by sub-proof #921.
% 151.67/22.23  | 
% 151.67/22.23  End of proof
% 151.67/22.23  
% 151.67/22.23  Sub-proof #181 shows that the following formulas are inconsistent:
% 151.67/22.23  ----------------------------------------------------------------
% 151.67/22.23    (1)   ~ (e3 = e1)
% 151.67/22.23    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.67/22.23         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.67/22.23    (3)  all_56_6 = e2
% 151.67/22.23    (4)  all_56_0 = e0
% 151.67/22.23    (5)   ~ (e1 = e0)
% 151.67/22.23    (6)   ~ (e2 = e1)
% 151.67/22.23    (7)  all_56_2 = e3
% 151.67/22.23    (8)  all_56_12 = e3
% 151.67/22.23  
% 151.67/22.23  Begin of proof
% 151.67/22.23  | 
% 151.67/22.23  | BETA: splitting (2) gives:
% 151.67/22.23  | 
% 151.67/22.23  | Case 1:
% 151.67/22.23  | | 
% 151.67/22.23  | |   (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 151.67/22.23  | | 
% 151.67/22.23  | | BETA: splitting (9) gives:
% 151.67/22.23  | | 
% 151.67/22.23  | | Case 1:
% 151.67/22.23  | | | 
% 151.67/22.23  | | |   (10)  all_56_0 = e1 & op(e3, e3) = e1
% 151.67/22.23  | | | 
% 151.67/22.23  | | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #214.
% 151.67/22.23  | | | 
% 151.67/22.23  | | Case 2:
% 151.67/22.23  | | | 
% 151.67/22.23  | | |   (11)  all_56_2 = e1 & op(e2, e3) = e1
% 151.67/22.23  | | | 
% 151.67/22.23  | | | REF_CLOSE: (1), (7), (11) are inconsistent by sub-proof #791.
% 151.67/22.23  | | | 
% 151.67/22.23  | | End of split
% 151.67/22.23  | | 
% 151.67/22.23  | Case 2:
% 151.67/22.23  | | 
% 151.67/22.23  | |   (12)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 151.67/22.23  | |           e1)
% 151.67/22.23  | | 
% 151.67/22.23  | | BETA: splitting (12) gives:
% 151.67/22.23  | | 
% 151.67/22.23  | | Case 1:
% 151.67/22.23  | | | 
% 151.67/22.23  | | |   (13)  all_56_6 = e1 & op(e1, e3) = e1
% 151.67/22.23  | | | 
% 151.67/22.23  | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #1058.
% 151.67/22.23  | | | 
% 151.67/22.23  | | Case 2:
% 151.67/22.23  | | | 
% 151.67/22.23  | | |   (14)  all_56_12 = e1 & op(e0, e3) = e1
% 151.67/22.23  | | | 
% 151.67/22.23  | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #992.
% 151.67/22.23  | | | 
% 151.67/22.23  | | End of split
% 151.67/22.23  | | 
% 151.67/22.23  | End of split
% 151.67/22.23  | 
% 151.67/22.23  End of proof
% 151.67/22.23  
% 151.67/22.23  Sub-proof #182 shows that the following formulas are inconsistent:
% 151.67/22.23  ----------------------------------------------------------------
% 151.67/22.23    (1)  op(e0, e1) = all_52_11
% 151.67/22.23    (2)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 151.67/22.23    (3)  all_56_8 = e3
% 151.67/22.23    (4)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 151.67/22.23         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 151.67/22.23    (5)   ~ (all_52_7 = all_52_11)
% 151.67/22.23    (6)  all_54_2 = all_52_8
% 151.67/22.23    (7)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 151.67/22.23         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 151.67/22.23    (8)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 151.67/22.23         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 151.67/22.23    (9)   ~ (all_52_11 = all_10_2)
% 151.67/22.23    (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 151.67/22.23          (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 151.67/22.23    (11)  op(e0, e0) = all_10_2
% 151.67/22.23    (12)  op(e3, e2) = all_52_4
% 151.67/22.23    (13)  op(e0, e2) = all_52_7
% 151.67/22.23    (14)   ~ (all_52_3 = all_52_7)
% 151.67/22.23    (15)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.23          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 151.67/22.23    (16)  all_56_11 = e1
% 151.67/22.23    (17)   ~ (all_10_2 = e1)
% 151.67/22.23    (18)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 151.67/22.23          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 151.67/22.23    (19)  all_42_2 = all_10_2
% 151.67/22.23    (20)   ~ (all_52_4 = all_52_12)
% 151.67/22.23    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 151.67/22.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 151.67/22.24    (22)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 151.67/22.24          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 151.67/22.24    (23)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 151.67/22.24          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 151.67/22.24    (24)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 151.67/22.24          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 151.67/22.24    (25)   ~ (all_52_12 = e1)
% 151.67/22.24    (26)   ~ (all_52_3 = all_52_11)
% 151.67/22.24    (27)   ~ (all_52_9 = e3)
% 151.67/22.24    (28)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.24              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 151.67/22.24                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 151.67/22.24                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 151.67/22.24    (29)   ~ (all_52_8 = all_52_12)
% 151.67/22.24    (30)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 151.67/22.24          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 151.67/22.24    (31)   ~ (e3 = e0)
% 151.67/22.24    (32)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 151.67/22.24          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 151.67/22.24    (33)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 151.67/22.24          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 151.67/22.24    (34)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 151.67/22.24          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 151.67/22.24    (35)   ~ (all_52_6 = e3)
% 151.67/22.24    (36)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 151.67/22.24          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 151.67/22.24    (37)   ~ (all_52_12 = all_52_13)
% 151.67/22.24    (38)  op(e1, e2) = all_52_6
% 151.67/22.24    (39)   ~ (all_52_12 = e3)
% 151.67/22.24    (40)  op(e2, e0) = all_52_13
% 151.67/22.24    (41)   ~ (all_52_9 = e2)
% 151.67/22.24    (42)   ~ (all_52_8 = e0)
% 151.67/22.24    (43)   ~ (all_52_4 = all_52_8)
% 151.67/22.24    (44)  op(e0, e3) = all_52_3
% 151.67/22.24    (45)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 151.67/22.24          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 151.67/22.24    (46)  op(e2, e2) = e2
% 151.67/22.24    (47)  op(e2, e1) = all_52_9
% 151.67/22.24    (48)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 151.67/22.24          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 151.67/22.24    (49)  op(e1, e1) = e3
% 151.67/22.24    (50)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 151.67/22.24    (51)  op(e1, e0) = e1
% 151.67/22.24    (52)   ~ (all_52_8 = e3)
% 151.67/22.24    (53)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 151.67/22.24          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 151.67/22.24            e2)
% 151.67/22.24    (54)  all_54_3 = all_52_12
% 151.67/22.24    (55)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.24          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 151.67/22.24    (56)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 151.67/22.24          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 151.67/22.24    (57)  all_56_12 = e2
% 151.67/22.24    (58)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 151.67/22.24    (59)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 151.67/22.24          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 151.67/22.24    (60)   ~ (all_52_12 = all_10_2)
% 151.67/22.24    (61)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 151.67/22.24          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 151.67/22.24    (62)   ~ (all_52_3 = all_10_2)
% 151.67/22.24    (63)  all_56_2 = e3
% 151.67/22.24    (64)  all_54_15 = all_10_2
% 151.67/22.24    (65)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 151.67/22.24          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 151.67/22.24    (66)  op(e1, e3) = all_52_2
% 151.67/22.24    (67)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 151.67/22.24              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 151.67/22.24            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 151.67/22.24            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 151.67/22.24            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 151.67/22.24            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 151.67/22.24            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 151.67/22.24            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 151.67/22.24            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 151.67/22.24            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 151.67/22.24            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 151.67/22.24            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 151.67/22.24            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.67/22.24            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 151.67/22.24            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 151.67/22.24            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 151.67/22.24            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 151.67/22.24            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 151.67/22.24            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 151.67/22.24            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 151.67/22.24            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 151.67/22.24            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 151.67/22.24            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 151.67/22.24            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 151.67/22.24            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.67/22.24            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 151.67/22.24            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.67/22.24            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 151.67/22.24            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.67/22.24            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 151.67/22.24            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 151.67/22.24            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 151.67/22.24            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 151.67/22.24            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 151.67/22.24            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 151.67/22.24            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 151.67/22.24            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.67/22.24            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 151.67/22.24            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 151.67/22.24            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 151.67/22.24            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 151.67/22.24            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 151.67/22.24            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.67/22.24            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 151.67/22.24            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 151.67/22.24            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 151.67/22.24            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 151.67/22.24            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 151.67/22.24              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 151.67/22.24            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 151.67/22.24            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 151.67/22.24              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 151.67/22.24            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 151.67/22.24            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 151.67/22.24                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 151.67/22.24                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 151.67/22.24                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 151.67/22.24                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 151.67/22.24                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 151.67/22.24                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.00/22.24                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.00/22.24              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.00/22.24                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.00/22.24                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.00/22.24                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.00/22.24                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.00/22.24                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.00/22.24                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.00/22.24                $i(all_57_7))))
% 152.00/22.24    (68)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.24          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.00/22.24    (69)   ~ (all_52_12 = e0)
% 152.00/22.24    (70)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.00/22.24          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.00/22.24            e1)
% 152.00/22.24    (71)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e2) & op(all_42_1, e0) = all_42_0 &
% 152.00/22.24            op(e0, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 152.00/22.24              e1) & op(e0, e3) = all_42_1 & $i(all_42_1))
% 152.00/22.24    (72)  op(e2, e3) = all_52_1
% 152.00/22.24    (73)   ~ (all_52_1 = e2)
% 152.00/22.24    (74)   ~ (all_52_6 = e2)
% 152.00/22.24  
% 152.00/22.24  Begin of proof
% 152.00/22.24  | 
% 152.00/22.24  | BETA: splitting (50) gives:
% 152.00/22.24  | 
% 152.00/22.24  | Case 1:
% 152.00/22.24  | | 
% 152.00/22.24  | |   (75)  all_54_3 = e2
% 152.00/22.24  | | 
% 152.00/22.24  | | COMBINE_EQS: (54), (75) imply:
% 152.00/22.24  | |   (76)  all_52_12 = e2
% 152.00/22.24  | | 
% 152.00/22.24  | | SIMP: (76) implies:
% 152.00/22.24  | |   (77)  all_52_12 = e2
% 152.00/22.24  | | 
% 152.00/22.24  | | REDUCE: (20), (77) imply:
% 152.00/22.24  | |   (78)   ~ (all_52_4 = e2)
% 152.00/22.24  | | 
% 152.00/22.24  | | REDUCE: (29), (77) imply:
% 152.00/22.24  | |   (79)   ~ (all_52_8 = e2)
% 152.00/22.24  | | 
% 152.00/22.24  | | REDUCE: (37), (77) imply:
% 152.00/22.24  | |   (80)   ~ (all_52_13 = e2)
% 152.00/22.24  | | 
% 152.00/22.24  | | SIMP: (80) implies:
% 152.00/22.24  | |   (81)   ~ (all_52_13 = e2)
% 152.00/22.24  | | 
% 152.00/22.24  | | REDUCE: (60), (77) imply:
% 152.00/22.24  | |   (82)   ~ (all_10_2 = e2)
% 152.00/22.24  | | 
% 152.00/22.24  | | SIMP: (82) implies:
% 152.00/22.24  | |   (83)   ~ (all_10_2 = e2)
% 152.00/22.24  | | 
% 152.00/22.24  | | REDUCE: (39), (77) imply:
% 152.00/22.24  | |   (84)   ~ (e3 = e2)
% 152.00/22.24  | | 
% 152.00/22.24  | | SIMP: (84) implies:
% 152.00/22.24  | |   (85)   ~ (e3 = e2)
% 152.00/22.24  | | 
% 152.00/22.24  | | REDUCE: (69), (77) imply:
% 152.00/22.24  | |   (86)   ~ (e2 = e0)
% 152.00/22.24  | | 
% 152.00/22.24  | | BETA: splitting (58) gives:
% 152.00/22.24  | | 
% 152.00/22.24  | | Case 1:
% 152.00/22.24  | | | 
% 152.00/22.24  | | |   (87)  all_54_2 = e3
% 152.00/22.24  | | | 
% 152.00/22.24  | | | REF_CLOSE: (6), (52), (87) are inconsistent by sub-proof #184.
% 152.00/22.24  | | | 
% 152.00/22.24  | | Case 2:
% 152.00/22.24  | | | 
% 152.00/22.24  | | |   (88)   ~ (all_54_2 = e3)
% 152.00/22.24  | | |   (89)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 152.00/22.24  | | | 
% 152.00/22.24  | | | BETA: splitting (89) gives:
% 152.00/22.24  | | | 
% 152.00/22.24  | | | Case 1:
% 152.00/22.24  | | | | 
% 152.00/22.24  | | | |   (90)  all_54_2 = e2
% 152.00/22.24  | | | | 
% 152.00/22.24  | | | | REF_CLOSE: (6), (79), (90) are inconsistent by sub-proof #183.
% 152.00/22.24  | | | | 
% 152.00/22.24  | | | Case 2:
% 152.00/22.24  | | | | 
% 152.00/22.24  | | | |   (91)   ~ (all_54_2 = e2)
% 152.00/22.24  | | | |   (92)  all_54_2 = e1 | all_54_2 = e0
% 152.00/22.24  | | | | 
% 152.00/22.24  | | | | BETA: splitting (92) gives:
% 152.00/22.24  | | | | 
% 152.00/22.24  | | | | Case 1:
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | |   (93)  all_54_2 = e1
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | | COMBINE_EQS: (6), (93) imply:
% 152.00/22.24  | | | | |   (94)  all_52_8 = e1
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | | SIMP: (94) implies:
% 152.00/22.24  | | | | |   (95)  all_52_8 = e1
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | | REDUCE: (43), (95) imply:
% 152.00/22.24  | | | | |   (96)   ~ (all_52_4 = e1)
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | | REDUCE: (52), (95) imply:
% 152.00/22.24  | | | | |   (97)   ~ (e3 = e1)
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | | SIMP: (97) implies:
% 152.00/22.24  | | | | |   (98)   ~ (e3 = e1)
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | | REDUCE: (79), (95) imply:
% 152.00/22.24  | | | | |   (99)   ~ (e2 = e1)
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | | SIMP: (99) implies:
% 152.00/22.24  | | | | |   (100)   ~ (e2 = e1)
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | | REDUCE: (42), (95) imply:
% 152.00/22.24  | | | | |   (101)   ~ (e1 = e0)
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | | BETA: splitting (7) gives:
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | | Case 1:
% 152.00/22.24  | | | | | | 
% 152.00/22.24  | | | | | |   (102)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2,
% 152.00/22.24  | | | | | |              e3) = e1)
% 152.00/22.24  | | | | | | 
% 152.00/22.24  | | | | | | BETA: splitting (102) gives:
% 152.00/22.24  | | | | | | 
% 152.00/22.24  | | | | | | Case 1:
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | |   (103)  all_56_0 = e1 & op(e3, e3) = e1
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | | ALPHA: (103) implies:
% 152.00/22.24  | | | | | | |   (104)  op(e3, e3) = e1
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12),
% 152.00/22.24  | | | | | | |            (13), (14), (15), (17), (18), (19), (21), (22), (23),
% 152.00/22.24  | | | | | | |            (24), (26), (27), (28), (30), (31), (32), (33), (34),
% 152.00/22.24  | | | | | | |            (35), (36), (38), (40), (41), (44), (45), (46), (47),
% 152.00/22.24  | | | | | | |            (48), (49), (53), (55), (56), (59), (61), (62), (64),
% 152.00/22.24  | | | | | | |            (65), (66), (67), (68), (70), (71), (72), (73), (74),
% 152.00/22.24  | | | | | | |            (78), (81), (83), (85), (86), (96), (100), (101), (104)
% 152.00/22.24  | | | | | | |            are inconsistent by sub-proof #277.
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | Case 2:
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | |   (105)  all_56_2 = e1 & op(e2, e3) = e1
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | | REF_CLOSE: (63), (98), (105) are inconsistent by sub-proof #791.
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | End of split
% 152.00/22.24  | | | | | | 
% 152.00/22.24  | | | | | Case 2:
% 152.00/22.24  | | | | | | 
% 152.00/22.24  | | | | | |   (106)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 &
% 152.00/22.24  | | | | | |            op(e0, e3) = e1)
% 152.00/22.24  | | | | | | 
% 152.00/22.24  | | | | | | BETA: splitting (106) gives:
% 152.00/22.24  | | | | | | 
% 152.00/22.24  | | | | | | Case 1:
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | |   (107)  all_56_6 = e1 & op(e1, e3) = e1
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | | ALPHA: (107) implies:
% 152.00/22.24  | | | | | | |   (108)  all_56_6 = e1
% 152.00/22.24  | | | | | | |   (109)  op(e1, e3) = e1
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | | REF_CLOSE: (16), (21), (31), (48), (49), (51), (61), (66), (85),
% 152.00/22.24  | | | | | | |            (86), (100), (101), (108), (109) are inconsistent by
% 152.00/22.24  | | | | | | |            sub-proof #232.
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | Case 2:
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | |   (110)  all_56_12 = e1 & op(e0, e3) = e1
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | | REF_CLOSE: (57), (100), (110) are inconsistent by sub-proof #789.
% 152.00/22.24  | | | | | | | 
% 152.00/22.24  | | | | | | End of split
% 152.00/22.24  | | | | | | 
% 152.00/22.24  | | | | | End of split
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | Case 2:
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | |   (111)  all_54_2 = e0
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | | REF_CLOSE: (6), (42), (111) are inconsistent by sub-proof #383.
% 152.00/22.24  | | | | | 
% 152.00/22.24  | | | | End of split
% 152.00/22.24  | | | | 
% 152.00/22.24  | | | End of split
% 152.00/22.24  | | | 
% 152.00/22.24  | | End of split
% 152.00/22.24  | | 
% 152.00/22.24  | Case 2:
% 152.00/22.24  | | 
% 152.00/22.24  | |   (112)  all_54_3 = e1 | all_54_3 = e0
% 152.00/22.24  | | 
% 152.00/22.24  | | REF_CLOSE: (25), (54), (69), (112) are inconsistent by sub-proof #759.
% 152.00/22.24  | | 
% 152.00/22.24  | End of split
% 152.00/22.24  | 
% 152.00/22.24  End of proof
% 152.00/22.24  
% 152.00/22.24  Sub-proof #183 shows that the following formulas are inconsistent:
% 152.00/22.24  ----------------------------------------------------------------
% 152.00/22.24    (1)  all_54_2 = all_52_8
% 152.00/22.24    (2)  all_54_2 = e2
% 152.00/22.24    (3)   ~ (all_52_8 = e2)
% 152.00/22.24  
% 152.00/22.24  Begin of proof
% 152.00/22.24  | 
% 152.00/22.24  | COMBINE_EQS: (1), (2) imply:
% 152.00/22.24  |   (4)  all_52_8 = e2
% 152.00/22.24  | 
% 152.00/22.24  | SIMP: (4) implies:
% 152.00/22.24  |   (5)  all_52_8 = e2
% 152.00/22.24  | 
% 152.00/22.24  | REDUCE: (3), (5) imply:
% 152.00/22.24  |   (6)  $false
% 152.00/22.24  | 
% 152.00/22.24  | CLOSE: (6) is inconsistent.
% 152.00/22.24  | 
% 152.00/22.24  End of proof
% 152.00/22.24  
% 152.00/22.24  Sub-proof #184 shows that the following formulas are inconsistent:
% 152.00/22.24  ----------------------------------------------------------------
% 152.00/22.24    (1)  all_54_2 = all_52_8
% 152.00/22.24    (2)  all_54_2 = e3
% 152.00/22.24    (3)   ~ (all_52_8 = e3)
% 152.00/22.24  
% 152.00/22.24  Begin of proof
% 152.00/22.24  | 
% 152.00/22.24  | COMBINE_EQS: (1), (2) imply:
% 152.00/22.24  |   (4)  all_52_8 = e3
% 152.00/22.24  | 
% 152.00/22.24  | SIMP: (4) implies:
% 152.00/22.24  |   (5)  all_52_8 = e3
% 152.00/22.24  | 
% 152.00/22.24  | REDUCE: (3), (5) imply:
% 152.00/22.24  |   (6)  $false
% 152.00/22.24  | 
% 152.00/22.24  | CLOSE: (6) is inconsistent.
% 152.00/22.24  | 
% 152.00/22.24  End of proof
% 152.00/22.24  
% 152.00/22.24  Sub-proof #185 shows that the following formulas are inconsistent:
% 152.00/22.24  ----------------------------------------------------------------
% 152.00/22.24    (1)  all_54_9 = all_52_6
% 152.00/22.24    (2)  all_54_9 = e2
% 152.00/22.24    (3)   ~ (all_52_6 = e2)
% 152.00/22.24  
% 152.00/22.24  Begin of proof
% 152.00/22.24  | 
% 152.00/22.24  | COMBINE_EQS: (1), (2) imply:
% 152.00/22.24  |   (4)  all_52_6 = e2
% 152.00/22.24  | 
% 152.00/22.24  | SIMP: (4) implies:
% 152.00/22.24  |   (5)  all_52_6 = e2
% 152.00/22.24  | 
% 152.00/22.24  | REDUCE: (3), (5) imply:
% 152.00/22.24  |   (6)  $false
% 152.00/22.24  | 
% 152.00/22.24  | CLOSE: (6) is inconsistent.
% 152.00/22.24  | 
% 152.00/22.24  End of proof
% 152.00/22.24  
% 152.00/22.24  Sub-proof #186 shows that the following formulas are inconsistent:
% 152.00/22.24  ----------------------------------------------------------------
% 152.00/22.24    (1)  all_54_9 = all_52_6
% 152.00/22.24    (2)  all_54_9 = e3
% 152.00/22.24    (3)   ~ (all_52_6 = e3)
% 152.00/22.24  
% 152.00/22.24  Begin of proof
% 152.00/22.24  | 
% 152.00/22.24  | COMBINE_EQS: (1), (2) imply:
% 152.00/22.24  |   (4)  all_52_6 = e3
% 152.00/22.24  | 
% 152.00/22.24  | SIMP: (4) implies:
% 152.00/22.24  |   (5)  all_52_6 = e3
% 152.00/22.24  | 
% 152.00/22.24  | REDUCE: (3), (5) imply:
% 152.00/22.24  |   (6)  $false
% 152.00/22.24  | 
% 152.00/22.24  | CLOSE: (6) is inconsistent.
% 152.00/22.24  | 
% 152.00/22.24  End of proof
% 152.00/22.24  
% 152.00/22.24  Sub-proof #187 shows that the following formulas are inconsistent:
% 152.00/22.24  ----------------------------------------------------------------
% 152.00/22.24    (1)  op(e0, e1) = all_52_11
% 152.00/22.24    (2)  all_56_8 = e3
% 152.00/22.24    (3)   ~ (all_52_7 = all_52_11)
% 152.00/22.24    (4)   ~ (e3 = e1)
% 152.00/22.24    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 152.00/22.24         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 152.00/22.24    (6)   ~ (all_52_11 = all_10_2)
% 152.00/22.24    (7)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 152.00/22.24    (8)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.00/22.24         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.00/22.24    (9)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 152.00/22.24         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.00/22.24    (10)  op(e0, e0) = all_10_2
% 152.00/22.24    (11)  op(e3, e2) = all_52_4
% 152.00/22.24    (12)  op(e0, e2) = all_52_7
% 152.00/22.24    (13)   ~ (all_52_9 = all_52_13)
% 152.00/22.24    (14)   ~ (all_52_3 = all_52_7)
% 152.00/22.24    (15)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.00/22.24          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.00/22.24    (16)   ~ (all_10_2 = e1)
% 152.00/22.24    (17)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.00/22.24          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.00/22.24    (18)   ~ (all_52_4 = all_52_12)
% 152.00/22.24    (19)   ~ (e2 = e0)
% 152.00/22.24    (20)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.00/22.24          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.00/22.24    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.24    (22)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.00/22.24          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.00/22.24    (23)   ~ (all_52_13 = e0)
% 152.00/22.24    (24)   ~ (all_52_1 = all_52_13)
% 152.00/22.24    (25)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.00/22.24          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.00/22.24    (26)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.00/22.24          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.00/22.24    (27)   ~ (all_52_3 = all_52_11)
% 152.00/22.24    (28)   ~ (all_52_9 = e3)
% 152.00/22.24    (29)   ~ (all_52_13 = all_52_14)
% 152.00/22.24    (30)   ~ (all_52_1 = all_52_9)
% 152.00/22.24    (31)  op(e1, e0) = all_52_14
% 152.00/22.24    (32)   ~ (all_52_12 = all_52_14)
% 152.00/22.24    (33)   ~ (e3 = e0)
% 152.00/22.24    (34)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.00/22.24          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.00/22.24    (35)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 152.00/22.24          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.00/22.24    (36)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.00/22.24          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.00/22.24    (37)   ~ (all_52_6 = e3)
% 152.00/22.24    (38)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 152.00/22.24          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 152.00/22.24    (39)  op(e3, e3) = e1
% 152.00/22.24    (40)   ~ (all_52_12 = all_52_13)
% 152.00/22.24    (41)  op(e1, e2) = all_52_6
% 152.00/22.24    (42)  op(e2, e0) = all_52_13
% 152.00/22.24    (43)   ~ (all_52_1 = all_52_3)
% 152.00/22.24    (44)  op(e0, e3) = all_52_3
% 152.00/22.24    (45)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 152.00/22.24    (46)  all_54_12 = all_52_3
% 152.00/22.24    (47)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.24          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.00/22.24    (48)  op(e2, e1) = all_52_9
% 152.00/22.24    (49)   ~ (all_52_1 = e1)
% 152.00/22.24    (50)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.00/22.24          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.00/22.25    (51)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 152.00/22.25              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.00/22.25            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 152.00/22.25                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 152.00/22.25              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.00/22.25          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 152.00/22.25              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.00/22.25            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 152.00/22.25                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 152.00/22.25              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.00/22.25          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 152.00/22.25              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.00/22.25            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 152.00/22.25                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 152.00/22.25              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.00/22.25          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 152.00/22.25              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.00/22.25            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 152.00/22.25                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 152.00/22.25                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.00/22.25                $i(all_57_14))))
% 152.00/22.25    (52)  op(e1, e1) = e3
% 152.00/22.25    (53)   ~ (e3 = e2)
% 152.00/22.25    (54)   ~ (all_52_14 = e3)
% 152.00/22.25    (55)   ~ (all_52_8 = e3)
% 152.00/22.25    (56)  all_54_3 = all_52_12
% 152.00/22.25    (57)   ~ (all_52_14 = all_10_2)
% 152.00/22.25    (58)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.00/22.25          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.00/22.25    (59)   ~ (all_52_7 = all_10_2)
% 152.00/22.25    (60)   ~ (all_52_6 = all_52_14)
% 152.00/22.25    (61)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.00/22.25          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.00/22.25    (62)   ~ (all_52_12 = all_10_2)
% 152.00/22.25    (63)  all_54_13 = all_52_7
% 152.00/22.25    (64)  op(e3, e1) = all_52_8
% 152.00/22.25    (65)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 152.00/22.25    (66)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.00/22.25          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.00/22.25    (67)   ~ (all_52_3 = all_10_2)
% 152.00/22.25    (68)   ~ (all_52_6 = all_52_7)
% 152.00/22.25    (69)  all_54_11 = all_52_14
% 152.00/22.25    (70)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.00/22.25    (71)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.00/22.25          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.00/22.25    (72)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.00/22.25              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.00/22.25            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.00/22.25            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.00/22.25            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.00/22.25            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.00/22.25            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.00/22.25            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.00/22.25            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.00/22.25            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.00/22.25            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.00/22.25            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.00/22.25            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.00/22.25            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.00/22.25            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.00/22.25            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.00/22.25            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.00/22.25            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.00/22.25            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.00/22.25            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.00/22.25            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.00/22.25            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.00/22.25            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.00/22.25            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.00/22.25            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.00/22.25            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.00/22.25            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.00/22.25            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.00/22.25            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.00/22.25            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.00/22.25            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.00/22.25            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.00/22.25            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.00/22.25            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.00/22.25            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.00/22.25            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.00/22.25            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.00/22.25            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.00/22.25            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.00/22.25            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.00/22.25            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.00/22.25            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.00/22.25            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.00/22.25            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.00/22.25            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.00/22.25            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.00/22.25            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.00/22.25            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.00/22.25              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.00/22.25            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.00/22.25            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.00/22.25              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.00/22.25            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.00/22.25            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.00/22.25                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.00/22.25                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.00/22.25                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.00/22.25                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.00/22.25                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.00/22.25                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.00/22.25                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.00/22.25              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.00/22.25                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.00/22.25                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.00/22.25                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.00/22.25                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.00/22.25                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.00/22.25                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.00/22.25                $i(all_57_7))))
% 152.00/22.25    (73)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.25          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.00/22.25    (74)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.00/22.25          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.00/22.25            e1)
% 152.00/22.25    (75)  op(e2, e2) = e0
% 152.00/22.25    (76)  op(e2, e3) = all_52_1
% 152.00/22.25  
% 152.00/22.25  Begin of proof
% 152.00/22.25  | 
% 152.00/22.25  | BETA: splitting (51) gives:
% 152.00/22.25  | 
% 152.00/22.25  | Case 1:
% 152.00/22.25  | | 
% 152.00/22.25  | |   (77)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 152.00/22.25  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 152.00/22.25  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 152.00/22.25  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 152.00/22.25  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 152.00/22.25  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 152.00/22.25  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 152.00/22.25  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.00/22.25  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 152.00/22.25  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 152.00/22.25  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 152.00/22.25  | |               $i(all_57_15))))
% 152.00/22.25  | | 
% 152.00/22.25  | | REF_CLOSE: (4), (19), (21), (39), (75), (77) are inconsistent by sub-proof
% 152.00/22.25  | |            #602.
% 152.00/22.25  | | 
% 152.00/22.25  | Case 2:
% 152.00/22.25  | | 
% 152.00/22.25  | |   (78)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 152.00/22.25  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.00/22.25  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 152.00/22.25  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.00/22.25  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 152.00/22.25  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 152.00/22.25  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 152.00/22.25  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.00/22.25  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 152.00/22.25  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 152.00/22.25  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 152.00/22.25  | |               all_57_14 & $i(all_57_14))))
% 152.00/22.25  | | 
% 152.00/22.25  | | BETA: splitting (78) gives:
% 152.00/22.25  | | 
% 152.00/22.25  | | Case 1:
% 152.00/22.25  | | | 
% 152.00/22.25  | | |   (79)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 152.00/22.25  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.00/22.25  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 152.00/22.25  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.00/22.25  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 152.00/22.25  | | |               e0) = all_57_15 & $i(all_57_15)))
% 152.00/22.25  | | | 
% 152.00/22.25  | | | ALPHA: (79) implies:
% 152.00/22.25  | | |   (80)  op(e1, e1) = e1
% 152.00/22.25  | | | 
% 152.00/22.25  | | | REF_CLOSE: (4), (21), (52), (80) are inconsistent by sub-proof #734.
% 152.00/22.25  | | | 
% 152.00/22.25  | | Case 2:
% 152.00/22.25  | | | 
% 152.00/22.25  | | |   (81)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 152.00/22.25  | | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.00/22.25  | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 152.00/22.25  | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.00/22.25  | | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 152.00/22.25  | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 152.00/22.25  | | | 
% 152.00/22.25  | | | ALPHA: (81) implies:
% 152.00/22.25  | | |   (82)  all_57_15 = e0
% 152.00/22.25  | | |   (83)  op(e0, e0) = e0
% 152.00/22.25  | | |   (84)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 152.00/22.25  | | |             e2) = all_57_12 & $i(all_57_12))
% 152.00/22.25  | | | 
% 152.00/22.25  | | | BETA: splitting (84) gives:
% 152.00/22.25  | | | 
% 152.00/22.25  | | | Case 1:
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | |   (85)  all_57_11 = e2 & op(e2, e0) = e2
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | ALPHA: (85) implies:
% 152.00/22.25  | | | |   (86)  op(e2, e0) = e2
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | GROUND_INST: instantiating (21) with all_10_2, e0, e0, e0, simplifying
% 152.00/22.25  | | | |              with (10), (83) gives:
% 152.00/22.25  | | | |   (87)  all_10_2 = e0
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | GROUND_INST: instantiating (21) with all_52_13, e2, e0, e2, simplifying
% 152.00/22.25  | | | |              with (42), (86) gives:
% 152.00/22.25  | | | |   (88)  all_52_13 = e2
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | REDUCE: (24), (88) imply:
% 152.00/22.25  | | | |   (89)   ~ (all_52_1 = e2)
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | REDUCE: (67), (87) imply:
% 152.00/22.25  | | | |   (90)   ~ (all_52_3 = e0)
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | REDUCE: (59), (87) imply:
% 152.00/22.25  | | | |   (91)   ~ (all_52_7 = e0)
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | REDUCE: (13), (88) imply:
% 152.00/22.25  | | | |   (92)   ~ (all_52_9 = e2)
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | REDUCE: (6), (87) imply:
% 152.00/22.25  | | | |   (93)   ~ (all_52_11 = e0)
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | REDUCE: (40), (88) imply:
% 152.00/22.25  | | | |   (94)   ~ (all_52_12 = e2)
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | REDUCE: (62), (87) imply:
% 152.00/22.25  | | | |   (95)   ~ (all_52_12 = e0)
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | REDUCE: (29), (88) imply:
% 152.00/22.25  | | | |   (96)   ~ (all_52_14 = e2)
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | SIMP: (96) implies:
% 152.00/22.25  | | | |   (97)   ~ (all_52_14 = e2)
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | REDUCE: (57), (87) imply:
% 152.00/22.25  | | | |   (98)   ~ (all_52_14 = e0)
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | BETA: splitting (7) gives:
% 152.00/22.25  | | | | 
% 152.00/22.25  | | | | Case 1:
% 152.00/22.25  | | | | | 
% 152.00/22.25  | | | | |   (99)  all_54_11 = e3
% 152.00/22.25  | | | | | 
% 152.00/22.25  | | | | | REF_CLOSE: (54), (69), (99) are inconsistent by sub-proof #661.
% 152.00/22.25  | | | | | 
% 152.00/22.25  | | | | Case 2:
% 152.00/22.25  | | | | | 
% 152.00/22.25  | | | | |   (100)   ~ (all_54_11 = e3)
% 152.00/22.25  | | | | |   (101)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 152.00/22.25  | | | | | 
% 152.00/22.25  | | | | | BETA: splitting (101) gives:
% 152.00/22.25  | | | | | 
% 152.00/22.25  | | | | | Case 1:
% 152.00/22.25  | | | | | | 
% 152.00/22.25  | | | | | |   (102)  all_54_11 = e2
% 152.00/22.25  | | | | | | 
% 152.00/22.25  | | | | | | REF_CLOSE: (69), (97), (102) are inconsistent by sub-proof #393.
% 152.00/22.25  | | | | | | 
% 152.00/22.25  | | | | | Case 2:
% 152.00/22.25  | | | | | | 
% 152.00/22.25  | | | | | |   (103)   ~ (all_54_11 = e2)
% 152.00/22.25  | | | | | |   (104)  all_54_11 = e1 | all_54_11 = e0
% 152.00/22.25  | | | | | | 
% 152.00/22.25  | | | | | | BETA: splitting (104) gives:
% 152.00/22.25  | | | | | | 
% 152.00/22.25  | | | | | | Case 1:
% 152.00/22.25  | | | | | | | 
% 152.00/22.25  | | | | | | |   (105)  all_54_11 = e1
% 152.00/22.25  | | | | | | | 
% 152.00/22.25  | | | | | | | COMBINE_EQS: (69), (105) imply:
% 152.00/22.25  | | | | | | |   (106)  all_52_14 = e1
% 152.00/22.25  | | | | | | | 
% 152.00/22.25  | | | | | | | SIMP: (106) implies:
% 152.00/22.25  | | | | | | |   (107)  all_52_14 = e1
% 152.00/22.25  | | | | | | | 
% 152.00/22.25  | | | | | | | REDUCE: (60), (107) imply:
% 152.00/22.25  | | | | | | |   (108)   ~ (all_52_6 = e1)
% 152.00/22.25  | | | | | | | 
% 152.00/22.25  | | | | | | | REDUCE: (32), (107) imply:
% 152.00/22.25  | | | | | | |   (109)   ~ (all_52_12 = e1)
% 152.00/22.25  | | | | | | | 
% 152.00/22.25  | | | | | | | REDUCE: (54), (107) imply:
% 152.00/22.25  | | | | | | |   (110)   ~ (e3 = e1)
% 152.00/22.25  | | | | | | | 
% 152.00/22.25  | | | | | | | REDUCE: (97), (107) imply:
% 152.00/22.25  | | | | | | |   (111)   ~ (e2 = e1)
% 152.00/22.25  | | | | | | | 
% 152.00/22.25  | | | | | | | SIMP: (111) implies:
% 152.00/22.25  | | | | | | |   (112)   ~ (e2 = e1)
% 152.00/22.25  | | | | | | | 
% 152.00/22.25  | | | | | | | REDUCE: (98), (107) imply:
% 152.00/22.25  | | | | | | |   (113)   ~ (e1 = e0)
% 152.00/22.25  | | | | | | | 
% 152.00/22.25  | | | | | | | BETA: splitting (71) gives:
% 152.00/22.25  | | | | | | | 
% 152.00/22.25  | | | | | | | Case 1:
% 152.00/22.25  | | | | | | | | 
% 152.00/22.25  | | | | | | | |   (114)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 &
% 152.00/22.25  | | | | | | | |            op(e2, e2) = e1)
% 152.00/22.25  | | | | | | | | 
% 152.00/22.25  | | | | | | | | BETA: splitting (114) gives:
% 152.00/22.25  | | | | | | | | 
% 152.00/22.25  | | | | | | | | Case 1:
% 152.00/22.25  | | | | | | | | | 
% 152.00/22.25  | | | | | | | | |   (115)  all_56_1 = e1 & op(e3, e2) = e1
% 152.00/22.25  | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | ALPHA: (115) implies:
% 152.00/22.25  | | | | | | | | |   (116)  all_56_1 = e1
% 152.00/22.25  | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | BETA: splitting (73) gives:
% 152.00/22.25  | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | Case 1:
% 152.00/22.25  | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | |   (117)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 152.00/22.25  | | | | | | | | | |            & op(e2, e2) = e3)
% 152.00/22.25  | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | REF_CLOSE: (4), (21), (33), (75), (116), (117) are
% 152.00/22.25  | | | | | | | | | |            inconsistent by sub-proof #465.
% 152.00/22.25  | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | Case 2:
% 152.00/22.25  | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | |   (118)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3
% 152.00/22.25  | | | | | | | | | |            & op(e0, e2) = e3)
% 152.00/22.25  | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | BETA: splitting (118) gives:
% 152.00/22.25  | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | Case 1:
% 152.00/22.25  | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | |   (119)  all_56_7 = e3 & op(e1, e2) = e3
% 152.00/22.25  | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | REF_CLOSE: (21), (37), (41), (119) are inconsistent by
% 152.00/22.25  | | | | | | | | | | |            sub-proof #925.
% 152.00/22.25  | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | Case 2:
% 152.00/22.25  | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | |   (120)  all_56_13 = e3 & op(e0, e2) = e3
% 152.00/22.25  | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | ALPHA: (120) implies:
% 152.00/22.25  | | | | | | | | | | |   (121)  all_56_13 = e3
% 152.00/22.25  | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | BETA: splitting (72) gives:
% 152.00/22.25  | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | Case 1:
% 152.00/22.25  | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | |   (122)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.00/22.25  | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.00/22.25  | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 152.00/22.25  | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 152.00/22.25  | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 152.00/22.25  | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.00/22.25  | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.00/22.25  | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.00/22.25  | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.00/22.25  | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.00/22.25  | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.00/22.25  | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 152.00/22.25  | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 152.00/22.25  | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 152.00/22.25  | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.00/22.25  | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.00/22.25  | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 152.00/22.25  | | | | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.00/22.25  | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.00/22.25  | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 152.00/22.25  | | | | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 152.00/22.25  | | | | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.00/22.25  | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.00/22.25  | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 152.00/22.25  | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.00/22.25  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 152.00/22.25  | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 152.00/22.25  | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 152.00/22.25  | | | | | | | | | | | |              e2) = e1 & op(e1, e1) = all_57_14 &
% 152.00/22.25  | | | | | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 152.00/22.25  | | | | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 152.00/22.25  | | | | | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 152.00/22.25  | | | | | | | | | | | |            = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 152.00/22.25  | | | | | | | | | | | |            = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 152.00/22.25  | | | | | | | | | | | |            = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.00/22.25  | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.00/22.25  | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 152.00/22.25  | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.00/22.25  | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | BETA: splitting (122) gives:
% 152.00/22.25  | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | Case 1:
% 152.00/22.25  | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | |   (123)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.00/22.25  | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.00/22.25  | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 152.00/22.25  | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 152.00/22.25  | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 152.00/22.25  | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.00/22.25  | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.00/22.25  | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.00/22.25  | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.00/22.25  | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.00/22.25  | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.00/22.25  | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 152.00/22.25  | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 152.00/22.25  | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 152.00/22.25  | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.00/22.25  | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.00/22.25  | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 152.00/22.25  | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | BETA: splitting (123) gives:
% 152.00/22.25  | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | Case 1:
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | |   (124)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.00/22.25  | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 152.00/22.25  | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 152.00/22.25  | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | | REF_CLOSE: (21), (76), (89), (124) are inconsistent by
% 152.00/22.25  | | | | | | | | | | | | | |            sub-proof #1180.
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | Case 2:
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | |   (125)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.00/22.25  | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.00/22.25  | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 152.00/22.25  | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 152.00/22.25  | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.00/22.25  | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | | REF_CLOSE: (21), (33), (52), (83), (125) are inconsistent by
% 152.00/22.25  | | | | | | | | | | | | | |            sub-proof #352.
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | End of split
% 152.00/22.25  | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | Case 2:
% 152.00/22.25  | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | |   (126)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.00/22.25  | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.00/22.25  | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.00/22.25  | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 152.00/22.25  | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 152.00/22.25  | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 152.00/22.25  | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.00/22.25  | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.00/22.25  | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 152.00/22.25  | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.00/22.25  | | | | | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.00/22.25  | | | | | | | | | | | | |            = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.00/22.25  | | | | | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.00/22.25  | | | | | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.00/22.25  | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.00/22.25  | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 152.00/22.25  | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 152.00/22.25  | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.00/22.25  | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.00/22.25  | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.00/22.25  | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.00/22.25  | | | | | | | | | | | | |            $i(all_57_10))
% 152.00/22.25  | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | BETA: splitting (126) gives:
% 152.00/22.25  | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | Case 1:
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | |   (127)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.00/22.25  | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.00/22.25  | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.00/22.25  | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 152.00/22.25  | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 152.00/22.25  | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.00/22.25  | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10))
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (52), (53), (83), (127) are
% 152.00/22.25  | | | | | | | | | | | | | |            inconsistent by sub-proof #245.
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | Case 2:
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | |   (128)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.00/22.25  | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 152.00/22.25  | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) &
% 152.00/22.25  | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 152.00/22.25  | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.00/22.25  | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 152.00/22.25  | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.00/22.25  | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.00/22.25  | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 152.00/22.25  | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 152.00/22.25  | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | | Case 1:
% 152.00/22.25  | | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | | |   (129)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.00/22.25  | | | | | | | | | | | | | | |            e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 152.00/22.25  | | | | | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 152.00/22.25  | | | | | | | | | | | | | | |            e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 152.00/22.25  | | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | | | ALPHA: (129) implies:
% 152.00/22.25  | | | | | | | | | | | | | | |   (130)  op(e3, e3) = e2
% 152.00/22.25  | | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | | | REF_CLOSE: (21), (39), (112), (130) are inconsistent by
% 152.00/22.25  | | | | | | | | | | | | | | |            sub-proof #1074.
% 152.00/22.25  | | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | | Case 2:
% 152.00/22.25  | | | | | | | | | | | | | | | 
% 152.00/22.25  | | | | | | | | | | | | | | |   (131)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.00/22.25  | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.00/22.25  | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 152.00/22.25  | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 152.00/22.25  | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.00/22.25  | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.00/22.25  | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.00/22.25  | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.00/22.25  | | | | | | | | | | | | | | |            $i(all_57_10))
% 152.00/22.25  | | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | | | REF_CLOSE: (8), (19), (21), (33), (53), (58), (83), (112),
% 152.00/22.26  | | | | | | | | | | | | | | |            (113), (116), (121), (131) are inconsistent by
% 152.00/22.26  | | | | | | | | | | | | | | |            sub-proof #207.
% 152.00/22.26  | | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | | End of split
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | End of split
% 152.00/22.26  | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | End of split
% 152.00/22.26  | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | Case 2:
% 152.00/22.26  | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | |   (132)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.00/22.26  | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.00/22.26  | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.00/22.26  | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.00/22.26  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 152.00/22.26  | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 152.00/22.26  | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 152.00/22.26  | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 152.00/22.26  | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.00/22.26  | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.00/22.26  | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.00/22.26  | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 152.00/22.26  | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.00/22.26  | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 152.00/22.26  | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 152.00/22.26  | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.00/22.26  | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.00/22.26  | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 152.00/22.26  | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 152.00/22.26  | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.00/22.26  | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.00/22.26  | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 152.00/22.26  | | | | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 152.00/22.26  | | | | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 152.00/22.26  | | | | | | | | | | | |            = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 152.00/22.26  | | | | | | | | | | | |            = e2 & $i(all_57_9) & $i(all_57_12)) |
% 152.00/22.26  | | | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 152.00/22.26  | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.00/22.26  | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 152.00/22.26  | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 152.00/22.26  | | | | | | | | | | | |          | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 152.00/22.26  | | | | | | | | | | | |              = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.00/22.26  | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.00/22.26  | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.00/22.26  | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 152.00/22.26  | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.00/22.26  | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.00/22.26  | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.00/22.26  | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.00/22.26  | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.00/22.26  | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.00/22.26  | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 152.00/22.26  | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.00/22.26  | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.00/22.26  | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.00/22.26  | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.00/22.26  | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.00/22.26  | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 152.00/22.26  | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 152.00/22.26  | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 152.00/22.26  | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.00/22.26  | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.00/22.26  | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 152.00/22.26  | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.00/22.26  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 152.00/22.26  | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 152.00/22.26  | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 152.00/22.26  | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 152.00/22.26  | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.00/22.26  | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.00/22.26  | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.00/22.26  | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | BETA: splitting (132) gives:
% 152.00/22.26  | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | Case 1:
% 152.00/22.26  | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | |   (133)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.00/22.26  | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.00/22.26  | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.00/22.26  | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.00/22.26  | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 152.00/22.26  | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 152.00/22.26  | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 152.00/22.26  | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 152.00/22.26  | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.00/22.26  | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.00/22.26  | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.00/22.26  | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 152.00/22.26  | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.00/22.26  | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 152.00/22.26  | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 152.00/22.26  | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.00/22.26  | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.00/22.26  | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 152.00/22.26  | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 152.00/22.26  | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.00/22.26  | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.00/22.26  | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 152.00/22.26  | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | BETA: splitting (133) gives:
% 152.00/22.26  | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | Case 1:
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | |   (134)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.00/22.26  | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.00/22.26  | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.00/22.26  | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.00/22.26  | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 152.00/22.26  | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 152.00/22.26  | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 152.00/22.26  | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 152.00/22.26  | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | | REF_CLOSE: (21), (48), (55), (64), (92), (134) are
% 152.00/22.26  | | | | | | | | | | | | | |            inconsistent by sub-proof #1083.
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | Case 2:
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | |   (135)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.00/22.26  | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 152.00/22.26  | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.00/22.26  | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.00/22.26  | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 152.00/22.26  | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 152.00/22.26  | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.00/22.26  | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.00/22.26  | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 152.00/22.26  | | | | | | | | | | | | | |            & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.00/22.26  | | | | | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 152.00/22.26  | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.00/22.26  | | | | | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | | REF_CLOSE: (21), (33), (52), (83), (84), (113), (135) are
% 152.00/22.26  | | | | | | | | | | | | | |            inconsistent by sub-proof #243.
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | End of split
% 152.00/22.26  | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | Case 2:
% 152.00/22.26  | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | |   (136)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 152.00/22.26  | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 152.00/22.26  | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 152.00/22.26  | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 152.00/22.26  | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 152.00/22.26  | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 152.00/22.26  | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 152.00/22.26  | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 152.00/22.26  | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 152.00/22.26  | | | | | | | | | | | | |            e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 152.00/22.26  | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.00/22.26  | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.00/22.26  | | | | | | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 152.00/22.26  | | | | | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 152.00/22.26  | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 152.00/22.26  | | | | | | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 152.00/22.26  | | | | | | | | | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 152.00/22.26  | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.00/22.26  | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 152.00/22.26  | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.00/22.26  | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 152.00/22.26  | | | | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 152.00/22.26  | | | | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.00/22.26  | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.00/22.26  | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.00/22.26  | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 152.00/22.26  | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 152.00/22.26  | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 152.00/22.26  | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.00/22.26  | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.00/22.26  | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 152.00/22.26  | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.00/22.26  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 152.00/22.26  | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 152.00/22.26  | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 152.00/22.26  | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 152.00/22.26  | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.00/22.26  | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.00/22.26  | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.00/22.26  | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | BETA: splitting (136) gives:
% 152.00/22.26  | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | Case 1:
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | |   (137)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 152.00/22.26  | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 152.00/22.26  | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 152.00/22.26  | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 152.00/22.26  | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 152.00/22.26  | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 152.00/22.26  | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 152.00/22.26  | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 152.00/22.26  | | | | | | | | | | | | | |            $i(all_57_14))
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | | REF_CLOSE: (21), (39), (113), (137) are inconsistent by
% 152.00/22.26  | | | | | | | | | | | | | |            sub-proof #956.
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | Case 2:
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | |   (138)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.00/22.26  | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.00/22.26  | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.00/22.26  | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.00/22.26  | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 152.00/22.26  | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.00/22.26  | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.00/22.26  | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.00/22.26  | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.00/22.26  | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.00/22.26  | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.00/22.26  | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 152.00/22.26  | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.00/22.26  | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.00/22.26  | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.00/22.26  | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.00/22.26  | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.00/22.26  | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 152.00/22.26  | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 152.00/22.26  | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 152.00/22.26  | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.00/22.26  | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.00/22.26  | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 152.00/22.26  | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.00/22.26  | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 152.00/22.26  | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 152.00/22.26  | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 152.00/22.26  | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 152.00/22.26  | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.00/22.26  | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.00/22.26  | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | | REF_CLOSE: (1), (12), (21), (33), (44), (52), (53), (84),
% 152.00/22.26  | | | | | | | | | | | | | |            (90), (91), (93), (138) are inconsistent by
% 152.00/22.26  | | | | | | | | | | | | | |            sub-proof #206.
% 152.00/22.26  | | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | | End of split
% 152.00/22.26  | | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | | End of split
% 152.00/22.26  | | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | | End of split
% 152.00/22.26  | | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | | End of split
% 152.00/22.26  | | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | End of split
% 152.00/22.26  | | | | | | | | | 
% 152.00/22.26  | | | | | | | | Case 2:
% 152.00/22.26  | | | | | | | | | 
% 152.00/22.26  | | | | | | | | |   (139)  all_56_3 = e1 & op(e2, e2) = e1
% 152.00/22.26  | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | ALPHA: (139) implies:
% 152.00/22.26  | | | | | | | | |   (140)  all_56_3 = e1
% 152.00/22.26  | | | | | | | | |   (141)  op(e2, e2) = e1
% 152.00/22.26  | | | | | | | | | 
% 152.00/22.26  | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (14),
% 152.00/22.26  | | | | | | | | |            (15), (16), (17), (19), (20), (21), (22), (24),
% 152.00/22.26  | | | | | | | | |            (25), (26), (27), (28), (30), (31), (33), (34),
% 152.00/22.26  | | | | | | | | |            (35), (36), (37), (38), (39), (41), (42), (43),
% 152.00/22.26  | | | | | | | | |            (44), (45), (46), (47), (48), (49), (50), (52),
% 152.00/22.26  | | | | | | | | |            (53), (55), (58), (59), (61), (63), (64), (66),
% 152.00/22.26  | | | | | | | | |            (67), (68), (70), (72), (73), (74), (76), (82),
% 152.00/22.26  | | | | | | | | |            (83), (84), (112), (113), (140), (141) are
% 152.00/22.26  | | | | | | | | |            inconsistent by sub-proof #241.
% 152.00/22.26  | | | | | | | | | 
% 152.00/22.26  | | | | | | | | End of split
% 152.00/22.26  | | | | | | | | 
% 152.00/22.26  | | | | | | | Case 2:
% 152.00/22.26  | | | | | | | | 
% 152.00/22.26  | | | | | | | |   (142)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 &
% 152.00/22.26  | | | | | | | |            op(e0, e2) = e1)
% 152.00/22.26  | | | | | | | | 
% 152.00/22.26  | | | | | | | | REF_CLOSE: (4), (11), (18), (21), (33), (37), (41), (56), (65),
% 152.00/22.26  | | | | | | | |            (73), (75), (94), (95), (108), (109), (142) are
% 152.00/22.26  | | | | | | | |            inconsistent by sub-proof #212.
% 152.00/22.26  | | | | | | | | 
% 152.00/22.26  | | | | | | | End of split
% 152.00/22.26  | | | | | | | 
% 152.00/22.26  | | | | | | Case 2:
% 152.00/22.26  | | | | | | | 
% 152.00/22.26  | | | | | | |   (143)  all_54_11 = e0
% 152.00/22.26  | | | | | | | 
% 152.00/22.26  | | | | | | | REF_CLOSE: (69), (98), (143) are inconsistent by sub-proof #211.
% 152.00/22.26  | | | | | | | 
% 152.00/22.26  | | | | | | End of split
% 152.00/22.26  | | | | | | 
% 152.00/22.26  | | | | | End of split
% 152.00/22.26  | | | | | 
% 152.00/22.26  | | | | End of split
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | Case 2:
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | |   (144)   ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12)
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | | ALPHA: (144) implies:
% 152.00/22.26  | | | |   (145)   ~ (all_57_12 = e0)
% 152.00/22.26  | | | |   (146)  op(e2, e2) = all_57_12
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | | REF_CLOSE: (21), (75), (145), (146) are inconsistent by sub-proof #856.
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | End of split
% 152.00/22.26  | | | 
% 152.00/22.26  | | End of split
% 152.00/22.26  | | 
% 152.00/22.26  | End of split
% 152.00/22.26  | 
% 152.00/22.26  End of proof
% 152.00/22.26  
% 152.00/22.26  Sub-proof #188 shows that the following formulas are inconsistent:
% 152.00/22.26  ----------------------------------------------------------------
% 152.00/22.26    (1)  all_56_14 = e1 & op(e0, e1) = e1
% 152.00/22.26    (2)  all_56_14 = e3
% 152.00/22.26    (3)   ~ (e3 = e1)
% 152.00/22.26  
% 152.00/22.26  Begin of proof
% 152.00/22.26  | 
% 152.00/22.26  | ALPHA: (1) implies:
% 152.00/22.26  |   (4)  all_56_14 = e1
% 152.00/22.26  | 
% 152.00/22.26  | COMBINE_EQS: (2), (4) imply:
% 152.00/22.26  |   (5)  e3 = e1
% 152.00/22.26  | 
% 152.00/22.26  | SIMP: (5) implies:
% 152.00/22.26  |   (6)  e3 = e1
% 152.00/22.26  | 
% 152.00/22.26  | REDUCE: (3), (6) imply:
% 152.00/22.26  |   (7)  $false
% 152.00/22.26  | 
% 152.00/22.26  | CLOSE: (7) is inconsistent.
% 152.00/22.26  | 
% 152.00/22.26  End of proof
% 152.00/22.26  
% 152.00/22.26  Sub-proof #189 shows that the following formulas are inconsistent:
% 152.00/22.26  ----------------------------------------------------------------
% 152.00/22.26    (1)   ~ (e3 = e1)
% 152.00/22.26    (2)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.00/22.26    (3)   ~ (e2 = e0)
% 152.00/22.26    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.26    (5)  op(e1, e3) = e1
% 152.00/22.26    (6)   ~ (e3 = e0)
% 152.00/22.26    (7)   ~ (e1 = e0)
% 152.00/22.26    (8)  all_56_7 = e2
% 152.00/22.26    (9)  op(e1, e1) = e3
% 152.00/22.26    (10)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.00/22.26          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.00/22.26    (11)  op(e1, e3) = all_52_2
% 152.00/22.26  
% 152.00/22.26  Begin of proof
% 152.00/22.26  | 
% 152.00/22.26  | BETA: splitting (2) gives:
% 152.00/22.26  | 
% 152.00/22.26  | Case 1:
% 152.00/22.26  | | 
% 152.00/22.26  | |   (12)  all_56_8 = e1 & op(e1, e1) = e1
% 152.00/22.26  | | 
% 152.00/22.26  | | ALPHA: (12) implies:
% 152.00/22.26  | |   (13)  op(e1, e1) = e1
% 152.00/22.26  | | 
% 152.00/22.26  | | REF_CLOSE: (1), (4), (9), (13) are inconsistent by sub-proof #734.
% 152.00/22.26  | | 
% 152.00/22.26  | Case 2:
% 152.00/22.26  | | 
% 152.00/22.26  | |   (14)  all_56_11 = e1 & op(e1, e0) = e1
% 152.00/22.26  | | 
% 152.00/22.26  | | ALPHA: (14) implies:
% 152.00/22.26  | |   (15)  all_56_11 = e1
% 152.00/22.26  | | 
% 152.00/22.26  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (15) are
% 152.00/22.26  | |            inconsistent by sub-proof #237.
% 152.00/22.26  | | 
% 152.00/22.26  | End of split
% 152.00/22.26  | 
% 152.00/22.26  End of proof
% 152.00/22.26  
% 152.00/22.26  Sub-proof #190 shows that the following formulas are inconsistent:
% 152.00/22.26  ----------------------------------------------------------------
% 152.00/22.26    (1)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.00/22.26    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.26    (3)  op(e2, e0) = e3
% 152.00/22.26    (4)   ~ (all_52_9 = e2)
% 152.00/22.26    (5)  op(e2, e1) = all_52_9
% 152.00/22.26    (6)   ~ (e3 = e2)
% 152.00/22.26  
% 152.00/22.26  Begin of proof
% 152.00/22.26  | 
% 152.00/22.26  | BETA: splitting (1) gives:
% 152.00/22.26  | 
% 152.00/22.26  | Case 1:
% 152.00/22.26  | | 
% 152.00/22.26  | |   (7)  all_56_5 = e2 & op(e2, e1) = e2
% 152.00/22.26  | | 
% 152.00/22.26  | | ALPHA: (7) implies:
% 152.00/22.26  | |   (8)  op(e2, e1) = e2
% 152.00/22.26  | | 
% 152.00/22.26  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #1157.
% 152.00/22.26  | | 
% 152.00/22.26  | Case 2:
% 152.00/22.26  | | 
% 152.00/22.26  | |   (9)  all_56_10 = e2 & op(e2, e0) = e2
% 152.00/22.26  | | 
% 152.00/22.26  | | ALPHA: (9) implies:
% 152.00/22.26  | |   (10)  op(e2, e0) = e2
% 152.00/22.26  | | 
% 152.00/22.26  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #854.
% 152.00/22.26  | | 
% 152.00/22.26  | End of split
% 152.00/22.26  | 
% 152.00/22.26  End of proof
% 152.00/22.26  
% 152.00/22.26  Sub-proof #191 shows that the following formulas are inconsistent:
% 152.00/22.26  ----------------------------------------------------------------
% 152.00/22.26    (1)   ~ (e2 = e0)
% 152.00/22.26    (2)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.00/22.26         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.00/22.26    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.26    (4)  op(e2, e3) = e1
% 152.00/22.26    (5)  op(e2, e0) = e3
% 152.00/22.26    (6)  all_56_5 = e0
% 152.00/22.26    (7)   ~ (e3 = e2)
% 152.00/22.26    (8)   ~ (e2 = e1)
% 152.00/22.26    (9)  op(e2, e2) = e0
% 152.00/22.26    (10)  op(e2, e3) = all_52_1
% 152.00/22.26  
% 152.00/22.26  Begin of proof
% 152.00/22.26  | 
% 152.00/22.26  | BETA: splitting (2) gives:
% 152.00/22.26  | 
% 152.00/22.26  | Case 1:
% 152.00/22.26  | | 
% 152.00/22.26  | |   (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 152.00/22.26  | |           e2)
% 152.00/22.26  | | 
% 152.00/22.26  | | REF_CLOSE: (1), (3), (4), (8), (9), (10), (11) are inconsistent by sub-proof
% 152.00/22.26  | |            #624.
% 152.00/22.26  | | 
% 152.00/22.26  | Case 2:
% 152.00/22.26  | | 
% 152.00/22.26  | |   (12)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 152.00/22.26  | |           e2)
% 152.00/22.26  | | 
% 152.00/22.26  | | BETA: splitting (12) gives:
% 152.00/22.26  | | 
% 152.00/22.26  | | Case 1:
% 152.00/22.26  | | | 
% 152.00/22.26  | | |   (13)  all_56_5 = e2 & op(e2, e1) = e2
% 152.00/22.26  | | | 
% 152.00/22.26  | | | REF_CLOSE: (1), (6), (13) are inconsistent by sub-proof #389.
% 152.00/22.26  | | | 
% 152.00/22.26  | | Case 2:
% 152.00/22.26  | | | 
% 152.00/22.26  | | |   (14)  all_56_10 = e2 & op(e2, e0) = e2
% 152.00/22.26  | | | 
% 152.00/22.26  | | | ALPHA: (14) implies:
% 152.00/22.26  | | |   (15)  op(e2, e0) = e2
% 152.00/22.26  | | | 
% 152.00/22.26  | | | REF_CLOSE: (3), (5), (7), (15) are inconsistent by sub-proof #854.
% 152.00/22.26  | | | 
% 152.00/22.26  | | End of split
% 152.00/22.26  | | 
% 152.00/22.26  | End of split
% 152.00/22.26  | 
% 152.00/22.26  End of proof
% 152.00/22.26  
% 152.00/22.26  Sub-proof #192 shows that the following formulas are inconsistent:
% 152.00/22.26  ----------------------------------------------------------------
% 152.00/22.26    (1)   ~ (e3 = e1)
% 152.00/22.26    (2)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.00/22.26    (3)   ~ (e2 = e0)
% 152.00/22.26    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.26    (5)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.00/22.26             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 152.00/22.26               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.00/22.26               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.00/22.26    (6)   ~ (e3 = e0)
% 152.00/22.26    (7)   ~ (e1 = e0)
% 152.00/22.26    (8)  all_56_13 = e3
% 152.00/22.26    (9)  op(e1, e1) = e3
% 152.00/22.26    (10)   ~ (e3 = e2)
% 152.00/22.26    (11)  all_56_15 = e2
% 152.00/22.26    (12)   ~ (e2 = e1)
% 152.00/22.26    (13)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.00/22.26          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.00/22.26            e1)
% 152.00/22.26  
% 152.00/22.26  Begin of proof
% 152.00/22.26  | 
% 152.00/22.26  | BETA: splitting (2) gives:
% 152.00/22.26  | 
% 152.00/22.26  | Case 1:
% 152.00/22.26  | | 
% 152.00/22.26  | |   (14)  all_56_8 = e2 & op(e1, e1) = e2
% 152.00/22.26  | | 
% 152.00/22.26  | | ALPHA: (14) implies:
% 152.00/22.26  | |   (15)  op(e1, e1) = e2
% 152.00/22.26  | | 
% 152.00/22.26  | | REF_CLOSE: (4), (9), (10), (15) are inconsistent by sub-proof #834.
% 152.00/22.26  | | 
% 152.00/22.26  | Case 2:
% 152.00/22.26  | | 
% 152.00/22.26  | |   (16)  all_56_14 = e2 & op(e0, e1) = e2
% 152.00/22.26  | | 
% 152.00/22.26  | | ALPHA: (16) implies:
% 152.00/22.26  | |   (17)  all_56_14 = e2
% 152.00/22.26  | | 
% 152.00/22.26  | | BETA: splitting (13) gives:
% 152.00/22.26  | | 
% 152.00/22.26  | | Case 1:
% 152.00/22.26  | | | 
% 152.00/22.26  | | |   (18)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2)
% 152.00/22.26  | | |           = e1)
% 152.00/22.26  | | | 
% 152.00/22.26  | | | BETA: splitting (18) gives:
% 152.00/22.26  | | | 
% 152.00/22.26  | | | Case 1:
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | |   (19)  all_56_12 = e1 & op(e0, e3) = e1
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | | ALPHA: (19) implies:
% 152.00/22.26  | | | |   (20)  all_56_12 = e1
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | | BETA: splitting (5) gives:
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | | Case 1:
% 152.00/22.26  | | | | | 
% 152.00/22.26  | | | | |   (21)  all_56_15 = e0 & op(e0, e0) = e0
% 152.00/22.26  | | | | | 
% 152.00/22.26  | | | | | ALPHA: (21) implies:
% 152.00/22.26  | | | | |   (22)  all_56_15 = e0
% 152.00/22.26  | | | | | 
% 152.00/22.26  | | | | | COMBINE_EQS: (11), (22) imply:
% 152.00/22.26  | | | | |   (23)  e2 = e0
% 152.00/22.26  | | | | | 
% 152.00/22.26  | | | | | REDUCE: (3), (23) imply:
% 152.00/22.26  | | | | |   (24)  $false
% 152.00/22.26  | | | | | 
% 152.00/22.26  | | | | | CLOSE: (24) is inconsistent.
% 152.00/22.26  | | | | | 
% 152.00/22.26  | | | | Case 2:
% 152.00/22.26  | | | | | 
% 152.00/22.26  | | | | |   (25)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 152.00/22.26  | | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 152.00/22.26  | | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 152.00/22.26  | | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 152.00/22.26  | | | | | 
% 152.00/22.26  | | | | | ALPHA: (25) implies:
% 152.00/22.26  | | | | |   (26)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 152.00/22.26  | | | | |             e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.00/22.26  | | | | | 
% 152.00/22.26  | | | | | REF_CLOSE: (3), (6), (7), (8), (17), (20), (26) are inconsistent by
% 152.00/22.26  | | | | |            sub-proof #1100.
% 152.00/22.26  | | | | | 
% 152.00/22.26  | | | | End of split
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | Case 2:
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | |   (27)  all_56_13 = e1 & op(e0, e2) = e1
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | | REF_CLOSE: (1), (8), (27) are inconsistent by sub-proof #878.
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | End of split
% 152.00/22.26  | | | 
% 152.00/22.26  | | Case 2:
% 152.00/22.26  | | | 
% 152.00/22.26  | | |   (28)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0)
% 152.00/22.26  | | |           = e1)
% 152.00/22.26  | | | 
% 152.00/22.26  | | | BETA: splitting (28) gives:
% 152.00/22.26  | | | 
% 152.00/22.26  | | | Case 1:
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | |   (29)  all_56_14 = e1 & op(e0, e1) = e1
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | | REF_CLOSE: (12), (17), (29) are inconsistent by sub-proof #357.
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | Case 2:
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | |   (30)  all_56_15 = e1 & op(e0, e0) = e1
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | | ALPHA: (30) implies:
% 152.00/22.26  | | | |   (31)  all_56_15 = e1
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | | COMBINE_EQS: (11), (31) imply:
% 152.00/22.26  | | | |   (32)  e2 = e1
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | | REDUCE: (12), (32) imply:
% 152.00/22.26  | | | |   (33)  $false
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | | CLOSE: (33) is inconsistent.
% 152.00/22.26  | | | | 
% 152.00/22.26  | | | End of split
% 152.00/22.26  | | | 
% 152.00/22.26  | | End of split
% 152.00/22.26  | | 
% 152.00/22.26  | End of split
% 152.00/22.26  | 
% 152.00/22.26  End of proof
% 152.00/22.26  
% 152.00/22.26  Sub-proof #193 shows that the following formulas are inconsistent:
% 152.00/22.26  ----------------------------------------------------------------
% 152.00/22.26    (1)   ~ (e3 = e1)
% 152.00/22.26    (2)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.00/22.26    (3)  op(e3, e2) = all_52_4
% 152.00/22.26    (4)  all_56_12 = e0
% 152.00/22.26    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.26    (6)   ~ (all_52_4 = e3)
% 152.00/22.26    (7)   ~ (e3 = e0)
% 152.00/22.26    (8)   ~ (all_52_6 = e3)
% 152.00/22.26    (9)  op(e1, e2) = all_52_6
% 152.00/22.26    (10)   ~ (e1 = e0)
% 152.00/22.27    (11)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.27          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.00/22.27    (12)  op(e2, e2) = e0
% 152.00/22.27  
% 152.00/22.27  Begin of proof
% 152.00/22.27  | 
% 152.00/22.27  | BETA: splitting (2) gives:
% 152.00/22.27  | 
% 152.00/22.27  | Case 1:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (13)  all_56_12 = e1 & op(e0, e3) = e1
% 152.00/22.27  | | 
% 152.00/22.27  | | ALPHA: (13) implies:
% 152.00/22.27  | |   (14)  all_56_12 = e1
% 152.00/22.27  | | 
% 152.00/22.27  | | COMBINE_EQS: (4), (14) imply:
% 152.00/22.27  | |   (15)  e1 = e0
% 152.00/22.27  | | 
% 152.00/22.27  | | REDUCE: (10), (15) imply:
% 152.00/22.27  | |   (16)  $false
% 152.00/22.27  | | 
% 152.00/22.27  | | CLOSE: (16) is inconsistent.
% 152.00/22.27  | | 
% 152.00/22.27  | Case 2:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (17)  all_56_13 = e1 & op(e0, e2) = e1
% 152.00/22.27  | | 
% 152.00/22.27  | | ALPHA: (17) implies:
% 152.00/22.27  | |   (18)  all_56_13 = e1
% 152.00/22.27  | | 
% 152.00/22.27  | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (11), (12), (18) are
% 152.00/22.27  | |            inconsistent by sub-proof #210.
% 152.00/22.27  | | 
% 152.00/22.27  | End of split
% 152.00/22.27  | 
% 152.00/22.27  End of proof
% 152.00/22.27  
% 152.00/22.27  Sub-proof #194 shows that the following formulas are inconsistent:
% 152.00/22.27  ----------------------------------------------------------------
% 152.00/22.27    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 152.00/22.27    (2)   ~ (e3 = e1)
% 152.00/22.27    (3)  all_56_10 = e3
% 152.00/22.27    (4)   ~ (e2 = e0)
% 152.00/22.27    (5)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.00/22.27         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.00/22.27    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.27    (7)  op(e2, e0) = e3
% 152.00/22.27    (8)   ~ (e3 = e0)
% 152.00/22.27    (9)   ~ (e1 = e0)
% 152.00/22.27    (10)   ~ (e3 = e2)
% 152.00/22.27    (11)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.00/22.27          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.00/22.27    (12)  op(e3, e3) = e3
% 152.00/22.27    (13)   ~ (e2 = e1)
% 152.00/22.27    (14)  op(e2, e2) = e0
% 152.00/22.27  
% 152.00/22.27  Begin of proof
% 152.00/22.27  | 
% 152.00/22.27  | BETA: splitting (1) gives:
% 152.00/22.27  | 
% 152.00/22.27  | Case 1:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (15)  all_56_0 = e0 & op(e3, e3) = e0
% 152.00/22.27  | | 
% 152.00/22.27  | | ALPHA: (15) implies:
% 152.00/22.27  | |   (16)  op(e3, e3) = e0
% 152.00/22.27  | | 
% 152.00/22.27  | | REF_CLOSE: (6), (8), (12), (16) are inconsistent by sub-proof #1141.
% 152.00/22.27  | | 
% 152.00/22.27  | Case 2:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (17)  all_56_2 = e0 & op(e2, e3) = e0
% 152.00/22.27  | | 
% 152.00/22.27  | | ALPHA: (17) implies:
% 152.00/22.27  | |   (18)  all_56_2 = e0
% 152.00/22.27  | | 
% 152.00/22.27  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14), (18)
% 152.00/22.27  | |            are inconsistent by sub-proof #670.
% 152.00/22.27  | | 
% 152.00/22.27  | End of split
% 152.00/22.27  | 
% 152.00/22.27  End of proof
% 152.00/22.27  
% 152.00/22.27  Sub-proof #195 shows that the following formulas are inconsistent:
% 152.00/22.27  ----------------------------------------------------------------
% 152.00/22.27    (1)   ~ (e3 = e1)
% 152.00/22.27    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.00/22.27         (all_56_14 = e0 & op(e0, e1) = e0)
% 152.00/22.27    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.00/22.27         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.00/22.27    (4)  all_56_4 = e0
% 152.00/22.27    (5)  op(e0, e0) = all_10_2
% 152.00/22.27    (6)  op(e0, e2) = all_52_7
% 152.00/22.27    (7)   ~ (all_52_3 = all_52_7)
% 152.00/22.27    (8)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.00/22.27         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.00/22.27    (9)   ~ (all_10_2 = e1)
% 152.00/22.27    (10)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.00/22.27          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.00/22.27    (11)   ~ (e2 = e0)
% 152.00/22.27    (12)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.00/22.27          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.00/22.27    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.27            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.27    (14)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.00/22.27          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.00/22.27    (15)  all_56_5 = e2
% 152.00/22.27    (16)   ~ (all_52_9 = e3)
% 152.00/22.27    (17)  op(e1, e3) = e1
% 152.00/22.27    (18)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.00/22.27          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.00/22.27    (19)   ~ (e3 = e0)
% 152.00/22.27    (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.00/22.27          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.00/22.27    (21)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 152.00/22.27          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.00/22.27    (22)   ~ (all_52_6 = e3)
% 152.00/22.27    (23)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 152.00/22.27          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 152.00/22.27    (24)  op(e1, e2) = all_52_6
% 152.00/22.27    (25)  op(e0, e3) = all_52_3
% 152.00/22.27    (26)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.27          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.00/22.27    (27)  all_56_11 = e0
% 152.00/22.27    (28)  op(e2, e1) = all_52_9
% 152.00/22.27    (29)   ~ (e1 = e0)
% 152.00/22.27    (30)  op(e1, e1) = e3
% 152.00/22.27    (31)   ~ (e3 = e2)
% 152.00/22.27    (32)  all_56_9 = e2
% 152.00/22.27    (33)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.00/22.27          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.00/22.27    (34)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.00/22.27          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.00/22.27    (35)  op(e3, e3) = e3
% 152.00/22.27    (36)   ~ (e2 = e1)
% 152.00/22.27    (37)  op(e1, e3) = all_52_2
% 152.00/22.27    (38)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.27          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.00/22.27    (39)  op(e2, e2) = e0
% 152.00/22.27  
% 152.00/22.27  Begin of proof
% 152.00/22.27  | 
% 152.00/22.27  | BETA: splitting (18) gives:
% 152.00/22.27  | 
% 152.00/22.27  | Case 1:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (40)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 152.00/22.27  | |           e1)
% 152.00/22.27  | | 
% 152.00/22.27  | | BETA: splitting (40) gives:
% 152.00/22.27  | | 
% 152.00/22.27  | | Case 1:
% 152.00/22.27  | | | 
% 152.00/22.27  | | |   (41)  all_56_0 = e1 & op(e3, e3) = e1
% 152.00/22.27  | | | 
% 152.00/22.27  | | | ALPHA: (41) implies:
% 152.00/22.27  | | |   (42)  op(e3, e3) = e1
% 152.00/22.27  | | | 
% 152.00/22.27  | | | REF_CLOSE: (1), (13), (35), (42) are inconsistent by sub-proof #1178.
% 152.00/22.27  | | | 
% 152.00/22.27  | | Case 2:
% 152.00/22.27  | | | 
% 152.00/22.27  | | |   (43)  all_56_1 = e1 & op(e3, e2) = e1
% 152.00/22.27  | | | 
% 152.00/22.27  | | | ALPHA: (43) implies:
% 152.00/22.27  | | |   (44)  all_56_1 = e1
% 152.00/22.27  | | | 
% 152.00/22.27  | | | BETA: splitting (21) gives:
% 152.00/22.27  | | | 
% 152.00/22.27  | | | Case 1:
% 152.00/22.27  | | | | 
% 152.00/22.27  | | | |   (45)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0)
% 152.00/22.27  | | | |           = e1)
% 152.00/22.27  | | | | 
% 152.00/22.27  | | | | BETA: splitting (45) gives:
% 152.00/22.27  | | | | 
% 152.00/22.27  | | | | Case 1:
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | |   (46)  all_56_9 = e1 & op(e3, e0) = e1
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | | REF_CLOSE: (32), (36), (46) are inconsistent by sub-proof #656.
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | Case 2:
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | |   (47)  all_56_10 = e1 & op(e2, e0) = e1
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | | ALPHA: (47) implies:
% 152.00/22.27  | | | | |   (48)  all_56_10 = e1
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | | BETA: splitting (26) gives:
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | | Case 1:
% 152.00/22.27  | | | | | | 
% 152.00/22.27  | | | | | |   (49)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2,
% 152.00/22.27  | | | | | |             e2) = e3)
% 152.00/22.27  | | | | | | 
% 152.00/22.27  | | | | | | BETA: splitting (49) gives:
% 152.00/22.27  | | | | | | 
% 152.00/22.27  | | | | | | Case 1:
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | |   (50)  all_56_2 = e3 & op(e2, e3) = e3
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | | ALPHA: (50) implies:
% 152.00/22.27  | | | | | | |   (51)  all_56_2 = e3
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | | BETA: splitting (34) gives:
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | 
% 152.00/22.27  | | | | | | | |   (52)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 &
% 152.00/22.27  | | | | | | | |           op(e2, e1) = e1)
% 152.00/22.27  | | | | | | | | 
% 152.00/22.27  | | | | | | | | BETA: splitting (52) gives:
% 152.00/22.27  | | | | | | | | 
% 152.00/22.27  | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | |   (53)  all_56_4 = e1 & op(e3, e1) = e1
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | ALPHA: (53) implies:
% 152.00/22.27  | | | | | | | | |   (54)  all_56_4 = e1
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | COMBINE_EQS: (4), (54) imply:
% 152.00/22.27  | | | | | | | | |   (55)  e1 = e0
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | COMBINE_EQS: (48), (55) imply:
% 152.00/22.27  | | | | | | | | |   (56)  all_56_10 = e0
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | REF_CLOSE: (1), (11), (12), (13), (29), (31), (33), (36),
% 152.00/22.27  | | | | | | | | |            (39), (51), (56) are inconsistent by sub-proof
% 152.00/22.27  | | | | | | | | |            #554.
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | |   (57)  all_56_5 = e1 & op(e2, e1) = e1
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | ALPHA: (57) implies:
% 152.00/22.27  | | | | | | | | |   (58)  all_56_5 = e1
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | REF_CLOSE: (1), (8), (11), (12), (13), (19), (26), (29), (31),
% 152.00/22.27  | | | | | | | | |            (36), (48), (51), (58) are inconsistent by
% 152.00/22.27  | | | | | | | | |            sub-proof #678.
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | 
% 152.00/22.27  | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | 
% 152.00/22.27  | | | | | | | |   (59)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 &
% 152.00/22.27  | | | | | | | |           op(e0, e1) = e1)
% 152.00/22.27  | | | | | | | | 
% 152.00/22.27  | | | | | | | | BETA: splitting (59) gives:
% 152.00/22.27  | | | | | | | | 
% 152.00/22.27  | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | |   (60)  all_56_8 = e1 & op(e1, e1) = e1
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | ALPHA: (60) implies:
% 152.00/22.27  | | | | | | | | |   (61)  op(e1, e1) = e1
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | REF_CLOSE: (1), (13), (30), (61) are inconsistent by sub-proof
% 152.00/22.27  | | | | | | | | |            #734.
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | |   (62)  all_56_14 = e1 & op(e0, e1) = e1
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | ALPHA: (62) implies:
% 152.00/22.27  | | | | | | | | |   (63)  all_56_14 = e1
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | BETA: splitting (23) gives:
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | |   (64)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 &
% 152.00/22.27  | | | | | | | | | |           op(e2, e3) = e2)
% 152.00/22.27  | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | BETA: splitting (64) gives:
% 152.00/22.27  | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | |   (65)  all_56_0 = e2 & op(e3, e3) = e2
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | ALPHA: (65) implies:
% 152.00/22.27  | | | | | | | | | | |   (66)  op(e3, e3) = e2
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | REF_CLOSE: (13), (31), (35), (66) are inconsistent by
% 152.00/22.27  | | | | | | | | | | |            sub-proof #1085.
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | |   (67)  all_56_2 = e2 & op(e2, e3) = e2
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | ALPHA: (67) implies:
% 152.00/22.27  | | | | | | | | | | |   (68)  all_56_2 = e2
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | REF_CLOSE: (31), (51), (68) are inconsistent by sub-proof
% 152.00/22.27  | | | | | | | | | | |            #685.
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | |   (69)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2
% 152.00/22.27  | | | | | | | | | |           & op(e0, e3) = e2)
% 152.00/22.27  | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | BETA: splitting (69) gives:
% 152.00/22.27  | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | |   (70)  all_56_6 = e2 & op(e1, e3) = e2
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | ALPHA: (70) implies:
% 152.00/22.27  | | | | | | | | | | |   (71)  all_56_6 = e2
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | BETA: splitting (3) gives:
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | |   (72)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 152.00/22.27  | | | | | | | | | | | |           & op(e2, e3) = e1)
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | BETA: splitting (72) gives:
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | |   (73)  all_56_0 = e1 & op(e3, e3) = e1
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | ALPHA: (73) implies:
% 152.00/22.27  | | | | | | | | | | | | |   (74)  op(e3, e3) = e1
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | REF_CLOSE: (1), (13), (35), (74) are inconsistent by
% 152.00/22.27  | | | | | | | | | | | | |            sub-proof #1178.
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | |   (75)  all_56_2 = e1 & op(e2, e3) = e1
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | ALPHA: (75) implies:
% 152.00/22.27  | | | | | | | | | | | | |   (76)  all_56_2 = e1
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | REF_CLOSE: (1), (51), (76) are inconsistent by sub-proof
% 152.00/22.27  | | | | | | | | | | | | |            #1053.
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | |   (77)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 152.00/22.27  | | | | | | | | | | | |           e1 & op(e0, e3) = e1)
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | BETA: splitting (77) gives:
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | |   (78)  all_56_6 = e1 & op(e1, e3) = e1
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | ALPHA: (78) implies:
% 152.00/22.27  | | | | | | | | | | | | |   (79)  all_56_6 = e1
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | COMBINE_EQS: (71), (79) imply:
% 152.00/22.27  | | | | | | | | | | | | |   (80)  e2 = e1
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | COMBINE_EQS: (15), (80) imply:
% 152.00/22.27  | | | | | | | | | | | | |   (81)  all_56_5 = e1
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | REF_CLOSE: (10), (11), (13), (14), (19), (29), (30), (31),
% 152.00/22.27  | | | | | | | | | | | | |            (36), (63), (81) are inconsistent by sub-proof
% 152.00/22.27  | | | | | | | | | | | | |            #247.
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | |   (82)  all_56_12 = e1 & op(e0, e3) = e1
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | ALPHA: (82) implies:
% 152.00/22.27  | | | | | | | | | | | | |   (83)  all_56_12 = e1
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | BETA: splitting (38) gives:
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | |   (84)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 152.00/22.27  | | | | | | | | | | | | | |           & op(e2, e2) = e3)
% 152.00/22.27  | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (19), (39), (44), (84) are inconsistent
% 152.00/22.27  | | | | | | | | | | | | | |            by sub-proof #465.
% 152.00/22.27  | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | |   (85)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 152.00/22.27  | | | | | | | | | | | | | |           e3 & op(e0, e2) = e3)
% 152.00/22.27  | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 152.00/22.27  | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | |   (86)  all_56_7 = e3 & op(e1, e2) = e3
% 152.00/22.27  | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | REF_CLOSE: (13), (22), (24), (86) are inconsistent by
% 152.00/22.27  | | | | | | | | | | | | | | |            sub-proof #925.
% 152.00/22.27  | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | |   (87)  all_56_13 = e3 & op(e0, e2) = e3
% 152.00/22.27  | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 152.00/22.27  | | | | | | | | | | | | | | |   (88)  all_56_13 = e3
% 152.00/22.27  | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 152.00/22.27  | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | |   (89)  all_56_12 = e0 & op(e0, e3) = e0
% 152.00/22.27  | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 152.00/22.27  | | | | | | | | | | | | | | | |   (90)  all_56_12 = e0
% 152.00/22.27  | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | | REF_CLOSE: (29), (83), (90) are inconsistent by sub-proof
% 152.00/22.27  | | | | | | | | | | | | | | | |            #1051.
% 152.00/22.27  | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | |   (91)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 152.00/22.27  | | | | | | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 152.00/22.27  | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 152.00/22.27  | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | | |   (92)  all_56_13 = e0 & op(e0, e2) = e0
% 152.00/22.27  | | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 152.00/22.27  | | | | | | | | | | | | | | | | |   (93)  all_56_13 = e0
% 152.00/22.27  | | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (88), (93) are inconsistent by sub-proof
% 152.00/22.27  | | | | | | | | | | | | | | | | |            #1094.
% 152.00/22.27  | | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | | |   (94)  all_56_14 = e0 & op(e0, e1) = e0
% 152.00/22.27  | | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (63), (94) are inconsistent by sub-proof
% 152.00/22.27  | | | | | | | | | | | | | | | | |            #1118.
% 152.00/22.27  | | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | |   (95)  all_56_12 = e2 & op(e0, e3) = e2
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | ALPHA: (95) implies:
% 152.00/22.27  | | | | | | | | | | |   (96)  all_56_12 = e2
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | BETA: splitting (20) gives:
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | |   (97)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 152.00/22.27  | | | | | | | | | | | |           & op(e2, e3) = e0)
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | BETA: splitting (97) gives:
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | |   (98)  all_56_0 = e0 & op(e3, e3) = e0
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | ALPHA: (98) implies:
% 152.00/22.27  | | | | | | | | | | | | |   (99)  op(e3, e3) = e0
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | REF_CLOSE: (13), (19), (35), (99) are inconsistent by
% 152.00/22.27  | | | | | | | | | | | | |            sub-proof #1141.
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | |   (100)  all_56_2 = e0 & op(e2, e3) = e0
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | ALPHA: (100) implies:
% 152.00/22.27  | | | | | | | | | | | | |   (101)  all_56_2 = e0
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | REF_CLOSE: (1), (11), (12), (13), (16), (19), (26), (28),
% 152.00/22.27  | | | | | | | | | | | | |            (29), (31), (33), (36), (39), (101) are
% 152.00/22.27  | | | | | | | | | | | | |            inconsistent by sub-proof #646.
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | |   (102)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 152.00/22.27  | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | BETA: splitting (102) gives:
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | Case 1:
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | |   (103)  all_56_6 = e0 & op(e1, e3) = e0
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | ALPHA: (103) implies:
% 152.00/22.27  | | | | | | | | | | | | |   (104)  op(e1, e3) = e0
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | REF_CLOSE: (13), (17), (29), (37), (104) are inconsistent by
% 152.00/22.27  | | | | | | | | | | | | |            sub-proof #1127.
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | Case 2:
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | |   (105)  all_56_12 = e0 & op(e0, e3) = e0
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | ALPHA: (105) implies:
% 152.00/22.27  | | | | | | | | | | | | |   (106)  op(e0, e3) = e0
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | | REF_CLOSE: (2), (6), (7), (11), (13), (25), (29), (63), (96),
% 152.00/22.27  | | | | | | | | | | | | |            (106) are inconsistent by sub-proof #1117.
% 152.00/22.27  | | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | | 
% 152.00/22.27  | | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | | 
% 152.00/22.27  | | | | | | | | End of split
% 152.00/22.27  | | | | | | | | 
% 152.00/22.27  | | | | | | | End of split
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | Case 2:
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | |   (107)  all_56_3 = e3 & op(e2, e2) = e3
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | | ALPHA: (107) implies:
% 152.00/22.27  | | | | | | |   (108)  op(e2, e2) = e3
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | | REF_CLOSE: (13), (19), (39), (108) are inconsistent by sub-proof
% 152.00/22.27  | | | | | | |            #719.
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | End of split
% 152.00/22.27  | | | | | | 
% 152.00/22.27  | | | | | Case 2:
% 152.00/22.27  | | | | | | 
% 152.00/22.27  | | | | | |   (109)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 &
% 152.00/22.27  | | | | | |            op(e2, e0) = e3)
% 152.00/22.27  | | | | | | 
% 152.00/22.27  | | | | | | BETA: splitting (109) gives:
% 152.00/22.27  | | | | | | 
% 152.00/22.27  | | | | | | Case 1:
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | |   (110)  all_56_5 = e3 & op(e2, e1) = e3
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | | REF_CLOSE: (13), (16), (28), (110) are inconsistent by sub-proof
% 152.00/22.27  | | | | | | |            #647.
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | Case 2:
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | |   (111)  all_56_10 = e3 & op(e2, e0) = e3
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | | REF_CLOSE: (1), (48), (111) are inconsistent by sub-proof #683.
% 152.00/22.27  | | | | | | | 
% 152.00/22.27  | | | | | | End of split
% 152.00/22.27  | | | | | | 
% 152.00/22.27  | | | | | End of split
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | End of split
% 152.00/22.27  | | | | 
% 152.00/22.27  | | | Case 2:
% 152.00/22.27  | | | | 
% 152.00/22.27  | | | |   (112)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0,
% 152.00/22.27  | | | |              e0) = e1)
% 152.00/22.27  | | | | 
% 152.00/22.27  | | | | BETA: splitting (112) gives:
% 152.00/22.27  | | | | 
% 152.00/22.27  | | | | Case 1:
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | |   (113)  all_56_11 = e1 & op(e1, e0) = e1
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | | ALPHA: (113) implies:
% 152.00/22.27  | | | | |   (114)  all_56_11 = e1
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | | REF_CLOSE: (27), (29), (114) are inconsistent by sub-proof #745.
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | Case 2:
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | |   (115)  all_56_15 = e1 & op(e0, e0) = e1
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | | ALPHA: (115) implies:
% 152.00/22.27  | | | | |   (116)  op(e0, e0) = e1
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | | REF_CLOSE: (5), (9), (13), (116) are inconsistent by sub-proof #1116.
% 152.00/22.27  | | | | | 
% 152.00/22.27  | | | | End of split
% 152.00/22.27  | | | | 
% 152.00/22.27  | | | End of split
% 152.00/22.27  | | | 
% 152.00/22.27  | | End of split
% 152.00/22.27  | | 
% 152.00/22.27  | Case 2:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (117)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 152.00/22.27  | |            e1)
% 152.00/22.27  | | 
% 152.00/22.27  | | REF_CLOSE: (4), (29), (32), (36), (117) are inconsistent by sub-proof #655.
% 152.00/22.27  | | 
% 152.00/22.27  | End of split
% 152.00/22.27  | 
% 152.00/22.27  End of proof
% 152.00/22.27  
% 152.00/22.27  Sub-proof #196 shows that the following formulas are inconsistent:
% 152.00/22.27  ----------------------------------------------------------------
% 152.00/22.27    (1)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 152.00/22.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.27    (3)   ~ (e3 = e0)
% 152.00/22.27    (4)  all_56_1 = e0
% 152.00/22.27    (5)  op(e2, e2) = e0
% 152.00/22.27  
% 152.00/22.27  Begin of proof
% 152.00/22.27  | 
% 152.00/22.27  | BETA: splitting (1) gives:
% 152.00/22.27  | 
% 152.00/22.27  | Case 1:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (6)  all_56_1 = e3 & op(e3, e2) = e3
% 152.00/22.27  | | 
% 152.00/22.27  | | ALPHA: (6) implies:
% 152.00/22.27  | |   (7)  all_56_1 = e3
% 152.00/22.27  | | 
% 152.00/22.27  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1065.
% 152.00/22.27  | | 
% 152.00/22.27  | Case 2:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (8)  all_56_3 = e3 & op(e2, e2) = e3
% 152.00/22.27  | | 
% 152.00/22.27  | | ALPHA: (8) implies:
% 152.00/22.27  | |   (9)  op(e2, e2) = e3
% 152.00/22.27  | | 
% 152.00/22.27  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #719.
% 152.00/22.27  | | 
% 152.00/22.27  | End of split
% 152.00/22.27  | 
% 152.00/22.27  End of proof
% 152.00/22.27  
% 152.00/22.27  Sub-proof #197 shows that the following formulas are inconsistent:
% 152.00/22.27  ----------------------------------------------------------------
% 152.00/22.27    (1)   ~ (e3 = e1)
% 152.00/22.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.27    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1)
% 152.00/22.27    (4)   ~ (e1 = e0)
% 152.00/22.27    (5)  all_56_1 = e0
% 152.00/22.27    (6)  op(e3, e3) = e3
% 152.00/22.27  
% 152.00/22.27  Begin of proof
% 152.00/22.27  | 
% 152.00/22.27  | BETA: splitting (3) gives:
% 152.00/22.27  | 
% 152.00/22.27  | Case 1:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 152.00/22.27  | | 
% 152.00/22.27  | | ALPHA: (7) implies:
% 152.00/22.27  | |   (8)  op(e3, e3) = e1
% 152.00/22.27  | | 
% 152.00/22.27  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #1178.
% 152.00/22.27  | | 
% 152.00/22.27  | Case 2:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (9)  all_56_1 = e1 & op(e3, e2) = e1
% 152.00/22.27  | | 
% 152.00/22.27  | | ALPHA: (9) implies:
% 152.00/22.27  | |   (10)  all_56_1 = e1
% 152.00/22.27  | | 
% 152.00/22.27  | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #1107.
% 152.00/22.27  | | 
% 152.00/22.27  | End of split
% 152.00/22.27  | 
% 152.00/22.27  End of proof
% 152.00/22.27  
% 152.00/22.27  Sub-proof #198 shows that the following formulas are inconsistent:
% 152.00/22.27  ----------------------------------------------------------------
% 152.00/22.27    (1)  op(e0, e1) = all_52_11
% 152.00/22.27    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.27    (3)   ~ (e3 = e0)
% 152.00/22.27    (4)   ~ (all_52_11 = e0)
% 152.00/22.27    (5)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.00/22.27    (6)  op(e1, e1) = e3
% 152.00/22.27  
% 152.00/22.27  Begin of proof
% 152.00/22.27  | 
% 152.00/22.27  | BETA: splitting (5) gives:
% 152.00/22.27  | 
% 152.00/22.27  | Case 1:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (7)  all_56_8 = e0 & op(e1, e1) = e0
% 152.00/22.27  | | 
% 152.00/22.27  | | ALPHA: (7) implies:
% 152.00/22.27  | |   (8)  op(e1, e1) = e0
% 152.00/22.27  | | 
% 152.00/22.27  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #896.
% 152.00/22.27  | | 
% 152.00/22.27  | Case 2:
% 152.00/22.27  | | 
% 152.00/22.27  | |   (9)  all_56_14 = e0 & op(e0, e1) = e0
% 152.00/22.27  | | 
% 152.00/22.27  | | ALPHA: (9) implies:
% 152.00/22.27  | |   (10)  op(e0, e1) = e0
% 152.00/22.27  | | 
% 152.00/22.27  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #1124.
% 152.00/22.27  | | 
% 152.00/22.27  | End of split
% 152.00/22.27  | 
% 152.00/22.27  End of proof
% 152.00/22.27  
% 152.00/22.27  Sub-proof #199 shows that the following formulas are inconsistent:
% 152.00/22.27  ----------------------------------------------------------------
% 152.00/22.27    (1)  all_56_11 = e0 & op(e1, e0) = e0
% 152.00/22.28    (2)  all_56_11 = e3
% 152.00/22.28    (3)   ~ (e3 = e0)
% 152.00/22.28  
% 152.00/22.28  Begin of proof
% 152.00/22.28  | 
% 152.00/22.28  | ALPHA: (1) implies:
% 152.00/22.28  |   (4)  all_56_11 = e0
% 152.00/22.28  | 
% 152.00/22.28  | COMBINE_EQS: (2), (4) imply:
% 152.00/22.28  |   (5)  e3 = e0
% 152.00/22.28  | 
% 152.00/22.28  | REDUCE: (3), (5) imply:
% 152.00/22.28  |   (6)  $false
% 152.00/22.28  | 
% 152.00/22.28  | CLOSE: (6) is inconsistent.
% 152.00/22.28  | 
% 152.00/22.28  End of proof
% 152.00/22.28  
% 152.00/22.28  Sub-proof #200 shows that the following formulas are inconsistent:
% 152.00/22.28  ----------------------------------------------------------------
% 152.00/22.28    (1)  all_56_8 = e3
% 152.00/22.28    (2)   ~ (e3 = e1)
% 152.00/22.28    (3)  all_56_11 = e2
% 152.00/22.28    (4)   ~ (e2 = e0)
% 152.00/22.28    (5)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.00/22.28         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.00/22.28    (6)   ~ (e3 = e0)
% 152.00/22.28    (7)   ~ (e1 = e0)
% 152.00/22.28    (8)  all_56_7 = e2
% 152.00/22.28    (9)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.00/22.28         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.00/22.28    (10)   ~ (e2 = e1)
% 152.00/22.28  
% 152.00/22.28  Begin of proof
% 152.00/22.28  | 
% 152.00/22.28  | BETA: splitting (5) gives:
% 152.00/22.28  | 
% 152.00/22.28  | Case 1:
% 152.00/22.28  | | 
% 152.00/22.28  | |   (11)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 152.00/22.28  | |           e1)
% 152.00/22.28  | | 
% 152.00/22.28  | | BETA: splitting (11) gives:
% 152.00/22.28  | | 
% 152.00/22.28  | | Case 1:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (12)  all_56_6 = e1 & op(e1, e3) = e1
% 152.00/22.28  | | | 
% 152.00/22.28  | | | ALPHA: (12) implies:
% 152.00/22.28  | | |   (13)  all_56_6 = e1
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (13) are inconsistent by
% 152.00/22.28  | | |            sub-proof #201.
% 152.00/22.28  | | | 
% 152.00/22.28  | | Case 2:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (14)  all_56_7 = e1 & op(e1, e2) = e1
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REF_CLOSE: (8), (10), (14) are inconsistent by sub-proof #612.
% 152.00/22.28  | | | 
% 152.00/22.28  | | End of split
% 152.00/22.28  | | 
% 152.00/22.28  | Case 2:
% 152.00/22.28  | | 
% 152.00/22.28  | |   (15)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 152.00/22.28  | |           e1)
% 152.00/22.28  | | 
% 152.00/22.28  | | REF_CLOSE: (1), (2), (3), (10), (15) are inconsistent by sub-proof #644.
% 152.00/22.28  | | 
% 152.00/22.28  | End of split
% 152.00/22.28  | 
% 152.00/22.28  End of proof
% 152.00/22.28  
% 152.00/22.28  Sub-proof #201 shows that the following formulas are inconsistent:
% 152.00/22.28  ----------------------------------------------------------------
% 152.00/22.28    (1)  all_56_8 = e3
% 152.00/22.28    (2)  all_56_11 = e2
% 152.00/22.28    (3)   ~ (e2 = e0)
% 152.00/22.28    (4)  all_56_6 = e1
% 152.00/22.28    (5)   ~ (e3 = e0)
% 152.00/22.28    (6)   ~ (e1 = e0)
% 152.00/22.28    (7)  all_56_7 = e2
% 152.00/22.28    (8)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.00/22.28         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.00/22.28  
% 152.00/22.28  Begin of proof
% 152.00/22.28  | 
% 152.00/22.28  | BETA: splitting (8) gives:
% 152.00/22.28  | 
% 152.00/22.28  | Case 1:
% 152.00/22.28  | | 
% 152.00/22.28  | |   (9)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0)
% 152.00/22.28  | | 
% 152.00/22.28  | | BETA: splitting (9) gives:
% 152.00/22.28  | | 
% 152.00/22.28  | | Case 1:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (10)  all_56_6 = e0 & op(e1, e3) = e0
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #1152.
% 152.00/22.28  | | | 
% 152.00/22.28  | | Case 2:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (11)  all_56_7 = e0 & op(e1, e2) = e0
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REF_CLOSE: (3), (7), (11) are inconsistent by sub-proof #611.
% 152.00/22.28  | | | 
% 152.00/22.28  | | End of split
% 152.00/22.28  | | 
% 152.00/22.28  | Case 2:
% 152.00/22.28  | | 
% 152.00/22.28  | |   (12)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 152.00/22.28  | |           e0)
% 152.00/22.28  | | 
% 152.00/22.28  | | BETA: splitting (12) gives:
% 152.00/22.28  | | 
% 152.00/22.28  | | Case 1:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (13)  all_56_8 = e0 & op(e1, e1) = e0
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REF_CLOSE: (1), (5), (13) are inconsistent by sub-proof #1150.
% 152.00/22.28  | | | 
% 152.00/22.28  | | Case 2:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (14)  all_56_11 = e0 & op(e1, e0) = e0
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REF_CLOSE: (2), (3), (14) are inconsistent by sub-proof #1149.
% 152.00/22.28  | | | 
% 152.00/22.28  | | End of split
% 152.00/22.28  | | 
% 152.00/22.28  | End of split
% 152.00/22.28  | 
% 152.00/22.28  End of proof
% 152.00/22.28  
% 152.00/22.28  Sub-proof #202 shows that the following formulas are inconsistent:
% 152.00/22.28  ----------------------------------------------------------------
% 152.00/22.28    (1)   ~ (all_52_14 = e0)
% 152.00/22.28    (2)  all_56_8 = e3
% 152.00/22.28    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.00/22.28         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.00/22.28    (4)   ~ (all_52_2 = all_52_6)
% 152.00/22.28    (5)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.00/22.28         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.00/22.28    (6)  op(e3, e2) = all_52_4
% 152.00/22.28    (7)  all_56_9 = e3
% 152.00/22.28    (8)   ~ (all_52_14 = e2)
% 152.00/22.28    (9)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.00/22.28         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.00/22.28    (10)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.00/22.28          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.00/22.28    (11)   ~ (all_52_4 = all_52_12)
% 152.00/22.28    (12)   ~ (e2 = e0)
% 152.00/22.28    (13)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.00/22.28          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.00/22.28    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.28            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.28    (15)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.00/22.28          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.00/22.28    (16)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 152.00/22.28    (17)   ~ (all_52_9 = e3)
% 152.00/22.28    (18)  op(e3, e3) = e2
% 152.00/22.28    (19)  all_56_14 = e2
% 152.00/22.28    (20)   ~ (all_52_8 = all_52_12)
% 152.00/22.28    (21)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.00/22.28          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.00/22.28    (22)  all_56_5 = e0
% 152.00/22.28    (23)   ~ (all_52_12 = all_52_14)
% 152.00/22.28    (24)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 152.00/22.28          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.00/22.28    (25)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.00/22.28          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.00/22.28    (26)   ~ (all_52_6 = e3)
% 152.00/22.28    (27)  op(e1, e2) = all_52_6
% 152.00/22.28    (28)  ( ~ (all_36_0 = e1) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 152.00/22.28            all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e3,
% 152.00/22.28              e2) = all_36_1 & $i(all_36_1))
% 152.00/22.28    (29)  op(e0, e1) = e2
% 152.00/22.28    (30)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.28          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.00/22.28    (31)  op(e2, e1) = all_52_9
% 152.00/22.28    (32)  all_56_7 = e2
% 152.00/22.28    (33)  op(e1, e1) = e3
% 152.00/22.28    (34)  all_54_3 = all_52_12
% 152.00/22.28    (35)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.00/22.28          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.00/22.28    (36)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.00/22.28          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.00/22.28    (37)   ~ (all_52_12 = e2)
% 152.00/22.28    (38)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.00/22.28          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.00/22.28    (39)  op(e3, e1) = all_52_8
% 152.00/22.28    (40)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 152.00/22.28    (41)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.00/22.28          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.00/22.28    (42)  all_54_11 = all_52_14
% 152.00/22.28    (43)  op(e0, e0) = e0
% 152.00/22.28    (44)  all_56_2 = e3
% 152.00/22.28    (45)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.00/22.28          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.00/22.28    (46)  op(e1, e3) = all_52_2
% 152.00/22.28    (47)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.28          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.00/22.28    (48)   ~ (all_52_12 = e0)
% 152.00/22.28    (49)  op(e2, e2) = e0
% 152.00/22.28  
% 152.00/22.28  Begin of proof
% 152.00/22.28  | 
% 152.00/22.28  | BETA: splitting (16) gives:
% 152.00/22.28  | 
% 152.00/22.28  | Case 1:
% 152.00/22.28  | | 
% 152.00/22.28  | |   (50)  all_54_11 = e2
% 152.00/22.28  | | 
% 152.00/22.28  | | REF_CLOSE: (8), (42), (50) are inconsistent by sub-proof #393.
% 152.00/22.28  | | 
% 152.00/22.28  | Case 2:
% 152.00/22.28  | | 
% 152.00/22.28  | |   (51)   ~ (all_54_11 = e2)
% 152.00/22.28  | |   (52)  all_54_11 = e1 | all_54_11 = e0
% 152.00/22.28  | | 
% 152.00/22.28  | | BETA: splitting (52) gives:
% 152.00/22.28  | | 
% 152.00/22.28  | | Case 1:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (53)  all_54_11 = e1
% 152.00/22.28  | | | 
% 152.00/22.28  | | | COMBINE_EQS: (42), (53) imply:
% 152.00/22.28  | | |   (54)  all_52_14 = e1
% 152.00/22.28  | | | 
% 152.00/22.28  | | | SIMP: (54) implies:
% 152.00/22.28  | | |   (55)  all_52_14 = e1
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REDUCE: (23), (55) imply:
% 152.00/22.28  | | |   (56)   ~ (all_52_12 = e1)
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REDUCE: (8), (55) imply:
% 152.00/22.28  | | |   (57)   ~ (e2 = e1)
% 152.00/22.28  | | | 
% 152.00/22.28  | | | SIMP: (57) implies:
% 152.00/22.28  | | |   (58)   ~ (e2 = e1)
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REDUCE: (1), (55) imply:
% 152.00/22.28  | | |   (59)   ~ (e1 = e0)
% 152.00/22.28  | | | 
% 152.00/22.28  | | | BETA: splitting (40) gives:
% 152.00/22.28  | | | 
% 152.00/22.28  | | | Case 1:
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | |   (60)  all_54_3 = e3
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | COMBINE_EQS: (34), (60) imply:
% 152.00/22.28  | | | |   (61)  all_52_12 = e3
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | REDUCE: (11), (61) imply:
% 152.00/22.28  | | | |   (62)   ~ (all_52_4 = e3)
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | REDUCE: (20), (61) imply:
% 152.00/22.28  | | | |   (63)   ~ (all_52_8 = e3)
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | REDUCE: (37), (61) imply:
% 152.00/22.28  | | | |   (64)   ~ (e3 = e2)
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | REDUCE: (56), (61) imply:
% 152.00/22.28  | | | |   (65)   ~ (e3 = e1)
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | REDUCE: (48), (61) imply:
% 152.00/22.28  | | | |   (66)   ~ (e3 = e0)
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | BETA: splitting (47) gives:
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | Case 1:
% 152.00/22.28  | | | | | 
% 152.00/22.28  | | | | |   (67)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2,
% 152.00/22.28  | | | | |             e2) = e3)
% 152.00/22.28  | | | | | 
% 152.00/22.28  | | | | | REF_CLOSE: (7), (12), (14), (18), (21), (25), (49), (58), (59), (65),
% 152.00/22.28  | | | | |            (66), (67) are inconsistent by sub-proof #219.
% 152.00/22.28  | | | | | 
% 152.00/22.28  | | | | Case 2:
% 152.00/22.28  | | | | | 
% 152.00/22.28  | | | | |   (68)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0,
% 152.00/22.28  | | | | |             e2) = e3)
% 152.00/22.28  | | | | | 
% 152.00/22.28  | | | | | BETA: splitting (68) gives:
% 152.00/22.28  | | | | | 
% 152.00/22.28  | | | | | Case 1:
% 152.00/22.28  | | | | | | 
% 152.00/22.28  | | | | | |   (69)  all_56_7 = e3 & op(e1, e2) = e3
% 152.00/22.28  | | | | | | 
% 152.00/22.28  | | | | | | REF_CLOSE: (14), (26), (27), (69) are inconsistent by sub-proof
% 152.00/22.28  | | | | | |            #925.
% 152.00/22.28  | | | | | | 
% 152.00/22.28  | | | | | Case 2:
% 152.00/22.28  | | | | | | 
% 152.00/22.28  | | | | | |   (70)  all_56_13 = e3 & op(e0, e2) = e3
% 152.00/22.28  | | | | | | 
% 152.00/22.28  | | | | | | ALPHA: (70) implies:
% 152.00/22.28  | | | | | |   (71)  all_56_13 = e3
% 152.00/22.28  | | | | | | 
% 152.00/22.28  | | | | | | BETA: splitting (25) gives:
% 152.00/22.28  | | | | | | 
% 152.00/22.28  | | | | | | Case 1:
% 152.00/22.28  | | | | | | | 
% 152.00/22.28  | | | | | | |   (72)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 &
% 152.00/22.28  | | | | | | |           op(e3, e2) = e0)
% 152.00/22.28  | | | | | | | 
% 152.00/22.28  | | | | | | | BETA: splitting (72) gives:
% 152.00/22.28  | | | | | | | 
% 152.00/22.28  | | | | | | | Case 1:
% 152.00/22.28  | | | | | | | | 
% 152.00/22.28  | | | | | | | |   (73)  all_56_0 = e0 & op(e3, e3) = e0
% 152.00/22.28  | | | | | | | | 
% 152.00/22.28  | | | | | | | | ALPHA: (73) implies:
% 152.00/22.28  | | | | | | | |   (74)  op(e3, e3) = e0
% 152.00/22.28  | | | | | | | | 
% 152.00/22.28  | | | | | | | | REF_CLOSE: (12), (14), (18), (74) are inconsistent by sub-proof
% 152.00/22.28  | | | | | | | |            #1073.
% 152.00/22.28  | | | | | | | | 
% 152.00/22.28  | | | | | | | Case 2:
% 152.00/22.28  | | | | | | | | 
% 152.00/22.28  | | | | | | | |   (75)  all_56_1 = e0 & op(e3, e2) = e0
% 152.00/22.28  | | | | | | | | 
% 152.00/22.28  | | | | | | | | ALPHA: (75) implies:
% 152.00/22.28  | | | | | | | |   (76)  all_56_1 = e0
% 152.00/22.28  | | | | | | | |   (77)  op(e3, e2) = e0
% 152.00/22.28  | | | | | | | | 
% 152.00/22.28  | | | | | | | | BETA: splitting (3) gives:
% 152.00/22.28  | | | | | | | | 
% 152.00/22.28  | | | | | | | | Case 1:
% 152.00/22.28  | | | | | | | | | 
% 152.00/22.28  | | | | | | | | |   (78)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 &
% 152.00/22.28  | | | | | | | | |           op(e2, e3) = e1)
% 152.00/22.28  | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | BETA: splitting (78) gives:
% 152.00/22.28  | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | Case 1:
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | |   (79)  all_56_0 = e1 & op(e3, e3) = e1
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | ALPHA: (79) implies:
% 152.00/22.28  | | | | | | | | | |   (80)  op(e3, e3) = e1
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | REF_CLOSE: (14), (18), (58), (80) are inconsistent by
% 152.00/22.28  | | | | | | | | | |            sub-proof #1074.
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | Case 2:
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | |   (81)  all_56_2 = e1 & op(e2, e3) = e1
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | ALPHA: (81) implies:
% 152.00/22.28  | | | | | | | | | |   (82)  all_56_2 = e1
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | COMBINE_EQS: (44), (82) imply:
% 152.00/22.28  | | | | | | | | | |   (83)  e3 = e1
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | COMBINE_EQS: (7), (83) imply:
% 152.00/22.28  | | | | | | | | | |   (84)  all_56_9 = e1
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | REF_CLOSE: (14), (15), (18), (39), (63), (64), (65), (66),
% 152.00/22.28  | | | | | | | | | |            (76), (84) are inconsistent by sub-proof #808.
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | End of split
% 152.00/22.28  | | | | | | | | | 
% 152.00/22.28  | | | | | | | | Case 2:
% 152.00/22.28  | | | | | | | | | 
% 152.00/22.28  | | | | | | | | |   (85)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 &
% 152.00/22.28  | | | | | | | | |           op(e0, e3) = e1)
% 152.00/22.28  | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | BETA: splitting (85) gives:
% 152.00/22.28  | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | Case 1:
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | |   (86)  all_56_6 = e1 & op(e1, e3) = e1
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | ALPHA: (86) implies:
% 152.00/22.28  | | | | | | | | | |   (87)  op(e1, e3) = e1
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | BETA: splitting (45) gives:
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | Case 1:
% 152.00/22.28  | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | |   (88)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 152.00/22.28  | | | | | | | | | | |           & op(e2, e2) = e1)
% 152.00/22.28  | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | BETA: splitting (88) gives:
% 152.00/22.28  | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | Case 1:
% 152.00/22.28  | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | |   (89)  all_56_1 = e1 & op(e3, e2) = e1
% 152.00/22.28  | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | ALPHA: (89) implies:
% 152.00/22.28  | | | | | | | | | | | |   (90)  all_56_1 = e1
% 152.00/22.28  | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | REF_CLOSE: (59), (76), (90) are inconsistent by sub-proof
% 152.00/22.28  | | | | | | | | | | | |            #1107.
% 152.00/22.28  | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | Case 2:
% 152.00/22.28  | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | |   (91)  all_56_3 = e1 & op(e2, e2) = e1
% 152.00/22.28  | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | ALPHA: (91) implies:
% 152.00/22.28  | | | | | | | | | | | |   (92)  all_56_3 = e1
% 152.00/22.28  | | | | | | | | | | | |   (93)  op(e2, e2) = e1
% 152.00/22.28  | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | BETA: splitting (24) gives:
% 152.00/22.28  | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | Case 1:
% 152.00/22.28  | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | |   (94)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 152.00/22.28  | | | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 152.00/22.28  | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | BETA: splitting (94) gives:
% 152.00/22.28  | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | Case 1:
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | |   (95)  all_56_9 = e1 & op(e3, e0) = e1
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | | ALPHA: (95) implies:
% 152.00/22.28  | | | | | | | | | | | | | |   (96)  all_56_9 = e1
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | | COMBINE_EQS: (7), (96) imply:
% 152.00/22.28  | | | | | | | | | | | | | |   (97)  e3 = e1
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | | REF_CLOSE: (5), (12), (14), (26), (27), (36), (47), (58),
% 152.00/22.28  | | | | | | | | | | | | | |            (59), (64), (65), (66), (71), (92), (93), (97) are
% 152.00/22.28  | | | | | | | | | | | | | |            inconsistent by sub-proof #259.
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | Case 2:
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | |   (98)  all_56_10 = e1 & op(e2, e0) = e1
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | | ALPHA: (98) implies:
% 152.00/22.28  | | | | | | | | | | | | | |   (99)  all_56_10 = e1
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | | REF_CLOSE: (9), (12), (13), (14), (17), (30), (31), (58),
% 152.00/22.28  | | | | | | | | | | | | | |            (59), (64), (65), (66), (92), (93), (99) are
% 152.00/22.28  | | | | | | | | | | | | | |            inconsistent by sub-proof #264.
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | End of split
% 152.00/22.28  | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | Case 2:
% 152.00/22.28  | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | |   (100)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 152.00/22.28  | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 152.00/22.28  | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | BETA: splitting (100) gives:
% 152.00/22.28  | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | Case 1:
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | |   (101)  all_56_11 = e1 & op(e1, e0) = e1
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | | ALPHA: (101) implies:
% 152.00/22.28  | | | | | | | | | | | | | |   (102)  all_56_11 = e1
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | | REF_CLOSE: (12), (14), (32), (33), (41), (46), (59), (66),
% 152.00/22.28  | | | | | | | | | | | | | |            (87), (102) are inconsistent by sub-proof #237.
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | Case 2:
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | |   (103)  all_56_15 = e1 & op(e0, e0) = e1
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | | ALPHA: (103) implies:
% 152.00/22.28  | | | | | | | | | | | | | |   (104)  op(e0, e0) = e1
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | | REF_CLOSE: (14), (43), (59), (104) are inconsistent by
% 152.00/22.28  | | | | | | | | | | | | | |            sub-proof #1040.
% 152.00/22.28  | | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | | End of split
% 152.00/22.28  | | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | | End of split
% 152.00/22.28  | | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | End of split
% 152.00/22.28  | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | Case 2:
% 152.00/22.28  | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | |   (105)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 152.00/22.28  | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 152.00/22.28  | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | | REF_CLOSE: (4), (6), (14), (26), (27), (46), (47), (49),
% 152.00/22.28  | | | | | | | | | | |            (62), (65), (66), (87), (105) are inconsistent by
% 152.00/22.28  | | | | | | | | | | |            sub-proof #204.
% 152.00/22.28  | | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | End of split
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | Case 2:
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | |   (106)  all_56_12 = e1 & op(e0, e3) = e1
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | ALPHA: (106) implies:
% 152.00/22.28  | | | | | | | | | |   (107)  op(e0, e3) = e1
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | | REF_CLOSE: (14), (28), (77), (107) are inconsistent by
% 152.00/22.28  | | | | | | | | | |            sub-proof #767.
% 152.00/22.28  | | | | | | | | | | 
% 152.00/22.28  | | | | | | | | | End of split
% 152.00/22.28  | | | | | | | | | 
% 152.00/22.28  | | | | | | | | End of split
% 152.00/22.28  | | | | | | | | 
% 152.00/22.28  | | | | | | | End of split
% 152.00/22.28  | | | | | | | 
% 152.00/22.28  | | | | | | Case 2:
% 152.00/22.28  | | | | | | | 
% 152.00/22.28  | | | | | | |   (108)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 &
% 152.00/22.28  | | | | | | |            op(e3, e0) = e0)
% 152.00/22.28  | | | | | | | 
% 152.00/22.28  | | | | | | | REF_CLOSE: (2), (6), (10), (12), (13), (14), (15), (17), (18),
% 152.00/22.28  | | | | | | |            (19), (22), (29), (30), (31), (33), (35), (38), (44),
% 152.00/22.28  | | | | | | |            (49), (58), (59), (62), (64), (65), (66), (108) are
% 152.00/22.28  | | | | | | |            inconsistent by sub-proof #203.
% 152.00/22.28  | | | | | | | 
% 152.00/22.28  | | | | | | End of split
% 152.00/22.28  | | | | | | 
% 152.00/22.28  | | | | | End of split
% 152.00/22.28  | | | | | 
% 152.00/22.28  | | | | End of split
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | Case 2:
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | |   (109)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | REF_CLOSE: (34), (37), (48), (56), (109) are inconsistent by sub-proof
% 152.00/22.28  | | | |            #758.
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | End of split
% 152.00/22.28  | | | 
% 152.00/22.28  | | Case 2:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (110)  all_54_11 = e0
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REF_CLOSE: (1), (42), (110) are inconsistent by sub-proof #211.
% 152.00/22.28  | | | 
% 152.00/22.28  | | End of split
% 152.00/22.28  | | 
% 152.00/22.28  | End of split
% 152.00/22.28  | 
% 152.00/22.28  End of proof
% 152.00/22.28  
% 152.00/22.28  Sub-proof #203 shows that the following formulas are inconsistent:
% 152.00/22.28  ----------------------------------------------------------------
% 152.00/22.28    (1)  all_56_8 = e3
% 152.00/22.28    (2)   ~ (e3 = e1)
% 152.00/22.28    (3)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.00/22.28    (4)  op(e3, e2) = all_52_4
% 152.00/22.28    (5)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.00/22.28         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.00/22.28    (6)   ~ (e2 = e0)
% 152.00/22.28    (7)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.00/22.28         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.00/22.28    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.28    (9)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.00/22.28         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.00/22.28    (10)   ~ (all_52_9 = e3)
% 152.00/22.28    (11)  op(e3, e3) = e2
% 152.00/22.28    (12)  all_56_14 = e2
% 152.00/22.28    (13)  all_56_5 = e0
% 152.00/22.28    (14)   ~ (all_52_4 = e3)
% 152.00/22.28    (15)   ~ (e3 = e0)
% 152.00/22.28    (16)  op(e0, e1) = e2
% 152.00/22.28    (17)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.28          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.00/22.28    (18)  op(e2, e1) = all_52_9
% 152.00/22.28    (19)   ~ (e1 = e0)
% 152.00/22.28    (20)  op(e1, e1) = e3
% 152.00/22.28    (21)   ~ (e3 = e2)
% 152.00/22.28    (22)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.00/22.28          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.00/22.28    (23)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.00/22.28          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.00/22.28    (24)   ~ (e2 = e1)
% 152.00/22.28    (25)  all_56_2 = e3
% 152.00/22.28    (26)  op(e2, e2) = e0
% 152.00/22.28  
% 152.00/22.28  Begin of proof
% 152.00/22.28  | 
% 152.00/22.28  | BETA: splitting (3) gives:
% 152.00/22.28  | 
% 152.00/22.28  | Case 1:
% 152.00/22.28  | | 
% 152.00/22.28  | |   (27)  all_56_4 = e0 & op(e3, e1) = e0
% 152.00/22.28  | | 
% 152.00/22.28  | | ALPHA: (27) implies:
% 152.00/22.28  | |   (28)  all_56_4 = e0
% 152.00/22.28  | | 
% 152.00/22.28  | | BETA: splitting (23) gives:
% 152.00/22.28  | | 
% 152.00/22.28  | | Case 1:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (29)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) =
% 152.00/22.28  | | |           e1)
% 152.00/22.28  | | | 
% 152.00/22.28  | | | BETA: splitting (29) gives:
% 152.00/22.28  | | | 
% 152.00/22.28  | | | Case 1:
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | |   (30)  all_56_4 = e1 & op(e3, e1) = e1
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | REF_CLOSE: (19), (28), (30) are inconsistent by sub-proof #309.
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | Case 2:
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | |   (31)  all_56_5 = e1 & op(e2, e1) = e1
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | ALPHA: (31) implies:
% 152.00/22.28  | | | |   (32)  all_56_5 = e1
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | | REF_CLOSE: (13), (19), (32) are inconsistent by sub-proof #682.
% 152.00/22.28  | | | | 
% 152.00/22.28  | | | End of split
% 152.00/22.28  | | | 
% 152.00/22.28  | | Case 2:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (33)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) =
% 152.00/22.28  | | |           e1)
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REF_CLOSE: (2), (8), (12), (20), (24), (33) are inconsistent by sub-proof
% 152.00/22.28  | | |            #356.
% 152.00/22.28  | | | 
% 152.00/22.28  | | End of split
% 152.00/22.28  | | 
% 152.00/22.28  | Case 2:
% 152.00/22.28  | | 
% 152.00/22.28  | |   (34)  all_56_9 = e0 & op(e3, e0) = e0
% 152.00/22.28  | | 
% 152.00/22.28  | | ALPHA: (34) implies:
% 152.00/22.28  | |   (35)  all_56_9 = e0
% 152.00/22.28  | | 
% 152.00/22.28  | | BETA: splitting (9) gives:
% 152.00/22.28  | | 
% 152.00/22.28  | | Case 1:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (36)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 152.00/22.28  | | |           e3)
% 152.00/22.28  | | | 
% 152.00/22.28  | | | REF_CLOSE: (4), (8), (11), (14), (21), (36) are inconsistent by sub-proof
% 152.00/22.28  | | |            #660.
% 152.00/22.28  | | | 
% 152.00/22.28  | | Case 2:
% 152.00/22.28  | | | 
% 152.00/22.28  | | |   (37)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 152.00/22.28  | | |           e3)
% 152.00/22.28  | | | 
% 152.00/22.28  | | | BETA: splitting (37) gives:
% 152.00/22.28  | | | 
% 152.00/22.28  | | | Case 1:
% 152.00/22.28  | | | | 
% 152.00/22.29  | | | |   (38)  all_56_4 = e3 & op(e3, e1) = e3
% 152.00/22.29  | | | | 
% 152.00/22.29  | | | | ALPHA: (38) implies:
% 152.00/22.29  | | | |   (39)  all_56_4 = e3
% 152.00/22.29  | | | | 
% 152.00/22.29  | | | | REF_CLOSE: (1), (2), (5), (6), (8), (12), (15), (16), (19), (20), (23),
% 152.00/22.29  | | | |            (24), (39) are inconsistent by sub-proof #354.
% 152.00/22.29  | | | | 
% 152.00/22.29  | | | Case 2:
% 152.00/22.29  | | | | 
% 152.00/22.29  | | | |   (40)  all_56_9 = e3 & op(e3, e0) = e3
% 152.00/22.29  | | | | 
% 152.00/22.29  | | | | ALPHA: (40) implies:
% 152.00/22.29  | | | |   (41)  all_56_9 = e3
% 152.00/22.29  | | | | 
% 152.00/22.29  | | | | COMBINE_EQS: (35), (41) imply:
% 152.00/22.29  | | | |   (42)  e3 = e0
% 152.00/22.29  | | | | 
% 152.00/22.29  | | | | SIMP: (42) implies:
% 152.00/22.29  | | | |   (43)  e3 = e0
% 152.00/22.29  | | | | 
% 152.00/22.29  | | | | COMBINE_EQS: (25), (43) imply:
% 152.00/22.29  | | | |   (44)  all_56_2 = e0
% 152.00/22.29  | | | | 
% 152.00/22.29  | | | | REF_CLOSE: (2), (6), (7), (8), (10), (15), (17), (18), (19), (21), (22),
% 152.00/22.29  | | | |            (24), (26), (44) are inconsistent by sub-proof #646.
% 152.00/22.29  | | | | 
% 152.00/22.29  | | | End of split
% 152.00/22.29  | | | 
% 152.00/22.29  | | End of split
% 152.00/22.29  | | 
% 152.00/22.29  | End of split
% 152.00/22.29  | 
% 152.00/22.29  End of proof
% 152.00/22.29  
% 152.00/22.29  Sub-proof #204 shows that the following formulas are inconsistent:
% 152.00/22.29  ----------------------------------------------------------------
% 152.00/22.29    (1)   ~ (e3 = e1)
% 152.00/22.29    (2)   ~ (all_52_2 = all_52_6)
% 152.00/22.29    (3)  op(e3, e2) = all_52_4
% 152.00/22.29    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.29    (5)  op(e1, e3) = e1
% 152.00/22.29    (6)   ~ (all_52_4 = e3)
% 152.00/22.29    (7)   ~ (e3 = e0)
% 152.00/22.29    (8)   ~ (all_52_6 = e3)
% 152.00/22.29    (9)  op(e1, e2) = all_52_6
% 152.00/22.29    (10)  op(e1, e3) = all_52_2
% 152.00/22.29    (11)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.29          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.00/22.29    (12)  op(e2, e2) = e0
% 152.00/22.29    (13)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.00/22.29  
% 152.00/22.29  Begin of proof
% 152.00/22.29  | 
% 152.00/22.29  | BETA: splitting (13) gives:
% 152.00/22.29  | 
% 152.00/22.29  | Case 1:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (14)  all_56_7 = e1 & op(e1, e2) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (14) implies:
% 152.00/22.29  | |   (15)  op(e1, e2) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (2), (4), (5), (9), (10), (15) are inconsistent by sub-proof
% 152.00/22.29  | |            #911.
% 152.00/22.29  | | 
% 152.00/22.29  | Case 2:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (16)  all_56_13 = e1 & op(e0, e2) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (16) implies:
% 152.00/22.29  | |   (17)  all_56_13 = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (11), (12), (17) are
% 152.00/22.29  | |            inconsistent by sub-proof #210.
% 152.00/22.29  | | 
% 152.00/22.29  | End of split
% 152.00/22.29  | 
% 152.00/22.29  End of proof
% 152.00/22.29  
% 152.00/22.29  Sub-proof #205 shows that the following formulas are inconsistent:
% 152.00/22.29  ----------------------------------------------------------------
% 152.00/22.29    (1)   ~ (all_52_6 = e1)
% 152.00/22.29    (2)   ~ (e3 = e1)
% 152.00/22.29    (3)  op(e3, e2) = all_52_4
% 152.00/22.29    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.29    (5)   ~ (all_52_4 = e3)
% 152.00/22.29    (6)   ~ (e3 = e0)
% 152.00/22.29    (7)   ~ (all_52_6 = e3)
% 152.00/22.29    (8)  op(e1, e2) = all_52_6
% 152.00/22.29    (9)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.29         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.00/22.29    (10)  op(e2, e2) = e0
% 152.00/22.29    (11)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.00/22.29  
% 152.00/22.29  Begin of proof
% 152.00/22.29  | 
% 152.00/22.29  | BETA: splitting (11) gives:
% 152.00/22.29  | 
% 152.00/22.29  | Case 1:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (12)  all_56_7 = e1 & op(e1, e2) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (12) implies:
% 152.00/22.29  | |   (13)  op(e1, e2) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (1), (4), (8), (13) are inconsistent by sub-proof #1042.
% 152.00/22.29  | | 
% 152.00/22.29  | Case 2:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (14)  all_56_13 = e1 & op(e0, e2) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (14) implies:
% 152.00/22.29  | |   (15)  all_56_13 = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (15) are
% 152.00/22.29  | |            inconsistent by sub-proof #210.
% 152.00/22.29  | | 
% 152.00/22.29  | End of split
% 152.00/22.29  | 
% 152.00/22.29  End of proof
% 152.00/22.29  
% 152.00/22.29  Sub-proof #206 shows that the following formulas are inconsistent:
% 152.00/22.29  ----------------------------------------------------------------
% 152.00/22.29    (1)  op(e0, e1) = all_52_11
% 152.00/22.29    (2)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 =
% 152.00/22.29             e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.00/22.29           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 =
% 152.00/22.29           e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.00/22.29           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 152.00/22.29           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.00/22.29           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 152.00/22.29               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 152.00/22.29               op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 152.00/22.29               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 152.00/22.29               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.00/22.29               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.00/22.29                 e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.00/22.29               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 152.00/22.29               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1,
% 152.00/22.29                 e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.00/22.29               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 152.00/22.29                 e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.00/22.29               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.00/22.29               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 152.00/22.29                 e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.00/22.29               $i(all_57_7))))
% 152.00/22.29    (3)  op(e0, e2) = all_52_7
% 152.00/22.29    (4)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 152.00/22.29           all_57_12 & $i(all_57_12))
% 152.00/22.29    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.29    (6)   ~ (e3 = e0)
% 152.00/22.29    (7)   ~ (all_52_11 = e0)
% 152.00/22.29    (8)  op(e0, e3) = all_52_3
% 152.00/22.29    (9)   ~ (all_52_7 = e0)
% 152.00/22.29    (10)  op(e1, e1) = e3
% 152.00/22.29    (11)   ~ (e3 = e2)
% 152.00/22.29    (12)   ~ (all_52_3 = e0)
% 152.00/22.29  
% 152.00/22.29  Begin of proof
% 152.00/22.29  | 
% 152.00/22.29  | BETA: splitting (2) gives:
% 152.00/22.29  | 
% 152.00/22.29  | Case 1:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (13)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 152.00/22.29  | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 152.00/22.29  | |           e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (13) implies:
% 152.00/22.29  | |   (14)  op(e1, e1) = e0
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (5), (6), (10), (14) are inconsistent by sub-proof #896.
% 152.00/22.29  | | 
% 152.00/22.29  | Case 2:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (15)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 152.00/22.29  | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.00/22.29  | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.00/22.29  | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.00/22.29  | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.00/22.29  | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.00/22.29  | |               op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.00/22.29  | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.00/22.29  | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.00/22.29  | |             (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.00/22.29  | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.00/22.29  | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 152.00/22.29  | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.00/22.29  | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.00/22.29  | |             (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.00/22.29  | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.00/22.29  | |               op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 152.00/22.29  | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 152.00/22.29  | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.00/22.29  | | 
% 152.00/22.29  | | BETA: splitting (15) gives:
% 152.00/22.29  | | 
% 152.00/22.29  | | Case 1:
% 152.00/22.29  | | | 
% 152.00/22.29  | | |   (16)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 152.00/22.29  | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.00/22.29  | | |         op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.00/22.29  | | |         $i(all_57_14)
% 152.00/22.29  | | | 
% 152.00/22.29  | | | ALPHA: (16) implies:
% 152.00/22.29  | | |   (17)  all_57_12 = e0
% 152.00/22.29  | | |   (18)   ~ (all_57_11 = e2)
% 152.00/22.29  | | | 
% 152.00/22.29  | | | REF_CLOSE: (4), (17), (18) are inconsistent by sub-proof #890.
% 152.00/22.29  | | | 
% 152.00/22.29  | | Case 2:
% 152.00/22.29  | | | 
% 152.00/22.29  | | |   (19)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.00/22.29  | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.00/22.29  | | |             op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.00/22.29  | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1
% 152.00/22.29  | | |               = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 152.00/22.29  | | |               e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 152.00/22.29  | | |             & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 152.00/22.29  | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.00/22.29  | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 152.00/22.29  | | |               = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 152.00/22.29  | | |               e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0
% 152.00/22.29  | | |             & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.00/22.29  | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.00/22.29  | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 152.00/22.29  | | |               = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.00/22.29  | | |             all_57_7 & op(e0, e1) = e0 & $i(all_57_7)))
% 152.00/22.29  | | | 
% 152.00/22.29  | | | ALPHA: (19) implies:
% 152.00/22.29  | | |   (20)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.00/22.29  | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.00/22.29  | | |           op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.00/22.29  | | |           e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.00/22.29  | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.00/22.29  | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.00/22.29  | | |           (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.00/22.29  | | |           op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 152.00/22.29  | | |           e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.00/22.29  | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.00/22.29  | | |         (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.00/22.29  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.00/22.29  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 152.00/22.29  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 152.00/22.29  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.00/22.29  | | | 
% 152.00/22.29  | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (11), (12), (20) are
% 152.00/22.29  | | |            inconsistent by sub-proof #240.
% 152.00/22.29  | | | 
% 152.00/22.29  | | End of split
% 152.00/22.29  | | 
% 152.00/22.29  | End of split
% 152.00/22.29  | 
% 152.00/22.29  End of proof
% 152.00/22.29  
% 152.00/22.29  Sub-proof #207 shows that the following formulas are inconsistent:
% 152.00/22.29  ----------------------------------------------------------------
% 152.00/22.29    (1)  all_56_1 = e1
% 152.00/22.29    (2)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.00/22.29         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.00/22.29    (3)   ~ (e2 = e0)
% 152.00/22.29    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.29    (5)   ~ (e3 = e0)
% 152.00/22.29    (6)   ~ (e1 = e0)
% 152.00/22.29    (7)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 152.00/22.29             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 152.00/22.29           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 152.00/22.29           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 152.00/22.29           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 152.00/22.29           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.00/22.29    (8)  all_56_13 = e3
% 152.00/22.29    (9)   ~ (e3 = e2)
% 152.00/22.29    (10)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.00/22.29          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.00/22.29    (11)   ~ (e2 = e1)
% 152.00/22.29    (12)  op(e0, e0) = e0
% 152.00/22.29  
% 152.00/22.29  Begin of proof
% 152.00/22.29  | 
% 152.00/22.29  | BETA: splitting (7) gives:
% 152.00/22.29  | 
% 152.00/22.29  | Case 1:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (13)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 152.00/22.29  | |           = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 152.00/22.29  | |         all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (13) implies:
% 152.00/22.29  | |   (14)  op(e0, e0) = e2
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (3), (4), (12), (14) are inconsistent by sub-proof #1043.
% 152.00/22.29  | | 
% 152.00/22.29  | Case 2:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (15)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 152.00/22.29  | |           = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1
% 152.00/22.29  | |         & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (15) implies:
% 152.00/22.29  | |   (16)  op(e2, e2) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (16) are
% 152.00/22.29  | |            inconsistent by sub-proof #505.
% 152.00/22.29  | | 
% 152.00/22.29  | End of split
% 152.00/22.29  | 
% 152.00/22.29  End of proof
% 152.00/22.29  
% 152.00/22.29  Sub-proof #208 shows that the following formulas are inconsistent:
% 152.00/22.29  ----------------------------------------------------------------
% 152.00/22.29    (1)   ~ (e3 = e1)
% 152.00/22.29    (2)  op(e3, e2) = all_52_4
% 152.00/22.29    (3)  all_56_9 = e3
% 152.00/22.29    (4)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.00/22.29         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.00/22.29    (5)  all_56_5 = e1
% 152.00/22.29    (6)   ~ (e2 = e0)
% 152.00/22.29    (7)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.00/22.29         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.00/22.29    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.29    (9)   ~ (all_52_4 = e3)
% 152.00/22.29    (10)   ~ (e3 = e0)
% 152.00/22.29    (11)   ~ (all_52_6 = e3)
% 152.00/22.29    (12)  op(e1, e2) = all_52_6
% 152.00/22.29    (13)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.29          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.00/22.29    (14)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.00/22.29    (15)   ~ (e1 = e0)
% 152.00/22.29    (16)  all_56_13 = e3
% 152.00/22.29    (17)   ~ (e3 = e2)
% 152.00/22.29    (18)   ~ (e2 = e1)
% 152.00/22.29    (19)  all_56_2 = e3
% 152.00/22.29    (20)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.29          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.00/22.29    (21)  op(e2, e2) = e0
% 152.00/22.29  
% 152.00/22.29  Begin of proof
% 152.00/22.29  | 
% 152.00/22.29  | BETA: splitting (14) gives:
% 152.00/22.29  | 
% 152.00/22.29  | Case 1:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (22)  all_56_9 = e1 & op(e3, e0) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (22) implies:
% 152.00/22.29  | |   (23)  all_56_9 = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | COMBINE_EQS: (3), (23) imply:
% 152.00/22.29  | |   (24)  e3 = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | SIMP: (24) implies:
% 152.00/22.29  | |   (25)  e3 = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | COMBINE_EQS: (16), (25) imply:
% 152.00/22.29  | |   (26)  all_56_13 = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (1), (2), (8), (9), (10), (11), (12), (20), (21), (26) are
% 152.00/22.29  | |            inconsistent by sub-proof #210.
% 152.00/22.29  | | 
% 152.00/22.29  | Case 2:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (27)  all_56_10 = e1 & op(e2, e0) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (27) implies:
% 152.00/22.29  | |   (28)  all_56_10 = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (10), (13), (15), (17), (18), (19),
% 152.00/22.29  | |            (28) are inconsistent by sub-proof #678.
% 152.00/22.29  | | 
% 152.00/22.29  | End of split
% 152.00/22.29  | 
% 152.00/22.29  End of proof
% 152.00/22.29  
% 152.00/22.29  Sub-proof #209 shows that the following formulas are inconsistent:
% 152.00/22.29  ----------------------------------------------------------------
% 152.00/22.29    (1)   ~ (e3 = e1)
% 152.00/22.29    (2)  op(e3, e2) = all_52_4
% 152.00/22.29    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.29    (4)  op(e3, e3) = e2
% 152.00/22.29    (5)   ~ (all_52_4 = e3)
% 152.00/22.29    (6)   ~ (e3 = e0)
% 152.00/22.29    (7)   ~ (all_52_6 = e3)
% 152.00/22.29    (8)  op(e1, e2) = all_52_6
% 152.00/22.29    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 152.00/22.29    (10)  all_56_13 = e3
% 152.00/22.29    (11)   ~ (e2 = e1)
% 152.00/22.29    (12)  all_56_2 = e3
% 152.00/22.29    (13)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.29          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.00/22.29    (14)  op(e2, e2) = e0
% 152.00/22.29  
% 152.00/22.29  Begin of proof
% 152.00/22.29  | 
% 152.00/22.29  | BETA: splitting (9) gives:
% 152.00/22.29  | 
% 152.00/22.29  | Case 1:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (15)  all_56_0 = e1 & op(e3, e3) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (15) implies:
% 152.00/22.29  | |   (16)  op(e3, e3) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (3), (4), (11), (16) are inconsistent by sub-proof #1074.
% 152.00/22.29  | | 
% 152.00/22.29  | Case 2:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (17)  all_56_2 = e1 & op(e2, e3) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (17) implies:
% 152.00/22.29  | |   (18)  all_56_2 = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | COMBINE_EQS: (12), (18) imply:
% 152.00/22.29  | |   (19)  e3 = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | COMBINE_EQS: (10), (19) imply:
% 152.00/22.29  | |   (20)  all_56_13 = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (13), (14), (20) are
% 152.00/22.29  | |            inconsistent by sub-proof #210.
% 152.00/22.29  | | 
% 152.00/22.29  | End of split
% 152.00/22.29  | 
% 152.00/22.29  End of proof
% 152.00/22.29  
% 152.00/22.29  Sub-proof #210 shows that the following formulas are inconsistent:
% 152.00/22.29  ----------------------------------------------------------------
% 152.00/22.29    (1)   ~ (e3 = e1)
% 152.00/22.29    (2)  op(e3, e2) = all_52_4
% 152.00/22.29    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.29    (4)  all_56_13 = e1
% 152.00/22.29    (5)   ~ (all_52_4 = e3)
% 152.00/22.29    (6)   ~ (e3 = e0)
% 152.00/22.29    (7)   ~ (all_52_6 = e3)
% 152.00/22.29    (8)  op(e1, e2) = all_52_6
% 152.00/22.29    (9)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.29         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.00/22.29    (10)  op(e2, e2) = e0
% 152.00/22.29  
% 152.00/22.29  Begin of proof
% 152.00/22.29  | 
% 152.00/22.29  | BETA: splitting (9) gives:
% 152.00/22.29  | 
% 152.00/22.29  | Case 1:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (11)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.00/22.29  | |           e3)
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (2), (3), (5), (6), (10), (11) are inconsistent by sub-proof
% 152.00/22.29  | |            #596.
% 152.00/22.29  | | 
% 152.00/22.29  | Case 2:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (12)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 152.00/22.29  | |           e3)
% 152.00/22.29  | | 
% 152.00/22.29  | | BETA: splitting (12) gives:
% 152.00/22.29  | | 
% 152.00/22.29  | | Case 1:
% 152.00/22.29  | | | 
% 152.00/22.29  | | |   (13)  all_56_7 = e3 & op(e1, e2) = e3
% 152.00/22.29  | | | 
% 152.00/22.29  | | | REF_CLOSE: (3), (7), (8), (13) are inconsistent by sub-proof #925.
% 152.00/22.29  | | | 
% 152.00/22.29  | | Case 2:
% 152.00/22.29  | | | 
% 152.00/22.29  | | |   (14)  all_56_13 = e3 & op(e0, e2) = e3
% 152.00/22.29  | | | 
% 152.00/22.29  | | | REF_CLOSE: (1), (4), (14) are inconsistent by sub-proof #585.
% 152.00/22.29  | | | 
% 152.00/22.29  | | End of split
% 152.00/22.29  | | 
% 152.00/22.29  | End of split
% 152.00/22.29  | 
% 152.00/22.29  End of proof
% 152.00/22.29  
% 152.00/22.29  Sub-proof #211 shows that the following formulas are inconsistent:
% 152.00/22.29  ----------------------------------------------------------------
% 152.00/22.29    (1)  all_54_11 = all_52_14
% 152.00/22.29    (2)  all_54_11 = e0
% 152.00/22.29    (3)   ~ (all_52_14 = e0)
% 152.00/22.29  
% 152.00/22.29  Begin of proof
% 152.00/22.29  | 
% 152.00/22.29  | COMBINE_EQS: (1), (2) imply:
% 152.00/22.29  |   (4)  all_52_14 = e0
% 152.00/22.29  | 
% 152.00/22.29  | SIMP: (4) implies:
% 152.00/22.29  |   (5)  all_52_14 = e0
% 152.00/22.29  | 
% 152.00/22.29  | REDUCE: (3), (5) imply:
% 152.00/22.29  |   (6)  $false
% 152.00/22.29  | 
% 152.00/22.29  | CLOSE: (6) is inconsistent.
% 152.00/22.29  | 
% 152.00/22.29  End of proof
% 152.00/22.29  
% 152.00/22.29  Sub-proof #212 shows that the following formulas are inconsistent:
% 152.00/22.29  ----------------------------------------------------------------
% 152.00/22.29    (1)   ~ (all_52_6 = e1)
% 152.00/22.29    (2)   ~ (e3 = e1)
% 152.00/22.29    (3)  op(e3, e2) = all_52_4
% 152.00/22.29    (4)   ~ (all_52_4 = all_52_12)
% 152.00/22.29    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.29    (6)   ~ (all_52_12 = e1)
% 152.00/22.29    (7)   ~ (e3 = e0)
% 152.00/22.29    (8)   ~ (all_52_6 = e3)
% 152.00/22.29    (9)  op(e1, e2) = all_52_6
% 152.00/22.29    (10)  all_54_3 = all_52_12
% 152.00/22.29    (11)   ~ (all_52_12 = e2)
% 152.00/22.29    (12)  all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 152.00/22.29    (13)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.00/22.29          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.00/22.29    (14)   ~ (all_52_12 = e0)
% 152.00/22.29    (15)  op(e2, e2) = e0
% 152.00/22.29    (16)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.00/22.29  
% 152.00/22.29  Begin of proof
% 152.00/22.29  | 
% 152.00/22.29  | BETA: splitting (16) gives:
% 152.00/22.29  | 
% 152.00/22.29  | Case 1:
% 152.00/22.29  | | 
% 152.00/22.29  | |   (17)  all_56_7 = e1 & op(e1, e2) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | ALPHA: (17) implies:
% 152.00/22.29  | |   (18)  op(e1, e2) = e1
% 152.00/22.29  | | 
% 152.00/22.29  | | REF_CLOSE: (1), (5), (9), (18) are inconsistent by sub-proof #1042.
% 152.00/22.29  | | 
% 152.00/22.29  | Case 2:
% 152.00/22.29  | | 
% 152.00/22.30  | |   (19)  all_56_13 = e1 & op(e0, e2) = e1
% 152.00/22.30  | | 
% 152.00/22.30  | | ALPHA: (19) implies:
% 152.00/22.30  | |   (20)  all_56_13 = e1
% 152.00/22.30  | | 
% 152.00/22.30  | | BETA: splitting (13) gives:
% 152.00/22.30  | | 
% 152.00/22.30  | | Case 1:
% 152.00/22.30  | | | 
% 152.00/22.30  | | |   (21)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.00/22.30  | | |           e3)
% 152.00/22.30  | | | 
% 152.00/22.30  | | | BETA: splitting (21) gives:
% 152.00/22.30  | | | 
% 152.00/22.30  | | | Case 1:
% 152.00/22.30  | | | | 
% 152.00/22.30  | | | |   (22)  all_56_1 = e3 & op(e3, e2) = e3
% 152.00/22.30  | | | | 
% 152.00/22.30  | | | | ALPHA: (22) implies:
% 152.00/22.30  | | | |   (23)  op(e3, e2) = e3
% 152.00/22.30  | | | | 
% 152.00/22.30  | | | | BETA: splitting (12) gives:
% 152.00/22.30  | | | | 
% 152.00/22.30  | | | | Case 1:
% 152.00/22.30  | | | | | 
% 152.00/22.30  | | | | |   (24)  all_54_3 = e3
% 152.00/22.30  | | | | | 
% 152.00/22.30  | | | | | COMBINE_EQS: (10), (24) imply:
% 152.00/22.30  | | | | |   (25)  all_52_12 = e3
% 152.00/22.30  | | | | | 
% 152.00/22.30  | | | | | REDUCE: (4), (25) imply:
% 152.00/22.30  | | | | |   (26)   ~ (all_52_4 = e3)
% 152.00/22.30  | | | | | 
% 152.00/22.30  | | | | | REF_CLOSE: (3), (5), (23), (26) are inconsistent by sub-proof #1166.
% 152.00/22.30  | | | | | 
% 152.00/22.30  | | | | Case 2:
% 152.00/22.30  | | | | | 
% 152.00/22.30  | | | | |   (27)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 152.00/22.30  | | | | | 
% 152.00/22.30  | | | | | REF_CLOSE: (6), (10), (11), (14), (27) are inconsistent by sub-proof
% 152.00/22.30  | | | | |            #758.
% 152.00/22.30  | | | | | 
% 152.00/22.30  | | | | End of split
% 152.00/22.30  | | | | 
% 152.00/22.30  | | | Case 2:
% 152.00/22.30  | | | | 
% 152.00/22.30  | | | |   (28)  all_56_3 = e3 & op(e2, e2) = e3
% 152.00/22.30  | | | | 
% 152.00/22.30  | | | | ALPHA: (28) implies:
% 152.00/22.30  | | | |   (29)  op(e2, e2) = e3
% 152.00/22.30  | | | | 
% 152.00/22.30  | | | | REF_CLOSE: (5), (7), (15), (29) are inconsistent by sub-proof #719.
% 152.00/22.30  | | | | 
% 152.00/22.30  | | | End of split
% 152.00/22.30  | | | 
% 152.00/22.30  | | Case 2:
% 152.00/22.30  | | | 
% 152.00/22.30  | | |   (30)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 152.00/22.30  | | |           e3)
% 152.00/22.30  | | | 
% 152.00/22.30  | | | REF_CLOSE: (2), (5), (8), (9), (20), (30) are inconsistent by sub-proof
% 152.00/22.30  | | |            #257.
% 152.00/22.30  | | | 
% 152.00/22.30  | | End of split
% 152.00/22.30  | | 
% 152.00/22.30  | End of split
% 152.00/22.30  | 
% 152.00/22.30  End of proof
% 152.00/22.30  
% 152.00/22.30  Sub-proof #213 shows that the following formulas are inconsistent:
% 152.00/22.30  ----------------------------------------------------------------
% 152.00/22.30    (1)   ~ (e3 = e1)
% 152.00/22.30    (2)  e2 = e0
% 152.00/22.30    (3)   ~ (e2 = e0)
% 152.00/22.30    (4)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.00/22.30         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.00/22.30    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.30    (6)   ~ (e1 = e0)
% 152.00/22.30    (7)   ~ (e3 = e2)
% 152.00/22.30    (8)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.00/22.30         (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.00/22.30    (9)   ~ (e2 = e1)
% 152.00/22.30    (10)  all_56_2 = e3
% 152.00/22.30    (11)  all_56_10 = e2
% 152.00/22.30    (12)  op(e2, e2) = e0
% 152.00/22.30  
% 152.00/22.30  Begin of proof
% 152.00/22.30  | 
% 152.00/22.30  | SIMP: (2) implies:
% 152.00/22.30  |   (13)  e2 = e0
% 152.00/22.30  | 
% 152.00/22.30  | COMBINE_EQS: (11), (13) imply:
% 152.00/22.30  |   (14)  all_56_10 = e0
% 152.00/22.30  | 
% 152.00/22.30  | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (14) are
% 152.00/22.30  |            inconsistent by sub-proof #554.
% 152.00/22.30  | 
% 152.00/22.30  End of proof
% 152.00/22.30  
% 152.00/22.30  Sub-proof #214 shows that the following formulas are inconsistent:
% 152.00/22.30  ----------------------------------------------------------------
% 152.00/22.30    (1)  all_56_0 = e1 & op(e3, e3) = e1
% 152.00/22.30    (2)  all_56_0 = e0
% 152.00/22.30    (3)   ~ (e1 = e0)
% 152.00/22.30  
% 152.00/22.30  Begin of proof
% 152.00/22.30  | 
% 152.00/22.30  | ALPHA: (1) implies:
% 152.00/22.30  |   (4)  all_56_0 = e1
% 152.00/22.30  | 
% 152.00/22.30  | COMBINE_EQS: (2), (4) imply:
% 152.00/22.30  |   (5)  e1 = e0
% 152.00/22.30  | 
% 152.00/22.30  | SIMP: (5) implies:
% 152.00/22.30  |   (6)  e1 = e0
% 152.00/22.30  | 
% 152.00/22.30  | REDUCE: (3), (6) imply:
% 152.00/22.30  |   (7)  $false
% 152.00/22.30  | 
% 152.00/22.30  | CLOSE: (7) is inconsistent.
% 152.00/22.30  | 
% 152.00/22.30  End of proof
% 152.00/22.30  
% 152.00/22.30  Sub-proof #215 shows that the following formulas are inconsistent:
% 152.00/22.30  ----------------------------------------------------------------
% 152.00/22.30    (1)  all_56_8 = e3
% 152.00/22.30    (2)   ~ (e3 = e1)
% 152.00/22.30    (3)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.00/22.30         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.00/22.30    (4)   ~ (e2 = e0)
% 152.00/22.30    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.00/22.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.00/22.30    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.00/22.30         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.00/22.30    (7)  op(e3, e3) = e2
% 152.00/22.30    (8)  all_56_14 = e2
% 152.00/22.30    (9)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.00/22.30         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.00/22.30    (10)   ~ (e3 = e0)
% 152.00/22.30    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.00/22.30          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.00/22.30    (12)  op(e0, e1) = e2
% 152.00/22.30    (13)   ~ (e1 = e0)
% 152.00/22.30    (14)  op(e1, e1) = e3
% 152.00/22.30    (15)   ~ (e3 = e2)
% 152.00/22.30    (16)  all_56_9 = e2
% 152.17/22.30    (17)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.17/22.30          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.17/22.30    (18)   ~ (e2 = e1)
% 152.17/22.30  
% 152.17/22.30  Begin of proof
% 152.17/22.30  | 
% 152.17/22.30  | BETA: splitting (6) gives:
% 152.17/22.30  | 
% 152.17/22.30  | Case 1:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (19)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 152.17/22.30  | |           e3)
% 152.17/22.30  | | 
% 152.17/22.30  | | REF_CLOSE: (2), (4), (5), (7), (9), (10), (11), (13), (15), (16), (18), (19)
% 152.17/22.30  | |            are inconsistent by sub-proof #653.
% 152.17/22.30  | | 
% 152.17/22.30  | Case 2:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (20)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 152.17/22.30  | |           e3)
% 152.17/22.30  | | 
% 152.17/22.30  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (12), (13), (14), (15), (16),
% 152.17/22.30  | |            (17), (18), (20) are inconsistent by sub-proof #353.
% 152.17/22.30  | | 
% 152.17/22.30  | End of split
% 152.17/22.30  | 
% 152.17/22.30  End of proof
% 152.17/22.30  
% 152.17/22.30  Sub-proof #216 shows that the following formulas are inconsistent:
% 152.17/22.30  ----------------------------------------------------------------
% 152.17/22.30    (1)   ~ (e3 = e1)
% 152.17/22.30    (2)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.17/22.30         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.17/22.30    (3)   ~ (e2 = e0)
% 152.17/22.30    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.30    (5)  all_56_4 = e2
% 152.17/22.30    (6)   ~ (e3 = e0)
% 152.17/22.30    (7)   ~ (e1 = e0)
% 152.17/22.30    (8)  op(e1, e1) = e3
% 152.17/22.30    (9)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.17/22.30         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.17/22.30    (10)   ~ (e2 = e1)
% 152.17/22.30    (11)  op(e0, e0) = e0
% 152.17/22.30    (12)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 152.17/22.30  
% 152.17/22.30  Begin of proof
% 152.17/22.30  | 
% 152.17/22.30  | BETA: splitting (12) gives:
% 152.17/22.30  | 
% 152.17/22.30  | Case 1:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (13)  all_56_14 = e2 & op(e0, e1) = e2
% 152.17/22.30  | | 
% 152.17/22.30  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13) are
% 152.17/22.30  | |            inconsistent by sub-proof #217.
% 152.17/22.30  | | 
% 152.17/22.30  | Case 2:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (14)  all_56_15 = e2 & op(e0, e0) = e2
% 152.17/22.30  | | 
% 152.17/22.30  | | ALPHA: (14) implies:
% 152.17/22.30  | |   (15)  op(e0, e0) = e2
% 152.17/22.30  | | 
% 152.17/22.30  | | REF_CLOSE: (3), (4), (11), (15) are inconsistent by sub-proof #1043.
% 152.17/22.30  | | 
% 152.17/22.30  | End of split
% 152.17/22.30  | 
% 152.17/22.30  End of proof
% 152.17/22.30  
% 152.17/22.30  Sub-proof #217 shows that the following formulas are inconsistent:
% 152.17/22.30  ----------------------------------------------------------------
% 152.17/22.30    (1)   ~ (e3 = e1)
% 152.17/22.30    (2)  all_56_14 = e2 & op(e0, e1) = e2
% 152.17/22.30    (3)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.17/22.30         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.17/22.30    (4)   ~ (e2 = e0)
% 152.17/22.30    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.30    (6)  all_56_4 = e2
% 152.17/22.30    (7)   ~ (e3 = e0)
% 152.17/22.30    (8)   ~ (e1 = e0)
% 152.17/22.30    (9)  op(e1, e1) = e3
% 152.17/22.30    (10)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.17/22.30          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.17/22.30    (11)   ~ (e2 = e1)
% 152.17/22.30  
% 152.17/22.30  Begin of proof
% 152.17/22.30  | 
% 152.17/22.30  | ALPHA: (2) implies:
% 152.17/22.30  |   (12)  all_56_14 = e2
% 152.17/22.30  |   (13)  op(e0, e1) = e2
% 152.17/22.30  | 
% 152.17/22.30  | BETA: splitting (10) gives:
% 152.17/22.30  | 
% 152.17/22.30  | Case 1:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (14)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) =
% 152.17/22.30  | |           e1)
% 152.17/22.30  | | 
% 152.17/22.30  | | BETA: splitting (14) gives:
% 152.17/22.30  | | 
% 152.17/22.30  | | Case 1:
% 152.17/22.30  | | | 
% 152.17/22.30  | | |   (15)  all_56_4 = e1 & op(e3, e1) = e1
% 152.17/22.30  | | | 
% 152.17/22.30  | | | REF_CLOSE: (6), (11), (15) are inconsistent by sub-proof #1066.
% 152.17/22.30  | | | 
% 152.17/22.30  | | Case 2:
% 152.17/22.30  | | | 
% 152.17/22.30  | | |   (16)  all_56_5 = e1 & op(e2, e1) = e1
% 152.17/22.30  | | | 
% 152.17/22.30  | | | ALPHA: (16) implies:
% 152.17/22.30  | | |   (17)  all_56_5 = e1
% 152.17/22.30  | | | 
% 152.17/22.30  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (13), (17) are inconsistent
% 152.17/22.30  | | |            by sub-proof #221.
% 152.17/22.30  | | | 
% 152.17/22.30  | | End of split
% 152.17/22.30  | | 
% 152.17/22.30  | Case 2:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (18)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) =
% 152.17/22.30  | |           e1)
% 152.17/22.30  | | 
% 152.17/22.30  | | REF_CLOSE: (1), (5), (9), (11), (12), (18) are inconsistent by sub-proof
% 152.17/22.30  | |            #356.
% 152.17/22.30  | | 
% 152.17/22.30  | End of split
% 152.17/22.30  | 
% 152.17/22.30  End of proof
% 152.17/22.30  
% 152.17/22.30  Sub-proof #218 shows that the following formulas are inconsistent:
% 152.17/22.30  ----------------------------------------------------------------
% 152.17/22.30    (1)  all_56_13 = e2
% 152.17/22.30    (2)   ~ (e3 = e1)
% 152.17/22.30    (3)  all_56_9 = e3
% 152.17/22.30    (4)   ~ (e2 = e0)
% 152.17/22.30    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.30    (6)  op(e3, e3) = e2
% 152.17/22.30    (7)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.17/22.30         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.17/22.30    (8)   ~ (e3 = e0)
% 152.17/22.30    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.17/22.30         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.17/22.30    (10)   ~ (all_52_6 = e3)
% 152.17/22.30    (11)  op(e1, e2) = all_52_6
% 152.17/22.30    (12)   ~ (e1 = e0)
% 152.17/22.30    (13)   ~ (e3 = e2)
% 152.17/22.30    (14)   ~ (e2 = e1)
% 152.17/22.30    (15)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.30          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.17/22.30    (16)  op(e2, e2) = e0
% 152.17/22.30  
% 152.17/22.30  Begin of proof
% 152.17/22.30  | 
% 152.17/22.30  | BETA: splitting (15) gives:
% 152.17/22.30  | 
% 152.17/22.30  | Case 1:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (17)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.17/22.30  | |           e3)
% 152.17/22.30  | | 
% 152.17/22.30  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (12), (14), (16), (17)
% 152.17/22.30  | |            are inconsistent by sub-proof #219.
% 152.17/22.30  | | 
% 152.17/22.30  | Case 2:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (18)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 152.17/22.30  | |           e3)
% 152.17/22.30  | | 
% 152.17/22.30  | | BETA: splitting (18) gives:
% 152.17/22.30  | | 
% 152.17/22.30  | | Case 1:
% 152.17/22.30  | | | 
% 152.17/22.30  | | |   (19)  all_56_7 = e3 & op(e1, e2) = e3
% 152.17/22.30  | | | 
% 152.17/22.30  | | | REF_CLOSE: (5), (10), (11), (19) are inconsistent by sub-proof #925.
% 152.17/22.30  | | | 
% 152.17/22.30  | | Case 2:
% 152.17/22.30  | | | 
% 152.17/22.30  | | |   (20)  all_56_13 = e3 & op(e0, e2) = e3
% 152.17/22.30  | | | 
% 152.17/22.30  | | | REF_CLOSE: (1), (13), (20) are inconsistent by sub-proof #563.
% 152.17/22.30  | | | 
% 152.17/22.30  | | End of split
% 152.17/22.30  | | 
% 152.17/22.30  | End of split
% 152.17/22.30  | 
% 152.17/22.30  End of proof
% 152.17/22.30  
% 152.17/22.30  Sub-proof #219 shows that the following formulas are inconsistent:
% 152.17/22.30  ----------------------------------------------------------------
% 152.17/22.30    (1)   ~ (e3 = e1)
% 152.17/22.30    (2)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 152.17/22.30    (3)  all_56_9 = e3
% 152.17/22.30    (4)   ~ (e2 = e0)
% 152.17/22.30    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.30    (6)  op(e3, e3) = e2
% 152.17/22.30    (7)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.17/22.30         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.17/22.30    (8)   ~ (e3 = e0)
% 152.17/22.30    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.17/22.30         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.17/22.30    (10)   ~ (e1 = e0)
% 152.17/22.30    (11)   ~ (e2 = e1)
% 152.17/22.30    (12)  op(e2, e2) = e0
% 152.17/22.30  
% 152.17/22.30  Begin of proof
% 152.17/22.30  | 
% 152.17/22.30  | BETA: splitting (2) gives:
% 152.17/22.30  | 
% 152.17/22.30  | Case 1:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (13)  all_56_1 = e3 & op(e3, e2) = e3
% 152.17/22.30  | | 
% 152.17/22.30  | | ALPHA: (13) implies:
% 152.17/22.30  | |   (14)  all_56_1 = e3
% 152.17/22.30  | | 
% 152.17/22.30  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (14) are
% 152.17/22.30  | |            inconsistent by sub-proof #345.
% 152.17/22.30  | | 
% 152.17/22.30  | Case 2:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (15)  all_56_3 = e3 & op(e2, e2) = e3
% 152.17/22.30  | | 
% 152.17/22.30  | | ALPHA: (15) implies:
% 152.17/22.30  | |   (16)  op(e2, e2) = e3
% 152.17/22.30  | | 
% 152.17/22.30  | | REF_CLOSE: (5), (8), (12), (16) are inconsistent by sub-proof #719.
% 152.17/22.30  | | 
% 152.17/22.30  | End of split
% 152.17/22.30  | 
% 152.17/22.30  End of proof
% 152.17/22.30  
% 152.17/22.30  Sub-proof #220 shows that the following formulas are inconsistent:
% 152.17/22.30  ----------------------------------------------------------------
% 152.17/22.30    (1)  all_56_8 = e3
% 152.17/22.30    (2)   ~ (e3 = e1)
% 152.17/22.30    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.17/22.30         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.17/22.30    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 152.17/22.30         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.17/22.30    (5)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.30         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.17/22.30    (6)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.17/22.30         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.17/22.30    (7)   ~ (e2 = e0)
% 152.17/22.30    (8)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.30         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.17/22.30    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.30    (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.17/22.30          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.17/22.30    (11)  all_56_4 = e2
% 152.17/22.30    (12)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.17/22.30          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.17/22.30    (13)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1)
% 152.17/22.30    (14)   ~ (all_52_9 = e3)
% 152.17/22.30    (15)  op(e3, e3) = e2
% 152.17/22.30    (16)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.17/22.30          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.17/22.30    (17)   ~ (e3 = e0)
% 152.17/22.30    (18)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.17/22.30          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.17/22.30    (19)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.17/22.30          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.17/22.30    (20)   ~ (all_52_6 = e3)
% 152.17/22.30    (21)  op(e1, e2) = all_52_6
% 152.17/22.30    (22)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.30          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.17/22.30    (23)  op(e2, e1) = all_52_9
% 152.17/22.30    (24)   ~ (e1 = e0)
% 152.17/22.30    (25)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.17/22.30          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.17/22.30    (26)  op(e1, e1) = e3
% 152.17/22.30    (27)   ~ (e3 = e2)
% 152.17/22.30    (28)   ~ (all_52_8 = e3)
% 152.17/22.30    (29)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.17/22.30          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 152.17/22.30            e2)
% 152.17/22.30    (30)  op(e3, e1) = all_52_8
% 152.17/22.30    (31)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.17/22.30          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.17/22.30    (32)   ~ (e2 = e1)
% 152.17/22.30    (33)  op(e0, e0) = e0
% 152.17/22.30    (34)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.30          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.17/22.30    (35)  op(e2, e2) = e0
% 152.17/22.30    (36)  op(e2, e3) = all_52_1
% 152.17/22.30    (37)   ~ (all_52_1 = e2)
% 152.17/22.30  
% 152.17/22.30  Begin of proof
% 152.17/22.30  | 
% 152.17/22.30  | BETA: splitting (13) gives:
% 152.17/22.30  | 
% 152.17/22.30  | Case 1:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (38)  all_56_4 = e1 & op(e3, e1) = e1
% 152.17/22.30  | | 
% 152.17/22.30  | | REF_CLOSE: (11), (32), (38) are inconsistent by sub-proof #1066.
% 152.17/22.30  | | 
% 152.17/22.30  | Case 2:
% 152.17/22.30  | | 
% 152.17/22.30  | |   (39)  all_56_5 = e1 & op(e2, e1) = e1
% 152.17/22.30  | | 
% 152.17/22.30  | | ALPHA: (39) implies:
% 152.17/22.30  | |   (40)  all_56_5 = e1
% 152.17/22.30  | | 
% 152.17/22.30  | | BETA: splitting (8) gives:
% 152.17/22.30  | | 
% 152.17/22.30  | | Case 1:
% 152.17/22.30  | | | 
% 152.17/22.30  | | |   (41)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 152.17/22.30  | | |           e2)
% 152.17/22.30  | | | 
% 152.17/22.30  | | | REF_CLOSE: (7), (9), (35), (36), (37), (41) are inconsistent by sub-proof
% 152.17/22.30  | | |            #613.
% 152.17/22.30  | | | 
% 152.17/22.30  | | Case 2:
% 152.17/22.30  | | | 
% 152.17/22.30  | | |   (42)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 152.17/22.30  | | |           e2)
% 152.17/22.30  | | | 
% 152.17/22.30  | | | BETA: splitting (42) gives:
% 152.17/22.30  | | | 
% 152.17/22.30  | | | Case 1:
% 152.17/22.30  | | | | 
% 152.17/22.30  | | | |   (43)  all_56_5 = e2 & op(e2, e1) = e2
% 152.17/22.30  | | | | 
% 152.17/22.30  | | | | REF_CLOSE: (32), (40), (43) are inconsistent by sub-proof #672.
% 152.17/22.30  | | | | 
% 152.17/22.30  | | | Case 2:
% 152.17/22.30  | | | | 
% 152.17/22.30  | | | |   (44)  all_56_10 = e2 & op(e2, e0) = e2
% 152.17/22.30  | | | | 
% 152.17/22.30  | | | | ALPHA: (44) implies:
% 152.17/22.30  | | | |   (45)  all_56_10 = e2
% 152.17/22.30  | | | |   (46)  op(e2, e0) = e2
% 152.17/22.30  | | | | 
% 152.17/22.30  | | | | BETA: splitting (29) gives:
% 152.17/22.30  | | | | 
% 152.17/22.30  | | | | Case 1:
% 152.17/22.30  | | | | | 
% 152.17/22.30  | | | | |   (47)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0,
% 152.17/22.30  | | | | |             e2) = e2)
% 152.17/22.30  | | | | | 
% 152.17/22.30  | | | | | BETA: splitting (47) gives:
% 152.17/22.30  | | | | | 
% 152.17/22.30  | | | | | Case 1:
% 152.17/22.30  | | | | | | 
% 152.17/22.30  | | | | | |   (48)  all_56_12 = e2 & op(e0, e3) = e2
% 152.17/22.30  | | | | | | 
% 152.17/22.30  | | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (12), (15), (17), (18),
% 152.17/22.30  | | | | | |            (24), (25), (26), (27), (31), (32), (48) are inconsistent
% 152.17/22.30  | | | | | |            by sub-proof #426.
% 152.17/22.30  | | | | | | 
% 152.17/22.30  | | | | | Case 2:
% 152.17/22.30  | | | | | | 
% 152.17/22.30  | | | | | |   (49)  all_56_13 = e2 & op(e0, e2) = e2
% 152.17/22.30  | | | | | | 
% 152.17/22.30  | | | | | | ALPHA: (49) implies:
% 152.17/22.30  | | | | | |   (50)  all_56_13 = e2
% 152.17/22.30  | | | | | | 
% 152.17/22.30  | | | | | | BETA: splitting (22) gives:
% 152.17/22.30  | | | | | | 
% 152.17/22.30  | | | | | | Case 1:
% 152.17/22.30  | | | | | | | 
% 152.17/22.30  | | | | | | |   (51)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 &
% 152.17/22.30  | | | | | | |           op(e2, e2) = e3)
% 152.17/22.30  | | | | | | | 
% 152.17/22.30  | | | | | | | BETA: splitting (51) gives:
% 152.17/22.30  | | | | | | | 
% 152.17/22.30  | | | | | | | Case 1:
% 152.17/22.30  | | | | | | | | 
% 152.17/22.30  | | | | | | | |   (52)  all_56_2 = e3 & op(e2, e3) = e3
% 152.17/22.30  | | | | | | | | 
% 152.17/22.30  | | | | | | | | ALPHA: (52) implies:
% 152.17/22.30  | | | | | | | |   (53)  all_56_2 = e3
% 152.17/22.30  | | | | | | | | 
% 152.17/22.30  | | | | | | | | BETA: splitting (16) gives:
% 152.17/22.30  | | | | | | | | 
% 152.17/22.30  | | | | | | | | Case 1:
% 152.17/22.30  | | | | | | | | | 
% 152.17/22.30  | | | | | | | | |   (54)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 &
% 152.17/22.30  | | | | | | | | |           op(e3, e2) = e1)
% 152.17/22.30  | | | | | | | | | 
% 152.17/22.30  | | | | | | | | | BETA: splitting (54) gives:
% 152.17/22.30  | | | | | | | | | 
% 152.17/22.30  | | | | | | | | | Case 1:
% 152.17/22.30  | | | | | | | | | | 
% 152.17/22.30  | | | | | | | | | |   (55)  all_56_0 = e1 & op(e3, e3) = e1
% 152.17/22.30  | | | | | | | | | | 
% 152.17/22.30  | | | | | | | | | | ALPHA: (55) implies:
% 152.17/22.30  | | | | | | | | | |   (56)  op(e3, e3) = e1
% 152.17/22.30  | | | | | | | | | | 
% 152.17/22.30  | | | | | | | | | | REF_CLOSE: (9), (15), (32), (56) are inconsistent by
% 152.17/22.30  | | | | | | | | | |            sub-proof #1074.
% 152.17/22.30  | | | | | | | | | | 
% 152.17/22.30  | | | | | | | | | Case 2:
% 152.17/22.30  | | | | | | | | | | 
% 152.17/22.30  | | | | | | | | | |   (57)  all_56_1 = e1 & op(e3, e2) = e1
% 152.17/22.30  | | | | | | | | | | 
% 152.17/22.30  | | | | | | | | | | ALPHA: (57) implies:
% 152.17/22.30  | | | | | | | | | |   (58)  all_56_1 = e1
% 152.17/22.30  | | | | | | | | | | 
% 152.17/22.30  | | | | | | | | | | REF_CLOSE: (2), (9), (17), (20), (21), (27), (34), (35),
% 152.17/22.30  | | | | | | | | | |            (50), (58) are inconsistent by sub-proof #464.
% 152.17/22.30  | | | | | | | | | | 
% 152.17/22.30  | | | | | | | | | End of split
% 152.17/22.30  | | | | | | | | | 
% 152.17/22.30  | | | | | | | | Case 2:
% 152.17/22.30  | | | | | | | | | 
% 152.17/22.30  | | | | | | | | |   (59)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 &
% 152.17/22.30  | | | | | | | | |           op(e3, e0) = e1)
% 152.17/22.30  | | | | | | | | | 
% 152.17/22.30  | | | | | | | | | BETA: splitting (59) gives:
% 152.17/22.30  | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | Case 1:
% 152.17/22.31  | | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | |   (60)  all_56_4 = e1 & op(e3, e1) = e1
% 152.17/22.31  | | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | | ALPHA: (60) implies:
% 152.17/22.31  | | | | | | | | | |   (61)  all_56_4 = e1
% 152.17/22.31  | | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | | COMBINE_EQS: (11), (61) imply:
% 152.17/22.31  | | | | | | | | | |   (62)  e2 = e1
% 152.17/22.31  | | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | | SIMP: (62) implies:
% 152.17/22.31  | | | | | | | | | |   (63)  e2 = e1
% 152.17/22.31  | | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | | COMBINE_EQS: (45), (63) imply:
% 152.17/22.31  | | | | | | | | | |   (64)  all_56_10 = e1
% 152.17/22.31  | | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (17), (22), (24), (27),
% 152.17/22.31  | | | | | | | | | |            (32), (40), (53), (64) are inconsistent by
% 152.17/22.31  | | | | | | | | | |            sub-proof #678.
% 152.17/22.31  | | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | Case 2:
% 152.17/22.31  | | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | |   (65)  all_56_9 = e1 & op(e3, e0) = e1
% 152.17/22.31  | | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | | ALPHA: (65) implies:
% 152.17/22.31  | | | | | | | | | |   (66)  all_56_9 = e1
% 152.17/22.31  | | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | | REF_CLOSE: (2), (7), (9), (10), (11), (15), (17), (19), (24),
% 152.17/22.31  | | | | | | | | | |            (27), (28), (30), (66) are inconsistent by
% 152.17/22.31  | | | | | | | | | |            sub-proof #484.
% 152.17/22.31  | | | | | | | | | | 
% 152.17/22.31  | | | | | | | | | End of split
% 152.17/22.31  | | | | | | | | | 
% 152.17/22.31  | | | | | | | | End of split
% 152.17/22.31  | | | | | | | | 
% 152.17/22.31  | | | | | | | Case 2:
% 152.17/22.31  | | | | | | | | 
% 152.17/22.31  | | | | | | | |   (67)  all_56_3 = e3 & op(e2, e2) = e3
% 152.17/22.31  | | | | | | | | 
% 152.17/22.31  | | | | | | | | ALPHA: (67) implies:
% 152.17/22.31  | | | | | | | |   (68)  op(e2, e2) = e3
% 152.17/22.31  | | | | | | | | 
% 152.17/22.31  | | | | | | | | REF_CLOSE: (9), (17), (35), (68) are inconsistent by sub-proof
% 152.17/22.31  | | | | | | | |            #719.
% 152.17/22.31  | | | | | | | | 
% 152.17/22.31  | | | | | | | End of split
% 152.17/22.31  | | | | | | | 
% 152.17/22.31  | | | | | | Case 2:
% 152.17/22.31  | | | | | | | 
% 152.17/22.31  | | | | | | |   (69)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 &
% 152.17/22.31  | | | | | | |           op(e2, e0) = e3)
% 152.17/22.31  | | | | | | | 
% 152.17/22.31  | | | | | | | REF_CLOSE: (9), (14), (23), (27), (46), (69) are inconsistent by
% 152.17/22.31  | | | | | | |            sub-proof #224.
% 152.17/22.31  | | | | | | | 
% 152.17/22.31  | | | | | | End of split
% 152.17/22.31  | | | | | | 
% 152.17/22.31  | | | | | End of split
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | Case 2:
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | |   (70)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0,
% 152.17/22.31  | | | | |             e0) = e2)
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | | BETA: splitting (70) gives:
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | | Case 1:
% 152.17/22.31  | | | | | | 
% 152.17/22.31  | | | | | |   (71)  all_56_14 = e2 & op(e0, e1) = e2
% 152.17/22.31  | | | | | | 
% 152.17/22.31  | | | | | | ALPHA: (71) implies:
% 152.17/22.31  | | | | | |   (72)  op(e0, e1) = e2
% 152.17/22.31  | | | | | | 
% 152.17/22.31  | | | | | | REF_CLOSE: (6), (7), (9), (11), (17), (24), (26), (40), (72) are
% 152.17/22.31  | | | | | |            inconsistent by sub-proof #221.
% 152.17/22.31  | | | | | | 
% 152.17/22.31  | | | | | Case 2:
% 152.17/22.31  | | | | | | 
% 152.17/22.31  | | | | | |   (73)  all_56_15 = e2 & op(e0, e0) = e2
% 152.17/22.31  | | | | | | 
% 152.17/22.31  | | | | | | ALPHA: (73) implies:
% 152.17/22.31  | | | | | |   (74)  op(e0, e0) = e2
% 152.17/22.31  | | | | | | 
% 152.17/22.31  | | | | | | REF_CLOSE: (7), (9), (33), (74) are inconsistent by sub-proof #1043.
% 152.17/22.31  | | | | | | 
% 152.17/22.31  | | | | | End of split
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | End of split
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | End of split
% 152.17/22.31  | | | 
% 152.17/22.31  | | End of split
% 152.17/22.31  | | 
% 152.17/22.31  | End of split
% 152.17/22.31  | 
% 152.17/22.31  End of proof
% 152.17/22.31  
% 152.17/22.31  Sub-proof #221 shows that the following formulas are inconsistent:
% 152.17/22.31  ----------------------------------------------------------------
% 152.17/22.31    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.17/22.31         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.17/22.31    (2)  all_56_5 = e1
% 152.17/22.31    (3)   ~ (e2 = e0)
% 152.17/22.31    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.31    (5)  all_56_4 = e2
% 152.17/22.31    (6)   ~ (e3 = e0)
% 152.17/22.31    (7)  op(e0, e1) = e2
% 152.17/22.31    (8)   ~ (e1 = e0)
% 152.17/22.31    (9)  op(e1, e1) = e3
% 152.17/22.31  
% 152.17/22.31  Begin of proof
% 152.17/22.31  | 
% 152.17/22.31  | BETA: splitting (1) gives:
% 152.17/22.31  | 
% 152.17/22.31  | Case 1:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (10)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 152.17/22.31  | |           e0)
% 152.17/22.31  | | 
% 152.17/22.31  | | BETA: splitting (10) gives:
% 152.17/22.31  | | 
% 152.17/22.31  | | Case 1:
% 152.17/22.31  | | | 
% 152.17/22.31  | | |   (11)  all_56_4 = e0 & op(e3, e1) = e0
% 152.17/22.31  | | | 
% 152.17/22.31  | | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #1070.
% 152.17/22.31  | | | 
% 152.17/22.31  | | Case 2:
% 152.17/22.31  | | | 
% 152.17/22.31  | | |   (12)  all_56_5 = e0 & op(e2, e1) = e0
% 152.17/22.31  | | | 
% 152.17/22.31  | | | REF_CLOSE: (2), (8), (12) are inconsistent by sub-proof #223.
% 152.17/22.31  | | | 
% 152.17/22.31  | | End of split
% 152.17/22.31  | | 
% 152.17/22.31  | Case 2:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (13)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 152.17/22.31  | |           e0)
% 152.17/22.31  | | 
% 152.17/22.31  | | REF_CLOSE: (3), (4), (6), (7), (9), (13) are inconsistent by sub-proof #222.
% 152.17/22.31  | | 
% 152.17/22.31  | End of split
% 152.17/22.31  | 
% 152.17/22.31  End of proof
% 152.17/22.31  
% 152.17/22.31  Sub-proof #222 shows that the following formulas are inconsistent:
% 152.17/22.31  ----------------------------------------------------------------
% 152.17/22.31    (1)   ~ (e2 = e0)
% 152.17/22.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.31    (3)   ~ (e3 = e0)
% 152.17/22.31    (4)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.17/22.31    (5)  op(e0, e1) = e2
% 152.17/22.31    (6)  op(e1, e1) = e3
% 152.17/22.31  
% 152.17/22.31  Begin of proof
% 152.17/22.31  | 
% 152.17/22.31  | BETA: splitting (4) gives:
% 152.17/22.31  | 
% 152.17/22.31  | Case 1:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (7)  all_56_8 = e0 & op(e1, e1) = e0
% 152.17/22.31  | | 
% 152.17/22.31  | | ALPHA: (7) implies:
% 152.17/22.31  | |   (8)  op(e1, e1) = e0
% 152.17/22.31  | | 
% 152.17/22.31  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #896.
% 152.17/22.31  | | 
% 152.17/22.31  | Case 2:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (9)  all_56_14 = e0 & op(e0, e1) = e0
% 152.17/22.31  | | 
% 152.17/22.31  | | ALPHA: (9) implies:
% 152.17/22.31  | |   (10)  op(e0, e1) = e0
% 152.17/22.31  | | 
% 152.17/22.31  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1008.
% 152.17/22.31  | | 
% 152.17/22.31  | End of split
% 152.17/22.31  | 
% 152.17/22.31  End of proof
% 152.17/22.31  
% 152.17/22.31  Sub-proof #223 shows that the following formulas are inconsistent:
% 152.17/22.31  ----------------------------------------------------------------
% 152.17/22.31    (1)  all_56_5 = e0 & op(e2, e1) = e0
% 152.17/22.31    (2)  all_56_5 = e1
% 152.17/22.31    (3)   ~ (e1 = e0)
% 152.17/22.31  
% 152.17/22.31  Begin of proof
% 152.17/22.31  | 
% 152.17/22.31  | ALPHA: (1) implies:
% 152.17/22.31  |   (4)  all_56_5 = e0
% 152.17/22.31  | 
% 152.17/22.31  | COMBINE_EQS: (2), (4) imply:
% 152.17/22.31  |   (5)  e1 = e0
% 152.17/22.31  | 
% 152.17/22.31  | REDUCE: (3), (5) imply:
% 152.17/22.31  |   (6)  $false
% 152.17/22.31  | 
% 152.17/22.31  | CLOSE: (6) is inconsistent.
% 152.17/22.31  | 
% 152.17/22.31  End of proof
% 152.17/22.31  
% 152.17/22.31  Sub-proof #224 shows that the following formulas are inconsistent:
% 152.17/22.31  ----------------------------------------------------------------
% 152.17/22.31    (1)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.17/22.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.31    (3)  op(e2, e0) = e2
% 152.17/22.31    (4)   ~ (all_52_9 = e3)
% 152.17/22.31    (5)  op(e2, e1) = all_52_9
% 152.17/22.31    (6)   ~ (e3 = e2)
% 152.17/22.31  
% 152.17/22.31  Begin of proof
% 152.17/22.31  | 
% 152.17/22.31  | BETA: splitting (1) gives:
% 152.17/22.31  | 
% 152.17/22.31  | Case 1:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (7)  all_56_5 = e3 & op(e2, e1) = e3
% 152.17/22.31  | | 
% 152.17/22.31  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #647.
% 152.17/22.31  | | 
% 152.17/22.31  | Case 2:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (8)  all_56_10 = e3 & op(e2, e0) = e3
% 152.17/22.31  | | 
% 152.17/22.31  | | ALPHA: (8) implies:
% 152.17/22.31  | |   (9)  op(e2, e0) = e3
% 152.17/22.31  | | 
% 152.17/22.31  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #854.
% 152.17/22.31  | | 
% 152.17/22.31  | End of split
% 152.17/22.31  | 
% 152.17/22.31  End of proof
% 152.17/22.31  
% 152.17/22.31  Sub-proof #225 shows that the following formulas are inconsistent:
% 152.17/22.31  ----------------------------------------------------------------
% 152.17/22.31    (1)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 152.17/22.31    (2)   ~ (all_14_2 = e0)
% 152.17/22.31    (3)  op(e3, e3) = all_14_2
% 152.17/22.31    (4)   ~ (all_10_2 = e1)
% 152.17/22.31    (5)   ~ (e2 = e0)
% 152.17/22.31    (6)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.31         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.17/22.31    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.31    (8)   ~ (all_52_9 = e3)
% 152.17/22.31    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.17/22.31         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.17/22.31    (10)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.17/22.31    (11)  op(e2, e0) = all_52_13
% 152.17/22.31    (12)  op(e0, e3) = all_52_3
% 152.17/22.31    (13)  all_54_0 = all_14_2
% 152.17/22.31    (14)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.31          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.17/22.31    (15)  op(e2, e1) = all_52_9
% 152.17/22.31    (16)   ~ (all_52_1 = all_14_2)
% 152.17/22.31    (17)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 152.17/22.31              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.17/22.31            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 152.17/22.31                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 152.17/22.31              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.17/22.31          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 152.17/22.31              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.31            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 152.17/22.31                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 152.17/22.31              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.17/22.31          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 152.17/22.31              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.31            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 152.17/22.31                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 152.17/22.31              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.17/22.31          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 152.17/22.31              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.31            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 152.17/22.31                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 152.17/22.31                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.17/22.31                $i(all_57_14))))
% 152.17/22.31    (18)   ~ (all_14_2 = e2)
% 152.17/22.31    (19)  op(e1, e1) = e3
% 152.17/22.31    (20)   ~ (all_14_2 = e1)
% 152.17/22.31    (21)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.17/22.31          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.17/22.31    (22)   ~ (all_10_2 = e2)
% 152.17/22.31    (23)   ~ (all_52_3 = all_10_2)
% 152.17/22.31    (24)   ~ (e2 = e1)
% 152.17/22.31    (25)   ~ (all_52_13 = all_10_2)
% 152.17/22.31    (26)  all_54_15 = all_10_2
% 152.17/22.31    (27)  op(e1, e3) = all_52_2
% 152.17/22.31    (28)  op(e2, e2) = e0
% 152.17/22.31    (29)  op(e2, e3) = all_52_1
% 152.17/22.31  
% 152.17/22.31  Begin of proof
% 152.17/22.31  | 
% 152.17/22.31  | BETA: splitting (10) gives:
% 152.17/22.31  | 
% 152.17/22.31  | Case 1:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (30)  all_54_0 = e3
% 152.17/22.31  | | 
% 152.17/22.31  | | COMBINE_EQS: (13), (30) imply:
% 152.17/22.31  | |   (31)  all_14_2 = e3
% 152.17/22.31  | | 
% 152.17/22.31  | | SIMP: (31) implies:
% 152.17/22.31  | |   (32)  all_14_2 = e3
% 152.17/22.31  | | 
% 152.17/22.31  | | REDUCE: (16), (32) imply:
% 152.17/22.31  | |   (33)   ~ (all_52_1 = e3)
% 152.17/22.31  | | 
% 152.17/22.31  | | REDUCE: (18), (32) imply:
% 152.17/22.31  | |   (34)   ~ (e3 = e2)
% 152.17/22.31  | | 
% 152.17/22.31  | | REDUCE: (20), (32) imply:
% 152.17/22.31  | |   (35)   ~ (e3 = e1)
% 152.17/22.31  | | 
% 152.17/22.31  | | REDUCE: (2), (32) imply:
% 152.17/22.31  | |   (36)   ~ (e3 = e0)
% 152.17/22.31  | | 
% 152.17/22.31  | | BETA: splitting (14) gives:
% 152.17/22.31  | | 
% 152.17/22.31  | | Case 1:
% 152.17/22.31  | | | 
% 152.17/22.31  | | |   (37)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.17/22.31  | | |           e3)
% 152.17/22.31  | | | 
% 152.17/22.31  | | | REF_CLOSE: (7), (28), (29), (33), (36), (37) are inconsistent by sub-proof
% 152.17/22.31  | | |            #690.
% 152.17/22.31  | | | 
% 152.17/22.31  | | Case 2:
% 152.17/22.31  | | | 
% 152.17/22.31  | | |   (38)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 152.17/22.31  | | |           e3)
% 152.17/22.31  | | | 
% 152.17/22.31  | | | BETA: splitting (38) gives:
% 152.17/22.31  | | | 
% 152.17/22.31  | | | Case 1:
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | |   (39)  all_56_5 = e3 & op(e2, e1) = e3
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | | REF_CLOSE: (7), (8), (15), (39) are inconsistent by sub-proof #647.
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | Case 2:
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | |   (40)  all_56_10 = e3 & op(e2, e0) = e3
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | | ALPHA: (40) implies:
% 152.17/22.31  | | | |   (41)  all_56_10 = e3
% 152.17/22.31  | | | |   (42)  op(e2, e0) = e3
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12),
% 152.17/22.31  | | | |            (13), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 152.17/22.31  | | | |            (26), (27), (28), (34), (35), (41), (42) are inconsistent by
% 152.17/22.31  | | | |            sub-proof #667.
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | End of split
% 152.17/22.31  | | | 
% 152.17/22.31  | | End of split
% 152.17/22.31  | | 
% 152.17/22.31  | Case 2:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (43)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.17/22.31  | | 
% 152.17/22.31  | | REF_CLOSE: (2), (13), (18), (20), (43) are inconsistent by sub-proof #1140.
% 152.17/22.31  | | 
% 152.17/22.31  | End of split
% 152.17/22.31  | 
% 152.17/22.31  End of proof
% 152.17/22.31  
% 152.17/22.31  Sub-proof #226 shows that the following formulas are inconsistent:
% 152.17/22.31  ----------------------------------------------------------------
% 152.17/22.31    (1)   ~ (e3 = e1)
% 152.17/22.31    (2)  op(e2, e2) = e1
% 152.17/22.31    (3)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.31         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.17/22.31    (4)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.31         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.17/22.31    (5)   ~ (e2 = e0)
% 152.17/22.31    (6)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.31         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.17/22.31    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.31    (8)   ~ (all_52_9 = e3)
% 152.17/22.31    (9)  all_56_13 = e1
% 152.17/22.31    (10)   ~ (e3 = e0)
% 152.17/22.31    (11)   ~ (all_52_6 = e3)
% 152.17/22.31    (12)  op(e1, e2) = all_52_6
% 152.17/22.31    (13)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.31          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.17/22.31    (14)  op(e2, e1) = all_52_9
% 152.17/22.31    (15)   ~ (e1 = e0)
% 152.17/22.31    (16)   ~ (e3 = e2)
% 152.17/22.31    (17)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.17/22.31          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.17/22.31    (18)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.31          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.17/22.31    (19)   ~ (e2 = e1)
% 152.17/22.31    (20)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.31          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.17/22.31    (21)  op(e2, e3) = all_52_1
% 152.17/22.31  
% 152.17/22.31  Begin of proof
% 152.17/22.31  | 
% 152.17/22.31  | BETA: splitting (20) gives:
% 152.17/22.31  | 
% 152.17/22.31  | Case 1:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (22)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.17/22.31  | |           e3)
% 152.17/22.31  | | 
% 152.17/22.31  | | BETA: splitting (22) gives:
% 152.17/22.31  | | 
% 152.17/22.31  | | Case 1:
% 152.17/22.31  | | | 
% 152.17/22.31  | | |   (23)  all_56_1 = e3 & op(e3, e2) = e3
% 152.17/22.31  | | | 
% 152.17/22.31  | | | ALPHA: (23) implies:
% 152.17/22.31  | | |   (24)  all_56_1 = e3
% 152.17/22.31  | | | 
% 152.17/22.31  | | | BETA: splitting (18) gives:
% 152.17/22.31  | | | 
% 152.17/22.31  | | | Case 1:
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | |   (25)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2)
% 152.17/22.31  | | | |           = e0)
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | | BETA: splitting (25) gives:
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | | Case 1:
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | |   (26)  all_56_1 = e0 & op(e3, e2) = e0
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | | REF_CLOSE: (10), (24), (26) are inconsistent by sub-proof #1114.
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | Case 2:
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | |   (27)  all_56_3 = e0 & op(e2, e2) = e0
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | | ALPHA: (27) implies:
% 152.17/22.31  | | | | |   (28)  op(e2, e2) = e0
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | | REF_CLOSE: (2), (7), (15), (28) are inconsistent by sub-proof #853.
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | End of split
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | Case 2:
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | |   (29)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2)
% 152.17/22.31  | | | |           = e0)
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | | BETA: splitting (29) gives:
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | | Case 1:
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | |   (30)  all_56_7 = e0 & op(e1, e2) = e0
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | | ALPHA: (30) implies:
% 152.17/22.31  | | | | |   (31)  all_56_7 = e0
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | | REF_CLOSE: (2), (3), (5), (7), (9), (16), (19), (24), (31) are
% 152.17/22.31  | | | | |            inconsistent by sub-proof #738.
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | Case 2:
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | |   (32)  all_56_13 = e0 & op(e0, e2) = e0
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | | REF_CLOSE: (9), (15), (32) are inconsistent by sub-proof #737.
% 152.17/22.31  | | | | | 
% 152.17/22.31  | | | | End of split
% 152.17/22.31  | | | | 
% 152.17/22.31  | | | End of split
% 152.17/22.31  | | | 
% 152.17/22.31  | | Case 2:
% 152.17/22.31  | | | 
% 152.17/22.31  | | |   (33)  all_56_3 = e3 & op(e2, e2) = e3
% 152.17/22.31  | | | 
% 152.17/22.31  | | | ALPHA: (33) implies:
% 152.17/22.31  | | |   (34)  all_56_3 = e3
% 152.17/22.31  | | |   (35)  op(e2, e2) = e3
% 152.17/22.31  | | | 
% 152.17/22.31  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 152.17/22.31  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (33),
% 152.17/22.31  | | |            (34), (35) are inconsistent by sub-proof #227.
% 152.17/22.31  | | | 
% 152.17/22.31  | | End of split
% 152.17/22.31  | | 
% 152.17/22.31  | Case 2:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (36)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 152.17/22.31  | |           e3)
% 152.17/22.31  | | 
% 152.17/22.31  | | REF_CLOSE: (1), (7), (9), (11), (12), (36) are inconsistent by sub-proof
% 152.17/22.31  | |            #257.
% 152.17/22.31  | | 
% 152.17/22.31  | End of split
% 152.17/22.31  | 
% 152.17/22.31  End of proof
% 152.17/22.31  
% 152.17/22.31  Sub-proof #227 shows that the following formulas are inconsistent:
% 152.17/22.31  ----------------------------------------------------------------
% 152.17/22.31    (1)   ~ (e3 = e1)
% 152.17/22.31    (2)  op(e2, e2) = e1
% 152.17/22.31    (3)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.31         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.17/22.31    (4)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.31         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.17/22.31    (5)   ~ (e2 = e0)
% 152.17/22.31    (6)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.31         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.17/22.31    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.31    (8)   ~ (all_52_9 = e3)
% 152.17/22.31    (9)  all_56_13 = e1
% 152.17/22.31    (10)  all_56_3 = e3 & op(e2, e2) = e3
% 152.17/22.31    (11)   ~ (e3 = e0)
% 152.17/22.31    (12)   ~ (all_52_6 = e3)
% 152.17/22.31    (13)  all_56_3 = e3
% 152.17/22.31    (14)  op(e1, e2) = all_52_6
% 152.17/22.31    (15)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.31          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.17/22.31    (16)  op(e2, e1) = all_52_9
% 152.17/22.31    (17)   ~ (e1 = e0)
% 152.17/22.31    (18)   ~ (e3 = e2)
% 152.17/22.31    (19)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.17/22.31          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.17/22.31    (20)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.31          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.17/22.31    (21)   ~ (e2 = e1)
% 152.17/22.31    (22)  op(e2, e2) = e3
% 152.17/22.31    (23)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.31          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.17/22.31    (24)  op(e2, e3) = all_52_1
% 152.17/22.31  
% 152.17/22.31  Begin of proof
% 152.17/22.31  | 
% 152.17/22.31  | BETA: splitting (19) gives:
% 152.17/22.31  | 
% 152.17/22.31  | Case 1:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (25)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 152.17/22.31  | |           e1)
% 152.17/22.31  | | 
% 152.17/22.31  | | BETA: splitting (25) gives:
% 152.17/22.31  | | 
% 152.17/22.31  | | Case 1:
% 152.17/22.31  | | | 
% 152.17/22.31  | | |   (26)  all_56_2 = e1 & op(e2, e3) = e1
% 152.17/22.31  | | | 
% 152.17/22.31  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (15), (16),
% 152.17/22.31  | | |            (17), (18), (21), (24), (26) are inconsistent by sub-proof
% 152.17/22.31  | | |            #272.
% 152.17/22.31  | | | 
% 152.17/22.31  | | Case 2:
% 152.17/22.31  | | | 
% 152.17/22.31  | | |   (27)  all_56_3 = e1 & op(e2, e2) = e1
% 152.17/22.31  | | | 
% 152.17/22.31  | | | ALPHA: (27) implies:
% 152.17/22.31  | | |   (28)  all_56_3 = e1
% 152.17/22.31  | | | 
% 152.17/22.31  | | | REF_CLOSE: (1), (2), (3), (5), (7), (9), (11), (12), (14), (17), (18),
% 152.17/22.31  | | |            (20), (21), (23), (28) are inconsistent by sub-proof #260.
% 152.17/22.31  | | | 
% 152.17/22.31  | | End of split
% 152.17/22.31  | | 
% 152.17/22.31  | Case 2:
% 152.17/22.31  | | 
% 152.17/22.31  | |   (29)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 152.17/22.31  | |           e1)
% 152.17/22.31  | | 
% 152.17/22.31  | | BETA: splitting (29) gives:
% 152.17/22.31  | | 
% 152.17/22.31  | | Case 1:
% 152.17/22.31  | | | 
% 152.17/22.31  | | | 
% 152.17/22.31  | | | GROUND_INST: instantiating (7) with e1, e3, e2, e2, simplifying with (2),
% 152.17/22.31  | | |              (22) gives:
% 152.17/22.31  | | |   (30)  e3 = e1
% 152.17/22.31  | | | 
% 152.17/22.31  | | | COMBINE_EQS: (13), (30) imply:
% 152.17/22.31  | | |   (31)  all_56_3 = e1
% 152.17/22.31  | | | 
% 152.17/22.31  | | | REF_CLOSE: (1), (2), (3), (5), (7), (9), (11), (12), (14), (17), (18),
% 152.17/22.31  | | |            (20), (21), (23), (31) are inconsistent by sub-proof #260.
% 152.17/22.31  | | | 
% 152.17/22.31  | | Case 2:
% 152.17/22.31  | | | 
% 152.17/22.31  | | |   (32)  all_56_10 = e1 & op(e2, e0) = e1
% 152.17/22.32  | | | 
% 152.17/22.32  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (15), (16),
% 152.17/22.32  | | |            (17), (18), (21), (32) are inconsistent by sub-proof #263.
% 152.17/22.32  | | | 
% 152.17/22.32  | | End of split
% 152.17/22.32  | | 
% 152.17/22.32  | End of split
% 152.17/22.32  | 
% 152.17/22.32  End of proof
% 152.17/22.32  
% 152.17/22.32  Sub-proof #228 shows that the following formulas are inconsistent:
% 152.17/22.32  ----------------------------------------------------------------
% 152.17/22.32    (1)  op(e0, e1) = all_52_11
% 152.17/22.32    (2)  all_56_8 = e3
% 152.17/22.32    (3)   ~ (all_52_7 = all_52_11)
% 152.17/22.32    (4)   ~ (e3 = e1)
% 152.17/22.32    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 152.17/22.32         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 152.17/22.32    (6)  op(e2, e2) = e1
% 152.17/22.32    (7)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.32         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.17/22.32    (8)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 152.17/22.32         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.17/22.32    (9)  op(e0, e0) = all_10_2
% 152.17/22.32    (10)   ~ (all_52_3 = all_52_7)
% 152.17/22.32    (11)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.32          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.17/22.32    (12)   ~ (all_10_2 = e1)
% 152.17/22.32    (13)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.17/22.32          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.17/22.32    (14)   ~ (e2 = e0)
% 152.17/22.32    (15)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.32          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.17/22.32    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.32    (17)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.17/22.32          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.17/22.32    (18)   ~ (all_52_1 = all_52_13)
% 152.17/22.32    (19)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.17/22.32          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.17/22.32    (20)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.17/22.32          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.17/22.32    (21)   ~ (all_52_3 = all_52_11)
% 152.17/22.32    (22)   ~ (all_52_9 = e3)
% 152.17/22.32    (23)   ~ (all_52_1 = all_52_9)
% 152.17/22.32    (24)  op(e1, e0) = all_52_14
% 152.17/22.32    (25)   ~ (e3 = e0)
% 152.17/22.32    (26)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.17/22.32          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.17/22.32    (27)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 152.17/22.32          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.17/22.32    (28)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.17/22.32          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.17/22.32    (29)   ~ (all_52_6 = e3)
% 152.17/22.32    (30)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 152.17/22.32          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 152.17/22.32    (31)  op(e3, e3) = e1
% 152.17/22.32    (32)  op(e1, e2) = all_52_6
% 152.17/22.32    (33)  op(e2, e0) = all_52_13
% 152.17/22.32    (34)  all_56_3 = e1
% 152.17/22.32    (35)   ~ (all_52_1 = all_52_3)
% 152.17/22.32    (36)  op(e0, e3) = all_52_3
% 152.17/22.32    (37)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 152.17/22.32    (38)  all_54_12 = all_52_3
% 152.17/22.32    (39)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.32          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.17/22.32    (40)  op(e2, e1) = all_52_9
% 152.17/22.32    (41)   ~ (e1 = e0)
% 152.17/22.32    (42)   ~ (all_52_1 = e1)
% 152.17/22.32    (43)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.17/22.32          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.17/22.32    (44)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 152.17/22.32              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.17/22.32            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 152.17/22.32                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 152.17/22.32              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.17/22.32          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 152.17/22.32              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.32            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 152.17/22.32                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 152.17/22.32              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.17/22.32          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 152.17/22.32              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.32            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 152.17/22.32                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 152.17/22.32              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.17/22.32          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 152.17/22.32              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.32            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 152.17/22.32                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 152.17/22.32                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.17/22.32                $i(all_57_14))))
% 152.17/22.32    (45)  op(e1, e1) = e3
% 152.17/22.32    (46)   ~ (e3 = e2)
% 152.17/22.32    (47)   ~ (all_52_8 = e3)
% 152.17/22.32    (48)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.32          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.17/22.32    (49)   ~ (all_52_7 = all_10_2)
% 152.17/22.32    (50)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.17/22.32          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.17/22.32    (51)  all_54_13 = all_52_7
% 152.17/22.32    (52)  op(e3, e1) = all_52_8
% 152.17/22.32    (53)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.17/22.32          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.17/22.32    (54)   ~ (all_52_3 = all_10_2)
% 152.17/22.32    (55)   ~ (all_52_6 = all_52_7)
% 152.17/22.32    (56)   ~ (e2 = e1)
% 152.17/22.32    (57)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.17/22.32    (58)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.17/22.32              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.17/22.32            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.17/22.32            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.17/22.32            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.17/22.32            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.17/22.32            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.17/22.32            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.17/22.32            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.17/22.32            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.17/22.32            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.17/22.32            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.17/22.32            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.32            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.17/22.32            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.17/22.32            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.32            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.17/22.32            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.17/22.32            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.17/22.32            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.17/22.32            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.17/22.32            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.32            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.17/22.32            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.17/22.32            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.17/22.32            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.17/22.32            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.17/22.32            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.17/22.32            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.32            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.17/22.32            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.17/22.32            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.17/22.32            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.17/22.32            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.17/22.32            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.32            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.17/22.32            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.32            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.17/22.32            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.17/22.32            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.32            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.17/22.32            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.17/22.32            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.17/22.32            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.17/22.32            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.17/22.32            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.17/22.32            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.17/22.32            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.17/22.32              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.17/22.32            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.17/22.32            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.17/22.32              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.17/22.32            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.17/22.32            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.17/22.32                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.17/22.32                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.32                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.17/22.32                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.17/22.32                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.17/22.32                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.17/22.32                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.17/22.32              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.17/22.32                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.17/22.32                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.17/22.32                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.17/22.32                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.17/22.32                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.17/22.32                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.17/22.32                $i(all_57_7))))
% 152.17/22.32    (59)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.32          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.17/22.32    (60)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.17/22.32          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.17/22.32            e1)
% 152.17/22.32    (61)  op(e2, e3) = all_52_1
% 152.17/22.32  
% 152.17/22.32  Begin of proof
% 152.17/22.32  | 
% 152.17/22.32  | BETA: splitting (44) gives:
% 152.17/22.32  | 
% 152.17/22.32  | Case 1:
% 152.17/22.32  | | 
% 152.17/22.32  | |   (62)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 152.17/22.32  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 152.17/22.32  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 152.17/22.32  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 152.17/22.32  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 152.17/22.32  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 152.17/22.32  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 152.17/22.32  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.32  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 152.17/22.32  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 152.17/22.32  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 152.17/22.32  | |               $i(all_57_15))))
% 152.17/22.32  | | 
% 152.17/22.32  | | REF_CLOSE: (4), (6), (16), (31), (56), (62) are inconsistent by sub-proof
% 152.17/22.32  | |            #898.
% 152.17/22.32  | | 
% 152.17/22.32  | Case 2:
% 152.17/22.32  | | 
% 152.17/22.32  | |   (63)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 152.17/22.32  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.17/22.32  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 152.17/22.32  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.17/22.32  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 152.17/22.32  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 152.17/22.32  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 152.17/22.32  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.32  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 152.17/22.32  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 152.17/22.32  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 152.17/22.32  | |               all_57_14 & $i(all_57_14))))
% 152.17/22.32  | | 
% 152.17/22.32  | | BETA: splitting (63) gives:
% 152.17/22.32  | | 
% 152.17/22.32  | | Case 1:
% 152.17/22.32  | | | 
% 152.17/22.32  | | |   (64)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 152.17/22.32  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.17/22.32  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 152.17/22.32  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.17/22.32  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 152.17/22.32  | | |               e0) = all_57_15 & $i(all_57_15)))
% 152.17/22.32  | | | 
% 152.17/22.32  | | | ALPHA: (64) implies:
% 152.17/22.32  | | |   (65)  op(e1, e1) = e1
% 152.17/22.32  | | | 
% 152.17/22.32  | | | REF_CLOSE: (4), (16), (45), (65) are inconsistent by sub-proof #734.
% 152.17/22.32  | | | 
% 152.17/22.32  | | Case 2:
% 152.17/22.32  | | | 
% 152.17/22.32  | | |   (66)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 152.17/22.32  | | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.17/22.32  | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 152.17/22.32  | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.17/22.32  | | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 152.17/22.32  | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 152.17/22.32  | | | 
% 152.17/22.32  | | | ALPHA: (66) implies:
% 152.17/22.32  | | |   (67)  all_57_15 = e0
% 152.17/22.32  | | |   (68)  op(e0, e0) = e0
% 152.17/22.32  | | |   (69)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 152.17/22.32  | | |             e2) = all_57_12 & $i(all_57_12))
% 152.17/22.32  | | | 
% 152.17/22.32  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 152.17/22.32  | | |            (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 152.17/22.32  | | |            (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 152.17/22.32  | | |            (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 152.17/22.32  | | |            (43), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 152.17/22.32  | | |            (54), (55), (56), (57), (58), (59), (60), (61), (67), (68),
% 152.17/22.32  | | |            (69) are inconsistent by sub-proof #241.
% 152.17/22.32  | | | 
% 152.17/22.32  | | End of split
% 152.17/22.32  | | 
% 152.17/22.32  | End of split
% 152.17/22.32  | 
% 152.17/22.32  End of proof
% 152.17/22.32  
% 152.17/22.32  Sub-proof #229 shows that the following formulas are inconsistent:
% 152.17/22.32  ----------------------------------------------------------------
% 152.17/22.32    (1)  op(e0, e1) = all_52_11
% 152.17/22.32    (2)  all_56_8 = e3
% 152.17/22.32    (3)   ~ (e3 = e1)
% 152.17/22.32    (4)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.17/22.32         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.17/22.32    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 152.17/22.32         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 152.17/22.32    (6)  op(e2, e2) = e1
% 152.17/22.32    (7)   ~ (all_14_2 = e0)
% 152.17/22.32    (8)   ~ (all_52_2 = all_52_6)
% 152.17/22.32    (9)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.32         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.17/22.32    (10)  op(e3, e3) = all_14_2
% 152.17/22.32    (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 152.17/22.32          (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.17/22.32    (12)  op(e0, e0) = all_10_2
% 152.17/22.32    (13)  op(e3, e2) = all_52_4
% 152.17/22.32    (14)  op(e0, e2) = all_52_7
% 152.17/22.32    (15)   ~ (all_52_14 = e2)
% 152.17/22.32    (16)   ~ (all_52_3 = all_52_7)
% 152.17/22.32    (17)   ~ (all_52_8 = all_14_2)
% 152.17/22.32    (18)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.32          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.17/22.32    (19)   ~ (all_10_2 = e1)
% 152.17/22.32    (20)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.17/22.32          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.17/22.32    (21)   ~ (e2 = e0)
% 152.17/22.32    (22)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.32          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.17/22.32    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.32            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.32    (24)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.17/22.32          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.17/22.32    (25)   ~ (all_52_12 = all_14_2)
% 152.17/22.32    (26)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.17/22.32          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.17/22.32    (27)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.17/22.32          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.17/22.32    (28)   ~ (all_52_3 = e2)
% 152.17/22.32    (29)   ~ (all_52_3 = all_52_11)
% 152.17/22.32    (30)   ~ (all_52_9 = e3)
% 152.17/22.32    (31)   ~ (all_52_4 = all_14_2)
% 152.17/22.32    (32)   ~ (all_52_3 = all_14_2)
% 152.17/22.32    (33)  op(e0, e0) = e2
% 152.17/22.32    (34)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.17/22.32              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.17/22.32                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.17/22.32                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.17/22.32    (35)  op(e1, e0) = all_52_14
% 152.17/22.32    (36)   ~ (all_52_13 = e2)
% 152.17/22.32    (37)  op(e3, e0) = all_52_12
% 152.17/22.32    (38)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.17/22.32          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.17/22.32    (39)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 152.17/22.32          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.17/22.32    (40)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.17/22.32          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.17/22.32    (41)   ~ (all_52_6 = e3)
% 152.17/22.32    (42)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 152.17/22.32          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 152.17/22.32    (43)  op(e1, e2) = all_52_6
% 152.17/22.32    (44)  op(e2, e0) = all_52_13
% 152.17/22.32    (45)  all_56_3 = e1
% 152.17/22.32    (46)  op(e0, e3) = all_52_3
% 152.17/22.32    (47)  all_54_12 = all_52_3
% 152.17/22.32    (48)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.32          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.17/22.32    (49)  op(e2, e1) = all_52_9
% 152.17/22.32    (50)   ~ (e1 = e0)
% 152.17/22.32    (51)   ~ (all_52_1 = all_14_2)
% 152.17/22.32    (52)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.17/22.32          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.17/22.33    (53)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 152.17/22.33              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.17/22.33            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 152.17/22.33                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 152.17/22.33              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.17/22.33          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 152.17/22.33              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.33            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 152.17/22.33                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 152.17/22.33              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.17/22.33          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 152.17/22.33              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.33            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 152.17/22.33                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 152.17/22.33              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.17/22.33          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 152.17/22.33              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.33            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 152.17/22.33                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 152.17/22.33                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.17/22.33                $i(all_57_14))))
% 152.17/22.33    (54)  op(e1, e1) = e3
% 152.17/22.33    (55)   ~ (e3 = e2)
% 152.17/22.33    (56)   ~ (all_14_2 = e1)
% 152.17/22.33    (57)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.33          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.17/22.33    (58)  op(e3, e1) = all_52_8
% 152.17/22.33    (59)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.17/22.33          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.17/22.33    (60)   ~ (all_52_2 = all_52_3)
% 152.17/22.33    (61)   ~ (e2 = e1)
% 152.17/22.33    (62)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.17/22.33    (63)  op(e1, e3) = all_52_2
% 152.17/22.33    (64)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.17/22.33              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.17/22.33            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.17/22.33            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.17/22.33            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.17/22.33            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.17/22.33            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.17/22.33            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.17/22.33            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.17/22.33            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.17/22.33            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.17/22.33            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.17/22.33            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.33            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.17/22.33            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.17/22.33            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.33            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.17/22.33            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.17/22.33            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.17/22.33            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.17/22.33            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.17/22.33            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.33            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.17/22.33            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.17/22.33            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.17/22.33            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.17/22.33            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.17/22.33            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.17/22.33            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.33            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.17/22.33            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.17/22.33            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.17/22.33            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.17/22.33            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.17/22.33            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.33            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.17/22.33            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.33            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.17/22.33            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.17/22.33            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.33            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.17/22.33            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.17/22.33            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.17/22.33            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.17/22.33            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.17/22.33            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.17/22.33            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.17/22.33            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.17/22.33              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.17/22.33            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.17/22.33            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.17/22.33              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.17/22.33            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.17/22.33            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.17/22.33                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.17/22.33                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.33                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.17/22.33                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.17/22.33                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.17/22.33                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.17/22.33                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.17/22.33              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.17/22.33                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.17/22.33                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.17/22.33                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.17/22.33                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.17/22.33                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.17/22.33                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.17/22.33                $i(all_57_7))))
% 152.17/22.33    (65)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.33          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.17/22.33    (66)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.17/22.33          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.17/22.33            e1)
% 152.17/22.33    (67)  op(e2, e3) = all_52_1
% 152.17/22.33  
% 152.17/22.33  Begin of proof
% 152.17/22.33  | 
% 152.17/22.33  | BETA: splitting (53) gives:
% 152.17/22.33  | 
% 152.17/22.33  | Case 1:
% 152.17/22.33  | | 
% 152.17/22.33  | |   (68)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 152.17/22.33  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 152.17/22.33  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 152.17/22.33  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 152.17/22.33  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 152.17/22.33  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 152.17/22.33  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 152.17/22.33  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.33  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 152.17/22.33  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 152.17/22.33  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 152.17/22.33  | |               $i(all_57_15))))
% 152.17/22.33  | | 
% 152.17/22.33  | | BETA: splitting (68) gives:
% 152.17/22.33  | | 
% 152.17/22.33  | | Case 1:
% 152.17/22.33  | | | 
% 152.17/22.33  | | |   (69)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 152.17/22.33  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 152.17/22.33  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 152.17/22.33  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 152.17/22.33  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 152.17/22.33  | | |               e0) = all_57_15 & $i(all_57_15)))
% 152.17/22.33  | | | 
% 152.17/22.33  | | | ALPHA: (69) implies:
% 152.17/22.33  | | |   (70)  op(e3, e3) = e3
% 152.17/22.33  | | |   (71)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 152.17/22.33  | | |             e0) = all_57_15 & $i(all_57_15))
% 152.17/22.33  | | |   (72)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 152.17/22.33  | | |             e1) = all_57_14 & $i(all_57_14))
% 152.17/22.33  | | |   (73)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2,
% 152.17/22.33  | | |             e2) = all_57_12 & $i(all_57_12))
% 152.17/22.33  | | | 
% 152.17/22.33  | | | BETA: splitting (72) gives:
% 152.17/22.33  | | | 
% 152.17/22.33  | | | Case 1:
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | |   (74)  all_57_1 = e1 & op(e1, e3) = e1
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | ALPHA: (74) implies:
% 152.17/22.33  | | | |   (75)  op(e1, e3) = e1
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | GROUND_INST: instantiating (23) with all_52_2, e1, e3, e1, simplifying
% 152.17/22.33  | | | |              with (63), (75) gives:
% 152.17/22.33  | | | |   (76)  all_52_2 = e1
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | GROUND_INST: instantiating (23) with all_14_2, e3, e3, e3, simplifying
% 152.17/22.33  | | | |              with (10), (70) gives:
% 152.17/22.33  | | | |   (77)  all_14_2 = e3
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | REDUCE: (51), (77) imply:
% 152.17/22.33  | | | |   (78)   ~ (all_52_1 = e3)
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | REDUCE: (60), (76) imply:
% 152.17/22.33  | | | |   (79)   ~ (all_52_3 = e1)
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | SIMP: (79) implies:
% 152.17/22.33  | | | |   (80)   ~ (all_52_3 = e1)
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | REDUCE: (32), (77) imply:
% 152.17/22.33  | | | |   (81)   ~ (all_52_3 = e3)
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | REDUCE: (31), (77) imply:
% 152.17/22.33  | | | |   (82)   ~ (all_52_4 = e3)
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | REDUCE: (17), (77) imply:
% 152.17/22.33  | | | |   (83)   ~ (all_52_8 = e3)
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | REDUCE: (25), (77) imply:
% 152.17/22.33  | | | |   (84)   ~ (all_52_12 = e3)
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | REDUCE: (7), (77) imply:
% 152.17/22.33  | | | |   (85)   ~ (e3 = e0)
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | BETA: splitting (26) gives:
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | Case 1:
% 152.17/22.33  | | | | | 
% 152.17/22.33  | | | | |   (86)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1,
% 152.17/22.33  | | | | |             e2) = e1)
% 152.17/22.33  | | | | | 
% 152.17/22.33  | | | | | BETA: splitting (86) gives:
% 152.17/22.33  | | | | | 
% 152.17/22.33  | | | | | Case 1:
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | |   (87)  all_56_6 = e1 & op(e1, e3) = e1
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | | ALPHA: (87) implies:
% 152.17/22.33  | | | | | |   (88)  all_56_6 = e1
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (12), (13), (14),
% 152.17/22.33  | | | | | |            (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 152.17/22.33  | | | | | |            (27), (28), (29), (30), (33), (34), (35), (36), (37),
% 152.17/22.33  | | | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 152.17/22.33  | | | | | |            (47), (48), (49), (50), (52), (54), (55), (57), (58),
% 152.17/22.33  | | | | | |            (59), (61), (62), (63), (64), (65), (66), (67), (70),
% 152.17/22.33  | | | | | |            (71), (72), (73), (75), (78), (80), (81), (82), (83),
% 152.17/22.33  | | | | | |            (84), (85), (88) are inconsistent by sub-proof #231.
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | Case 2:
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | |   (89)  all_56_7 = e1 & op(e1, e2) = e1
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | | ALPHA: (89) implies:
% 152.17/22.33  | | | | | |   (90)  op(e1, e2) = e1
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | | REF_CLOSE: (8), (23), (43), (63), (75), (90) are inconsistent by
% 152.17/22.33  | | | | | |            sub-proof #911.
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | End of split
% 152.17/22.33  | | | | | 
% 152.17/22.33  | | | | Case 2:
% 152.17/22.33  | | | | | 
% 152.17/22.33  | | | | |   (91)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1,
% 152.17/22.33  | | | | |             e0) = e1)
% 152.17/22.33  | | | | | 
% 152.17/22.33  | | | | | BETA: splitting (91) gives:
% 152.17/22.33  | | | | | 
% 152.17/22.33  | | | | | Case 1:
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | |   (92)  all_56_8 = e1 & op(e1, e1) = e1
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | | ALPHA: (92) implies:
% 152.17/22.33  | | | | | |   (93)  op(e1, e1) = e1
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | | REF_CLOSE: (3), (23), (54), (93) are inconsistent by sub-proof #734.
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | Case 2:
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | |   (94)  all_56_11 = e1 & op(e1, e0) = e1
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | | ALPHA: (94) implies:
% 152.17/22.33  | | | | | |   (95)  all_56_11 = e1
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | | BETA: splitting (65) gives:
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | | Case 1:
% 152.17/22.33  | | | | | | | 
% 152.17/22.33  | | | | | | |   (96)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 &
% 152.17/22.33  | | | | | | |           op(e2, e2) = e3)
% 152.17/22.33  | | | | | | | 
% 152.17/22.33  | | | | | | | REF_CLOSE: (3), (13), (23), (45), (82), (96) are inconsistent by
% 152.17/22.33  | | | | | | |            sub-proof #261.
% 152.17/22.33  | | | | | | | 
% 152.17/22.33  | | | | | | Case 2:
% 152.17/22.33  | | | | | | | 
% 152.17/22.33  | | | | | | |   (97)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 &
% 152.17/22.33  | | | | | | |           op(e0, e2) = e3)
% 152.17/22.33  | | | | | | | 
% 152.17/22.33  | | | | | | | BETA: splitting (97) gives:
% 152.17/22.33  | | | | | | | 
% 152.17/22.33  | | | | | | | Case 1:
% 152.17/22.33  | | | | | | | | 
% 152.17/22.33  | | | | | | | |   (98)  all_56_7 = e3 & op(e1, e2) = e3
% 152.17/22.33  | | | | | | | | 
% 152.17/22.33  | | | | | | | | REF_CLOSE: (23), (41), (43), (98) are inconsistent by sub-proof
% 152.17/22.33  | | | | | | | |            #925.
% 152.17/22.33  | | | | | | | | 
% 152.17/22.33  | | | | | | | Case 2:
% 152.17/22.33  | | | | | | | | 
% 152.17/22.33  | | | | | | | |   (99)  all_56_13 = e3 & op(e0, e2) = e3
% 152.17/22.33  | | | | | | | | 
% 152.17/22.33  | | | | | | | | ALPHA: (99) implies:
% 152.17/22.33  | | | | | | | |   (100)  all_56_13 = e3
% 152.17/22.33  | | | | | | | | 
% 152.17/22.33  | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (11), (12), (13),
% 152.17/22.33  | | | | | | | |            (15), (18), (19), (21), (22), (23), (26), (28), (29),
% 152.17/22.33  | | | | | | | |            (30), (33), (35), (36), (37), (38), (41), (42), (43),
% 152.17/22.33  | | | | | | | |            (44), (45), (47), (48), (49), (50), (52), (54), (55),
% 152.17/22.33  | | | | | | | |            (57), (58), (59), (61), (62), (63), (64), (65), (67),
% 152.17/22.33  | | | | | | | |            (70), (71), (72), (73), (75), (78), (80), (81), (82),
% 152.17/22.33  | | | | | | | |            (83), (84), (85), (95), (100) are inconsistent by
% 152.17/22.33  | | | | | | | |            sub-proof #230.
% 152.17/22.33  | | | | | | | | 
% 152.17/22.33  | | | | | | | End of split
% 152.17/22.33  | | | | | | | 
% 152.17/22.33  | | | | | | End of split
% 152.17/22.33  | | | | | | 
% 152.17/22.33  | | | | | End of split
% 152.17/22.33  | | | | | 
% 152.17/22.33  | | | | End of split
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | Case 2:
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | |   (101)   ~ (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14)
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | ALPHA: (101) implies:
% 152.17/22.33  | | | |   (102)   ~ (all_57_14 = e3)
% 152.17/22.33  | | | |   (103)  op(e1, e1) = all_57_14
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | | REF_CLOSE: (23), (54), (102), (103) are inconsistent by sub-proof #816.
% 152.17/22.33  | | | | 
% 152.17/22.33  | | | End of split
% 152.17/22.33  | | | 
% 152.17/22.33  | | Case 2:
% 152.17/22.33  | | | 
% 152.17/22.33  | | |   (104)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 152.17/22.33  | | |              e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.33  | | |              $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 152.17/22.33  | | |              (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 152.17/22.33  | | |          ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) &
% 152.17/22.33  | | |              op(e0, e0) = all_57_15 & $i(all_57_15)))
% 152.17/22.33  | | | 
% 152.17/22.33  | | | ALPHA: (104) implies:
% 152.17/22.33  | | |   (105)  op(e2, e2) = e2
% 152.17/22.33  | | | 
% 152.17/22.33  | | | REF_CLOSE: (6), (23), (61), (105) are inconsistent by sub-proof #1158.
% 152.17/22.33  | | | 
% 152.17/22.33  | | End of split
% 152.17/22.33  | | 
% 152.17/22.33  | Case 2:
% 152.17/22.33  | | 
% 152.17/22.33  | |   (106)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 152.17/22.33  | |                e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.17/22.33  | |                $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 152.17/22.33  | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.17/22.33  | |            ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) &
% 152.17/22.33  | |                op(e0, e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 152.17/22.33  | |            op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 152.17/22.33  | |                (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.17/22.33  | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 152.17/22.33  | |                op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 152.17/22.33  | |                op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 152.17/22.33  | |                all_57_14 & $i(all_57_14))))
% 152.17/22.33  | | 
% 152.17/22.33  | | REF_CLOSE: (3), (21), (23), (33), (54), (106) are inconsistent by sub-proof
% 152.17/22.33  | |            #291.
% 152.17/22.33  | | 
% 152.17/22.33  | End of split
% 152.17/22.33  | 
% 152.17/22.33  End of proof
% 152.17/22.33  
% 152.17/22.33  Sub-proof #230 shows that the following formulas are inconsistent:
% 152.17/22.33  ----------------------------------------------------------------
% 152.17/22.33    (1)  op(e0, e1) = all_52_11
% 152.17/22.33    (2)  all_56_8 = e3
% 152.17/22.33    (3)   ~ (e3 = e1)
% 152.17/22.33    (4)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.17/22.33         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.17/22.33    (5)  op(e2, e2) = e1
% 152.17/22.33    (6)   ~ (all_52_2 = all_52_6)
% 152.17/22.33    (7)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.33         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.17/22.33    (8)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 152.17/22.33         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.17/22.33    (9)  op(e0, e0) = all_10_2
% 152.17/22.33    (10)  op(e3, e2) = all_52_4
% 152.17/22.33    (11)   ~ (all_52_14 = e2)
% 152.17/22.33    (12)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.33          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.17/22.33    (13)  all_56_11 = e1
% 152.17/22.33    (14)   ~ (all_10_2 = e1)
% 152.17/22.33    (15)   ~ (e2 = e0)
% 152.17/22.33    (16)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.33          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.17/22.33    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.33    (18)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.17/22.33          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.17/22.33    (19)   ~ (all_52_3 = e2)
% 152.17/22.33    (20)   ~ (all_52_3 = all_52_11)
% 152.17/22.33    (21)   ~ (all_52_9 = e3)
% 152.17/22.33    (22)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 152.17/22.33            all_57_14 & $i(all_57_14))
% 152.17/22.33    (23)  op(e0, e0) = e2
% 152.17/22.33    (24)  op(e1, e3) = e1
% 152.17/22.33    (25)   ~ (all_52_1 = e3)
% 152.17/22.33    (26)  op(e1, e0) = all_52_14
% 152.17/22.33    (27)   ~ (all_52_13 = e2)
% 152.17/22.33    (28)   ~ (all_52_4 = e3)
% 152.17/22.33    (29)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 152.17/22.33            all_57_12 & $i(all_57_12))
% 152.17/22.33    (30)  op(e3, e0) = all_52_12
% 152.17/22.33    (31)   ~ (e3 = e0)
% 152.17/22.33    (32)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 152.17/22.33            all_57_15 & $i(all_57_15))
% 152.17/22.33    (33)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.17/22.33          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.17/22.33    (34)   ~ (all_52_6 = e3)
% 152.17/22.33    (35)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 152.17/22.33          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 152.17/22.33    (36)  op(e1, e2) = all_52_6
% 152.17/22.33    (37)   ~ (all_52_12 = e3)
% 152.17/22.33    (38)  op(e2, e0) = all_52_13
% 152.17/22.33    (39)  all_56_3 = e1
% 152.17/22.33    (40)   ~ (all_52_3 = e3)
% 152.17/22.33    (41)   ~ (all_52_3 = e1)
% 152.17/22.33    (42)  all_54_12 = all_52_3
% 152.17/22.33    (43)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.33          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.17/22.33    (44)  op(e2, e1) = all_52_9
% 152.17/22.33    (45)   ~ (e1 = e0)
% 152.17/22.33    (46)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.17/22.33          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.17/22.33    (47)  all_56_13 = e3
% 152.17/22.33    (48)  op(e1, e1) = e3
% 152.17/22.33    (49)   ~ (e3 = e2)
% 152.17/22.33    (50)   ~ (all_52_8 = e3)
% 152.17/22.33    (51)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.33          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.17/22.33    (52)  op(e3, e1) = all_52_8
% 152.17/22.33    (53)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.17/22.33          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.17/22.33    (54)  op(e3, e3) = e3
% 152.17/22.33    (55)   ~ (e2 = e1)
% 152.17/22.33    (56)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.17/22.33    (57)  op(e1, e3) = all_52_2
% 152.17/22.34    (58)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.17/22.34              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.17/22.34            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.17/22.34            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.17/22.34            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.17/22.34            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.17/22.34            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.17/22.34            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.17/22.34            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.17/22.34            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.17/22.34            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.17/22.34            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.17/22.34            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.34            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.17/22.34            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.17/22.34            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.34            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.17/22.34            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.17/22.34            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.17/22.34            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.17/22.34            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.17/22.34            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.34            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.17/22.34            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.17/22.34            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.17/22.34            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.17/22.34            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.17/22.34            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.17/22.34            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.34            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.17/22.34            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.17/22.34            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.17/22.34            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.17/22.34            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.17/22.34            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.34            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.17/22.34            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.34            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.17/22.34            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.17/22.34            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.34            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.17/22.34            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.17/22.34            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.17/22.34            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.17/22.34            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.17/22.34            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.17/22.34            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.17/22.34            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.17/22.34              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.17/22.34            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.17/22.34            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.17/22.34              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.17/22.34            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.17/22.34            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.17/22.34                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.17/22.34                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.34                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.17/22.34                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.17/22.34                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.17/22.34                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.17/22.34                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.17/22.34              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.17/22.34                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.17/22.34                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.17/22.34                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.17/22.34                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.17/22.34                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.17/22.34                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.17/22.34                $i(all_57_7))))
% 152.17/22.34    (59)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.34          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.17/22.34    (60)  op(e2, e3) = all_52_1
% 152.17/22.34  
% 152.17/22.34  Begin of proof
% 152.17/22.34  | 
% 152.17/22.34  | BETA: splitting (43) gives:
% 152.17/22.34  | 
% 152.17/22.34  | Case 1:
% 152.17/22.34  | | 
% 152.17/22.34  | |   (61)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.17/22.34  | |           e3)
% 152.17/22.34  | | 
% 152.17/22.34  | | REF_CLOSE: (3), (5), (7), (15), (17), (25), (31), (34), (36), (39), (45),
% 152.17/22.34  | |            (47), (49), (51), (55), (59), (60), (61) are inconsistent by
% 152.17/22.34  | |            sub-proof #239.
% 152.17/22.34  | | 
% 152.17/22.34  | Case 2:
% 152.17/22.34  | | 
% 152.17/22.34  | |   (62)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 152.17/22.34  | |           e3)
% 152.17/22.34  | | 
% 152.17/22.34  | | BETA: splitting (62) gives:
% 152.17/22.34  | | 
% 152.17/22.34  | | Case 1:
% 152.17/22.34  | | | 
% 152.17/22.34  | | |   (63)  all_56_5 = e3 & op(e2, e1) = e3
% 152.17/22.34  | | | 
% 152.17/22.34  | | | REF_CLOSE: (17), (21), (44), (63) are inconsistent by sub-proof #647.
% 152.17/22.34  | | | 
% 152.17/22.34  | | Case 2:
% 152.17/22.34  | | | 
% 152.17/22.34  | | |   (64)  all_56_10 = e3 & op(e2, e0) = e3
% 152.17/22.34  | | | 
% 152.17/22.34  | | | ALPHA: (64) implies:
% 152.17/22.34  | | |   (65)  all_56_10 = e3
% 152.17/22.34  | | | 
% 152.17/22.34  | | | BETA: splitting (53) gives:
% 152.17/22.34  | | | 
% 152.17/22.34  | | | Case 1:
% 152.17/22.34  | | | | 
% 152.17/22.34  | | | |   (66)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2)
% 152.17/22.34  | | | |           = e0)
% 152.17/22.34  | | | | 
% 152.17/22.34  | | | | BETA: splitting (66) gives:
% 152.17/22.34  | | | | 
% 152.17/22.34  | | | | Case 1:
% 152.17/22.34  | | | | | 
% 152.17/22.34  | | | | |   (67)  all_56_6 = e0 & op(e1, e3) = e0
% 152.17/22.34  | | | | | 
% 152.17/22.34  | | | | | ALPHA: (67) implies:
% 152.17/22.34  | | | | |   (68)  op(e1, e3) = e0
% 152.17/22.34  | | | | | 
% 152.17/22.34  | | | | | REF_CLOSE: (17), (24), (45), (57), (68) are inconsistent by sub-proof
% 152.17/22.34  | | | | |            #1127.
% 152.17/22.34  | | | | | 
% 152.17/22.34  | | | | Case 2:
% 152.17/22.34  | | | | | 
% 152.17/22.34  | | | | |   (69)  all_56_7 = e0 & op(e1, e2) = e0
% 152.17/22.34  | | | | | 
% 152.17/22.34  | | | | | ALPHA: (69) implies:
% 152.17/22.34  | | | | |   (70)  all_56_7 = e0
% 152.17/22.34  | | | | | 
% 152.17/22.34  | | | | | BETA: splitting (4) gives:
% 152.17/22.34  | | | | | 
% 152.17/22.34  | | | | | Case 1:
% 152.17/22.34  | | | | | | 
% 152.17/22.34  | | | | | |   (71)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2,
% 152.17/22.34  | | | | | |             e3) = e1)
% 152.17/22.34  | | | | | | 
% 152.17/22.34  | | | | | | BETA: splitting (71) gives:
% 152.17/22.34  | | | | | | 
% 152.17/22.34  | | | | | | Case 1:
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | |   (72)  all_56_0 = e1 & op(e3, e3) = e1
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | | ALPHA: (72) implies:
% 152.17/22.34  | | | | | | |   (73)  op(e3, e3) = e1
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | | REF_CLOSE: (3), (17), (54), (73) are inconsistent by sub-proof
% 152.17/22.34  | | | | | | |            #1178.
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | Case 2:
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | |   (74)  all_56_2 = e1 & op(e2, e3) = e1
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | | ALPHA: (74) implies:
% 152.17/22.34  | | | | | | |   (75)  all_56_2 = e1
% 152.17/22.34  | | | | | | |   (76)  op(e2, e3) = e1
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | | REF_CLOSE: (5), (12), (15), (16), (17), (31), (39), (45), (49),
% 152.17/22.34  | | | | | | |            (55), (60), (65), (75), (76) are inconsistent by
% 152.17/22.34  | | | | | | |            sub-proof #387.
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | End of split
% 152.17/22.34  | | | | | | 
% 152.17/22.34  | | | | | Case 2:
% 152.17/22.34  | | | | | | 
% 152.17/22.34  | | | | | |   (77)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0,
% 152.17/22.34  | | | | | |             e3) = e1)
% 152.17/22.34  | | | | | | 
% 152.17/22.34  | | | | | | BETA: splitting (77) gives:
% 152.17/22.34  | | | | | | 
% 152.17/22.34  | | | | | | Case 1:
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | |   (78)  all_56_6 = e1 & op(e1, e3) = e1
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | | ALPHA: (78) implies:
% 152.17/22.34  | | | | | | |   (79)  all_56_6 = e1
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | | REF_CLOSE: (11), (15), (17), (26), (46), (48), (49), (55), (70),
% 152.17/22.34  | | | | | | |            (79) are inconsistent by sub-proof #238.
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | Case 2:
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | |   (80)  all_56_12 = e1 & op(e0, e3) = e1
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | | ALPHA: (80) implies:
% 152.17/22.34  | | | | | | |   (81)  all_56_12 = e1
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | | BETA: splitting (58) gives:
% 152.17/22.34  | | | | | | | 
% 152.17/22.34  | | | | | | | Case 1:
% 152.17/22.34  | | | | | | | | 
% 152.17/22.34  | | | | | | | |   (82)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.17/22.34  | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.17/22.34  | | | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.17/22.34  | | | | | | | |           $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 &
% 152.17/22.34  | | | | | | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 152.17/22.34  | | | | | | | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.17/22.34  | | | | | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2)
% 152.17/22.34  | | | | | | | |           & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3 & 
% 152.17/22.34  | | | | | | | |           ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.17/22.34  | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 152.17/22.34  | | | | | | | |             e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.17/22.34  | | | | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) & 
% 152.17/22.34  | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 152.17/22.34  | | | | | | | |           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.17/22.34  | | | | | | | |           $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 152.17/22.34  | | | | | | | |           all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 152.17/22.34  | | | | | | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.17/22.34  | | | | | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4)
% 152.17/22.34  | | | | | | | |           & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 & 
% 152.17/22.34  | | | | | | | |           ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.17/22.34  | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 152.17/22.34  | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 152.17/22.34  | | | | | | | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 152.17/22.34  | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.17/22.34  | | | | | | | |           all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.34  | | | | | | | |           $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 152.17/22.34  | | | | | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 152.17/22.34  | | | | | | | |             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.34  | | | | | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5)
% 152.17/22.34  | | | | | | | |           & $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 & 
% 152.17/22.34  | | | | | | | |           ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.17/22.34  | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2,
% 152.17/22.34  | | | | | | | |             e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.17/22.34  | | | | | | | | 
% 152.17/22.34  | | | | | | | | BETA: splitting (82) gives:
% 152.17/22.34  | | | | | | | | 
% 152.17/22.34  | | | | | | | | Case 1:
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | |   (83)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 152.17/22.34  | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.17/22.34  | | | | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3
% 152.17/22.34  | | | | | | | | |           & $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 &
% 152.17/22.34  | | | | | | | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 152.17/22.34  | | | | | | | | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.17/22.34  | | | | | | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.17/22.34  | | | | | | | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.17/22.34  | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 152.17/22.34  | | | | | | | | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.17/22.34  | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.34  | | | | | | | | |           $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 152.17/22.34  | | | | | | | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 152.17/22.34  | | | | | | | | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.34  | | | | | | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.17/22.34  | | | | | | | | |           $i(all_57_2) & $i(all_57_14))
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | BETA: splitting (83) gives:
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | Case 1:
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | |   (84)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.17/22.34  | | | | | | | | | |             e2) = all_57_12 & op(e1, e3) = all_57_1 & op(e1,
% 152.17/22.34  | | | | | | | | | |             e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 152.17/22.34  | | | | | | | | | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.17/22.34  | | | | | | | | | |             e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0,
% 152.17/22.34  | | | | | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | REF_CLOSE: (17), (22), (32), (84) are inconsistent by
% 152.17/22.34  | | | | | | | | | |            sub-proof #814.
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | Case 2:
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | |   (85)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_14 = e3) & op(e2, e3) = all_57_0 &
% 152.17/22.34  | | | | | | | | | |           op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.17/22.34  | | | | | | | | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.17/22.34  | | | | | | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.17/22.34  | | | | | | | | | |             e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 152.17/22.34  | | | | | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | REF_CLOSE: (17), (29), (32), (85) are inconsistent by
% 152.17/22.34  | | | | | | | | | |            sub-proof #831.
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | End of split
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | Case 2:
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | |   (86)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &
% 152.17/22.34  | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.34  | | | | | | | | |           op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1)
% 152.17/22.34  | | | | | | | | |           = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3 =
% 152.17/22.34  | | | | | | | | |           e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 152.17/22.34  | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 152.17/22.34  | | | | | | | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2
% 152.17/22.34  | | | | | | | | |           & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 152.17/22.34  | | | | | | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 152.17/22.34  | | | | | | | | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.17/22.34  | | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.34  | | | | | | | | |           $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 152.17/22.34  | | | | | | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 152.17/22.34  | | | | | | | | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.34  | | | | | | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.17/22.34  | | | | | | | | |           $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 152.17/22.34  | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 152.17/22.34  | | | | | | | | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.17/22.34  | | | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.17/22.34  | | | | | | | | |           $i(all_57_7) & $i(all_57_10))
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | BETA: splitting (86) gives:
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | Case 1:
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | |   (87)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.34  | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 152.17/22.34  | | | | | | | | | |             e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 152.17/22.34  | | | | | | | | | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.34  | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 152.17/22.34  | | | | | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | REF_CLOSE: (10), (17), (28), (48), (49), (87) are
% 152.17/22.34  | | | | | | | | | |            inconsistent by sub-proof #294.
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | Case 2:
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | |   (88)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3,
% 152.17/22.34  | | | | | | | | | |             e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.17/22.34  | | | | | | | | | |           all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.17/22.34  | | | | | | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.17/22.34  | | | | | | | | | |             e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 152.17/22.34  | | | | | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 152.17/22.34  | | | | | | | | | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.17/22.34  | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 152.17/22.34  | | | | | | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | BETA: splitting (88) gives:
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | Case 1:
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | |   (89)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.17/22.34  | | | | | | | | | | |           e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 152.17/22.34  | | | | | | | | | | |         op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 152.17/22.34  | | | | | | | | | | |           e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | | ALPHA: (89) implies:
% 152.17/22.34  | | | | | | | | | | |   (90)  op(e3, e3) = e2
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | | REF_CLOSE: (17), (49), (54), (90) are inconsistent by
% 152.17/22.34  | | | | | | | | | | |            sub-proof #1085.
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | Case 2:
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | |   (91)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.17/22.34  | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.17/22.34  | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 152.17/22.34  | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 152.17/22.34  | | | | | | | | | | |         | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.17/22.34  | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.17/22.34  | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.17/22.34  | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.17/22.34  | | | | | | | | | | |           $i(all_57_10))
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | | REF_CLOSE: (6), (17), (24), (36), (50), (52), (57), (91) are
% 152.17/22.34  | | | | | | | | | | |            inconsistent by sub-proof #234.
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | End of split
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | End of split
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | End of split
% 152.17/22.34  | | | | | | | | 
% 152.17/22.34  | | | | | | | Case 2:
% 152.17/22.34  | | | | | | | | 
% 152.17/22.34  | | | | | | | |   (92)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) & 
% 152.17/22.34  | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 152.17/22.34  | | | | | | | |             e1) = e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 152.17/22.34  | | | | | | | |           $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 &
% 152.17/22.34  | | | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 152.17/22.34  | | | | | | | |             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.17/22.34  | | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.17/22.34  | | | | | | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.17/22.34  | | | | | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 152.17/22.34  | | | | | | | |             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.17/22.34  | | | | | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8)
% 152.17/22.34  | | | | | | | |           & $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 & 
% 152.17/22.34  | | | | | | | |           ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3)
% 152.17/22.34  | | | | | | | |           = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.17/22.34  | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.17/22.34  | | | | | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 152.17/22.34  | | | | | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 152.17/22.34  | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1,
% 152.17/22.34  | | | | | | | |             e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)) |
% 152.17/22.34  | | | | | | | |         (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) & 
% 152.17/22.34  | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 152.17/22.34  | | | | | | | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.17/22.34  | | | | | | | |           $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 &
% 152.17/22.34  | | | | | | | |           all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 152.17/22.34  | | | | | | | |             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.17/22.34  | | | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.17/22.34  | | | | | | | |           $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 152.17/22.34  | | | | | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 =
% 152.17/22.34  | | | | | | | |             e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.17/22.34  | | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.17/22.34  | | | | | | | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 152.17/22.34  | | | | | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 =
% 152.17/22.34  | | | | | | | |             e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.17/22.34  | | | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.17/22.34  | | | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.17/22.34  | | | | | | | |           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.17/22.34  | | | | | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.17/22.34  | | | | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 152.17/22.34  | | | | | | | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 152.17/22.34  | | | | | | | |             (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 152.17/22.34  | | | | | | | |               &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.17/22.34  | | | | | | | |               op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 152.17/22.34  | | | | | | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.17/22.34  | | | | | | | |                 e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 152.17/22.34  | | | | | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.17/22.34  | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 & 
% 152.17/22.34  | | | | | | | |               ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1,
% 152.17/22.34  | | | | | | | |                 e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.17/22.34  | | | | | | | |               e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 =
% 152.17/22.34  | | | | | | | |               e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.17/22.34  | | | | | | | |               op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.17/22.34  | | | | | | | |                 e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.17/22.34  | | | | | | | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.17/22.34  | | | | | | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.17/22.34  | | | | | | | |               all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.17/22.34  | | | | | | | | 
% 152.17/22.34  | | | | | | | | BETA: splitting (92) gives:
% 152.17/22.34  | | | | | | | | 
% 152.17/22.34  | | | | | | | | Case 1:
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | |   (93)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &
% 152.17/22.34  | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.17/22.34  | | | | | | | | |           op(e3, e1) = e3 & op(e0, e1) = all_57_8 & op(e0, e0)
% 152.17/22.34  | | | | | | | | |           = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7 =
% 152.17/22.34  | | | | | | | | |           e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.17/22.34  | | | | | | | | |           (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.17/22.34  | | | | | | | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 152.17/22.34  | | | | | | | | |           & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.17/22.34  | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 152.17/22.34  | | | | | | | | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.17/22.34  | | | | | | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 152.17/22.34  | | | | | | | | |           $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 152.17/22.34  | | | | | | | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 152.17/22.34  | | | | | | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.34  | | | | | | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.17/22.34  | | | | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 152.17/22.34  | | | | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 152.17/22.34  | | | | | | | | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.34  | | | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.17/22.34  | | | | | | | | |           $i(all_57_10) & $i(all_57_13))
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | BETA: splitting (93) gives:
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | Case 1:
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | |   (94)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.17/22.34  | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e1) = all_57_8 & op(e0,
% 152.17/22.34  | | | | | | | | | |             e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 152.17/22.34  | | | | | | | | | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3,
% 152.17/22.34  | | | | | | | | | |             e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2,
% 152.17/22.34  | | | | | | | | | |             e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | BETA: splitting (94) gives:
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | Case 1:
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | |   (95)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.17/22.34  | | | | | | | | | | |           e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.17/22.34  | | | | | | | | | | |         all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.17/22.34  | | | | | | | | | | |         all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.34  | | | | | | | | | | |         $i(all_57_10)
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | | ALPHA: (95) implies:
% 152.17/22.34  | | | | | | | | | | |   (96)  op(e3, e1) = e3
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | | REF_CLOSE: (17), (50), (52), (96) are inconsistent by
% 152.17/22.34  | | | | | | | | | | |            sub-proof #1164.
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | Case 2:
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | |   (97)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 152.17/22.34  | | | | | | | | | | |           e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 152.17/22.34  | | | | | | | | | | |         op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 152.17/22.34  | | | | | | | | | | |         op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | | ALPHA: (97) implies:
% 152.17/22.34  | | | | | | | | | | |   (98)  op(e3, e3) = e1
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | | REF_CLOSE: (2), (3), (8), (15), (17), (18), (31), (33), (35),
% 152.17/22.34  | | | | | | | | | | |            (45), (46), (48), (49), (53), (55), (81), (98) are
% 152.17/22.34  | | | | | | | | | | |            inconsistent by sub-proof #569.
% 152.17/22.34  | | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | End of split
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | Case 2:
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | |   (99)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.17/22.34  | | | | | | | | | |           &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.17/22.34  | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 152.17/22.34  | | | | | | | | | |             e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.17/22.34  | | | | | | | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 152.17/22.34  | | | | | | | | | |             e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 152.17/22.34  | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.17/22.34  | | | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.17/22.34  | | | | | | | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &
% 152.17/22.34  | | | | | | | | | |            ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3,
% 152.17/22.34  | | | | | | | | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 152.17/22.34  | | | | | | | | | |           e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.17/22.34  | | | | | | | | | |           $i(all_57_13))
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | REF_CLOSE: (9), (14), (17), (30), (37), (99) are inconsistent
% 152.17/22.34  | | | | | | | | | |            by sub-proof #1080.
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | End of split
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | Case 2:
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | |   (100)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.17/22.34  | | | | | | | | |            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3,
% 152.17/22.34  | | | | | | | | |              e0) = all_57_9 & op(e2, e2) = all_57_12 & op(e2,
% 152.17/22.34  | | | | | | | | |              e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 152.17/22.34  | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.17/22.34  | | | | | | | | |            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3,
% 152.17/22.34  | | | | | | | | |              e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1,
% 152.17/22.34  | | | | | | | | |              e0) = e1 & $i(all_57_9) & $i(all_57_14)) |
% 152.17/22.34  | | | | | | | | |          (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.17/22.34  | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.17/22.34  | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.17/22.34  | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.17/22.34  | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &
% 152.17/22.34  | | | | | | | | |             ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2,
% 152.17/22.34  | | | | | | | | |              e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 152.17/22.34  | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.17/22.34  | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 152.17/22.34  | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 & 
% 152.17/22.34  | | | | | | | | |                ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.17/22.34  | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.17/22.34  | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 =
% 152.17/22.34  | | | | | | | | |                e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.17/22.34  | | | | | | | | |                (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.17/22.34  | | | | | | | | |                op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.17/22.34  | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 152.17/22.34  | | | | | | | | |                &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 152.17/22.34  | | | | | | | | |                op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.17/22.34  | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 =
% 152.17/22.34  | | | | | | | | |                e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.17/22.34  | | | | | | | | |                (all_57_15 = e2) & op(e1, e2) = all_57_4 &
% 152.17/22.34  | | | | | | | | |                op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.17/22.34  | | | | | | | | |                $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 152.17/22.34  | | | | | | | | |                &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.17/22.34  | | | | | | | | |                op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.17/22.34  | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.17/22.34  | | | | | | | | |                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.17/22.34  | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 152.17/22.34  | | | | | | | | |                = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | BETA: splitting (100) gives:
% 152.17/22.34  | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | Case 1:
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | |   (101)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 152.17/22.34  | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 152.17/22.34  | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 152.17/22.34  | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 152.17/22.34  | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 152.17/22.34  | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.17/22.34  | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 152.17/22.34  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | | REF_CLOSE: (17), (31), (54), (101) are inconsistent by
% 152.17/22.34  | | | | | | | | | |            sub-proof #975.
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.34  | | | | | | | | | Case 2:
% 152.17/22.34  | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | |   (102)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.17/22.35  | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.17/22.35  | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.17/22.35  | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.17/22.35  | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 152.17/22.35  | | | | | | | | | |            &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.17/22.35  | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1,
% 152.17/22.35  | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 &
% 152.17/22.35  | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.17/22.35  | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.17/22.35  | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.17/22.35  | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 152.17/22.35  | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.35  | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.17/22.35  | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 152.17/22.35  | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.17/22.35  | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 152.17/22.35  | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.17/22.35  | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 152.17/22.35  | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 152.17/22.35  | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 152.17/22.35  | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 152.17/22.35  | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.17/22.35  | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 152.17/22.35  | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.17/22.35  | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.17/22.35  | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 152.17/22.35  | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 152.17/22.35  | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 152.17/22.35  | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.17/22.35  | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7))))
% 152.17/22.35  | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | BETA: splitting (102) gives:
% 152.17/22.35  | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | Case 1:
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | |   (103)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.17/22.35  | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.17/22.35  | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.17/22.35  | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.17/22.35  | | | | | | | | | | |          $i(all_57_13)
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | ALPHA: (103) implies:
% 152.17/22.35  | | | | | | | | | | |   (104)  op(e2, e0) = e2
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | REF_CLOSE: (17), (27), (38), (104) are inconsistent by
% 152.17/22.35  | | | | | | | | | | |            sub-proof #1156.
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | Case 2:
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | |   (105)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.17/22.35  | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.17/22.35  | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 152.17/22.35  | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 152.17/22.35  | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 152.17/22.35  | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 152.17/22.35  | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.17/22.35  | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.17/22.35  | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 152.17/22.35  | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 152.17/22.35  | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 152.17/22.35  | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.17/22.35  | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 152.17/22.35  | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 152.17/22.35  | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.17/22.35  | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.17/22.35  | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 152.17/22.35  | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.17/22.35  | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 152.17/22.35  | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 152.17/22.35  | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 152.17/22.35  | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.17/22.35  | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.17/22.35  | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 152.17/22.35  | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 152.17/22.35  | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 152.17/22.35  | | | | | | | | | | |                & $i(all_57_7))))
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | BETA: splitting (105) gives:
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | Case 1:
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | |   (106)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.17/22.35  | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.17/22.35  | | | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 152.17/22.35  | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | ALPHA: (106) implies:
% 152.17/22.35  | | | | | | | | | | | |   (107)  op(e2, e2) = e0
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | REF_CLOSE: (5), (17), (45), (107) are inconsistent by
% 152.17/22.35  | | | | | | | | | | | |            sub-proof #853.
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | Case 2:
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | |   (108)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.17/22.35  | | | | | | | | | | | |          ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.17/22.35  | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.17/22.35  | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.35  | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.17/22.35  | | | | | | | | | | | |              e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 152.17/22.35  | | | | | | | | | | | |              & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.17/22.35  | | | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 152.17/22.35  | | | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.17/22.35  | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 152.17/22.35  | | | | | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 &
% 152.17/22.35  | | | | | | | | | | | |              $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 152.17/22.35  | | | | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 152.17/22.35  | | | | | | | | | | | |              & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.17/22.35  | | | | | | | | | | | |              op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 152.17/22.35  | | | | | | | | | | | |              e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.17/22.35  | | | | | | | | | | | |              (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.17/22.35  | | | | | | | | | | | |                e1) = all_57_6 & op(e0, e1) = e0 &
% 152.17/22.35  | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 152.17/22.35  | | | | | | | | | | | |              e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 152.17/22.35  | | | | | | | | | | | |              & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.17/22.35  | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_7)))
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | ALPHA: (108) implies:
% 152.17/22.35  | | | | | | | | | | | |   (109)  op(e0, e0) = all_57_15
% 152.17/22.35  | | | | | | | | | | | |   (110)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.17/22.35  | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.17/22.35  | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.35  | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 152.17/22.35  | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 152.17/22.35  | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.17/22.35  | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 152.17/22.35  | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.17/22.35  | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.17/22.35  | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.17/22.35  | | | | | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.17/22.35  | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.17/22.35  | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.17/22.35  | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 152.17/22.35  | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.17/22.35  | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.17/22.35  | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.17/22.35  | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.17/22.35  | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 152.17/22.35  | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | BETA: splitting (56) gives:
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | Case 1:
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | |   (111)  all_54_12 = e3
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | REF_CLOSE: (40), (42), (111) are inconsistent by sub-proof
% 152.17/22.35  | | | | | | | | | | | | |            #1093.
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | Case 2:
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | |   (112)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | BETA: splitting (112) gives:
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | Case 1:
% 152.17/22.35  | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | |   (113)  all_54_12 = e2
% 152.17/22.35  | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | REF_CLOSE: (19), (42), (113) are inconsistent by sub-proof
% 152.17/22.35  | | | | | | | | | | | | | |            #882.
% 152.17/22.35  | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | Case 2:
% 152.17/22.35  | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | |   (114)  all_54_12 = e1 | all_54_12 = e0
% 152.17/22.35  | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | BETA: splitting (114) gives:
% 152.17/22.35  | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | Case 1:
% 152.17/22.35  | | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | |   (115)  all_54_12 = e1
% 152.17/22.35  | | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | | REF_CLOSE: (41), (42), (115) are inconsistent by sub-proof
% 152.17/22.35  | | | | | | | | | | | | | | |            #1091.
% 152.17/22.35  | | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | Case 2:
% 152.17/22.35  | | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | |   (116)  all_54_12 = e0
% 152.17/22.35  | | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | | COMBINE_EQS: (42), (116) imply:
% 152.17/22.35  | | | | | | | | | | | | | | |   (117)  all_52_3 = e0
% 152.17/22.35  | | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | | SIMP: (117) implies:
% 152.17/22.35  | | | | | | | | | | | | | | |   (118)  all_52_3 = e0
% 152.17/22.35  | | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | | REDUCE: (20), (118) imply:
% 152.17/22.35  | | | | | | | | | | | | | | |   (119)   ~ (all_52_11 = e0)
% 152.17/22.35  | | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | | SIMP: (119) implies:
% 152.17/22.35  | | | | | | | | | | | | | | |   (120)   ~ (all_52_11 = e0)
% 152.17/22.35  | | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (22), (23), (29), (48), (49), (109),
% 152.17/22.35  | | | | | | | | | | | | | | |            (110), (120) are inconsistent by sub-proof #233.
% 152.17/22.35  | | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | | End of split
% 152.17/22.35  | | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | End of split
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | End of split
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | End of split
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | End of split
% 152.17/22.35  | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | End of split
% 152.17/22.35  | | | | | | | | | 
% 152.17/22.35  | | | | | | | | End of split
% 152.17/22.35  | | | | | | | | 
% 152.17/22.35  | | | | | | | End of split
% 152.17/22.35  | | | | | | | 
% 152.17/22.35  | | | | | | End of split
% 152.17/22.35  | | | | | | 
% 152.17/22.35  | | | | | End of split
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | End of split
% 152.17/22.35  | | | | 
% 152.17/22.35  | | | Case 2:
% 152.17/22.35  | | | | 
% 152.17/22.35  | | | |   (121)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1,
% 152.17/22.35  | | | |              e0) = e0)
% 152.17/22.35  | | | | 
% 152.17/22.35  | | | | REF_CLOSE: (13), (17), (31), (45), (48), (121) are inconsistent by
% 152.17/22.35  | | | |            sub-proof #610.
% 152.17/22.35  | | | | 
% 152.17/22.35  | | | End of split
% 152.17/22.35  | | | 
% 152.17/22.35  | | End of split
% 152.17/22.35  | | 
% 152.17/22.35  | End of split
% 152.17/22.35  | 
% 152.17/22.35  End of proof
% 152.17/22.35  
% 152.17/22.35  Sub-proof #231 shows that the following formulas are inconsistent:
% 152.17/22.35  ----------------------------------------------------------------
% 152.17/22.35    (1)  op(e0, e1) = all_52_11
% 152.17/22.35    (2)   ~ (e3 = e1)
% 152.17/22.35    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.17/22.35         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.17/22.35    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 152.17/22.35         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 152.17/22.35    (5)  op(e2, e2) = e1
% 152.17/22.35    (6)   ~ (all_52_2 = all_52_6)
% 152.17/22.35    (7)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.35         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.17/22.35    (8)  op(e0, e0) = all_10_2
% 152.17/22.35    (9)  op(e3, e2) = all_52_4
% 152.17/22.35    (10)  op(e0, e2) = all_52_7
% 152.17/22.35    (11)   ~ (all_52_14 = e2)
% 152.17/22.35    (12)   ~ (all_52_3 = all_52_7)
% 152.17/22.35    (13)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.35          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.17/22.35    (14)   ~ (all_10_2 = e1)
% 152.17/22.35    (15)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.17/22.35          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.17/22.35    (16)   ~ (e2 = e0)
% 152.17/22.35    (17)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.17/22.35          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.17/22.35    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.35            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.35    (19)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.17/22.35          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.17/22.35    (20)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.17/22.35          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.17/22.35    (21)  all_56_6 = e1
% 152.17/22.35    (22)   ~ (all_52_3 = e2)
% 152.17/22.35    (23)   ~ (all_52_3 = all_52_11)
% 152.17/22.35    (24)   ~ (all_52_9 = e3)
% 152.17/22.35    (25)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 152.17/22.35            all_57_14 & $i(all_57_14))
% 152.17/22.35    (26)  op(e0, e0) = e2
% 152.17/22.35    (27)  op(e1, e3) = e1
% 152.17/22.35    (28)   ~ (all_52_1 = e3)
% 152.17/22.35    (29)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.17/22.35              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.17/22.35                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.17/22.35                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.17/22.35    (30)  op(e1, e0) = all_52_14
% 152.17/22.35    (31)   ~ (all_52_13 = e2)
% 152.17/22.35    (32)   ~ (all_52_4 = e3)
% 152.17/22.35    (33)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 152.17/22.35            all_57_12 & $i(all_57_12))
% 152.17/22.35    (34)  op(e3, e0) = all_52_12
% 152.17/22.35    (35)   ~ (e3 = e0)
% 152.17/22.35    (36)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 152.17/22.35            all_57_15 & $i(all_57_15))
% 152.17/22.35    (37)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.17/22.35          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.17/22.35    (38)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 152.17/22.35          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.17/22.35    (39)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.17/22.35          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.17/22.35    (40)   ~ (all_52_6 = e3)
% 152.17/22.35    (41)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 152.17/22.35          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 152.17/22.35    (42)  op(e1, e2) = all_52_6
% 152.17/22.35    (43)   ~ (all_52_12 = e3)
% 152.17/22.35    (44)  op(e2, e0) = all_52_13
% 152.17/22.35    (45)  all_56_3 = e1
% 152.17/22.35    (46)   ~ (all_52_3 = e3)
% 152.17/22.35    (47)   ~ (all_52_3 = e1)
% 152.17/22.35    (48)  op(e0, e3) = all_52_3
% 152.17/22.35    (49)  all_54_12 = all_52_3
% 152.17/22.35    (50)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.35          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.17/22.35    (51)  op(e2, e1) = all_52_9
% 152.17/22.35    (52)   ~ (e1 = e0)
% 152.17/22.35    (53)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.17/22.35          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.17/22.35    (54)  op(e1, e1) = e3
% 152.17/22.35    (55)   ~ (e3 = e2)
% 152.17/22.35    (56)   ~ (all_52_8 = e3)
% 152.17/22.35    (57)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.17/22.35          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.17/22.35    (58)  op(e3, e1) = all_52_8
% 152.17/22.35    (59)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.17/22.35          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.17/22.35    (60)  op(e3, e3) = e3
% 152.17/22.35    (61)   ~ (e2 = e1)
% 152.17/22.35    (62)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.17/22.35    (63)  op(e1, e3) = all_52_2
% 152.17/22.35    (64)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.17/22.35              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.17/22.35            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.17/22.35            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.17/22.35            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.17/22.35            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.17/22.35            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.17/22.35            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.17/22.35            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.17/22.35            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.17/22.35            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.17/22.35            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.17/22.35            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.35            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.17/22.35            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.17/22.35            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.35            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.17/22.35            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.17/22.35            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.17/22.35            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.17/22.35            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.17/22.35            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.35            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.17/22.35            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.17/22.35            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.17/22.35            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.17/22.35            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.17/22.35            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.17/22.35            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.35            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.17/22.35            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.17/22.35            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.17/22.35            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.17/22.35            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.17/22.35            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.35            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.17/22.35            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.35            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.17/22.35            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.17/22.35            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.35            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.17/22.35            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.17/22.35            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.17/22.35            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.17/22.35            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.17/22.35            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.17/22.35            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.17/22.35            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.17/22.35              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.17/22.35            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.17/22.35            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.17/22.35              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.17/22.35            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.17/22.35            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.17/22.35                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.17/22.35                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.35                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.17/22.35                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.17/22.35                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.17/22.35                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.17/22.35                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.17/22.35              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.17/22.35                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.17/22.35                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.17/22.35                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.17/22.35                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.17/22.35                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.17/22.35                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.17/22.35                $i(all_57_7))))
% 152.17/22.35    (65)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.17/22.35          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.17/22.35    (66)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.17/22.35          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.17/22.35            e1)
% 152.17/22.35    (67)  op(e2, e3) = all_52_1
% 152.17/22.35  
% 152.17/22.35  Begin of proof
% 152.17/22.35  | 
% 152.17/22.35  | BETA: splitting (38) gives:
% 152.17/22.35  | 
% 152.17/22.35  | Case 1:
% 152.17/22.35  | | 
% 152.17/22.35  | |   (68)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 152.17/22.35  | |           e1)
% 152.17/22.35  | | 
% 152.17/22.35  | | BETA: splitting (68) gives:
% 152.17/22.35  | | 
% 152.17/22.35  | | Case 1:
% 152.17/22.35  | | | 
% 152.17/22.35  | | |   (69)  all_56_9 = e1 & op(e3, e0) = e1
% 152.17/22.35  | | | 
% 152.17/22.35  | | | ALPHA: (69) implies:
% 152.17/22.35  | | |   (70)  all_56_9 = e1
% 152.17/22.35  | | | 
% 152.17/22.35  | | | BETA: splitting (65) gives:
% 152.17/22.35  | | | 
% 152.17/22.35  | | | Case 1:
% 152.17/22.35  | | | | 
% 152.17/22.35  | | | |   (71)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2)
% 152.17/22.35  | | | |           = e3)
% 152.17/22.35  | | | | 
% 152.17/22.35  | | | | BETA: splitting (71) gives:
% 152.17/22.35  | | | | 
% 152.17/22.35  | | | | Case 1:
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | |   (72)  all_56_1 = e3 & op(e3, e2) = e3
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | | ALPHA: (72) implies:
% 152.17/22.35  | | | | |   (73)  op(e3, e2) = e3
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | | REF_CLOSE: (9), (18), (32), (73) are inconsistent by sub-proof #1166.
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | Case 2:
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | |   (74)  all_56_3 = e3 & op(e2, e2) = e3
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | | REF_CLOSE: (2), (45), (74) are inconsistent by sub-proof #270.
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | End of split
% 152.17/22.35  | | | | 
% 152.17/22.35  | | | Case 2:
% 152.17/22.35  | | | | 
% 152.17/22.35  | | | |   (75)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2)
% 152.17/22.35  | | | |           = e3)
% 152.17/22.35  | | | | 
% 152.17/22.35  | | | | BETA: splitting (75) gives:
% 152.17/22.35  | | | | 
% 152.17/22.35  | | | | Case 1:
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | |   (76)  all_56_7 = e3 & op(e1, e2) = e3
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | | REF_CLOSE: (18), (40), (42), (76) are inconsistent by sub-proof #925.
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | Case 2:
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | |   (77)  all_56_13 = e3 & op(e0, e2) = e3
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | | ALPHA: (77) implies:
% 152.17/22.35  | | | | |   (78)  all_56_13 = e3
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | | BETA: splitting (50) gives:
% 152.17/22.35  | | | | | 
% 152.17/22.35  | | | | | Case 1:
% 152.17/22.35  | | | | | | 
% 152.17/22.35  | | | | | |   (79)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2,
% 152.17/22.35  | | | | | |             e2) = e3)
% 152.17/22.35  | | | | | | 
% 152.17/22.35  | | | | | | REF_CLOSE: (2), (5), (7), (16), (18), (28), (35), (40), (42), (45),
% 152.17/22.35  | | | | | |            (52), (55), (57), (61), (65), (67), (78), (79) are
% 152.17/22.35  | | | | | |            inconsistent by sub-proof #239.
% 152.17/22.35  | | | | | | 
% 152.17/22.35  | | | | | Case 2:
% 152.17/22.35  | | | | | | 
% 152.17/22.35  | | | | | |   (80)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2,
% 152.17/22.35  | | | | | |             e0) = e3)
% 152.17/22.35  | | | | | | 
% 152.17/22.35  | | | | | | BETA: splitting (80) gives:
% 152.17/22.35  | | | | | | 
% 152.17/22.35  | | | | | | Case 1:
% 152.17/22.35  | | | | | | | 
% 152.17/22.35  | | | | | | |   (81)  all_56_5 = e3 & op(e2, e1) = e3
% 152.17/22.35  | | | | | | | 
% 152.17/22.35  | | | | | | | REF_CLOSE: (18), (24), (51), (81) are inconsistent by sub-proof
% 152.17/22.35  | | | | | | |            #647.
% 152.17/22.35  | | | | | | | 
% 152.17/22.35  | | | | | | Case 2:
% 152.17/22.35  | | | | | | | 
% 152.17/22.35  | | | | | | |   (82)  all_56_10 = e3 & op(e2, e0) = e3
% 152.17/22.35  | | | | | | | 
% 152.17/22.35  | | | | | | | ALPHA: (82) implies:
% 152.17/22.35  | | | | | | |   (83)  all_56_10 = e3
% 152.17/22.35  | | | | | | | 
% 152.17/22.35  | | | | | | | BETA: splitting (66) gives:
% 152.17/22.35  | | | | | | | 
% 152.17/22.35  | | | | | | | Case 1:
% 152.17/22.35  | | | | | | | | 
% 152.17/22.35  | | | | | | | |   (84)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 &
% 152.17/22.35  | | | | | | | |           op(e0, e2) = e1)
% 152.17/22.35  | | | | | | | | 
% 152.17/22.35  | | | | | | | | BETA: splitting (84) gives:
% 152.17/22.35  | | | | | | | | 
% 152.17/22.35  | | | | | | | | Case 1:
% 152.17/22.35  | | | | | | | | | 
% 152.17/22.35  | | | | | | | | |   (85)  all_56_12 = e1 & op(e0, e3) = e1
% 152.17/22.35  | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | ALPHA: (85) implies:
% 152.17/22.35  | | | | | | | | |   (86)  all_56_12 = e1
% 152.17/22.35  | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | BETA: splitting (53) gives:
% 152.17/22.35  | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | Case 1:
% 152.17/22.35  | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | |   (87)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 &
% 152.17/22.35  | | | | | | | | | |           op(e1, e2) = e2)
% 152.17/22.35  | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | BETA: splitting (87) gives:
% 152.17/22.35  | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | Case 1:
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | |   (88)  all_56_6 = e2 & op(e1, e3) = e2
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | ALPHA: (88) implies:
% 152.17/22.35  | | | | | | | | | | |   (89)  all_56_6 = e2
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | REF_CLOSE: (21), (61), (89) are inconsistent by sub-proof
% 152.17/22.35  | | | | | | | | | | |            #1172.
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | Case 2:
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | |   (90)  all_56_7 = e2 & op(e1, e2) = e2
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | ALPHA: (90) implies:
% 152.17/22.35  | | | | | | | | | | |   (91)  all_56_7 = e2
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | BETA: splitting (41) gives:
% 152.17/22.35  | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | Case 1:
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | |   (92)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 152.17/22.35  | | | | | | | | | | | |           & op(e2, e3) = e2)
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | BETA: splitting (92) gives:
% 152.17/22.35  | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | Case 1:
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | |   (93)  all_56_0 = e2 & op(e3, e3) = e2
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | ALPHA: (93) implies:
% 152.17/22.35  | | | | | | | | | | | | |   (94)  op(e3, e3) = e2
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | | REF_CLOSE: (18), (55), (60), (94) are inconsistent by
% 152.17/22.35  | | | | | | | | | | | | |            sub-proof #1085.
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | Case 2:
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.35  | | | | | | | | | | | | |   (95)  all_56_2 = e2 & op(e2, e3) = e2
% 152.17/22.35  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | ALPHA: (95) implies:
% 152.17/22.36  | | | | | | | | | | | | |   (96)  all_56_2 = e2
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | BETA: splitting (37) gives:
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | |   (97)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 152.17/22.36  | | | | | | | | | | | | | |           & op(e2, e3) = e0)
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | |   (98)  all_56_0 = e0 & op(e3, e3) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 152.17/22.36  | | | | | | | | | | | | | | |   (99)  op(e3, e3) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | REF_CLOSE: (18), (35), (60), (99) are inconsistent by
% 152.17/22.36  | | | | | | | | | | | | | | |            sub-proof #1141.
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | |   (100)  all_56_2 = e0 & op(e2, e3) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 152.17/22.36  | | | | | | | | | | | | | | |   (101)  all_56_2 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | COMBINE_EQS: (96), (101) imply:
% 152.17/22.36  | | | | | | | | | | | | | | |   (102)  e2 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | SIMP: (102) implies:
% 152.17/22.36  | | | | | | | | | | | | | | |   (103)  e2 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | COMBINE_EQS: (91), (103) imply:
% 152.17/22.36  | | | | | | | | | | | | | | |   (104)  all_56_7 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (18), (21), (30), (53), (54), (55),
% 152.17/22.36  | | | | | | | | | | | | | | |            (61), (104) are inconsistent by sub-proof #238.
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | |   (105)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 152.17/22.36  | | | | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | |   (106)  all_56_6 = e0 & op(e1, e3) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 152.17/22.36  | | | | | | | | | | | | | | |   (107)  op(e1, e3) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | REF_CLOSE: (18), (27), (52), (63), (107) are inconsistent by
% 152.17/22.36  | | | | | | | | | | | | | | |            sub-proof #1127.
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | |   (108)  all_56_12 = e0 & op(e0, e3) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | REF_CLOSE: (52), (86), (108) are inconsistent by sub-proof
% 152.17/22.36  | | | | | | | | | | | | | | |            #1103.
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | |   (109)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 152.17/22.36  | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 152.17/22.36  | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | BETA: splitting (109) gives:
% 152.17/22.36  | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | |   (110)  all_56_6 = e2 & op(e1, e3) = e2
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | ALPHA: (110) implies:
% 152.17/22.36  | | | | | | | | | | | | |   (111)  all_56_6 = e2
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | REF_CLOSE: (21), (61), (111) are inconsistent by sub-proof
% 152.17/22.36  | | | | | | | | | | | | |            #1172.
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | |   (112)  all_56_12 = e2 & op(e0, e3) = e2
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | ALPHA: (112) implies:
% 152.17/22.36  | | | | | | | | | | | | |   (113)  all_56_12 = e2
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | BETA: splitting (66) gives:
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | REF_CLOSE: (61), (85), (113) are inconsistent by sub-proof
% 152.17/22.36  | | | | | | | | | | | | | | |            #789.
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | |   (114)  all_56_13 = e1 & op(e0, e2) = e1
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 152.17/22.36  | | | | | | | | | | | | | | |   (115)  all_56_13 = e1
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (16), (18), (35), (40), (42), (45),
% 152.17/22.36  | | | | | | | | | | | | | | |            (52), (55), (57), (61), (65), (115) are
% 152.17/22.36  | | | | | | | | | | | | | | |            inconsistent by sub-proof #260.
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | |   (116)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 152.17/22.36  | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | |   (117)  all_56_14 = e1 & op(e0, e1) = e1
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 152.17/22.36  | | | | | | | | | | | | | | |   (118)  all_56_14 = e1
% 152.17/22.36  | | | | | | | | | | | | | | |   (119)  op(e0, e1) = e1
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (12), (13),
% 152.17/22.36  | | | | | | | | | | | | | | |            (14), (15), (16), (17), (18), (20), (24), (26),
% 152.17/22.36  | | | | | | | | | | | | | | |            (29), (31), (35), (37), (38), (40), (42), (44),
% 152.17/22.36  | | | | | | | | | | | | | | |            (45), (48), (50), (51), (52), (54), (55), (59),
% 152.17/22.36  | | | | | | | | | | | | | | |            (60), (61), (63), (65), (67), (113), (118), (119)
% 152.17/22.36  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #235.
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | |   (120)  all_56_15 = e1 & op(e0, e0) = e1
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 152.17/22.36  | | | | | | | | | | | | | | |   (121)  op(e0, e0) = e1
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | REF_CLOSE: (8), (14), (18), (121) are inconsistent by
% 152.17/22.36  | | | | | | | | | | | | | | |            sub-proof #1116.
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | |   (122)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2
% 152.17/22.36  | | | | | | | | | |            & op(e1, e0) = e2)
% 152.17/22.36  | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | REF_CLOSE: (11), (18), (30), (54), (55), (122) are
% 152.17/22.36  | | | | | | | | | |            inconsistent by sub-proof #289.
% 152.17/22.36  | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | 
% 152.17/22.36  | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | 
% 152.17/22.36  | | | | | | | | |   (123)  all_56_13 = e1 & op(e0, e2) = e1
% 152.17/22.36  | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | ALPHA: (123) implies:
% 152.17/22.36  | | | | | | | | |   (124)  all_56_13 = e1
% 152.17/22.36  | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | REF_CLOSE: (2), (5), (7), (16), (18), (35), (40), (42), (45),
% 152.17/22.36  | | | | | | | | |            (52), (55), (57), (61), (65), (124) are
% 152.17/22.36  | | | | | | | | |            inconsistent by sub-proof #260.
% 152.17/22.36  | | | | | | | | | 
% 152.17/22.36  | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | 
% 152.17/22.36  | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | 
% 152.17/22.36  | | | | | | | |   (125)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 &
% 152.17/22.36  | | | | | | | |            op(e0, e0) = e1)
% 152.17/22.36  | | | | | | | | 
% 152.17/22.36  | | | | | | | | BETA: splitting (125) gives:
% 152.17/22.36  | | | | | | | | 
% 152.17/22.36  | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | 
% 152.17/22.36  | | | | | | | | |   (126)  all_56_14 = e1 & op(e0, e1) = e1
% 152.17/22.36  | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | ALPHA: (126) implies:
% 152.17/22.36  | | | | | | | | |   (127)  all_56_14 = e1
% 152.17/22.36  | | | | | | | | |   (128)  op(e0, e1) = e1
% 152.17/22.36  | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | BETA: splitting (53) gives:
% 152.17/22.36  | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | |   (129)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 152.17/22.36  | | | | | | | | | |            & op(e1, e2) = e2)
% 152.17/22.36  | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | BETA: splitting (129) gives:
% 152.17/22.36  | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | |   (130)  all_56_6 = e2 & op(e1, e3) = e2
% 152.17/22.36  | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | ALPHA: (130) implies:
% 152.17/22.36  | | | | | | | | | | |   (131)  all_56_6 = e2
% 152.17/22.36  | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | REF_CLOSE: (21), (61), (131) are inconsistent by sub-proof
% 152.17/22.36  | | | | | | | | | | |            #1172.
% 152.17/22.36  | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | |   (132)  all_56_7 = e2 & op(e1, e2) = e2
% 152.17/22.36  | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | ALPHA: (132) implies:
% 152.17/22.36  | | | | | | | | | | |   (133)  all_56_7 = e2
% 152.17/22.36  | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | BETA: splitting (41) gives:
% 152.17/22.36  | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | |   (134)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 152.17/22.36  | | | | | | | | | | | |            & op(e2, e3) = e2)
% 152.17/22.36  | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | BETA: splitting (134) gives:
% 152.17/22.36  | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | |   (135)  all_56_0 = e2 & op(e3, e3) = e2
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | ALPHA: (135) implies:
% 152.17/22.36  | | | | | | | | | | | | |   (136)  op(e3, e3) = e2
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | REF_CLOSE: (18), (55), (60), (136) are inconsistent by
% 152.17/22.36  | | | | | | | | | | | | |            sub-proof #1085.
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | |   (137)  all_56_2 = e2 & op(e2, e3) = e2
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | ALPHA: (137) implies:
% 152.17/22.36  | | | | | | | | | | | | |   (138)  all_56_2 = e2
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | BETA: splitting (62) gives:
% 152.17/22.36  | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | |   (139)  all_54_12 = e3
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | REF_CLOSE: (46), (49), (139) are inconsistent by sub-proof
% 152.17/22.36  | | | | | | | | | | | | | |            #1093.
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | |   (140)   ~ (all_54_12 = e3)
% 152.17/22.36  | | | | | | | | | | | | | |   (141)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 152.17/22.36  | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | |   (142)  all_54_12 = e2
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | REF_CLOSE: (22), (49), (142) are inconsistent by sub-proof
% 152.17/22.36  | | | | | | | | | | | | | | |            #882.
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | |   (143)   ~ (all_54_12 = e2)
% 152.17/22.36  | | | | | | | | | | | | | | |   (144)  all_54_12 = e1 | all_54_12 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | |   (145)  all_54_12 = e1
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | REF_CLOSE: (47), (49), (145) are inconsistent by sub-proof
% 152.17/22.36  | | | | | | | | | | | | | | | |            #1091.
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | |   (146)  all_54_12 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (146) imply:
% 152.17/22.36  | | | | | | | | | | | | | | | |   (147)  all_52_3 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | SIMP: (147) implies:
% 152.17/22.36  | | | | | | | | | | | | | | | |   (148)  all_52_3 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | REDUCE: (23), (148) imply:
% 152.17/22.36  | | | | | | | | | | | | | | | |   (149)   ~ (all_52_11 = e0)
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | SIMP: (149) implies:
% 152.17/22.36  | | | | | | | | | | | | | | | |   (150)   ~ (all_52_11 = e0)
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | REDUCE: (46), (148) imply:
% 152.17/22.36  | | | | | | | | | | | | | | | |   (151)   ~ (e3 = e0)
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | REDUCE: (22), (148) imply:
% 152.17/22.36  | | | | | | | | | | | | | | | |   (152)   ~ (e2 = e0)
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | REDUCE: (47), (148) imply:
% 152.17/22.36  | | | | | | | | | | | | | | | |   (153)   ~ (e1 = e0)
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | |   (154)  all_56_15 = e0 & op(e0, e0) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 152.17/22.36  | | | | | | | | | | | | | | | | |   (155)  op(e0, e0) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (18), (26), (155) are inconsistent by
% 152.17/22.36  | | | | | | | | | | | | | | | | |            sub-proof #1043.
% 152.17/22.36  | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | |   (156)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 152.17/22.36  | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 152.17/22.36  | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 152.17/22.36  | | | | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 152.17/22.36  | | | | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 152.17/22.36  | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 152.17/22.36  | | | | | | | | | | | | | | | | |   (157)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 152.17/22.36  | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 152.17/22.36  | | | | | | | | | | | | | | | | |              e1) = e0)
% 152.17/22.36  | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | |   (158)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 152.17/22.36  | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | |   (159)  all_56_2 = e0 & op(e2, e3) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | |   (160)  all_56_2 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (138), (160) imply:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | |   (161)  e2 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (161) imply:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | |   (162)  all_56_7 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (18), (21), (30), (53), (54), (55),
% 152.17/22.36  | | | | | | | | | | | | | | | | | | |            (61), (162) are inconsistent by sub-proof #238.
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | |   (163)  all_56_3 = e0 & op(e2, e2) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | ALPHA: (163) implies:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | |   (164)  op(e2, e2) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (18), (52), (164) are inconsistent by
% 152.17/22.36  | | | | | | | | | | | | | | | | | | |            sub-proof #853.
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | |   (165)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 152.17/22.36  | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | |   (166)  all_56_5 = e0 & op(e2, e1) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | |   (167)  all_56_5 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | |   (168)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | |   (169)  all_56_4 = e2 & op(e3, e1) = e2
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | ALPHA: (169) implies:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | |   (170)  all_56_4 = e2
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |   (171)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |   (172)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |   (173)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (25), (36), (173) are inconsistent by
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #814.
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |   (174)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (54), (174) are inconsistent by sub-proof
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            #368.
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |   (175)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (175) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |   (176)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (18), (32), (54), (55), (176) are
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #294.
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |   (177)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (178)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (179)  op(e3, e3) = e2
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (16), (18), (19), (35), (39), (52), (55),
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            (56), (58), (70), (170), (179) are inconsistent by
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #484.
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |   (180)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18), (27), (42), (56), (58), (63), (180) are
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #234.
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |   (181)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_9) & $i(all_57_12)) |
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |          | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.36  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |   (182)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (183)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (184)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (185)  op(e3, e1) = e3
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (56), (58), (185) are inconsistent by
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1164.
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (187)  op(e3, e3) = e1
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (16), (18), (19), (35), (39), (52),
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            (55), (61), (70), (170), (187) are inconsistent by
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #941.
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (188)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (14), (18), (34), (43), (188) are
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1080.
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |   (189)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (190)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (35), (60), (190) are inconsistent by
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #975.
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |   (191)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (192)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_13)
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (193)  op(e2, e0) = e2
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (31), (44), (193) are inconsistent by
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1156.
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |   (194)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_7))))
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  op(e2, e2) = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (18), (52), (196) are inconsistent by
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #853.
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (197)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_6 & op(e0, e1) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_7)))
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (198)  op(e0, e0) = all_57_15
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |   (199)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (25), (26), (33), (54), (55), (150),
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | |            (198), (199) are inconsistent by sub-proof #233.
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |   (200)  all_56_5 = e2 & op(e2, e1) = e2
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |   (201)  all_56_5 = e2
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (201) imply:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |   (202)  e2 = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (133), (202) imply:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |   (203)  all_56_7 = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (16), (18), (21), (30), (53), (54), (55),
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |            (61), (203) are inconsistent by sub-proof #238.
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | |   (204)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |   (205)  all_56_8 = e2 & op(e1, e1) = e2
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | ALPHA: (205) implies:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |   (206)  op(e1, e1) = e2
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (54), (55), (206) are inconsistent by
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |            sub-proof #834.
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |   (207)  all_56_14 = e2 & op(e0, e1) = e2
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |   (208)  all_56_14 = e2
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (8), (14), (16), (18), (35), (52), (61),
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |            (66), (78), (157), (208) are inconsistent by
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1098.
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | |   (209)  all_56_10 = e0 & op(e2, e0) = e0
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (83), (209) are inconsistent by sub-proof
% 152.17/22.37  | | | | | | | | | | | | | | | | | | |            #749.
% 152.17/22.37  | | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | |   (210)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 152.17/22.37  | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 152.17/22.37  | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | BETA: splitting (210) gives:
% 152.17/22.37  | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | Case 1:
% 152.17/22.37  | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | |   (211)  all_56_6 = e2 & op(e1, e3) = e2
% 152.17/22.37  | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | ALPHA: (211) implies:
% 152.17/22.37  | | | | | | | | | | | | |   (212)  all_56_6 = e2
% 152.17/22.37  | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | REF_CLOSE: (21), (61), (212) are inconsistent by sub-proof
% 152.17/22.37  | | | | | | | | | | | | |            #1172.
% 152.17/22.37  | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | |   (213)  all_56_12 = e2 & op(e0, e3) = e2
% 152.17/22.37  | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | ALPHA: (213) implies:
% 152.17/22.37  | | | | | | | | | | | | |   (214)  all_56_12 = e2
% 152.17/22.37  | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (10), (12), (13),
% 152.17/22.37  | | | | | | | | | | | | |            (14), (15), (16), (17), (18), (20), (24), (26),
% 152.17/22.37  | | | | | | | | | | | | |            (29), (31), (35), (37), (38), (40), (42), (44),
% 152.17/22.37  | | | | | | | | | | | | |            (45), (48), (50), (51), (52), (54), (55), (59),
% 152.17/22.37  | | | | | | | | | | | | |            (60), (61), (63), (65), (67), (127), (128), (214)
% 152.17/22.37  | | | | | | | | | | | | |            are inconsistent by sub-proof #235.
% 152.17/22.37  | | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | |   (215)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2
% 152.17/22.37  | | | | | | | | | |            & op(e1, e0) = e2)
% 152.17/22.37  | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | | REF_CLOSE: (11), (18), (30), (54), (55), (215) are
% 152.17/22.37  | | | | | | | | | |            inconsistent by sub-proof #289.
% 152.17/22.37  | | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | | 
% 152.17/22.37  | | | | | | | | Case 2:
% 152.17/22.37  | | | | | | | | | 
% 152.17/22.37  | | | | | | | | |   (216)  all_56_15 = e1 & op(e0, e0) = e1
% 152.17/22.37  | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | ALPHA: (216) implies:
% 152.17/22.37  | | | | | | | | |   (217)  op(e0, e0) = e1
% 152.17/22.37  | | | | | | | | | 
% 152.17/22.37  | | | | | | | | | REF_CLOSE: (8), (14), (18), (217) are inconsistent by
% 152.17/22.37  | | | | | | | | |            sub-proof #1116.
% 152.17/22.37  | | | | | | | | | 
% 152.17/22.37  | | | | | | | | End of split
% 152.17/22.37  | | | | | | | | 
% 152.17/22.37  | | | | | | | End of split
% 152.17/22.37  | | | | | | | 
% 152.17/22.37  | | | | | | End of split
% 152.17/22.37  | | | | | | 
% 152.17/22.37  | | | | | End of split
% 152.17/22.37  | | | | | 
% 152.17/22.37  | | | | End of split
% 152.17/22.37  | | | | 
% 152.17/22.37  | | | End of split
% 152.17/22.37  | | | 
% 152.17/22.37  | | Case 2:
% 152.17/22.37  | | | 
% 152.17/22.37  | | |   (218)  all_56_10 = e1 & op(e2, e0) = e1
% 152.17/22.37  | | | 
% 152.17/22.37  | | | ALPHA: (218) implies:
% 152.17/22.37  | | |   (219)  all_56_10 = e1
% 152.17/22.37  | | | 
% 152.17/22.37  | | | REF_CLOSE: (2), (5), (13), (16), (17), (18), (24), (35), (45), (50), (51),
% 152.17/22.37  | | |            (52), (55), (61), (219) are inconsistent by sub-proof #264.
% 152.17/22.37  | | | 
% 152.17/22.37  | | End of split
% 152.17/22.37  | | 
% 152.17/22.37  | Case 2:
% 152.17/22.37  | | 
% 152.17/22.37  | |   (220)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.17/22.37  | |            e1)
% 152.17/22.37  | | 
% 152.17/22.37  | | BETA: splitting (220) gives:
% 152.17/22.37  | | 
% 152.17/22.37  | | Case 1:
% 152.17/22.37  | | | 
% 152.17/22.37  | | |   (221)  all_56_11 = e1 & op(e1, e0) = e1
% 152.17/22.37  | | | 
% 152.17/22.37  | | | ALPHA: (221) implies:
% 152.17/22.37  | | |   (222)  all_56_11 = e1
% 152.17/22.37  | | |   (223)  op(e1, e0) = e1
% 152.17/22.37  | | | 
% 152.17/22.37  | | | REF_CLOSE: (16), (18), (21), (27), (35), (52), (53), (54), (55), (59),
% 152.17/22.37  | | |            (61), (63), (222), (223) are inconsistent by sub-proof #232.
% 152.17/22.37  | | | 
% 152.17/22.37  | | Case 2:
% 152.17/22.37  | | | 
% 152.17/22.37  | | |   (224)  all_56_15 = e1 & op(e0, e0) = e1
% 152.17/22.37  | | | 
% 152.17/22.37  | | | ALPHA: (224) implies:
% 152.17/22.37  | | |   (225)  op(e0, e0) = e1
% 152.17/22.37  | | | 
% 152.17/22.37  | | | REF_CLOSE: (8), (14), (18), (225) are inconsistent by sub-proof #1116.
% 152.17/22.37  | | | 
% 152.17/22.37  | | End of split
% 152.17/22.37  | | 
% 152.17/22.37  | End of split
% 152.17/22.37  | 
% 152.17/22.37  End of proof
% 152.17/22.37  
% 152.17/22.37  Sub-proof #232 shows that the following formulas are inconsistent:
% 152.17/22.37  ----------------------------------------------------------------
% 152.17/22.37    (1)  all_56_11 = e1
% 152.17/22.37    (2)   ~ (e2 = e0)
% 152.17/22.37    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.37    (4)  all_56_6 = e1
% 152.17/22.37    (5)  op(e1, e3) = e1
% 152.17/22.37    (6)   ~ (e3 = e0)
% 152.17/22.37    (7)   ~ (e1 = e0)
% 152.17/22.37    (8)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.17/22.37         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.17/22.37    (9)  op(e1, e1) = e3
% 152.17/22.37    (10)   ~ (e3 = e2)
% 152.17/22.37    (11)  op(e1, e0) = e1
% 152.17/22.37    (12)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.17/22.37          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.17/22.37    (13)   ~ (e2 = e1)
% 152.17/22.37    (14)  op(e1, e3) = all_52_2
% 152.17/22.37  
% 152.17/22.37  Begin of proof
% 152.17/22.37  | 
% 152.17/22.37  | BETA: splitting (8) gives:
% 152.17/22.37  | 
% 152.17/22.37  | Case 1:
% 152.17/22.37  | | 
% 152.17/22.37  | |   (15)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 152.17/22.37  | |           e2)
% 152.17/22.37  | | 
% 152.17/22.37  | | BETA: splitting (15) gives:
% 152.17/22.37  | | 
% 152.17/22.37  | | Case 1:
% 152.17/22.37  | | | 
% 152.17/22.37  | | |   (16)  all_56_6 = e2 & op(e1, e3) = e2
% 152.17/22.37  | | | 
% 152.17/22.37  | | | ALPHA: (16) implies:
% 152.17/22.37  | | |   (17)  all_56_6 = e2
% 152.17/22.37  | | | 
% 152.17/22.37  | | | REF_CLOSE: (4), (13), (17) are inconsistent by sub-proof #1172.
% 152.17/22.37  | | | 
% 152.17/22.37  | | Case 2:
% 152.17/22.37  | | | 
% 152.17/22.37  | | |   (18)  all_56_7 = e2 & op(e1, e2) = e2
% 152.17/22.37  | | | 
% 152.17/22.37  | | | ALPHA: (18) implies:
% 152.17/22.37  | | |   (19)  all_56_7 = e2
% 152.17/22.37  | | | 
% 152.17/22.37  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (12), (14), (19) are
% 152.17/22.37  | | |            inconsistent by sub-proof #237.
% 152.17/22.37  | | | 
% 152.17/22.37  | | End of split
% 152.17/22.37  | | 
% 152.17/22.37  | Case 2:
% 152.17/22.37  | | 
% 152.17/22.37  | |   (20)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 152.17/22.37  | |           e2)
% 152.17/22.37  | | 
% 152.17/22.37  | | REF_CLOSE: (3), (9), (10), (11), (13), (20) are inconsistent by sub-proof
% 152.17/22.37  | |            #280.
% 152.17/22.37  | | 
% 152.17/22.37  | End of split
% 152.17/22.37  | 
% 152.17/22.37  End of proof
% 152.17/22.37  
% 152.17/22.37  Sub-proof #233 shows that the following formulas are inconsistent:
% 152.17/22.37  ----------------------------------------------------------------
% 152.17/22.37    (1)  op(e0, e1) = all_52_11
% 152.17/22.37    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.17/22.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.17/22.37    (3)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 152.17/22.37           all_57_14 & $i(all_57_14))
% 152.17/22.37    (4)  op(e0, e0) = e2
% 152.17/22.37    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 152.17/22.37             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.17/22.37           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.17/22.37           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.17/22.37             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.17/22.37           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.17/22.37           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.17/22.37           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 152.17/22.37           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.17/22.37           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 152.17/22.37           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.17/22.37         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.17/22.37             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.17/22.37           $i(all_57_7))
% 152.17/22.37    (6)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 152.17/22.37           all_57_12 & $i(all_57_12))
% 152.17/22.37    (7)   ~ (all_52_11 = e0)
% 152.17/22.37    (8)  op(e1, e1) = e3
% 152.17/22.37    (9)  op(e0, e0) = all_57_15
% 152.17/22.37    (10)   ~ (e3 = e2)
% 152.17/22.37  
% 152.17/22.37  Begin of proof
% 152.42/22.37  | 
% 152.42/22.37  | BETA: splitting (5) gives:
% 152.42/22.37  | 
% 152.42/22.37  | Case 1:
% 152.42/22.37  | | 
% 152.42/22.37  | |   (11)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 152.42/22.37  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 152.42/22.37  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.42/22.37  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.42/22.37  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 152.42/22.37  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 152.42/22.37  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.42/22.37  | |           $i(all_57_3))
% 152.42/22.37  | | 
% 152.42/22.37  | | REF_CLOSE: (2), (3), (4), (6), (9), (11) are inconsistent by sub-proof #627.
% 152.42/22.37  | | 
% 152.42/22.37  | Case 2:
% 152.42/22.37  | | 
% 152.42/22.37  | |   (12)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.42/22.37  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.42/22.37  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.42/22.37  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.42/22.37  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.42/22.37  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.42/22.37  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.37  | |           $i(all_57_7))
% 152.42/22.37  | | 
% 152.42/22.37  | | REF_CLOSE: (1), (2), (7), (8), (10), (12) are inconsistent by sub-proof
% 152.42/22.37  | |            #696.
% 152.42/22.37  | | 
% 152.42/22.37  | End of split
% 152.42/22.37  | 
% 152.42/22.37  End of proof
% 152.42/22.37  
% 152.42/22.37  Sub-proof #234 shows that the following formulas are inconsistent:
% 152.42/22.37  ----------------------------------------------------------------
% 152.42/22.37    (1)   ~ (all_52_2 = all_52_6)
% 152.42/22.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.38    (3)  op(e1, e3) = e1
% 152.42/22.38    (4)  op(e1, e2) = all_52_6
% 152.42/22.38    (5)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 152.42/22.38             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 152.42/22.38           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 152.42/22.38           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 152.42/22.38           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 152.42/22.38           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.42/22.38    (6)   ~ (all_52_8 = e3)
% 152.42/22.38    (7)  op(e3, e1) = all_52_8
% 152.42/22.38    (8)  op(e1, e3) = all_52_2
% 152.42/22.38  
% 152.42/22.38  Begin of proof
% 152.42/22.38  | 
% 152.42/22.38  | BETA: splitting (5) gives:
% 152.42/22.38  | 
% 152.42/22.38  | Case 1:
% 152.42/22.38  | | 
% 152.42/22.38  | |   (9)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 152.42/22.38  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 152.42/22.38  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 152.42/22.38  | | 
% 152.42/22.38  | | ALPHA: (9) implies:
% 152.42/22.38  | |   (10)  op(e1, e2) = e1
% 152.42/22.38  | | 
% 152.42/22.38  | | REF_CLOSE: (1), (2), (3), (4), (8), (10) are inconsistent by sub-proof #911.
% 152.42/22.38  | | 
% 152.42/22.38  | Case 2:
% 152.42/22.38  | | 
% 152.42/22.38  | |   (11)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 152.42/22.38  | |           = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1
% 152.42/22.38  | |         & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 152.42/22.38  | | 
% 152.42/22.38  | | ALPHA: (11) implies:
% 152.42/22.38  | |   (12)  op(e3, e1) = e3
% 152.42/22.38  | | 
% 152.42/22.38  | | REF_CLOSE: (2), (6), (7), (12) are inconsistent by sub-proof #1164.
% 152.42/22.38  | | 
% 152.42/22.38  | End of split
% 152.42/22.38  | 
% 152.42/22.38  End of proof
% 152.42/22.38  
% 152.42/22.38  Sub-proof #235 shows that the following formulas are inconsistent:
% 152.42/22.38  ----------------------------------------------------------------
% 152.42/22.38    (1)  op(e0, e1) = e1
% 152.42/22.38    (2)   ~ (e3 = e1)
% 152.42/22.38    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.42/22.38         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.42/22.38    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 152.42/22.38         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 152.42/22.38    (5)  op(e2, e2) = e1
% 152.42/22.38    (6)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.38         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.42/22.38    (7)  op(e0, e0) = all_10_2
% 152.42/22.38    (8)  op(e0, e2) = all_52_7
% 152.42/22.38    (9)   ~ (all_52_3 = all_52_7)
% 152.42/22.38    (10)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.38          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.42/22.38    (11)   ~ (all_10_2 = e1)
% 152.42/22.38    (12)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.42/22.38          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.38    (13)   ~ (e2 = e0)
% 152.42/22.38    (14)  all_56_14 = e1
% 152.42/22.38    (15)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.38          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.42/22.38    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.38            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.38    (17)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.42/22.38          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.38    (18)   ~ (all_52_9 = e3)
% 152.42/22.38    (19)  op(e0, e0) = e2
% 152.42/22.38    (20)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.42/22.38              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.42/22.38                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.42/22.38                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.42/22.38    (21)   ~ (all_52_13 = e2)
% 152.42/22.38    (22)   ~ (e3 = e0)
% 152.42/22.38    (23)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.42/22.38          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.42/22.38    (24)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 152.42/22.38          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.42/22.38    (25)   ~ (all_52_6 = e3)
% 152.42/22.38    (26)  op(e1, e2) = all_52_6
% 152.42/22.38    (27)  op(e2, e0) = all_52_13
% 152.42/22.38    (28)  all_56_3 = e1
% 152.42/22.38    (29)  op(e0, e3) = all_52_3
% 152.42/22.38    (30)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.38          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.42/22.38    (31)  op(e2, e1) = all_52_9
% 152.42/22.38    (32)   ~ (e1 = e0)
% 152.42/22.38    (33)  op(e1, e1) = e3
% 152.42/22.38    (34)   ~ (e3 = e2)
% 152.42/22.38    (35)  all_56_12 = e2
% 152.42/22.38    (36)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.42/22.38          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.42/22.38    (37)  op(e3, e3) = e3
% 152.42/22.38    (38)   ~ (e2 = e1)
% 152.42/22.38    (39)  op(e1, e3) = all_52_2
% 152.42/22.38    (40)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.38          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.38    (41)  op(e2, e3) = all_52_1
% 152.42/22.38  
% 152.42/22.38  Begin of proof
% 152.42/22.38  | 
% 152.42/22.38  | BETA: splitting (3) gives:
% 152.42/22.38  | 
% 152.42/22.38  | Case 1:
% 152.42/22.38  | | 
% 152.42/22.38  | |   (42)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 152.42/22.38  | |           e1)
% 152.42/22.38  | | 
% 152.42/22.38  | | BETA: splitting (42) gives:
% 152.42/22.38  | | 
% 152.42/22.38  | | Case 1:
% 152.42/22.38  | | | 
% 152.42/22.38  | | |   (43)  all_56_0 = e1 & op(e3, e3) = e1
% 152.42/22.38  | | | 
% 152.42/22.38  | | | ALPHA: (43) implies:
% 152.42/22.38  | | |   (44)  op(e3, e3) = e1
% 152.42/22.38  | | | 
% 152.42/22.38  | | | REF_CLOSE: (2), (16), (37), (44) are inconsistent by sub-proof #1178.
% 152.42/22.38  | | | 
% 152.42/22.38  | | Case 2:
% 152.42/22.38  | | | 
% 152.42/22.38  | | |   (45)  all_56_2 = e1 & op(e2, e3) = e1
% 152.42/22.38  | | | 
% 152.42/22.38  | | | ALPHA: (45) implies:
% 152.42/22.38  | | |   (46)  all_56_2 = e1
% 152.42/22.38  | | |   (47)  op(e2, e3) = e1
% 152.42/22.38  | | | 
% 152.42/22.38  | | | REF_CLOSE: (2), (5), (10), (13), (15), (16), (18), (22), (28), (30), (31),
% 152.42/22.38  | | |            (32), (34), (38), (41), (46), (47) are inconsistent by
% 152.42/22.38  | | |            sub-proof #273.
% 152.42/22.38  | | | 
% 152.42/22.38  | | End of split
% 152.42/22.38  | | 
% 152.42/22.38  | Case 2:
% 152.42/22.38  | | 
% 152.42/22.38  | |   (48)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 152.42/22.38  | |           e1)
% 152.42/22.38  | | 
% 152.42/22.38  | | BETA: splitting (48) gives:
% 152.42/22.38  | | 
% 152.42/22.38  | | Case 1:
% 152.42/22.38  | | | 
% 152.42/22.38  | | |   (49)  all_56_6 = e1 & op(e1, e3) = e1
% 152.42/22.38  | | | 
% 152.42/22.38  | | | ALPHA: (49) implies:
% 152.42/22.38  | | |   (50)  op(e1, e3) = e1
% 152.42/22.38  | | | 
% 152.42/22.38  | | | BETA: splitting (20) gives:
% 152.42/22.38  | | | 
% 152.42/22.38  | | | Case 1:
% 152.42/22.38  | | | | 
% 152.42/22.38  | | | |   (51)  all_56_15 = e0 & op(e0, e0) = e0
% 152.42/22.38  | | | | 
% 152.42/22.38  | | | | ALPHA: (51) implies:
% 152.42/22.38  | | | |   (52)  op(e0, e0) = e0
% 152.42/22.38  | | | | 
% 152.42/22.38  | | | | REF_CLOSE: (13), (16), (19), (52) are inconsistent by sub-proof #1043.
% 152.42/22.38  | | | | 
% 152.42/22.38  | | | Case 2:
% 152.42/22.38  | | | | 
% 152.42/22.38  | | | |   (53)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 152.42/22.38  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 152.42/22.38  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 152.42/22.38  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 152.42/22.38  | | | | 
% 152.42/22.38  | | | | ALPHA: (53) implies:
% 152.42/22.38  | | | |   (54)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 152.42/22.38  | | | |             e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.38  | | | | 
% 152.42/22.38  | | | | BETA: splitting (54) gives:
% 152.42/22.38  | | | | 
% 152.42/22.38  | | | | Case 1:
% 152.42/22.38  | | | | | 
% 152.42/22.38  | | | | |   (55)  all_56_12 = e0 & op(e0, e3) = e0
% 152.42/22.38  | | | | | 
% 152.42/22.38  | | | | | ALPHA: (55) implies:
% 152.42/22.38  | | | | |   (56)  op(e0, e3) = e0
% 152.42/22.38  | | | | | 
% 152.42/22.38  | | | | | REF_CLOSE: (8), (9), (13), (14), (16), (29), (32), (35), (54), (56)
% 152.42/22.38  | | | | |            are inconsistent by sub-proof #1117.
% 152.42/22.38  | | | | | 
% 152.42/22.38  | | | | Case 2:
% 152.42/22.38  | | | | | 
% 152.42/22.38  | | | | |   (57)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 152.42/22.38  | | | | |             e1) = e0)
% 152.42/22.38  | | | | | 
% 152.42/22.38  | | | | | BETA: splitting (57) gives:
% 152.42/22.38  | | | | | 
% 152.42/22.38  | | | | | Case 1:
% 152.42/22.38  | | | | | | 
% 152.42/22.38  | | | | | |   (58)  all_56_13 = e0 & op(e0, e2) = e0
% 152.42/22.38  | | | | | | 
% 152.42/22.38  | | | | | | ALPHA: (58) implies:
% 152.42/22.38  | | | | | |   (59)  all_56_13 = e0
% 152.42/22.38  | | | | | |   (60)  op(e0, e2) = e0
% 152.42/22.38  | | | | | | 
% 152.42/22.38  | | | | | | BETA: splitting (23) gives:
% 152.42/22.38  | | | | | | 
% 152.42/22.38  | | | | | | Case 1:
% 152.42/22.38  | | | | | | | 
% 152.42/22.38  | | | | | | |   (61)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 &
% 152.42/22.38  | | | | | | |           op(e2, e3) = e0)
% 152.42/22.38  | | | | | | | 
% 152.42/22.38  | | | | | | | BETA: splitting (61) gives:
% 152.42/22.38  | | | | | | | 
% 152.42/22.38  | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | |   (62)  all_56_0 = e0 & op(e3, e3) = e0
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | | ALPHA: (62) implies:
% 152.42/22.38  | | | | | | | |   (63)  op(e3, e3) = e0
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | | REF_CLOSE: (16), (22), (37), (63) are inconsistent by sub-proof
% 152.42/22.38  | | | | | | | |            #1141.
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | |   (64)  all_56_2 = e0 & op(e2, e3) = e0
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | | ALPHA: (64) implies:
% 152.42/22.38  | | | | | | | |   (65)  all_56_2 = e0
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | | BETA: splitting (40) gives:
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | 
% 152.42/22.38  | | | | | | | | |   (66)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 &
% 152.42/22.38  | | | | | | | | |           op(e2, e2) = e3)
% 152.42/22.38  | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | BETA: splitting (66) gives:
% 152.42/22.38  | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | |   (67)  all_56_1 = e3 & op(e3, e2) = e3
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | ALPHA: (67) implies:
% 152.42/22.38  | | | | | | | | | |   (68)  all_56_1 = e3
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | BETA: splitting (6) gives:
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | |   (69)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 152.42/22.38  | | | | | | | | | | |           & op(e2, e2) = e2)
% 152.42/22.38  | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | BETA: splitting (69) gives:
% 152.42/22.38  | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | |   (70)  all_56_1 = e2 & op(e3, e2) = e2
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | REF_CLOSE: (34), (68), (70) are inconsistent by sub-proof
% 152.42/22.38  | | | | | | | | | | | |            #907.
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | |   (71)  all_56_3 = e2 & op(e2, e2) = e2
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | ALPHA: (71) implies:
% 152.42/22.38  | | | | | | | | | | | |   (72)  op(e2, e2) = e2
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | REF_CLOSE: (5), (16), (38), (72) are inconsistent by
% 152.42/22.38  | | | | | | | | | | | |            sub-proof #1158.
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | |   (73)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 152.42/22.38  | | | | | | | | | | |           e2 & op(e0, e2) = e2)
% 152.42/22.38  | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | BETA: splitting (73) gives:
% 152.42/22.38  | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | |   (74)  all_56_7 = e2 & op(e1, e2) = e2
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | ALPHA: (74) implies:
% 152.42/22.38  | | | | | | | | | | | |   (75)  all_56_7 = e2
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | BETA: splitting (15) gives:
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | |   (76)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 152.42/22.38  | | | | | | | | | | | | |           & op(e2, e2) = e2)
% 152.42/22.38  | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | BETA: splitting (76) gives:
% 152.42/22.38  | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | |   (77)  all_56_2 = e2 & op(e2, e3) = e2
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | REF_CLOSE: (13), (65), (77) are inconsistent by sub-proof
% 152.42/22.38  | | | | | | | | | | | | | |            #994.
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | |   (78)  all_56_3 = e2 & op(e2, e2) = e2
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | ALPHA: (78) implies:
% 152.42/22.38  | | | | | | | | | | | | | |   (79)  op(e2, e2) = e2
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (38), (79) are inconsistent by
% 152.42/22.38  | | | | | | | | | | | | | |            sub-proof #1158.
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | |   (80)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 152.42/22.38  | | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 152.42/22.38  | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | BETA: splitting (80) gives:
% 152.42/22.38  | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | |   (81)  all_56_5 = e2 & op(e2, e1) = e2
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | ALPHA: (81) implies:
% 152.42/22.38  | | | | | | | | | | | | | |   (82)  all_56_5 = e2
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | |   (83)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 152.42/22.38  | | | | | | | | | | | | | | |           & op(e2, e1) = e0)
% 152.42/22.38  | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | BETA: splitting (83) gives:
% 152.42/22.38  | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | |   (84)  all_56_4 = e0 & op(e3, e1) = e0
% 152.42/22.38  | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | ALPHA: (84) implies:
% 152.42/22.38  | | | | | | | | | | | | | | | |   (85)  all_56_4 = e0
% 152.42/22.38  | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | BETA: splitting (24) gives:
% 152.42/22.38  | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | |   (86)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 152.42/22.38  | | | | | | | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 152.42/22.38  | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | BETA: splitting (86) gives:
% 152.42/22.38  | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | |   (87)  all_56_9 = e1 & op(e3, e0) = e1
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 152.42/22.38  | | | | | | | | | | | | | | | | | |   (88)  all_56_9 = e1
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | |   (89)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2
% 152.42/22.38  | | | | | | | | | | | | | | | | | | |           & op(e3, e2) = e2)
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |   (90)  all_56_0 = e2 & op(e3, e3) = e2
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | ALPHA: (90) implies:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |   (91)  op(e3, e3) = e2
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (34), (37), (91) are inconsistent by
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |            sub-proof #1085.
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |   (92)  all_56_1 = e2 & op(e3, e2) = e2
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (68), (92) are inconsistent by sub-proof
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |            #907.
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | |   (93)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2
% 152.42/22.38  | | | | | | | | | | | | | | | | | | |           & op(e3, e0) = e2)
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | BETA: splitting (93) gives:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |   (94)  all_56_4 = e2 & op(e3, e1) = e2
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (85), (94) are inconsistent by sub-proof
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |            #949.
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |   (95)  all_56_9 = e2 & op(e3, e0) = e2
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |   (96)  all_56_9 = e2
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (88), (96) imply:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |   (97)  e2 = e1
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (82), (97) imply:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |   (98)  all_56_5 = e1
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (13), (14), (16), (17), (22), (32), (33),
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |            (34), (38), (98) are inconsistent by sub-proof
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | |            #247.
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | |   (99)  all_56_10 = e1 & op(e2, e0) = e1
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 152.42/22.38  | | | | | | | | | | | | | | | | | |   (100)  all_56_10 = e1
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (13), (15), (16), (18), (22),
% 152.42/22.38  | | | | | | | | | | | | | | | | | |            (28), (30), (31), (32), (34), (38), (100) are
% 152.42/22.38  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #264.
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | |   (101)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 152.42/22.38  | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 152.42/22.38  | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 152.42/22.38  | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | |   (102)  all_56_11 = e1 & op(e1, e0) = e1
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 152.42/22.38  | | | | | | | | | | | | | | | | | |   (103)  all_56_11 = e1
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (22), (32), (33), (36), (39), (50),
% 152.42/22.38  | | | | | | | | | | | | | | | | | |            (75), (103) are inconsistent by sub-proof #237.
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | |   (104)  all_56_15 = e1 & op(e0, e0) = e1
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | ALPHA: (104) implies:
% 152.42/22.38  | | | | | | | | | | | | | | | | | |   (105)  op(e0, e0) = e1
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (11), (16), (105) are inconsistent by
% 152.42/22.38  | | | | | | | | | | | | | | | | | |            sub-proof #1116.
% 152.42/22.38  | | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | |   (106)  all_56_5 = e0 & op(e2, e1) = e0
% 152.42/22.38  | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 152.42/22.38  | | | | | | | | | | | | | | | |   (107)  all_56_5 = e0
% 152.42/22.38  | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (82), (107) are inconsistent by sub-proof
% 152.42/22.38  | | | | | | | | | | | | | | | |            #509.
% 152.42/22.38  | | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | |   (108)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 152.42/22.38  | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 152.42/22.38  | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (22), (32), (33), (108) are
% 152.42/22.38  | | | | | | | | | | | | | | |            inconsistent by sub-proof #236.
% 152.42/22.38  | | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | |   (109)  all_56_10 = e2 & op(e2, e0) = e2
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | ALPHA: (109) implies:
% 152.42/22.38  | | | | | | | | | | | | | |   (110)  op(e2, e0) = e2
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | | REF_CLOSE: (16), (21), (27), (110) are inconsistent by
% 152.42/22.38  | | | | | | | | | | | | | |            sub-proof #1156.
% 152.42/22.38  | | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | |   (111)  all_56_13 = e2 & op(e0, e2) = e2
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | ALPHA: (111) implies:
% 152.42/22.38  | | | | | | | | | | | |   (112)  all_56_13 = e2
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | COMBINE_EQS: (59), (112) imply:
% 152.42/22.38  | | | | | | | | | | | |   (113)  e2 = e0
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | REDUCE: (13), (113) imply:
% 152.42/22.38  | | | | | | | | | | | |   (114)  $false
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | | CLOSE: (114) is inconsistent.
% 152.42/22.38  | | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | |   (115)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | REF_CLOSE: (2), (28), (115) are inconsistent by sub-proof
% 152.42/22.38  | | | | | | | | | |            #274.
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | 
% 152.42/22.38  | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | 
% 152.42/22.38  | | | | | | | | |   (116)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 &
% 152.42/22.38  | | | | | | | | |            op(e0, e2) = e3)
% 152.42/22.38  | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | BETA: splitting (116) gives:
% 152.42/22.38  | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | |   (117)  all_56_7 = e3 & op(e1, e2) = e3
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | REF_CLOSE: (16), (25), (26), (117) are inconsistent by
% 152.42/22.38  | | | | | | | | | |            sub-proof #925.
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | |   (118)  all_56_13 = e3 & op(e0, e2) = e3
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | ALPHA: (118) implies:
% 152.42/22.38  | | | | | | | | | |   (119)  all_56_13 = e3
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | | REF_CLOSE: (22), (59), (119) are inconsistent by sub-proof
% 152.42/22.38  | | | | | | | | | |            #1094.
% 152.42/22.38  | | | | | | | | | | 
% 152.42/22.38  | | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | | 
% 152.42/22.38  | | | | | | | | End of split
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | End of split
% 152.42/22.38  | | | | | | | 
% 152.42/22.38  | | | | | | Case 2:
% 152.42/22.38  | | | | | | | 
% 152.42/22.38  | | | | | | |   (120)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 &
% 152.42/22.38  | | | | | | |            op(e0, e3) = e0)
% 152.42/22.38  | | | | | | | 
% 152.42/22.38  | | | | | | | BETA: splitting (120) gives:
% 152.42/22.38  | | | | | | | 
% 152.42/22.38  | | | | | | | Case 1:
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | |   (121)  all_56_6 = e0 & op(e1, e3) = e0
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | | ALPHA: (121) implies:
% 152.42/22.38  | | | | | | | |   (122)  op(e1, e3) = e0
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | | REF_CLOSE: (16), (32), (39), (50), (122) are inconsistent by
% 152.42/22.38  | | | | | | | |            sub-proof #1127.
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | Case 2:
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | |   (123)  all_56_12 = e0 & op(e0, e3) = e0
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | | ALPHA: (123) implies:
% 152.42/22.38  | | | | | | | |   (124)  op(e0, e3) = e0
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | | REF_CLOSE: (8), (9), (16), (29), (60), (124) are inconsistent by
% 152.42/22.38  | | | | | | | |            sub-proof #1123.
% 152.42/22.38  | | | | | | | | 
% 152.42/22.38  | | | | | | | End of split
% 152.42/22.38  | | | | | | | 
% 152.42/22.38  | | | | | | End of split
% 152.42/22.38  | | | | | | 
% 152.42/22.38  | | | | | Case 2:
% 152.42/22.38  | | | | | | 
% 152.42/22.38  | | | | | |   (125)  all_56_14 = e0 & op(e0, e1) = e0
% 152.42/22.38  | | | | | | 
% 152.42/22.38  | | | | | | ALPHA: (125) implies:
% 152.42/22.38  | | | | | |   (126)  op(e0, e1) = e0
% 152.42/22.38  | | | | | | 
% 152.42/22.38  | | | | | | REF_CLOSE: (1), (16), (32), (126) are inconsistent by sub-proof
% 152.42/22.38  | | | | | |            #899.
% 152.42/22.38  | | | | | | 
% 152.42/22.38  | | | | | End of split
% 152.42/22.38  | | | | | 
% 152.42/22.38  | | | | End of split
% 152.42/22.38  | | | | 
% 152.42/22.38  | | | End of split
% 152.42/22.38  | | | 
% 152.42/22.38  | | Case 2:
% 152.42/22.38  | | | 
% 152.42/22.38  | | |   (127)  all_56_12 = e1 & op(e0, e3) = e1
% 152.42/22.38  | | | 
% 152.42/22.38  | | | REF_CLOSE: (35), (38), (127) are inconsistent by sub-proof #789.
% 152.42/22.38  | | | 
% 152.42/22.38  | | End of split
% 152.42/22.38  | | 
% 152.42/22.38  | End of split
% 152.42/22.38  | 
% 152.42/22.38  End of proof
% 152.42/22.38  
% 152.42/22.38  Sub-proof #236 shows that the following formulas are inconsistent:
% 152.42/22.38  ----------------------------------------------------------------
% 152.42/22.38    (1)  op(e0, e1) = e1
% 152.42/22.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.38    (3)   ~ (e3 = e0)
% 152.42/22.38    (4)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.38    (5)   ~ (e1 = e0)
% 152.42/22.38    (6)  op(e1, e1) = e3
% 152.42/22.38  
% 152.42/22.38  Begin of proof
% 152.42/22.38  | 
% 152.42/22.38  | BETA: splitting (4) gives:
% 152.42/22.38  | 
% 152.42/22.38  | Case 1:
% 152.42/22.38  | | 
% 152.42/22.38  | |   (7)  all_56_8 = e0 & op(e1, e1) = e0
% 152.42/22.38  | | 
% 152.42/22.38  | | ALPHA: (7) implies:
% 152.42/22.38  | |   (8)  op(e1, e1) = e0
% 152.42/22.38  | | 
% 152.42/22.38  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #896.
% 152.42/22.38  | | 
% 152.42/22.38  | Case 2:
% 152.42/22.38  | | 
% 152.42/22.38  | |   (9)  all_56_14 = e0 & op(e0, e1) = e0
% 152.42/22.38  | | 
% 152.42/22.38  | | ALPHA: (9) implies:
% 152.42/22.38  | |   (10)  op(e0, e1) = e0
% 152.42/22.38  | | 
% 152.42/22.38  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #899.
% 152.42/22.38  | | 
% 152.42/22.38  | End of split
% 152.42/22.38  | 
% 152.42/22.38  End of proof
% 152.42/22.38  
% 152.42/22.38  Sub-proof #237 shows that the following formulas are inconsistent:
% 152.42/22.38  ----------------------------------------------------------------
% 152.42/22.38    (1)  all_56_11 = e1
% 152.42/22.38    (2)   ~ (e2 = e0)
% 152.42/22.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.38    (4)  op(e1, e3) = e1
% 152.42/22.38    (5)   ~ (e3 = e0)
% 152.42/22.38    (6)   ~ (e1 = e0)
% 152.42/22.38    (7)  all_56_7 = e2
% 152.42/22.38    (8)  op(e1, e1) = e3
% 152.42/22.38    (9)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.42/22.38         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.42/22.38    (10)  op(e1, e3) = all_52_2
% 152.42/22.38  
% 152.42/22.38  Begin of proof
% 152.42/22.38  | 
% 152.42/22.38  | BETA: splitting (9) gives:
% 152.42/22.38  | 
% 152.42/22.38  | Case 1:
% 152.42/22.38  | | 
% 152.42/22.38  | |   (11)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) =
% 152.42/22.38  | |           e0)
% 152.42/22.38  | | 
% 152.42/22.38  | | BETA: splitting (11) gives:
% 152.42/22.38  | | 
% 152.42/22.38  | | Case 1:
% 152.42/22.38  | | | 
% 152.42/22.38  | | |   (12)  all_56_6 = e0 & op(e1, e3) = e0
% 152.42/22.38  | | | 
% 152.42/22.38  | | | ALPHA: (12) implies:
% 152.42/22.38  | | |   (13)  op(e1, e3) = e0
% 152.42/22.38  | | | 
% 152.42/22.39  | | | REF_CLOSE: (3), (4), (6), (10), (13) are inconsistent by sub-proof #1127.
% 152.42/22.39  | | | 
% 152.42/22.39  | | Case 2:
% 152.42/22.39  | | | 
% 152.42/22.39  | | |   (14)  all_56_7 = e0 & op(e1, e2) = e0
% 152.42/22.39  | | | 
% 152.42/22.39  | | | ALPHA: (14) implies:
% 152.42/22.39  | | |   (15)  all_56_7 = e0
% 152.42/22.39  | | | 
% 152.42/22.39  | | | REF_CLOSE: (2), (7), (15) are inconsistent by sub-proof #483.
% 152.42/22.39  | | | 
% 152.42/22.39  | | End of split
% 152.42/22.39  | | 
% 152.42/22.39  | Case 2:
% 152.42/22.39  | | 
% 152.42/22.39  | |   (16)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 152.42/22.39  | |           e0)
% 152.42/22.39  | | 
% 152.42/22.39  | | REF_CLOSE: (1), (3), (5), (6), (8), (16) are inconsistent by sub-proof #362.
% 152.42/22.39  | | 
% 152.42/22.39  | End of split
% 152.42/22.39  | 
% 152.42/22.39  End of proof
% 152.42/22.39  
% 152.42/22.39  Sub-proof #238 shows that the following formulas are inconsistent:
% 152.42/22.39  ----------------------------------------------------------------
% 152.42/22.39    (1)   ~ (all_52_14 = e2)
% 152.42/22.39    (2)   ~ (e2 = e0)
% 152.42/22.39    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.39    (4)  all_56_6 = e1
% 152.42/22.39    (5)  op(e1, e0) = all_52_14
% 152.42/22.39    (6)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.42/22.39         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.42/22.39    (7)  op(e1, e1) = e3
% 152.42/22.39    (8)   ~ (e3 = e2)
% 152.42/22.39    (9)  all_56_7 = e0
% 152.42/22.39    (10)   ~ (e2 = e1)
% 152.42/22.39  
% 152.42/22.39  Begin of proof
% 152.42/22.39  | 
% 152.42/22.39  | BETA: splitting (6) gives:
% 152.42/22.39  | 
% 152.42/22.39  | Case 1:
% 152.42/22.39  | | 
% 152.42/22.39  | |   (11)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 152.42/22.39  | |           e2)
% 152.42/22.39  | | 
% 152.42/22.39  | | BETA: splitting (11) gives:
% 152.42/22.39  | | 
% 152.42/22.39  | | Case 1:
% 152.42/22.39  | | | 
% 152.42/22.39  | | |   (12)  all_56_6 = e2 & op(e1, e3) = e2
% 152.42/22.39  | | | 
% 152.42/22.39  | | | ALPHA: (12) implies:
% 152.42/22.39  | | |   (13)  all_56_6 = e2
% 152.42/22.39  | | | 
% 152.42/22.39  | | | REF_CLOSE: (4), (10), (13) are inconsistent by sub-proof #1172.
% 152.42/22.39  | | | 
% 152.42/22.39  | | Case 2:
% 152.42/22.39  | | | 
% 152.42/22.39  | | |   (14)  all_56_7 = e2 & op(e1, e2) = e2
% 152.42/22.39  | | | 
% 152.42/22.39  | | | REF_CLOSE: (2), (9), (14) are inconsistent by sub-proof #740.
% 152.42/22.39  | | | 
% 152.42/22.39  | | End of split
% 152.42/22.39  | | 
% 152.42/22.39  | Case 2:
% 152.42/22.39  | | 
% 152.42/22.39  | |   (15)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 152.42/22.39  | |           e2)
% 152.42/22.39  | | 
% 152.42/22.39  | | REF_CLOSE: (1), (3), (5), (7), (8), (15) are inconsistent by sub-proof #289.
% 152.42/22.39  | | 
% 152.42/22.39  | End of split
% 152.42/22.39  | 
% 152.42/22.39  End of proof
% 152.42/22.39  
% 152.42/22.39  Sub-proof #239 shows that the following formulas are inconsistent:
% 152.42/22.39  ----------------------------------------------------------------
% 152.42/22.39    (1)   ~ (e3 = e1)
% 152.42/22.39    (2)  op(e2, e2) = e1
% 152.42/22.39    (3)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.39         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.42/22.39    (4)   ~ (e2 = e0)
% 152.42/22.39    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.39    (6)   ~ (all_52_1 = e3)
% 152.42/22.39    (7)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 152.42/22.39    (8)   ~ (e3 = e0)
% 152.42/22.39    (9)   ~ (all_52_6 = e3)
% 152.42/22.39    (10)  op(e1, e2) = all_52_6
% 152.42/22.39    (11)  all_56_3 = e1
% 152.42/22.39    (12)   ~ (e1 = e0)
% 152.42/22.39    (13)  all_56_13 = e3
% 152.42/22.39    (14)   ~ (e3 = e2)
% 152.42/22.39    (15)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.39          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.42/22.39    (16)   ~ (e2 = e1)
% 152.42/22.39    (17)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.39          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.39    (18)  op(e2, e3) = all_52_1
% 152.42/22.39  
% 152.42/22.39  Begin of proof
% 152.42/22.39  | 
% 152.42/22.39  | BETA: splitting (7) gives:
% 152.42/22.39  | 
% 152.42/22.39  | Case 1:
% 152.42/22.39  | | 
% 152.42/22.39  | |   (19)  all_56_2 = e3 & op(e2, e3) = e3
% 152.42/22.39  | | 
% 152.42/22.39  | | REF_CLOSE: (5), (6), (18), (19) are inconsistent by sub-proof #917.
% 152.42/22.39  | | 
% 152.42/22.39  | Case 2:
% 152.42/22.39  | | 
% 152.42/22.39  | |   (20)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.39  | | 
% 152.42/22.39  | | ALPHA: (20) implies:
% 152.42/22.39  | |   (21)  all_56_3 = e3
% 152.42/22.39  | | 
% 152.42/22.39  | | COMBINE_EQS: (11), (21) imply:
% 152.42/22.39  | |   (22)  e3 = e1
% 152.42/22.39  | | 
% 152.42/22.39  | | COMBINE_EQS: (13), (22) imply:
% 152.42/22.39  | |   (23)  all_56_13 = e1
% 152.42/22.39  | | 
% 152.42/22.39  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (14), (15),
% 152.42/22.39  | |            (16), (17), (23) are inconsistent by sub-proof #260.
% 152.42/22.39  | | 
% 152.42/22.39  | End of split
% 152.42/22.39  | 
% 152.42/22.39  End of proof
% 152.42/22.39  
% 152.42/22.39  Sub-proof #240 shows that the following formulas are inconsistent:
% 152.42/22.39  ----------------------------------------------------------------
% 152.42/22.39    (1)  op(e0, e1) = all_52_11
% 152.42/22.39    (2)  op(e0, e2) = all_52_7
% 152.42/22.39    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.39    (4)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 152.42/22.39             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.42/22.39           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.42/22.39           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.42/22.39             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.42/22.39           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.42/22.39           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.42/22.39           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 152.42/22.39           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.42/22.39           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 152.42/22.39           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.42/22.39         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.42/22.39             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.39           $i(all_57_7))
% 152.42/22.39    (5)   ~ (all_52_11 = e0)
% 152.42/22.39    (6)  op(e0, e3) = all_52_3
% 152.42/22.39    (7)   ~ (all_52_7 = e0)
% 152.42/22.39    (8)  op(e1, e1) = e3
% 152.42/22.39    (9)   ~ (e3 = e2)
% 152.42/22.39    (10)   ~ (all_52_3 = e0)
% 152.42/22.39  
% 152.42/22.39  Begin of proof
% 152.42/22.39  | 
% 152.42/22.39  | BETA: splitting (4) gives:
% 152.42/22.39  | 
% 152.42/22.39  | Case 1:
% 152.42/22.39  | | 
% 152.42/22.39  | |   (11)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 152.42/22.39  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 152.42/22.39  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.42/22.39  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.42/22.39  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 152.42/22.39  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 152.42/22.39  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.42/22.39  | |           $i(all_57_3))
% 152.42/22.39  | | 
% 152.42/22.39  | | REF_CLOSE: (2), (3), (6), (7), (10), (11) are inconsistent by sub-proof
% 152.42/22.39  | |            #1035.
% 152.42/22.39  | | 
% 152.42/22.39  | Case 2:
% 152.42/22.39  | | 
% 152.42/22.39  | |   (12)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.42/22.39  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.42/22.39  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.42/22.39  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.42/22.39  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.42/22.39  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.42/22.39  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.39  | |           $i(all_57_7))
% 152.42/22.39  | | 
% 152.42/22.39  | | REF_CLOSE: (1), (3), (5), (8), (9), (12) are inconsistent by sub-proof #696.
% 152.42/22.39  | | 
% 152.42/22.39  | End of split
% 152.42/22.39  | 
% 152.42/22.39  End of proof
% 152.42/22.39  
% 152.42/22.39  Sub-proof #241 shows that the following formulas are inconsistent:
% 152.42/22.39  ----------------------------------------------------------------
% 152.42/22.39    (1)  op(e0, e1) = all_52_11
% 152.42/22.39    (2)  all_56_8 = e3
% 152.42/22.39    (3)   ~ (all_52_7 = all_52_11)
% 152.42/22.39    (4)   ~ (e3 = e1)
% 152.42/22.39    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 152.42/22.39         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 152.42/22.39    (6)  op(e2, e2) = e1
% 152.42/22.39    (7)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.39         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.42/22.39    (8)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 152.42/22.39         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.42/22.39    (9)  op(e0, e0) = all_10_2
% 152.42/22.39    (10)   ~ (all_52_3 = all_52_7)
% 152.42/22.39    (11)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.39          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.42/22.39    (12)   ~ (all_10_2 = e1)
% 152.42/22.39    (13)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.42/22.39          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.39    (14)   ~ (e2 = e0)
% 152.42/22.39    (15)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 152.42/22.39            all_57_12 & $i(all_57_12))
% 152.42/22.39    (16)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.39          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.42/22.39    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.39            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.39    (18)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.42/22.39          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.42/22.39    (19)   ~ (all_52_1 = all_52_13)
% 152.42/22.39    (20)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.42/22.39          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.42/22.39    (21)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.42/22.39          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.39    (22)   ~ (all_52_3 = all_52_11)
% 152.42/22.39    (23)   ~ (all_52_9 = e3)
% 152.42/22.39    (24)   ~ (all_52_1 = all_52_9)
% 152.42/22.39    (25)  op(e1, e0) = all_52_14
% 152.42/22.39    (26)   ~ (e3 = e0)
% 152.42/22.39    (27)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.42/22.39          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.42/22.39    (28)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 152.42/22.39          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.42/22.39    (29)  all_57_15 = e0
% 152.42/22.39    (30)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.42/22.39          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.42/22.39    (31)   ~ (all_52_6 = e3)
% 152.42/22.39    (32)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 152.42/22.39          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 152.42/22.39    (33)  op(e3, e3) = e1
% 152.42/22.39    (34)  op(e1, e2) = all_52_6
% 152.42/22.39    (35)  op(e2, e0) = all_52_13
% 152.42/22.39    (36)  all_56_3 = e1
% 152.42/22.39    (37)   ~ (all_52_1 = all_52_3)
% 152.42/22.39    (38)  op(e0, e3) = all_52_3
% 152.42/22.39    (39)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 152.42/22.39    (40)  all_54_12 = all_52_3
% 152.42/22.39    (41)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.39          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.42/22.39    (42)  op(e2, e1) = all_52_9
% 152.42/22.39    (43)   ~ (e1 = e0)
% 152.42/22.39    (44)   ~ (all_52_1 = e1)
% 152.42/22.39    (45)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.42/22.39          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.42/22.39    (46)  op(e1, e1) = e3
% 152.42/22.39    (47)   ~ (e3 = e2)
% 152.42/22.39    (48)   ~ (all_52_8 = e3)
% 152.42/22.39    (49)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.39          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.42/22.39    (50)   ~ (all_52_7 = all_10_2)
% 152.42/22.39    (51)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.42/22.39          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.42/22.39    (52)  all_54_13 = all_52_7
% 152.42/22.39    (53)  op(e3, e1) = all_52_8
% 152.42/22.39    (54)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.42/22.39          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.42/22.39    (55)   ~ (all_52_3 = all_10_2)
% 152.42/22.39    (56)   ~ (all_52_6 = all_52_7)
% 152.42/22.39    (57)   ~ (e2 = e1)
% 152.42/22.39    (58)  op(e0, e0) = e0
% 152.42/22.39    (59)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.42/22.39    (60)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.42/22.39              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.42/22.39            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.42/22.39            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.42/22.39            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.42/22.39            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.42/22.39            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.42/22.39            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.39            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.42/22.39            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.42/22.39            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.42/22.39            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.42/22.39            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.39            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.42/22.39            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.42/22.39            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.39            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.42/22.39            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.42/22.39            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.42/22.39            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.42/22.39            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.42/22.39            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.39            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.42/22.39            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.42/22.39            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.42/22.39            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.42/22.39            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.42/22.39            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.42/22.39            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.42/22.39            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.42/22.39            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.42/22.39            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.42/22.39            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.42/22.39            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.42/22.39            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.42/22.39            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.42/22.39            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.39            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.42/22.39            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.42/22.39            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.39            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.42/22.39            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.42/22.39            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.42/22.39            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.42/22.39            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.42/22.39            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.42/22.39            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.42/22.39            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.42/22.39              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.42/22.39            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.42/22.39            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.42/22.39              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.42/22.39            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.42/22.39            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.42/22.39                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.42/22.39                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.42/22.39                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.42/22.39                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.42/22.39                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.42/22.39                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.42/22.39                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.42/22.39              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.42/22.39                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.42/22.39                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.42/22.39                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.42/22.39                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.42/22.39                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.42/22.39                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.39                $i(all_57_7))))
% 152.42/22.39    (61)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.39          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.39    (62)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.42/22.39          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.42/22.39            e1)
% 152.42/22.39    (63)  op(e2, e3) = all_52_1
% 152.42/22.39  
% 152.42/22.39  Begin of proof
% 152.42/22.39  | 
% 152.42/22.39  | BETA: splitting (28) gives:
% 152.42/22.39  | 
% 152.42/22.39  | Case 1:
% 152.42/22.39  | | 
% 152.42/22.39  | |   (64)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 152.42/22.39  | |           e1)
% 152.42/22.39  | | 
% 152.42/22.39  | | BETA: splitting (64) gives:
% 152.42/22.39  | | 
% 152.42/22.39  | | Case 1:
% 152.42/22.39  | | | 
% 152.42/22.39  | | |   (65)  all_56_9 = e1 & op(e3, e0) = e1
% 152.42/22.39  | | | 
% 152.42/22.39  | | | ALPHA: (65) implies:
% 152.42/22.39  | | |   (66)  all_56_9 = e1
% 152.42/22.39  | | | 
% 152.42/22.39  | | | BETA: splitting (51) gives:
% 152.42/22.39  | | | 
% 152.42/22.39  | | | Case 1:
% 152.42/22.39  | | | | 
% 152.42/22.39  | | | |   (67)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1)
% 152.42/22.39  | | | |           = e1)
% 152.42/22.39  | | | | 
% 152.42/22.39  | | | | BETA: splitting (67) gives:
% 152.42/22.39  | | | | 
% 152.42/22.39  | | | | Case 1:
% 152.42/22.39  | | | | | 
% 152.42/22.39  | | | | |   (68)  all_56_4 = e1 & op(e3, e1) = e1
% 152.42/22.39  | | | | | 
% 152.42/22.39  | | | | | ALPHA: (68) implies:
% 152.42/22.39  | | | | |   (69)  all_56_4 = e1
% 152.42/22.39  | | | | | 
% 152.42/22.39  | | | | | BETA: splitting (62) gives:
% 152.42/22.39  | | | | | 
% 152.42/22.39  | | | | | Case 1:
% 152.42/22.39  | | | | | | 
% 152.42/22.39  | | | | | |   (70)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 &
% 152.42/22.39  | | | | | |           op(e0, e2) = e1)
% 152.42/22.39  | | | | | | 
% 152.42/22.39  | | | | | | BETA: splitting (70) gives:
% 152.42/22.39  | | | | | | 
% 152.42/22.39  | | | | | | Case 1:
% 152.42/22.39  | | | | | | | 
% 152.42/22.39  | | | | | | |   (71)  all_56_12 = e1 & op(e0, e3) = e1
% 152.42/22.39  | | | | | | | 
% 152.42/22.39  | | | | | | | ALPHA: (71) implies:
% 152.42/22.39  | | | | | | |   (72)  all_56_12 = e1
% 152.42/22.39  | | | | | | | 
% 152.42/22.39  | | | | | | | REF_CLOSE: (2), (4), (8), (14), (17), (20), (26), (27), (32),
% 152.42/22.39  | | | | | | |            (33), (43), (45), (46), (47), (54), (57), (72) are
% 152.42/22.39  | | | | | | |            inconsistent by sub-proof #569.
% 152.42/22.39  | | | | | | | 
% 152.42/22.39  | | | | | | Case 2:
% 152.42/22.39  | | | | | | | 
% 152.42/22.39  | | | | | | |   (73)  all_56_13 = e1 & op(e0, e2) = e1
% 152.42/22.39  | | | | | | | 
% 152.42/22.39  | | | | | | | ALPHA: (73) implies:
% 152.42/22.39  | | | | | | |   (74)  all_56_13 = e1
% 152.42/22.39  | | | | | | | 
% 152.42/22.39  | | | | | | | BETA: splitting (61) gives:
% 152.42/22.39  | | | | | | | 
% 152.42/22.39  | | | | | | | Case 1:
% 152.42/22.39  | | | | | | | | 
% 152.42/22.39  | | | | | | | |   (75)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 &
% 152.42/22.39  | | | | | | | |           op(e2, e2) = e3)
% 152.42/22.39  | | | | | | | | 
% 152.42/22.39  | | | | | | | | BETA: splitting (75) gives:
% 152.42/22.39  | | | | | | | | 
% 152.42/22.39  | | | | | | | | Case 1:
% 152.42/22.39  | | | | | | | | | 
% 152.42/22.39  | | | | | | | | |   (76)  all_56_1 = e3 & op(e3, e2) = e3
% 152.42/22.39  | | | | | | | | | 
% 152.42/22.39  | | | | | | | | | ALPHA: (76) implies:
% 152.42/22.39  | | | | | | | | |   (77)  all_56_1 = e3
% 152.42/22.39  | | | | | | | | | 
% 152.42/22.39  | | | | | | | | | BETA: splitting (30) gives:
% 152.42/22.39  | | | | | | | | | 
% 152.42/22.39  | | | | | | | | | Case 1:
% 152.42/22.39  | | | | | | | | | | 
% 152.42/22.39  | | | | | | | | | |   (78)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 &
% 152.42/22.39  | | | | | | | | | |           op(e3, e2) = e0)
% 152.42/22.39  | | | | | | | | | | 
% 152.42/22.39  | | | | | | | | | | REF_CLOSE: (17), (26), (33), (43), (77), (78) are
% 152.42/22.39  | | | | | | | | | |            inconsistent by sub-proof #951.
% 152.42/22.39  | | | | | | | | | | 
% 152.42/22.39  | | | | | | | | | Case 2:
% 152.42/22.39  | | | | | | | | | | 
% 152.42/22.39  | | | | | | | | | |   (79)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 &
% 152.42/22.39  | | | | | | | | | |           op(e3, e0) = e0)
% 152.42/22.39  | | | | | | | | | | 
% 152.42/22.39  | | | | | | | | | | BETA: splitting (79) gives:
% 152.42/22.40  | | | | | | | | | | 
% 152.42/22.40  | | | | | | | | | | Case 1:
% 152.42/22.40  | | | | | | | | | | | 
% 152.42/22.40  | | | | | | | | | | |   (80)  all_56_4 = e0 & op(e3, e1) = e0
% 152.42/22.40  | | | | | | | | | | | 
% 152.42/22.40  | | | | | | | | | | | ALPHA: (80) implies:
% 152.42/22.40  | | | | | | | | | | |   (81)  all_56_4 = e0
% 152.42/22.40  | | | | | | | | | | | 
% 152.42/22.40  | | | | | | | | | | | REF_CLOSE: (43), (69), (81) are inconsistent by sub-proof
% 152.42/22.40  | | | | | | | | | | |            #657.
% 152.42/22.40  | | | | | | | | | | | 
% 152.42/22.40  | | | | | | | | | | Case 2:
% 152.42/22.40  | | | | | | | | | | | 
% 152.42/22.40  | | | | | | | | | | |   (82)  all_56_9 = e0 & op(e3, e0) = e0
% 152.42/22.40  | | | | | | | | | | | 
% 152.42/22.40  | | | | | | | | | | | REF_CLOSE: (43), (66), (82) are inconsistent by sub-proof
% 152.42/22.40  | | | | | | | | | | |            #1063.
% 152.42/22.40  | | | | | | | | | | | 
% 152.42/22.40  | | | | | | | | | | End of split
% 152.42/22.40  | | | | | | | | | | 
% 152.42/22.40  | | | | | | | | | End of split
% 152.42/22.40  | | | | | | | | | 
% 152.42/22.40  | | | | | | | | Case 2:
% 152.42/22.40  | | | | | | | | | 
% 152.42/22.40  | | | | | | | | |   (83)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.40  | | | | | | | | | 
% 152.42/22.40  | | | | | | | | | REF_CLOSE: (4), (36), (83) are inconsistent by sub-proof #270.
% 152.42/22.40  | | | | | | | | | 
% 152.42/22.40  | | | | | | | | End of split
% 152.42/22.40  | | | | | | | | 
% 152.42/22.40  | | | | | | | Case 2:
% 152.42/22.40  | | | | | | | | 
% 152.42/22.40  | | | | | | | |   (84)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 &
% 152.42/22.40  | | | | | | | |           op(e0, e2) = e3)
% 152.42/22.40  | | | | | | | | 
% 152.42/22.40  | | | | | | | | REF_CLOSE: (4), (17), (31), (34), (74), (84) are inconsistent by
% 152.42/22.40  | | | | | | | |            sub-proof #257.
% 152.42/22.40  | | | | | | | | 
% 152.42/22.40  | | | | | | | End of split
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | End of split
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | Case 2:
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | |   (85)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 &
% 152.42/22.40  | | | | | |           op(e0, e0) = e1)
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | | REF_CLOSE: (13), (14), (17), (21), (26), (43), (46), (47), (57),
% 152.42/22.40  | | | | | |            (58), (69), (85) are inconsistent by sub-proof #253.
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | End of split
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | Case 2:
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | |   (86)  all_56_5 = e1 & op(e2, e1) = e1
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | ALPHA: (86) implies:
% 152.42/22.40  | | | | |   (87)  all_56_5 = e1
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | BETA: splitting (62) gives:
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | Case 1:
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | |   (88)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 &
% 152.42/22.40  | | | | | |           op(e0, e2) = e1)
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | | BETA: splitting (88) gives:
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | | Case 1:
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | |   (89)  all_56_12 = e1 & op(e0, e3) = e1
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | | ALPHA: (89) implies:
% 152.42/22.40  | | | | | | |   (90)  all_56_12 = e1
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | | REF_CLOSE: (2), (4), (8), (14), (17), (20), (26), (27), (32),
% 152.42/22.40  | | | | | | |            (33), (43), (45), (46), (47), (54), (57), (90) are
% 152.42/22.40  | | | | | | |            inconsistent by sub-proof #569.
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | Case 2:
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | |   (91)  all_56_13 = e1 & op(e0, e2) = e1
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | | REF_CLOSE: (4), (5), (14), (17), (26), (30), (31), (33), (34),
% 152.42/22.40  | | | | | | |            (36), (43), (47), (57), (61), (66), (91) are
% 152.42/22.40  | | | | | | |            inconsistent by sub-proof #252.
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | End of split
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | Case 2:
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | |   (92)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 &
% 152.42/22.40  | | | | | |           op(e0, e0) = e1)
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | | BETA: splitting (92) gives:
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | | Case 1:
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | |   (93)  all_56_14 = e1 & op(e0, e1) = e1
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | | ALPHA: (93) implies:
% 152.42/22.40  | | | | | | |   (94)  all_56_14 = e1
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | | REF_CLOSE: (4), (5), (14), (17), (18), (21), (26), (30), (33),
% 152.42/22.40  | | | | | | |            (43), (46), (47), (57), (66), (87), (94) are
% 152.42/22.40  | | | | | | |            inconsistent by sub-proof #251.
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | Case 2:
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | |   (95)  all_56_15 = e1 & op(e0, e0) = e1
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | | ALPHA: (95) implies:
% 152.42/22.40  | | | | | | |   (96)  op(e0, e0) = e1
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | | REF_CLOSE: (17), (43), (58), (96) are inconsistent by sub-proof
% 152.42/22.40  | | | | | | |            #1040.
% 152.42/22.40  | | | | | | | 
% 152.42/22.40  | | | | | | End of split
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | End of split
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | End of split
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | Case 2:
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | |   (97)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1)
% 152.42/22.40  | | | |           = e1)
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | | BETA: splitting (97) gives:
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | | Case 1:
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | |   (98)  all_56_8 = e1 & op(e1, e1) = e1
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | ALPHA: (98) implies:
% 152.42/22.40  | | | | |   (99)  op(e1, e1) = e1
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | REF_CLOSE: (4), (17), (46), (99) are inconsistent by sub-proof #734.
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | Case 2:
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | |   (100)  all_56_14 = e1 & op(e0, e1) = e1
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | REF_CLOSE: (2), (4), (5), (13), (14), (17), (18), (21), (26), (30),
% 152.42/22.40  | | | | |            (33), (43), (46), (47), (51), (57), (66), (100) are
% 152.42/22.40  | | | | |            inconsistent by sub-proof #250.
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | End of split
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | End of split
% 152.42/22.40  | | | 
% 152.42/22.40  | | Case 2:
% 152.42/22.40  | | | 
% 152.42/22.40  | | |   (101)  all_56_10 = e1 & op(e2, e0) = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | ALPHA: (101) implies:
% 152.42/22.40  | | |   (102)  all_56_10 = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | REF_CLOSE: (4), (6), (11), (14), (16), (17), (23), (26), (36), (41), (42),
% 152.42/22.40  | | |            (43), (47), (57), (102) are inconsistent by sub-proof #264.
% 152.42/22.40  | | | 
% 152.42/22.40  | | End of split
% 152.42/22.40  | | 
% 152.42/22.40  | Case 2:
% 152.42/22.40  | | 
% 152.42/22.40  | |   (103)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.42/22.40  | |            e1)
% 152.42/22.40  | | 
% 152.42/22.40  | | BETA: splitting (103) gives:
% 152.42/22.40  | | 
% 152.42/22.40  | | Case 1:
% 152.42/22.40  | | | 
% 152.42/22.40  | | |   (104)  all_56_11 = e1 & op(e1, e0) = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | ALPHA: (104) implies:
% 152.42/22.40  | | |   (105)  op(e1, e0) = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14),
% 152.42/22.40  | | |            (15), (16), (17), (19), (20), (21), (22), (24), (25), (26),
% 152.42/22.40  | | |            (27), (29), (31), (32), (33), (34), (35), (36), (37), (38),
% 152.42/22.40  | | |            (39), (40), (42), (43), (44), (45), (46), (47), (48), (49),
% 152.42/22.40  | | |            (50), (51), (52), (53), (54), (55), (56), (57), (58), (59),
% 152.42/22.40  | | |            (60), (61), (62), (63), (105) are inconsistent by sub-proof
% 152.42/22.40  | | |            #242.
% 152.42/22.40  | | | 
% 152.42/22.40  | | Case 2:
% 152.42/22.40  | | | 
% 152.42/22.40  | | |   (106)  all_56_15 = e1 & op(e0, e0) = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | ALPHA: (106) implies:
% 152.42/22.40  | | |   (107)  op(e0, e0) = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | REF_CLOSE: (17), (43), (58), (107) are inconsistent by sub-proof #1040.
% 152.42/22.40  | | | 
% 152.42/22.40  | | End of split
% 152.42/22.40  | | 
% 152.42/22.40  | End of split
% 152.42/22.40  | 
% 152.42/22.40  End of proof
% 152.42/22.40  
% 152.42/22.40  Sub-proof #242 shows that the following formulas are inconsistent:
% 152.42/22.40  ----------------------------------------------------------------
% 152.42/22.40    (1)  op(e0, e1) = all_52_11
% 152.42/22.40    (2)  all_56_8 = e3
% 152.42/22.40    (3)   ~ (all_52_7 = all_52_11)
% 152.42/22.40    (4)   ~ (e3 = e1)
% 152.42/22.40    (5)  op(e2, e2) = e1
% 152.42/22.40    (6)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.40         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.42/22.40    (7)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 152.42/22.40         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.42/22.40    (8)  op(e0, e0) = all_10_2
% 152.42/22.40    (9)   ~ (all_52_3 = all_52_7)
% 152.42/22.40    (10)   ~ (all_10_2 = e1)
% 152.42/22.40    (11)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.42/22.40          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.40    (12)   ~ (e2 = e0)
% 152.42/22.40    (13)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 152.42/22.40            all_57_12 & $i(all_57_12))
% 152.42/22.40    (14)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.40          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.42/22.40    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.40            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.40    (16)   ~ (all_52_1 = all_52_13)
% 152.42/22.40    (17)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.42/22.40          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.42/22.40    (18)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.42/22.40          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.40    (19)   ~ (all_52_3 = all_52_11)
% 152.42/22.40    (20)   ~ (all_52_1 = all_52_9)
% 152.42/22.40    (21)  op(e1, e0) = all_52_14
% 152.42/22.40    (22)   ~ (e3 = e0)
% 152.42/22.40    (23)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.42/22.40          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.42/22.40    (24)  all_57_15 = e0
% 152.42/22.40    (25)   ~ (all_52_6 = e3)
% 152.42/22.40    (26)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 152.42/22.40          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 152.42/22.40    (27)  op(e3, e3) = e1
% 152.42/22.40    (28)  op(e1, e2) = all_52_6
% 152.42/22.40    (29)  op(e2, e0) = all_52_13
% 152.42/22.40    (30)  all_56_3 = e1
% 152.42/22.40    (31)   ~ (all_52_1 = all_52_3)
% 152.42/22.40    (32)  op(e0, e3) = all_52_3
% 152.42/22.40    (33)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 152.42/22.40    (34)  all_54_12 = all_52_3
% 152.42/22.40    (35)  op(e2, e1) = all_52_9
% 152.42/22.40    (36)   ~ (e1 = e0)
% 152.42/22.40    (37)   ~ (all_52_1 = e1)
% 152.42/22.40    (38)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.42/22.40          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.42/22.40    (39)  op(e1, e1) = e3
% 152.42/22.40    (40)   ~ (e3 = e2)
% 152.42/22.40    (41)  op(e1, e0) = e1
% 152.42/22.40    (42)   ~ (all_52_8 = e3)
% 152.42/22.40    (43)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.40          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.42/22.40    (44)   ~ (all_52_7 = all_10_2)
% 152.42/22.40    (45)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.42/22.40          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.42/22.40    (46)  all_54_13 = all_52_7
% 152.42/22.40    (47)  op(e3, e1) = all_52_8
% 152.42/22.40    (48)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.42/22.40          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.42/22.40    (49)   ~ (all_52_3 = all_10_2)
% 152.42/22.40    (50)   ~ (all_52_6 = all_52_7)
% 152.42/22.40    (51)   ~ (e2 = e1)
% 152.42/22.40    (52)  op(e0, e0) = e0
% 152.42/22.40    (53)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.42/22.40    (54)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.42/22.40              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.42/22.40            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.42/22.40            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.42/22.40            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.42/22.40            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.42/22.40            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.42/22.40            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.40            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.42/22.40            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.42/22.40            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.42/22.40            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.42/22.40            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.40            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.42/22.40            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.42/22.40            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.40            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.42/22.40            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.42/22.40            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.42/22.40            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.42/22.40            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.42/22.40            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.40            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.42/22.40            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.42/22.40            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.42/22.40            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.42/22.40            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.42/22.40            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.42/22.40            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.42/22.40            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.42/22.40            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.42/22.40            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.42/22.40            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.42/22.40            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.42/22.40            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.42/22.40            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.42/22.40            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.40            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.42/22.40            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.42/22.40            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.40            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.42/22.40            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.42/22.40            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.42/22.40            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.42/22.40            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.42/22.40            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.42/22.40            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.42/22.40            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.42/22.40              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.42/22.40            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.42/22.40            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.42/22.40              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.42/22.40            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.42/22.40            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.42/22.40                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.42/22.40                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.42/22.40                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.42/22.40                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.42/22.40                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.42/22.40                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.42/22.40                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.42/22.40              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.42/22.40                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.42/22.40                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.42/22.40                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.42/22.40                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.42/22.40                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.42/22.40                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.40                $i(all_57_7))))
% 152.42/22.40    (55)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.40          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.40    (56)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.42/22.40          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.42/22.40            e1)
% 152.42/22.40    (57)  op(e2, e3) = all_52_1
% 152.42/22.40  
% 152.42/22.40  Begin of proof
% 152.42/22.40  | 
% 152.42/22.40  | BETA: splitting (45) gives:
% 152.42/22.40  | 
% 152.42/22.40  | Case 1:
% 152.42/22.40  | | 
% 152.42/22.40  | |   (58)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) =
% 152.42/22.40  | |           e1)
% 152.42/22.40  | | 
% 152.42/22.40  | | BETA: splitting (58) gives:
% 152.42/22.40  | | 
% 152.42/22.40  | | Case 1:
% 152.42/22.40  | | | 
% 152.42/22.40  | | |   (59)  all_56_4 = e1 & op(e3, e1) = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | ALPHA: (59) implies:
% 152.42/22.40  | | |   (60)  all_56_4 = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | BETA: splitting (56) gives:
% 152.42/22.40  | | | 
% 152.42/22.40  | | | Case 1:
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | |   (61)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0,
% 152.42/22.40  | | | |             e2) = e1)
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | | BETA: splitting (61) gives:
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | | Case 1:
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | |   (62)  all_56_12 = e1 & op(e0, e3) = e1
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | ALPHA: (62) implies:
% 152.42/22.40  | | | | |   (63)  all_56_12 = e1
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | REF_CLOSE: (2), (4), (7), (12), (15), (17), (22), (23), (26), (27),
% 152.42/22.40  | | | | |            (36), (38), (39), (40), (48), (51), (63) are inconsistent
% 152.42/22.40  | | | | |            by sub-proof #569.
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | Case 2:
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | |   (64)  all_56_13 = e1 & op(e0, e2) = e1
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | ALPHA: (64) implies:
% 152.42/22.40  | | | | |   (65)  all_56_13 = e1
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | REF_CLOSE: (4), (5), (6), (12), (15), (22), (25), (28), (30), (36),
% 152.42/22.40  | | | | |            (40), (43), (51), (55), (65) are inconsistent by sub-proof
% 152.42/22.40  | | | | |            #260.
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | End of split
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | Case 2:
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | |   (66)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0,
% 152.42/22.40  | | | |             e0) = e1)
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | | REF_CLOSE: (11), (12), (15), (18), (22), (36), (39), (40), (51), (52),
% 152.42/22.40  | | | |            (60), (66) are inconsistent by sub-proof #253.
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | End of split
% 152.42/22.40  | | | 
% 152.42/22.40  | | Case 2:
% 152.42/22.40  | | | 
% 152.42/22.40  | | |   (67)  all_56_5 = e1 & op(e2, e1) = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | ALPHA: (67) implies:
% 152.42/22.40  | | |   (68)  all_56_5 = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | REF_CLOSE: (2), (4), (5), (6), (7), (11), (12), (15), (17), (18), (22),
% 152.42/22.40  | | |            (23), (25), (26), (27), (28), (30), (36), (38), (39), (40),
% 152.42/22.40  | | |            (43), (48), (51), (52), (55), (56), (68) are inconsistent by
% 152.42/22.40  | | |            sub-proof #246.
% 152.42/22.40  | | | 
% 152.42/22.40  | | End of split
% 152.42/22.40  | | 
% 152.42/22.40  | Case 2:
% 152.42/22.40  | | 
% 152.42/22.40  | |   (69)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) =
% 152.42/22.40  | |           e1)
% 152.42/22.40  | | 
% 152.42/22.40  | | BETA: splitting (69) gives:
% 152.42/22.40  | | 
% 152.42/22.40  | | Case 1:
% 152.42/22.40  | | | 
% 152.42/22.40  | | |   (70)  all_56_8 = e1 & op(e1, e1) = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | ALPHA: (70) implies:
% 152.42/22.40  | | |   (71)  op(e1, e1) = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | REF_CLOSE: (4), (15), (39), (71) are inconsistent by sub-proof #734.
% 152.42/22.40  | | | 
% 152.42/22.40  | | Case 2:
% 152.42/22.40  | | | 
% 152.42/22.40  | | |   (72)  all_56_14 = e1 & op(e0, e1) = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | ALPHA: (72) implies:
% 152.42/22.40  | | |   (73)  op(e0, e1) = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | GROUND_INST: instantiating (15) with all_10_2, e0, e0, e0, simplifying
% 152.42/22.40  | | |              with (8), (52) gives:
% 152.42/22.40  | | |   (74)  all_10_2 = e0
% 152.42/22.40  | | | 
% 152.42/22.40  | | | GROUND_INST: instantiating (15) with all_52_11, e1, e1, e0, simplifying
% 152.42/22.40  | | |              with (1), (73) gives:
% 152.42/22.40  | | |   (75)  all_52_11 = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | GROUND_INST: instantiating (15) with all_52_14, e1, e0, e1, simplifying
% 152.42/22.40  | | |              with (21), (41) gives:
% 152.42/22.40  | | |   (76)  all_52_14 = e1
% 152.42/22.40  | | | 
% 152.42/22.40  | | | REDUCE: (19), (75) imply:
% 152.42/22.40  | | |   (77)   ~ (all_52_3 = e1)
% 152.42/22.40  | | | 
% 152.42/22.40  | | | REDUCE: (49), (74) imply:
% 152.42/22.40  | | |   (78)   ~ (all_52_3 = e0)
% 152.42/22.40  | | | 
% 152.42/22.40  | | | REDUCE: (3), (75) imply:
% 152.42/22.40  | | |   (79)   ~ (all_52_7 = e1)
% 152.42/22.40  | | | 
% 152.42/22.40  | | | REDUCE: (44), (74) imply:
% 152.42/22.40  | | |   (80)   ~ (all_52_7 = e0)
% 152.42/22.40  | | | 
% 152.42/22.40  | | | REDUCE: (10), (74) imply:
% 152.42/22.40  | | |   (81)   ~ (e1 = e0)
% 152.42/22.40  | | | 
% 152.42/22.40  | | | BETA: splitting (54) gives:
% 152.42/22.40  | | | 
% 152.42/22.40  | | | Case 1:
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | |   (82)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.42/22.40  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.42/22.40  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 152.42/22.40  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 152.42/22.40  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.42/22.40  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 152.42/22.40  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.42/22.40  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 152.42/22.40  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.42/22.40  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.42/22.40  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 152.42/22.40  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.40  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 152.42/22.40  | | | |           $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.42/22.40  | | | |           (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 152.42/22.40  | | | |           & op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.42/22.40  | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 =
% 152.42/22.40  | | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.42/22.40  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 152.42/22.40  | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 152.42/22.40  | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 152.42/22.40  | | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 152.42/22.40  | | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.42/22.40  | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 152.42/22.40  | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.40  | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.42/22.40  | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 152.42/22.40  | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 152.42/22.40  | | | |           & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.42/22.40  | | | |           $i(all_57_7) & $i(all_57_10))
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | | BETA: splitting (82) gives:
% 152.42/22.40  | | | | 
% 152.42/22.40  | | | | Case 1:
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | |   (83)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.42/22.40  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 152.42/22.40  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 152.42/22.40  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 152.42/22.40  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.42/22.40  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 152.42/22.40  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.42/22.40  | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 152.42/22.40  | | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.42/22.40  | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.42/22.40  | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 152.42/22.40  | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 152.42/22.40  | | | | |           & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 152.42/22.40  | | | | |           $i(all_57_14))
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | BETA: splitting (83) gives:
% 152.42/22.40  | | | | | 
% 152.42/22.40  | | | | | Case 1:
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | |   (84)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.42/22.40  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.40  | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.42/22.40  | | | | | |           $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 & all_57_15
% 152.42/22.40  | | | | | |           = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2,
% 152.42/22.40  | | | | | |             e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 152.42/22.40  | | | | | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | | BETA: splitting (84) gives:
% 152.42/22.40  | | | | | | 
% 152.42/22.40  | | | | | | Case 1:
% 152.42/22.40  | | | | | | | 
% 152.42/22.41  | | | | | | |   (85)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.42/22.41  | | | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.41  | | | | | | |         all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.42/22.41  | | | | | | |         $i(all_57_1) & $i(all_57_12)
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | ALPHA: (85) implies:
% 152.42/22.41  | | | | | | |   (86)  op(e2, e2) = all_57_12
% 152.42/22.41  | | | | | | |   (87)  op(e2, e3) = e2
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | GROUND_INST: instantiating (15) with e1, all_57_12, e2, e2,
% 152.42/22.41  | | | | | | |              simplifying with (5), (86) gives:
% 152.42/22.41  | | | | | | |   (88)  all_57_12 = e1
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | GROUND_INST: instantiating (15) with all_52_1, e2, e3, e2,
% 152.42/22.41  | | | | | | |              simplifying with (57), (87) gives:
% 152.42/22.41  | | | | | | |   (89)  all_52_1 = e2
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | REDUCE: (31), (89) imply:
% 152.42/22.41  | | | | | | |   (90)   ~ (all_52_3 = e2)
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | SIMP: (90) implies:
% 152.42/22.41  | | | | | | |   (91)   ~ (all_52_3 = e2)
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | REDUCE: (20), (89) imply:
% 152.42/22.41  | | | | | | |   (92)   ~ (all_52_9 = e2)
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | SIMP: (92) implies:
% 152.42/22.41  | | | | | | |   (93)   ~ (all_52_9 = e2)
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | REDUCE: (16), (89) imply:
% 152.42/22.41  | | | | | | |   (94)   ~ (all_52_13 = e2)
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | SIMP: (94) implies:
% 152.42/22.41  | | | | | | |   (95)   ~ (all_52_13 = e2)
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | BETA: splitting (23) gives:
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | Case 1:
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | |   (96)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 &
% 152.42/22.41  | | | | | | | |           op(e2, e3) = e0)
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | | BETA: splitting (96) gives:
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | | Case 1:
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | |   (97)  all_56_0 = e0 & op(e3, e3) = e0
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | ALPHA: (97) implies:
% 152.42/22.41  | | | | | | | | |   (98)  op(e3, e3) = e0
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | REF_CLOSE: (15), (27), (36), (98) are inconsistent by
% 152.42/22.41  | | | | | | | | |            sub-proof #957.
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | Case 2:
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | |   (99)  all_56_2 = e0 & op(e2, e3) = e0
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | ALPHA: (99) implies:
% 152.42/22.41  | | | | | | | | |   (100)  all_56_2 = e0
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | REF_CLOSE: (5), (12), (14), (15), (29), (35), (51), (93),
% 152.42/22.41  | | | | | | | | |            (95), (100) are inconsistent by sub-proof #1154.
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | End of split
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | Case 2:
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | |   (101)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 &
% 152.42/22.41  | | | | | | | |            op(e0, e3) = e0)
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | | BETA: splitting (101) gives:
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | | Case 1:
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | |   (102)  all_56_6 = e0 & op(e1, e3) = e0
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | ALPHA: (102) implies:
% 152.42/22.41  | | | | | | | | |   (103)  all_56_6 = e0
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | BETA: splitting (38) gives:
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | Case 1:
% 152.42/22.41  | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | |   (104)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 152.42/22.41  | | | | | | | | | |            & op(e1, e2) = e2)
% 152.42/22.41  | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | BETA: splitting (104) gives:
% 152.42/22.41  | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | Case 1:
% 152.42/22.41  | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | |   (105)  all_56_6 = e2 & op(e1, e3) = e2
% 152.42/22.41  | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | ALPHA: (105) implies:
% 152.42/22.41  | | | | | | | | | | |   (106)  all_56_6 = e2
% 152.42/22.41  | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | REF_CLOSE: (12), (103), (106) are inconsistent by sub-proof
% 152.42/22.41  | | | | | | | | | | |            #724.
% 152.42/22.41  | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | Case 2:
% 152.42/22.41  | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | |   (107)  all_56_7 = e2 & op(e1, e2) = e2
% 152.42/22.41  | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | ALPHA: (107) implies:
% 152.42/22.41  | | | | | | | | | | |   (108)  op(e1, e2) = e2
% 152.42/22.41  | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | BETA: splitting (53) gives:
% 152.42/22.41  | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | Case 1:
% 152.42/22.41  | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | |   (109)  all_54_12 = e3
% 152.42/22.41  | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | COMBINE_EQS: (34), (109) imply:
% 152.42/22.41  | | | | | | | | | | | |   (110)  all_52_3 = e3
% 152.42/22.41  | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | SIMP: (110) implies:
% 152.42/22.41  | | | | | | | | | | | |   (111)  all_52_3 = e3
% 152.42/22.41  | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | REDUCE: (9), (111) imply:
% 152.42/22.41  | | | | | | | | | | | |   (112)   ~ (all_52_7 = e3)
% 152.42/22.41  | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | SIMP: (112) implies:
% 152.42/22.41  | | | | | | | | | | | |   (113)   ~ (all_52_7 = e3)
% 152.42/22.41  | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | BETA: splitting (33) gives:
% 152.42/22.41  | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | Case 1:
% 152.42/22.41  | | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | |   (114)  all_54_13 = e3
% 152.42/22.41  | | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | | REF_CLOSE: (46), (113), (114) are inconsistent by sub-proof
% 152.42/22.41  | | | | | | | | | | | | |            #845.
% 152.42/22.41  | | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | Case 2:
% 152.42/22.41  | | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | |   (115)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 152.42/22.41  | | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | | REF_CLOSE: (15), (28), (46), (50), (79), (80), (108), (115)
% 152.42/22.41  | | | | | | | | | | | | |            are inconsistent by sub-proof #836.
% 152.42/22.41  | | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | End of split
% 152.42/22.41  | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | Case 2:
% 152.42/22.41  | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | |   (116)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 152.42/22.41  | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | | REF_CLOSE: (34), (77), (78), (91), (116) are inconsistent by
% 152.42/22.41  | | | | | | | | | | | |            sub-proof #881.
% 152.42/22.41  | | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | | End of split
% 152.42/22.41  | | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | End of split
% 152.42/22.41  | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | Case 2:
% 152.42/22.41  | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | |   (117)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2
% 152.42/22.41  | | | | | | | | | |            & op(e1, e0) = e2)
% 152.42/22.41  | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | | REF_CLOSE: (15), (39), (40), (41), (51), (117) are
% 152.42/22.41  | | | | | | | | | |            inconsistent by sub-proof #280.
% 152.42/22.41  | | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | End of split
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | Case 2:
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | |   (118)  all_56_12 = e0 & op(e0, e3) = e0
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | ALPHA: (118) implies:
% 152.42/22.41  | | | | | | | | |   (119)  op(e0, e3) = e0
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | | REF_CLOSE: (15), (32), (78), (119) are inconsistent by
% 152.42/22.41  | | | | | | | | |            sub-proof #1142.
% 152.42/22.41  | | | | | | | | | 
% 152.42/22.41  | | | | | | | | End of split
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | End of split
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | Case 2:
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | |   (120)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 152.42/22.41  | | | | | | |          (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.41  | | | | | | |          all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.42/22.41  | | | | | | |          $i(all_57_2) & $i(all_57_12)
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | ALPHA: (120) implies:
% 152.42/22.41  | | | | | | |   (121)  op(e0, e0) = e3
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | REF_CLOSE: (15), (22), (52), (121) are inconsistent by sub-proof
% 152.42/22.41  | | | | | | |            #1143.
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | End of split
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | Case 2:
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | |   (122)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.42/22.41  | | | | | |            (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 152.42/22.41  | | | | | |            e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.41  | | | | | |            $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 152.42/22.41  | | | | | |            all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3)
% 152.42/22.41  | | | | | |            & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 152.42/22.41  | | | | | |            all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 152.42/22.41  | | | | | |            $i(all_57_14))
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | | REF_CLOSE: (15), (22), (39), (52), (122) are inconsistent by
% 152.42/22.41  | | | | | |            sub-proof #352.
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | End of split
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | Case 2:
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | |   (123)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.42/22.41  | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.42/22.41  | | | | |            & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 152.42/22.41  | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.42/22.41  | | | | |            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.42/22.41  | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 152.42/22.41  | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4
% 152.42/22.41  | | | | |            = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 152.42/22.41  | | | | |              = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 152.42/22.41  | | | | |              e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.42/22.41  | | | | |            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 152.42/22.41  | | | | |            (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.42/22.41  | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 152.42/22.41  | | | | |            = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 152.42/22.41  | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 152.42/22.41  | | | | |            op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1
% 152.42/22.41  | | | | |            & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | | BETA: splitting (123) gives:
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | | Case 1:
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | |   (124)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.42/22.41  | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 152.42/22.41  | | | | | |            e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.42/22.41  | | | | | |            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 &
% 152.42/22.41  | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2)
% 152.42/22.41  | | | | | |            & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 152.42/22.41  | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.42/22.41  | | | | | |            $i(all_57_10))
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | | REF_CLOSE: (12), (15), (39), (40), (52), (124) are inconsistent by
% 152.42/22.41  | | | | | |            sub-proof #245.
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | Case 2:
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | |   (125)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.42/22.41  | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.42/22.41  | | | | | |            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.41  | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 152.42/22.41  | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2)
% 152.42/22.41  | | | | | |            & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 152.42/22.41  | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.42/22.41  | | | | | |            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 152.42/22.41  | | | | | |            (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.42/22.41  | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2,
% 152.42/22.41  | | | | | |              e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | | BETA: splitting (125) gives:
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | | Case 1:
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | |   (126)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.42/22.41  | | | | | | |          (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.42/22.41  | | | | | | |          all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.41  | | | | | | |          $i(all_57_3) & $i(all_57_14)
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | ALPHA: (126) implies:
% 152.42/22.41  | | | | | | |   (127)  op(e3, e3) = e2
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | REF_CLOSE: (15), (27), (51), (127) are inconsistent by sub-proof
% 152.42/22.41  | | | | | | |            #1074.
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | Case 2:
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | |   (128)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 152.42/22.41  | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 152.42/22.41  | | | | | | |            all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.42/22.41  | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 152.42/22.41  | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 152.42/22.41  | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.42/22.41  | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7)
% 152.42/22.41  | | | | | | |            & $i(all_57_10))
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | REF_CLOSE: (12), (15), (42), (47), (52), (128) are inconsistent by
% 152.42/22.41  | | | | | | |            sub-proof #244.
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | End of split
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | End of split
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | End of split
% 152.42/22.41  | | | | 
% 152.42/22.41  | | | Case 2:
% 152.42/22.41  | | | | 
% 152.42/22.41  | | | |   (129)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.42/22.41  | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.42/22.41  | | | |            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.42/22.41  | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 152.42/22.41  | | | |            (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 152.42/22.41  | | | |            op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 152.42/22.41  | | | |            e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.42/22.41  | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 152.42/22.41  | | | |            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.42/22.41  | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.42/22.41  | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.42/22.41  | | | |            (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.41  | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.42/22.41  | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 152.42/22.41  | | | |            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 152.42/22.41  | | | |            all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.42/22.41  | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 152.42/22.41  | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 = e0) &
% 152.42/22.41  | | | |            op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 152.42/22.41  | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 152.42/22.41  | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 152.42/22.41  | | | |            (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.42/22.41  | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.42/22.41  | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 152.42/22.41  | | | |            (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.42/22.41  | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 152.42/22.41  | | | |            all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 152.42/22.41  | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0)
% 152.42/22.41  | | | |            & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 152.42/22.41  | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14))
% 152.42/22.41  | | | |          | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.42/22.41  | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3)
% 152.42/22.41  | | | |                & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 152.42/22.41  | | | |                e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.42/22.41  | | | |                (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.42/22.41  | | | |                all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.42/22.41  | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.42/22.41  | | | |                (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 152.42/22.41  | | | |                op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.42/22.41  | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.42/22.41  | | | |                (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 152.42/22.41  | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.42/22.41  | | | |                all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 152.42/22.41  | | | |                & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 152.42/22.41  | | | |                e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.42/22.41  | | | |                (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 152.42/22.41  | | | |                op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.42/22.41  | | | | 
% 152.42/22.41  | | | | BETA: splitting (129) gives:
% 152.42/22.41  | | | | 
% 152.42/22.41  | | | | Case 1:
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | |   (130)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.42/22.41  | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.42/22.41  | | | | |            & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.42/22.41  | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 152.42/22.41  | | | | |            (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 152.42/22.41  | | | | |            op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 152.42/22.41  | | | | |            = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.42/22.41  | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 152.42/22.41  | | | | |            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.42/22.41  | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12))
% 152.42/22.41  | | | | |          | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.42/22.41  | | | | |            (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.42/22.41  | | | | |            & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10)
% 152.42/22.41  | | | | |            & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 152.42/22.41  | | | | |            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 152.42/22.41  | | | | |            all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 152.42/22.41  | | | | |            = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | | BETA: splitting (130) gives:
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | | Case 1:
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | |   (131)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.42/22.41  | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 152.42/22.41  | | | | | |            e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 152.42/22.41  | | | | | |            $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 &
% 152.42/22.41  | | | | | |            all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1)
% 152.42/22.41  | | | | | |            & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 152.42/22.41  | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.42/22.41  | | | | | |            $i(all_57_12))
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | | REF_CLOSE: (5), (15), (36), (52), (131) are inconsistent by
% 152.42/22.41  | | | | | |            sub-proof #891.
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | Case 2:
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | |   (132)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.42/22.41  | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 152.42/22.41  | | | | | |            e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 152.42/22.41  | | | | | |            $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 152.42/22.41  | | | | | |            all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 152.42/22.41  | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 152.42/22.41  | | | | | |              e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.42/22.41  | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 152.42/22.41  | | | | | |            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 152.42/22.41  | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1,
% 152.42/22.41  | | | | | |              e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | | REF_CLOSE: (13), (15), (22), (36), (39), (52), (132) are
% 152.42/22.41  | | | | | |            inconsistent by sub-proof #243.
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | End of split
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | Case 2:
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | |   (133)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 152.42/22.41  | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9
% 152.42/22.41  | | | | |            & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.42/22.41  | | | | |            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 152.42/22.41  | | | | |            (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.42/22.41  | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 152.42/22.41  | | | | |            = e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 152.42/22.41  | | | | |            all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1)
% 152.42/22.41  | | | | |            & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) =
% 152.42/22.41  | | | | |            e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.42/22.41  | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 152.42/22.41  | | | | |            (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.42/22.41  | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 152.42/22.41  | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.42/22.41  | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 =
% 152.42/22.41  | | | | |                e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2,
% 152.42/22.41  | | | | |                  e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.42/22.41  | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.42/22.41  | | | | |                (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.42/22.41  | | | | |                all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.42/22.41  | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.42/22.41  | | | | |                (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.42/22.41  | | | | |                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.42/22.41  | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 152.42/22.41  | | | | |                (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.42/22.41  | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.42/22.41  | | | | |                $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.42/22.41  | | | | |                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 152.42/22.41  | | | | |                & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.42/22.41  | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.42/22.41  | | | | |                (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 152.42/22.41  | | | | |                & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.41  | | | | |                $i(all_57_7))))
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | | BETA: splitting (133) gives:
% 152.42/22.41  | | | | | 
% 152.42/22.41  | | | | | Case 1:
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | |   (134)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 152.42/22.41  | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 152.42/22.41  | | | | | |            all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.42/22.41  | | | | | |            $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 &
% 152.42/22.41  | | | | | |            all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 = e0)
% 152.42/22.41  | | | | | |            & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 152.42/22.41  | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.42/22.41  | | | | | |            $i(all_57_14))
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | | REF_CLOSE: (15), (27), (36), (134) are inconsistent by sub-proof
% 152.42/22.41  | | | | | |            #956.
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | Case 2:
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | |   (135)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 152.42/22.41  | | | | | |            (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.42/22.41  | | | | | |            e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.42/22.41  | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 152.42/22.41  | | | | | |            all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 =
% 152.42/22.41  | | | | | |              e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1,
% 152.42/22.41  | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.42/22.41  | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15)
% 152.42/22.41  | | | | | |            & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &
% 152.42/22.41  | | | | | |                 ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 152.42/22.41  | | | | | |                  e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 152.42/22.41  | | | | | |              (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.42/22.41  | | | | | |                ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 152.42/22.41  | | | | | |                  e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.42/22.41  | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 152.42/22.41  | | | | | |                ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.42/22.41  | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.42/22.41  | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) & 
% 152.42/22.41  | | | | | |                ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 152.42/22.41  | | | | | |                  e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.42/22.41  | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 152.42/22.41  | | | | | |                ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.42/22.41  | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.42/22.41  | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 152.42/22.41  | | | | | |                ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.42/22.41  | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | | BETA: splitting (135) gives:
% 152.42/22.41  | | | | | | 
% 152.42/22.41  | | | | | | Case 1:
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | |   (136)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) & 
% 152.42/22.41  | | | | | | |          ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0)
% 152.42/22.41  | | | | | | |          = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.42/22.41  | | | | | | |          $i(all_57_12) & $i(all_57_13)
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | ALPHA: (136) implies:
% 152.42/22.41  | | | | | | |   (137)  op(e1, e1) = e0
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | REF_CLOSE: (15), (22), (39), (137) are inconsistent by sub-proof
% 152.42/22.41  | | | | | | |            #896.
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | Case 2:
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | |   (138)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 152.42/22.41  | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 152.42/22.41  | | | | | | |            all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.41  | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.42/22.41  | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12
% 152.42/22.41  | | | | | | |                = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.42/22.41  | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 152.42/22.41  | | | | | | |                  e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 152.42/22.41  | | | | | | |                all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 152.42/22.41  | | | | | | |                  = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.42/22.41  | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 152.42/22.41  | | | | | | |                all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15
% 152.42/22.41  | | | | | | |                  = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.42/22.41  | | | | | | |                op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 152.42/22.41  | | | | | | |                all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.42/22.41  | | | | | | |                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.42/22.41  | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.42/22.41  | | | | | | |                all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 152.42/22.41  | | | | | | |                  = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.42/22.41  | | | | | | |                op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.42/22.41  | | | | | | |                all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15
% 152.42/22.41  | | | | | | |                  = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.42/22.41  | | | | | | |                op(e0, e1) = e0 & $i(all_57_7))))
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | BETA: splitting (138) gives:
% 152.42/22.41  | | | | | | | 
% 152.42/22.41  | | | | | | | Case 1:
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | |   (139)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &
% 152.42/22.41  | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 152.42/22.41  | | | | | | | |          all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.41  | | | | | | | |          $i(all_57_11) & $i(all_57_14)
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | | ALPHA: (139) implies:
% 152.42/22.41  | | | | | | | |   (140)  all_57_12 = e0
% 152.42/22.41  | | | | | | | |   (141)   ~ (all_57_11 = e2)
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | | REF_CLOSE: (13), (140), (141) are inconsistent by sub-proof
% 152.42/22.41  | | | | | | | |            #890.
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | Case 2:
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | |   (142)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 =
% 152.42/22.41  | | | | | | | |              e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.42/22.41  | | | | | | | |              (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 152.42/22.41  | | | | | | | |                e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 152.42/22.41  | | | | | | | |            (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 152.42/22.41  | | | | | | | |              &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.42/22.41  | | | | | | | |              op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.42/22.41  | | | | | | | |            (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3)
% 152.42/22.41  | | | | | | | |              &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 152.42/22.41  | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 152.42/22.41  | | | | | | | |            | (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.42/22.41  | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 152.42/22.41  | | | | | | | |              & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4))
% 152.42/22.41  | | | | | | | |            | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 152.42/22.41  | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 152.42/22.41  | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.42/22.41  | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 & 
% 152.42/22.41  | | | | | | | |              ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 152.42/22.41  | | | | | | | |                e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) =
% 152.42/22.41  | | | | | | | |              e0 & $i(all_57_7)))
% 152.42/22.41  | | | | | | | | 
% 152.42/22.41  | | | | | | | | ALPHA: (142) implies:
% 152.42/22.42  | | | | | | | |   (143)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 152.42/22.42  | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 152.42/22.42  | | | | | | | |              e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 152.42/22.42  | | | | | | | |          (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.42/22.42  | | | | | | | |            ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 152.42/22.42  | | | | | | | |              e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.42/22.42  | | | | | | | |          (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 152.42/22.42  | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.42/22.42  | | | | | | | |            all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.42/22.42  | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) & 
% 152.42/22.42  | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 152.42/22.42  | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.42/22.42  | | | | | | | |          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 152.42/22.42  | | | | | | | |            ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.42/22.42  | | | | | | | |            all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.42/22.42  | | | | | | | |          (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 152.42/22.42  | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.42/22.42  | | | | | | | |            all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.42/22.42  | | | | | | | | 
% 152.42/22.42  | | | | | | | | BETA: splitting (143) gives:
% 152.42/22.42  | | | | | | | | 
% 152.42/22.42  | | | | | | | | Case 1:
% 152.42/22.42  | | | | | | | | | 
% 152.42/22.42  | | | | | | | | |   (144)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2)
% 152.42/22.42  | | | | | | | | |            &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 152.42/22.42  | | | | | | | | |            op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 152.42/22.42  | | | | | | | | |          (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 152.42/22.42  | | | | | | | | |            &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.42/22.42  | | | | | | | | |            op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.42/22.42  | | | | | | | | |          (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3)
% 152.42/22.42  | | | | | | | | |            &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 152.42/22.42  | | | | | | | | |              e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 152.42/22.42  | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | REF_CLOSE: (15), (27), (32), (51), (78), (144) are
% 152.42/22.42  | | | | | | | | |            inconsistent by sub-proof #955.
% 152.42/22.42  | | | | | | | | | 
% 152.42/22.42  | | | | | | | | Case 2:
% 152.42/22.42  | | | | | | | | | 
% 152.42/22.42  | | | | | | | | |   (145)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1)
% 152.42/22.42  | | | | | | | | |            &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 &
% 152.42/22.42  | | | | | | | | |            op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.42/22.42  | | | | | | | | |          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.42/22.42  | | | | | | | | |            &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.42/22.42  | | | | | | | | |              e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6))
% 152.42/22.42  | | | | | | | | |          | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.42/22.42  | | | | | | | | |              e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 152.42/22.42  | | | | | | | | |            op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.42  | | | | | | | | |            $i(all_57_7))
% 152.42/22.42  | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | BETA: splitting (145) gives:
% 152.42/22.42  | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | Case 1:
% 152.42/22.42  | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | |   (146)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1)
% 152.42/22.42  | | | | | | | | | |          &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 &
% 152.42/22.42  | | | | | | | | | |          op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)
% 152.42/22.42  | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | ALPHA: (146) implies:
% 152.42/22.42  | | | | | | | | | |   (147)  op(e1, e1) = e2
% 152.42/22.42  | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | REF_CLOSE: (15), (39), (40), (147) are inconsistent by
% 152.42/22.42  | | | | | | | | | |            sub-proof #834.
% 152.42/22.42  | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | Case 2:
% 152.42/22.42  | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | |   (148)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 152.42/22.42  | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 152.42/22.42  | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.42/22.42  | | | | | | | | | |            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &
% 152.42/22.42  | | | | | | | | | |             ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 152.42/22.42  | | | | | | | | | |              e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) =
% 152.42/22.42  | | | | | | | | | |            e0 & $i(all_57_7))
% 152.42/22.42  | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | BETA: splitting (148) gives:
% 152.42/22.42  | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | Case 1:
% 152.42/22.42  | | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | |   (149)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 152.42/22.42  | | | | | | | | | | |            e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 152.42/22.42  | | | | | | | | | | |          op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.42/22.42  | | | | | | | | | | |          $i(all_57_6)
% 152.42/22.42  | | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | | ALPHA: (149) implies:
% 152.42/22.42  | | | | | | | | | | |   (150)   ~ (all_57_15 = e1)
% 152.42/22.42  | | | | | | | | | | |   (151)  op(e0, e1) = e0
% 152.42/22.42  | | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | | GROUND_INST: instantiating (15) with e1, e0, e1, e0,
% 152.42/22.42  | | | | | | | | | | |              simplifying with (73), (151) gives:
% 152.42/22.42  | | | | | | | | | | |   (152)  e1 = e0
% 152.42/22.42  | | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | | REDUCE: (36), (152) imply:
% 152.42/22.42  | | | | | | | | | | |   (153)  $false
% 152.42/22.42  | | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 152.42/22.42  | | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | Case 2:
% 152.42/22.42  | | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | |   (154)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.42/22.42  | | | | | | | | | | |            e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 152.42/22.42  | | | | | | | | | | |          op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.42  | | | | | | | | | | |          $i(all_57_7)
% 152.42/22.42  | | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | | ALPHA: (154) implies:
% 152.42/22.42  | | | | | | | | | | |   (155)  op(e0, e1) = e0
% 152.42/22.42  | | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | | REF_CLOSE: (15), (36), (73), (155) are inconsistent by
% 152.42/22.42  | | | | | | | | | | |            sub-proof #899.
% 152.42/22.42  | | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | | End of split
% 152.42/22.42  | | | | | | | | | | 
% 152.42/22.42  | | | | | | | | | End of split
% 152.42/22.42  | | | | | | | | | 
% 152.42/22.42  | | | | | | | | End of split
% 152.42/22.42  | | | | | | | | 
% 152.42/22.42  | | | | | | | End of split
% 152.42/22.42  | | | | | | | 
% 152.42/22.42  | | | | | | End of split
% 152.42/22.42  | | | | | | 
% 152.42/22.42  | | | | | End of split
% 152.42/22.42  | | | | | 
% 152.42/22.42  | | | | End of split
% 152.42/22.42  | | | | 
% 152.42/22.42  | | | End of split
% 152.42/22.42  | | | 
% 152.42/22.42  | | End of split
% 152.42/22.42  | | 
% 152.42/22.42  | End of split
% 152.42/22.42  | 
% 152.42/22.42  End of proof
% 152.42/22.42  
% 152.42/22.42  Sub-proof #243 shows that the following formulas are inconsistent:
% 152.42/22.42  ----------------------------------------------------------------
% 152.42/22.42    (1)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 152.42/22.42           all_57_12 & $i(all_57_12))
% 152.42/22.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.42    (3)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 152.42/22.42             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.42/22.42           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 152.42/22.42           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 152.42/22.42           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 152.42/22.42           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 152.42/22.42           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 152.42/22.42           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.42/22.42           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.42/22.42    (4)   ~ (e3 = e0)
% 152.42/22.42    (5)   ~ (e1 = e0)
% 152.42/22.42    (6)  op(e1, e1) = e3
% 152.42/22.42    (7)  op(e0, e0) = e0
% 152.42/22.42  
% 152.42/22.42  Begin of proof
% 152.42/22.42  | 
% 152.42/22.42  | BETA: splitting (3) gives:
% 152.42/22.42  | 
% 152.42/22.42  | Case 1:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (8)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 152.42/22.42  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.42/22.42  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 152.42/22.42  | | 
% 152.42/22.42  | | ALPHA: (8) implies:
% 152.42/22.42  | |   (9)  op(e0, e0) = e1
% 152.42/22.42  | | 
% 152.42/22.42  | | REF_CLOSE: (2), (5), (7), (9) are inconsistent by sub-proof #1040.
% 152.42/22.42  | | 
% 152.42/22.42  | Case 2:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (10)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.42/22.42  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.42  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.42/22.42  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 152.42/22.42  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 152.42/22.42  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.42/22.42  | |           $i(all_57_13))
% 152.42/22.42  | | 
% 152.42/22.42  | | BETA: splitting (10) gives:
% 152.42/22.42  | | 
% 152.42/22.42  | | Case 1:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (11)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.42/22.42  | | |         (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.42  | | |         op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.42/22.42  | | |         $i(all_57_11)
% 152.42/22.42  | | | 
% 152.42/22.42  | | | ALPHA: (11) implies:
% 152.42/22.42  | | |   (12)  all_57_12 = e0
% 152.42/22.42  | | |   (13)   ~ (all_57_11 = e2)
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (1), (12), (13) are inconsistent by sub-proof #890.
% 152.42/22.42  | | | 
% 152.42/22.42  | | Case 2:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (14)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.42/22.42  | | |         (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.42  | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.42/22.42  | | |         $i(all_57_13)
% 152.42/22.42  | | | 
% 152.42/22.42  | | | ALPHA: (14) implies:
% 152.42/22.42  | | |   (15)  op(e1, e1) = e0
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (2), (4), (6), (15) are inconsistent by sub-proof #896.
% 152.42/22.42  | | | 
% 152.42/22.42  | | End of split
% 152.42/22.42  | | 
% 152.42/22.42  | End of split
% 152.42/22.42  | 
% 152.42/22.42  End of proof
% 152.42/22.42  
% 152.42/22.42  Sub-proof #244 shows that the following formulas are inconsistent:
% 152.42/22.42  ----------------------------------------------------------------
% 152.42/22.42    (1)   ~ (e2 = e0)
% 152.42/22.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.42    (3)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 152.42/22.42             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 152.42/22.42           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 152.42/22.42           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 152.42/22.42           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 152.42/22.42           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.42/22.42    (4)   ~ (all_52_8 = e3)
% 152.42/22.42    (5)  op(e3, e1) = all_52_8
% 152.42/22.42    (6)  op(e0, e0) = e0
% 152.42/22.42  
% 152.42/22.42  Begin of proof
% 152.42/22.42  | 
% 152.42/22.42  | BETA: splitting (3) gives:
% 152.42/22.42  | 
% 152.42/22.42  | Case 1:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 152.42/22.42  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 152.42/22.42  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 152.42/22.42  | | 
% 152.42/22.42  | | ALPHA: (7) implies:
% 152.42/22.42  | |   (8)  op(e0, e0) = e2
% 152.42/22.42  | | 
% 152.42/22.42  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #1043.
% 152.42/22.42  | | 
% 152.42/22.42  | Case 2:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 152.42/22.42  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.42/22.42  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 152.42/22.42  | | 
% 152.42/22.42  | | ALPHA: (9) implies:
% 152.42/22.42  | |   (10)  op(e3, e1) = e3
% 152.42/22.42  | | 
% 152.42/22.42  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #1164.
% 152.42/22.42  | | 
% 152.42/22.42  | End of split
% 152.42/22.42  | 
% 152.42/22.42  End of proof
% 152.42/22.42  
% 152.42/22.42  Sub-proof #245 shows that the following formulas are inconsistent:
% 152.42/22.42  ----------------------------------------------------------------
% 152.42/22.42    (1)   ~ (e2 = e0)
% 152.42/22.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.42    (3)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 152.42/22.42             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.42/22.42           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 152.42/22.42           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 152.42/22.42           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 152.42/22.42           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 152.42/22.42    (4)  op(e1, e1) = e3
% 152.42/22.42    (5)   ~ (e3 = e2)
% 152.42/22.42    (6)  op(e0, e0) = e0
% 152.42/22.42  
% 152.42/22.42  Begin of proof
% 152.42/22.42  | 
% 152.42/22.42  | BETA: splitting (3) gives:
% 152.42/22.42  | 
% 152.42/22.42  | Case 1:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (7)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 152.42/22.42  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.42/22.42  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 152.42/22.42  | | 
% 152.42/22.42  | | ALPHA: (7) implies:
% 152.42/22.42  | |   (8)  op(e1, e1) = e2
% 152.42/22.42  | | 
% 152.42/22.42  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #834.
% 152.42/22.42  | | 
% 152.42/22.42  | Case 2:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (9)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 152.42/22.42  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 152.42/22.42  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 152.42/22.42  | | 
% 152.42/22.42  | | ALPHA: (9) implies:
% 152.42/22.42  | |   (10)  op(e0, e0) = e2
% 152.42/22.42  | | 
% 152.42/22.42  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #1043.
% 152.42/22.42  | | 
% 152.42/22.42  | End of split
% 152.42/22.42  | 
% 152.42/22.42  End of proof
% 152.42/22.42  
% 152.42/22.42  Sub-proof #246 shows that the following formulas are inconsistent:
% 152.42/22.42  ----------------------------------------------------------------
% 152.42/22.42    (1)  all_56_8 = e3
% 152.42/22.42    (2)   ~ (e3 = e1)
% 152.42/22.42    (3)  op(e2, e2) = e1
% 152.42/22.42    (4)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.42         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.42/22.42    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 152.42/22.42         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.42/22.42    (6)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.42/22.42         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.42    (7)  all_56_5 = e1
% 152.42/22.42    (8)   ~ (e2 = e0)
% 152.42/22.42    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.42    (10)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.42/22.42          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.42/22.42    (11)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.42/22.42          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.42    (12)   ~ (e3 = e0)
% 152.42/22.42    (13)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.42/22.42          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.42/22.42    (14)   ~ (all_52_6 = e3)
% 152.42/22.42    (15)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 152.42/22.42          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 152.42/22.42    (16)  op(e3, e3) = e1
% 152.42/22.42    (17)  op(e1, e2) = all_52_6
% 152.42/22.42    (18)  all_56_3 = e1
% 152.42/22.42    (19)   ~ (e1 = e0)
% 152.42/22.42    (20)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.42/22.42          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.42/22.42    (21)  op(e1, e1) = e3
% 152.42/22.42    (22)   ~ (e3 = e2)
% 152.42/22.42    (23)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.42          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.42/22.42    (24)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.42/22.42          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.42/22.42    (25)   ~ (e2 = e1)
% 152.42/22.42    (26)  op(e0, e0) = e0
% 152.42/22.42    (27)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.42          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.42    (28)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.42/22.42          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.42/22.42            e1)
% 152.42/22.42  
% 152.42/22.42  Begin of proof
% 152.42/22.42  | 
% 152.42/22.42  | BETA: splitting (28) gives:
% 152.42/22.42  | 
% 152.42/22.42  | Case 1:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (29)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 152.42/22.42  | |           e1)
% 152.42/22.42  | | 
% 152.42/22.42  | | BETA: splitting (29) gives:
% 152.42/22.42  | | 
% 152.42/22.42  | | Case 1:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (30)  all_56_12 = e1 & op(e0, e3) = e1
% 152.42/22.42  | | | 
% 152.42/22.42  | | | ALPHA: (30) implies:
% 152.42/22.42  | | |   (31)  all_56_12 = e1
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (1), (2), (5), (8), (9), (10), (12), (13), (15), (16), (19),
% 152.42/22.42  | | |            (20), (21), (22), (24), (25), (31) are inconsistent by
% 152.42/22.42  | | |            sub-proof #569.
% 152.42/22.42  | | | 
% 152.42/22.42  | | Case 2:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (32)  all_56_13 = e1 & op(e0, e2) = e1
% 152.42/22.42  | | | 
% 152.42/22.42  | | | ALPHA: (32) implies:
% 152.42/22.42  | | |   (33)  all_56_13 = e1
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (2), (3), (4), (8), (9), (12), (14), (17), (18), (19), (22),
% 152.42/22.42  | | |            (23), (25), (27), (33) are inconsistent by sub-proof #260.
% 152.42/22.42  | | | 
% 152.42/22.42  | | End of split
% 152.42/22.42  | | 
% 152.42/22.42  | Case 2:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (34)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.42/22.42  | |           e1)
% 152.42/22.42  | | 
% 152.42/22.42  | | BETA: splitting (34) gives:
% 152.42/22.42  | | 
% 152.42/22.42  | | Case 1:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (35)  all_56_14 = e1 & op(e0, e1) = e1
% 152.42/22.42  | | | 
% 152.42/22.42  | | | ALPHA: (35) implies:
% 152.42/22.42  | | |   (36)  all_56_14 = e1
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (6), (7), (8), (9), (11), (12), (19), (21), (22), (25), (36)
% 152.42/22.42  | | |            are inconsistent by sub-proof #247.
% 152.42/22.42  | | | 
% 152.42/22.42  | | Case 2:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (37)  all_56_15 = e1 & op(e0, e0) = e1
% 152.42/22.42  | | | 
% 152.42/22.42  | | | ALPHA: (37) implies:
% 152.42/22.42  | | |   (38)  op(e0, e0) = e1
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (9), (19), (26), (38) are inconsistent by sub-proof #1040.
% 152.42/22.42  | | | 
% 152.42/22.42  | | End of split
% 152.42/22.42  | | 
% 152.42/22.42  | End of split
% 152.42/22.42  | 
% 152.42/22.42  End of proof
% 152.42/22.42  
% 152.42/22.42  Sub-proof #247 shows that the following formulas are inconsistent:
% 152.42/22.42  ----------------------------------------------------------------
% 152.42/22.42    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.42/22.42         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.42    (2)  all_56_5 = e1
% 152.42/22.42    (3)   ~ (e2 = e0)
% 152.42/22.42    (4)  all_56_14 = e1
% 152.42/22.42    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.42    (6)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.42/22.42         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.42    (7)   ~ (e3 = e0)
% 152.42/22.42    (8)   ~ (e1 = e0)
% 152.42/22.42    (9)  op(e1, e1) = e3
% 152.42/22.42    (10)   ~ (e3 = e2)
% 152.42/22.42    (11)   ~ (e2 = e1)
% 152.42/22.42  
% 152.42/22.42  Begin of proof
% 152.42/22.42  | 
% 152.42/22.42  | BETA: splitting (6) gives:
% 152.42/22.42  | 
% 152.42/22.42  | Case 1:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (12)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) =
% 152.42/22.42  | |           e2)
% 152.42/22.42  | | 
% 152.42/22.42  | | BETA: splitting (12) gives:
% 152.42/22.42  | | 
% 152.42/22.42  | | Case 1:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (13)  all_56_4 = e2 & op(e3, e1) = e2
% 152.42/22.42  | | | 
% 152.42/22.42  | | | ALPHA: (13) implies:
% 152.42/22.42  | | |   (14)  all_56_4 = e2
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (14) are inconsistent
% 152.42/22.42  | | |            by sub-proof #249.
% 152.42/22.42  | | | 
% 152.42/22.42  | | Case 2:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (15)  all_56_5 = e2 & op(e2, e1) = e2
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (2), (11), (15) are inconsistent by sub-proof #672.
% 152.42/22.42  | | | 
% 152.42/22.42  | | End of split
% 152.42/22.42  | | 
% 152.42/22.42  | Case 2:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (16)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) =
% 152.42/22.42  | |           e2)
% 152.42/22.42  | | 
% 152.42/22.42  | | BETA: splitting (16) gives:
% 152.42/22.42  | | 
% 152.42/22.42  | | Case 1:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (17)  all_56_8 = e2 & op(e1, e1) = e2
% 152.42/22.42  | | | 
% 152.42/22.42  | | | ALPHA: (17) implies:
% 152.42/22.42  | | |   (18)  op(e1, e1) = e2
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (5), (9), (10), (18) are inconsistent by sub-proof #834.
% 152.42/22.42  | | | 
% 152.42/22.42  | | Case 2:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (19)  all_56_14 = e2 & op(e0, e1) = e2
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (4), (11), (19) are inconsistent by sub-proof #248.
% 152.42/22.42  | | | 
% 152.42/22.42  | | End of split
% 152.42/22.42  | | 
% 152.42/22.42  | End of split
% 152.42/22.42  | 
% 152.42/22.42  End of proof
% 152.42/22.42  
% 152.42/22.42  Sub-proof #248 shows that the following formulas are inconsistent:
% 152.42/22.42  ----------------------------------------------------------------
% 152.42/22.42    (1)  all_56_14 = e2 & op(e0, e1) = e2
% 152.42/22.42    (2)  all_56_14 = e1
% 152.42/22.42    (3)   ~ (e2 = e1)
% 152.42/22.42  
% 152.42/22.42  Begin of proof
% 152.42/22.42  | 
% 152.42/22.42  | ALPHA: (1) implies:
% 152.42/22.42  |   (4)  all_56_14 = e2
% 152.42/22.42  | 
% 152.42/22.42  | COMBINE_EQS: (2), (4) imply:
% 152.42/22.42  |   (5)  e2 = e1
% 152.42/22.42  | 
% 152.42/22.42  | REDUCE: (3), (5) imply:
% 152.42/22.42  |   (6)  $false
% 152.42/22.42  | 
% 152.42/22.42  | CLOSE: (6) is inconsistent.
% 152.42/22.42  | 
% 152.42/22.42  End of proof
% 152.42/22.42  
% 152.42/22.42  Sub-proof #249 shows that the following formulas are inconsistent:
% 152.42/22.42  ----------------------------------------------------------------
% 152.42/22.42    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.42/22.42         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.42    (2)  all_56_5 = e1
% 152.42/22.42    (3)   ~ (e2 = e0)
% 152.42/22.42    (4)  all_56_14 = e1
% 152.42/22.42    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.42    (6)  all_56_4 = e2
% 152.42/22.42    (7)   ~ (e3 = e0)
% 152.42/22.42    (8)   ~ (e1 = e0)
% 152.42/22.42    (9)  op(e1, e1) = e3
% 152.42/22.42  
% 152.42/22.42  Begin of proof
% 152.42/22.42  | 
% 152.42/22.42  | BETA: splitting (1) gives:
% 152.42/22.42  | 
% 152.42/22.42  | Case 1:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (10)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 152.42/22.42  | |           e0)
% 152.42/22.42  | | 
% 152.42/22.42  | | BETA: splitting (10) gives:
% 152.42/22.42  | | 
% 152.42/22.42  | | Case 1:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (11)  all_56_4 = e0 & op(e3, e1) = e0
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #1070.
% 152.42/22.42  | | | 
% 152.42/22.42  | | Case 2:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (12)  all_56_5 = e0 & op(e2, e1) = e0
% 152.42/22.42  | | | 
% 152.42/22.42  | | | ALPHA: (12) implies:
% 152.42/22.42  | | |   (13)  all_56_5 = e0
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #682.
% 152.42/22.42  | | | 
% 152.42/22.42  | | End of split
% 152.42/22.42  | | 
% 152.42/22.42  | Case 2:
% 152.42/22.42  | | 
% 152.42/22.42  | |   (14)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 152.42/22.42  | |           e0)
% 152.42/22.42  | | 
% 152.42/22.42  | | BETA: splitting (14) gives:
% 152.42/22.42  | | 
% 152.42/22.42  | | Case 1:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (15)  all_56_8 = e0 & op(e1, e1) = e0
% 152.42/22.42  | | | 
% 152.42/22.42  | | | ALPHA: (15) implies:
% 152.42/22.42  | | |   (16)  op(e1, e1) = e0
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (5), (7), (9), (16) are inconsistent by sub-proof #896.
% 152.42/22.42  | | | 
% 152.42/22.42  | | Case 2:
% 152.42/22.42  | | | 
% 152.42/22.42  | | |   (17)  all_56_14 = e0 & op(e0, e1) = e0
% 152.42/22.42  | | | 
% 152.42/22.42  | | | REF_CLOSE: (4), (8), (17) are inconsistent by sub-proof #279.
% 152.42/22.42  | | | 
% 152.42/22.42  | | End of split
% 152.42/22.42  | | 
% 152.42/22.42  | End of split
% 152.42/22.42  | 
% 152.42/22.42  End of proof
% 152.42/22.42  
% 152.42/22.42  Sub-proof #250 shows that the following formulas are inconsistent:
% 152.42/22.42  ----------------------------------------------------------------
% 152.42/22.42    (1)  all_56_14 = e1 & op(e0, e1) = e1
% 152.42/22.42    (2)  all_56_8 = e3
% 152.42/22.42    (3)   ~ (e3 = e1)
% 152.42/22.42    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 152.42/22.42         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 152.42/22.42    (5)  all_56_9 = e1
% 152.42/22.42    (6)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.42/22.42         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.42    (7)   ~ (e2 = e0)
% 152.42/22.42    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.42    (9)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.42/22.42         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.42/22.43    (10)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.42/22.43          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.43    (11)   ~ (e3 = e0)
% 152.42/22.43    (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.42/22.43          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.42/22.43    (13)  op(e3, e3) = e1
% 152.42/22.43    (14)   ~ (e1 = e0)
% 152.42/22.43    (15)  op(e1, e1) = e3
% 152.42/22.43    (16)   ~ (e3 = e2)
% 152.42/22.43    (17)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.42/22.43          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.42/22.43    (18)   ~ (e2 = e1)
% 152.42/22.43  
% 152.42/22.43  Begin of proof
% 152.42/22.43  | 
% 152.42/22.43  | ALPHA: (1) implies:
% 152.42/22.43  |   (19)  all_56_14 = e1
% 152.42/22.43  | 
% 152.42/22.43  | BETA: splitting (9) gives:
% 152.42/22.43  | 
% 152.42/22.43  | Case 1:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (20)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 152.42/22.43  | |           e3)
% 152.42/22.43  | | 
% 152.42/22.43  | | REF_CLOSE: (3), (4), (5), (7), (8), (11), (12), (13), (14), (16), (18), (20)
% 152.42/22.43  | |            are inconsistent by sub-proof #944.
% 152.42/22.43  | | 
% 152.42/22.43  | Case 2:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (21)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 152.42/22.43  | |           e3)
% 152.42/22.43  | | 
% 152.42/22.43  | | BETA: splitting (21) gives:
% 152.42/22.43  | | 
% 152.42/22.43  | | Case 1:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (22)  all_56_4 = e3 & op(e3, e1) = e3
% 152.42/22.43  | | | 
% 152.42/22.43  | | | ALPHA: (22) implies:
% 152.42/22.43  | | |   (23)  all_56_4 = e3
% 152.42/22.43  | | | 
% 152.42/22.43  | | | BETA: splitting (12) gives:
% 152.42/22.43  | | | 
% 152.42/22.43  | | | Case 1:
% 152.42/22.43  | | | | 
% 152.42/22.43  | | | |   (24)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2)
% 152.42/22.43  | | | |           = e0)
% 152.42/22.43  | | | | 
% 152.42/22.43  | | | | BETA: splitting (24) gives:
% 152.42/22.43  | | | | 
% 152.42/22.43  | | | | Case 1:
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | |   (25)  all_56_0 = e0 & op(e3, e3) = e0
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | | ALPHA: (25) implies:
% 152.42/22.43  | | | | |   (26)  op(e3, e3) = e0
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | | REF_CLOSE: (8), (13), (14), (26) are inconsistent by sub-proof #957.
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | Case 2:
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | |   (27)  all_56_1 = e0 & op(e3, e2) = e0
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | | ALPHA: (27) implies:
% 152.42/22.43  | | | | |   (28)  all_56_1 = e0
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | | BETA: splitting (10) gives:
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | | Case 1:
% 152.42/22.43  | | | | | | 
% 152.42/22.43  | | | | | |   (29)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2,
% 152.42/22.43  | | | | | |             e1) = e2)
% 152.42/22.43  | | | | | | 
% 152.42/22.43  | | | | | | BETA: splitting (29) gives:
% 152.42/22.43  | | | | | | 
% 152.42/22.43  | | | | | | Case 1:
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | |   (30)  all_56_4 = e2 & op(e3, e1) = e2
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | | ALPHA: (30) implies:
% 152.42/22.43  | | | | | | |   (31)  all_56_4 = e2
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (11), (12), (13), (14),
% 152.42/22.43  | | | | | | |            (16), (18), (31) are inconsistent by sub-proof #941.
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | Case 2:
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | |   (32)  all_56_5 = e2 & op(e2, e1) = e2
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | | ALPHA: (32) implies:
% 152.42/22.43  | | | | | | |   (33)  all_56_5 = e2
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | | BETA: splitting (4) gives:
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | | Case 1:
% 152.42/22.43  | | | | | | | | 
% 152.42/22.43  | | | | | | | |   (34)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 &
% 152.42/22.43  | | | | | | | |           op(e3, e2) = e2)
% 152.42/22.43  | | | | | | | | 
% 152.42/22.43  | | | | | | | | BETA: splitting (34) gives:
% 152.42/22.43  | | | | | | | | 
% 152.42/22.43  | | | | | | | | Case 1:
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | |   (35)  all_56_0 = e2 & op(e3, e3) = e2
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | ALPHA: (35) implies:
% 152.42/22.43  | | | | | | | | |   (36)  op(e3, e3) = e2
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | REF_CLOSE: (8), (13), (18), (36) are inconsistent by sub-proof
% 152.42/22.43  | | | | | | | | |            #1074.
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | Case 2:
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | |   (37)  all_56_1 = e2 & op(e3, e2) = e2
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | ALPHA: (37) implies:
% 152.42/22.43  | | | | | | | | |   (38)  all_56_1 = e2
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | COMBINE_EQS: (28), (38) imply:
% 152.42/22.43  | | | | | | | | |   (39)  e2 = e0
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | REDUCE: (7), (39) imply:
% 152.42/22.43  | | | | | | | | |   (40)  $false
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | CLOSE: (40) is inconsistent.
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | End of split
% 152.42/22.43  | | | | | | | | 
% 152.42/22.43  | | | | | | | Case 2:
% 152.42/22.43  | | | | | | | | 
% 152.42/22.43  | | | | | | | |   (41)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 &
% 152.42/22.43  | | | | | | | |           op(e3, e0) = e2)
% 152.42/22.43  | | | | | | | | 
% 152.42/22.43  | | | | | | | | BETA: splitting (41) gives:
% 152.42/22.43  | | | | | | | | 
% 152.42/22.43  | | | | | | | | Case 1:
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | |   (42)  all_56_4 = e2 & op(e3, e1) = e2
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | ALPHA: (42) implies:
% 152.42/22.43  | | | | | | | | |   (43)  all_56_4 = e2
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (11), (12), (13),
% 152.42/22.43  | | | | | | | | |            (14), (16), (18), (43) are inconsistent by
% 152.42/22.43  | | | | | | | | |            sub-proof #941.
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | Case 2:
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | |   (44)  all_56_9 = e2 & op(e3, e0) = e2
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | ALPHA: (44) implies:
% 152.42/22.43  | | | | | | | | |   (45)  all_56_9 = e2
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | COMBINE_EQS: (5), (45) imply:
% 152.42/22.43  | | | | | | | | |   (46)  e2 = e1
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | SIMP: (46) implies:
% 152.42/22.43  | | | | | | | | |   (47)  e2 = e1
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | COMBINE_EQS: (33), (47) imply:
% 152.42/22.43  | | | | | | | | |   (48)  all_56_5 = e1
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 152.42/22.43  | | | | | | | | |            (13), (14), (15), (16), (18), (19), (48) are
% 152.42/22.43  | | | | | | | | |            inconsistent by sub-proof #251.
% 152.42/22.43  | | | | | | | | | 
% 152.42/22.43  | | | | | | | | End of split
% 152.42/22.43  | | | | | | | | 
% 152.42/22.43  | | | | | | | End of split
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | End of split
% 152.42/22.43  | | | | | | 
% 152.42/22.43  | | | | | Case 2:
% 152.42/22.43  | | | | | | 
% 152.42/22.43  | | | | | |   (49)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0,
% 152.42/22.43  | | | | | |             e1) = e2)
% 152.42/22.43  | | | | | | 
% 152.42/22.43  | | | | | | BETA: splitting (49) gives:
% 152.42/22.43  | | | | | | 
% 152.42/22.43  | | | | | | Case 1:
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | |   (50)  all_56_8 = e2 & op(e1, e1) = e2
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | | ALPHA: (50) implies:
% 152.42/22.43  | | | | | | |   (51)  op(e1, e1) = e2
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | | REF_CLOSE: (8), (15), (16), (51) are inconsistent by sub-proof
% 152.42/22.43  | | | | | | |            #834.
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | Case 2:
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | |   (52)  all_56_14 = e2 & op(e0, e1) = e2
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | | ALPHA: (52) implies:
% 152.42/22.43  | | | | | | |   (53)  all_56_14 = e2
% 152.42/22.43  | | | | | | |   (54)  op(e0, e1) = e2
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | | REF_CLOSE: (2), (3), (6), (7), (8), (11), (14), (15), (17), (18),
% 152.42/22.43  | | | | | | |            (23), (53), (54) are inconsistent by sub-proof #354.
% 152.42/22.43  | | | | | | | 
% 152.42/22.43  | | | | | | End of split
% 152.42/22.43  | | | | | | 
% 152.42/22.43  | | | | | End of split
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | End of split
% 152.42/22.43  | | | | 
% 152.42/22.43  | | | Case 2:
% 152.42/22.43  | | | | 
% 152.42/22.43  | | | |   (55)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0)
% 152.42/22.43  | | | |           = e0)
% 152.42/22.43  | | | | 
% 152.42/22.43  | | | | BETA: splitting (55) gives:
% 152.42/22.43  | | | | 
% 152.42/22.43  | | | | Case 1:
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | |   (56)  all_56_4 = e0 & op(e3, e1) = e0
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | | REF_CLOSE: (11), (23), (56) are inconsistent by sub-proof #361.
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | Case 2:
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | |   (57)  all_56_9 = e0 & op(e3, e0) = e0
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | | ALPHA: (57) implies:
% 152.42/22.43  | | | | |   (58)  all_56_9 = e0
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | | REF_CLOSE: (5), (14), (58) are inconsistent by sub-proof #946.
% 152.42/22.43  | | | | | 
% 152.42/22.43  | | | | End of split
% 152.42/22.43  | | | | 
% 152.42/22.43  | | | End of split
% 152.42/22.43  | | | 
% 152.42/22.43  | | Case 2:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (59)  all_56_9 = e3 & op(e3, e0) = e3
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (3), (5), (59) are inconsistent by sub-proof #942.
% 152.42/22.43  | | | 
% 152.42/22.43  | | End of split
% 152.42/22.43  | | 
% 152.42/22.43  | End of split
% 152.42/22.43  | 
% 152.42/22.43  End of proof
% 152.42/22.43  
% 152.42/22.43  Sub-proof #251 shows that the following formulas are inconsistent:
% 152.42/22.43  ----------------------------------------------------------------
% 152.42/22.43    (1)   ~ (e3 = e1)
% 152.42/22.43    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 152.42/22.43         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 152.42/22.43    (3)  all_56_9 = e1
% 152.42/22.43    (4)  all_56_5 = e1
% 152.42/22.43    (5)   ~ (e2 = e0)
% 152.42/22.43    (6)  all_56_14 = e1
% 152.42/22.43    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.43    (8)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.42/22.43         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.42/22.43    (9)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.42/22.43         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.43    (10)   ~ (e3 = e0)
% 152.42/22.43    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.42/22.43          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.42/22.43    (12)  op(e3, e3) = e1
% 152.42/22.43    (13)   ~ (e1 = e0)
% 152.42/22.43    (14)  op(e1, e1) = e3
% 152.42/22.43    (15)   ~ (e3 = e2)
% 152.42/22.43    (16)   ~ (e2 = e1)
% 152.42/22.43  
% 152.42/22.43  Begin of proof
% 152.42/22.43  | 
% 152.42/22.43  | BETA: splitting (9) gives:
% 152.42/22.43  | 
% 152.42/22.43  | Case 1:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (17)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) =
% 152.42/22.43  | |           e2)
% 152.42/22.43  | | 
% 152.42/22.43  | | BETA: splitting (17) gives:
% 152.42/22.43  | | 
% 152.42/22.43  | | Case 1:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (18)  all_56_4 = e2 & op(e3, e1) = e2
% 152.42/22.43  | | | 
% 152.42/22.43  | | | ALPHA: (18) implies:
% 152.42/22.43  | | |   (19)  all_56_4 = e2
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (10), (11), (12), (13), (15),
% 152.42/22.43  | | |            (16), (19) are inconsistent by sub-proof #941.
% 152.42/22.43  | | | 
% 152.42/22.43  | | Case 2:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (20)  all_56_5 = e2 & op(e2, e1) = e2
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (4), (16), (20) are inconsistent by sub-proof #672.
% 152.42/22.43  | | | 
% 152.42/22.43  | | End of split
% 152.42/22.43  | | 
% 152.42/22.43  | Case 2:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (21)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) =
% 152.42/22.43  | |           e2)
% 152.42/22.43  | | 
% 152.42/22.43  | | REF_CLOSE: (6), (7), (14), (15), (16), (21) are inconsistent by sub-proof
% 152.42/22.43  | |            #255.
% 152.42/22.43  | | 
% 152.42/22.43  | End of split
% 152.42/22.43  | 
% 152.42/22.43  End of proof
% 152.42/22.43  
% 152.42/22.43  Sub-proof #252 shows that the following formulas are inconsistent:
% 152.42/22.43  ----------------------------------------------------------------
% 152.42/22.43    (1)  all_56_13 = e1 & op(e0, e2) = e1
% 152.42/22.43    (2)   ~ (e3 = e1)
% 152.42/22.43    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 152.42/22.43         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 152.42/22.43    (4)  all_56_9 = e1
% 152.42/22.43    (5)   ~ (e2 = e0)
% 152.42/22.43    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.43    (7)   ~ (e3 = e0)
% 152.42/22.43    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.42/22.43         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.42/22.43    (9)   ~ (all_52_6 = e3)
% 152.42/22.43    (10)  op(e3, e3) = e1
% 152.42/22.43    (11)  op(e1, e2) = all_52_6
% 152.42/22.43    (12)  all_56_3 = e1
% 152.42/22.43    (13)   ~ (e1 = e0)
% 152.42/22.43    (14)   ~ (e3 = e2)
% 152.42/22.43    (15)   ~ (e2 = e1)
% 152.42/22.43    (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.43          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.43  
% 152.42/22.43  Begin of proof
% 152.42/22.43  | 
% 152.42/22.43  | ALPHA: (1) implies:
% 152.42/22.43  |   (17)  all_56_13 = e1
% 152.42/22.43  | 
% 152.42/22.43  | BETA: splitting (16) gives:
% 152.42/22.43  | 
% 152.42/22.43  | Case 1:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (18)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.42/22.43  | |           e3)
% 152.42/22.43  | | 
% 152.42/22.43  | | BETA: splitting (18) gives:
% 152.42/22.43  | | 
% 152.42/22.43  | | Case 1:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (19)  all_56_1 = e3 & op(e3, e2) = e3
% 152.42/22.43  | | | 
% 152.42/22.43  | | | ALPHA: (19) implies:
% 152.42/22.43  | | |   (20)  all_56_1 = e3
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (10), (13), (14), (15), (20) are
% 152.42/22.43  | | |            inconsistent by sub-proof #945.
% 152.42/22.43  | | | 
% 152.42/22.43  | | Case 2:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (21)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (2), (12), (21) are inconsistent by sub-proof #270.
% 152.42/22.43  | | | 
% 152.42/22.43  | | End of split
% 152.42/22.43  | | 
% 152.42/22.43  | Case 2:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (22)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 152.42/22.43  | |           e3)
% 152.42/22.43  | | 
% 152.42/22.43  | | BETA: splitting (22) gives:
% 152.42/22.43  | | 
% 152.42/22.43  | | Case 1:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (23)  all_56_7 = e3 & op(e1, e2) = e3
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (6), (9), (11), (23) are inconsistent by sub-proof #925.
% 152.42/22.43  | | | 
% 152.42/22.43  | | Case 2:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (24)  all_56_13 = e3 & op(e0, e2) = e3
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (2), (17), (24) are inconsistent by sub-proof #585.
% 152.42/22.43  | | | 
% 152.42/22.43  | | End of split
% 152.42/22.43  | | 
% 152.42/22.43  | End of split
% 152.42/22.43  | 
% 152.42/22.43  End of proof
% 152.42/22.43  
% 152.42/22.43  Sub-proof #253 shows that the following formulas are inconsistent:
% 152.42/22.43  ----------------------------------------------------------------
% 152.42/22.43    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.42/22.43         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.43    (2)   ~ (e2 = e0)
% 152.42/22.43    (3)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.42/22.43    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.43    (5)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.42/22.43         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.43    (6)   ~ (e3 = e0)
% 152.42/22.43    (7)  all_56_4 = e1
% 152.42/22.43    (8)   ~ (e1 = e0)
% 152.42/22.43    (9)  op(e1, e1) = e3
% 152.42/22.43    (10)   ~ (e3 = e2)
% 152.42/22.43    (11)   ~ (e2 = e1)
% 152.42/22.43    (12)  op(e0, e0) = e0
% 152.42/22.43  
% 152.42/22.43  Begin of proof
% 152.42/22.43  | 
% 152.42/22.43  | BETA: splitting (3) gives:
% 152.42/22.43  | 
% 152.42/22.43  | Case 1:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (13)  all_56_14 = e1 & op(e0, e1) = e1
% 152.42/22.43  | | 
% 152.42/22.43  | | ALPHA: (13) implies:
% 152.42/22.43  | |   (14)  all_56_14 = e1
% 152.42/22.43  | | 
% 152.42/22.43  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (14) are
% 152.42/22.43  | |            inconsistent by sub-proof #254.
% 152.42/22.43  | | 
% 152.42/22.43  | Case 2:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (15)  all_56_15 = e1 & op(e0, e0) = e1
% 152.42/22.43  | | 
% 152.42/22.43  | | ALPHA: (15) implies:
% 152.42/22.43  | |   (16)  op(e0, e0) = e1
% 152.42/22.43  | | 
% 152.42/22.43  | | REF_CLOSE: (4), (8), (12), (16) are inconsistent by sub-proof #1040.
% 152.42/22.43  | | 
% 152.42/22.43  | End of split
% 152.42/22.43  | 
% 152.42/22.43  End of proof
% 152.42/22.43  
% 152.42/22.43  Sub-proof #254 shows that the following formulas are inconsistent:
% 152.42/22.43  ----------------------------------------------------------------
% 152.42/22.43    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.42/22.43         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.43    (2)   ~ (e2 = e0)
% 152.42/22.43    (3)  all_56_14 = e1
% 152.42/22.43    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.43    (5)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.42/22.43         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.43    (6)   ~ (e3 = e0)
% 152.42/22.43    (7)  all_56_4 = e1
% 152.42/22.43    (8)   ~ (e1 = e0)
% 152.42/22.43    (9)  op(e1, e1) = e3
% 152.42/22.43    (10)   ~ (e3 = e2)
% 152.42/22.43    (11)   ~ (e2 = e1)
% 152.42/22.43  
% 152.42/22.43  Begin of proof
% 152.42/22.43  | 
% 152.42/22.43  | BETA: splitting (5) gives:
% 152.42/22.43  | 
% 152.42/22.43  | Case 1:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (12)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) =
% 152.42/22.43  | |           e2)
% 152.42/22.43  | | 
% 152.42/22.43  | | BETA: splitting (12) gives:
% 152.42/22.43  | | 
% 152.42/22.43  | | Case 1:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (13)  all_56_4 = e2 & op(e3, e1) = e2
% 152.42/22.43  | | | 
% 152.42/22.43  | | | ALPHA: (13) implies:
% 152.42/22.43  | | |   (14)  all_56_4 = e2
% 152.42/22.43  | | | 
% 152.42/22.43  | | | COMBINE_EQS: (7), (14) imply:
% 152.42/22.43  | | |   (15)  e2 = e1
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REDUCE: (11), (15) imply:
% 152.42/22.43  | | |   (16)  $false
% 152.42/22.43  | | | 
% 152.42/22.43  | | | CLOSE: (16) is inconsistent.
% 152.42/22.43  | | | 
% 152.42/22.43  | | Case 2:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (17)  all_56_5 = e2 & op(e2, e1) = e2
% 152.42/22.43  | | | 
% 152.42/22.43  | | | ALPHA: (17) implies:
% 152.42/22.43  | | |   (18)  all_56_5 = e2
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (18) are inconsistent
% 152.42/22.43  | | |            by sub-proof #256.
% 152.42/22.43  | | | 
% 152.42/22.43  | | End of split
% 152.42/22.43  | | 
% 152.42/22.43  | Case 2:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (19)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) =
% 152.42/22.43  | |           e2)
% 152.42/22.43  | | 
% 152.42/22.43  | | REF_CLOSE: (3), (4), (9), (10), (11), (19) are inconsistent by sub-proof
% 152.42/22.43  | |            #255.
% 152.42/22.43  | | 
% 152.42/22.43  | End of split
% 152.42/22.43  | 
% 152.42/22.43  End of proof
% 152.42/22.43  
% 152.42/22.43  Sub-proof #255 shows that the following formulas are inconsistent:
% 152.42/22.43  ----------------------------------------------------------------
% 152.42/22.43    (1)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.43    (2)  all_56_14 = e1
% 152.42/22.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.43    (4)  op(e1, e1) = e3
% 152.42/22.43    (5)   ~ (e3 = e2)
% 152.42/22.43    (6)   ~ (e2 = e1)
% 152.42/22.43  
% 152.42/22.43  Begin of proof
% 152.42/22.43  | 
% 152.42/22.43  | BETA: splitting (1) gives:
% 152.42/22.43  | 
% 152.42/22.43  | Case 1:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (7)  all_56_8 = e2 & op(e1, e1) = e2
% 152.42/22.43  | | 
% 152.42/22.43  | | ALPHA: (7) implies:
% 152.42/22.43  | |   (8)  op(e1, e1) = e2
% 152.42/22.43  | | 
% 152.42/22.43  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #834.
% 152.42/22.43  | | 
% 152.42/22.43  | Case 2:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (9)  all_56_14 = e2 & op(e0, e1) = e2
% 152.42/22.43  | | 
% 152.42/22.43  | | ALPHA: (9) implies:
% 152.42/22.43  | |   (10)  all_56_14 = e2
% 152.42/22.43  | | 
% 152.42/22.43  | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #1099.
% 152.42/22.43  | | 
% 152.42/22.43  | End of split
% 152.42/22.43  | 
% 152.42/22.43  End of proof
% 152.42/22.43  
% 152.42/22.43  Sub-proof #256 shows that the following formulas are inconsistent:
% 152.42/22.43  ----------------------------------------------------------------
% 152.42/22.43    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.42/22.43         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.43    (2)   ~ (e2 = e0)
% 152.42/22.43    (3)  all_56_14 = e1
% 152.42/22.43    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.43    (5)  all_56_5 = e2
% 152.42/22.43    (6)   ~ (e3 = e0)
% 152.42/22.43    (7)  all_56_4 = e1
% 152.42/22.43    (8)   ~ (e1 = e0)
% 152.42/22.43    (9)  op(e1, e1) = e3
% 152.42/22.43  
% 152.42/22.43  Begin of proof
% 152.42/22.43  | 
% 152.42/22.43  | BETA: splitting (1) gives:
% 152.42/22.43  | 
% 152.42/22.43  | Case 1:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (10)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 152.42/22.43  | |           e0)
% 152.42/22.43  | | 
% 152.42/22.43  | | BETA: splitting (10) gives:
% 152.42/22.43  | | 
% 152.42/22.43  | | Case 1:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (11)  all_56_4 = e0 & op(e3, e1) = e0
% 152.42/22.43  | | | 
% 152.42/22.43  | | | ALPHA: (11) implies:
% 152.42/22.43  | | |   (12)  all_56_4 = e0
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (7), (8), (12) are inconsistent by sub-proof #657.
% 152.42/22.43  | | | 
% 152.42/22.43  | | Case 2:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (13)  all_56_5 = e0 & op(e2, e1) = e0
% 152.42/22.43  | | | 
% 152.42/22.43  | | | ALPHA: (13) implies:
% 152.42/22.43  | | |   (14)  all_56_5 = e0
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (2), (5), (14) are inconsistent by sub-proof #509.
% 152.42/22.43  | | | 
% 152.42/22.43  | | End of split
% 152.42/22.43  | | 
% 152.42/22.43  | Case 2:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (15)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 152.42/22.43  | |           e0)
% 152.42/22.43  | | 
% 152.42/22.43  | | BETA: splitting (15) gives:
% 152.42/22.43  | | 
% 152.42/22.43  | | Case 1:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (16)  all_56_8 = e0 & op(e1, e1) = e0
% 152.42/22.43  | | | 
% 152.42/22.43  | | | ALPHA: (16) implies:
% 152.42/22.43  | | |   (17)  op(e1, e1) = e0
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (4), (6), (9), (17) are inconsistent by sub-proof #896.
% 152.42/22.43  | | | 
% 152.42/22.43  | | Case 2:
% 152.42/22.43  | | | 
% 152.42/22.43  | | |   (18)  all_56_14 = e0 & op(e0, e1) = e0
% 152.42/22.43  | | | 
% 152.42/22.43  | | | REF_CLOSE: (3), (8), (18) are inconsistent by sub-proof #1118.
% 152.42/22.43  | | | 
% 152.42/22.43  | | End of split
% 152.42/22.43  | | 
% 152.42/22.43  | End of split
% 152.42/22.43  | 
% 152.42/22.43  End of proof
% 152.42/22.43  
% 152.42/22.43  Sub-proof #257 shows that the following formulas are inconsistent:
% 152.42/22.43  ----------------------------------------------------------------
% 152.42/22.43    (1)   ~ (e3 = e1)
% 152.42/22.43    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.43    (3)  all_56_13 = e1
% 152.42/22.43    (4)   ~ (all_52_6 = e3)
% 152.42/22.43    (5)  op(e1, e2) = all_52_6
% 152.42/22.43    (6)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.43  
% 152.42/22.43  Begin of proof
% 152.42/22.43  | 
% 152.42/22.43  | BETA: splitting (6) gives:
% 152.42/22.43  | 
% 152.42/22.43  | Case 1:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (7)  all_56_7 = e3 & op(e1, e2) = e3
% 152.42/22.43  | | 
% 152.42/22.43  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #925.
% 152.42/22.43  | | 
% 152.42/22.43  | Case 2:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (8)  all_56_13 = e3 & op(e0, e2) = e3
% 152.42/22.43  | | 
% 152.42/22.43  | | ALPHA: (8) implies:
% 152.42/22.43  | |   (9)  all_56_13 = e3
% 152.42/22.43  | | 
% 152.42/22.43  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1121.
% 152.42/22.43  | | 
% 152.42/22.43  | End of split
% 152.42/22.43  | 
% 152.42/22.43  End of proof
% 152.42/22.43  
% 152.42/22.43  Sub-proof #258 shows that the following formulas are inconsistent:
% 152.42/22.43  ----------------------------------------------------------------
% 152.42/22.43    (1)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.42/22.43    (2)  all_56_10 = e3
% 152.42/22.43    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.43    (4)   ~ (all_52_9 = e2)
% 152.42/22.43    (5)  op(e2, e1) = all_52_9
% 152.42/22.43    (6)   ~ (e3 = e2)
% 152.42/22.43  
% 152.42/22.43  Begin of proof
% 152.42/22.43  | 
% 152.42/22.43  | BETA: splitting (1) gives:
% 152.42/22.43  | 
% 152.42/22.43  | Case 1:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (7)  all_56_5 = e2 & op(e2, e1) = e2
% 152.42/22.43  | | 
% 152.42/22.43  | | ALPHA: (7) implies:
% 152.42/22.43  | |   (8)  op(e2, e1) = e2
% 152.42/22.43  | | 
% 152.42/22.43  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1157.
% 152.42/22.43  | | 
% 152.42/22.43  | Case 2:
% 152.42/22.43  | | 
% 152.42/22.43  | |   (9)  all_56_10 = e2 & op(e2, e0) = e2
% 152.42/22.43  | | 
% 152.42/22.43  | | ALPHA: (9) implies:
% 152.42/22.43  | |   (10)  all_56_10 = e2
% 152.42/22.43  | | 
% 152.42/22.43  | | COMBINE_EQS: (2), (10) imply:
% 152.42/22.43  | |   (11)  e3 = e2
% 152.42/22.43  | | 
% 152.42/22.43  | | SIMP: (11) implies:
% 152.42/22.43  | |   (12)  e3 = e2
% 152.42/22.43  | | 
% 152.42/22.43  | | REDUCE: (6), (12) imply:
% 152.42/22.43  | |   (13)  $false
% 152.42/22.43  | | 
% 152.42/22.43  | | CLOSE: (13) is inconsistent.
% 152.42/22.43  | | 
% 152.42/22.43  | End of split
% 152.42/22.43  | 
% 152.42/22.43  End of proof
% 152.42/22.43  
% 152.42/22.43  Sub-proof #259 shows that the following formulas are inconsistent:
% 152.42/22.43  ----------------------------------------------------------------
% 152.42/22.43    (1)   ~ (e3 = e1)
% 152.42/22.43    (2)  op(e2, e2) = e1
% 152.42/22.43    (3)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.43         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.42/22.43    (4)   ~ (e2 = e0)
% 152.42/22.43    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.43           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.43    (6)  e3 = e1
% 152.42/22.43    (7)   ~ (e3 = e0)
% 152.42/22.44    (8)   ~ (all_52_6 = e3)
% 152.42/22.44    (9)  op(e1, e2) = all_52_6
% 152.42/22.44    (10)  all_56_3 = e1
% 152.42/22.44    (11)   ~ (e1 = e0)
% 152.42/22.44    (12)  all_56_13 = e3
% 152.42/22.44    (13)   ~ (e3 = e2)
% 152.42/22.44    (14)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.44          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.42/22.44    (15)   ~ (e2 = e1)
% 152.42/22.44    (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.44          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.44  
% 152.42/22.44  Begin of proof
% 152.42/22.44  | 
% 152.42/22.44  | SIMP: (6) implies:
% 152.42/22.44  |   (17)  e3 = e1
% 152.42/22.44  | 
% 152.42/22.44  | COMBINE_EQS: (12), (17) imply:
% 152.42/22.44  |   (18)  all_56_13 = e1
% 152.42/22.44  | 
% 152.42/22.44  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 152.42/22.44  |            (15), (16), (18) are inconsistent by sub-proof #260.
% 152.42/22.44  | 
% 152.42/22.44  End of proof
% 152.42/22.44  
% 152.42/22.44  Sub-proof #260 shows that the following formulas are inconsistent:
% 152.42/22.44  ----------------------------------------------------------------
% 152.42/22.44    (1)   ~ (e3 = e1)
% 152.42/22.44    (2)  op(e2, e2) = e1
% 152.42/22.44    (3)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.44         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.42/22.44    (4)   ~ (e2 = e0)
% 152.42/22.44    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.44    (6)  all_56_13 = e1
% 152.42/22.44    (7)   ~ (e3 = e0)
% 152.42/22.44    (8)   ~ (all_52_6 = e3)
% 152.42/22.44    (9)  op(e1, e2) = all_52_6
% 152.42/22.44    (10)  all_56_3 = e1
% 152.42/22.44    (11)   ~ (e1 = e0)
% 152.42/22.44    (12)   ~ (e3 = e2)
% 152.42/22.44    (13)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.44          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.42/22.44    (14)   ~ (e2 = e1)
% 152.42/22.44    (15)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.44          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.44  
% 152.42/22.44  Begin of proof
% 152.42/22.44  | 
% 152.42/22.44  | BETA: splitting (15) gives:
% 152.42/22.44  | 
% 152.42/22.44  | Case 1:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.42/22.44  | |           e3)
% 152.42/22.44  | | 
% 152.42/22.44  | | BETA: splitting (16) gives:
% 152.42/22.44  | | 
% 152.42/22.44  | | Case 1:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (17)  all_56_1 = e3 & op(e3, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | ALPHA: (17) implies:
% 152.42/22.44  | | |   (18)  all_56_1 = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10), (11), (12), (13), (14),
% 152.42/22.44  | | |            (18) are inconsistent by sub-proof #736.
% 152.42/22.44  | | | 
% 152.42/22.44  | | Case 2:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (19)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | REF_CLOSE: (1), (10), (19) are inconsistent by sub-proof #270.
% 152.42/22.44  | | | 
% 152.42/22.44  | | End of split
% 152.42/22.44  | | 
% 152.42/22.44  | Case 2:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (20)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 152.42/22.44  | |           e3)
% 152.42/22.44  | | 
% 152.42/22.44  | | BETA: splitting (20) gives:
% 152.42/22.44  | | 
% 152.42/22.44  | | Case 1:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (21)  all_56_7 = e3 & op(e1, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | REF_CLOSE: (5), (8), (9), (21) are inconsistent by sub-proof #925.
% 152.42/22.44  | | | 
% 152.42/22.44  | | Case 2:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (22)  all_56_13 = e3 & op(e0, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | REF_CLOSE: (1), (6), (22) are inconsistent by sub-proof #585.
% 152.42/22.44  | | | 
% 152.42/22.44  | | End of split
% 152.42/22.44  | | 
% 152.42/22.44  | End of split
% 152.42/22.44  | 
% 152.42/22.44  End of proof
% 152.42/22.44  
% 152.42/22.44  Sub-proof #261 shows that the following formulas are inconsistent:
% 152.42/22.44  ----------------------------------------------------------------
% 152.42/22.44    (1)   ~ (e3 = e1)
% 152.42/22.44    (2)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 152.42/22.44    (3)  op(e3, e2) = all_52_4
% 152.42/22.44    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.44    (5)   ~ (all_52_4 = e3)
% 152.42/22.44    (6)  all_56_3 = e1
% 152.42/22.44  
% 152.42/22.44  Begin of proof
% 152.42/22.44  | 
% 152.42/22.44  | BETA: splitting (2) gives:
% 152.42/22.44  | 
% 152.42/22.44  | Case 1:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (7)  all_56_1 = e3 & op(e3, e2) = e3
% 152.42/22.44  | | 
% 152.42/22.44  | | ALPHA: (7) implies:
% 152.42/22.44  | |   (8)  op(e3, e2) = e3
% 152.42/22.44  | | 
% 152.42/22.44  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1166.
% 152.42/22.44  | | 
% 152.42/22.44  | Case 2:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (9)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.44  | | 
% 152.42/22.44  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #274.
% 152.42/22.44  | | 
% 152.42/22.44  | End of split
% 152.42/22.44  | 
% 152.42/22.44  End of proof
% 152.42/22.44  
% 152.42/22.44  Sub-proof #262 shows that the following formulas are inconsistent:
% 152.42/22.44  ----------------------------------------------------------------
% 152.42/22.44    (1)  all_56_1 = e1
% 152.42/22.44    (2)   ~ (e3 = e1)
% 152.42/22.44    (3)  op(e2, e2) = e1
% 152.42/22.44    (4)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.44         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.42/22.44    (5)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.44         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.42/22.44    (6)   ~ (e2 = e0)
% 152.42/22.44    (7)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.44         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.42/22.44    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.44    (9)   ~ (all_52_9 = e3)
% 152.42/22.44    (10)   ~ (e3 = e0)
% 152.42/22.44    (11)   ~ (all_52_6 = e3)
% 152.42/22.44    (12)  op(e1, e2) = all_52_6
% 152.42/22.44    (13)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.44          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.42/22.44    (14)  op(e2, e1) = all_52_9
% 152.42/22.44    (15)   ~ (e1 = e0)
% 152.42/22.44    (16)   ~ (e3 = e2)
% 152.42/22.44    (17)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.42/22.44          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.42/22.44    (18)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.44          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.42/22.44    (19)   ~ (e2 = e1)
% 152.42/22.44    (20)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.44          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.44    (21)  op(e2, e3) = all_52_1
% 152.42/22.44  
% 152.42/22.44  Begin of proof
% 152.42/22.44  | 
% 152.42/22.44  | BETA: splitting (20) gives:
% 152.42/22.44  | 
% 152.42/22.44  | Case 1:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (22)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.42/22.44  | |           e3)
% 152.42/22.44  | | 
% 152.42/22.44  | | BETA: splitting (22) gives:
% 152.42/22.44  | | 
% 152.42/22.44  | | Case 1:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (23)  all_56_1 = e3 & op(e3, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | ALPHA: (23) implies:
% 152.42/22.44  | | |   (24)  all_56_1 = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | REF_CLOSE: (1), (2), (24) are inconsistent by sub-proof #1069.
% 152.42/22.44  | | | 
% 152.42/22.44  | | Case 2:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (25)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | ALPHA: (25) implies:
% 152.42/22.44  | | |   (26)  all_56_3 = e3
% 152.42/22.44  | | |   (27)  op(e2, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | BETA: splitting (17) gives:
% 152.42/22.44  | | | 
% 152.42/22.44  | | | Case 1:
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | |   (28)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2)
% 152.42/22.44  | | | |           = e1)
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | | BETA: splitting (28) gives:
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | | Case 1:
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | |   (29)  all_56_2 = e1 & op(e2, e3) = e1
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (13), (14), (15),
% 152.42/22.44  | | | | |            (16), (19), (21), (25), (29) are inconsistent by sub-proof
% 152.42/22.44  | | | | |            #272.
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | Case 2:
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | |   (30)  all_56_3 = e1 & op(e2, e2) = e1
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | ALPHA: (30) implies:
% 152.42/22.44  | | | | |   (31)  all_56_3 = e1
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (11), (12), (15), (16),
% 152.42/22.44  | | | | |            (18), (19), (20), (31) are inconsistent by sub-proof #268.
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | End of split
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | Case 2:
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | |   (32)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0)
% 152.42/22.44  | | | |           = e1)
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | | BETA: splitting (32) gives:
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | | Case 1:
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | GROUND_INST: instantiating (8) with e1, e3, e2, e2, simplifying with
% 152.42/22.44  | | | | |              (3), (27) gives:
% 152.42/22.44  | | | | |   (33)  e3 = e1
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | COMBINE_EQS: (26), (33) imply:
% 152.42/22.44  | | | | |   (34)  all_56_3 = e1
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (11), (12), (15), (16),
% 152.42/22.44  | | | | |            (18), (19), (20), (34) are inconsistent by sub-proof #268.
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | Case 2:
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | |   (35)  all_56_10 = e1 & op(e2, e0) = e1
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (13), (14), (15),
% 152.42/22.44  | | | | |            (16), (19), (25), (35) are inconsistent by sub-proof #263.
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | End of split
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | End of split
% 152.42/22.44  | | | 
% 152.42/22.44  | | End of split
% 152.42/22.44  | | 
% 152.42/22.44  | Case 2:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (36)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 152.42/22.44  | |           e3)
% 152.42/22.44  | | 
% 152.42/22.44  | | BETA: splitting (36) gives:
% 152.42/22.44  | | 
% 152.42/22.44  | | Case 1:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (37)  all_56_7 = e3 & op(e1, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | REF_CLOSE: (8), (11), (12), (37) are inconsistent by sub-proof #925.
% 152.42/22.44  | | | 
% 152.42/22.44  | | Case 2:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (38)  all_56_13 = e3 & op(e0, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | ALPHA: (38) implies:
% 152.42/22.44  | | |   (39)  all_56_13 = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | REF_CLOSE: (1), (3), (4), (6), (8), (10), (15), (16), (18), (19), (39) are
% 152.42/22.44  | | |            inconsistent by sub-proof #505.
% 152.42/22.44  | | | 
% 152.42/22.44  | | End of split
% 152.42/22.44  | | 
% 152.42/22.44  | End of split
% 152.42/22.44  | 
% 152.42/22.44  End of proof
% 152.42/22.44  
% 152.42/22.44  Sub-proof #263 shows that the following formulas are inconsistent:
% 152.42/22.44  ----------------------------------------------------------------
% 152.42/22.44    (1)   ~ (e3 = e1)
% 152.42/22.44    (2)  op(e2, e2) = e1
% 152.42/22.44    (3)  all_56_10 = e1 & op(e2, e0) = e1
% 152.42/22.44    (4)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.44         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.42/22.44    (5)   ~ (e2 = e0)
% 152.42/22.44    (6)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.44         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.42/22.44    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.44    (8)   ~ (all_52_9 = e3)
% 152.42/22.44    (9)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.44    (10)   ~ (e3 = e0)
% 152.42/22.44    (11)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.44          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.42/22.44    (12)  op(e2, e1) = all_52_9
% 152.42/22.44    (13)   ~ (e1 = e0)
% 152.42/22.44    (14)   ~ (e3 = e2)
% 152.42/22.44    (15)   ~ (e2 = e1)
% 152.42/22.44  
% 152.42/22.44  Begin of proof
% 152.42/22.44  | 
% 152.42/22.44  | ALPHA: (3) implies:
% 152.42/22.44  |   (16)  all_56_10 = e1
% 152.42/22.44  | 
% 152.42/22.44  | ALPHA: (9) implies:
% 152.42/22.44  |   (17)  all_56_3 = e3
% 152.42/22.44  |   (18)  op(e2, e2) = e3
% 152.42/22.44  | 
% 152.42/22.44  | GROUND_INST: instantiating (7) with e1, e3, e2, e2, simplifying with (2), (18)
% 152.42/22.44  |              gives:
% 152.42/22.44  |   (19)  e3 = e1
% 152.42/22.44  | 
% 152.42/22.44  | COMBINE_EQS: (17), (19) imply:
% 152.42/22.44  |   (20)  all_56_3 = e1
% 152.42/22.44  | 
% 152.42/22.44  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 152.42/22.44  |            (15), (16), (20) are inconsistent by sub-proof #264.
% 152.42/22.44  | 
% 152.42/22.44  End of proof
% 152.42/22.44  
% 152.42/22.44  Sub-proof #264 shows that the following formulas are inconsistent:
% 152.42/22.44  ----------------------------------------------------------------
% 152.42/22.44    (1)   ~ (e3 = e1)
% 152.42/22.44    (2)  op(e2, e2) = e1
% 152.42/22.44    (3)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.44         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.42/22.44    (4)   ~ (e2 = e0)
% 152.42/22.44    (5)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.44         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.42/22.44    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.44    (7)   ~ (all_52_9 = e3)
% 152.42/22.44    (8)  all_56_10 = e1
% 152.42/22.44    (9)   ~ (e3 = e0)
% 152.42/22.44    (10)  all_56_3 = e1
% 152.42/22.44    (11)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.44          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.42/22.44    (12)  op(e2, e1) = all_52_9
% 152.42/22.44    (13)   ~ (e1 = e0)
% 152.42/22.44    (14)   ~ (e3 = e2)
% 152.42/22.44    (15)   ~ (e2 = e1)
% 152.42/22.44  
% 152.42/22.44  Begin of proof
% 152.42/22.44  | 
% 152.42/22.44  | BETA: splitting (11) gives:
% 152.42/22.44  | 
% 152.42/22.44  | Case 1:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (16)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.42/22.44  | |           e3)
% 152.42/22.44  | | 
% 152.42/22.44  | | BETA: splitting (16) gives:
% 152.42/22.44  | | 
% 152.42/22.44  | | Case 1:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (17)  all_56_2 = e3 & op(e2, e3) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | ALPHA: (17) implies:
% 152.42/22.44  | | |   (18)  all_56_2 = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | BETA: splitting (5) gives:
% 152.42/22.44  | | | 
% 152.42/22.44  | | | Case 1:
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | |   (19)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2)
% 152.42/22.44  | | | |           = e2)
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | | REF_CLOSE: (2), (6), (14), (15), (18), (19) are inconsistent by
% 152.42/22.44  | | | |            sub-proof #267.
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | Case 2:
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | |   (20)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0)
% 152.42/22.44  | | | |           = e2)
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | | BETA: splitting (20) gives:
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | | Case 1:
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | |   (21)  all_56_5 = e2 & op(e2, e1) = e2
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | ALPHA: (21) implies:
% 152.42/22.44  | | | | |   (22)  all_56_5 = e2
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | BETA: splitting (3) gives:
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | Case 1:
% 152.42/22.44  | | | | | | 
% 152.42/22.44  | | | | | |   (23)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2,
% 152.42/22.44  | | | | | |             e2) = e0)
% 152.42/22.44  | | | | | | 
% 152.42/22.44  | | | | | | BETA: splitting (23) gives:
% 152.42/22.44  | | | | | | 
% 152.42/22.44  | | | | | | Case 1:
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | |   (24)  all_56_2 = e0 & op(e2, e3) = e0
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | | ALPHA: (24) implies:
% 152.42/22.44  | | | | | | |   (25)  all_56_2 = e0
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | | REF_CLOSE: (9), (18), (25) are inconsistent by sub-proof #1137.
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | Case 2:
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | |   (26)  all_56_3 = e0 & op(e2, e2) = e0
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | | REF_CLOSE: (10), (13), (26) are inconsistent by sub-proof #741.
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | End of split
% 152.42/22.44  | | | | | | 
% 152.42/22.44  | | | | | Case 2:
% 152.42/22.44  | | | | | | 
% 152.42/22.44  | | | | | |   (27)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2,
% 152.42/22.44  | | | | | |             e0) = e0)
% 152.42/22.44  | | | | | | 
% 152.42/22.44  | | | | | | BETA: splitting (27) gives:
% 152.42/22.44  | | | | | | 
% 152.42/22.44  | | | | | | Case 1:
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | |   (28)  all_56_5 = e0 & op(e2, e1) = e0
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | | ALPHA: (28) implies:
% 152.42/22.44  | | | | | | |   (29)  all_56_5 = e0
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | | REF_CLOSE: (4), (22), (29) are inconsistent by sub-proof #509.
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | Case 2:
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | |   (30)  all_56_10 = e0 & op(e2, e0) = e0
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | | REF_CLOSE: (8), (13), (30) are inconsistent by sub-proof #884.
% 152.42/22.44  | | | | | | | 
% 152.42/22.44  | | | | | | End of split
% 152.42/22.44  | | | | | | 
% 152.42/22.44  | | | | | End of split
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | Case 2:
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | |   (31)  all_56_10 = e2 & op(e2, e0) = e2
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | REF_CLOSE: (8), (15), (31) are inconsistent by sub-proof #266.
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | End of split
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | End of split
% 152.42/22.44  | | | 
% 152.42/22.44  | | Case 2:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (32)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | REF_CLOSE: (1), (10), (32) are inconsistent by sub-proof #274.
% 152.42/22.44  | | | 
% 152.42/22.44  | | End of split
% 152.42/22.44  | | 
% 152.42/22.44  | Case 2:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (33)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 152.42/22.44  | |           e3)
% 152.42/22.44  | | 
% 152.42/22.44  | | REF_CLOSE: (1), (6), (7), (8), (12), (33) are inconsistent by sub-proof
% 152.42/22.44  | |            #265.
% 152.42/22.44  | | 
% 152.42/22.44  | End of split
% 152.42/22.44  | 
% 152.42/22.44  End of proof
% 152.42/22.44  
% 152.42/22.44  Sub-proof #265 shows that the following formulas are inconsistent:
% 152.42/22.44  ----------------------------------------------------------------
% 152.42/22.44    (1)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.42/22.44    (2)   ~ (e3 = e1)
% 152.42/22.44    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.44    (4)   ~ (all_52_9 = e3)
% 152.42/22.44    (5)  all_56_10 = e1
% 152.42/22.44    (6)  op(e2, e1) = all_52_9
% 152.42/22.44  
% 152.42/22.44  Begin of proof
% 152.42/22.44  | 
% 152.42/22.44  | BETA: splitting (1) gives:
% 152.42/22.44  | 
% 152.42/22.44  | Case 1:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (7)  all_56_5 = e3 & op(e2, e1) = e3
% 152.42/22.44  | | 
% 152.42/22.44  | | REF_CLOSE: (3), (4), (6), (7) are inconsistent by sub-proof #647.
% 152.42/22.44  | | 
% 152.42/22.44  | Case 2:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (8)  all_56_10 = e3 & op(e2, e0) = e3
% 152.42/22.44  | | 
% 152.42/22.44  | | ALPHA: (8) implies:
% 152.42/22.44  | |   (9)  all_56_10 = e3
% 152.42/22.44  | | 
% 152.42/22.44  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #677.
% 152.42/22.44  | | 
% 152.42/22.44  | End of split
% 152.42/22.44  | 
% 152.42/22.44  End of proof
% 152.42/22.44  
% 152.42/22.44  Sub-proof #266 shows that the following formulas are inconsistent:
% 152.42/22.44  ----------------------------------------------------------------
% 152.42/22.44    (1)  all_56_10 = e2 & op(e2, e0) = e2
% 152.42/22.44    (2)  all_56_10 = e1
% 152.42/22.44    (3)   ~ (e2 = e1)
% 152.42/22.44  
% 152.42/22.44  Begin of proof
% 152.42/22.44  | 
% 152.42/22.44  | ALPHA: (1) implies:
% 152.42/22.44  |   (4)  all_56_10 = e2
% 152.42/22.44  | 
% 152.42/22.44  | COMBINE_EQS: (2), (4) imply:
% 152.42/22.44  |   (5)  e2 = e1
% 152.42/22.44  | 
% 152.42/22.44  | REDUCE: (3), (5) imply:
% 152.42/22.44  |   (6)  $false
% 152.42/22.44  | 
% 152.42/22.44  | CLOSE: (6) is inconsistent.
% 152.42/22.44  | 
% 152.42/22.44  End of proof
% 152.42/22.44  
% 152.42/22.44  Sub-proof #267 shows that the following formulas are inconsistent:
% 152.42/22.44  ----------------------------------------------------------------
% 152.42/22.44    (1)  op(e2, e2) = e1
% 152.42/22.44    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.44    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 152.42/22.44    (4)   ~ (e3 = e2)
% 152.42/22.44    (5)   ~ (e2 = e1)
% 152.42/22.44    (6)  all_56_2 = e3
% 152.42/22.44  
% 152.42/22.44  Begin of proof
% 152.42/22.44  | 
% 152.42/22.44  | BETA: splitting (3) gives:
% 152.42/22.44  | 
% 152.42/22.44  | Case 1:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (7)  all_56_2 = e2 & op(e2, e3) = e2
% 152.42/22.44  | | 
% 152.42/22.44  | | ALPHA: (7) implies:
% 152.42/22.44  | |   (8)  all_56_2 = e2
% 152.42/22.44  | | 
% 152.42/22.44  | | REF_CLOSE: (4), (6), (8) are inconsistent by sub-proof #685.
% 152.42/22.44  | | 
% 152.42/22.44  | Case 2:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (9)  all_56_3 = e2 & op(e2, e2) = e2
% 152.42/22.44  | | 
% 152.42/22.44  | | ALPHA: (9) implies:
% 152.42/22.44  | |   (10)  op(e2, e2) = e2
% 152.42/22.44  | | 
% 152.42/22.44  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1158.
% 152.42/22.44  | | 
% 152.42/22.44  | End of split
% 152.42/22.44  | 
% 152.42/22.44  End of proof
% 152.42/22.44  
% 152.42/22.44  Sub-proof #268 shows that the following formulas are inconsistent:
% 152.42/22.44  ----------------------------------------------------------------
% 152.42/22.44    (1)  all_56_1 = e1
% 152.42/22.44    (2)   ~ (e3 = e1)
% 152.42/22.44    (3)  op(e2, e2) = e1
% 152.42/22.44    (4)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.44         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.42/22.44    (5)   ~ (e2 = e0)
% 152.42/22.44    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.44           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.44    (7)   ~ (e3 = e0)
% 152.42/22.44    (8)   ~ (all_52_6 = e3)
% 152.42/22.44    (9)  op(e1, e2) = all_52_6
% 152.42/22.44    (10)  all_56_3 = e1
% 152.42/22.44    (11)   ~ (e1 = e0)
% 152.42/22.44    (12)   ~ (e3 = e2)
% 152.42/22.44    (13)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.44          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.42/22.44    (14)   ~ (e2 = e1)
% 152.42/22.44    (15)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.44          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.44  
% 152.42/22.44  Begin of proof
% 152.42/22.44  | 
% 152.42/22.44  | BETA: splitting (15) gives:
% 152.42/22.44  | 
% 152.42/22.44  | Case 1:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.42/22.44  | |           e3)
% 152.42/22.44  | | 
% 152.42/22.44  | | BETA: splitting (16) gives:
% 152.42/22.44  | | 
% 152.42/22.44  | | Case 1:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (17)  all_56_1 = e3 & op(e3, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | ALPHA: (17) implies:
% 152.42/22.44  | | |   (18)  all_56_1 = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | REF_CLOSE: (1), (2), (18) are inconsistent by sub-proof #1069.
% 152.42/22.44  | | | 
% 152.42/22.44  | | Case 2:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (19)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | REF_CLOSE: (2), (10), (19) are inconsistent by sub-proof #274.
% 152.42/22.44  | | | 
% 152.42/22.44  | | End of split
% 152.42/22.44  | | 
% 152.42/22.44  | Case 2:
% 152.42/22.44  | | 
% 152.42/22.44  | |   (20)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 152.42/22.44  | |           e3)
% 152.42/22.44  | | 
% 152.42/22.44  | | BETA: splitting (20) gives:
% 152.42/22.44  | | 
% 152.42/22.44  | | Case 1:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (21)  all_56_7 = e3 & op(e1, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | REF_CLOSE: (6), (8), (9), (21) are inconsistent by sub-proof #925.
% 152.42/22.44  | | | 
% 152.42/22.44  | | Case 2:
% 152.42/22.44  | | | 
% 152.42/22.44  | | |   (22)  all_56_13 = e3 & op(e0, e2) = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | ALPHA: (22) implies:
% 152.42/22.44  | | |   (23)  all_56_13 = e3
% 152.42/22.44  | | | 
% 152.42/22.44  | | | BETA: splitting (4) gives:
% 152.42/22.44  | | | 
% 152.42/22.44  | | | Case 1:
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | |   (24)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2)
% 152.42/22.44  | | | |           = e2)
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | | REF_CLOSE: (1), (3), (6), (14), (24) are inconsistent by sub-proof #507.
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | Case 2:
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | |   (25)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2)
% 152.42/22.44  | | | |           = e2)
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | | BETA: splitting (25) gives:
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | | Case 1:
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | |   (26)  all_56_7 = e2 & op(e1, e2) = e2
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | ALPHA: (26) implies:
% 152.42/22.44  | | | | |   (27)  all_56_7 = e2
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | REF_CLOSE: (1), (5), (7), (10), (11), (13), (23), (27) are
% 152.42/22.44  | | | | |            inconsistent by sub-proof #271.
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | Case 2:
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | |   (28)  all_56_13 = e2 & op(e0, e2) = e2
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | ALPHA: (28) implies:
% 152.42/22.44  | | | | |   (29)  all_56_13 = e2
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | | REF_CLOSE: (1), (2), (6), (8), (9), (10), (12), (15), (29) are
% 152.42/22.44  | | | | |            inconsistent by sub-proof #269.
% 152.42/22.44  | | | | | 
% 152.42/22.44  | | | | End of split
% 152.42/22.44  | | | | 
% 152.42/22.44  | | | End of split
% 152.42/22.44  | | | 
% 152.42/22.44  | | End of split
% 152.42/22.44  | | 
% 152.42/22.44  | End of split
% 152.42/22.44  | 
% 152.42/22.44  End of proof
% 152.42/22.44  
% 152.42/22.44  Sub-proof #269 shows that the following formulas are inconsistent:
% 152.42/22.44  ----------------------------------------------------------------
% 152.42/22.45    (1)  all_56_13 = e2
% 152.42/22.45    (2)  all_56_1 = e1
% 152.42/22.45    (3)   ~ (e3 = e1)
% 152.42/22.45    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.45    (5)   ~ (all_52_6 = e3)
% 152.42/22.45    (6)  op(e1, e2) = all_52_6
% 152.42/22.45    (7)  all_56_3 = e1
% 152.42/22.45    (8)   ~ (e3 = e2)
% 152.42/22.45    (9)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.45         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.45  
% 152.42/22.45  Begin of proof
% 152.42/22.45  | 
% 152.42/22.45  | BETA: splitting (9) gives:
% 152.42/22.45  | 
% 152.42/22.45  | Case 1:
% 152.42/22.45  | | 
% 152.42/22.45  | |   (10)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.42/22.45  | |           e3)
% 152.42/22.45  | | 
% 152.42/22.45  | | BETA: splitting (10) gives:
% 152.42/22.45  | | 
% 152.42/22.45  | | Case 1:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (11)  all_56_1 = e3 & op(e3, e2) = e3
% 152.42/22.45  | | | 
% 152.42/22.45  | | | ALPHA: (11) implies:
% 152.42/22.45  | | |   (12)  all_56_1 = e3
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #1069.
% 152.42/22.45  | | | 
% 152.42/22.45  | | Case 2:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (13)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (3), (7), (13) are inconsistent by sub-proof #270.
% 152.42/22.45  | | | 
% 152.42/22.45  | | End of split
% 152.42/22.45  | | 
% 152.42/22.45  | Case 2:
% 152.42/22.45  | | 
% 152.42/22.45  | |   (14)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 152.42/22.45  | |           e3)
% 152.42/22.45  | | 
% 152.42/22.45  | | BETA: splitting (14) gives:
% 152.42/22.45  | | 
% 152.42/22.45  | | Case 1:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (15)  all_56_7 = e3 & op(e1, e2) = e3
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (4), (5), (6), (15) are inconsistent by sub-proof #925.
% 152.42/22.45  | | | 
% 152.42/22.45  | | Case 2:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (16)  all_56_13 = e3 & op(e0, e2) = e3
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (1), (8), (16) are inconsistent by sub-proof #563.
% 152.42/22.45  | | | 
% 152.42/22.45  | | End of split
% 152.42/22.45  | | 
% 152.42/22.45  | End of split
% 152.42/22.45  | 
% 152.42/22.45  End of proof
% 152.42/22.45  
% 152.42/22.45  Sub-proof #270 shows that the following formulas are inconsistent:
% 152.42/22.45  ----------------------------------------------------------------
% 152.42/22.45    (1)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.45    (2)  all_56_3 = e1
% 152.42/22.45    (3)   ~ (e3 = e1)
% 152.42/22.45  
% 152.42/22.45  Begin of proof
% 152.42/22.45  | 
% 152.42/22.45  | ALPHA: (1) implies:
% 152.42/22.45  |   (4)  all_56_3 = e3
% 152.42/22.45  | 
% 152.42/22.45  | COMBINE_EQS: (2), (4) imply:
% 152.42/22.45  |   (5)  e3 = e1
% 152.42/22.45  | 
% 152.42/22.45  | REDUCE: (3), (5) imply:
% 152.42/22.45  |   (6)  $false
% 152.42/22.45  | 
% 152.42/22.45  | CLOSE: (6) is inconsistent.
% 152.42/22.45  | 
% 152.42/22.45  End of proof
% 152.42/22.45  
% 152.42/22.45  Sub-proof #271 shows that the following formulas are inconsistent:
% 152.42/22.45  ----------------------------------------------------------------
% 152.42/22.45    (1)  all_56_1 = e1
% 152.42/22.45    (2)   ~ (e2 = e0)
% 152.42/22.45    (3)   ~ (e3 = e0)
% 152.42/22.45    (4)  all_56_3 = e1
% 152.42/22.45    (5)   ~ (e1 = e0)
% 152.42/22.45    (6)  all_56_7 = e2
% 152.42/22.45    (7)  all_56_13 = e3
% 152.42/22.45    (8)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.45         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.42/22.45  
% 152.42/22.45  Begin of proof
% 152.42/22.45  | 
% 152.42/22.45  | BETA: splitting (8) gives:
% 152.42/22.45  | 
% 152.42/22.45  | Case 1:
% 152.42/22.45  | | 
% 152.42/22.45  | |   (9)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 152.42/22.45  | | 
% 152.42/22.45  | | BETA: splitting (9) gives:
% 152.42/22.45  | | 
% 152.42/22.45  | | Case 1:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (10)  all_56_1 = e0 & op(e3, e2) = e0
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #1072.
% 152.42/22.45  | | | 
% 152.42/22.45  | | Case 2:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (11)  all_56_3 = e0 & op(e2, e2) = e0
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (4), (5), (11) are inconsistent by sub-proof #741.
% 152.42/22.45  | | | 
% 152.42/22.45  | | End of split
% 152.42/22.45  | | 
% 152.42/22.45  | Case 2:
% 152.42/22.45  | | 
% 152.42/22.45  | |   (12)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 152.42/22.45  | |           e0)
% 152.42/22.45  | | 
% 152.42/22.45  | | BETA: splitting (12) gives:
% 152.42/22.45  | | 
% 152.42/22.45  | | Case 1:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (13)  all_56_7 = e0 & op(e1, e2) = e0
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (2), (6), (13) are inconsistent by sub-proof #611.
% 152.42/22.45  | | | 
% 152.42/22.45  | | Case 2:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (14)  all_56_13 = e0 & op(e0, e2) = e0
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (3), (7), (14) are inconsistent by sub-proof #1102.
% 152.42/22.45  | | | 
% 152.42/22.45  | | End of split
% 152.42/22.45  | | 
% 152.42/22.45  | End of split
% 152.42/22.45  | 
% 152.42/22.45  End of proof
% 152.42/22.45  
% 152.42/22.45  Sub-proof #272 shows that the following formulas are inconsistent:
% 152.42/22.45  ----------------------------------------------------------------
% 152.42/22.45    (1)   ~ (e3 = e1)
% 152.42/22.45    (2)  op(e2, e2) = e1
% 152.42/22.45    (3)  all_56_2 = e1 & op(e2, e3) = e1
% 152.42/22.45    (4)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.45         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.42/22.45    (5)   ~ (e2 = e0)
% 152.42/22.45    (6)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.45         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.42/22.45    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.45    (8)   ~ (all_52_9 = e3)
% 152.42/22.45    (9)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.45    (10)   ~ (e3 = e0)
% 152.42/22.45    (11)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.45          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.42/22.45    (12)  op(e2, e1) = all_52_9
% 152.42/22.45    (13)   ~ (e1 = e0)
% 152.42/22.45    (14)   ~ (e3 = e2)
% 152.42/22.45    (15)   ~ (e2 = e1)
% 152.42/22.45    (16)  op(e2, e3) = all_52_1
% 152.42/22.45  
% 152.42/22.45  Begin of proof
% 152.42/22.45  | 
% 152.42/22.45  | ALPHA: (3) implies:
% 152.42/22.45  |   (17)  all_56_2 = e1
% 152.42/22.45  |   (18)  op(e2, e3) = e1
% 152.42/22.45  | 
% 152.42/22.45  | ALPHA: (9) implies:
% 152.42/22.45  |   (19)  all_56_3 = e3
% 152.42/22.45  |   (20)  op(e2, e2) = e3
% 152.42/22.45  | 
% 152.42/22.45  | GROUND_INST: instantiating (7) with e1, e3, e2, e2, simplifying with (2), (20)
% 152.42/22.45  |              gives:
% 152.42/22.45  |   (21)  e3 = e1
% 152.42/22.45  | 
% 152.42/22.45  | COMBINE_EQS: (19), (21) imply:
% 152.42/22.45  |   (22)  all_56_3 = e1
% 152.42/22.45  | 
% 152.42/22.45  | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 152.42/22.45  |            (15), (16), (17), (18), (22) are inconsistent by sub-proof #273.
% 152.42/22.45  | 
% 152.42/22.45  End of proof
% 152.42/22.45  
% 152.42/22.45  Sub-proof #273 shows that the following formulas are inconsistent:
% 152.42/22.45  ----------------------------------------------------------------
% 152.42/22.45    (1)   ~ (e3 = e1)
% 152.42/22.45    (2)  op(e2, e2) = e1
% 152.42/22.45    (3)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.45         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.42/22.45    (4)   ~ (e2 = e0)
% 152.42/22.45    (5)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 152.42/22.45         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 152.42/22.45    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.45    (7)  op(e2, e3) = e1
% 152.42/22.45    (8)   ~ (all_52_9 = e3)
% 152.42/22.45    (9)   ~ (e3 = e0)
% 152.42/22.45    (10)  all_56_3 = e1
% 152.42/22.45    (11)  all_56_2 = e1
% 152.42/22.45    (12)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.45          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.42/22.45    (13)  op(e2, e1) = all_52_9
% 152.42/22.45    (14)   ~ (e1 = e0)
% 152.42/22.45    (15)   ~ (e3 = e2)
% 152.42/22.45    (16)   ~ (e2 = e1)
% 152.42/22.45    (17)  op(e2, e3) = all_52_1
% 152.42/22.45  
% 152.42/22.45  Begin of proof
% 152.42/22.45  | 
% 152.42/22.45  | BETA: splitting (12) gives:
% 152.42/22.45  | 
% 152.42/22.45  | Case 1:
% 152.42/22.45  | | 
% 152.42/22.45  | |   (18)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 152.42/22.45  | |           e3)
% 152.42/22.45  | | 
% 152.42/22.45  | | BETA: splitting (18) gives:
% 152.42/22.45  | | 
% 152.42/22.45  | | Case 1:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (19)  all_56_2 = e3 & op(e2, e3) = e3
% 152.42/22.45  | | | 
% 152.42/22.45  | | | ALPHA: (19) implies:
% 152.42/22.45  | | |   (20)  all_56_2 = e3
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (1), (11), (20) are inconsistent by sub-proof #1053.
% 152.42/22.45  | | | 
% 152.42/22.45  | | Case 2:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (21)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (1), (10), (21) are inconsistent by sub-proof #274.
% 152.42/22.45  | | | 
% 152.42/22.45  | | End of split
% 152.42/22.45  | | 
% 152.42/22.45  | Case 2:
% 152.42/22.45  | | 
% 152.42/22.45  | |   (22)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 152.42/22.45  | |           e3)
% 152.42/22.45  | | 
% 152.42/22.45  | | BETA: splitting (22) gives:
% 152.42/22.45  | | 
% 152.42/22.45  | | Case 1:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (23)  all_56_5 = e3 & op(e2, e1) = e3
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (6), (8), (13), (23) are inconsistent by sub-proof #647.
% 152.42/22.45  | | | 
% 152.42/22.45  | | Case 2:
% 152.42/22.45  | | | 
% 152.42/22.45  | | |   (24)  all_56_10 = e3 & op(e2, e0) = e3
% 152.42/22.45  | | | 
% 152.42/22.45  | | | ALPHA: (24) implies:
% 152.42/22.45  | | |   (25)  all_56_10 = e3
% 152.42/22.45  | | | 
% 152.42/22.45  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (14), (15),
% 152.42/22.45  | | |            (16), (17), (25) are inconsistent by sub-proof #387.
% 152.42/22.45  | | | 
% 152.42/22.45  | | End of split
% 152.42/22.45  | | 
% 152.42/22.45  | End of split
% 152.42/22.45  | 
% 152.42/22.45  End of proof
% 152.42/22.45  
% 152.42/22.45  Sub-proof #274 shows that the following formulas are inconsistent:
% 152.42/22.45  ----------------------------------------------------------------
% 152.42/22.45    (1)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.45    (2)  all_56_3 = e1
% 152.42/22.45    (3)   ~ (e3 = e1)
% 152.42/22.45  
% 152.42/22.45  Begin of proof
% 152.42/22.45  | 
% 152.42/22.45  | ALPHA: (1) implies:
% 152.42/22.45  |   (4)  all_56_3 = e3
% 152.42/22.45  | 
% 152.42/22.45  | COMBINE_EQS: (2), (4) imply:
% 152.42/22.45  |   (5)  e3 = e1
% 152.42/22.45  | 
% 152.42/22.45  | SIMP: (5) implies:
% 152.42/22.45  |   (6)  e3 = e1
% 152.42/22.45  | 
% 152.42/22.45  | REDUCE: (3), (6) imply:
% 152.42/22.45  |   (7)  $false
% 152.42/22.45  | 
% 152.42/22.45  | CLOSE: (7) is inconsistent.
% 152.42/22.45  | 
% 152.42/22.45  End of proof
% 152.42/22.45  
% 152.42/22.45  Sub-proof #275 shows that the following formulas are inconsistent:
% 152.42/22.45  ----------------------------------------------------------------
% 152.42/22.45    (1)  op(e0, e1) = all_52_11
% 152.42/22.45    (2)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.45    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.45    (4)  op(e1, e1) = e3
% 152.42/22.45    (5)   ~ (e3 = e2)
% 152.42/22.45    (6)   ~ (all_52_11 = e2)
% 152.42/22.45  
% 152.42/22.45  Begin of proof
% 152.42/22.45  | 
% 152.42/22.45  | BETA: splitting (2) gives:
% 152.42/22.45  | 
% 152.42/22.45  | Case 1:
% 152.42/22.45  | | 
% 152.42/22.45  | |   (7)  all_56_8 = e2 & op(e1, e1) = e2
% 152.42/22.45  | | 
% 152.42/22.45  | | ALPHA: (7) implies:
% 152.42/22.45  | |   (8)  op(e1, e1) = e2
% 152.42/22.45  | | 
% 152.42/22.45  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #834.
% 152.42/22.45  | | 
% 152.42/22.45  | Case 2:
% 152.42/22.45  | | 
% 152.42/22.45  | |   (9)  all_56_14 = e2 & op(e0, e1) = e2
% 152.42/22.45  | | 
% 152.42/22.45  | | ALPHA: (9) implies:
% 152.42/22.45  | |   (10)  op(e0, e1) = e2
% 152.42/22.45  | | 
% 152.42/22.45  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #1092.
% 152.42/22.45  | | 
% 152.42/22.45  | End of split
% 152.42/22.45  | 
% 152.42/22.45  End of proof
% 152.42/22.45  
% 152.42/22.45  Sub-proof #276 shows that the following formulas are inconsistent:
% 152.42/22.45  ----------------------------------------------------------------
% 152.42/22.45    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.45           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.45    (2)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 152.42/22.45             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.42/22.45           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 152.42/22.45           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 152.42/22.45           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 152.42/22.45           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 152.42/22.45    (3)  all_57_5 = e0
% 152.42/22.45    (4)  op(e1, e1) = e3
% 152.42/22.45    (5)   ~ (e3 = e2)
% 152.42/22.45  
% 152.42/22.45  Begin of proof
% 152.42/22.45  | 
% 152.42/22.45  | BETA: splitting (2) gives:
% 152.42/22.45  | 
% 152.42/22.45  | Case 1:
% 152.42/22.45  | | 
% 152.42/22.45  | |   (6)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 152.42/22.45  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.42/22.45  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 152.42/22.45  | | 
% 152.42/22.45  | | ALPHA: (6) implies:
% 152.42/22.45  | |   (7)  op(e1, e1) = e2
% 152.42/22.45  | | 
% 152.42/22.45  | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #834.
% 152.42/22.45  | | 
% 152.42/22.45  | Case 2:
% 152.42/22.45  | | 
% 152.42/22.45  | |   (8)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 152.42/22.45  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 152.42/22.45  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 152.42/22.45  | | 
% 152.42/22.45  | | ALPHA: (8) implies:
% 152.42/22.45  | |   (9)   ~ (all_57_5 = e0)
% 152.42/22.45  | | 
% 152.42/22.45  | | REDUCE: (3), (9) imply:
% 152.42/22.45  | |   (10)  $false
% 152.42/22.45  | | 
% 152.42/22.45  | | CLOSE: (10) is inconsistent.
% 152.42/22.45  | | 
% 152.42/22.45  | End of split
% 152.42/22.45  | 
% 152.42/22.45  End of proof
% 152.42/22.45  
% 152.42/22.45  Sub-proof #277 shows that the following formulas are inconsistent:
% 152.42/22.45  ----------------------------------------------------------------
% 152.42/22.45    (1)  op(e0, e1) = all_52_11
% 152.42/22.45    (2)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 152.42/22.45    (3)  all_56_8 = e3
% 152.42/22.45    (4)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 152.42/22.45         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 152.42/22.45    (5)   ~ (all_52_7 = all_52_11)
% 152.42/22.45    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 152.42/22.45         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 152.42/22.45    (7)   ~ (all_52_11 = all_10_2)
% 152.42/22.45    (8)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 152.42/22.45         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.42/22.45    (9)  op(e0, e0) = all_10_2
% 152.42/22.45    (10)  op(e3, e2) = all_52_4
% 152.42/22.45    (11)  op(e0, e2) = all_52_7
% 152.42/22.45    (12)   ~ (all_52_3 = all_52_7)
% 152.42/22.45    (13)   ~ (all_52_4 = e2)
% 152.42/22.45    (14)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.45          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.42/22.45    (15)   ~ (all_10_2 = e1)
% 152.42/22.45    (16)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.42/22.45          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.42/22.45    (17)  all_42_2 = all_10_2
% 152.42/22.45    (18)   ~ (e2 = e0)
% 152.42/22.45    (19)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.42/22.45            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.42/22.45    (20)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.42/22.45          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.42/22.45    (21)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.42/22.45          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.42/22.45    (22)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.42/22.45          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.42/22.45    (23)   ~ (all_52_3 = all_52_11)
% 152.42/22.45    (24)   ~ (all_52_9 = e3)
% 152.42/22.45    (25)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.42/22.45              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.42/22.45                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.42/22.45                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.42/22.45    (26)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.42/22.45          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.42/22.45    (27)   ~ (all_52_13 = e2)
% 152.42/22.45    (28)   ~ (e3 = e0)
% 152.42/22.45    (29)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.42/22.45          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.42/22.45    (30)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 152.42/22.45          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.42/22.45    (31)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.42/22.45          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.42/22.45    (32)   ~ (all_52_6 = e3)
% 152.42/22.45    (33)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 152.42/22.45          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 152.42/22.45    (34)  op(e3, e3) = e1
% 152.42/22.45    (35)  op(e1, e2) = all_52_6
% 152.42/22.45    (36)  op(e2, e0) = all_52_13
% 152.42/22.45    (37)   ~ (all_52_9 = e2)
% 152.42/22.45    (38)  op(e0, e3) = all_52_3
% 152.42/22.45    (39)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.45          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.42/22.45    (40)  op(e2, e2) = e2
% 152.42/22.45    (41)  op(e2, e1) = all_52_9
% 152.42/22.45    (42)   ~ (e1 = e0)
% 152.42/22.45    (43)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.42/22.45          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.42/22.45    (44)   ~ (all_52_4 = e1)
% 152.42/22.45    (45)  op(e1, e1) = e3
% 152.42/22.45    (46)   ~ (e3 = e2)
% 152.42/22.45    (47)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 152.42/22.45          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 152.42/22.45            e2)
% 152.42/22.45    (48)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.42/22.45          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.42/22.45    (49)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.42/22.45          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.42/22.45    (50)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.42/22.45          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.42/22.45    (51)   ~ (all_10_2 = e2)
% 152.42/22.45    (52)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.42/22.45          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.42/22.45    (53)   ~ (all_52_3 = all_10_2)
% 152.42/22.45    (54)   ~ (e2 = e1)
% 152.42/22.45    (55)  all_54_15 = all_10_2
% 152.42/22.45    (56)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.42/22.45          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.42/22.45    (57)  op(e1, e3) = all_52_2
% 152.42/22.46    (58)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.42/22.46              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.42/22.46            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.42/22.46            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.42/22.46            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.42/22.46            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.42/22.46            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.42/22.46            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.46            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.42/22.46            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.42/22.46            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.42/22.46            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.42/22.46            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.46            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.42/22.46            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.42/22.46            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.42/22.46            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.42/22.46            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.42/22.46            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.42/22.46            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.42/22.46            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.42/22.46            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.42/22.46            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.42/22.46            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.42/22.46            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.42/22.46            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.42/22.46            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.42/22.46            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.42/22.46            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.42/22.46            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.42/22.46            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.42/22.46            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.42/22.46            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.42/22.46            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.42/22.46            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.42/22.46            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.42/22.46            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.46            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.42/22.46            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.42/22.46            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.46            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.42/22.46            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.42/22.46            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.42/22.46            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.42/22.46            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.42/22.46            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.42/22.46            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.42/22.46            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.42/22.46              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.42/22.46            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.42/22.46            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.42/22.46              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.42/22.46            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.42/22.46            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.42/22.46                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.42/22.46                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.42/22.46                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.42/22.46                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.42/22.46                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.42/22.46                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.42/22.46                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.42/22.46              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.42/22.46                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.42/22.46                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.42/22.46                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.42/22.46                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.42/22.46                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.42/22.46                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.46                $i(all_57_7))))
% 152.42/22.46    (59)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.42/22.46          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.42/22.46    (60)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.42/22.46          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.42/22.46            e1)
% 152.42/22.46    (61)   ~ (all_42_2 = e3) | ( ~ (all_42_0 = e2) & op(all_42_1, e0) = all_42_0 &
% 152.42/22.46            op(e0, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 152.42/22.46              e1) & op(e0, e3) = all_42_1 & $i(all_42_1))
% 152.42/22.46    (62)  op(e2, e3) = all_52_1
% 152.42/22.46    (63)   ~ (all_52_1 = e2)
% 152.42/22.46    (64)   ~ (all_52_6 = e2)
% 152.42/22.46  
% 152.42/22.46  Begin of proof
% 152.42/22.46  | 
% 152.42/22.46  | BETA: splitting (58) gives:
% 152.42/22.46  | 
% 152.42/22.46  | Case 1:
% 152.42/22.46  | | 
% 152.42/22.46  | |   (65)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 152.42/22.46  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.42/22.46  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 152.42/22.46  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 152.42/22.46  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 152.42/22.46  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 152.42/22.46  | |         (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 152.42/22.46  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 152.42/22.46  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.42/22.46  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 152.42/22.46  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 152.42/22.46  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) |
% 152.42/22.46  | |         (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 152.42/22.46  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.42/22.46  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 152.42/22.46  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 152.42/22.46  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 152.42/22.46  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 152.42/22.46  | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 152.42/22.46  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 152.42/22.46  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.42/22.46  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 152.42/22.46  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 152.42/22.46  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 152.42/22.46  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 152.42/22.46  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 152.42/22.46  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.42/22.46  | | 
% 152.42/22.46  | | BETA: splitting (65) gives:
% 152.42/22.46  | | 
% 152.42/22.46  | | Case 1:
% 152.42/22.46  | | | 
% 152.42/22.46  | | |   (66)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.42/22.46  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.42/22.46  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 152.42/22.46  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 152.42/22.46  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.42/22.46  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.42/22.46  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 152.42/22.46  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.42/22.46  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.42/22.46  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 152.42/22.46  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 152.42/22.46  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 152.42/22.46  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 152.42/22.46  | | | 
% 152.42/22.46  | | | BETA: splitting (66) gives:
% 152.42/22.46  | | | 
% 152.42/22.46  | | | Case 1:
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | |   (67)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.42/22.46  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.42/22.46  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 152.42/22.46  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 152.42/22.46  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.42/22.46  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 152.42/22.46  | | | |           e3 & $i(all_57_2) & $i(all_57_12))
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | | REF_CLOSE: (19), (62), (63), (67) are inconsistent by sub-proof #1180.
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | Case 2:
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | |   (68)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.42/22.46  | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.42/22.46  | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 152.42/22.46  | | | |           $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 152.42/22.46  | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.42/22.46  | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 152.42/22.46  | | | |           e3 & $i(all_57_2) & $i(all_57_14))
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | | REF_CLOSE: (19), (45), (68) are inconsistent by sub-proof #368.
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | End of split
% 152.42/22.46  | | | 
% 152.42/22.46  | | Case 2:
% 152.42/22.46  | | | 
% 152.42/22.46  | | |   (69)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.42/22.46  | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.42/22.46  | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 152.42/22.46  | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5
% 152.42/22.46  | | |             = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 152.42/22.46  | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.42/22.46  | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 152.42/22.46  | | |           &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 152.42/22.46  | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 152.42/22.46  | | |           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 =
% 152.42/22.46  | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 152.42/22.46  | | |           & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 152.42/22.46  | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 152.42/22.46  | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.42/22.46  | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 152.42/22.46  | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.42/22.46  | | | 
% 152.42/22.46  | | | BETA: splitting (69) gives:
% 152.42/22.46  | | | 
% 152.42/22.46  | | | Case 1:
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | |   (70)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.42/22.46  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.42/22.46  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 152.42/22.46  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.42/22.46  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 152.42/22.46  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.42/22.46  | | | |           $i(all_57_5) & $i(all_57_10))
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | | REF_CLOSE: (9), (19), (45), (46), (51), (70) are inconsistent by
% 152.42/22.46  | | | |            sub-proof #367.
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | Case 2:
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | |   (71)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.42/22.46  | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.42/22.46  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.42/22.46  | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 152.42/22.46  | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.42/22.46  | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 152.42/22.46  | | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 152.42/22.46  | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 152.42/22.46  | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.42/22.46  | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | | BETA: splitting (71) gives:
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | | Case 1:
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | |   (72)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.42/22.46  | | | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.42/22.46  | | | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.42/22.46  | | | | |         $i(all_57_14)
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | | ALPHA: (72) implies:
% 152.42/22.46  | | | | |   (73)  op(e3, e3) = e2
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | | REF_CLOSE: (19), (34), (54), (73) are inconsistent by sub-proof #1074.
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | Case 2:
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | |   (74)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 152.42/22.46  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 152.42/22.46  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.42/22.46  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 152.42/22.46  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.42/22.46  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 152.42/22.46  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | | REF_CLOSE: (9), (19), (40), (51), (54), (74) are inconsistent by
% 152.42/22.46  | | | | |            sub-proof #1084.
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | End of split
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | End of split
% 152.42/22.46  | | | 
% 152.42/22.46  | | End of split
% 152.42/22.46  | | 
% 152.42/22.46  | Case 2:
% 152.42/22.46  | | 
% 152.42/22.46  | |   (75)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 152.42/22.46  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.42/22.46  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 152.42/22.46  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 152.42/22.46  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 152.42/22.46  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 152.42/22.46  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 152.42/22.46  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.42/22.46  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.42/22.46  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.42/22.46  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.46  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.42/22.46  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 152.42/22.46  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 152.42/22.46  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.42/22.46  | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 152.42/22.46  | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 152.42/22.46  | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 152.42/22.46  | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 152.42/22.46  | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 152.42/22.46  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 152.42/22.46  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 152.42/22.46  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 152.42/22.46  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.42/22.46  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 152.42/22.46  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.42/22.46  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.42/22.46  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 152.42/22.46  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.42/22.46  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 152.42/22.46  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 152.42/22.46  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 152.42/22.46  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.42/22.46  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 152.42/22.46  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.42/22.46  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 152.42/22.46  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 152.42/22.46  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.42/22.46  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 152.42/22.46  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.42/22.46  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.42/22.46  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.42/22.46  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.46  | |               $i(all_57_7))))
% 152.42/22.46  | | 
% 152.42/22.46  | | BETA: splitting (75) gives:
% 152.42/22.46  | | 
% 152.42/22.46  | | Case 1:
% 152.42/22.46  | | | 
% 152.42/22.46  | | |   (76)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.42/22.46  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.42/22.46  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.42/22.46  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 152.42/22.46  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.42/22.46  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.42/22.46  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 152.42/22.46  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 152.42/22.46  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 152.42/22.46  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 152.42/22.46  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 152.42/22.46  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.42/22.46  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 152.42/22.46  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.42/22.46  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.42/22.46  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.42/22.46  | | |           $i(all_57_13))
% 152.42/22.46  | | | 
% 152.42/22.46  | | | BETA: splitting (76) gives:
% 152.42/22.46  | | | 
% 152.42/22.46  | | | Case 1:
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | |   (77)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.42/22.46  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.42/22.46  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.42/22.46  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 152.42/22.46  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 152.42/22.46  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 152.42/22.46  | | | |           e2 & $i(all_57_6) & $i(all_57_12))
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | | REF_CLOSE: (9), (15), (19), (37), (41), (77) are inconsistent by
% 152.42/22.46  | | | |            sub-proof #544.
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | Case 2:
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | |   (78)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.42/22.46  | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.42/22.46  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.42/22.46  | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 152.42/22.46  | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 152.42/22.46  | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 152.42/22.46  | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 152.42/22.46  | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 152.42/22.46  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 152.42/22.46  | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | | REF_CLOSE: (9), (15), (18), (19), (28), (40), (45), (78) are
% 152.42/22.46  | | | |            inconsistent by sub-proof #293.
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | End of split
% 152.42/22.46  | | | 
% 152.42/22.46  | | Case 2:
% 152.42/22.46  | | | 
% 152.42/22.46  | | |   (79)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 152.42/22.46  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.42/22.46  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.42/22.46  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 152.42/22.46  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 152.42/22.46  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.42/22.46  | | |           $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0
% 152.42/22.46  | | |           &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.42/22.46  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 152.42/22.46  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 152.42/22.46  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.42/22.46  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 152.42/22.46  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 152.42/22.46  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.42/22.46  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.42/22.46  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.42/22.46  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.42/22.46  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.42/22.46  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 152.42/22.46  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.42/22.46  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.42/22.46  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.42/22.46  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 152.42/22.46  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.42/22.46  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.42/22.46  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 152.42/22.46  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.42/22.46  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.42/22.46  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.42/22.46  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 152.42/22.46  | | | 
% 152.42/22.46  | | | BETA: splitting (79) gives:
% 152.42/22.46  | | | 
% 152.42/22.46  | | | Case 1:
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | |   (80)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 152.42/22.46  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.42/22.46  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.42/22.46  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 152.42/22.46  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.42/22.46  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 152.42/22.46  | | | |           e1 & $i(all_57_9) & $i(all_57_14))
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | | REF_CLOSE: (19), (34), (42), (80) are inconsistent by sub-proof #956.
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | Case 2:
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | |   (81)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 152.42/22.46  | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.42/22.46  | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.42/22.46  | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 152.42/22.46  | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.42/22.46  | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 152.42/22.46  | | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 152.42/22.46  | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 152.42/22.46  | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.42/22.46  | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.42/22.46  | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.42/22.46  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.42/22.46  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.42/22.46  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.42/22.46  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 152.42/22.46  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.42/22.46  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.42/22.46  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 152.42/22.46  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.42/22.46  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 152.42/22.46  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 152.42/22.46  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.42/22.46  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 152.42/22.46  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | | BETA: splitting (81) gives:
% 152.42/22.46  | | | | 
% 152.42/22.46  | | | | Case 1:
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | |   (82)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 152.42/22.46  | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.42/22.46  | | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.42/22.46  | | | | |         $i(all_57_13)
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | | ALPHA: (82) implies:
% 152.42/22.46  | | | | |   (83)  op(e2, e0) = e2
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | | REF_CLOSE: (19), (27), (36), (83) are inconsistent by sub-proof #1156.
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | Case 2:
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | |   (84)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 152.42/22.46  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.42/22.46  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.42/22.46  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.42/22.46  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.42/22.46  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 152.42/22.46  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 152.42/22.46  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.42/22.46  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.42/22.46  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.42/22.46  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 152.42/22.46  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.42/22.46  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 152.42/22.46  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.42/22.46  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.42/22.46  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.42/22.46  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 152.42/22.46  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.42/22.46  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.42/22.46  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 152.42/22.46  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.46  | | | | |               $i(all_57_7))))
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | | BETA: splitting (84) gives:
% 152.42/22.46  | | | | | 
% 152.42/22.46  | | | | | Case 1:
% 152.42/22.46  | | | | | | 
% 152.42/22.46  | | | | | |   (85)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 152.42/22.46  | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.42/22.46  | | | | | |         & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.42/22.46  | | | | | |         $i(all_57_14)
% 152.42/22.46  | | | | | | 
% 152.42/22.46  | | | | | | ALPHA: (85) implies:
% 152.42/22.46  | | | | | |   (86)  op(e2, e2) = e0
% 152.42/22.46  | | | | | | 
% 152.42/22.46  | | | | | | REF_CLOSE: (18), (19), (40), (86) are inconsistent by sub-proof
% 152.42/22.46  | | | | | |            #1145.
% 152.42/22.46  | | | | | | 
% 152.42/22.46  | | | | | Case 2:
% 152.42/22.46  | | | | | | 
% 152.42/22.46  | | | | | |   (87)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.42/22.46  | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 152.42/22.46  | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 152.42/22.46  | | | | | |               e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 152.42/22.46  | | | | | |             = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1,
% 152.42/22.46  | | | | | |               e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.42/22.46  | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.42/22.46  | | | | | |             (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.42/22.46  | | | | | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.42/22.46  | | | | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 152.42/22.46  | | | | | |             (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.42/22.46  | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.42/22.46  | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.42/22.46  | | | | | |             (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 152.42/22.46  | | | | | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.42/22.46  | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.42/22.46  | | | | | |             (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 152.42/22.46  | | | | | |             & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.46  | | | | | |             $i(all_57_7)))
% 152.42/22.46  | | | | | | 
% 152.42/22.46  | | | | | | ALPHA: (87) implies:
% 152.42/22.46  | | | | | |   (88)  op(e0, e0) = all_57_15
% 152.42/22.46  | | | | | |   (89)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.42/22.46  | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 152.42/22.46  | | | | | |           & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 152.42/22.46  | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 152.42/22.46  | | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 152.42/22.46  | | | | | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.42/22.46  | | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 152.42/22.46  | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.42/22.46  | | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.42/22.46  | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 152.42/22.46  | | | | | |           & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.42/22.46  | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 152.42/22.46  | | | | | |           & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 152.42/22.46  | | | | | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.42/22.46  | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 152.42/22.46  | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.42/22.46  | | | | | | 
% 152.42/22.46  | | | | | | GROUND_INST: instantiating (19) with all_10_2, all_57_15, e0, e0,
% 152.42/22.46  | | | | | |              simplifying with (9), (88) gives:
% 152.42/22.46  | | | | | |   (90)  all_57_15 = all_10_2
% 152.42/22.46  | | | | | | 
% 152.42/22.46  | | | | | | BETA: splitting (61) gives:
% 152.42/22.46  | | | | | | 
% 152.42/22.46  | | | | | | Case 1:
% 152.42/22.46  | | | | | | | 
% 152.42/22.46  | | | | | | |   (91)   ~ (all_42_2 = e3)
% 152.42/22.46  | | | | | | | 
% 152.42/22.46  | | | | | | | REDUCE: (17), (91) imply:
% 152.42/22.46  | | | | | | |   (92)   ~ (all_10_2 = e3)
% 152.42/22.46  | | | | | | | 
% 152.42/22.46  | | | | | | | BETA: splitting (2) gives:
% 152.42/22.46  | | | | | | | 
% 152.42/22.46  | | | | | | | Case 1:
% 152.42/22.46  | | | | | | | | 
% 152.42/22.46  | | | | | | | |   (93)  all_54_15 = e3
% 152.42/22.46  | | | | | | | | 
% 152.42/22.46  | | | | | | | | COMBINE_EQS: (55), (93) imply:
% 152.42/22.46  | | | | | | | |   (94)  all_10_2 = e3
% 152.42/22.46  | | | | | | | | 
% 152.42/22.46  | | | | | | | | REDUCE: (92), (94) imply:
% 152.42/22.46  | | | | | | | |   (95)  $false
% 152.42/22.46  | | | | | | | | 
% 152.42/22.46  | | | | | | | | CLOSE: (95) is inconsistent.
% 152.42/22.46  | | | | | | | | 
% 152.42/22.46  | | | | | | | Case 2:
% 152.42/22.46  | | | | | | | | 
% 152.42/22.46  | | | | | | | |   (96)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 152.42/22.46  | | | | | | | | 
% 152.42/22.46  | | | | | | | | REF_CLOSE: (1), (7), (15), (19), (34), (38), (40), (45), (46),
% 152.42/22.46  | | | | | | | |            (51), (53), (54), (55), (89), (96) are inconsistent
% 152.42/22.46  | | | | | | | |            by sub-proof #286.
% 152.42/22.46  | | | | | | | | 
% 152.42/22.46  | | | | | | | End of split
% 152.42/22.46  | | | | | | | 
% 152.42/22.46  | | | | | | Case 2:
% 152.42/22.46  | | | | | | | 
% 152.42/22.46  | | | | | | |   (97)  all_42_2 = e3
% 152.42/22.46  | | | | | | | 
% 152.42/22.46  | | | | | | | COMBINE_EQS: (17), (97) imply:
% 152.42/22.47  | | | | | | |   (98)  all_10_2 = e3
% 152.42/22.47  | | | | | | | 
% 152.42/22.47  | | | | | | | COMBINE_EQS: (90), (98) imply:
% 152.42/22.47  | | | | | | |   (99)  all_57_15 = e3
% 152.42/22.47  | | | | | | | 
% 152.42/22.47  | | | | | | | REDUCE: (7), (98) imply:
% 152.42/22.47  | | | | | | |   (100)   ~ (all_52_11 = e3)
% 152.42/22.47  | | | | | | | 
% 152.42/22.47  | | | | | | | REDUCE: (15), (98) imply:
% 152.42/22.47  | | | | | | |   (101)   ~ (e3 = e1)
% 152.42/22.47  | | | | | | | 
% 152.42/22.47  | | | | | | | REDUCE: (9), (98) imply:
% 152.42/22.47  | | | | | | |   (102)  op(e0, e0) = e3
% 152.42/22.47  | | | | | | | 
% 152.42/22.47  | | | | | | | BETA: splitting (59) gives:
% 152.42/22.47  | | | | | | | 
% 152.42/22.47  | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | 
% 152.42/22.47  | | | | | | | |   (103)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 &
% 152.42/22.47  | | | | | | | |            op(e2, e2) = e3)
% 152.42/22.47  | | | | | | | | 
% 152.42/22.47  | | | | | | | | BETA: splitting (103) gives:
% 152.42/22.47  | | | | | | | | 
% 152.42/22.47  | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | 
% 152.42/22.47  | | | | | | | | |   (104)  all_56_1 = e3 & op(e3, e2) = e3
% 152.42/22.47  | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | ALPHA: (104) implies:
% 152.42/22.47  | | | | | | | | |   (105)  all_56_1 = e3
% 152.42/22.47  | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | BETA: splitting (39) gives:
% 152.42/22.47  | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | |   (106)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 152.42/22.47  | | | | | | | | | |            & op(e2, e2) = e3)
% 152.42/22.47  | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | BETA: splitting (106) gives:
% 152.42/22.47  | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | |   (107)  all_56_2 = e3 & op(e2, e3) = e3
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | ALPHA: (107) implies:
% 152.42/22.47  | | | | | | | | | | |   (108)  all_56_2 = e3
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | BETA: splitting (89) gives:
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | |   (109)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.42/22.47  | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.42/22.47  | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.42/22.47  | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 152.42/22.47  | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 152.42/22.47  | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.42/22.47  | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 152.42/22.47  | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.42/22.47  | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.42/22.47  | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | REF_CLOSE: (19), (34), (54), (88), (102), (109) are
% 152.42/22.47  | | | | | | | | | | | |            inconsistent by sub-proof #952.
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | |   (110)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.42/22.47  | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.42/22.47  | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.42/22.47  | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 152.42/22.47  | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.42/22.47  | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.42/22.47  | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.42/22.47  | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.42/22.47  | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 152.42/22.47  | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | BETA: splitting (110) gives:
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | |   (111)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.42/22.47  | | | | | | | | | | | | |            e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.42/22.47  | | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.42/22.47  | | | | | | | | | | | | |          $i(all_57_4)
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | ALPHA: (111) implies:
% 152.42/22.47  | | | | | | | | | | | | |   (112)  op(e1, e1) = e2
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | REF_CLOSE: (19), (45), (46), (112) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | |            sub-proof #834.
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | |   (113)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 152.42/22.47  | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 152.42/22.47  | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.42/22.47  | | | | | | | | | | | | |            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 152.42/22.47  | | | | | | | | | | | | |            &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.42/22.47  | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 152.42/22.47  | | | | | | | | | | | | |              e1) = e0 & $i(all_57_7))
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | BETA: splitting (113) gives:
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | |   (114)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 152.42/22.47  | | | | | | | | | | | | | |            e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 152.42/22.47  | | | | | | | | | | | | | |          op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.42/22.47  | | | | | | | | | | | | | |          $i(all_57_6)
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | ALPHA: (114) implies:
% 152.42/22.47  | | | | | | | | | | | | | |   (115)   ~ (all_57_15 = e1)
% 152.42/22.47  | | | | | | | | | | | | | |   (116)  op(e0, e1) = e0
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (9), (10), (11), (12), (13),
% 152.42/22.47  | | | | | | | | | | | | | |            (14), (15), (16), (18), (19), (20), (21), (22),
% 152.42/22.47  | | | | | | | | | | | | | |            (23), (25), (26), (28), (29), (30), (31), (32),
% 152.42/22.47  | | | | | | | | | | | | | |            (33), (34), (35), (37), (38), (39), (40), (41),
% 152.42/22.47  | | | | | | | | | | | | | |            (42), (43), (44), (45), (46), (48), (49), (50),
% 152.42/22.47  | | | | | | | | | | | | | |            (52), (54), (56), (57), (59), (60), (62), (63),
% 152.42/22.47  | | | | | | | | | | | | | |            (64), (89), (100), (101), (102), (105), (108),
% 152.42/22.47  | | | | | | | | | | | | | |            (116) are inconsistent by sub-proof #282.
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | |   (117)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.42/22.47  | | | | | | | | | | | | | |            e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 152.42/22.47  | | | | | | | | | | | | | |          op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.42/22.47  | | | | | | | | | | | | | |          $i(all_57_7)
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | ALPHA: (117) implies:
% 152.42/22.47  | | | | | | | | | | | | | |   (118)  op(e2, e2) = e1
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | REF_CLOSE: (19), (40), (54), (118) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | |            sub-proof #1158.
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | |   (119)  all_56_3 = e3 & op(e2, e2) = e3
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | ALPHA: (119) implies:
% 152.42/22.47  | | | | | | | | | | |   (120)  op(e2, e2) = e3
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | REF_CLOSE: (19), (40), (46), (120) are inconsistent by
% 152.42/22.47  | | | | | | | | | | |            sub-proof #1179.
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | |   (121)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3
% 152.42/22.47  | | | | | | | | | |            & op(e2, e0) = e3)
% 152.42/22.47  | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | BETA: splitting (121) gives:
% 152.42/22.47  | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | |   (122)  all_56_5 = e3 & op(e2, e1) = e3
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | REF_CLOSE: (19), (24), (41), (122) are inconsistent by
% 152.42/22.47  | | | | | | | | | | |            sub-proof #647.
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | |   (123)  all_56_10 = e3 & op(e2, e0) = e3
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | ALPHA: (123) implies:
% 152.42/22.47  | | | | | | | | | | |   (124)  all_56_10 = e3
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | BETA: splitting (30) gives:
% 152.42/22.47  | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | |   (125)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 152.42/22.47  | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | BETA: splitting (125) gives:
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | |   (126)  all_56_9 = e1 & op(e3, e0) = e1
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | ALPHA: (126) implies:
% 152.42/22.47  | | | | | | | | | | | | |   (127)  all_56_9 = e1
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | REF_CLOSE: (4), (9), (18), (19), (25), (27), (28), (36),
% 152.42/22.47  | | | | | | | | | | | | |            (42), (51), (54), (102), (124), (127) are
% 152.42/22.47  | | | | | | | | | | | | |            inconsistent by sub-proof #747.
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | |   (128)  all_56_10 = e1 & op(e2, e0) = e1
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | ALPHA: (128) implies:
% 152.42/22.47  | | | | | | | | | | | | |   (129)  all_56_10 = e1
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | REF_CLOSE: (101), (124), (129) are inconsistent by sub-proof
% 152.42/22.47  | | | | | | | | | | | | |            #677.
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | |   (130)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 152.42/22.47  | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | BETA: splitting (130) gives:
% 152.42/22.47  | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | |   (131)  all_56_11 = e1 & op(e1, e0) = e1
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | ALPHA: (131) implies:
% 152.42/22.47  | | | | | | | | | | | | |   (132)  all_56_11 = e1
% 152.42/22.47  | | | | | | | | | | | | |   (133)  op(e1, e0) = e1
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | BETA: splitting (25) gives:
% 152.42/22.47  | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | |   (134)  all_56_15 = e0 & op(e0, e0) = e0
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | ALPHA: (134) implies:
% 152.42/22.47  | | | | | | | | | | | | | |   (135)  op(e0, e0) = e0
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | REF_CLOSE: (19), (28), (102), (135) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | |            sub-proof #1143.
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | |   (136)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 152.42/22.47  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 152.42/22.47  | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 152.42/22.47  | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 152.42/22.47  | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | ALPHA: (136) implies:
% 152.42/22.47  | | | | | | | | | | | | | |   (137)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 152.42/22.47  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 152.42/22.47  | | | | | | | | | | | | | |              e1) = e0)
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 152.42/22.47  | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | |   (138)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.42/22.47  | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.42/22.47  | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.42/22.47  | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 152.42/22.47  | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 152.42/22.47  | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.42/22.47  | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 152.42/22.47  | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.42/22.47  | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.42/22.47  | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 152.42/22.47  | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | REF_CLOSE: (19), (34), (54), (88), (102), (138) are
% 152.42/22.47  | | | | | | | | | | | | | | |            inconsistent by sub-proof #952.
% 152.42/22.47  | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | |   (139)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.42/22.47  | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.42/22.47  | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.42/22.47  | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 152.42/22.47  | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.42/22.47  | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.42/22.47  | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.42/22.47  | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.42/22.47  | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 152.42/22.47  | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.42/22.47  | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | |   (140)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.42/22.47  | | | | | | | | | | | | | | | |            e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.42/22.47  | | | | | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.42/22.47  | | | | | | | | | | | | | | | |          $i(all_57_4)
% 152.42/22.47  | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | |   (141)  op(e1, e1) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | REF_CLOSE: (19), (45), (46), (141) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | | | |            sub-proof #834.
% 152.42/22.47  | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | |   (142)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 152.42/22.47  | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 152.42/22.47  | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.42/22.47  | | | | | | | | | | | | | | | |            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 152.42/22.47  | | | | | | | | | | | | | | | |            &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.42/22.47  | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 152.42/22.47  | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_7))
% 152.42/22.47  | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | |   (143)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 152.42/22.47  | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 152.42/22.47  | | | | | | | | | | | | | | | | |          op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.42/22.47  | | | | | | | | | | | | | | | | |          $i(all_57_6)
% 152.42/22.47  | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | |   (144)   ~ (all_57_15 = e1)
% 152.42/22.47  | | | | | | | | | | | | | | | | |   (145)  op(e0, e1) = e0
% 152.42/22.47  | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | BETA: splitting (43) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | |   (146)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e2)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | |   (147)  all_56_6 = e2 & op(e1, e3) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | |   (148)  all_56_6 = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | |   (149)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | |   (150)  all_56_6 = e0 & op(e1, e3) = e0
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (148), (150) are inconsistent by sub-proof
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | |            #1054.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | |   (151)  all_56_7 = e0 & op(e1, e2) = e0
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | |   (152)  all_56_7 = e0
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | |   (153)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |   (154)  all_56_0 = e3 & op(e3, e3) = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (154) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |   (155)  op(e3, e3) = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (34), (101), (155) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1178.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |   (156)  all_56_2 = e3 & op(e2, e3) = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |   (157)  all_56_2 = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (5), (6), (9), (10), (11), (12), (13),
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |            (14), (15), (16), (18), (19), (20), (21), (22),
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |            (23), (25), (26), (28), (29), (30), (31), (32),
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |            (33), (34), (35), (37), (38), (39), (40), (41),
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |            (42), (43), (44), (45), (46), (48), (49), (50),
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |            (52), (54), (56), (57), (59), (60), (62), (63),
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |            (64), (89), (100), (101), (102), (105), (145),
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |            (157) are inconsistent by sub-proof #282.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | |   (158)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |   (159)  all_56_6 = e3 & op(e1, e3) = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (159) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |   (160)  all_56_6 = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (18), (19), (21), (28), (42), (43), (45),
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |            (46), (52), (54), (101), (160) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #607.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |   (161)  all_56_12 = e3 & op(e0, e3) = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | |   (162)  all_56_12 = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (56) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | |   (163)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (164)  all_56_1 = e1 & op(e3, e2) = e1
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (165)  all_56_1 = e1
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (105), (165) imply:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (166)  e3 = e1
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (166) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (167)  e3 = e1
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (162), (167) imply:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (168)  all_56_12 = e1
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (169)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (170)  all_56_0 = e3 & op(e3, e3) = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (170) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (171)  op(e3, e3) = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (34), (101), (171) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1178.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (172)  all_56_2 = e3 & op(e2, e3) = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (172) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (173)  all_56_2 = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (28), (29), (33), (34), (42), (54),
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (62), (63), (168), (173) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #754.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (158) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (174)  all_56_6 = e3 & op(e1, e3) = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (174) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (175)  all_56_6 = e3
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (18), (19), (21), (28), (42), (43), (45),
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (46), (52), (54), (101), (175) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #607.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (101), (162), (168) are inconsistent by sub-proof
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1056.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (176)  all_56_3 = e1 & op(e2, e2) = e1
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (177)  op(e2, e2) = e1
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (40), (54), (177) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1158.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | |   (178)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (178) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (179)  all_56_7 = e1 & op(e1, e2) = e1
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (152), (179) are inconsistent by sub-proof
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |            #1111.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (180)  all_56_13 = e1 & op(e0, e2) = e1
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | |   (181)  all_56_13 = e1
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (182)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 =
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e2, e0) = e2)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (182) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (183)  all_56_9 = e2 & op(e3, e0) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (184)  all_56_9 = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (185)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (28), (34), (42), (105), (185) are
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #951.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (186)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (186) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (187)  all_56_4 = e0 & op(e3, e1) = e0
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (187) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_56_4 = e0
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (189)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (190)  all_56_4 = e2 & op(e3, e1) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (191)  all_56_4 = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (188), (191) are inconsistent by sub-proof
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #936.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (192)  all_56_5 = e2 & op(e2, e1) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (193)  op(e2, e1) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (37), (41), (193) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1157.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (194)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  all_56_8 = e2 & op(e1, e1) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  op(e1, e1) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (45), (46), (196) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #834.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (197)  all_56_14 = e2 & op(e0, e1) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (198)  op(e0, e1) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (28), (42), (137), (162), (181), (198)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #633.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (199)  all_56_9 = e0 & op(e3, e0) = e0
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (200)  all_56_9 = e0
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (184), (200) are inconsistent by sub-proof
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #776.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (201)  all_56_10 = e2 & op(e2, e0) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (202)  op(e2, e0) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (27), (36), (202) are inconsistent by
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1156.
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |   (203)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 =
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (204)  all_56_11 = e2 & op(e1, e0) = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_56_11 = e2
% 152.42/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (18), (21), (28), (42), (52), (54), (101),
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (148), (205) are inconsistent by sub-proof #281.
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (206)  all_56_15 = e2 & op(e0, e0) = e2
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (207)  op(e0, e0) = e2
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (19), (51), (207) are inconsistent by
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1097.
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | |   (208)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (28), (42), (45), (132), (208) are
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #362.
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | |   (209)  all_56_7 = e2 & op(e1, e2) = e2
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 152.69/22.47  | | | | | | | | | | | | | | | | | | |   (210)  op(e1, e2) = e2
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (35), (64), (210) are inconsistent by
% 152.69/22.47  | | | | | | | | | | | | | | | | | | |            sub-proof #1171.
% 152.69/22.47  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.47  | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | |   (211)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 152.69/22.47  | | | | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 152.69/22.47  | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (45), (46), (54), (133), (211) are
% 152.69/22.47  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #280.
% 152.69/22.47  | | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.47  | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | |   (212)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.69/22.47  | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 152.69/22.47  | | | | | | | | | | | | | | | | |          op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.69/22.47  | | | | | | | | | | | | | | | | |          $i(all_57_7)
% 152.69/22.47  | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 152.69/22.47  | | | | | | | | | | | | | | | | |   (213)  op(e2, e2) = e1
% 152.69/22.47  | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (40), (54), (213) are inconsistent by
% 152.69/22.47  | | | | | | | | | | | | | | | | |            sub-proof #1158.
% 152.69/22.47  | | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | Case 2:
% 152.69/22.47  | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | |   (214)  all_56_15 = e1 & op(e0, e0) = e1
% 152.69/22.47  | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | ALPHA: (214) implies:
% 152.69/22.47  | | | | | | | | | | | | |   (215)  op(e0, e0) = e1
% 152.69/22.47  | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | | REF_CLOSE: (9), (15), (19), (215) are inconsistent by
% 152.69/22.47  | | | | | | | | | | | | |            sub-proof #1116.
% 152.69/22.47  | | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | | End of split
% 152.69/22.47  | | | | | | | | | | | | 
% 152.69/22.47  | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | |   (216)  all_56_3 = e3 & op(e2, e2) = e3
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | ALPHA: (216) implies:
% 152.69/22.48  | | | | | | | | |   (217)  op(e2, e2) = e3
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | REF_CLOSE: (19), (40), (46), (217) are inconsistent by
% 152.69/22.48  | | | | | | | | |            sub-proof #1179.
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | 
% 152.69/22.48  | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | 
% 152.69/22.48  | | | | | | | |   (218)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 &
% 152.69/22.48  | | | | | | | |            op(e0, e2) = e3)
% 152.69/22.48  | | | | | | | | 
% 152.69/22.48  | | | | | | | | BETA: splitting (218) gives:
% 152.69/22.48  | | | | | | | | 
% 152.69/22.48  | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | |   (219)  all_56_7 = e3 & op(e1, e2) = e3
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | REF_CLOSE: (19), (32), (35), (219) are inconsistent by
% 152.69/22.48  | | | | | | | | |            sub-proof #925.
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | |   (220)  all_56_13 = e3 & op(e0, e2) = e3
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | ALPHA: (220) implies:
% 152.69/22.48  | | | | | | | | |   (221)  all_56_13 = e3
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | BETA: splitting (39) gives:
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | |   (222)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 152.69/22.48  | | | | | | | | | |            & op(e2, e2) = e3)
% 152.69/22.48  | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | BETA: splitting (222) gives:
% 152.69/22.48  | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | |   (223)  all_56_2 = e3 & op(e2, e3) = e3
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | ALPHA: (223) implies:
% 152.69/22.48  | | | | | | | | | | |   (224)  all_56_2 = e3
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | BETA: splitting (60) gives:
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | |   (225)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 152.69/22.48  | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | BETA: splitting (225) gives:
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | |   (226)  all_56_12 = e1 & op(e0, e3) = e1
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | ALPHA: (226) implies:
% 152.69/22.48  | | | | | | | | | | | | |   (227)  all_56_12 = e1
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | REF_CLOSE: (18), (19), (28), (29), (33), (34), (42), (54),
% 152.69/22.48  | | | | | | | | | | | | |            (62), (63), (224), (227) are inconsistent by
% 152.69/22.48  | | | | | | | | | | | | |            sub-proof #754.
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | |   (228)  all_56_13 = e1 & op(e0, e2) = e1
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | REF_CLOSE: (101), (221), (228) are inconsistent by sub-proof
% 152.69/22.48  | | | | | | | | | | | | |            #878.
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | |   (229)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 152.69/22.48  | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | BETA: splitting (229) gives:
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | |   (230)  all_56_14 = e1 & op(e0, e1) = e1
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | ALPHA: (230) implies:
% 152.69/22.48  | | | | | | | | | | | | |   (231)  all_56_14 = e1
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | BETA: splitting (25) gives:
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | |   (232)  all_56_15 = e0 & op(e0, e0) = e0
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | ALPHA: (232) implies:
% 152.69/22.48  | | | | | | | | | | | | | |   (233)  op(e0, e0) = e0
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | REF_CLOSE: (19), (28), (102), (233) are inconsistent by
% 152.69/22.48  | | | | | | | | | | | | | |            sub-proof #1143.
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | |   (234)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 152.69/22.48  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 152.69/22.48  | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 152.69/22.48  | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 152.69/22.48  | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | ALPHA: (234) implies:
% 152.69/22.48  | | | | | | | | | | | | | |   (235)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 152.69/22.48  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 152.69/22.48  | | | | | | | | | | | | | |              e1) = e0)
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | |   (236)  all_56_12 = e0 & op(e0, e3) = e0
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (12), (15), (18), (19), (28), (38),
% 152.69/22.48  | | | | | | | | | | | | | | |            (40), (42), (46), (47), (49), (51), (54), (56),
% 152.69/22.48  | | | | | | | | | | | | | | |            (59), (60), (101), (221), (235), (236) are
% 152.69/22.48  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1095.
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | |   (237)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 152.69/22.48  | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | |   (238)  all_56_13 = e0 & op(e0, e2) = e0
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | | REF_CLOSE: (28), (221), (238) are inconsistent by sub-proof
% 152.69/22.48  | | | | | | | | | | | | | | | |            #1102.
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | |   (239)  all_56_14 = e0 & op(e0, e1) = e0
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | | REF_CLOSE: (42), (231), (239) are inconsistent by sub-proof
% 152.69/22.48  | | | | | | | | | | | | | | | |            #279.
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | |   (240)  all_56_15 = e1 & op(e0, e0) = e1
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | ALPHA: (240) implies:
% 152.69/22.48  | | | | | | | | | | | | |   (241)  op(e0, e0) = e1
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | REF_CLOSE: (9), (15), (19), (241) are inconsistent by
% 152.69/22.48  | | | | | | | | | | | | |            sub-proof #1116.
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | |   (242)  all_56_3 = e3 & op(e2, e2) = e3
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | ALPHA: (242) implies:
% 152.69/22.48  | | | | | | | | | | |   (243)  op(e2, e2) = e3
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | REF_CLOSE: (19), (40), (46), (243) are inconsistent by
% 152.69/22.48  | | | | | | | | | | |            sub-proof #1179.
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | |   (244)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3
% 152.69/22.48  | | | | | | | | | |            & op(e2, e0) = e3)
% 152.69/22.48  | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | BETA: splitting (244) gives:
% 152.69/22.48  | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | |   (245)  all_56_5 = e3 & op(e2, e1) = e3
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | REF_CLOSE: (19), (24), (41), (245) are inconsistent by
% 152.69/22.48  | | | | | | | | | | |            sub-proof #647.
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | |   (246)  all_56_10 = e3 & op(e2, e0) = e3
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | ALPHA: (246) implies:
% 152.69/22.48  | | | | | | | | | | |   (247)  all_56_10 = e3
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | BETA: splitting (8) gives:
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | |   (248)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 152.69/22.48  | | | | | | | | | | | |            & op(e2, e3) = e3)
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | REF_CLOSE: (14), (18), (19), (28), (34), (40), (42), (48),
% 152.69/22.48  | | | | | | | | | | | |            (54), (101), (247), (248) are inconsistent by
% 152.69/22.48  | | | | | | | | | | | |            sub-proof #278.
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | |   (249)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 152.69/22.48  | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | BETA: splitting (249) gives:
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | |   (250)  all_56_6 = e3 & op(e1, e3) = e3
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | ALPHA: (250) implies:
% 152.69/22.48  | | | | | | | | | | | | |   (251)  all_56_6 = e3
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | REF_CLOSE: (3), (18), (19), (21), (28), (42), (43), (45),
% 152.69/22.48  | | | | | | | | | | | | |            (46), (52), (54), (101), (251) are inconsistent by
% 152.69/22.48  | | | | | | | | | | | | |            sub-proof #607.
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | |   (252)  all_56_12 = e3 & op(e0, e3) = e3
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | ALPHA: (252) implies:
% 152.69/22.48  | | | | | | | | | | | | |   (253)  all_56_12 = e3
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | BETA: splitting (25) gives:
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | |   (254)  all_56_15 = e0 & op(e0, e0) = e0
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | ALPHA: (254) implies:
% 152.69/22.48  | | | | | | | | | | | | | |   (255)  op(e0, e0) = e0
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | REF_CLOSE: (19), (28), (102), (255) are inconsistent by
% 152.69/22.48  | | | | | | | | | | | | | |            sub-proof #1143.
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | |   (256)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 152.69/22.48  | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 152.69/22.48  | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 152.69/22.48  | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 152.69/22.48  | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | ALPHA: (256) implies:
% 152.69/22.48  | | | | | | | | | | | | | |   (257)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 152.69/22.48  | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 152.69/22.48  | | | | | | | | | | | | | |              e1) = e0)
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | |   (258)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 =
% 152.69/22.48  | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | Case 1:
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | |   (259)  all_56_12 = e2 & op(e0, e3) = e2
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 152.69/22.48  | | | | | | | | | | | | | | | |   (260)  all_56_12 = e2
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | | COMBINE_EQS: (253), (260) imply:
% 152.69/22.48  | | | | | | | | | | | | | | | |   (261)  e3 = e2
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | | COMBINE_EQS: (221), (261) imply:
% 152.69/22.48  | | | | | | | | | | | | | | | |   (262)  all_56_13 = e2
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (28), (40), (42), (46), (49), (54),
% 152.69/22.48  | | | | | | | | | | | | | | | |            (56), (59), (101), (262) are inconsistent by
% 152.69/22.48  | | | | | | | | | | | | | | | |            sub-proof #1104.
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | |   (263)  all_56_13 = e2 & op(e0, e2) = e2
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | | ALPHA: (263) implies:
% 152.69/22.48  | | | | | | | | | | | | | | | |   (264)  all_56_13 = e2
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | | REF_CLOSE: (18), (19), (28), (40), (42), (46), (49), (54),
% 152.69/22.48  | | | | | | | | | | | | | | | |            (56), (59), (101), (264) are inconsistent by
% 152.69/22.48  | | | | | | | | | | | | | | | |            sub-proof #1104.
% 152.69/22.48  | | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | Case 2:
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | |   (265)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 =
% 152.69/22.48  | | | | | | | | | | | | | | |            e2 & op(e0, e0) = e2)
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | | REF_CLOSE: (9), (15), (18), (19), (28), (42), (51), (54),
% 152.69/22.48  | | | | | | | | | | | | | | |            (60), (101), (221), (257), (265) are inconsistent
% 152.69/22.48  | | | | | | | | | | | | | | |            by sub-proof #1096.
% 152.69/22.48  | | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | | 
% 152.69/22.48  | | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | | 
% 152.69/22.48  | | | | | | | | End of split
% 152.69/22.48  | | | | | | | | 
% 152.69/22.48  | | | | | | | End of split
% 152.69/22.48  | | | | | | | 
% 152.69/22.48  | | | | | | End of split
% 152.69/22.48  | | | | | | 
% 152.69/22.48  | | | | | End of split
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | End of split
% 152.69/22.48  | | | | 
% 152.69/22.48  | | | End of split
% 152.69/22.48  | | | 
% 152.69/22.48  | | End of split
% 152.69/22.48  | | 
% 152.69/22.48  | End of split
% 152.69/22.48  | 
% 152.69/22.48  End of proof
% 152.69/22.48  
% 152.69/22.48  Sub-proof #278 shows that the following formulas are inconsistent:
% 152.69/22.48  ----------------------------------------------------------------
% 152.69/22.48    (1)   ~ (e3 = e1)
% 152.69/22.48    (2)  all_56_10 = e3
% 152.69/22.48    (3)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.69/22.48         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.69/22.48    (4)   ~ (e2 = e0)
% 152.69/22.48    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.69/22.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.69/22.48    (6)   ~ (e3 = e0)
% 152.69/22.48    (7)  op(e3, e3) = e1
% 152.69/22.48    (8)  op(e2, e2) = e2
% 152.69/22.48    (9)   ~ (e1 = e0)
% 152.69/22.48    (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 152.69/22.48    (11)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.69/22.48          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.69/22.48    (12)   ~ (e2 = e1)
% 152.69/22.48  
% 152.69/22.48  Begin of proof
% 152.69/22.48  | 
% 152.69/22.48  | BETA: splitting (10) gives:
% 152.69/22.48  | 
% 152.69/22.48  | Case 1:
% 152.69/22.48  | | 
% 152.69/22.48  | |   (13)  all_56_0 = e3 & op(e3, e3) = e3
% 152.69/22.48  | | 
% 152.69/22.48  | | ALPHA: (13) implies:
% 152.69/22.48  | |   (14)  op(e3, e3) = e3
% 152.69/22.48  | | 
% 152.69/22.48  | | REF_CLOSE: (1), (5), (7), (14) are inconsistent by sub-proof #1178.
% 152.69/22.48  | | 
% 152.69/22.48  | Case 2:
% 152.69/22.48  | | 
% 152.69/22.48  | |   (15)  all_56_2 = e3 & op(e2, e3) = e3
% 152.69/22.48  | | 
% 152.69/22.48  | | ALPHA: (15) implies:
% 152.69/22.48  | |   (16)  all_56_2 = e3
% 152.69/22.48  | | 
% 152.69/22.48  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (16) are
% 152.69/22.48  | |            inconsistent by sub-proof #363.
% 152.69/22.48  | | 
% 152.69/22.48  | End of split
% 152.69/22.48  | 
% 152.69/22.48  End of proof
% 152.69/22.48  
% 152.69/22.48  Sub-proof #279 shows that the following formulas are inconsistent:
% 152.69/22.48  ----------------------------------------------------------------
% 152.69/22.48    (1)  all_56_14 = e0 & op(e0, e1) = e0
% 152.69/22.48    (2)  all_56_14 = e1
% 152.69/22.48    (3)   ~ (e1 = e0)
% 152.69/22.48  
% 152.69/22.48  Begin of proof
% 152.69/22.48  | 
% 152.69/22.48  | ALPHA: (1) implies:
% 152.69/22.48  |   (4)  all_56_14 = e0
% 152.69/22.48  | 
% 152.69/22.48  | COMBINE_EQS: (2), (4) imply:
% 152.69/22.48  |   (5)  e1 = e0
% 152.69/22.48  | 
% 152.69/22.48  | REDUCE: (3), (5) imply:
% 152.69/22.48  |   (6)  $false
% 152.69/22.48  | 
% 152.69/22.48  | CLOSE: (6) is inconsistent.
% 152.69/22.48  | 
% 152.69/22.48  End of proof
% 152.69/22.48  
% 152.69/22.48  Sub-proof #280 shows that the following formulas are inconsistent:
% 152.69/22.48  ----------------------------------------------------------------
% 152.69/22.48    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.69/22.48           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.69/22.48    (2)  op(e1, e1) = e3
% 152.69/22.48    (3)   ~ (e3 = e2)
% 152.69/22.48    (4)  op(e1, e0) = e1
% 152.69/22.48    (5)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.69/22.48    (6)   ~ (e2 = e1)
% 152.69/22.48  
% 152.69/22.48  Begin of proof
% 152.69/22.48  | 
% 152.69/22.48  | BETA: splitting (5) gives:
% 152.69/22.48  | 
% 152.69/22.48  | Case 1:
% 152.69/22.48  | | 
% 152.69/22.48  | |   (7)  all_56_8 = e2 & op(e1, e1) = e2
% 152.69/22.48  | | 
% 152.69/22.48  | | ALPHA: (7) implies:
% 152.69/22.48  | |   (8)  op(e1, e1) = e2
% 152.69/22.48  | | 
% 152.69/22.48  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #834.
% 152.69/22.48  | | 
% 152.69/22.48  | Case 2:
% 152.69/22.48  | | 
% 152.69/22.48  | |   (9)  all_56_11 = e2 & op(e1, e0) = e2
% 152.69/22.48  | | 
% 152.69/22.48  | | ALPHA: (9) implies:
% 152.69/22.48  | |   (10)  op(e1, e0) = e2
% 152.69/22.48  | | 
% 152.69/22.48  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #1125.
% 152.69/22.48  | | 
% 152.69/22.48  | End of split
% 152.69/22.48  | 
% 152.69/22.48  End of proof
% 152.69/22.48  
% 152.69/22.48  Sub-proof #281 shows that the following formulas are inconsistent:
% 152.69/22.48  ----------------------------------------------------------------
% 152.69/22.48    (1)  all_56_8 = e3
% 152.69/22.48    (2)   ~ (e3 = e1)
% 152.69/22.48    (3)  all_56_6 = e2
% 152.69/22.48    (4)  all_56_11 = e2
% 152.69/22.48    (5)   ~ (e2 = e0)
% 152.69/22.48    (6)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.69/22.48         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.69/22.48    (7)   ~ (e3 = e0)
% 152.69/22.48    (8)   ~ (e1 = e0)
% 152.69/22.48    (9)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.69/22.48         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.69/22.48    (10)   ~ (e2 = e1)
% 152.69/22.48  
% 152.69/22.48  Begin of proof
% 152.69/22.48  | 
% 152.69/22.48  | BETA: splitting (6) gives:
% 152.69/22.48  | 
% 152.69/22.48  | Case 1:
% 152.69/22.48  | | 
% 152.69/22.48  | |   (11)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 152.69/22.48  | |           e1)
% 152.69/22.48  | | 
% 152.69/22.48  | | BETA: splitting (11) gives:
% 152.69/22.48  | | 
% 152.69/22.48  | | Case 1:
% 152.69/22.48  | | | 
% 152.69/22.48  | | |   (12)  all_56_6 = e1 & op(e1, e3) = e1
% 152.69/22.48  | | | 
% 152.69/22.48  | | | REF_CLOSE: (3), (10), (12) are inconsistent by sub-proof #1058.
% 152.69/22.48  | | | 
% 152.69/22.48  | | Case 2:
% 152.69/22.48  | | | 
% 152.69/22.48  | | |   (13)  all_56_7 = e1 & op(e1, e2) = e1
% 152.69/22.48  | | | 
% 152.69/22.48  | | | ALPHA: (13) implies:
% 152.69/22.48  | | |   (14)  all_56_7 = e1
% 152.69/22.48  | | | 
% 152.69/22.48  | | | BETA: splitting (9) gives:
% 152.69/22.48  | | | 
% 152.69/22.48  | | | Case 1:
% 152.69/22.48  | | | | 
% 152.69/22.48  | | | |   (15)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2)
% 152.69/22.48  | | | |           = e0)
% 152.69/22.48  | | | | 
% 152.69/22.48  | | | | BETA: splitting (15) gives:
% 152.69/22.48  | | | | 
% 152.69/22.48  | | | | Case 1:
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | |   (16)  all_56_6 = e0 & op(e1, e3) = e0
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | | REF_CLOSE: (3), (5), (16) are inconsistent by sub-proof #1054.
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | Case 2:
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | |   (17)  all_56_7 = e0 & op(e1, e2) = e0
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | | REF_CLOSE: (8), (14), (17) are inconsistent by sub-proof #880.
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | End of split
% 152.69/22.48  | | | | 
% 152.69/22.48  | | | Case 2:
% 152.69/22.48  | | | | 
% 152.69/22.48  | | | |   (18)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.69/22.48  | | | |           = e0)
% 152.69/22.48  | | | | 
% 152.69/22.48  | | | | BETA: splitting (18) gives:
% 152.69/22.48  | | | | 
% 152.69/22.48  | | | | Case 1:
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | |   (19)  all_56_8 = e0 & op(e1, e1) = e0
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | | REF_CLOSE: (1), (7), (19) are inconsistent by sub-proof #1150.
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | Case 2:
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | |   (20)  all_56_11 = e0 & op(e1, e0) = e0
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | | REF_CLOSE: (4), (5), (20) are inconsistent by sub-proof #1149.
% 152.69/22.48  | | | | | 
% 152.69/22.48  | | | | End of split
% 152.69/22.48  | | | | 
% 152.69/22.48  | | | End of split
% 152.69/22.48  | | | 
% 152.69/22.48  | | End of split
% 152.69/22.48  | | 
% 152.69/22.48  | Case 2:
% 152.69/22.48  | | 
% 152.69/22.48  | |   (21)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 152.69/22.48  | |           e1)
% 152.69/22.48  | | 
% 152.69/22.48  | | REF_CLOSE: (1), (2), (4), (10), (21) are inconsistent by sub-proof #644.
% 152.69/22.48  | | 
% 152.69/22.48  | End of split
% 152.69/22.48  | 
% 152.69/22.48  End of proof
% 152.69/22.48  
% 152.69/22.48  Sub-proof #282 shows that the following formulas are inconsistent:
% 152.69/22.48  ----------------------------------------------------------------
% 152.69/22.48    (1)  op(e0, e1) = all_52_11
% 152.69/22.48    (2)  all_56_8 = e3
% 152.69/22.48    (3)   ~ (all_52_7 = all_52_11)
% 152.69/22.48    (4)   ~ (e3 = e1)
% 152.69/22.48    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 152.69/22.48         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 152.69/22.48    (6)  op(e0, e0) = all_10_2
% 152.69/22.48    (7)  op(e3, e2) = all_52_4
% 152.69/22.48    (8)  op(e0, e2) = all_52_7
% 152.69/22.48    (9)   ~ (all_52_3 = all_52_7)
% 152.69/22.48    (10)   ~ (all_52_4 = e2)
% 152.69/22.48    (11)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.69/22.48          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.69/22.48    (12)   ~ (all_10_2 = e1)
% 152.69/22.48    (13)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.69/22.48          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.69/22.48    (14)   ~ (e2 = e0)
% 152.69/22.48    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.69/22.48            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.69/22.48    (16)  op(e0, e0) = e3
% 152.69/22.48    (17)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.69/22.48          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.69/22.48    (18)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.69/22.48          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.69/22.48    (19)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.69/22.48          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.69/22.48    (20)   ~ (all_52_3 = all_52_11)
% 152.69/22.48    (21)   ~ (all_52_11 = e3)
% 152.69/22.48    (22)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.69/22.48              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.69/22.48                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.69/22.48                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.69/22.48    (23)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.69/22.48          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.69/22.48    (24)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 152.69/22.48              e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.69/22.48            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 152.69/22.48             ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.69/22.48              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.69/22.48            (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.69/22.48            all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 152.69/22.48            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 152.69/22.48            = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.69/22.48          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 152.69/22.48              e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.69/22.48            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 152.69/22.48             ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 152.69/22.48              e1) = e0 & $i(all_57_7))
% 152.69/22.48    (25)  op(e0, e1) = e0
% 152.69/22.48    (26)   ~ (e3 = e0)
% 152.69/22.48    (27)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 152.69/22.48          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 152.69/22.48    (28)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 152.69/22.48          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.69/22.48    (29)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.69/22.48          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.69/22.48    (30)   ~ (all_52_6 = e3)
% 152.69/22.48    (31)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 152.69/22.48          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 152.69/22.48    (32)  op(e3, e3) = e1
% 152.69/22.48    (33)  op(e1, e2) = all_52_6
% 152.69/22.48    (34)   ~ (all_52_9 = e2)
% 152.69/22.48    (35)  op(e0, e3) = all_52_3
% 152.69/22.48    (36)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.69/22.48          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.69/22.48    (37)  op(e2, e2) = e2
% 152.69/22.48    (38)  op(e2, e1) = all_52_9
% 152.69/22.48    (39)   ~ (e1 = e0)
% 152.69/22.48    (40)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.69/22.48          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.69/22.48    (41)   ~ (all_52_4 = e1)
% 152.69/22.48    (42)  op(e1, e1) = e3
% 152.69/22.48    (43)   ~ (e3 = e2)
% 152.69/22.48    (44)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.69/22.48          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.69/22.48    (45)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.69/22.48          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.69/22.48    (46)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.69/22.48          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.69/22.48    (47)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.69/22.48          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.69/22.48    (48)   ~ (e2 = e1)
% 152.69/22.48    (49)  all_56_2 = e3
% 152.69/22.48    (50)  all_56_1 = e3
% 152.69/22.48    (51)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.69/22.48          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.69/22.48    (52)  op(e1, e3) = all_52_2
% 152.69/22.48    (53)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.69/22.48          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.69/22.48    (54)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.69/22.48          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.69/22.48            e1)
% 152.69/22.48    (55)  op(e2, e3) = all_52_1
% 152.69/22.48    (56)   ~ (all_52_1 = e2)
% 152.69/22.48    (57)   ~ (all_52_6 = e2)
% 152.69/22.49  
% 152.69/22.49  Begin of proof
% 152.69/22.49  | 
% 152.69/22.49  | BETA: splitting (17) gives:
% 152.69/22.49  | 
% 152.69/22.49  | Case 1:
% 152.69/22.49  | | 
% 152.69/22.49  | |   (58)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 152.69/22.49  | |           e3)
% 152.69/22.49  | | 
% 152.69/22.49  | | BETA: splitting (58) gives:
% 152.69/22.49  | | 
% 152.69/22.49  | | Case 1:
% 152.69/22.49  | | | 
% 152.69/22.49  | | |   (59)  all_56_0 = e3 & op(e3, e3) = e3
% 152.69/22.49  | | | 
% 152.69/22.49  | | | ALPHA: (59) implies:
% 152.69/22.49  | | |   (60)  op(e3, e3) = e3
% 152.69/22.49  | | | 
% 152.69/22.49  | | | REF_CLOSE: (4), (15), (32), (60) are inconsistent by sub-proof #1178.
% 152.69/22.49  | | | 
% 152.69/22.49  | | Case 2:
% 152.69/22.49  | | | 
% 152.69/22.49  | | |   (61)  all_56_1 = e3 & op(e3, e2) = e3
% 152.69/22.49  | | | 
% 152.69/22.49  | | | ALPHA: (61) implies:
% 152.69/22.49  | | |   (62)  op(e3, e2) = e3
% 152.69/22.49  | | | 
% 152.69/22.49  | | | GROUND_INST: instantiating (15) with all_52_11, e0, e1, e0, simplifying
% 152.69/22.49  | | |              with (1), (25) gives:
% 152.69/22.49  | | |   (63)  all_52_11 = e0
% 152.69/22.49  | | | 
% 152.69/22.49  | | | GROUND_INST: instantiating (15) with all_52_4, e3, e2, e3, simplifying
% 152.69/22.49  | | |              with (7), (62) gives:
% 152.69/22.49  | | |   (64)  all_52_4 = e3
% 152.69/22.49  | | | 
% 152.69/22.49  | | | REDUCE: (20), (63) imply:
% 152.69/22.49  | | |   (65)   ~ (all_52_3 = e0)
% 152.69/22.49  | | | 
% 152.69/22.49  | | | REDUCE: (3), (63) imply:
% 152.69/22.49  | | |   (66)   ~ (all_52_7 = e0)
% 152.69/22.49  | | | 
% 152.69/22.49  | | | REDUCE: (21), (63) imply:
% 152.69/22.49  | | |   (67)   ~ (e3 = e0)
% 152.69/22.49  | | | 
% 152.69/22.49  | | | BETA: splitting (46) gives:
% 152.69/22.49  | | | 
% 152.69/22.49  | | | Case 1:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | |   (68)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1)
% 152.69/22.49  | | | |           = e1)
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | BETA: splitting (68) gives:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | Case 1:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | |   (69)  all_56_4 = e1 & op(e3, e1) = e1
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | ALPHA: (69) implies:
% 152.69/22.49  | | | | |   (70)  all_56_4 = e1
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | BETA: splitting (27) gives:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | Case 1:
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | |   (71)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2,
% 152.69/22.49  | | | | | |             e3) = e0)
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | | REF_CLOSE: (15), (26), (32), (39), (49), (71) are inconsistent by
% 152.69/22.49  | | | | | |            sub-proof #931.
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | Case 2:
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | |   (72)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0,
% 152.69/22.49  | | | | | |             e3) = e0)
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | | BETA: splitting (72) gives:
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | | Case 1:
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | |   (73)  all_56_6 = e0 & op(e1, e3) = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | ALPHA: (73) implies:
% 152.69/22.49  | | | | | | |   (74)  all_56_6 = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | BETA: splitting (31) gives:
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | |   (75)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 &
% 152.69/22.49  | | | | | | | |           op(e2, e3) = e2)
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | | REF_CLOSE: (15), (32), (48), (55), (56), (75) are inconsistent
% 152.69/22.49  | | | | | | | |            by sub-proof #938.
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | |   (76)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 &
% 152.69/22.49  | | | | | | | |           op(e0, e3) = e2)
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | | BETA: splitting (76) gives:
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | |   (77)  all_56_6 = e2 & op(e1, e3) = e2
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | REF_CLOSE: (14), (74), (77) are inconsistent by sub-proof
% 152.69/22.49  | | | | | | | | |            #1129.
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | |   (78)  all_56_12 = e2 & op(e0, e3) = e2
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | ALPHA: (78) implies:
% 152.69/22.49  | | | | | | | | |   (79)  all_56_12 = e2
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | BETA: splitting (19) gives:
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | |   (80)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 &
% 152.69/22.49  | | | | | | | | | |           op(e2, e1) = e2)
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | BETA: splitting (80) gives:
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | |   (81)  all_56_4 = e2 & op(e3, e1) = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | ALPHA: (81) implies:
% 152.69/22.49  | | | | | | | | | | |   (82)  all_56_4 = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | COMBINE_EQS: (70), (82) imply:
% 152.69/22.49  | | | | | | | | | | |   (83)  e2 = e1
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | COMBINE_EQS: (79), (83) imply:
% 152.69/22.49  | | | | | | | | | | |   (84)  all_56_12 = e1
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | REF_CLOSE: (14), (15), (26), (27), (31), (32), (39), (48),
% 152.69/22.49  | | | | | | | | | | |            (49), (55), (56), (84) are inconsistent by
% 152.69/22.49  | | | | | | | | | | |            sub-proof #754.
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | |   (85)  all_56_5 = e2 & op(e2, e1) = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | ALPHA: (85) implies:
% 152.69/22.49  | | | | | | | | | | |   (86)  op(e2, e1) = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | REF_CLOSE: (15), (34), (38), (86) are inconsistent by
% 152.69/22.49  | | | | | | | | | | |            sub-proof #1157.
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | |   (87)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2
% 152.69/22.49  | | | | | | | | | |           & op(e0, e1) = e2)
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | REF_CLOSE: (8), (14), (15), (24), (35), (37), (42), (43),
% 152.69/22.49  | | | | | | | | | |            (48), (65), (66), (87) are inconsistent by
% 152.69/22.49  | | | | | | | | | |            sub-proof #285.
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | End of split
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | Case 2:
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | |   (88)  all_56_12 = e0 & op(e0, e3) = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | ALPHA: (88) implies:
% 152.69/22.49  | | | | | | |   (89)  op(e0, e3) = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | REF_CLOSE: (15), (35), (65), (89) are inconsistent by sub-proof
% 152.69/22.49  | | | | | | |            #1142.
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | End of split
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | End of split
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | Case 2:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | |   (90)  all_56_5 = e1 & op(e2, e1) = e1
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | ALPHA: (90) implies:
% 152.69/22.49  | | | | |   (91)  all_56_5 = e1
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | BETA: splitting (27) gives:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | Case 1:
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | |   (92)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2,
% 152.69/22.49  | | | | | |             e3) = e0)
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | | REF_CLOSE: (15), (26), (32), (39), (49), (92) are inconsistent by
% 152.69/22.49  | | | | | |            sub-proof #931.
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | Case 2:
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | |   (93)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0,
% 152.69/22.49  | | | | | |             e3) = e0)
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | | BETA: splitting (93) gives:
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | | Case 1:
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | |   (94)  all_56_6 = e0 & op(e1, e3) = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | ALPHA: (94) implies:
% 152.69/22.49  | | | | | | |   (95)  all_56_6 = e0
% 152.69/22.49  | | | | | | |   (96)  op(e1, e3) = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | BETA: splitting (31) gives:
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | |   (97)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 &
% 152.69/22.49  | | | | | | | |           op(e2, e3) = e2)
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | | REF_CLOSE: (15), (32), (48), (55), (56), (97) are inconsistent
% 152.69/22.49  | | | | | | | |            by sub-proof #938.
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | |   (98)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 &
% 152.69/22.49  | | | | | | | |           op(e0, e3) = e2)
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | | BETA: splitting (98) gives:
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | |   (99)  all_56_6 = e2 & op(e1, e3) = e2
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | REF_CLOSE: (14), (95), (99) are inconsistent by sub-proof
% 152.69/22.49  | | | | | | | | |            #1129.
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | |   (100)  all_56_12 = e2 & op(e0, e3) = e2
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | ALPHA: (100) implies:
% 152.69/22.49  | | | | | | | | |   (101)  all_56_12 = e2
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | BETA: splitting (40) gives:
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | |   (102)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 152.69/22.49  | | | | | | | | | |            & op(e1, e2) = e2)
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | REF_CLOSE: (14), (15), (33), (57), (95), (102) are
% 152.69/22.49  | | | | | | | | | |            inconsistent by sub-proof #284.
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | |   (103)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2
% 152.69/22.49  | | | | | | | | | |            & op(e1, e0) = e2)
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | BETA: splitting (103) gives:
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | |   (104)  all_56_8 = e2 & op(e1, e1) = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | ALPHA: (104) implies:
% 152.69/22.49  | | | | | | | | | | |   (105)  op(e1, e1) = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | REF_CLOSE: (15), (42), (43), (105) are inconsistent by
% 152.69/22.49  | | | | | | | | | | |            sub-proof #834.
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | |   (106)  all_56_11 = e2 & op(e1, e0) = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | ALPHA: (106) implies:
% 152.69/22.49  | | | | | | | | | | |   (107)  all_56_11 = e2
% 152.69/22.49  | | | | | | | | | | |   (108)  op(e1, e0) = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | BETA: splitting (19) gives:
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | |   (109)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 152.69/22.49  | | | | | | | | | | | |            & op(e2, e1) = e2)
% 152.69/22.49  | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | BETA: splitting (109) gives:
% 152.69/22.49  | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | |   (110)  all_56_4 = e2 & op(e3, e1) = e2
% 152.69/22.49  | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | ALPHA: (110) implies:
% 152.69/22.49  | | | | | | | | | | | | |   (111)  all_56_4 = e2
% 152.69/22.49  | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | BETA: splitting (54) gives:
% 152.69/22.49  | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | |   (112)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 =
% 152.69/22.49  | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 152.69/22.49  | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | BETA: splitting (112) gives:
% 152.69/22.49  | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | |   (113)  all_56_12 = e1 & op(e0, e3) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | ALPHA: (113) implies:
% 152.69/22.49  | | | | | | | | | | | | | | |   (114)  all_56_12 = e1
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (26), (27), (31), (32), (39), (48),
% 152.69/22.49  | | | | | | | | | | | | | | |            (49), (55), (56), (114) are inconsistent by
% 152.69/22.49  | | | | | | | | | | | | | | |            sub-proof #754.
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | |   (115)  all_56_13 = e1 & op(e0, e2) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | ALPHA: (115) implies:
% 152.69/22.49  | | | | | | | | | | | | | | |   (116)  all_56_13 = e1
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | BETA: splitting (18) gives:
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | |   (117)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1
% 152.69/22.49  | | | | | | | | | | | | | | | |            & op(e1, e2) = e1)
% 152.69/22.49  | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | BETA: splitting (117) gives:
% 152.69/22.49  | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | |   (118)  all_56_6 = e1 & op(e1, e3) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 152.69/22.49  | | | | | | | | | | | | | | | | |   (119)  op(e1, e3) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (39), (52), (96), (119) are inconsistent by
% 152.69/22.49  | | | | | | | | | | | | | | | | |            sub-proof #1127.
% 152.69/22.49  | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | |   (120)  all_56_7 = e1 & op(e1, e2) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 152.69/22.49  | | | | | | | | | | | | | | | | |   (121)  all_56_7 = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 152.69/22.49  | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | |   (122)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 152.69/22.49  | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 152.69/22.49  | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |   (123)  all_56_9 = e1 & op(e3, e0) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | ALPHA: (123) implies:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |   (124)  all_56_9 = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | BETA: splitting (29) gives:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | |   (125)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |   (126)  all_56_0 = e0 & op(e3, e3) = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |   (127)  op(e3, e3) = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (32), (39), (127) are inconsistent by
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |            sub-proof #957.
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |   (128)  all_56_1 = e0 & op(e3, e2) = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |   (129)  all_56_1 = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (4), (14), (15), (18), (26), (37), (39),
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |            (43), (47), (48), (53), (107), (116), (129) are
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #351.
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | |   (130)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |   (131)  all_56_4 = e0 & op(e3, e1) = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (111), (131) are inconsistent by sub-proof
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |            #1070.
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |   (132)  all_56_9 = e0 & op(e3, e0) = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | ALPHA: (132) implies:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |   (133)  all_56_9 = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (124), (133) imply:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |   (134)  e1 = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | SIMP: (134) implies:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |   (135)  e1 = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (121), (135) imply:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |   (136)  all_56_7 = e0
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (18), (39), (42), (48), (52), (96),
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | |            (108), (136) are inconsistent by sub-proof #349.
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |   (137)  all_56_10 = e1 & op(e2, e0) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |   (138)  all_56_10 = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11), (14), (15), (26), (36), (37), (39),
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |            (43), (91), (138) are inconsistent by sub-proof
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |            #681.
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | |   (139)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 152.69/22.49  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 152.69/22.49  | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |   (140)  all_56_11 = e1 & op(e1, e0) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | ALPHA: (140) implies:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |   (141)  op(e1, e0) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (15), (48), (108), (141) are inconsistent by
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |            sub-proof #1125.
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |   (142)  all_56_15 = e1 & op(e0, e0) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |   (143)  op(e0, e0) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (15), (143) are inconsistent by
% 152.69/22.49  | | | | | | | | | | | | | | | | | | |            sub-proof #1116.
% 152.69/22.49  | | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | |   (144)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 =
% 152.69/22.49  | | | | | | | | | | | | | | | |            e1 & op(e1, e0) = e1)
% 152.69/22.49  | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | | REF_CLOSE: (4), (15), (42), (48), (108), (144) are
% 152.69/22.49  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #350.
% 152.69/22.49  | | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | |   (145)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 =
% 152.69/22.49  | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 152.69/22.49  | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 152.69/22.49  | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | |   (146)  all_56_14 = e1 & op(e0, e1) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 152.69/22.49  | | | | | | | | | | | | | | |   (147)  all_56_14 = e1
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (14), (15), (16), (18), (22), (26),
% 152.69/22.49  | | | | | | | | | | | | | | |            (35), (39), (42), (48), (52), (66), (96), (101),
% 152.69/22.49  | | | | | | | | | | | | | | |            (108), (147) are inconsistent by sub-proof #283.
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | |   (148)  all_56_15 = e1 & op(e0, e0) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | ALPHA: (148) implies:
% 152.69/22.49  | | | | | | | | | | | | | | |   (149)  op(e0, e0) = e1
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | | REF_CLOSE: (6), (12), (15), (149) are inconsistent by
% 152.69/22.49  | | | | | | | | | | | | | | |            sub-proof #1116.
% 152.69/22.49  | | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | |   (150)  all_56_5 = e2 & op(e2, e1) = e2
% 152.69/22.49  | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | ALPHA: (150) implies:
% 152.69/22.49  | | | | | | | | | | | | |   (151)  op(e2, e1) = e2
% 152.69/22.49  | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | | REF_CLOSE: (15), (34), (38), (151) are inconsistent by
% 152.69/22.49  | | | | | | | | | | | | |            sub-proof #1157.
% 152.69/22.49  | | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | |   (152)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 152.69/22.49  | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 152.69/22.49  | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | | REF_CLOSE: (8), (14), (15), (24), (35), (37), (42), (43),
% 152.69/22.49  | | | | | | | | | | | |            (48), (65), (66), (152) are inconsistent by
% 152.69/22.49  | | | | | | | | | | | |            sub-proof #285.
% 152.69/22.49  | | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | End of split
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | Case 2:
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | |   (153)  all_56_12 = e0 & op(e0, e3) = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | ALPHA: (153) implies:
% 152.69/22.49  | | | | | | |   (154)  op(e0, e3) = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | REF_CLOSE: (15), (35), (65), (154) are inconsistent by sub-proof
% 152.69/22.49  | | | | | | |            #1142.
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | End of split
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | End of split
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | End of split
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | Case 2:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | |   (155)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0,
% 152.69/22.49  | | | |              e1) = e1)
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | BETA: splitting (155) gives:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | Case 1:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | |   (156)  all_56_8 = e1 & op(e1, e1) = e1
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | ALPHA: (156) implies:
% 152.69/22.49  | | | | |   (157)  op(e1, e1) = e1
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | REF_CLOSE: (4), (15), (42), (157) are inconsistent by sub-proof #734.
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | Case 2:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | |   (158)  all_56_14 = e1 & op(e0, e1) = e1
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | ALPHA: (158) implies:
% 152.69/22.49  | | | | |   (159)  all_56_14 = e1
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | BETA: splitting (27) gives:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | Case 1:
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | |   (160)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2,
% 152.69/22.49  | | | | | |              e3) = e0)
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | | REF_CLOSE: (15), (26), (32), (39), (49), (160) are inconsistent by
% 152.69/22.49  | | | | | |            sub-proof #931.
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | Case 2:
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | |   (161)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 &
% 152.69/22.49  | | | | | |            op(e0, e3) = e0)
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | | BETA: splitting (161) gives:
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | | Case 1:
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | |   (162)  all_56_6 = e0 & op(e1, e3) = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | ALPHA: (162) implies:
% 152.69/22.49  | | | | | | |   (163)  all_56_6 = e0
% 152.69/22.49  | | | | | | |   (164)  op(e1, e3) = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | BETA: splitting (31) gives:
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | |   (165)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 &
% 152.69/22.49  | | | | | | | |            op(e2, e3) = e2)
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | | REF_CLOSE: (15), (32), (48), (55), (56), (165) are inconsistent
% 152.69/22.49  | | | | | | | |            by sub-proof #938.
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | |   (166)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 &
% 152.69/22.49  | | | | | | | |            op(e0, e3) = e2)
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | | BETA: splitting (166) gives:
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | |   (167)  all_56_6 = e2 & op(e1, e3) = e2
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | REF_CLOSE: (14), (163), (167) are inconsistent by sub-proof
% 152.69/22.49  | | | | | | | | |            #1129.
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | |   (168)  all_56_12 = e2 & op(e0, e3) = e2
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | ALPHA: (168) implies:
% 152.69/22.49  | | | | | | | | |   (169)  all_56_12 = e2
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | BETA: splitting (40) gives:
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | |   (170)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 152.69/22.49  | | | | | | | | | |            & op(e1, e2) = e2)
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | REF_CLOSE: (14), (15), (33), (57), (163), (170) are
% 152.69/22.49  | | | | | | | | | |            inconsistent by sub-proof #284.
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | |   (171)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2
% 152.69/22.49  | | | | | | | | | |            & op(e1, e0) = e2)
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | BETA: splitting (171) gives:
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | Case 1:
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | |   (172)  all_56_8 = e2 & op(e1, e1) = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | ALPHA: (172) implies:
% 152.69/22.49  | | | | | | | | | | |   (173)  op(e1, e1) = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | REF_CLOSE: (15), (42), (43), (173) are inconsistent by
% 152.69/22.49  | | | | | | | | | | |            sub-proof #834.
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | Case 2:
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | |   (174)  all_56_11 = e2 & op(e1, e0) = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | ALPHA: (174) implies:
% 152.69/22.49  | | | | | | | | | | |   (175)  op(e1, e0) = e2
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | | REF_CLOSE: (4), (8), (9), (14), (15), (16), (18), (22), (26),
% 152.69/22.49  | | | | | | | | | | |            (35), (39), (42), (48), (52), (66), (159), (164),
% 152.69/22.49  | | | | | | | | | | |            (169), (175) are inconsistent by sub-proof #283.
% 152.69/22.49  | | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | | 
% 152.69/22.49  | | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | | 
% 152.69/22.49  | | | | | | | | End of split
% 152.69/22.49  | | | | | | | | 
% 152.69/22.49  | | | | | | | End of split
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | Case 2:
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | |   (176)  all_56_12 = e0 & op(e0, e3) = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | ALPHA: (176) implies:
% 152.69/22.49  | | | | | | |   (177)  op(e0, e3) = e0
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | | REF_CLOSE: (15), (35), (65), (177) are inconsistent by sub-proof
% 152.69/22.49  | | | | | | |            #1142.
% 152.69/22.49  | | | | | | | 
% 152.69/22.49  | | | | | | End of split
% 152.69/22.49  | | | | | | 
% 152.69/22.49  | | | | | End of split
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | End of split
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | End of split
% 152.69/22.49  | | | 
% 152.69/22.49  | | End of split
% 152.69/22.49  | | 
% 152.69/22.49  | Case 2:
% 152.69/22.49  | | 
% 152.69/22.49  | |   (178)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 152.69/22.49  | |            e3)
% 152.69/22.49  | | 
% 152.69/22.49  | | BETA: splitting (178) gives:
% 152.69/22.49  | | 
% 152.69/22.49  | | Case 1:
% 152.69/22.49  | | | 
% 152.69/22.49  | | |   (179)  all_56_4 = e3 & op(e3, e1) = e3
% 152.69/22.49  | | | 
% 152.69/22.49  | | | ALPHA: (179) implies:
% 152.69/22.49  | | |   (180)  all_56_4 = e3
% 152.69/22.49  | | | 
% 152.69/22.49  | | | BETA: splitting (19) gives:
% 152.69/22.49  | | | 
% 152.69/22.49  | | | Case 1:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | |   (181)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1)
% 152.69/22.49  | | | |            = e2)
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | BETA: splitting (181) gives:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | Case 1:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | |   (182)  all_56_4 = e2 & op(e3, e1) = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | ALPHA: (182) implies:
% 152.69/22.49  | | | | |   (183)  all_56_4 = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | REF_CLOSE: (43), (180), (183) are inconsistent by sub-proof #1068.
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | Case 2:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | |   (184)  all_56_5 = e2 & op(e2, e1) = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | ALPHA: (184) implies:
% 152.69/22.49  | | | | |   (185)  op(e2, e1) = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | REF_CLOSE: (15), (34), (38), (185) are inconsistent by sub-proof
% 152.69/22.49  | | | | |            #1157.
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | End of split
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | Case 2:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | |   (186)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0,
% 152.69/22.49  | | | |              e1) = e2)
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | BETA: splitting (186) gives:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | Case 1:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | |   (187)  all_56_8 = e2 & op(e1, e1) = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | ALPHA: (187) implies:
% 152.69/22.49  | | | | |   (188)  op(e1, e1) = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | REF_CLOSE: (15), (42), (43), (188) are inconsistent by sub-proof #834.
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | Case 2:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | |   (189)  all_56_14 = e2 & op(e0, e1) = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | ALPHA: (189) implies:
% 152.69/22.49  | | | | |   (190)  all_56_14 = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | REF_CLOSE: (2), (4), (11), (13), (14), (15), (26), (36), (37), (39),
% 152.69/22.49  | | | | |            (43), (44), (46), (48), (49), (180), (190) are inconsistent
% 152.69/22.49  | | | | |            by sub-proof #312.
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | End of split
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | End of split
% 152.69/22.49  | | | 
% 152.69/22.49  | | Case 2:
% 152.69/22.49  | | | 
% 152.69/22.49  | | |   (191)  all_56_9 = e3 & op(e3, e0) = e3
% 152.69/22.49  | | | 
% 152.69/22.49  | | | ALPHA: (191) implies:
% 152.69/22.49  | | |   (192)  all_56_9 = e3
% 152.69/22.49  | | | 
% 152.69/22.49  | | | BETA: splitting (5) gives:
% 152.69/22.49  | | | 
% 152.69/22.49  | | | Case 1:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | |   (193)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2)
% 152.69/22.49  | | | |            = e2)
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | BETA: splitting (193) gives:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | Case 1:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | |   (194)  all_56_0 = e2 & op(e3, e3) = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | ALPHA: (194) implies:
% 152.69/22.49  | | | | |   (195)  op(e3, e3) = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | REF_CLOSE: (4), (14), (15), (23), (26), (29), (39), (48), (50), (192),
% 152.69/22.49  | | | | |            (195) are inconsistent by sub-proof #345.
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | Case 2:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | |   (196)  all_56_1 = e2 & op(e3, e2) = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | ALPHA: (196) implies:
% 152.69/22.49  | | | | |   (197)  all_56_1 = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | REF_CLOSE: (4), (14), (15), (26), (30), (33), (37), (39), (43), (45),
% 152.69/22.49  | | | | |            (48), (51), (53), (197) are inconsistent by sub-proof #921.
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | End of split
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | Case 2:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | |   (198)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0)
% 152.69/22.49  | | | |            = e2)
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | BETA: splitting (198) gives:
% 152.69/22.49  | | | | 
% 152.69/22.49  | | | | Case 1:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | |   (199)  all_56_4 = e2 & op(e3, e1) = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | ALPHA: (199) implies:
% 152.69/22.49  | | | | |   (200)  all_56_4 = e2
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | BETA: splitting (29) gives:
% 152.69/22.49  | | | | | 
% 152.69/22.49  | | | | | Case 1:
% 152.69/22.49  | | | | | | 
% 152.69/22.50  | | | | | |   (201)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3,
% 152.69/22.50  | | | | | |              e2) = e0)
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | | BETA: splitting (201) gives:
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | | Case 1:
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | |   (202)  all_56_0 = e0 & op(e3, e3) = e0
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | | ALPHA: (202) implies:
% 152.69/22.50  | | | | | | |   (203)  op(e3, e3) = e0
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | | REF_CLOSE: (15), (32), (39), (203) are inconsistent by sub-proof
% 152.69/22.50  | | | | | | |            #957.
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | Case 2:
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | |   (204)  all_56_1 = e0 & op(e3, e2) = e0
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | | REF_CLOSE: (26), (50), (204) are inconsistent by sub-proof #1114.
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | End of split
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | Case 2:
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | |   (205)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3,
% 152.69/22.50  | | | | | |              e0) = e0)
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | | BETA: splitting (205) gives:
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | | Case 1:
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | |   (206)  all_56_4 = e0 & op(e3, e1) = e0
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | | REF_CLOSE: (14), (200), (206) are inconsistent by sub-proof #1070.
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | Case 2:
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | |   (207)  all_56_9 = e0 & op(e3, e0) = e0
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | | REF_CLOSE: (26), (192), (207) are inconsistent by sub-proof #446.
% 152.69/22.50  | | | | | | | 
% 152.69/22.50  | | | | | | End of split
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | End of split
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | Case 2:
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | |   (208)  all_56_9 = e2 & op(e3, e0) = e2
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | | ALPHA: (208) implies:
% 152.69/22.50  | | | | |   (209)  all_56_9 = e2
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | | COMBINE_EQS: (192), (209) imply:
% 152.69/22.50  | | | | |   (210)  e3 = e2
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | | COMBINE_EQS: (50), (210) imply:
% 152.69/22.50  | | | | |   (211)  all_56_1 = e2
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | | REF_CLOSE: (4), (14), (15), (26), (30), (33), (37), (39), (43), (45),
% 152.69/22.50  | | | | |            (48), (51), (53), (211) are inconsistent by sub-proof #921.
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | End of split
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | End of split
% 152.69/22.50  | | | 
% 152.69/22.50  | | End of split
% 152.69/22.50  | | 
% 152.69/22.50  | End of split
% 152.69/22.50  | 
% 152.69/22.50  End of proof
% 152.69/22.50  
% 152.69/22.50  Sub-proof #283 shows that the following formulas are inconsistent:
% 152.69/22.50  ----------------------------------------------------------------
% 152.69/22.50    (1)   ~ (e3 = e1)
% 152.69/22.50    (2)  op(e0, e2) = all_52_7
% 152.69/22.50    (3)   ~ (all_52_3 = all_52_7)
% 152.69/22.50    (4)   ~ (e2 = e0)
% 152.69/22.50    (5)  all_56_14 = e1
% 152.69/22.50    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.69/22.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.69/22.50    (7)  op(e0, e0) = e3
% 152.69/22.50    (8)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.69/22.50         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.69/22.50    (9)  op(e1, e3) = e0
% 152.69/22.50    (10)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.69/22.50              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.69/22.50                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.69/22.50                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.69/22.50    (11)   ~ (e3 = e0)
% 152.69/22.50    (12)  op(e0, e3) = all_52_3
% 152.69/22.50    (13)   ~ (all_52_7 = e0)
% 152.69/22.50    (14)   ~ (e1 = e0)
% 152.69/22.50    (15)  op(e1, e1) = e3
% 152.69/22.50    (16)  op(e1, e0) = e2
% 152.69/22.50    (17)  all_56_12 = e2
% 152.69/22.50    (18)   ~ (e2 = e1)
% 152.69/22.50    (19)  op(e1, e3) = all_52_2
% 152.69/22.50  
% 152.69/22.50  Begin of proof
% 152.69/22.50  | 
% 152.69/22.50  | BETA: splitting (8) gives:
% 152.69/22.50  | 
% 152.69/22.50  | Case 1:
% 152.69/22.50  | | 
% 152.69/22.50  | |   (20)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 152.69/22.50  | |           e1)
% 152.69/22.50  | | 
% 152.69/22.50  | | BETA: splitting (20) gives:
% 152.69/22.50  | | 
% 152.69/22.50  | | Case 1:
% 152.69/22.50  | | | 
% 152.69/22.50  | | |   (21)  all_56_6 = e1 & op(e1, e3) = e1
% 152.69/22.50  | | | 
% 152.69/22.50  | | | ALPHA: (21) implies:
% 152.69/22.50  | | |   (22)  op(e1, e3) = e1
% 152.69/22.50  | | | 
% 152.69/22.50  | | | REF_CLOSE: (6), (9), (14), (19), (22) are inconsistent by sub-proof #1127.
% 152.69/22.50  | | | 
% 152.69/22.50  | | Case 2:
% 152.69/22.50  | | | 
% 152.69/22.50  | | |   (23)  all_56_7 = e1 & op(e1, e2) = e1
% 152.69/22.50  | | | 
% 152.69/22.50  | | | ALPHA: (23) implies:
% 152.69/22.50  | | |   (24)  all_56_7 = e1
% 152.69/22.50  | | | 
% 152.69/22.50  | | | BETA: splitting (10) gives:
% 152.69/22.50  | | | 
% 152.69/22.50  | | | Case 1:
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | |   (25)  all_56_15 = e0 & op(e0, e0) = e0
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | | ALPHA: (25) implies:
% 152.69/22.50  | | | |   (26)  op(e0, e0) = e0
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | | REF_CLOSE: (6), (7), (11), (26) are inconsistent by sub-proof #1143.
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | Case 2:
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | |   (27)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 152.69/22.50  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 152.69/22.50  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 152.69/22.50  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | | ALPHA: (27) implies:
% 152.69/22.50  | | | |   (28)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 152.69/22.50  | | | |             e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | | BETA: splitting (28) gives:
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | | Case 1:
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | |   (29)  all_56_12 = e0 & op(e0, e3) = e0
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | | ALPHA: (29) implies:
% 152.69/22.50  | | | | |   (30)  op(e0, e3) = e0
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | | REF_CLOSE: (2), (3), (4), (5), (6), (12), (14), (17), (28), (30) are
% 152.69/22.50  | | | | |            inconsistent by sub-proof #1117.
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | Case 2:
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | |   (31)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 152.69/22.50  | | | | |             e1) = e0)
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | | BETA: splitting (31) gives:
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | | Case 1:
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | |   (32)  all_56_13 = e0 & op(e0, e2) = e0
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | | ALPHA: (32) implies:
% 152.69/22.50  | | | | | |   (33)  op(e0, e2) = e0
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | | REF_CLOSE: (2), (6), (13), (33) are inconsistent by sub-proof #1036.
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | Case 2:
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | |   (34)  all_56_14 = e0 & op(e0, e1) = e0
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | | ALPHA: (34) implies:
% 152.69/22.50  | | | | | |   (35)  all_56_14 = e0
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | | COMBINE_EQS: (5), (35) imply:
% 152.69/22.50  | | | | | |   (36)  e1 = e0
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | | COMBINE_EQS: (24), (36) imply:
% 152.69/22.50  | | | | | |   (37)  all_56_7 = e0
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | | REF_CLOSE: (1), (6), (8), (9), (14), (15), (16), (18), (19), (37)
% 152.69/22.50  | | | | | |            are inconsistent by sub-proof #349.
% 152.69/22.50  | | | | | | 
% 152.69/22.50  | | | | | End of split
% 152.69/22.50  | | | | | 
% 152.69/22.50  | | | | End of split
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | End of split
% 152.69/22.50  | | | 
% 152.69/22.50  | | End of split
% 152.69/22.50  | | 
% 152.69/22.50  | Case 2:
% 152.69/22.50  | | 
% 152.69/22.50  | |   (38)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 152.69/22.50  | |           e1)
% 152.69/22.50  | | 
% 152.69/22.50  | | REF_CLOSE: (1), (6), (15), (16), (18), (38) are inconsistent by sub-proof
% 152.69/22.50  | |            #350.
% 152.69/22.50  | | 
% 152.69/22.50  | End of split
% 152.69/22.50  | 
% 152.69/22.50  End of proof
% 152.69/22.50  
% 152.69/22.50  Sub-proof #284 shows that the following formulas are inconsistent:
% 152.69/22.50  ----------------------------------------------------------------
% 152.69/22.50    (1)   ~ (e2 = e0)
% 152.69/22.50    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.69/22.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.69/22.50    (3)  all_56_6 = e0
% 152.69/22.50    (4)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2)
% 152.69/22.50    (5)  op(e1, e2) = all_52_6
% 152.69/22.50    (6)   ~ (all_52_6 = e2)
% 152.69/22.50  
% 152.69/22.50  Begin of proof
% 152.69/22.50  | 
% 152.69/22.50  | BETA: splitting (4) gives:
% 152.69/22.50  | 
% 152.69/22.50  | Case 1:
% 152.69/22.50  | | 
% 152.69/22.50  | |   (7)  all_56_6 = e2 & op(e1, e3) = e2
% 152.69/22.50  | | 
% 152.69/22.50  | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #1129.
% 152.69/22.50  | | 
% 152.69/22.50  | Case 2:
% 152.69/22.50  | | 
% 152.69/22.50  | |   (8)  all_56_7 = e2 & op(e1, e2) = e2
% 152.69/22.50  | | 
% 152.69/22.50  | | ALPHA: (8) implies:
% 152.69/22.50  | |   (9)  op(e1, e2) = e2
% 152.69/22.50  | | 
% 152.69/22.50  | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #1171.
% 152.69/22.50  | | 
% 152.69/22.50  | End of split
% 152.69/22.50  | 
% 152.69/22.50  End of proof
% 152.69/22.50  
% 152.69/22.50  Sub-proof #285 shows that the following formulas are inconsistent:
% 152.69/22.50  ----------------------------------------------------------------
% 152.69/22.50    (1)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.69/22.50    (2)  op(e0, e2) = all_52_7
% 152.69/22.50    (3)   ~ (e2 = e0)
% 152.69/22.50    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.69/22.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.69/22.50    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 152.69/22.50             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.69/22.50           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.69/22.50           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.69/22.50             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.69/22.50           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.69/22.50           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.69/22.50           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 152.69/22.50           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.69/22.50           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 152.69/22.50           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.69/22.50         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.69/22.50             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.69/22.50           $i(all_57_7))
% 152.69/22.50    (6)  op(e0, e3) = all_52_3
% 152.69/22.50    (7)  op(e2, e2) = e2
% 152.69/22.50    (8)   ~ (all_52_7 = e0)
% 152.69/22.50    (9)  op(e1, e1) = e3
% 152.69/22.50    (10)   ~ (e3 = e2)
% 152.69/22.50    (11)   ~ (all_52_3 = e0)
% 152.69/22.50    (12)   ~ (e2 = e1)
% 152.69/22.50  
% 152.69/22.50  Begin of proof
% 152.69/22.50  | 
% 152.69/22.50  | BETA: splitting (1) gives:
% 152.69/22.50  | 
% 152.69/22.50  | Case 1:
% 152.69/22.50  | | 
% 152.69/22.50  | |   (13)  all_56_8 = e2 & op(e1, e1) = e2
% 152.69/22.50  | | 
% 152.69/22.50  | | ALPHA: (13) implies:
% 152.69/22.50  | |   (14)  op(e1, e1) = e2
% 152.69/22.50  | | 
% 152.69/22.50  | | REF_CLOSE: (4), (9), (10), (14) are inconsistent by sub-proof #834.
% 152.69/22.50  | | 
% 152.69/22.50  | Case 2:
% 152.69/22.50  | | 
% 152.69/22.50  | |   (15)  all_56_14 = e2 & op(e0, e1) = e2
% 152.69/22.50  | | 
% 152.69/22.50  | | ALPHA: (15) implies:
% 152.69/22.50  | |   (16)  op(e0, e1) = e2
% 152.69/22.50  | | 
% 152.69/22.50  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (16)
% 152.69/22.50  | |            are inconsistent by sub-proof #348.
% 152.69/22.50  | | 
% 152.69/22.50  | End of split
% 152.69/22.50  | 
% 152.69/22.50  End of proof
% 152.69/22.50  
% 152.69/22.50  Sub-proof #286 shows that the following formulas are inconsistent:
% 152.69/22.50  ----------------------------------------------------------------
% 152.69/22.50    (1)  op(e0, e1) = all_52_11
% 152.69/22.50    (2)   ~ (all_52_11 = all_10_2)
% 152.69/22.50    (3)   ~ (all_10_2 = e1)
% 152.69/22.50    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.69/22.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.69/22.50    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 152.69/22.50             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.69/22.50           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.69/22.50           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.69/22.50             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.69/22.50           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.69/22.50           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.69/22.50           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 152.69/22.50           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.69/22.50           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 152.69/22.50           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.69/22.50         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.69/22.50             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.69/22.50           $i(all_57_7))
% 152.69/22.50    (6)  op(e3, e3) = e1
% 152.69/22.50    (7)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 152.69/22.50    (8)  op(e0, e3) = all_52_3
% 152.69/22.50    (9)  op(e2, e2) = e2
% 152.69/22.50    (10)  op(e1, e1) = e3
% 152.69/22.50    (11)   ~ (e3 = e2)
% 152.69/22.50    (12)   ~ (all_10_2 = e2)
% 152.69/22.50    (13)   ~ (all_52_3 = all_10_2)
% 152.69/22.50    (14)   ~ (e2 = e1)
% 152.69/22.50    (15)  all_54_15 = all_10_2
% 152.69/22.50  
% 152.69/22.50  Begin of proof
% 152.69/22.50  | 
% 152.69/22.50  | BETA: splitting (7) gives:
% 152.69/22.50  | 
% 152.69/22.50  | Case 1:
% 152.69/22.50  | | 
% 152.69/22.50  | |   (16)  all_54_15 = e2
% 152.69/22.50  | | 
% 152.69/22.50  | | COMBINE_EQS: (15), (16) imply:
% 152.69/22.50  | |   (17)  all_10_2 = e2
% 152.69/22.50  | | 
% 152.69/22.50  | | REDUCE: (12), (17) imply:
% 152.69/22.50  | |   (18)  $false
% 152.69/22.50  | | 
% 152.69/22.50  | | CLOSE: (18) is inconsistent.
% 152.69/22.50  | | 
% 152.69/22.50  | Case 2:
% 152.69/22.50  | | 
% 152.69/22.50  | |   (19)  all_54_15 = e1 | all_54_15 = e0
% 152.69/22.50  | | 
% 152.69/22.50  | | BETA: splitting (19) gives:
% 152.69/22.50  | | 
% 152.69/22.50  | | Case 1:
% 152.69/22.50  | | | 
% 152.69/22.50  | | |   (20)  all_54_15 = e1
% 152.69/22.50  | | | 
% 152.69/22.50  | | | COMBINE_EQS: (15), (20) imply:
% 152.69/22.50  | | |   (21)  all_10_2 = e1
% 152.69/22.50  | | | 
% 152.69/22.50  | | | REDUCE: (3), (21) imply:
% 152.69/22.50  | | |   (22)  $false
% 152.69/22.50  | | | 
% 152.69/22.50  | | | CLOSE: (22) is inconsistent.
% 152.69/22.50  | | | 
% 152.69/22.50  | | Case 2:
% 152.69/22.50  | | | 
% 152.69/22.50  | | |   (23)  all_54_15 = e0
% 152.69/22.50  | | | 
% 152.69/22.50  | | | COMBINE_EQS: (15), (23) imply:
% 152.69/22.50  | | |   (24)  all_10_2 = e0
% 152.69/22.50  | | | 
% 152.69/22.50  | | | REDUCE: (13), (24) imply:
% 152.69/22.50  | | |   (25)   ~ (all_52_3 = e0)
% 152.69/22.50  | | | 
% 152.69/22.50  | | | REDUCE: (2), (24) imply:
% 152.69/22.50  | | |   (26)   ~ (all_52_11 = e0)
% 152.69/22.50  | | | 
% 152.69/22.50  | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (11), (14), (25), (26) are
% 152.69/22.50  | | |            inconsistent by sub-proof #287.
% 152.69/22.50  | | | 
% 152.69/22.50  | | End of split
% 152.69/22.50  | | 
% 152.69/22.50  | End of split
% 152.69/22.50  | 
% 152.69/22.50  End of proof
% 152.69/22.50  
% 152.69/22.50  Sub-proof #287 shows that the following formulas are inconsistent:
% 152.69/22.50  ----------------------------------------------------------------
% 152.69/22.50    (1)  op(e0, e1) = all_52_11
% 152.69/22.50    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.69/22.50           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.69/22.50    (3)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 152.69/22.50             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.69/22.50           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.69/22.50           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.69/22.50             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.69/22.50           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.69/22.50           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.69/22.50           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 152.69/22.50           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.69/22.50           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 152.69/22.50           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.69/22.50         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.69/22.50             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.69/22.50           $i(all_57_7))
% 152.69/22.50    (4)   ~ (all_52_11 = e0)
% 152.69/22.50    (5)  op(e3, e3) = e1
% 152.69/22.50    (6)  op(e0, e3) = all_52_3
% 152.69/22.50    (7)  op(e2, e2) = e2
% 152.69/22.50    (8)  op(e1, e1) = e3
% 152.69/22.50    (9)   ~ (e3 = e2)
% 152.69/22.50    (10)   ~ (all_52_3 = e0)
% 152.69/22.50    (11)   ~ (e2 = e1)
% 152.69/22.50  
% 152.69/22.50  Begin of proof
% 152.69/22.50  | 
% 152.69/22.50  | BETA: splitting (3) gives:
% 152.69/22.50  | 
% 152.69/22.50  | Case 1:
% 152.69/22.50  | | 
% 152.69/22.50  | |   (12)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 152.69/22.50  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 152.69/22.50  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.69/22.50  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.69/22.50  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 152.69/22.50  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 152.69/22.50  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.69/22.50  | |           $i(all_57_3))
% 152.69/22.50  | | 
% 152.69/22.50  | | REF_CLOSE: (2), (5), (6), (10), (11), (12) are inconsistent by sub-proof
% 152.69/22.50  | |            #955.
% 152.69/22.50  | | 
% 152.69/22.50  | Case 2:
% 152.69/22.50  | | 
% 152.69/22.50  | |   (13)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.69/22.50  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.69/22.50  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.69/22.50  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.69/22.50  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.69/22.50  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.69/22.50  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.69/22.50  | |           $i(all_57_7))
% 152.69/22.50  | | 
% 152.69/22.50  | | BETA: splitting (13) gives:
% 152.69/22.50  | | 
% 152.69/22.50  | | Case 1:
% 152.69/22.50  | | | 
% 152.69/22.50  | | |   (14)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.69/22.50  | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.69/22.50  | | |         op(e0, e2) = e0 & $i(all_57_4)
% 152.69/22.50  | | | 
% 152.69/22.50  | | | ALPHA: (14) implies:
% 152.69/22.50  | | |   (15)  op(e1, e1) = e2
% 152.69/22.50  | | | 
% 152.69/22.50  | | | REF_CLOSE: (2), (8), (9), (15) are inconsistent by sub-proof #834.
% 152.69/22.50  | | | 
% 152.69/22.50  | | Case 2:
% 152.69/22.50  | | | 
% 152.69/22.50  | | |   (16)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.69/22.50  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.69/22.50  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 152.69/22.50  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 152.69/22.50  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.69/22.50  | | | 
% 152.69/22.50  | | | BETA: splitting (16) gives:
% 152.69/22.50  | | | 
% 152.69/22.50  | | | Case 1:
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | |   (17)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.69/22.50  | | | |         (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.69/22.50  | | | |         op(e0, e1) = e0 & $i(all_57_6)
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | | ALPHA: (17) implies:
% 152.69/22.50  | | | |   (18)  op(e0, e1) = e0
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | | GROUND_INST: instantiating (2) with all_52_11, e0, e1, e0, simplifying
% 152.69/22.50  | | | |              with (1), (18) gives:
% 152.69/22.50  | | | |   (19)  all_52_11 = e0
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | | REDUCE: (4), (19) imply:
% 152.69/22.50  | | | |   (20)  $false
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | | CLOSE: (20) is inconsistent.
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | Case 2:
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | |   (21)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.69/22.50  | | | |         (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.69/22.50  | | | |         op(e0, e1) = e0 & $i(all_57_7)
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | | ALPHA: (21) implies:
% 152.69/22.50  | | | |   (22)  op(e2, e2) = e1
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | | REF_CLOSE: (2), (7), (11), (22) are inconsistent by sub-proof #1158.
% 152.69/22.50  | | | | 
% 152.69/22.50  | | | End of split
% 152.69/22.50  | | | 
% 152.69/22.50  | | End of split
% 152.69/22.50  | | 
% 152.69/22.50  | End of split
% 152.69/22.50  | 
% 152.69/22.50  End of proof
% 152.69/22.50  
% 152.69/22.50  Sub-proof #288 shows that the following formulas are inconsistent:
% 152.69/22.50  ----------------------------------------------------------------
% 152.69/22.50    (1)  op(e0, e1) = all_52_11
% 152.69/22.50    (2)   ~ (all_14_2 = e0)
% 152.69/22.50    (3)   ~ (all_52_2 = all_52_6)
% 152.69/22.50    (4)  op(e3, e3) = all_14_2
% 152.69/22.50    (5)  op(e0, e0) = all_10_2
% 152.69/22.50    (6)  op(e3, e2) = all_52_4
% 152.69/22.50    (7)  op(e0, e2) = all_52_7
% 152.69/22.50    (8)   ~ (all_52_14 = e2)
% 152.69/22.50    (9)   ~ (all_52_3 = all_52_7)
% 152.69/22.50    (10)   ~ (all_52_8 = all_14_2)
% 152.69/22.50    (11)   ~ (all_10_2 = e1)
% 152.69/22.50    (12)   ~ (e2 = e0)
% 152.69/22.50    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.69/22.50            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.69/22.50    (14)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.69/22.50          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.69/22.50    (15)   ~ (all_52_4 = all_14_2)
% 152.69/22.50    (16)  op(e0, e0) = e2
% 152.69/22.50    (17)  op(e1, e0) = all_52_14
% 152.69/22.50    (18)   ~ (all_52_13 = e2)
% 152.69/22.50    (19)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.69/22.50    (20)  op(e1, e2) = all_52_6
% 152.69/22.50    (21)  op(e2, e0) = all_52_13
% 152.69/22.50    (22)   ~ (all_52_9 = e2)
% 152.69/22.50    (23)  op(e0, e3) = all_52_3
% 152.69/22.50    (24)  all_54_0 = all_14_2
% 152.69/22.50    (25)  op(e2, e2) = e2
% 152.69/22.50    (26)  op(e2, e1) = all_52_9
% 152.69/22.50    (27)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 152.69/22.50          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.69/22.50    (28)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 152.69/22.50              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.69/22.50            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 152.69/22.50                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 152.69/22.50              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.69/22.50          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 152.69/22.50              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.69/22.50            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 152.69/22.50                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 152.69/22.50              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.69/22.50          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 152.69/22.50              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.69/22.50            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 152.69/22.50                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 152.69/22.50              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.69/22.50          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 152.69/22.50              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.69/22.50            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 152.69/22.50                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 152.69/22.50                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.69/22.50                $i(all_57_14))))
% 152.69/22.50    (29)  op(e1, e1) = e3
% 152.69/22.50    (30)   ~ (e3 = e2)
% 152.69/22.50    (31)   ~ (all_52_1 = all_52_2)
% 152.69/22.50    (32)   ~ (all_14_2 = e1)
% 152.69/22.50    (33)  op(e3, e1) = all_52_8
% 152.69/22.50    (34)   ~ (e2 = e1)
% 152.69/22.50    (35)   ~ (all_52_8 = all_52_9)
% 152.69/22.50    (36)  op(e1, e3) = all_52_2
% 152.69/22.50    (37)   ~ (all_52_11 = e2)
% 152.69/22.51    (38)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.69/22.51              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.69/22.51            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.69/22.51            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.69/22.51            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.69/22.51            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.69/22.51            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.69/22.51            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.69/22.51            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.69/22.51            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.69/22.51            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.69/22.51            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.69/22.51            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.69/22.51            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.69/22.51            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.69/22.51            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.69/22.51            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.69/22.51            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.69/22.51            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.69/22.51            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.69/22.51            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.69/22.51            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.69/22.51            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.69/22.51            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.69/22.51            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.69/22.51            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.69/22.51            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.69/22.51            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.69/22.51            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.69/22.51            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.69/22.51            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.69/22.51            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.69/22.51            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.69/22.51            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.69/22.51            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.69/22.51            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.69/22.51            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.69/22.51            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.69/22.51            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.69/22.51            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.69/22.51            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.69/22.51            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.69/22.51            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.69/22.51            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.69/22.51            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.69/22.51            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.69/22.51            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.69/22.51            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.69/22.51              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.69/22.51            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.69/22.51            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.69/22.51              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.69/22.51            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.69/22.51            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.69/22.51                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.69/22.51                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.69/22.51                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.69/22.51                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.69/22.51                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.69/22.51                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.69/22.51                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.69/22.51              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.69/22.51                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.69/22.51                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.69/22.51                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.69/22.51                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.69/22.51                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.69/22.51                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.69/22.51                $i(all_57_7))))
% 152.69/22.51    (39)  op(e2, e3) = all_52_1
% 152.69/22.51    (40)   ~ (all_52_6 = e2)
% 152.69/22.51  
% 152.69/22.51  Begin of proof
% 152.69/22.51  | 
% 152.69/22.51  | BETA: splitting (27) gives:
% 152.69/22.51  | 
% 152.69/22.51  | Case 1:
% 152.69/22.51  | | 
% 152.69/22.51  | |   (41)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 152.69/22.51  | |           e2)
% 152.69/22.51  | | 
% 152.69/22.51  | | BETA: splitting (41) gives:
% 152.69/22.51  | | 
% 152.69/22.51  | | Case 1:
% 152.69/22.51  | | | 
% 152.69/22.51  | | |   (42)  all_56_6 = e2 & op(e1, e3) = e2
% 152.69/22.51  | | | 
% 152.69/22.51  | | | ALPHA: (42) implies:
% 152.69/22.51  | | |   (43)  op(e1, e3) = e2
% 152.69/22.51  | | | 
% 152.69/22.51  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 152.69/22.51  | | |            (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 152.69/22.51  | | |            (25), (26), (28), (29), (30), (31), (32), (33), (34), (35),
% 152.69/22.51  | | |            (36), (37), (38), (39), (43) are inconsistent by sub-proof
% 152.69/22.51  | | |            #290.
% 152.69/22.51  | | | 
% 152.69/22.51  | | Case 2:
% 152.69/22.51  | | | 
% 152.69/22.51  | | |   (44)  all_56_7 = e2 & op(e1, e2) = e2
% 152.69/22.51  | | | 
% 152.69/22.51  | | | ALPHA: (44) implies:
% 152.69/22.51  | | |   (45)  op(e1, e2) = e2
% 152.69/22.51  | | | 
% 152.69/22.51  | | | REF_CLOSE: (13), (20), (40), (45) are inconsistent by sub-proof #1171.
% 152.69/22.51  | | | 
% 152.69/22.51  | | End of split
% 152.69/22.51  | | 
% 152.69/22.51  | Case 2:
% 152.69/22.51  | | 
% 152.69/22.51  | |   (46)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 152.69/22.51  | |           e2)
% 152.69/22.51  | | 
% 152.69/22.51  | | REF_CLOSE: (8), (13), (17), (29), (30), (46) are inconsistent by sub-proof
% 152.69/22.51  | |            #289.
% 152.69/22.51  | | 
% 152.69/22.51  | End of split
% 152.69/22.51  | 
% 152.69/22.51  End of proof
% 152.69/22.51  
% 152.69/22.51  Sub-proof #289 shows that the following formulas are inconsistent:
% 152.69/22.51  ----------------------------------------------------------------
% 152.69/22.51    (1)   ~ (all_52_14 = e2)
% 152.69/22.51    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.69/22.51           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.69/22.51    (3)  op(e1, e0) = all_52_14
% 152.69/22.51    (4)  op(e1, e1) = e3
% 152.69/22.51    (5)   ~ (e3 = e2)
% 152.69/22.51    (6)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 152.69/22.51  
% 152.69/22.51  Begin of proof
% 152.69/22.51  | 
% 152.69/22.51  | BETA: splitting (6) gives:
% 152.69/22.51  | 
% 152.69/22.51  | Case 1:
% 152.69/22.51  | | 
% 152.69/22.51  | |   (7)  all_56_8 = e2 & op(e1, e1) = e2
% 152.69/22.51  | | 
% 152.69/22.51  | | ALPHA: (7) implies:
% 152.69/22.51  | |   (8)  op(e1, e1) = e2
% 152.69/22.51  | | 
% 152.69/22.51  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #834.
% 152.69/22.51  | | 
% 152.69/22.51  | Case 2:
% 152.69/22.51  | | 
% 152.69/22.51  | |   (9)  all_56_11 = e2 & op(e1, e0) = e2
% 152.69/22.51  | | 
% 152.69/22.51  | | ALPHA: (9) implies:
% 152.69/22.51  | |   (10)  op(e1, e0) = e2
% 152.69/22.51  | | 
% 152.69/22.51  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #974.
% 152.69/22.51  | | 
% 152.69/22.51  | End of split
% 152.69/22.51  | 
% 152.69/22.51  End of proof
% 152.69/22.51  
% 152.69/22.51  Sub-proof #290 shows that the following formulas are inconsistent:
% 152.69/22.51  ----------------------------------------------------------------
% 152.69/22.51    (1)  op(e0, e1) = all_52_11
% 152.69/22.51    (2)  op(e1, e3) = e2
% 152.69/22.51    (3)   ~ (all_14_2 = e0)
% 152.69/22.51    (4)   ~ (all_52_2 = all_52_6)
% 152.69/22.51    (5)  op(e3, e3) = all_14_2
% 152.69/22.51    (6)  op(e0, e0) = all_10_2
% 152.69/22.51    (7)  op(e3, e2) = all_52_4
% 152.69/22.51    (8)  op(e0, e2) = all_52_7
% 152.69/22.51    (9)   ~ (all_52_3 = all_52_7)
% 152.69/22.51    (10)   ~ (all_52_8 = all_14_2)
% 152.69/22.51    (11)   ~ (all_10_2 = e1)
% 152.69/22.51    (12)   ~ (e2 = e0)
% 152.69/22.51    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.69/22.51            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.69/22.51    (14)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 152.69/22.51          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 152.69/22.51    (15)   ~ (all_52_4 = all_14_2)
% 152.69/22.51    (16)  op(e0, e0) = e2
% 152.69/22.51    (17)   ~ (all_52_13 = e2)
% 152.69/22.51    (18)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.69/22.51    (19)  op(e1, e2) = all_52_6
% 152.69/22.51    (20)  op(e2, e0) = all_52_13
% 152.69/22.51    (21)   ~ (all_52_9 = e2)
% 152.69/22.51    (22)  op(e0, e3) = all_52_3
% 152.69/22.51    (23)  all_54_0 = all_14_2
% 152.69/22.51    (24)  op(e2, e2) = e2
% 152.69/22.51    (25)  op(e2, e1) = all_52_9
% 152.69/22.51    (26)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 152.69/22.51              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 152.69/22.51            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 152.69/22.51                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 152.69/22.51              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.69/22.51          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 152.69/22.51              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.69/22.51            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 152.69/22.51                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 152.69/22.51              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.69/22.51          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 152.69/22.51              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.69/22.51            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 152.69/22.51                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 152.69/22.51              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.69/22.51          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 152.69/22.51              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.69/22.51            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 152.69/22.51                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 152.69/22.51                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.69/22.51                $i(all_57_14))))
% 152.69/22.51    (27)  op(e1, e1) = e3
% 152.69/22.51    (28)   ~ (e3 = e2)
% 152.69/22.51    (29)   ~ (all_52_1 = all_52_2)
% 152.69/22.51    (30)   ~ (all_14_2 = e1)
% 152.69/22.51    (31)  op(e3, e1) = all_52_8
% 152.69/22.51    (32)   ~ (e2 = e1)
% 152.69/22.51    (33)   ~ (all_52_8 = all_52_9)
% 152.69/22.51    (34)  op(e1, e3) = all_52_2
% 152.69/22.51    (35)   ~ (all_52_11 = e2)
% 152.69/22.51    (36)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.69/22.51              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.69/22.51            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.69/22.51            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.69/22.51            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.69/22.51            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.69/22.51            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.69/22.51            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.69/22.51            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.69/22.51            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.69/22.51            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.69/22.51            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.69/22.51            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.69/22.51            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.69/22.51            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.69/22.51            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.69/22.51            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.69/22.51            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.69/22.51            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.69/22.51            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.69/22.51            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.69/22.51            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.69/22.51            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.69/22.51            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.69/22.51            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.69/22.51            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.69/22.51            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.69/22.51            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.69/22.51            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.69/22.51            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.69/22.51            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.69/22.51            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.69/22.51            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.69/22.51            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.69/22.51            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.69/22.51            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.69/22.51            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.69/22.51            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.69/22.51            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.69/22.51            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.69/22.51            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.69/22.51            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.69/22.51            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.69/22.51            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.69/22.51            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.69/22.51            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.69/22.51            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.69/22.51            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.69/22.51              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.69/22.51            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.69/22.51            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.69/22.51              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.69/22.51            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.69/22.51            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.69/22.51                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.69/22.51                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.69/22.51                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.69/22.51                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.69/22.51                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.69/22.51                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.69/22.51                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.69/22.51              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.69/22.51                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.69/22.51                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.69/22.51                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.69/22.51                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.69/22.51                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.69/22.51                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.69/22.51                $i(all_57_7))))
% 152.69/22.51    (37)  op(e2, e3) = all_52_1
% 152.69/22.51  
% 152.69/22.51  Begin of proof
% 152.69/22.51  | 
% 152.69/22.51  | BETA: splitting (14) gives:
% 152.69/22.51  | 
% 152.69/22.51  | Case 1:
% 152.69/22.51  | | 
% 152.69/22.51  | |   (38)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) =
% 152.69/22.51  | |           e2)
% 152.69/22.51  | | 
% 152.69/22.51  | | BETA: splitting (38) gives:
% 152.69/22.51  | | 
% 152.69/22.51  | | Case 1:
% 152.69/22.51  | | | 
% 152.69/22.51  | | |   (39)  all_56_4 = e2 & op(e3, e1) = e2
% 152.69/22.51  | | | 
% 152.69/22.51  | | | ALPHA: (39) implies:
% 152.69/22.51  | | |   (40)  op(e3, e1) = e2
% 152.69/22.51  | | | 
% 152.69/22.51  | | | GROUND_INST: instantiating (13) with all_52_2, e2, e3, e1, simplifying
% 152.69/22.51  | | |              with (2), (34) gives:
% 152.69/22.51  | | |   (41)  all_52_2 = e2
% 152.69/22.51  | | | 
% 152.69/22.51  | | | GROUND_INST: instantiating (13) with all_52_8, e2, e1, e3, simplifying
% 152.69/22.51  | | |              with (31), (40) gives:
% 152.69/22.51  | | |   (42)  all_52_8 = e2
% 152.69/22.51  | | | 
% 152.69/22.51  | | | REDUCE: (29), (41) imply:
% 152.69/22.51  | | |   (43)   ~ (all_52_1 = e2)
% 152.69/22.51  | | | 
% 152.69/22.51  | | | REDUCE: (33), (42) imply:
% 152.69/22.51  | | |   (44)   ~ (all_52_9 = e2)
% 152.69/22.51  | | | 
% 152.69/22.51  | | | REDUCE: (10), (42) imply:
% 152.69/22.51  | | |   (45)   ~ (all_14_2 = e2)
% 152.69/22.51  | | | 
% 152.69/22.51  | | | SIMP: (45) implies:
% 152.69/22.51  | | |   (46)   ~ (all_14_2 = e2)
% 152.69/22.51  | | | 
% 152.69/22.51  | | | BETA: splitting (18) gives:
% 152.69/22.51  | | | 
% 152.69/22.51  | | | Case 1:
% 152.69/22.51  | | | | 
% 152.69/22.51  | | | |   (47)  all_54_0 = e3
% 152.69/22.51  | | | | 
% 152.69/22.51  | | | | COMBINE_EQS: (23), (47) imply:
% 152.69/22.51  | | | |   (48)  all_14_2 = e3
% 152.69/22.51  | | | | 
% 152.69/22.51  | | | | REDUCE: (15), (48) imply:
% 152.69/22.51  | | | |   (49)   ~ (all_52_4 = e3)
% 152.69/22.51  | | | | 
% 152.69/22.51  | | | | REDUCE: (30), (48) imply:
% 152.69/22.51  | | | |   (50)   ~ (e3 = e1)
% 152.69/22.51  | | | | 
% 152.69/22.51  | | | | REDUCE: (3), (48) imply:
% 152.69/22.51  | | | |   (51)   ~ (e3 = e0)
% 152.69/22.51  | | | | 
% 152.69/22.51  | | | | REDUCE: (5), (48) imply:
% 152.69/22.51  | | | |   (52)  op(e3, e3) = e3
% 152.69/22.51  | | | | 
% 152.69/22.51  | | | | BETA: splitting (26) gives:
% 152.69/22.51  | | | | 
% 152.69/22.51  | | | | Case 1:
% 152.69/22.51  | | | | | 
% 152.69/22.51  | | | | |   (53)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2,
% 152.69/22.51  | | | | |                 e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 152.69/22.51  | | | | |               all_57_12 & $i(all_57_12))) & ((all_57_1 = e1 & op(e1,
% 152.69/22.51  | | | | |                 e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 152.69/22.51  | | | | |               all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 152.69/22.51  | | | | |                 e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 152.69/22.51  | | | | |               all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 & op(e2,
% 152.69/22.51  | | | | |             e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 152.69/22.51  | | | | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.69/22.51  | | | | |               $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | (
% 152.69/22.51  | | | | |               ~ (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 152.69/22.51  | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0) | (
% 152.69/22.51  | | | | |               ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 152.69/22.51  | | | | |               $i(all_57_15))))
% 152.69/22.51  | | | | | 
% 152.69/22.51  | | | | | BETA: splitting (53) gives:
% 152.69/22.51  | | | | | 
% 152.69/22.51  | | | | | Case 1:
% 152.69/22.51  | | | | | | 
% 152.69/22.51  | | | | | |   (54)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2,
% 152.69/22.51  | | | | | |               e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 152.69/22.51  | | | | | |             all_57_12 & $i(all_57_12))) & ((all_57_1 = e1 & op(e1,
% 152.69/22.51  | | | | | |               e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 152.69/22.51  | | | | | |             all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 152.69/22.51  | | | | | |               e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 152.69/22.51  | | | | | |             all_57_15 & $i(all_57_15)))
% 152.69/22.51  | | | | | | 
% 152.69/22.51  | | | | | | ALPHA: (54) implies:
% 152.69/22.51  | | | | | |   (55)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) &
% 152.69/22.51  | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_14))
% 152.69/22.51  | | | | | | 
% 152.69/22.51  | | | | | | BETA: splitting (55) gives:
% 152.69/22.51  | | | | | | 
% 152.69/22.51  | | | | | | Case 1:
% 152.69/22.51  | | | | | | | 
% 152.69/22.51  | | | | | | |   (56)  all_57_1 = e1 & op(e1, e3) = e1
% 152.69/22.51  | | | | | | | 
% 152.69/22.51  | | | | | | | ALPHA: (56) implies:
% 152.69/22.51  | | | | | | |   (57)  all_57_1 = e1
% 152.69/22.51  | | | | | | |   (58)  op(e1, e3) = e1
% 152.69/22.51  | | | | | | | 
% 152.69/22.51  | | | | | | | BETA: splitting (36) gives:
% 152.69/22.51  | | | | | | | 
% 152.69/22.51  | | | | | | | Case 1:
% 152.69/22.51  | | | | | | | | 
% 152.69/22.51  | | | | | | | |   (59)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.69/22.51  | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.69/22.51  | | | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.69/22.51  | | | | | | | |           $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 &
% 152.69/22.51  | | | | | | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 152.69/22.51  | | | | | | | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.69/22.51  | | | | | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2)
% 152.69/22.51  | | | | | | | |           & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3 & 
% 152.69/22.51  | | | | | | | |           ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.69/22.51  | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 152.69/22.51  | | | | | | | |             e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.69/22.51  | | | | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) & 
% 152.69/22.51  | | | | | | | |           ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 152.69/22.51  | | | | | | | |           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.69/22.51  | | | | | | | |           $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 152.69/22.51  | | | | | | | |           all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 152.69/22.51  | | | | | | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.69/22.51  | | | | | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4)
% 152.69/22.51  | | | | | | | |           & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 & 
% 152.69/22.51  | | | | | | | |           ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.69/22.51  | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 152.69/22.51  | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 152.69/22.51  | | | | | | | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 152.69/22.51  | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.69/22.51  | | | | | | | |           all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.69/22.51  | | | | | | | |           $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 152.69/22.51  | | | | | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 152.69/22.51  | | | | | | | |             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.69/22.51  | | | | | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5)
% 152.69/22.51  | | | | | | | |           & $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 & 
% 152.69/22.51  | | | | | | | |           ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.69/22.51  | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2,
% 152.69/22.51  | | | | | | | |             e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.69/22.51  | | | | | | | | 
% 152.69/22.51  | | | | | | | | BETA: splitting (59) gives:
% 152.69/22.51  | | | | | | | | 
% 152.69/22.51  | | | | | | | | Case 1:
% 152.69/22.51  | | | | | | | | | 
% 152.69/22.51  | | | | | | | | |   (60)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 152.69/22.51  | | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.69/22.51  | | | | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3
% 152.69/22.51  | | | | | | | | |           & $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 &
% 152.69/22.51  | | | | | | | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 152.69/22.51  | | | | | | | | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.69/22.51  | | | | | | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.69/22.51  | | | | | | | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.69/22.51  | | | | | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 152.69/22.51  | | | | | | | | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.69/22.51  | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.69/22.51  | | | | | | | | |           $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 152.69/22.51  | | | | | | | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 152.69/22.51  | | | | | | | | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.69/22.51  | | | | | | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.69/22.51  | | | | | | | | |           $i(all_57_2) & $i(all_57_14))
% 152.69/22.51  | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | BETA: splitting (60) gives:
% 152.69/22.51  | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | Case 1:
% 152.69/22.51  | | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | |   (61)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 152.69/22.51  | | | | | | | | | |           &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.69/22.51  | | | | | | | | | |             e2) = all_57_12 & op(e1, e3) = all_57_1 & op(e1,
% 152.69/22.51  | | | | | | | | | |             e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 152.69/22.51  | | | | | | | | | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0)
% 152.69/22.51  | | | | | | | | | |           &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.69/22.51  | | | | | | | | | |             e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0,
% 152.69/22.51  | | | | | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.69/22.51  | | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | | REF_CLOSE: (13), (37), (43), (61) are inconsistent by
% 152.69/22.51  | | | | | | | | | |            sub-proof #1180.
% 152.69/22.51  | | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | Case 2:
% 152.69/22.51  | | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | |   (62)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2)
% 152.69/22.51  | | | | | | | | | |           &  ~ (all_57_14 = e3) & op(e2, e3) = all_57_0 &
% 152.69/22.51  | | | | | | | | | |           op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.69/22.51  | | | | | | | | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.69/22.51  | | | | | | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0)
% 152.69/22.51  | | | | | | | | | |           &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.69/22.51  | | | | | | | | | |             e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 152.69/22.51  | | | | | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 152.69/22.51  | | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | | REF_CLOSE: (13), (27), (62) are inconsistent by sub-proof
% 152.69/22.51  | | | | | | | | | |            #368.
% 152.69/22.51  | | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | End of split
% 152.69/22.51  | | | | | | | | | 
% 152.69/22.51  | | | | | | | | Case 2:
% 152.69/22.51  | | | | | | | | | 
% 152.69/22.51  | | | | | | | | |   (63)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &
% 152.69/22.51  | | | | | | | | |            ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.69/22.51  | | | | | | | | |           op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1)
% 152.69/22.51  | | | | | | | | |           = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3 =
% 152.69/22.51  | | | | | | | | |           e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 152.69/22.51  | | | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 152.69/22.51  | | | | | | | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2
% 152.69/22.51  | | | | | | | | |           & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 152.69/22.51  | | | | | | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 152.69/22.51  | | | | | | | | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.69/22.51  | | | | | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.69/22.51  | | | | | | | | |           $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 152.69/22.51  | | | | | | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 152.69/22.51  | | | | | | | | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.69/22.51  | | | | | | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.69/22.51  | | | | | | | | |           $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 152.69/22.51  | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 152.69/22.51  | | | | | | | | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.69/22.51  | | | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.69/22.51  | | | | | | | | |           $i(all_57_7) & $i(all_57_10))
% 152.69/22.51  | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | BETA: splitting (63) gives:
% 152.69/22.51  | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | Case 1:
% 152.69/22.51  | | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | |   (64)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1)
% 152.69/22.51  | | | | | | | | | |           &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.69/22.51  | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 152.69/22.51  | | | | | | | | | |             e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 152.69/22.51  | | | | | | | | | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.69/22.51  | | | | | | | | | |           &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.69/22.51  | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 152.69/22.51  | | | | | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 152.69/22.51  | | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | | REF_CLOSE: (7), (13), (27), (28), (49), (64) are inconsistent
% 152.69/22.51  | | | | | | | | | |            by sub-proof #294.
% 152.69/22.51  | | | | | | | | | | 
% 152.69/22.51  | | | | | | | | | Case 2:
% 152.69/22.51  | | | | | | | | | | 
% 152.69/22.52  | | | | | | | | | |   (65)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3)
% 152.69/22.52  | | | | | | | | | |           &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3,
% 152.69/22.52  | | | | | | | | | |             e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.69/22.52  | | | | | | | | | |           all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.69/22.52  | | | | | | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.69/22.52  | | | | | | | | | |           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.69/22.52  | | | | | | | | | |             e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 152.69/22.52  | | | | | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 152.69/22.52  | | | | | | | | | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.69/22.52  | | | | | | | | | |           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.69/22.52  | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 152.69/22.52  | | | | | | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.69/22.52  | | | | | | | | | | 
% 152.69/22.52  | | | | | | | | | | BETA: splitting (65) gives:
% 152.69/22.52  | | | | | | | | | | 
% 152.69/22.52  | | | | | | | | | | Case 1:
% 152.69/22.52  | | | | | | | | | | | 
% 152.69/22.52  | | | | | | | | | | |   (66)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.69/22.52  | | | | | | | | | | |           e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 152.69/22.52  | | | | | | | | | | |         op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 152.69/22.52  | | | | | | | | | | |           e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 152.69/22.52  | | | | | | | | | | | 
% 152.69/22.52  | | | | | | | | | | | ALPHA: (66) implies:
% 152.69/22.52  | | | | | | | | | | |   (67)  op(e3, e3) = e2
% 152.69/22.52  | | | | | | | | | | | 
% 152.69/22.52  | | | | | | | | | | | REF_CLOSE: (13), (28), (52), (67) are inconsistent by
% 152.69/22.52  | | | | | | | | | | |            sub-proof #1085.
% 152.69/22.52  | | | | | | | | | | | 
% 152.69/22.52  | | | | | | | | | | Case 2:
% 152.69/22.52  | | | | | | | | | | | 
% 152.69/22.52  | | | | | | | | | | |   (68)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.69/22.52  | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.69/22.52  | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 152.69/22.52  | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 152.69/22.52  | | | | | | | | | | |         | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.69/22.52  | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.69/22.52  | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.69/22.52  | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.69/22.52  | | | | | | | | | | |           $i(all_57_10))
% 152.77/22.52  | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | BETA: splitting (68) gives:
% 152.77/22.52  | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | |   (69)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.77/22.52  | | | | | | | | | | | |           e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.77/22.52  | | | | | | | | | | | |         op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 152.77/22.52  | | | | | | | | | | | |         op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | ALPHA: (69) implies:
% 152.77/22.52  | | | | | | | | | | | |   (70)  op(e1, e2) = e1
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | REF_CLOSE: (4), (13), (19), (34), (58), (70) are inconsistent
% 152.77/22.52  | | | | | | | | | | | |            by sub-proof #911.
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | Case 2:
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | |   (71)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.77/22.52  | | | | | | | | | | | |           e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.77/22.52  | | | | | | | | | | | |         all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.77/22.52  | | | | | | | | | | | |         op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.77/22.52  | | | | | | | | | | | |         $i(all_57_10)
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | ALPHA: (71) implies:
% 152.77/22.52  | | | | | | | | | | | |   (72)  op(e2, e2) = e1
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | REF_CLOSE: (13), (24), (32), (72) are inconsistent by
% 152.77/22.52  | | | | | | | | | | | |            sub-proof #1158.
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | 
% 152.77/22.52  | | | | | | | Case 2:
% 152.77/22.52  | | | | | | | | 
% 152.77/22.52  | | | | | | | |   (73)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) & 
% 152.77/22.52  | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 152.77/22.52  | | | | | | | |             e1) = e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 152.77/22.52  | | | | | | | |           $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 &
% 152.77/22.52  | | | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 152.77/22.52  | | | | | | | |             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.77/22.52  | | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.77/22.52  | | | | | | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.77/22.52  | | | | | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 152.77/22.52  | | | | | | | |             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.77/22.52  | | | | | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8)
% 152.77/22.52  | | | | | | | |           & $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 & 
% 152.77/22.52  | | | | | | | |           ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3)
% 152.77/22.52  | | | | | | | |           = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.77/22.52  | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.77/22.52  | | | | | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 152.77/22.52  | | | | | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 152.77/22.52  | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1,
% 152.77/22.52  | | | | | | | |             e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)) |
% 152.77/22.52  | | | | | | | |         (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) & 
% 152.77/22.52  | | | | | | | |           ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 152.77/22.52  | | | | | | | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.77/22.52  | | | | | | | |           $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 &
% 152.77/22.52  | | | | | | | |           all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 152.77/22.52  | | | | | | | |             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.77/22.52  | | | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.77/22.52  | | | | | | | |           $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 152.77/22.52  | | | | | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 =
% 152.77/22.52  | | | | | | | |             e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.77/22.52  | | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.77/22.52  | | | | | | | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 152.77/22.52  | | | | | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 =
% 152.77/22.52  | | | | | | | |             e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.77/22.52  | | | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.77/22.52  | | | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.77/22.52  | | | | | | | |           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.77/22.52  | | | | | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.77/22.52  | | | | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 152.77/22.52  | | | | | | | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 152.77/22.52  | | | | | | | |             (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 152.77/22.52  | | | | | | | |               &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.77/22.52  | | | | | | | |               op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 152.77/22.52  | | | | | | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.77/22.52  | | | | | | | |                 e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 152.77/22.52  | | | | | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.77/22.52  | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 & 
% 152.77/22.52  | | | | | | | |               ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1,
% 152.77/22.52  | | | | | | | |                 e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.77/22.52  | | | | | | | |               e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 =
% 152.77/22.52  | | | | | | | |               e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.77/22.52  | | | | | | | |               op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.77/22.52  | | | | | | | |                 e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.77/22.52  | | | | | | | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.77/22.52  | | | | | | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.77/22.52  | | | | | | | |               all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.77/22.52  | | | | | | | | 
% 152.77/22.52  | | | | | | | | BETA: splitting (73) gives:
% 152.77/22.52  | | | | | | | | 
% 152.77/22.52  | | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | |   (74)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &
% 152.77/22.52  | | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.77/22.52  | | | | | | | | |           op(e3, e1) = e3 & op(e0, e1) = all_57_8 & op(e0, e0)
% 152.77/22.52  | | | | | | | | |           = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7 =
% 152.77/22.52  | | | | | | | | |           e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.77/22.52  | | | | | | | | |           (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.77/22.52  | | | | | | | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 152.77/22.52  | | | | | | | | |           & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.77/22.52  | | | | | | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 152.77/22.52  | | | | | | | | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.77/22.52  | | | | | | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 152.77/22.52  | | | | | | | | |           $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 152.77/22.52  | | | | | | | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 152.77/22.52  | | | | | | | | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.77/22.52  | | | | | | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.77/22.52  | | | | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 152.77/22.52  | | | | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 152.77/22.52  | | | | | | | | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.77/22.52  | | | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.77/22.52  | | | | | | | | |           $i(all_57_10) & $i(all_57_13))
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | BETA: splitting (74) gives:
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | |   (75)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.77/22.52  | | | | | | | | | |           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.77/22.52  | | | | | | | | | |           op(e3, e1) = e3 & op(e0, e1) = all_57_8 & op(e0,
% 152.77/22.52  | | | | | | | | | |             e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 152.77/22.52  | | | | | | | | | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.77/22.52  | | | | | | | | | |           &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3,
% 152.77/22.52  | | | | | | | | | |             e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2,
% 152.77/22.52  | | | | | | | | | |             e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | REF_CLOSE: (6), (11), (13), (21), (25), (75) are inconsistent
% 152.77/22.52  | | | | | | | | | |            by sub-proof #544.
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | Case 2:
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | |   (76)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.77/22.52  | | | | | | | | | |           &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.77/22.52  | | | | | | | | | |           op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 152.77/22.52  | | | | | | | | | |             e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.77/22.52  | | | | | | | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 152.77/22.52  | | | | | | | | | |             e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 152.77/22.52  | | | | | | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.77/22.52  | | | | | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.77/22.52  | | | | | | | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &
% 152.77/22.52  | | | | | | | | | |            ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3,
% 152.77/22.52  | | | | | | | | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 152.77/22.52  | | | | | | | | | |           e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.77/22.52  | | | | | | | | | |           $i(all_57_13))
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (24), (27), (51), (76) are
% 152.77/22.52  | | | | | | | | | |            inconsistent by sub-proof #293.
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | Case 2:
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | |   (77)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.77/22.52  | | | | | | | | |           &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 152.77/22.52  | | | | | | | | |           = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.77/22.52  | | | | | | | | |           e2 & $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0
% 152.77/22.52  | | | | | | | | |           & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 152.77/22.52  | | | | | | | | |           (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 152.77/22.52  | | | | | | | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.77/22.52  | | | | | | | | |           & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 152.77/22.52  | | | | | | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13
% 152.77/22.52  | | | | | | | | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.77/22.52  | | | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.77/22.52  | | | | | | | | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 152.77/22.52  | | | | | | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14
% 152.77/22.52  | | | | | | | | |             = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.77/22.52  | | | | | | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.77/22.52  | | | | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.77/22.52  | | | | | | | | |           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.77/22.52  | | | | | | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.77/22.52  | | | | | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 152.77/22.52  | | | | | | | | |               op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.77/22.52  | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 152.77/22.52  | | | | | | | | |               &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 152.77/22.52  | | | | | | | | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.77/22.52  | | | | | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 152.77/22.52  | | | | | | | | |               all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.77/22.52  | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.77/22.52  | | | | | | | | |               = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.77/22.52  | | | | | | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.77/22.52  | | | | | | | | |                 e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.77/22.52  | | | | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.77/22.52  | | | | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 152.77/22.52  | | | | | | | | |               &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.77/22.52  | | | | | | | | |               op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.77/22.52  | | | | | | | | |                 e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.77/22.52  | | | | | | | | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.77/22.52  | | | | | | | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 152.77/22.52  | | | | | | | | |               = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | BETA: splitting (77) gives:
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | |   (78)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 152.77/22.52  | | | | | | | | | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 152.77/22.52  | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 152.77/22.52  | | | | | | | | | |           op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 152.77/22.52  | | | | | | | | | |         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 152.77/22.52  | | | | | | | | | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.77/22.52  | | | | | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 152.77/22.52  | | | | | | | | | |           op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | REF_CLOSE: (13), (51), (52), (78) are inconsistent by
% 152.77/22.52  | | | | | | | | | |            sub-proof #975.
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | Case 2:
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | |   (79)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.77/22.52  | | | | | | | | | |             e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.77/22.52  | | | | | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.77/22.52  | | | | | | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.77/22.52  | | | | | | | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 152.77/22.52  | | | | | | | | | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.77/22.52  | | | | | | | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1,
% 152.77/22.52  | | | | | | | | | |             e1) = all_57_14 & op(e1, e0) = e1 &
% 152.77/22.52  | | | | | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.77/22.52  | | | | | | | | | |           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.77/22.52  | | | | | | | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.77/22.52  | | | | | | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 152.77/22.52  | | | | | | | | | |               op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.77/22.52  | | | | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.77/22.52  | | | | | | | | | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 152.77/22.52  | | | | | | | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.77/22.52  | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 152.77/22.52  | | | | | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.77/22.52  | | | | | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 152.77/22.52  | | | | | | | | | |                 e2) = all_57_3 & op(e0, e2) = e0 &
% 152.77/22.52  | | | | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 152.77/22.52  | | | | | | | | | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 152.77/22.52  | | | | | | | | | |               & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.77/22.52  | | | | | | | | | |               op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 152.77/22.52  | | | | | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.77/22.52  | | | | | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.77/22.52  | | | | | | | | | |                 e1) = all_57_6 & op(e0, e1) = e0 &
% 152.77/22.52  | | | | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 152.77/22.52  | | | | | | | | | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 152.77/22.52  | | | | | | | | | |               & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.77/22.52  | | | | | | | | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | BETA: splitting (79) gives:
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | |   (80)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.77/22.52  | | | | | | | | | | |           e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.77/22.52  | | | | | | | | | | |         all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.77/22.52  | | | | | | | | | | |         op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.77/22.52  | | | | | | | | | | |         $i(all_57_13)
% 152.77/22.52  | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | ALPHA: (80) implies:
% 152.77/22.52  | | | | | | | | | | |   (81)  op(e2, e0) = e2
% 152.77/22.52  | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | REF_CLOSE: (13), (17), (20), (81) are inconsistent by
% 152.77/22.52  | | | | | | | | | | |            sub-proof #1156.
% 152.77/22.52  | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | Case 2:
% 152.77/22.52  | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | |   (82)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.77/22.52  | | | | | | | | | | |             e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.77/22.52  | | | | | | | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 152.77/22.52  | | | | | | | | | | |           & op(e1, e0) = e1 & $i(all_57_11) &
% 152.77/22.52  | | | | | | | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 152.77/22.52  | | | | | | | | | | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 152.77/22.52  | | | | | | | | | | |               &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.77/22.52  | | | | | | | | | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.77/22.52  | | | | | | | | | | |               op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 152.77/22.52  | | | | | | | | | | |               = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 152.77/22.52  | | | | | | | | | | |                ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 152.77/22.52  | | | | | | | | | | |               & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.77/22.52  | | | | | | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 152.77/22.52  | | | | | | | | | | |               e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 152.77/22.52  | | | | | | | | | | |                 e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.77/22.52  | | | | | | | | | | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.77/22.52  | | | | | | | | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 152.77/22.52  | | | | | | | | | | |                 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.77/22.52  | | | | | | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 152.77/22.52  | | | | | | | | | | |               & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 152.77/22.52  | | | | | | | | | | |               = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 152.77/22.52  | | | | | | | | | | |                 e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.77/22.52  | | | | | | | | | | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.77/22.52  | | | | | | | | | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 152.77/22.52  | | | | | | | | | | |                 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 152.77/22.52  | | | | | | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 152.77/22.52  | | | | | | | | | | |               & $i(all_57_7))))
% 152.77/22.52  | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | BETA: splitting (82) gives:
% 152.77/22.52  | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | |   (83)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.77/22.52  | | | | | | | | | | | |           e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.77/22.52  | | | | | | | | | | | |         op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 152.77/22.52  | | | | | | | | | | | |         op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | ALPHA: (83) implies:
% 152.77/22.52  | | | | | | | | | | | |   (84)  op(e2, e2) = e0
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | REF_CLOSE: (12), (13), (24), (84) are inconsistent by
% 152.77/22.52  | | | | | | | | | | | |            sub-proof #1145.
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | Case 2:
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | |   (85)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.77/22.52  | | | | | | | | | | | |         ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.77/22.52  | | | | | | | | | | | |               e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.77/22.52  | | | | | | | | | | | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.77/22.52  | | | | | | | | | | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.77/22.52  | | | | | | | | | | | |             e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 152.77/22.52  | | | | | | | | | | | |             & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.77/22.52  | | | | | | | | | | | |             op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 152.77/22.52  | | | | | | | | | | | |             e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.77/22.52  | | | | | | | | | | | |             (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 152.77/22.52  | | | | | | | | | | | |               e2) = all_57_3 & op(e0, e2) = e0 &
% 152.77/22.52  | | | | | | | | | | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 152.77/22.52  | | | | | | | | | | | |             e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 152.77/22.52  | | | | | | | | | | | |             & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.77/22.52  | | | | | | | | | | | |             op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 152.77/22.52  | | | | | | | | | | | |             e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.77/22.52  | | | | | | | | | | | |             (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.77/22.52  | | | | | | | | | | | |               e1) = all_57_6 & op(e0, e1) = e0 &
% 152.77/22.52  | | | | | | | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 152.77/22.52  | | | | | | | | | | | |             e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 152.77/22.52  | | | | | | | | | | | |             & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.77/22.52  | | | | | | | | | | | |             op(e0, e1) = e0 & $i(all_57_7)))
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | ALPHA: (85) implies:
% 152.77/22.52  | | | | | | | | | | | |   (86)  op(e0, e0) = all_57_15
% 152.77/22.52  | | | | | | | | | | | |   (87)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.77/22.52  | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.77/22.52  | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.77/22.52  | | | | | | | | | | | |           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 152.77/22.52  | | | | | | | | | | | |           &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 152.77/22.52  | | | | | | | | | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.77/22.52  | | | | | | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 152.77/22.52  | | | | | | | | | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.77/22.52  | | | | | | | | | | | |           (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.77/22.52  | | | | | | | | | | | |           = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.77/22.52  | | | | | | | | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.77/22.52  | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.77/22.52  | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.77/22.52  | | | | | | | | | | | |           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 152.77/22.52  | | | | | | | | | | | |           &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.77/22.52  | | | | | | | | | | | |           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.77/22.52  | | | | | | | | | | | |             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.77/22.52  | | | | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.77/22.52  | | | | | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 152.77/22.52  | | | | | | | | | | | |           = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | BETA: splitting (87) gives:
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | |   (88)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.77/22.52  | | | | | | | | | | | | |             e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.77/22.52  | | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.77/22.52  | | | | | | | | | | | | |           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 152.77/22.52  | | | | | | | | | | | | |           &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 152.77/22.52  | | | | | | | | | | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.77/22.52  | | | | | | | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 152.77/22.52  | | | | | | | | | | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.77/22.52  | | | | | | | | | | | | |           (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.77/22.52  | | | | | | | | | | | | |           = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 152.77/22.52  | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | BETA: splitting (88) gives:
% 152.77/22.52  | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | |   (89)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.77/22.52  | | | | | | | | | | | | | |           e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.77/22.52  | | | | | | | | | | | | | |         all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.77/22.52  | | | | | | | | | | | | | |         $i(all_57_0)
% 152.77/22.52  | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | ALPHA: (89) implies:
% 152.77/22.52  | | | | | | | | | | | | | |   (90)  op(e2, e2) = e3
% 152.77/22.52  | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | REF_CLOSE: (13), (24), (28), (90) are inconsistent by
% 152.77/22.52  | | | | | | | | | | | | | |            sub-proof #1179.
% 152.77/22.52  | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | Case 2:
% 152.77/22.52  | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | |   (91)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.77/22.52  | | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.77/22.52  | | | | | | | | | | | | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.77/22.52  | | | | | | | | | | | | | |           $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 152.77/22.52  | | | | | | | | | | | | | |           &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 152.77/22.52  | | | | | | | | | | | | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 152.77/22.52  | | | | | | | | | | | | | |             e2) = e0 & $i(all_57_3))
% 152.77/22.52  | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 152.77/22.52  | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | |   (92)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.77/22.52  | | | | | | | | | | | | | | |           e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.77/22.52  | | | | | | | | | | | | | | |         all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.77/22.52  | | | | | | | | | | | | | | |         $i(all_57_1)
% 152.77/22.52  | | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 152.77/22.52  | | | | | | | | | | | | | | |   (93)   ~ (all_57_1 = e1)
% 152.77/22.52  | | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | | REDUCE: (57), (93) imply:
% 152.77/22.52  | | | | | | | | | | | | | | |   (94)  $false
% 152.77/22.52  | | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | | CLOSE: (94) is inconsistent.
% 152.77/22.52  | | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | Case 2:
% 152.77/22.52  | | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | |   (95)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.77/22.52  | | | | | | | | | | | | | | |           e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 152.77/22.52  | | | | | | | | | | | | | | |         op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.77/22.52  | | | | | | | | | | | | | | |         $i(all_57_3)
% 152.77/22.52  | | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | | ALPHA: (95) implies:
% 152.77/22.52  | | | | | | | | | | | | | | |   (96)   ~ (all_57_15 = e2)
% 152.77/22.52  | | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (86), (96) are inconsistent by
% 152.77/22.52  | | | | | | | | | | | | | | |            sub-proof #901.
% 152.77/22.52  | | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | Case 2:
% 152.77/22.52  | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | |   (97)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.77/22.52  | | | | | | | | | | | | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.77/22.52  | | | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.77/22.52  | | | | | | | | | | | | |           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 152.77/22.52  | | | | | | | | | | | | |           &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.77/22.52  | | | | | | | | | | | | |           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.77/22.52  | | | | | | | | | | | | |             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.77/22.52  | | | | | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.77/22.52  | | | | | | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 152.77/22.52  | | | | | | | | | | | | |           = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.77/22.52  | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | | REF_CLOSE: (13), (24), (27), (28), (32), (50), (52), (97) are
% 152.77/22.52  | | | | | | | | | | | | |            inconsistent by sub-proof #292.
% 152.77/22.52  | | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | End of split
% 152.77/22.52  | | | | | | | | 
% 152.77/22.52  | | | | | | | End of split
% 152.77/22.52  | | | | | | | 
% 152.77/22.52  | | | | | | Case 2:
% 152.77/22.52  | | | | | | | 
% 152.77/22.52  | | | | | | |   (98)   ~ (all_57_14 = e3) & op(e1, e1) = all_57_14 &
% 152.77/22.52  | | | | | | |         $i(all_57_14)
% 152.77/22.52  | | | | | | | 
% 152.77/22.52  | | | | | | | ALPHA: (98) implies:
% 152.77/22.52  | | | | | | |   (99)   ~ (all_57_14 = e3)
% 152.77/22.52  | | | | | | |   (100)  op(e1, e1) = all_57_14
% 152.77/22.52  | | | | | | | 
% 152.77/22.52  | | | | | | | REF_CLOSE: (13), (27), (99), (100) are inconsistent by sub-proof
% 152.77/22.52  | | | | | | |            #816.
% 152.77/22.52  | | | | | | | 
% 152.77/22.52  | | | | | | End of split
% 152.77/22.52  | | | | | | 
% 152.77/22.52  | | | | | Case 2:
% 152.77/22.52  | | | | | | 
% 152.77/22.52  | | | | | |   (101)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3,
% 152.77/22.52  | | | | | |                e2) = e3) | ( ~ (all_57_10 = e2) & op(e3, e3) =
% 152.77/22.52  | | | | | |              all_57_10 & $i(all_57_10))) & ((all_57_4 = e1 & op(e1,
% 152.77/22.52  | | | | | |                e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 152.77/22.52  | | | | | |              all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 152.77/22.52  | | | | | |                e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 152.77/22.52  | | | | | |              all_57_15 & $i(all_57_15)))
% 152.77/22.52  | | | | | | 
% 152.77/22.52  | | | | | | ALPHA: (101) implies:
% 152.77/22.52  | | | | | |   (102)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) &
% 152.77/22.52  | | | | | |            op(e0, e0) = all_57_15 & $i(all_57_15))
% 152.77/22.52  | | | | | | 
% 152.77/22.52  | | | | | | BETA: splitting (102) gives:
% 152.77/22.52  | | | | | | 
% 152.77/22.52  | | | | | | Case 1:
% 152.77/22.52  | | | | | | | 
% 152.77/22.52  | | | | | | |   (103)  all_57_5 = e0 & op(e0, e2) = e0
% 152.77/22.52  | | | | | | | 
% 152.77/22.52  | | | | | | | ALPHA: (103) implies:
% 152.77/22.52  | | | | | | |   (104)  all_57_5 = e0
% 152.77/22.52  | | | | | | |   (105)  op(e0, e2) = e0
% 152.77/22.52  | | | | | | | 
% 152.77/22.52  | | | | | | | BETA: splitting (36) gives:
% 152.77/22.52  | | | | | | | 
% 152.77/22.52  | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | 
% 152.77/22.52  | | | | | | | |   (106)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.77/22.52  | | | | | | | |            ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.77/22.52  | | | | | | | |            all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.77/22.52  | | | | | | | |            $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 &
% 152.77/22.52  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 152.77/22.52  | | | | | | | |              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.77/22.52  | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.77/22.52  | | | | | | | |            $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.77/22.52  | | | | | | | |            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 152.77/22.52  | | | | | | | |              e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.77/22.52  | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.77/22.52  | | | | | | | |            $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 152.77/22.52  | | | | | | | |            all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 152.77/22.52  | | | | | | | |              e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.77/22.52  | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.77/22.52  | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 152.77/22.52  | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 152.77/22.52  | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.77/22.52  | | | | | | | |            op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.77/22.52  | | | | | | | |            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 &
% 152.77/22.52  | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 152.77/22.52  | | | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.77/22.52  | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.77/22.52  | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 152.77/22.52  | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 152.77/22.52  | | | | | | | |              e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.77/22.52  | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.77/22.52  | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 152.77/22.52  | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 152.77/22.52  | | | | | | | |              e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.77/22.52  | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.77/22.52  | | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 152.77/22.52  | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 152.77/22.52  | | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.77/22.52  | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.77/22.52  | | | | | | | |            $i(all_57_7) & $i(all_57_10))
% 152.77/22.52  | | | | | | | | 
% 152.77/22.52  | | | | | | | | BETA: splitting (106) gives:
% 152.77/22.52  | | | | | | | | 
% 152.77/22.52  | | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | |   (107)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 152.77/22.52  | | | | | | | | |            &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.77/22.52  | | | | | | | | |              e2) = all_57_12 & op(e1, e3) = all_57_1 & op(e1,
% 152.77/22.52  | | | | | | | | |              e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 152.77/22.52  | | | | | | | | |          (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0)
% 152.77/22.52  | | | | | | | | |            &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.77/22.52  | | | | | | | | |              e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0,
% 152.77/22.52  | | | | | | | | |              e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 152.77/22.52  | | | | | | | | |          (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2)
% 152.77/22.52  | | | | | | | | |            &  ~ (all_57_14 = e3) & op(e2, e3) = all_57_0 &
% 152.77/22.52  | | | | | | | | |            op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.77/22.52  | | | | | | | | |            all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.77/22.52  | | | | | | | | |          (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0)
% 152.77/22.52  | | | | | | | | |            &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.77/22.52  | | | | | | | | |              e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 152.77/22.52  | | | | | | | | |              e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | BETA: splitting (107) gives:
% 152.77/22.52  | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | Case 1:
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | |   (108)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.77/22.52  | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.77/22.52  | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 152.77/22.52  | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 152.77/22.52  | | | | | | | | | |          (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 152.77/22.52  | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.77/22.52  | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.77/22.52  | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | | REF_CLOSE: (13), (37), (43), (108) are inconsistent by
% 152.77/22.52  | | | | | | | | | |            sub-proof #1180.
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.52  | | | | | | | | | Case 2:
% 152.77/22.52  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | |   (109)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.77/22.53  | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.77/22.53  | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.77/22.53  | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 152.77/22.53  | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 152.77/22.53  | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 152.77/22.53  | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0,
% 152.77/22.53  | | | | | | | | | |              e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2)
% 152.77/22.53  | | | | | | | | | |            & $i(all_57_14))
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | REF_CLOSE: (13), (27), (109) are inconsistent by sub-proof
% 152.77/22.53  | | | | | | | | | |            #368.
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | End of split
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | Case 2:
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | |   (110)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.77/22.53  | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 152.77/22.53  | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 152.77/22.53  | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.77/22.53  | | | | | | | | |            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 152.77/22.53  | | | | | | | | |              e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 152.77/22.53  | | | | | | | | |          (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3,
% 152.77/22.53  | | | | | | | | |              e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.77/22.53  | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.77/22.53  | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.77/22.53  | | | | | | | | |              e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 152.77/22.53  | | | | | | | | |              e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 152.77/22.53  | | | | | | | | |          (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.77/22.53  | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 152.77/22.53  | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | BETA: splitting (110) gives:
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | Case 1:
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | |   (111)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.77/22.53  | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.77/22.53  | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.77/22.53  | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 152.77/22.53  | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 152.77/22.53  | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 152.77/22.53  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0,
% 152.77/22.53  | | | | | | | | | |              e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5)
% 152.77/22.53  | | | | | | | | | |            & $i(all_57_10))
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | REF_CLOSE: (7), (13), (27), (28), (49), (111) are
% 152.77/22.53  | | | | | | | | | |            inconsistent by sub-proof #294.
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | Case 2:
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | |   (112)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.77/22.53  | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 152.77/22.53  | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 152.77/22.53  | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) & $i(all_57_14))
% 152.77/22.53  | | | | | | | | | |          | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.77/22.53  | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.77/22.53  | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 152.77/22.53  | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 152.77/22.53  | | | | | | | | | |          (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.77/22.53  | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.77/22.53  | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.77/22.53  | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.77/22.53  | | | | | | | | | |            $i(all_57_10))
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | BETA: splitting (112) gives:
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | Case 1:
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | |   (113)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 152.77/22.53  | | | | | | | | | | |            e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 152.77/22.53  | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 152.77/22.53  | | | | | | | | | | |            e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | ALPHA: (113) implies:
% 152.77/22.53  | | | | | | | | | | |   (114)  op(e3, e3) = e2
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | REF_CLOSE: (13), (28), (52), (114) are inconsistent by
% 152.77/22.53  | | | | | | | | | | |            sub-proof #1085.
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | Case 2:
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | |   (115)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.77/22.53  | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.77/22.53  | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 152.77/22.53  | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 152.77/22.53  | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.77/22.53  | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.77/22.53  | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.77/22.53  | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.77/22.53  | | | | | | | | | | |            $i(all_57_10))
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | REF_CLOSE: (13), (24), (32), (104), (115) are inconsistent by
% 152.77/22.53  | | | | | | | | | | |            sub-proof #532.
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | End of split
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | End of split
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | End of split
% 152.77/22.53  | | | | | | | | 
% 152.77/22.53  | | | | | | | Case 2:
% 152.77/22.53  | | | | | | | | 
% 152.77/22.53  | | | | | | | |   (116)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) & 
% 152.77/22.53  | | | | | | | |            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 152.77/22.53  | | | | | | | |              e1) = e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1
% 152.77/22.53  | | | | | | | |            & $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 &
% 152.77/22.53  | | | | | | | |            all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 152.77/22.53  | | | | | | | |              e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.77/22.53  | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.77/22.53  | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.77/22.53  | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 152.77/22.53  | | | | | | | |              e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.77/22.53  | | | | | | | |            op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 152.77/22.53  | | | | | | | |            $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 152.77/22.53  | | | | | | | |            all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 152.77/22.53  | | | | | | | |              = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.77/22.53  | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.77/22.53  | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 152.77/22.53  | | | | | | | |            all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 152.77/22.53  | | | | | | | |              = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.77/22.53  | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.77/22.53  | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0 &
% 152.77/22.53  | | | | | | | |            all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 =
% 152.77/22.53  | | | | | | | |              e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.77/22.53  | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.77/22.53  | | | | | | | |            $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 &
% 152.77/22.53  | | | | | | | |            all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 152.77/22.53  | | | | | | | |              e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.77/22.53  | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.77/22.53  | | | | | | | |            $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 152.77/22.53  | | | | | | | |            all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13
% 152.77/22.53  | | | | | | | |              = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.77/22.53  | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.77/22.53  | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 152.77/22.53  | | | | | | | |            all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14
% 152.77/22.53  | | | | | | | |              = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.77/22.53  | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.77/22.53  | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.77/22.53  | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.77/22.53  | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.77/22.53  | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 152.77/22.53  | | | | | | | |                  e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 152.77/22.53  | | | | | | | |              (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.77/22.53  | | | | | | | |                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.77/22.53  | | | | | | | |                all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.77/22.53  | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &
% 152.77/22.53  | | | | | | | |                 ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 152.77/22.53  | | | | | | | |                  e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) =
% 152.77/22.53  | | | | | | | |                e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 152.77/22.53  | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 152.77/22.53  | | | | | | | |                op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0,
% 152.77/22.53  | | | | | | | |                  e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.77/22.53  | | | | | | | |                all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.77/22.53  | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.77/22.53  | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.77/22.53  | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.77/22.53  | | | | | | | |                  e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 152.77/22.53  | | | | | | | |                op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.77/22.53  | | | | | | | |                $i(all_57_7))))
% 152.77/22.53  | | | | | | | | 
% 152.77/22.53  | | | | | | | | BETA: splitting (116) gives:
% 152.77/22.53  | | | | | | | | 
% 152.77/22.53  | | | | | | | | Case 1:
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | |   (117)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.77/22.53  | | | | | | | | |            op(e3, e1) = e3 & op(e0, e1) = all_57_8 & op(e0,
% 152.77/22.53  | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 152.77/22.53  | | | | | | | | |          (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3,
% 152.77/22.53  | | | | | | | | |              e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2,
% 152.77/22.53  | | | | | | | | |              e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 152.77/22.53  | | | | | | | | |          (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.77/22.53  | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 152.77/22.53  | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.77/22.53  | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 152.77/22.53  | | | | | | | | |            op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 152.77/22.53  | | | | | | | | |            all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 152.77/22.53  | | | | | | | | |          (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 152.77/22.53  | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.77/22.53  | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | BETA: splitting (117) gives:
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | Case 1:
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | |   (118)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.77/22.53  | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.77/22.53  | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.77/22.53  | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.77/22.53  | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 152.77/22.53  | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 152.77/22.53  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 152.77/22.53  | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 152.77/22.53  | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | REF_CLOSE: (6), (11), (13), (21), (25), (118) are
% 152.77/22.53  | | | | | | | | | |            inconsistent by sub-proof #544.
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | Case 2:
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | |   (119)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.77/22.53  | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 152.77/22.53  | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.77/22.53  | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.77/22.53  | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 152.77/22.53  | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 152.77/22.53  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 152.77/22.53  | | | | | | | | | |              e2) = e0 & op(e2, e0) = all_57_11 &
% 152.77/22.53  | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 152.77/22.53  | | | | | | | | | |            all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.77/22.53  | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 152.77/22.53  | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.77/22.53  | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | REF_CLOSE: (6), (11), (12), (13), (24), (27), (51), (119) are
% 152.77/22.53  | | | | | | | | | |            inconsistent by sub-proof #293.
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | End of split
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | Case 2:
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | |   (120)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3,
% 152.77/22.53  | | | | | | | | |              e0) = all_57_9 & op(e2, e2) = all_57_12 & op(e2,
% 152.77/22.53  | | | | | | | | |              e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 152.77/22.53  | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.77/22.53  | | | | | | | | |            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3,
% 152.77/22.53  | | | | | | | | |              e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1,
% 152.77/22.53  | | | | | | | | |              e0) = e1 & $i(all_57_9) & $i(all_57_14)) |
% 152.77/22.53  | | | | | | | | |          (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.77/22.53  | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.77/22.53  | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.77/22.53  | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.77/22.53  | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &
% 152.77/22.53  | | | | | | | | |             ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2,
% 152.77/22.53  | | | | | | | | |              e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 152.77/22.53  | | | | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.77/22.53  | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 152.77/22.53  | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 & 
% 152.77/22.53  | | | | | | | | |                ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.77/22.53  | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.77/22.53  | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 =
% 152.77/22.53  | | | | | | | | |                e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.77/22.53  | | | | | | | | |                (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.77/22.53  | | | | | | | | |                op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.77/22.53  | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 152.77/22.53  | | | | | | | | |                &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 152.77/22.53  | | | | | | | | |                op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.77/22.53  | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 =
% 152.77/22.53  | | | | | | | | |                e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.77/22.53  | | | | | | | | |                (all_57_15 = e2) & op(e1, e2) = all_57_4 &
% 152.77/22.53  | | | | | | | | |                op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.77/22.53  | | | | | | | | |                $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 152.77/22.53  | | | | | | | | |                &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.77/22.53  | | | | | | | | |                op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.77/22.53  | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.77/22.53  | | | | | | | | |                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.77/22.53  | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 152.77/22.53  | | | | | | | | |                = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | BETA: splitting (120) gives:
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | Case 1:
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | |   (121)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 152.77/22.53  | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 152.77/22.53  | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 152.77/22.53  | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 152.77/22.53  | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 152.77/22.53  | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.77/22.53  | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 152.77/22.53  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | REF_CLOSE: (13), (51), (52), (121) are inconsistent by
% 152.77/22.53  | | | | | | | | | |            sub-proof #975.
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | Case 2:
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | |   (122)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.77/22.53  | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.77/22.53  | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.77/22.53  | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.77/22.53  | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 152.77/22.53  | | | | | | | | | |            &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.77/22.53  | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1,
% 152.77/22.53  | | | | | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 &
% 152.77/22.53  | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.77/22.53  | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.77/22.53  | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.77/22.53  | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 152.77/22.53  | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.77/22.53  | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.77/22.53  | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 152.77/22.53  | | | | | | | | | |                & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.77/22.53  | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 152.77/22.53  | | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.77/22.53  | | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 152.77/22.53  | | | | | | | | | |                  e2) = all_57_3 & op(e0, e2) = e0 &
% 152.77/22.53  | | | | | | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 152.77/22.53  | | | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 152.77/22.53  | | | | | | | | | |                & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.77/22.53  | | | | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 152.77/22.53  | | | | | | | | | |                e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.77/22.53  | | | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.77/22.53  | | | | | | | | | |                  e1) = all_57_6 & op(e0, e1) = e0 &
% 152.77/22.53  | | | | | | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 152.77/22.53  | | | | | | | | | |                e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 152.77/22.53  | | | | | | | | | |                & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.77/22.53  | | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_7))))
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | BETA: splitting (122) gives:
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | Case 1:
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | |   (123)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.77/22.53  | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.77/22.53  | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.77/22.53  | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.77/22.53  | | | | | | | | | | |          $i(all_57_13)
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | ALPHA: (123) implies:
% 152.77/22.53  | | | | | | | | | | |   (124)  op(e2, e0) = e2
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | REF_CLOSE: (13), (17), (20), (124) are inconsistent by
% 152.77/22.53  | | | | | | | | | | |            sub-proof #1156.
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | Case 2:
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | |   (125)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.77/22.53  | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.77/22.53  | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 152.77/22.53  | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 152.77/22.53  | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 152.77/22.53  | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 152.77/22.53  | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.77/22.53  | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.77/22.53  | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 152.77/22.53  | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 152.77/22.53  | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 152.77/22.53  | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.77/22.53  | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 152.77/22.53  | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 152.77/22.53  | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.77/22.53  | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.77/22.53  | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 152.77/22.53  | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.77/22.53  | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 152.77/22.53  | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 152.77/22.53  | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 152.77/22.53  | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.77/22.53  | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.77/22.53  | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 152.77/22.53  | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 152.77/22.53  | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 152.77/22.53  | | | | | | | | | | |                & $i(all_57_7))))
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | BETA: splitting (125) gives:
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | Case 1:
% 152.77/22.53  | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | |   (126)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.77/22.53  | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.77/22.53  | | | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 152.77/22.53  | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 152.77/22.53  | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | | ALPHA: (126) implies:
% 152.77/22.53  | | | | | | | | | | | |   (127)  op(e2, e2) = e0
% 152.77/22.53  | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | | REF_CLOSE: (12), (13), (24), (127) are inconsistent by
% 152.77/22.53  | | | | | | | | | | | |            sub-proof #1145.
% 152.77/22.53  | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | Case 2:
% 152.77/22.53  | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | |   (128)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.77/22.53  | | | | | | | | | | | |          ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.77/22.53  | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.77/22.53  | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.77/22.53  | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.77/22.53  | | | | | | | | | | | |              e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 152.77/22.53  | | | | | | | | | | | |              & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.77/22.53  | | | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 152.77/22.53  | | | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.77/22.53  | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 152.77/22.53  | | | | | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 &
% 152.77/22.53  | | | | | | | | | | | |              $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 152.77/22.53  | | | | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 152.77/22.53  | | | | | | | | | | | |              & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.77/22.53  | | | | | | | | | | | |              op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 152.77/22.53  | | | | | | | | | | | |              e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.77/22.53  | | | | | | | | | | | |              (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.77/22.53  | | | | | | | | | | | |                e1) = all_57_6 & op(e0, e1) = e0 &
% 152.77/22.53  | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 152.77/22.53  | | | | | | | | | | | |              e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 152.77/22.53  | | | | | | | | | | | |              & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.77/22.53  | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_7)))
% 152.77/22.53  | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | | ALPHA: (128) implies:
% 152.77/22.53  | | | | | | | | | | | |   (129)  op(e0, e0) = all_57_15
% 152.77/22.53  | | | | | | | | | | | |   (130)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.77/22.53  | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.77/22.53  | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.77/22.53  | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 152.77/22.53  | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 152.77/22.53  | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.77/22.53  | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 152.77/22.53  | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.77/22.53  | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.77/22.53  | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.77/22.53  | | | | | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.77/22.53  | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.77/22.53  | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.77/22.53  | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 152.77/22.53  | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.77/22.53  | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.77/22.53  | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.77/22.53  | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.77/22.53  | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 152.77/22.53  | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.77/22.53  | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | | BETA: splitting (130) gives:
% 152.77/22.53  | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | | Case 1:
% 152.77/22.53  | | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | | |   (131)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.77/22.53  | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.77/22.53  | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.77/22.53  | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 152.77/22.53  | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 152.77/22.53  | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.77/22.53  | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 152.77/22.53  | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.77/22.53  | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.77/22.53  | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 152.77/22.53  | | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | | | REF_CLOSE: (8), (9), (13), (16), (22), (105), (129), (131)
% 152.77/22.53  | | | | | | | | | | | | |            are inconsistent by sub-proof #529.
% 152.77/22.53  | | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | | Case 2:
% 152.77/22.53  | | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | | |   (132)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.77/22.53  | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.77/22.53  | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.77/22.53  | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 152.77/22.53  | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 152.77/22.53  | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.77/22.53  | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.77/22.53  | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.77/22.53  | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 152.77/22.53  | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.77/22.53  | | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | | | REF_CLOSE: (13), (24), (27), (28), (32), (50), (52), (132)
% 152.77/22.53  | | | | | | | | | | | | |            are inconsistent by sub-proof #292.
% 152.77/22.53  | | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | | End of split
% 152.77/22.53  | | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | | End of split
% 152.77/22.53  | | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | | End of split
% 152.77/22.53  | | | | | | | | | | 
% 152.77/22.53  | | | | | | | | | End of split
% 152.77/22.53  | | | | | | | | | 
% 152.77/22.53  | | | | | | | | End of split
% 152.77/22.53  | | | | | | | | 
% 152.77/22.53  | | | | | | | End of split
% 152.77/22.53  | | | | | | | 
% 152.77/22.53  | | | | | | Case 2:
% 152.77/22.53  | | | | | | | 
% 152.77/22.53  | | | | | | |   (133)   ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 152.77/22.53  | | | | | | |          $i(all_57_15)
% 152.77/22.53  | | | | | | | 
% 152.77/22.53  | | | | | | | ALPHA: (133) implies:
% 152.77/22.53  | | | | | | |   (134)   ~ (all_57_15 = e2)
% 152.77/22.53  | | | | | | |   (135)  op(e0, e0) = all_57_15
% 152.77/22.53  | | | | | | | 
% 152.77/22.53  | | | | | | | REF_CLOSE: (13), (16), (134), (135) are inconsistent by sub-proof
% 152.77/22.53  | | | | | | |            #901.
% 152.77/22.53  | | | | | | | 
% 152.77/22.53  | | | | | | End of split
% 152.77/22.53  | | | | | | 
% 152.77/22.53  | | | | | End of split
% 152.77/22.53  | | | | | 
% 152.77/22.53  | | | | Case 2:
% 152.77/22.53  | | | | | 
% 152.77/22.53  | | | | |   (136)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3,
% 152.77/22.53  | | | | |                  e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 152.77/22.53  | | | | |                all_57_10 & $i(all_57_10))) & ((all_57_7 = e2 & op(e2,
% 152.77/22.53  | | | | |                  e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 152.77/22.53  | | | | |                all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 152.77/22.53  | | | | |                  e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 152.77/22.53  | | | | |                all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 & op(e0,
% 152.77/22.53  | | | | |              e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 152.77/22.53  | | | | |                (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 152.77/22.53  | | | | |                $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) |
% 152.77/22.53  | | | | |              ( ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 152.77/22.53  | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1) |
% 152.77/22.53  | | | | |              ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.77/22.53  | | | | |                $i(all_57_14))))
% 152.77/22.53  | | | | | 
% 152.77/22.53  | | | | | REF_CLOSE: (12), (13), (16), (27), (50), (136) are inconsistent by
% 152.77/22.53  | | | | |            sub-proof #291.
% 152.77/22.53  | | | | | 
% 152.77/22.53  | | | | End of split
% 152.77/22.53  | | | | 
% 152.77/22.53  | | | Case 2:
% 152.77/22.53  | | | | 
% 152.77/22.53  | | | |   (137)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 152.77/22.53  | | | | 
% 152.77/22.53  | | | | REF_CLOSE: (3), (23), (30), (46), (137) are inconsistent by sub-proof
% 152.77/22.53  | | | |            #1140.
% 152.77/22.53  | | | | 
% 152.77/22.53  | | | End of split
% 152.77/22.53  | | | 
% 152.77/22.53  | | Case 2:
% 152.77/22.53  | | | 
% 152.77/22.53  | | |   (138)  all_56_5 = e2 & op(e2, e1) = e2
% 152.77/22.53  | | | 
% 152.77/22.53  | | | ALPHA: (138) implies:
% 152.77/22.53  | | |   (139)  op(e2, e1) = e2
% 152.77/22.53  | | | 
% 152.77/22.53  | | | REF_CLOSE: (13), (21), (25), (139) are inconsistent by sub-proof #1157.
% 152.77/22.53  | | | 
% 152.77/22.53  | | End of split
% 152.77/22.53  | | 
% 152.77/22.53  | Case 2:
% 152.77/22.53  | | 
% 152.77/22.53  | |   (140)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) =
% 152.77/22.53  | |            e2)
% 152.77/22.53  | | 
% 152.77/22.53  | | BETA: splitting (140) gives:
% 152.77/22.53  | | 
% 152.77/22.53  | | Case 1:
% 152.77/22.53  | | | 
% 152.77/22.53  | | |   (141)  all_56_8 = e2 & op(e1, e1) = e2
% 152.77/22.53  | | | 
% 152.77/22.53  | | | ALPHA: (141) implies:
% 152.77/22.53  | | |   (142)  op(e1, e1) = e2
% 152.77/22.53  | | | 
% 152.77/22.53  | | | REF_CLOSE: (13), (27), (28), (142) are inconsistent by sub-proof #834.
% 152.77/22.53  | | | 
% 152.77/22.53  | | Case 2:
% 152.77/22.53  | | | 
% 152.77/22.53  | | |   (143)  all_56_14 = e2 & op(e0, e1) = e2
% 152.77/22.53  | | | 
% 152.77/22.53  | | | ALPHA: (143) implies:
% 152.77/22.53  | | |   (144)  op(e0, e1) = e2
% 152.77/22.53  | | | 
% 152.77/22.53  | | | GROUND_INST: instantiating (13) with all_52_11, e2, e1, e0, simplifying
% 152.77/22.53  | | |              with (1), (144) gives:
% 152.77/22.53  | | |   (145)  all_52_11 = e2
% 152.77/22.53  | | | 
% 152.77/22.53  | | | REDUCE: (35), (145) imply:
% 152.77/22.53  | | |   (146)  $false
% 152.77/22.53  | | | 
% 152.77/22.53  | | | CLOSE: (146) is inconsistent.
% 152.77/22.53  | | | 
% 152.77/22.53  | | End of split
% 152.77/22.53  | | 
% 152.77/22.53  | End of split
% 152.77/22.53  | 
% 152.77/22.53  End of proof
% 152.77/22.53  
% 152.77/22.53  Sub-proof #291 shows that the following formulas are inconsistent:
% 152.77/22.53  ----------------------------------------------------------------
% 152.77/22.53    (1)   ~ (e3 = e1)
% 152.77/22.53    (2)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 152.77/22.53             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.77/22.53           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 152.77/22.53               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 152.77/22.53             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.77/22.53         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 152.77/22.53             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.77/22.53           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 152.77/22.53               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 152.77/22.53             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 152.77/22.53    (3)   ~ (e2 = e0)
% 152.77/22.53    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.77/22.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.77/22.53    (5)  op(e0, e0) = e2
% 152.77/22.53    (6)  op(e1, e1) = e3
% 152.77/22.53  
% 152.77/22.53  Begin of proof
% 152.77/22.53  | 
% 152.77/22.53  | BETA: splitting (2) gives:
% 152.77/22.53  | 
% 152.77/22.53  | Case 1:
% 152.77/22.53  | | 
% 152.77/22.53  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3)
% 152.77/22.53  | |          | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.77/22.53  | |        ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 152.77/22.53  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 152.77/22.53  | |              e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 152.77/22.53  | |            $i(all_57_15)))
% 152.77/22.53  | | 
% 152.77/22.53  | | ALPHA: (7) implies:
% 152.77/22.53  | |   (8)  op(e1, e1) = e1
% 152.77/22.53  | | 
% 152.77/22.53  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #734.
% 152.77/22.53  | | 
% 152.77/22.53  | Case 2:
% 152.77/22.53  | | 
% 152.77/22.53  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3)
% 152.77/22.53  | |          | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.77/22.53  | |        ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 152.77/22.53  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 152.77/22.53  | |              e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.77/22.53  | |            $i(all_57_14)))
% 152.77/22.53  | | 
% 152.77/22.53  | | ALPHA: (9) implies:
% 152.77/22.53  | |   (10)  op(e0, e0) = e0
% 152.77/22.53  | | 
% 152.77/22.53  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #1043.
% 152.77/22.53  | | 
% 152.77/22.53  | End of split
% 152.77/22.53  | 
% 152.77/22.53  End of proof
% 152.77/22.53  
% 152.77/22.53  Sub-proof #292 shows that the following formulas are inconsistent:
% 152.77/22.53  ----------------------------------------------------------------
% 152.77/22.53    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.77/22.53             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.77/22.53           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 152.77/22.53           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 152.77/22.53             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.77/22.53           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.77/22.53           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.77/22.53    (2)   ~ (e3 = e1)
% 152.77/22.53    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.77/22.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.77/22.53    (4)  op(e2, e2) = e2
% 152.77/22.53    (5)  op(e1, e1) = e3
% 152.77/22.53    (6)   ~ (e3 = e2)
% 152.77/22.53    (7)  op(e3, e3) = e3
% 152.77/22.53    (8)   ~ (e2 = e1)
% 152.77/22.53  
% 152.77/22.53  Begin of proof
% 152.77/22.53  | 
% 152.77/22.53  | BETA: splitting (1) gives:
% 152.77/22.53  | 
% 152.77/22.53  | Case 1:
% 152.77/22.53  | | 
% 152.77/22.53  | |   (9)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.77/22.53  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.77/22.53  | |        $i(all_57_4)
% 152.77/22.53  | | 
% 152.77/22.53  | | ALPHA: (9) implies:
% 152.77/22.53  | |   (10)  op(e1, e1) = e2
% 152.77/22.53  | | 
% 152.77/22.53  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #834.
% 152.77/22.53  | | 
% 152.77/22.53  | Case 2:
% 152.77/22.53  | | 
% 152.77/22.53  | |   (11)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 152.77/22.53  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 152.77/22.53  | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.77/22.53  | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2,
% 152.77/22.53  | |             e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.77/22.53  | | 
% 152.77/22.53  | | REF_CLOSE: (2), (3), (4), (7), (8), (11) are inconsistent by sub-proof
% 152.77/22.53  | |            #1076.
% 152.77/22.53  | | 
% 152.77/22.53  | End of split
% 152.77/22.53  | 
% 152.77/22.53  End of proof
% 152.77/22.53  
% 152.77/22.53  Sub-proof #293 shows that the following formulas are inconsistent:
% 152.77/22.53  ----------------------------------------------------------------
% 152.77/22.53    (1)  op(e0, e0) = all_10_2
% 152.77/22.53    (2)   ~ (all_10_2 = e1)
% 152.77/22.53    (3)   ~ (e2 = e0)
% 152.77/22.53    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.77/22.53           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.77/22.54    (5)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 152.77/22.54             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.77/22.54           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 152.77/22.54           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 152.77/22.54           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 152.77/22.54           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 152.77/22.54           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 152.77/22.54           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.77/22.54           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.77/22.54    (6)   ~ (e3 = e0)
% 152.77/22.54    (7)  op(e2, e2) = e2
% 152.77/22.54    (8)  op(e1, e1) = e3
% 152.77/22.54  
% 152.77/22.54  Begin of proof
% 152.77/22.54  | 
% 152.77/22.54  | BETA: splitting (5) gives:
% 152.77/22.54  | 
% 152.77/22.54  | Case 1:
% 152.77/22.54  | | 
% 152.77/22.54  | |   (9)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 152.77/22.54  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.77/22.54  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 152.77/22.54  | | 
% 152.77/22.54  | | ALPHA: (9) implies:
% 152.77/22.54  | |   (10)  op(e0, e0) = e1
% 152.77/22.54  | | 
% 152.77/22.54  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #1116.
% 152.77/22.54  | | 
% 152.77/22.54  | Case 2:
% 152.77/22.54  | | 
% 152.77/22.54  | |   (11)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.77/22.54  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.77/22.54  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.77/22.54  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 152.77/22.54  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 152.77/22.54  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.77/22.54  | |           $i(all_57_13))
% 152.77/22.54  | | 
% 152.77/22.54  | | REF_CLOSE: (3), (4), (6), (7), (8), (11) are inconsistent by sub-proof #434.
% 152.77/22.54  | | 
% 152.77/22.54  | End of split
% 152.77/22.54  | 
% 152.77/22.54  End of proof
% 152.77/22.54  
% 152.77/22.54  Sub-proof #294 shows that the following formulas are inconsistent:
% 152.77/22.54  ----------------------------------------------------------------
% 152.77/22.54    (1)  op(e3, e2) = all_52_4
% 152.77/22.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.77/22.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.77/22.54    (3)   ~ (all_52_4 = e3)
% 152.77/22.54    (4)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 152.77/22.54             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.77/22.54           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 152.77/22.54           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 152.77/22.54           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 152.77/22.54           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 152.77/22.54    (5)  op(e1, e1) = e3
% 152.77/22.54    (6)   ~ (e3 = e2)
% 152.77/22.54  
% 152.77/22.54  Begin of proof
% 152.77/22.54  | 
% 152.77/22.54  | BETA: splitting (4) gives:
% 152.77/22.54  | 
% 152.77/22.54  | Case 1:
% 152.77/22.54  | | 
% 152.77/22.54  | |   (7)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 152.77/22.54  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.77/22.54  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 152.77/22.54  | | 
% 152.77/22.54  | | ALPHA: (7) implies:
% 152.77/22.54  | |   (8)  op(e1, e1) = e2
% 152.77/22.54  | | 
% 152.77/22.54  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #834.
% 152.77/22.54  | | 
% 152.77/22.54  | Case 2:
% 152.77/22.54  | | 
% 152.77/22.54  | |   (9)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 152.77/22.54  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 152.77/22.54  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 152.77/22.54  | | 
% 152.77/22.54  | | ALPHA: (9) implies:
% 152.77/22.54  | |   (10)  op(e3, e2) = e3
% 152.77/22.54  | | 
% 152.77/22.54  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #1166.
% 152.77/22.54  | | 
% 152.77/22.54  | End of split
% 152.77/22.54  | 
% 152.77/22.54  End of proof
% 152.77/22.54  
% 152.77/22.54  Sub-proof #295 shows that the following formulas are inconsistent:
% 152.77/22.54  ----------------------------------------------------------------
% 152.77/22.54    (1)   ~ (e3 = e1)
% 152.77/22.54    (2)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 152.77/22.54             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.77/22.54           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 152.77/22.54               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 152.77/22.54             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 152.77/22.54         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 152.77/22.54             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.77/22.54           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 152.77/22.54               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 152.77/22.54             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 152.77/22.54    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.77/22.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.77/22.54    (4)  op(e0, e0) = e3
% 152.77/22.54    (5)   ~ (e3 = e0)
% 152.77/22.54    (6)  op(e1, e1) = e3
% 152.77/22.54  
% 152.77/22.54  Begin of proof
% 152.77/22.54  | 
% 152.77/22.54  | BETA: splitting (2) gives:
% 152.77/22.54  | 
% 152.77/22.54  | Case 1:
% 152.77/22.54  | | 
% 152.77/22.54  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3)
% 152.77/22.54  | |          | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.77/22.54  | |        ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 152.77/22.54  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 152.77/22.54  | |              e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 152.77/22.54  | |            $i(all_57_15)))
% 152.77/22.54  | | 
% 152.77/22.54  | | ALPHA: (7) implies:
% 152.77/22.54  | |   (8)  op(e1, e1) = e1
% 152.77/22.54  | | 
% 152.77/22.54  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #734.
% 152.77/22.54  | | 
% 152.77/22.54  | Case 2:
% 152.77/22.54  | | 
% 152.77/22.54  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3)
% 152.77/22.54  | |          | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 152.77/22.54  | |        ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 152.77/22.54  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 152.77/22.54  | |              e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 152.77/22.54  | |            $i(all_57_14)))
% 152.77/22.54  | | 
% 152.77/22.54  | | ALPHA: (9) implies:
% 152.77/22.54  | |   (10)  op(e0, e0) = e0
% 152.77/22.54  | | 
% 152.77/22.54  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #1143.
% 152.77/22.54  | | 
% 152.77/22.54  | End of split
% 152.77/22.54  | 
% 152.77/22.54  End of proof
% 152.77/22.54  
% 152.77/22.54  Sub-proof #296 shows that the following formulas are inconsistent:
% 152.77/22.54  ----------------------------------------------------------------
% 152.77/22.54    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.77/22.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.77/22.54    (2)  op(e2, e3) = e2
% 152.77/22.54    (3)  op(e0, e0) = e3
% 152.77/22.54    (4)  op(e0, e0) = e1
% 152.77/22.54    (5)  op(e2, e3) = e3
% 152.77/22.54    (6)   ~ (e2 = e1)
% 152.77/22.54    (7)  op(e2, e3) = all_52_1
% 152.77/22.54  
% 152.77/22.54  Begin of proof
% 152.77/22.54  | 
% 152.77/22.54  | GROUND_INST: instantiating (1) with e1, e3, e0, e0, simplifying with (3), (4)
% 152.77/22.54  |              gives:
% 152.77/22.54  |   (8)  e3 = e1
% 152.77/22.54  | 
% 152.77/22.54  | GROUND_INST: instantiating (1) with all_52_1, e2, e3, e2, simplifying with
% 152.77/22.54  |              (2), (7) gives:
% 152.77/22.54  |   (9)  all_52_1 = e2
% 152.77/22.54  | 
% 152.77/22.54  | GROUND_INST: instantiating (1) with all_52_1, e3, e3, e2, simplifying with
% 152.77/22.54  |              (5), (7) gives:
% 152.77/22.54  |   (10)  all_52_1 = e3
% 152.77/22.54  | 
% 152.77/22.54  | COMBINE_EQS: (9), (10) imply:
% 152.77/22.54  |   (11)  e3 = e2
% 152.77/22.54  | 
% 152.77/22.54  | COMBINE_EQS: (8), (11) imply:
% 152.77/22.54  |   (12)  e2 = e1
% 152.77/22.54  | 
% 152.77/22.54  | SIMP: (12) implies:
% 152.77/22.54  |   (13)  e2 = e1
% 152.77/22.54  | 
% 152.77/22.54  | REDUCE: (6), (13) imply:
% 152.77/22.54  |   (14)  $false
% 152.77/22.54  | 
% 152.77/22.54  | CLOSE: (14) is inconsistent.
% 152.77/22.54  | 
% 152.77/22.54  End of proof
% 152.77/22.54  
% 152.77/22.54  Sub-proof #297 shows that the following formulas are inconsistent:
% 152.77/22.54  ----------------------------------------------------------------
% 152.77/22.54    (1)  op(e0, e2) = all_52_7
% 152.77/22.54    (2)   ~ (all_52_3 = all_52_7)
% 152.77/22.54    (3)   ~ (e2 = e0)
% 152.77/22.54    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.77/22.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.77/22.54    (5)  op(e0, e0) = e3
% 152.77/22.54    (6)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 152.77/22.54           all_57_14 & $i(all_57_14))
% 152.77/22.54    (7)   ~ (all_57_10 = e2)
% 152.83/22.54    (8)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 152.83/22.54             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.83/22.54           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.83/22.54           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.83/22.54             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.83/22.54           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.83/22.54           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.83/22.54           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 152.83/22.54           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.83/22.54           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 152.83/22.54           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.83/22.54         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.83/22.54             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.54           $i(all_57_7))
% 152.83/22.54    (9)  op(e0, e1) = e2
% 152.83/22.54    (10)  op(e0, e3) = all_52_3
% 152.83/22.54    (11)  op(e2, e2) = e2
% 152.83/22.54    (12)  op(e0, e0) = all_57_15
% 152.83/22.54    (13)   ~ (e2 = e1)
% 152.83/22.54  
% 152.83/22.54  Begin of proof
% 152.83/22.54  | 
% 152.83/22.54  | BETA: splitting (8) gives:
% 152.83/22.54  | 
% 152.83/22.54  | Case 1:
% 152.83/22.54  | | 
% 152.83/22.54  | |   (14)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 152.83/22.54  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 152.83/22.54  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.83/22.54  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.83/22.54  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 152.83/22.54  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 152.83/22.54  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.83/22.54  | |           $i(all_57_3))
% 152.83/22.54  | | 
% 152.83/22.54  | | BETA: splitting (14) gives:
% 152.83/22.54  | | 
% 152.83/22.54  | | Case 1:
% 152.83/22.54  | | | 
% 152.83/22.54  | | |   (15)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.83/22.54  | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.83/22.54  | | |         op(e0, e3) = e0 & $i(all_57_0)
% 152.83/22.54  | | | 
% 152.83/22.54  | | | ALPHA: (15) implies:
% 152.83/22.54  | | |   (16)  op(e0, e3) = e0
% 152.83/22.54  | | | 
% 152.83/22.54  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 152.83/22.54  | | |            (16) are inconsistent by sub-proof #298.
% 152.83/22.54  | | | 
% 152.83/22.54  | | Case 2:
% 152.83/22.54  | | | 
% 152.83/22.54  | | |   (17)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.54  | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.83/22.54  | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 152.83/22.54  | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.83/22.54  | | |           & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 152.83/22.54  | | | 
% 152.83/22.54  | | | BETA: splitting (17) gives:
% 152.83/22.54  | | | 
% 152.83/22.54  | | | Case 1:
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | |   (18)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.54  | | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.83/22.54  | | | |         op(e0, e3) = e0 & $i(all_57_1)
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | | ALPHA: (18) implies:
% 152.83/22.54  | | | |   (19)  op(e0, e3) = e0
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 152.83/22.54  | | | |            (13), (19) are inconsistent by sub-proof #298.
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | Case 2:
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | |   (20)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.83/22.54  | | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.83/22.54  | | | |         op(e0, e2) = e0 & $i(all_57_3)
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | | ALPHA: (20) implies:
% 152.83/22.54  | | | |   (21)  all_57_10 = e2
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | | REDUCE: (7), (21) imply:
% 152.83/22.54  | | | |   (22)  $false
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | | CLOSE: (22) is inconsistent.
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | End of split
% 152.83/22.54  | | | 
% 152.83/22.54  | | End of split
% 152.83/22.54  | | 
% 152.83/22.54  | Case 2:
% 152.83/22.54  | | 
% 152.83/22.54  | |   (23)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.83/22.54  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.83/22.54  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.54  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.83/22.54  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.83/22.54  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.83/22.54  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.54  | |           $i(all_57_7))
% 152.83/22.54  | | 
% 152.83/22.54  | | REF_CLOSE: (3), (4), (6), (9), (11), (13), (23) are inconsistent by
% 152.83/22.54  | |            sub-proof #1004.
% 152.83/22.54  | | 
% 152.83/22.54  | End of split
% 152.83/22.54  | 
% 152.83/22.54  End of proof
% 152.83/22.54  
% 152.83/22.54  Sub-proof #298 shows that the following formulas are inconsistent:
% 152.83/22.54  ----------------------------------------------------------------
% 152.83/22.54    (1)  op(e0, e2) = all_52_7
% 152.83/22.54    (2)   ~ (all_52_3 = all_52_7)
% 152.83/22.54    (3)   ~ (e2 = e0)
% 152.83/22.54    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.54    (5)  op(e0, e0) = e3
% 152.83/22.54    (6)  op(e0, e3) = e0
% 152.83/22.54    (7)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 152.83/22.54           all_57_14 & $i(all_57_14))
% 152.83/22.54    (8)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 152.83/22.54             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.83/22.54           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.83/22.54           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.83/22.54             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.83/22.54           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.83/22.54           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.83/22.54           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 152.83/22.54           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.83/22.54           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 152.83/22.54           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.83/22.54         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.83/22.54             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.54           $i(all_57_7))
% 152.83/22.54    (9)  op(e0, e1) = e2
% 152.83/22.54    (10)  op(e0, e3) = all_52_3
% 152.83/22.54    (11)  op(e2, e2) = e2
% 152.83/22.54    (12)  op(e0, e0) = all_57_15
% 152.83/22.54    (13)   ~ (e2 = e1)
% 152.83/22.54  
% 152.83/22.54  Begin of proof
% 152.83/22.54  | 
% 152.83/22.54  | BETA: splitting (8) gives:
% 152.83/22.54  | 
% 152.83/22.54  | Case 1:
% 152.83/22.54  | | 
% 152.83/22.54  | |   (14)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 152.83/22.54  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 152.83/22.54  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.83/22.54  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.83/22.54  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 152.83/22.54  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 152.83/22.54  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.83/22.54  | |           $i(all_57_3))
% 152.83/22.54  | | 
% 152.83/22.54  | | BETA: splitting (14) gives:
% 152.83/22.54  | | 
% 152.83/22.54  | | Case 1:
% 152.83/22.54  | | | 
% 152.83/22.54  | | |   (15)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.83/22.54  | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.83/22.54  | | |         op(e0, e3) = e0 & $i(all_57_0)
% 152.83/22.54  | | | 
% 152.83/22.54  | | | ALPHA: (15) implies:
% 152.83/22.54  | | |   (16)   ~ (all_57_15 = e3)
% 152.83/22.54  | | | 
% 152.83/22.54  | | | REF_CLOSE: (4), (5), (12), (16) are inconsistent by sub-proof #1019.
% 152.83/22.54  | | | 
% 152.83/22.54  | | Case 2:
% 152.83/22.54  | | | 
% 152.83/22.54  | | |   (17)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.54  | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.83/22.54  | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 152.83/22.54  | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.83/22.54  | | |           & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 152.83/22.54  | | | 
% 152.83/22.54  | | | BETA: splitting (17) gives:
% 152.83/22.54  | | | 
% 152.83/22.54  | | | Case 1:
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | |   (18)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.54  | | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.83/22.54  | | | |         op(e0, e3) = e0 & $i(all_57_1)
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | | ALPHA: (18) implies:
% 152.83/22.54  | | | |   (19)   ~ (all_57_15 = e3)
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | | REF_CLOSE: (4), (5), (12), (19) are inconsistent by sub-proof #1019.
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | Case 2:
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | |   (20)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.83/22.54  | | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.83/22.54  | | | |         op(e0, e2) = e0 & $i(all_57_3)
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | | ALPHA: (20) implies:
% 152.83/22.54  | | | |   (21)  op(e0, e2) = e0
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | | REF_CLOSE: (1), (2), (4), (6), (10), (21) are inconsistent by sub-proof
% 152.83/22.54  | | | |            #1123.
% 152.83/22.54  | | | | 
% 152.83/22.54  | | | End of split
% 152.83/22.54  | | | 
% 152.83/22.54  | | End of split
% 152.83/22.54  | | 
% 152.83/22.54  | Case 2:
% 152.83/22.54  | | 
% 152.83/22.54  | |   (22)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.83/22.54  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.83/22.54  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.54  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.83/22.54  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.83/22.54  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.83/22.54  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.54  | |           $i(all_57_7))
% 152.83/22.54  | | 
% 152.83/22.54  | | REF_CLOSE: (3), (4), (7), (9), (11), (13), (22) are inconsistent by
% 152.83/22.54  | |            sub-proof #1004.
% 152.83/22.54  | | 
% 152.83/22.54  | End of split
% 152.83/22.54  | 
% 152.83/22.54  End of proof
% 152.83/22.54  
% 152.83/22.54  Sub-proof #299 shows that the following formulas are inconsistent:
% 152.83/22.54  ----------------------------------------------------------------
% 152.83/22.54    (1)  op(e0, e0) = all_10_2
% 152.83/22.54    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.54           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.54    (3)   ~ (all_57_10 = e2)
% 152.83/22.54    (4)  op(e2, e2) = e2
% 152.83/22.54    (5)   ~ (all_10_2 = e2)
% 152.83/22.54    (6)   ~ (e2 = e1)
% 152.83/22.54    (7)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 152.83/22.54             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 152.83/22.54           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 152.83/22.54           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 152.83/22.54             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 152.83/22.54             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 152.83/22.54           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.83/22.54           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.83/22.54           $i(all_57_7) & $i(all_57_10))
% 152.83/22.54  
% 152.83/22.54  Begin of proof
% 152.83/22.54  | 
% 152.83/22.54  | BETA: splitting (7) gives:
% 152.83/22.54  | 
% 152.83/22.54  | Case 1:
% 152.83/22.54  | | 
% 152.83/22.54  | |   (8)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 152.83/22.54  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 152.83/22.54  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 152.83/22.54  | | 
% 152.83/22.54  | | ALPHA: (8) implies:
% 152.83/22.54  | |   (9)  all_57_10 = e2
% 152.83/22.54  | | 
% 152.83/22.54  | | REDUCE: (3), (9) imply:
% 152.83/22.54  | |   (10)  $false
% 152.83/22.54  | | 
% 152.83/22.54  | | CLOSE: (10) is inconsistent.
% 152.83/22.54  | | 
% 152.83/22.54  | Case 2:
% 152.83/22.54  | | 
% 152.83/22.54  | |   (11)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 152.83/22.54  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 152.83/22.54  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 152.83/22.54  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 152.83/22.54  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 152.83/22.54  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.83/22.54  | | 
% 152.83/22.54  | | REF_CLOSE: (1), (2), (4), (5), (6), (11) are inconsistent by sub-proof
% 152.83/22.54  | |            #1084.
% 152.83/22.54  | | 
% 152.83/22.54  | End of split
% 152.83/22.54  | 
% 152.83/22.54  End of proof
% 152.83/22.54  
% 152.83/22.54  Sub-proof #300 shows that the following formulas are inconsistent:
% 152.83/22.54  ----------------------------------------------------------------
% 152.83/22.54    (1)  all_56_8 = e3
% 152.83/22.54    (2)   ~ (e3 = e1)
% 152.83/22.54    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.83/22.54         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.83/22.54    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 152.83/22.54         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.83/22.54    (5)  all_56_11 = e2
% 152.83/22.54    (6)  op(e0, e0) = all_10_2
% 152.83/22.54    (7)  op(e3, e2) = all_52_4
% 152.83/22.54    (8)  op(e0, e2) = all_52_7
% 152.83/22.54    (9)  op(e3, e2) = e3
% 152.83/22.54    (10)   ~ (all_52_3 = all_52_7)
% 152.83/22.54    (11)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.54          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.83/22.54    (12)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.83/22.54          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.54    (13)   ~ (e2 = e0)
% 152.83/22.54    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.54            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.54    (15)  op(e0, e0) = e3
% 152.83/22.54    (16)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 152.83/22.54          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 152.83/22.54    (17)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.83/22.54          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.83/22.54    (18)  op(e3, e3) = e2
% 152.83/22.54    (19)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 152.83/22.54            all_57_14 & $i(all_57_14))
% 152.83/22.54    (20)  all_56_14 = e2
% 152.83/22.54    (21)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.54              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.83/22.54                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.83/22.54                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.83/22.54    (22)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.83/22.54          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.83/22.54    (23)  all_57_3 = e3
% 152.83/22.54    (24)  op(e3, e0) = all_52_12
% 152.83/22.54    (25)   ~ (e3 = e0)
% 152.83/22.54    (26)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 152.83/22.54          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 152.83/22.54    (27)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.83/22.54          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.54    (28)   ~ (all_52_9 = e2)
% 152.83/22.54    (29)  op(e0, e1) = e2
% 152.83/22.54    (30)  op(e0, e3) = all_52_3
% 152.83/22.54    (31)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.83/22.54          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.83/22.54    (32)  op(e2, e2) = e2
% 152.83/22.54    (33)  op(e2, e1) = all_52_9
% 152.83/22.54    (34)   ~ (e1 = e0)
% 152.83/22.54    (35)  all_56_13 = e3
% 152.83/22.54    (36)  op(e1, e1) = e3
% 152.83/22.54    (37)  all_57_12 = e2
% 152.83/22.54    (38)  op(e1, e0) = e2
% 152.83/22.54    (39)   ~ (e3 = e2)
% 152.83/22.54    (40)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.54          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.83/22.54    (41)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.54          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.83/22.54    (42)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.83/22.54          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.54    (43)   ~ (all_10_2 = e2)
% 152.83/22.54    (44)  op(e3, e1) = all_52_8
% 152.83/22.54    (45)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 152.83/22.54          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 152.83/22.54    (46)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.54          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.54    (47)   ~ (e2 = e1)
% 152.83/22.54    (48)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 152.83/22.54            all_57_15 & $i(all_57_15))
% 152.83/22.54    (49)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.54          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.54    (50)  op(e1, e3) = all_52_2
% 152.83/22.55    (51)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.83/22.55              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.83/22.55            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.83/22.55            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.83/22.55            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.83/22.55            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.83/22.55            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.83/22.55            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.83/22.55            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.83/22.55            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.83/22.55            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.83/22.55            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.83/22.55            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.83/22.55            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.83/22.55            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.83/22.55            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.83/22.55            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.83/22.55            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.83/22.55            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.83/22.55            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.83/22.55            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.83/22.55            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.83/22.55            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.83/22.55            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.83/22.55            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.55            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.83/22.55            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.83/22.55            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.55            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.55            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.83/22.55            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.83/22.55            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.83/22.55            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.83/22.55            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.83/22.55            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.55            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.83/22.55            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.55            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.83/22.55            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.83/22.55            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.55            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.83/22.55            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.83/22.55            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.55            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.83/22.55            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.83/22.55            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.55            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.83/22.55            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.83/22.55              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.83/22.55            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.83/22.55            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.83/22.55              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.83/22.55            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.83/22.55            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.83/22.55                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.83/22.55                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.83/22.55                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.83/22.55                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.83/22.55                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.83/22.55                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.83/22.55                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.83/22.55              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.83/22.55                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.83/22.55                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.55                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.83/22.55                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.83/22.55                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.83/22.55                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.55                $i(all_57_7))))
% 152.83/22.55    (52)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.83/22.55          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.83/22.55    (53)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.55          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.83/22.55            e1)
% 152.83/22.55    (54)  op(e2, e3) = all_52_1
% 152.83/22.55  
% 152.83/22.55  Begin of proof
% 152.83/22.55  | 
% 152.83/22.55  | BETA: splitting (48) gives:
% 152.83/22.55  | 
% 152.83/22.55  | Case 1:
% 152.83/22.55  | | 
% 152.83/22.55  | |   (55)  all_57_5 = e0 & op(e0, e2) = e0
% 152.83/22.55  | | 
% 152.83/22.55  | | REF_CLOSE: (8), (10), (13), (14), (15), (21), (25), (29), (30), (35), (55)
% 152.83/22.55  | |            are inconsistent by sub-proof #313.
% 152.83/22.55  | | 
% 152.83/22.55  | Case 2:
% 152.83/22.55  | | 
% 152.83/22.55  | |   (56)   ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)
% 152.83/22.55  | | 
% 152.83/22.55  | | ALPHA: (56) implies:
% 152.83/22.55  | |   (57)   ~ (all_57_15 = e2)
% 152.83/22.55  | |   (58)  op(e0, e0) = all_57_15
% 152.83/22.55  | | 
% 152.83/22.55  | | BETA: splitting (4) gives:
% 152.83/22.55  | | 
% 152.83/22.55  | | Case 1:
% 152.83/22.55  | | | 
% 152.83/22.55  | | |   (59)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 152.83/22.55  | | |           e3)
% 152.83/22.55  | | | 
% 152.83/22.55  | | | BETA: splitting (59) gives:
% 152.83/22.55  | | | 
% 152.83/22.55  | | | Case 1:
% 152.83/22.55  | | | | 
% 152.83/22.55  | | | |   (60)  all_56_0 = e3 & op(e3, e3) = e3
% 152.83/22.55  | | | | 
% 152.83/22.55  | | | | ALPHA: (60) implies:
% 152.83/22.55  | | | |   (61)  op(e3, e3) = e3
% 152.83/22.55  | | | | 
% 152.83/22.55  | | | | REF_CLOSE: (14), (18), (39), (61) are inconsistent by sub-proof #1085.
% 152.83/22.55  | | | | 
% 152.83/22.55  | | | Case 2:
% 152.83/22.55  | | | | 
% 152.83/22.55  | | | |   (62)  all_56_2 = e3 & op(e2, e3) = e3
% 152.83/22.55  | | | | 
% 152.83/22.55  | | | | ALPHA: (62) implies:
% 152.83/22.55  | | | |   (63)  all_56_2 = e3
% 152.83/22.55  | | | |   (64)  op(e2, e3) = e3
% 152.83/22.55  | | | | 
% 152.83/22.55  | | | | BETA: splitting (16) gives:
% 152.83/22.55  | | | | 
% 152.83/22.55  | | | | Case 1:
% 152.83/22.55  | | | | | 
% 152.83/22.55  | | | | |   (65)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3,
% 152.83/22.55  | | | | |             e2) = e3)
% 152.83/22.55  | | | | | 
% 152.83/22.55  | | | | | BETA: splitting (65) gives:
% 152.83/22.55  | | | | | 
% 152.83/22.55  | | | | | Case 1:
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | |   (66)  all_56_0 = e3 & op(e3, e3) = e3
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | | ALPHA: (66) implies:
% 152.83/22.55  | | | | | |   (67)  op(e3, e3) = e3
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | | REF_CLOSE: (14), (18), (39), (67) are inconsistent by sub-proof
% 152.83/22.55  | | | | | |            #1085.
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | Case 2:
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | |   (68)  all_56_1 = e3 & op(e3, e2) = e3
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | | ALPHA: (68) implies:
% 152.83/22.55  | | | | | |   (69)  all_56_1 = e3
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | | REF_CLOSE: (1), (2), (5), (6), (11), (13), (14), (17), (18), (19),
% 152.83/22.55  | | | | | |            (22), (23), (25), (27), (28), (29), (31), (32), (33),
% 152.83/22.55  | | | | | |            (34), (36), (37), (38), (39), (40), (41), (43), (45),
% 152.83/22.55  | | | | | |            (46), (47), (49), (51), (52), (54), (62), (63), (69) are
% 152.83/22.55  | | | | | |            inconsistent by sub-proof #336.
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | End of split
% 152.83/22.55  | | | | | 
% 152.83/22.55  | | | | Case 2:
% 152.83/22.55  | | | | | 
% 152.83/22.55  | | | | |   (70)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3,
% 152.83/22.55  | | | | |             e0) = e3)
% 152.83/22.55  | | | | | 
% 152.83/22.55  | | | | | BETA: splitting (70) gives:
% 152.83/22.55  | | | | | 
% 152.83/22.55  | | | | | Case 1:
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | |   (71)  all_56_4 = e3 & op(e3, e1) = e3
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | | ALPHA: (71) implies:
% 152.83/22.55  | | | | | |   (72)  all_56_4 = e3
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | | REF_CLOSE: (1), (2), (11), (12), (13), (14), (20), (25), (31), (32),
% 152.83/22.55  | | | | | |            (34), (39), (40), (42), (47), (63), (72) are inconsistent
% 152.83/22.55  | | | | | |            by sub-proof #312.
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | Case 2:
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | |   (73)  all_56_9 = e3 & op(e3, e0) = e3
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | | ALPHA: (73) implies:
% 152.83/22.55  | | | | | |   (74)  all_56_9 = e3
% 152.83/22.55  | | | | | |   (75)  op(e3, e0) = e3
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | | BETA: splitting (26) gives:
% 152.83/22.55  | | | | | | 
% 152.83/22.55  | | | | | | Case 1:
% 152.83/22.55  | | | | | | | 
% 152.83/22.55  | | | | | | |   (76)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 &
% 152.83/22.55  | | | | | | |           op(e2, e0) = e1)
% 152.83/22.55  | | | | | | | 
% 152.83/22.55  | | | | | | | BETA: splitting (76) gives:
% 152.83/22.55  | | | | | | | 
% 152.83/22.55  | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | |   (77)  all_56_9 = e1 & op(e3, e0) = e1
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | | ALPHA: (77) implies:
% 152.83/22.55  | | | | | | | |   (78)  all_56_9 = e1
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | | REF_CLOSE: (2), (74), (78) are inconsistent by sub-proof #1064.
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | |   (79)  all_56_10 = e1 & op(e2, e0) = e1
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | | REF_CLOSE: (2), (3), (5), (11), (13), (14), (15), (18), (20),
% 152.83/22.55  | | | | | | | |            (21), (24), (25), (27), (31), (32), (34), (35), (36),
% 152.83/22.55  | | | | | | | |            (39), (42), (46), (47), (49), (50), (53), (63), (75),
% 152.83/22.55  | | | | | | | |            (79) are inconsistent by sub-proof #306.
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | End of split
% 152.83/22.55  | | | | | | | 
% 152.83/22.55  | | | | | | Case 2:
% 152.83/22.55  | | | | | | | 
% 152.83/22.55  | | | | | | |   (80)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 &
% 152.83/22.55  | | | | | | |           op(e0, e0) = e1)
% 152.83/22.55  | | | | | | | 
% 152.83/22.55  | | | | | | | BETA: splitting (80) gives:
% 152.83/22.55  | | | | | | | 
% 152.83/22.55  | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | |   (81)  all_56_11 = e1 & op(e1, e0) = e1
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | | ALPHA: (81) implies:
% 152.83/22.55  | | | | | | | |   (82)  op(e1, e0) = e1
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | | REF_CLOSE: (14), (38), (47), (82) are inconsistent by sub-proof
% 152.83/22.55  | | | | | | | |            #1125.
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | |   (83)  all_56_15 = e1 & op(e0, e0) = e1
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | | ALPHA: (83) implies:
% 152.83/22.55  | | | | | | | |   (84)  op(e0, e0) = e1
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | | BETA: splitting (21) gives:
% 152.83/22.55  | | | | | | | | 
% 152.83/22.55  | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | 
% 152.83/22.55  | | | | | | | | |   (85)  all_56_15 = e0 & op(e0, e0) = e0
% 152.83/22.55  | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | ALPHA: (85) implies:
% 152.83/22.55  | | | | | | | | |   (86)  op(e0, e0) = e0
% 152.83/22.55  | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | REF_CLOSE: (14), (15), (25), (86) are inconsistent by
% 152.83/22.55  | | | | | | | | |            sub-proof #1143.
% 152.83/22.55  | | | | | | | | | 
% 152.83/22.55  | | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | | 
% 152.83/22.55  | | | | | | | | |   (87)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 &
% 152.83/22.55  | | | | | | | | |             op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 152.83/22.55  | | | | | | | | |             e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) |
% 152.83/22.55  | | | | | | | | |           (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0
% 152.83/22.55  | | | | | | | | |             & op(e0, e1) = e0))
% 152.83/22.55  | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | ALPHA: (87) implies:
% 152.83/22.55  | | | | | | | | |   (88)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.83/22.55  | | | | | | | | |           op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 152.83/22.55  | | | | | | | | |           e0)
% 152.83/22.55  | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | BETA: splitting (51) gives:
% 152.83/22.55  | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | |   (89)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 152.83/22.55  | | | | | | | | | |           &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.83/22.55  | | | | | | | | | |             e2) = all_57_12 & op(e1, e3) = all_57_1 & op(e1,
% 152.83/22.55  | | | | | | | | | |             e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 152.83/22.55  | | | | | | | | | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0)
% 152.83/22.55  | | | | | | | | | |           &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2,
% 152.83/22.55  | | | | | | | | | |             e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0,
% 152.83/22.55  | | | | | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 152.83/22.55  | | | | | | | | | |         (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2)
% 152.83/22.55  | | | | | | | | | |           &  ~ (all_57_14 = e3) & op(e2, e3) = all_57_0 &
% 152.83/22.55  | | | | | | | | | |           op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.83/22.55  | | | | | | | | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.83/22.55  | | | | | | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0)
% 152.83/22.55  | | | | | | | | | |           &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1,
% 152.83/22.55  | | | | | | | | | |             e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 152.83/22.55  | | | | | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_14)) |
% 152.83/22.55  | | | | | | | | | |         (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1)
% 152.83/22.55  | | | | | | | | | |           &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.83/22.55  | | | | | | | | | |           op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 152.83/22.55  | | | | | | | | | |             e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 152.83/22.55  | | | | | | | | | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.83/22.55  | | | | | | | | | |           &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.83/22.55  | | | | | | | | | |           op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 152.83/22.55  | | | | | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 152.83/22.55  | | | | | | | | | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3)
% 152.83/22.55  | | | | | | | | | |           &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3,
% 152.83/22.55  | | | | | | | | | |             e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.83/22.55  | | | | | | | | | |           all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.83/22.55  | | | | | | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.83/22.55  | | | | | | | | | |           &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1,
% 152.83/22.55  | | | | | | | | | |             e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 152.83/22.55  | | | | | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 152.83/22.55  | | | | | | | | | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.83/22.55  | | | | | | | | | |           &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 152.83/22.55  | | | | | | | | | |           op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 152.83/22.55  | | | | | | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.83/22.55  | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | BETA: splitting (89) gives:
% 152.83/22.55  | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | |   (90)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.83/22.55  | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.83/22.55  | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 152.83/22.55  | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 152.83/22.55  | | | | | | | | | | |         | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 152.83/22.55  | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.83/22.55  | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.83/22.55  | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.83/22.55  | | | | | | | | | | |         | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.83/22.55  | | | | | | | | | | |             e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.83/22.55  | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.83/22.55  | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) &
% 152.83/22.55  | | | | | | | | | | |           $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 152.83/22.55  | | | | | | | | | | |           &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 152.83/22.55  | | | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.83/22.55  | | | | | | | | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.83/22.55  | | | | | | | | | | |           $i(all_57_2) & $i(all_57_14))
% 152.83/22.55  | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | BETA: splitting (90) gives:
% 152.83/22.55  | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | |   (91)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.83/22.55  | | | | | | | | | | | |             e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.83/22.55  | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 152.83/22.55  | | | | | | | | | | | |           op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 152.83/22.55  | | | | | | | | | | | |         | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 152.83/22.55  | | | | | | | | | | | |             e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.83/22.55  | | | | | | | | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.83/22.55  | | | | | | | | | | | |           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.83/22.55  | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | BETA: splitting (91) gives:
% 152.83/22.55  | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | |   (92)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.83/22.55  | | | | | | | | | | | | |           e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.83/22.55  | | | | | | | | | | | | |         op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 152.83/22.55  | | | | | | | | | | | | |         op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | ALPHA: (92) implies:
% 152.83/22.55  | | | | | | | | | | | | |   (93)  op(e2, e3) = e2
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (7), (9), (13), (14), (15), (18),
% 152.83/22.55  | | | | | | | | | | | | |            (20), (25), (32), (34), (35), (36), (46), (47),
% 152.83/22.55  | | | | | | | | | | | | |            (49), (50), (54), (64), (84), (88), (93) are
% 152.83/22.55  | | | | | | | | | | | | |            inconsistent by sub-proof #305.
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | |   (94)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 152.83/22.55  | | | | | | | | | | | | |           e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.83/22.55  | | | | | | | | | | | | |         op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.83/22.55  | | | | | | | | | | | | |         op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | ALPHA: (94) implies:
% 152.83/22.55  | | | | | | | | | | | | |   (95)  all_57_15 = e3
% 152.83/22.55  | | | | | | | | | | | | |   (96)  op(e2, e2) = all_57_12
% 152.83/22.55  | | | | | | | | | | | | |   (97)  op(e2, e3) = e2
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | REF_CLOSE: (2), (3), (5), (7), (9), (13), (14), (15), (18),
% 152.83/22.55  | | | | | | | | | | | | |            (20), (25), (32), (34), (35), (36), (46), (47),
% 152.83/22.55  | | | | | | | | | | | | |            (49), (50), (54), (64), (84), (88), (97) are
% 152.83/22.55  | | | | | | | | | | | | |            inconsistent by sub-proof #305.
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | End of split
% 152.83/22.55  | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | |   (98)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.83/22.55  | | | | | | | | | | | |             e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.83/22.55  | | | | | | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.83/22.55  | | | | | | | | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) &
% 152.83/22.55  | | | | | | | | | | | |           $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 152.83/22.55  | | | | | | | | | | | |           &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 152.83/22.55  | | | | | | | | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.83/22.55  | | | | | | | | | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.83/22.55  | | | | | | | | | | | |           $i(all_57_2) & $i(all_57_14))
% 152.83/22.55  | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | REF_CLOSE: (14), (36), (98) are inconsistent by sub-proof
% 152.83/22.55  | | | | | | | | | | | |            #368.
% 152.83/22.55  | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | End of split
% 152.83/22.55  | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | |   (99)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 152.83/22.55  | | | | | | | | | | |             e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.83/22.55  | | | | | | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 152.83/22.55  | | | | | | | | | | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 152.83/22.55  | | | | | | | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 152.83/22.55  | | | | | | | | | | |           &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 152.83/22.55  | | | | | | | | | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.83/22.55  | | | | | | | | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.83/22.55  | | | | | | | | | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 152.83/22.55  | | | | | | | | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.83/22.55  | | | | | | | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.83/22.55  | | | | | | | | | | |           = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.83/22.55  | | | | | | | | | | |           all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.83/22.55  | | | | | | | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 152.83/22.55  | | | | | | | | | | |             e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 152.83/22.55  | | | | | | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 152.83/22.55  | | | | | | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 152.83/22.55  | | | | | | | | | | |         | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 152.83/22.55  | | | | | | | | | | |             e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.83/22.55  | | | | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 152.83/22.55  | | | | | | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.83/22.55  | | | | | | | | | | |           $i(all_57_10))
% 152.83/22.55  | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | REF_CLOSE: (6), (14), (19), (23), (32), (43), (47), (99) are
% 152.83/22.55  | | | | | | | | | | |            inconsistent by sub-proof #339.
% 152.83/22.55  | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | End of split
% 152.83/22.55  | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | |   (100)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.83/22.55  | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.83/22.55  | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.83/22.55  | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.55  | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 152.83/22.55  | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 152.83/22.55  | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 152.83/22.55  | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 152.83/22.55  | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.83/22.55  | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.83/22.55  | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.83/22.55  | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 152.83/22.55  | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.83/22.55  | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 152.83/22.55  | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 152.83/22.55  | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.83/22.55  | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.83/22.55  | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 152.83/22.55  | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 152.83/22.55  | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1,
% 152.83/22.55  | | | | | | | | | |              e1) = e0 & op(e1, e0) = all_57_13 &
% 152.83/22.55  | | | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 152.83/22.55  | | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 152.83/22.55  | | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 152.83/22.55  | | | | | | | | | |            all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.83/22.55  | | | | | | | | | |            e2 & $i(all_57_9) & $i(all_57_12)) | (all_57_10 =
% 152.83/22.55  | | | | | | | | | |            e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 152.83/22.55  | | | | | | | | | |            (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 152.83/22.55  | | | | | | | | | |            all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 152.83/22.55  | | | | | | | | | |            e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 =
% 152.83/22.55  | | | | | | | | | |            e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 152.83/22.55  | | | | | | | | | |            (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 152.83/22.55  | | | | | | | | | |            op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 152.83/22.55  | | | | | | | | | |            all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 152.83/22.55  | | | | | | | | | |          (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.83/22.55  | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.83/22.55  | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 152.83/22.55  | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14))
% 152.83/22.55  | | | | | | | | | |          | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.83/22.55  | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 152.83/22.55  | | | | | | | | | |                  e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.83/22.55  | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 152.83/22.55  | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 152.83/22.55  | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.83/22.55  | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.83/22.55  | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.83/22.55  | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 152.83/22.55  | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 152.83/22.55  | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 152.83/22.55  | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.83/22.55  | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.83/22.55  | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 152.83/22.55  | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.83/22.55  | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 152.83/22.55  | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 152.83/22.55  | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 152.83/22.55  | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 152.83/22.55  | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.83/22.55  | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.83/22.55  | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.83/22.55  | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | BETA: splitting (100) gives:
% 152.83/22.55  | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | |   (101)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.83/22.55  | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.83/22.55  | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.83/22.55  | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.55  | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 152.83/22.55  | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 152.83/22.55  | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 152.83/22.55  | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 152.83/22.55  | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.83/22.55  | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.83/22.55  | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 152.83/22.55  | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 152.83/22.55  | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.83/22.55  | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 152.83/22.55  | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 152.83/22.55  | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.83/22.55  | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.83/22.55  | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 152.83/22.55  | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 152.83/22.55  | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.55  | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.83/22.55  | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 152.83/22.55  | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | BETA: splitting (101) gives:
% 152.83/22.55  | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | |   (102)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.83/22.55  | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.83/22.55  | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.83/22.55  | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.55  | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 152.83/22.55  | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 152.83/22.55  | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 152.83/22.55  | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 152.83/22.55  | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 152.83/22.55  | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | BETA: splitting (102) gives:
% 152.83/22.55  | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | |   (103)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.83/22.55  | | | | | | | | | | | | |            e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.83/22.55  | | | | | | | | | | | | |          all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.83/22.55  | | | | | | | | | | | | |          all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.55  | | | | | | | | | | | | |          $i(all_57_10)
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | ALPHA: (103) implies:
% 152.83/22.55  | | | | | | | | | | | | |   (104)  all_57_15 = e1
% 152.83/22.55  | | | | | | | | | | | | |   (105)  op(e3, e1) = e3
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | REDUCE: (57), (104) imply:
% 152.83/22.55  | | | | | | | | | | | | |   (106)   ~ (e2 = e1)
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | BETA: splitting (3) gives:
% 152.83/22.55  | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | |   (107)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1
% 152.83/22.55  | | | | | | | | | | | | | |            & op(e2, e3) = e1)
% 152.83/22.55  | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | REF_CLOSE: (2), (14), (18), (47), (63), (107) are
% 152.83/22.55  | | | | | | | | | | | | | |            inconsistent by sub-proof #310.
% 152.83/22.55  | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | |   (108)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 =
% 152.83/22.55  | | | | | | | | | | | | | |            e1 & op(e0, e3) = e1)
% 152.83/22.55  | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | BETA: splitting (108) gives:
% 152.83/22.55  | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | |   (109)  all_56_6 = e1 & op(e1, e3) = e1
% 152.83/22.55  | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 152.83/22.55  | | | | | | | | | | | | | | |   (110)  op(e1, e3) = e1
% 152.83/22.55  | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | BETA: splitting (40) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | |   (111)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 152.83/22.55  | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 152.83/22.55  | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | |   (112)  all_56_2 = e1 & op(e2, e3) = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 152.83/22.55  | | | | | | | | | | | | | | | | |   (113)  all_56_2 = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (63), (113) are inconsistent by sub-proof
% 152.83/22.55  | | | | | | | | | | | | | | | | |            #1053.
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | |   (114)  all_56_3 = e1 & op(e2, e2) = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | ALPHA: (114) implies:
% 152.83/22.55  | | | | | | | | | | | | | | | | |   (115)  op(e2, e2) = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (32), (47), (115) are inconsistent by
% 152.83/22.55  | | | | | | | | | | | | | | | | |            sub-proof #1158.
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | End of split
% 152.83/22.55  | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | |   (116)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 152.83/22.55  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 152.83/22.55  | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | |   (117)  all_56_5 = e1 & op(e2, e1) = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 152.83/22.55  | | | | | | | | | | | | | | | | |   (118)  all_56_5 = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | |   (119)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e1)
% 152.83/22.55  | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | |   (120)  all_56_1 = e1 & op(e3, e2) = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | |   (121)  all_56_1 = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | | |   (122)  op(e3, e2) = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | |   (123)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | |            & op(e3, e2) = e0)
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (13), (14), (18), (20), (34), (36), (42),
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | |            (44), (47), (105), (118), (121), (123) are
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #304.
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | |   (124)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = e0)
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | |   (125)  all_56_4 = e0 & op(e3, e1) = e0
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | |   (126)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e1)
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |   (127)  all_56_4 = e1 & op(e3, e1) = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |   (128)  op(e3, e1) = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (14), (44), (105), (128) are inconsistent by
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #439.
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |   (129)  op(e3, e1) = e0
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_52_8, e0, e1, e3,
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (44), (129) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |   (130)  all_52_8 = e0
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_52_8, e3, e1, e3,
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (44), (105) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |   (131)  all_52_8 = e3
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_52_4, e1, e2, e3,
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (7), (122) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |   (132)  all_52_4 = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (14) with all_52_4, e3, e2, e3,
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |              simplifying with (7), (9) gives:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |   (133)  all_52_4 = e3
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (132), (133) imply:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |   (134)  e3 = e1
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (130), (131) imply:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |   (135)  e3 = e0
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | SIMP: (135) implies:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |   (136)  e3 = e0
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (14), (20), (34), (36), (42), (44), (47),
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |            (105), (118), (134), (136) are inconsistent by
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #303.
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | End of split
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | |   (137)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 =
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e1) = e1)
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (14), (20), (36), (47), (137) are
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #326.
% 152.83/22.55  | | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | | Case 2:
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | | |   (138)  all_56_9 = e0 & op(e3, e0) = e0
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (15), (24), (34), (75), (84), (138) are
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #323.
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | Case 2:
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | |   (139)  all_56_3 = e1 & op(e2, e2) = e1
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 152.83/22.56  | | | | | | | | | | | | | | | | | | |   (140)  op(e2, e2) = e1
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (32), (47), (140) are inconsistent by
% 152.83/22.56  | | | | | | | | | | | | | | | | | | |            sub-proof #1158.
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | Case 2:
% 152.83/22.56  | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | |   (141)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 =
% 152.83/22.56  | | | | | | | | | | | | | | | | | |            e1 & op(e0, e2) = e1)
% 152.83/22.56  | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 152.83/22.56  | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | Case 1:
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | |   (142)  all_56_7 = e1 & op(e1, e2) = e1
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (14), (15), (34), (36), (46), (50),
% 152.83/22.56  | | | | | | | | | | | | | | | | | | |            (84), (110), (142) are inconsistent by sub-proof
% 152.83/22.56  | | | | | | | | | | | | | | | | | | |            #329.
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | Case 2:
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | |   (143)  all_56_13 = e1 & op(e0, e2) = e1
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (35), (143) are inconsistent by sub-proof
% 152.83/22.56  | | | | | | | | | | | | | | | | | | |            #878.
% 152.83/22.56  | | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | Case 2:
% 152.83/22.56  | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | |   (144)  all_56_10 = e1 & op(e2, e0) = e1
% 152.83/22.56  | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 152.83/22.56  | | | | | | | | | | | | | | | | |   (145)  all_56_10 = e1
% 152.83/22.56  | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (11), (13), (14), (15), (18), (20),
% 152.83/22.56  | | | | | | | | | | | | | | | | |            (24), (25), (27), (31), (32), (34), (35), (36),
% 152.83/22.56  | | | | | | | | | | | | | | | | |            (39), (42), (46), (47), (49), (50), (75), (84),
% 152.83/22.56  | | | | | | | | | | | | | | | | |            (110), (145) are inconsistent by sub-proof #308.
% 152.83/22.56  | | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | Case 2:
% 152.83/22.56  | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | |   (146)  all_56_12 = e1 & op(e0, e3) = e1
% 152.83/22.56  | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 152.83/22.56  | | | | | | | | | | | | | | |   (147)  all_56_12 = e1
% 152.83/22.56  | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | | REF_CLOSE: (13), (20), (25), (34), (35), (88), (147) are
% 152.83/22.56  | | | | | | | | | | | | | | |            inconsistent by sub-proof #1100.
% 152.83/22.56  | | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | Case 2:
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | |   (148)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 152.83/22.56  | | | | | | | | | | | | |            e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 152.83/22.56  | | | | | | | | | | | | |          op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 152.83/22.56  | | | | | | | | | | | | |          op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | ALPHA: (148) implies:
% 152.83/22.56  | | | | | | | | | | | | |   (149)  op(e2, e1) = e2
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | REF_CLOSE: (14), (28), (33), (149) are inconsistent by
% 152.83/22.56  | | | | | | | | | | | | |            sub-proof #1157.
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | Case 2:
% 152.83/22.56  | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | |   (150)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 152.83/22.56  | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 152.83/22.56  | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.83/22.56  | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.56  | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 152.83/22.56  | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 152.83/22.56  | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.56  | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.83/22.56  | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 152.83/22.56  | | | | | | | | | | | |            & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.83/22.56  | | | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 152.83/22.56  | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.83/22.56  | | | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.83/22.56  | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (28), (32), (33), (34), (36),
% 152.83/22.56  | | | | | | | | | | | |            (84), (150) are inconsistent by sub-proof #302.
% 152.83/22.56  | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | Case 2:
% 152.83/22.56  | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | |   (151)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 152.83/22.56  | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 152.83/22.56  | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 152.83/22.56  | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 152.83/22.56  | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 152.83/22.56  | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 152.83/22.56  | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 152.83/22.56  | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 152.83/22.56  | | | | | | | | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 152.83/22.56  | | | | | | | | | | |            e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 152.83/22.56  | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.83/22.56  | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.83/22.56  | | | | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 152.83/22.56  | | | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 152.83/22.56  | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 152.83/22.56  | | | | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 152.83/22.56  | | | | | | | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 152.83/22.56  | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.83/22.56  | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 152.83/22.56  | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.83/22.56  | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 152.83/22.56  | | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 152.83/22.56  | | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.83/22.56  | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.83/22.56  | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.83/22.56  | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 152.83/22.56  | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 152.83/22.56  | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 152.83/22.56  | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.83/22.56  | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.83/22.56  | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 152.83/22.56  | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.83/22.56  | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 152.83/22.56  | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 152.83/22.56  | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 152.83/22.56  | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 152.83/22.56  | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.83/22.56  | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.83/22.56  | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.83/22.56  | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | BETA: splitting (151) gives:
% 152.83/22.56  | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | Case 1:
% 152.83/22.56  | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | |   (152)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 152.83/22.56  | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 152.83/22.56  | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 152.83/22.56  | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 152.83/22.56  | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 152.83/22.56  | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 152.83/22.56  | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 152.83/22.56  | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 152.83/22.56  | | | | | | | | | | | |            $i(all_57_14))
% 152.83/22.56  | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | REF_CLOSE: (13), (14), (18), (152) are inconsistent by
% 152.83/22.56  | | | | | | | | | | | |            sub-proof #1037.
% 152.83/22.56  | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | Case 2:
% 152.83/22.56  | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | |   (153)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.83/22.56  | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.83/22.56  | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.83/22.56  | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.83/22.56  | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 152.83/22.56  | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.83/22.56  | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.83/22.56  | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.83/22.56  | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.83/22.56  | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.83/22.56  | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.83/22.56  | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 152.83/22.56  | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.83/22.56  | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 152.83/22.56  | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.83/22.56  | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.83/22.56  | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.83/22.56  | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 152.83/22.56  | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 152.83/22.56  | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 152.83/22.56  | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.83/22.56  | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.83/22.56  | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 152.83/22.56  | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.83/22.56  | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 152.83/22.56  | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 152.83/22.56  | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 152.83/22.56  | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 152.83/22.56  | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.83/22.56  | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.83/22.56  | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.83/22.56  | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | BETA: splitting (153) gives:
% 152.83/22.56  | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | Case 1:
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | |   (154)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.83/22.56  | | | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.83/22.56  | | | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.83/22.56  | | | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.83/22.56  | | | | | | | | | | | | |          $i(all_57_13)
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | ALPHA: (154) implies:
% 152.83/22.56  | | | | | | | | | | | | |   (155)  op(e1, e1) = e0
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | REF_CLOSE: (14), (15), (34), (36), (84), (155) are
% 152.83/22.56  | | | | | | | | | | | | |            inconsistent by sub-proof #331.
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | Case 2:
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | |   (156)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.83/22.56  | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.83/22.56  | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 152.83/22.56  | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 152.83/22.56  | | | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 152.83/22.56  | | | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 152.83/22.56  | | | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.83/22.56  | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.83/22.56  | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 152.83/22.56  | | | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 152.83/22.56  | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 152.83/22.56  | | | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.83/22.56  | | | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 152.83/22.56  | | | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 152.83/22.56  | | | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.83/22.56  | | | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.83/22.56  | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 152.83/22.56  | | | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.83/22.56  | | | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 152.83/22.56  | | | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 152.83/22.56  | | | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 152.83/22.56  | | | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.83/22.56  | | | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.83/22.56  | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 152.83/22.56  | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 152.83/22.56  | | | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 152.83/22.56  | | | | | | | | | | | | |                & $i(all_57_7))))
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | | REF_CLOSE: (13), (14), (15), (19), (23), (29), (32), (38),
% 152.83/22.56  | | | | | | | | | | | | |            (39), (47), (156) are inconsistent by sub-proof
% 152.83/22.56  | | | | | | | | | | | | |            #1002.
% 152.83/22.56  | | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | | 
% 152.83/22.56  | | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | | 
% 152.83/22.56  | | | | | | | | End of split
% 152.83/22.56  | | | | | | | | 
% 152.83/22.56  | | | | | | | End of split
% 152.83/22.56  | | | | | | | 
% 152.83/22.56  | | | | | | End of split
% 152.83/22.56  | | | | | | 
% 152.83/22.56  | | | | | End of split
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | End of split
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | End of split
% 152.83/22.56  | | | 
% 152.83/22.56  | | Case 2:
% 152.83/22.56  | | | 
% 152.83/22.56  | | |   (157)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3)
% 152.83/22.56  | | |            = e3)
% 152.83/22.56  | | | 
% 152.83/22.56  | | | REF_CLOSE: (1), (2), (5), (13), (14), (15), (17), (20), (21), (25), (29),
% 152.83/22.56  | | |            (30), (34), (35), (46), (47), (53), (58), (157) are
% 152.83/22.56  | | |            inconsistent by sub-proof #301.
% 152.83/22.56  | | | 
% 152.83/22.56  | | End of split
% 152.83/22.56  | | 
% 152.83/22.56  | End of split
% 152.83/22.56  | 
% 152.83/22.56  End of proof
% 152.83/22.56  
% 152.83/22.56  Sub-proof #301 shows that the following formulas are inconsistent:
% 152.83/22.56  ----------------------------------------------------------------
% 152.83/22.56    (1)  all_56_8 = e3
% 152.83/22.56    (2)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.83/22.56    (3)   ~ (e3 = e1)
% 152.83/22.56    (4)  all_56_11 = e2
% 152.83/22.56    (5)   ~ (e2 = e0)
% 152.83/22.56    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.56    (7)  op(e0, e0) = e3
% 152.83/22.56    (8)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.83/22.56         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.83/22.56    (9)  all_56_14 = e2
% 152.83/22.56    (10)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.56              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.83/22.56                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.83/22.56                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.83/22.56    (11)   ~ (e3 = e0)
% 152.83/22.56    (12)  op(e0, e1) = e2
% 152.83/22.56    (13)  op(e0, e3) = all_52_3
% 152.83/22.56    (14)   ~ (e1 = e0)
% 152.83/22.56    (15)  all_56_13 = e3
% 152.83/22.56    (16)  op(e0, e0) = all_57_15
% 152.83/22.56    (17)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.56          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.56    (18)   ~ (e2 = e1)
% 152.83/22.56    (19)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.56          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.83/22.56            e1)
% 152.83/22.56  
% 152.83/22.56  Begin of proof
% 152.83/22.56  | 
% 152.83/22.56  | BETA: splitting (2) gives:
% 152.83/22.56  | 
% 152.83/22.56  | Case 1:
% 152.83/22.56  | | 
% 152.83/22.56  | |   (20)  all_56_6 = e3 & op(e1, e3) = e3
% 152.83/22.56  | | 
% 152.83/22.56  | | ALPHA: (20) implies:
% 152.83/22.56  | |   (21)  all_56_6 = e3
% 152.83/22.56  | | 
% 152.83/22.56  | | REF_CLOSE: (1), (3), (4), (5), (8), (11), (14), (17), (18), (21) are
% 152.83/22.56  | |            inconsistent by sub-proof #608.
% 152.83/22.56  | | 
% 152.83/22.56  | Case 2:
% 152.83/22.56  | | 
% 152.83/22.56  | |   (22)  all_56_12 = e3 & op(e0, e3) = e3
% 152.83/22.56  | | 
% 152.83/22.56  | | ALPHA: (22) implies:
% 152.83/22.56  | |   (23)  all_56_12 = e3
% 152.83/22.56  | |   (24)  op(e0, e3) = e3
% 152.83/22.56  | | 
% 152.83/22.56  | | BETA: splitting (19) gives:
% 152.83/22.56  | | 
% 152.83/22.56  | | Case 1:
% 152.83/22.56  | | | 
% 152.83/22.56  | | |   (25)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2)
% 152.83/22.56  | | |           = e1)
% 152.83/22.56  | | | 
% 152.83/22.56  | | | BETA: splitting (25) gives:
% 152.83/22.56  | | | 
% 152.83/22.56  | | | Case 1:
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | |   (26)  all_56_12 = e1 & op(e0, e3) = e1
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | ALPHA: (26) implies:
% 152.83/22.56  | | | |   (27)  all_56_12 = e1
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | COMBINE_EQS: (23), (27) imply:
% 152.83/22.56  | | | |   (28)  e3 = e1
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | COMBINE_EQS: (15), (28) imply:
% 152.83/22.56  | | | |   (29)  all_56_13 = e1
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | REF_CLOSE: (5), (6), (7), (10), (11), (12), (14), (23), (29) are
% 152.83/22.56  | | | |            inconsistent by sub-proof #335.
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | Case 2:
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | |   (30)  all_56_13 = e1 & op(e0, e2) = e1
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | ALPHA: (30) implies:
% 152.83/22.56  | | | |   (31)  all_56_13 = e1
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | REF_CLOSE: (5), (6), (7), (10), (11), (12), (14), (23), (31) are
% 152.83/22.56  | | | |            inconsistent by sub-proof #335.
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | End of split
% 152.83/22.56  | | | 
% 152.83/22.56  | | Case 2:
% 152.83/22.56  | | | 
% 152.83/22.56  | | |   (32)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0)
% 152.83/22.56  | | |           = e1)
% 152.83/22.56  | | | 
% 152.83/22.56  | | | BETA: splitting (32) gives:
% 152.83/22.56  | | | 
% 152.83/22.56  | | | Case 1:
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | |   (33)  all_56_14 = e1 & op(e0, e1) = e1
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | REF_CLOSE: (9), (18), (33) are inconsistent by sub-proof #357.
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | Case 2:
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | |   (34)  all_56_15 = e1 & op(e0, e0) = e1
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | ALPHA: (34) implies:
% 152.83/22.56  | | | |   (35)  op(e0, e0) = e1
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | BETA: splitting (10) gives:
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | Case 1:
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | |   (36)  all_56_15 = e0 & op(e0, e0) = e0
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | | ALPHA: (36) implies:
% 152.83/22.56  | | | | |   (37)  op(e0, e0) = e0
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | | REF_CLOSE: (6), (7), (11), (37) are inconsistent by sub-proof #1143.
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | Case 2:
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | |   (38)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 152.83/22.56  | | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 152.83/22.56  | | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 152.83/22.56  | | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | | ALPHA: (38) implies:
% 152.83/22.56  | | | | |   (39)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 152.83/22.56  | | | | |             e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | | BETA: splitting (39) gives:
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | | Case 1:
% 152.83/22.56  | | | | | | 
% 152.83/22.56  | | | | | |   (40)  all_56_12 = e0 & op(e0, e3) = e0
% 152.83/22.56  | | | | | | 
% 152.83/22.56  | | | | | | ALPHA: (40) implies:
% 152.83/22.56  | | | | | |   (41)  op(e0, e3) = e0
% 152.83/22.56  | | | | | | 
% 152.83/22.56  | | | | | | REF_CLOSE: (6), (7), (13), (14), (16), (24), (35), (41) are
% 152.83/22.56  | | | | | |            inconsistent by sub-proof #319.
% 152.83/22.56  | | | | | | 
% 152.83/22.56  | | | | | Case 2:
% 152.83/22.56  | | | | | | 
% 152.83/22.56  | | | | | |   (42)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 &
% 152.83/22.56  | | | | | |           op(e0, e1) = e0)
% 152.83/22.56  | | | | | | 
% 152.83/22.56  | | | | | | REF_CLOSE: (5), (6), (11), (12), (15), (42) are inconsistent by
% 152.83/22.56  | | | | | |            sub-proof #315.
% 152.83/22.56  | | | | | | 
% 152.83/22.56  | | | | | End of split
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | End of split
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | End of split
% 152.83/22.56  | | | 
% 152.83/22.56  | | End of split
% 152.83/22.56  | | 
% 152.83/22.56  | End of split
% 152.83/22.56  | 
% 152.83/22.56  End of proof
% 152.83/22.56  
% 152.83/22.56  Sub-proof #302 shows that the following formulas are inconsistent:
% 152.83/22.56  ----------------------------------------------------------------
% 152.83/22.56    (1)   ~ (e2 = e0)
% 152.83/22.56    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.56    (3)  op(e0, e0) = e3
% 152.83/22.56    (4)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 152.83/22.56             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.83/22.56           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 152.83/22.56           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 152.83/22.56           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 152.83/22.56           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 152.83/22.56           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 152.83/22.56           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.83/22.56           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.83/22.56    (5)  op(e0, e0) = e1
% 152.83/22.56    (6)   ~ (all_52_9 = e2)
% 152.83/22.56    (7)  op(e2, e2) = e2
% 152.83/22.56    (8)  op(e2, e1) = all_52_9
% 152.83/22.56    (9)   ~ (e1 = e0)
% 152.83/22.56    (10)  op(e1, e1) = e3
% 152.83/22.56  
% 152.83/22.56  Begin of proof
% 152.83/22.56  | 
% 152.83/22.56  | BETA: splitting (4) gives:
% 152.83/22.56  | 
% 152.83/22.56  | Case 1:
% 152.83/22.56  | | 
% 152.83/22.56  | |   (11)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 152.83/22.56  | |           = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.83/22.56  | |         all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 152.83/22.56  | | 
% 152.83/22.56  | | ALPHA: (11) implies:
% 152.83/22.56  | |   (12)  op(e2, e1) = e2
% 152.83/22.56  | | 
% 152.83/22.56  | | REF_CLOSE: (2), (6), (8), (12) are inconsistent by sub-proof #1157.
% 152.83/22.56  | | 
% 152.83/22.56  | Case 2:
% 152.83/22.56  | | 
% 152.83/22.56  | |   (13)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.83/22.56  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.56  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.83/22.56  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 152.83/22.56  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 152.83/22.56  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.83/22.56  | |           $i(all_57_13))
% 152.83/22.56  | | 
% 152.83/22.56  | | BETA: splitting (13) gives:
% 152.83/22.56  | | 
% 152.83/22.56  | | Case 1:
% 152.83/22.56  | | | 
% 152.83/22.56  | | |   (14)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.83/22.56  | | |         (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.56  | | |         op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.83/22.56  | | |         $i(all_57_11)
% 152.83/22.56  | | | 
% 152.83/22.56  | | | ALPHA: (14) implies:
% 152.83/22.56  | | |   (15)  op(e2, e2) = e0
% 152.83/22.56  | | | 
% 152.83/22.56  | | | REF_CLOSE: (1), (2), (7), (15) are inconsistent by sub-proof #1145.
% 152.83/22.56  | | | 
% 152.83/22.56  | | Case 2:
% 152.83/22.56  | | | 
% 152.83/22.56  | | |   (16)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.83/22.56  | | |         (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.56  | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.83/22.56  | | |         $i(all_57_13)
% 152.83/22.56  | | | 
% 152.83/22.56  | | | ALPHA: (16) implies:
% 152.83/22.56  | | |   (17)  op(e1, e1) = e0
% 152.83/22.56  | | | 
% 152.83/22.56  | | | REF_CLOSE: (2), (3), (5), (9), (10), (17) are inconsistent by sub-proof
% 152.83/22.56  | | |            #331.
% 152.83/22.56  | | | 
% 152.83/22.56  | | End of split
% 152.83/22.56  | | 
% 152.83/22.56  | End of split
% 152.83/22.56  | 
% 152.83/22.56  End of proof
% 152.83/22.56  
% 152.83/22.56  Sub-proof #303 shows that the following formulas are inconsistent:
% 152.83/22.56  ----------------------------------------------------------------
% 152.83/22.56    (1)   ~ (e3 = e1)
% 152.83/22.56    (2)  e3 = e1
% 152.83/22.56    (3)  all_56_5 = e1
% 152.83/22.56    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.56    (5)  op(e3, e1) = e3
% 152.83/22.56    (6)  all_56_14 = e2
% 152.83/22.56    (7)  e3 = e0
% 152.83/22.56    (8)   ~ (e1 = e0)
% 152.83/22.56    (9)  op(e1, e1) = e3
% 152.83/22.56    (10)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.83/22.56          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.56    (11)  op(e3, e1) = all_52_8
% 152.83/22.56    (12)   ~ (e2 = e1)
% 152.83/22.56  
% 152.83/22.56  Begin of proof
% 152.83/22.56  | 
% 152.83/22.56  | COMBINE_EQS: (2), (7) imply:
% 152.83/22.56  |   (13)  e1 = e0
% 152.83/22.56  | 
% 152.83/22.56  | SIMP: (13) implies:
% 152.83/22.56  |   (14)  e1 = e0
% 152.83/22.56  | 
% 152.83/22.56  | COMBINE_EQS: (3), (14) imply:
% 152.83/22.56  |   (15)  all_56_5 = e0
% 152.83/22.56  | 
% 152.83/22.56  | REF_CLOSE: (1), (4), (5), (6), (8), (9), (10), (11), (12), (15) are
% 152.83/22.56  |            inconsistent by sub-proof #325.
% 152.83/22.56  | 
% 152.83/22.56  End of proof
% 152.83/22.56  
% 152.83/22.56  Sub-proof #304 shows that the following formulas are inconsistent:
% 152.83/22.56  ----------------------------------------------------------------
% 152.83/22.56    (1)  all_56_1 = e1
% 152.83/22.56    (2)   ~ (e3 = e1)
% 152.83/22.56    (3)  all_56_5 = e1
% 152.83/22.56    (4)   ~ (e2 = e0)
% 152.83/22.56    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.56    (6)  op(e3, e3) = e2
% 152.83/22.56    (7)  op(e3, e1) = e3
% 152.83/22.56    (8)  all_56_14 = e2
% 152.83/22.56    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 152.83/22.56    (10)   ~ (e1 = e0)
% 152.83/22.56    (11)  op(e1, e1) = e3
% 152.83/22.56    (12)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.83/22.56          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.56    (13)  op(e3, e1) = all_52_8
% 152.83/22.56    (14)   ~ (e2 = e1)
% 152.83/22.56  
% 152.83/22.56  Begin of proof
% 152.83/22.56  | 
% 152.83/22.56  | BETA: splitting (9) gives:
% 152.83/22.56  | 
% 152.83/22.56  | Case 1:
% 152.83/22.56  | | 
% 152.83/22.56  | |   (15)  all_56_0 = e0 & op(e3, e3) = e0
% 152.83/22.56  | | 
% 152.83/22.56  | | ALPHA: (15) implies:
% 152.83/22.56  | |   (16)  op(e3, e3) = e0
% 152.83/22.56  | | 
% 152.83/22.56  | | REF_CLOSE: (4), (5), (6), (16) are inconsistent by sub-proof #1073.
% 152.83/22.56  | | 
% 152.83/22.56  | Case 2:
% 152.83/22.56  | | 
% 152.83/22.56  | |   (17)  all_56_1 = e0 & op(e3, e2) = e0
% 152.83/22.56  | | 
% 152.83/22.56  | | ALPHA: (17) implies:
% 152.83/22.56  | |   (18)  all_56_1 = e0
% 152.83/22.56  | | 
% 152.83/22.56  | | COMBINE_EQS: (1), (18) imply:
% 152.83/22.56  | |   (19)  e1 = e0
% 152.83/22.56  | | 
% 152.83/22.56  | | SIMP: (19) implies:
% 152.83/22.56  | |   (20)  e1 = e0
% 152.83/22.56  | | 
% 152.83/22.56  | | COMBINE_EQS: (3), (20) imply:
% 152.83/22.56  | |   (21)  all_56_5 = e0
% 152.83/22.56  | | 
% 152.83/22.56  | | REF_CLOSE: (2), (5), (7), (8), (10), (11), (12), (13), (14), (21) are
% 152.83/22.56  | |            inconsistent by sub-proof #325.
% 152.83/22.56  | | 
% 152.83/22.56  | End of split
% 152.83/22.56  | 
% 152.83/22.56  End of proof
% 152.83/22.56  
% 152.83/22.56  Sub-proof #305 shows that the following formulas are inconsistent:
% 152.83/22.56  ----------------------------------------------------------------
% 152.83/22.56    (1)   ~ (e3 = e1)
% 152.83/22.56    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.83/22.56         (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.56    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.83/22.56         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.83/22.56    (4)  all_56_11 = e2
% 152.83/22.56    (5)  op(e3, e2) = all_52_4
% 152.83/22.56    (6)  op(e3, e2) = e3
% 152.83/22.56    (7)   ~ (e2 = e0)
% 152.83/22.56    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.56           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.56    (9)  op(e2, e3) = e2
% 152.83/22.56    (10)  op(e0, e0) = e3
% 152.83/22.56    (11)  op(e3, e3) = e2
% 152.83/22.56    (12)  all_56_14 = e2
% 152.83/22.56    (13)  op(e0, e0) = e1
% 152.83/22.56    (14)   ~ (e3 = e0)
% 152.83/22.56    (15)  op(e2, e2) = e2
% 152.83/22.56    (16)   ~ (e1 = e0)
% 152.83/22.56    (17)  all_56_13 = e3
% 152.83/22.56    (18)  op(e1, e1) = e3
% 152.83/22.56    (19)  op(e2, e3) = e3
% 152.83/22.56    (20)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.56          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.56    (21)   ~ (e2 = e1)
% 152.83/22.56    (22)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.56          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.56    (23)  op(e1, e3) = all_52_2
% 152.83/22.56    (24)  op(e2, e3) = all_52_1
% 152.83/22.56  
% 152.83/22.56  Begin of proof
% 152.83/22.56  | 
% 152.83/22.56  | BETA: splitting (3) gives:
% 152.83/22.56  | 
% 152.83/22.56  | Case 1:
% 152.83/22.56  | | 
% 152.83/22.56  | |   (25)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 152.83/22.56  | |           e1)
% 152.83/22.56  | | 
% 152.83/22.56  | | BETA: splitting (25) gives:
% 152.83/22.56  | | 
% 152.83/22.56  | | Case 1:
% 152.83/22.56  | | | 
% 152.83/22.56  | | |   (26)  all_56_0 = e1 & op(e3, e3) = e1
% 152.83/22.56  | | | 
% 152.83/22.56  | | | ALPHA: (26) implies:
% 152.83/22.56  | | |   (27)  op(e3, e3) = e1
% 152.83/22.56  | | | 
% 152.83/22.56  | | | REF_CLOSE: (8), (11), (21), (27) are inconsistent by sub-proof #1074.
% 152.83/22.56  | | | 
% 152.83/22.56  | | Case 2:
% 152.83/22.56  | | | 
% 152.83/22.56  | | |   (28)  all_56_2 = e1 & op(e2, e3) = e1
% 152.83/22.56  | | | 
% 152.83/22.56  | | | ALPHA: (28) implies:
% 152.83/22.56  | | |   (29)  op(e2, e3) = e1
% 152.83/22.56  | | | 
% 152.83/22.56  | | | REF_CLOSE: (8), (9), (21), (24), (29) are inconsistent by sub-proof #842.
% 152.83/22.56  | | | 
% 152.83/22.56  | | End of split
% 152.83/22.56  | | 
% 152.83/22.56  | Case 2:
% 152.83/22.56  | | 
% 152.83/22.56  | |   (30)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 152.83/22.56  | |           e1)
% 152.83/22.56  | | 
% 152.83/22.56  | | BETA: splitting (30) gives:
% 152.83/22.56  | | 
% 152.83/22.56  | | Case 1:
% 152.83/22.56  | | | 
% 152.83/22.56  | | |   (31)  all_56_6 = e1 & op(e1, e3) = e1
% 152.83/22.56  | | | 
% 152.83/22.56  | | | ALPHA: (31) implies:
% 152.83/22.56  | | |   (32)  op(e1, e3) = e1
% 152.83/22.56  | | | 
% 152.83/22.56  | | | BETA: splitting (22) gives:
% 152.83/22.56  | | | 
% 152.83/22.56  | | | Case 1:
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | |   (33)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2)
% 152.83/22.56  | | | |           = e1)
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | BETA: splitting (33) gives:
% 152.83/22.56  | | | | 
% 152.83/22.56  | | | | Case 1:
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | |   (34)  all_56_1 = e1 & op(e3, e2) = e1
% 152.83/22.56  | | | | | 
% 152.83/22.56  | | | | | ALPHA: (34) implies:
% 152.83/22.56  | | | | |   (35)  op(e3, e2) = e1
% 152.83/22.56  | | | | | 
% 152.83/22.57  | | | | | GROUND_INST: instantiating (8) with all_52_1, e2, e3, e2, simplifying
% 152.83/22.57  | | | | |              with (9), (24) gives:
% 152.83/22.57  | | | | |   (36)  all_52_1 = e2
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | GROUND_INST: instantiating (8) with all_52_1, e3, e3, e2, simplifying
% 152.83/22.57  | | | | |              with (19), (24) gives:
% 152.83/22.57  | | | | |   (37)  all_52_1 = e3
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | GROUND_INST: instantiating (8) with all_52_4, e1, e2, e3, simplifying
% 152.83/22.57  | | | | |              with (5), (35) gives:
% 152.83/22.57  | | | | |   (38)  all_52_4 = e1
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | GROUND_INST: instantiating (8) with all_52_4, e3, e2, e3, simplifying
% 152.83/22.57  | | | | |              with (5), (6) gives:
% 152.83/22.57  | | | | |   (39)  all_52_4 = e3
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | COMBINE_EQS: (36), (37) imply:
% 152.83/22.57  | | | | |   (40)  e3 = e2
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | COMBINE_EQS: (38), (39) imply:
% 152.83/22.57  | | | | |   (41)  e3 = e1
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | COMBINE_EQS: (40), (41) imply:
% 152.83/22.57  | | | | |   (42)  e2 = e1
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | REDUCE: (21), (42) imply:
% 152.83/22.57  | | | | |   (43)  $false
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | CLOSE: (43) is inconsistent.
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | Case 2:
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | |   (44)  all_56_3 = e1 & op(e2, e2) = e1
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | ALPHA: (44) implies:
% 152.83/22.57  | | | | |   (45)  op(e2, e2) = e1
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | REF_CLOSE: (8), (15), (21), (45) are inconsistent by sub-proof #1158.
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | End of split
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | Case 2:
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | |   (46)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2)
% 152.83/22.57  | | | |           = e1)
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | BETA: splitting (46) gives:
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | Case 1:
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | |   (47)  all_56_7 = e1 & op(e1, e2) = e1
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | REF_CLOSE: (4), (7), (8), (10), (13), (16), (18), (20), (23), (32),
% 152.83/22.57  | | | | |            (47) are inconsistent by sub-proof #329.
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | Case 2:
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | |   (48)  all_56_13 = e1 & op(e0, e2) = e1
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | REF_CLOSE: (1), (17), (48) are inconsistent by sub-proof #878.
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | End of split
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | End of split
% 152.83/22.57  | | | 
% 152.83/22.57  | | Case 2:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (49)  all_56_12 = e1 & op(e0, e3) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | ALPHA: (49) implies:
% 152.83/22.57  | | |   (50)  all_56_12 = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | REF_CLOSE: (2), (7), (12), (14), (16), (17), (50) are inconsistent by
% 152.83/22.57  | | |            sub-proof #1100.
% 152.83/22.57  | | | 
% 152.83/22.57  | | End of split
% 152.83/22.57  | | 
% 152.83/22.57  | End of split
% 152.83/22.57  | 
% 152.83/22.57  End of proof
% 152.83/22.57  
% 152.83/22.57  Sub-proof #306 shows that the following formulas are inconsistent:
% 152.83/22.57  ----------------------------------------------------------------
% 152.83/22.57    (1)   ~ (e3 = e1)
% 152.83/22.57    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.83/22.57         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.83/22.57    (3)  op(e3, e0) = e3
% 152.83/22.57    (4)  all_56_11 = e2
% 152.83/22.57    (5)  all_56_10 = e1 & op(e2, e0) = e1
% 152.83/22.57    (6)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.57         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.83/22.57    (7)   ~ (e2 = e0)
% 152.83/22.57    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.57    (9)  op(e0, e0) = e3
% 152.83/22.57    (10)  op(e3, e3) = e2
% 152.83/22.57    (11)  all_56_14 = e2
% 152.83/22.57    (12)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.57              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.83/22.57                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.83/22.57                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.83/22.57    (13)  op(e3, e0) = all_52_12
% 152.83/22.57    (14)   ~ (e3 = e0)
% 152.83/22.57    (15)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.83/22.57          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.57    (16)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.83/22.57          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.83/22.57    (17)  op(e2, e2) = e2
% 152.83/22.57    (18)   ~ (e1 = e0)
% 152.83/22.57    (19)  all_56_13 = e3
% 152.83/22.57    (20)  op(e1, e1) = e3
% 152.83/22.57    (21)   ~ (e3 = e2)
% 152.83/22.57    (22)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.83/22.57          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.57    (23)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.57          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.57    (24)   ~ (e2 = e1)
% 152.83/22.57    (25)  all_56_2 = e3
% 152.83/22.57    (26)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.57          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.57    (27)  op(e1, e3) = all_52_2
% 152.83/22.57    (28)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.57          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.83/22.57            e1)
% 152.83/22.57  
% 152.83/22.57  Begin of proof
% 152.83/22.57  | 
% 152.83/22.57  | ALPHA: (5) implies:
% 152.83/22.57  |   (29)  all_56_10 = e1
% 152.83/22.57  | 
% 152.83/22.57  | BETA: splitting (28) gives:
% 152.83/22.57  | 
% 152.83/22.57  | Case 1:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (30)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 152.83/22.57  | |           e1)
% 152.83/22.57  | | 
% 152.83/22.57  | | BETA: splitting (30) gives:
% 152.83/22.57  | | 
% 152.83/22.57  | | Case 1:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (31)  all_56_12 = e1 & op(e0, e3) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | ALPHA: (31) implies:
% 152.83/22.57  | | |   (32)  all_56_12 = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | REF_CLOSE: (7), (8), (9), (11), (12), (14), (18), (19), (32) are
% 152.83/22.57  | | |            inconsistent by sub-proof #311.
% 152.83/22.57  | | | 
% 152.83/22.57  | | Case 2:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (33)  all_56_13 = e1 & op(e0, e2) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | REF_CLOSE: (1), (19), (33) are inconsistent by sub-proof #878.
% 152.83/22.57  | | | 
% 152.83/22.57  | | End of split
% 152.83/22.57  | | 
% 152.83/22.57  | Case 2:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (34)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.83/22.57  | |           e1)
% 152.83/22.57  | | 
% 152.83/22.57  | | BETA: splitting (34) gives:
% 152.83/22.57  | | 
% 152.83/22.57  | | Case 1:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (35)  all_56_14 = e1 & op(e0, e1) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | REF_CLOSE: (11), (24), (35) are inconsistent by sub-proof #357.
% 152.83/22.57  | | | 
% 152.83/22.57  | | Case 2:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (36)  all_56_15 = e1 & op(e0, e0) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | ALPHA: (36) implies:
% 152.83/22.57  | | |   (37)  op(e0, e0) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | BETA: splitting (12) gives:
% 152.83/22.57  | | | 
% 152.83/22.57  | | | Case 1:
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | |   (38)  all_56_15 = e0 & op(e0, e0) = e0
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | ALPHA: (38) implies:
% 152.83/22.57  | | | |   (39)  op(e0, e0) = e0
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | REF_CLOSE: (8), (9), (14), (39) are inconsistent by sub-proof #1143.
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | Case 2:
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | |   (40)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 152.83/22.57  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 152.83/22.57  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 152.83/22.57  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | ALPHA: (40) implies:
% 152.83/22.57  | | | |   (41)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 152.83/22.57  | | | |             e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (13),
% 152.83/22.57  | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 152.83/22.57  | | | |            (24), (25), (26), (27), (29), (37), (41) are inconsistent by
% 152.83/22.57  | | | |            sub-proof #307.
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | End of split
% 152.83/22.57  | | | 
% 152.83/22.57  | | End of split
% 152.83/22.57  | | 
% 152.83/22.57  | End of split
% 152.83/22.57  | 
% 152.83/22.57  End of proof
% 152.83/22.57  
% 152.83/22.57  Sub-proof #307 shows that the following formulas are inconsistent:
% 152.83/22.57  ----------------------------------------------------------------
% 152.83/22.57    (1)   ~ (e3 = e1)
% 152.83/22.57    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.83/22.57         (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.57    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.83/22.57         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.83/22.57    (4)  op(e3, e0) = e3
% 152.83/22.57    (5)  all_56_11 = e2
% 152.83/22.57    (6)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.57         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.83/22.57    (7)   ~ (e2 = e0)
% 152.83/22.57    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.57    (9)  op(e0, e0) = e3
% 152.83/22.57    (10)  op(e3, e3) = e2
% 152.83/22.57    (11)  all_56_14 = e2
% 152.83/22.57    (12)  op(e0, e0) = e1
% 152.83/22.57    (13)  all_56_10 = e1
% 152.83/22.57    (14)  op(e3, e0) = all_52_12
% 152.83/22.57    (15)   ~ (e3 = e0)
% 152.83/22.57    (16)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.83/22.57          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.57    (17)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.83/22.57          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.83/22.57    (18)  op(e2, e2) = e2
% 152.83/22.57    (19)   ~ (e1 = e0)
% 152.83/22.57    (20)  all_56_13 = e3
% 152.83/22.57    (21)  op(e1, e1) = e3
% 152.83/22.57    (22)   ~ (e3 = e2)
% 152.83/22.57    (23)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.83/22.57          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.57    (24)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.57          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.57    (25)   ~ (e2 = e1)
% 152.83/22.57    (26)  all_56_2 = e3
% 152.83/22.57    (27)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.57          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.57    (28)  op(e1, e3) = all_52_2
% 152.83/22.57  
% 152.83/22.57  Begin of proof
% 152.83/22.57  | 
% 152.83/22.57  | BETA: splitting (3) gives:
% 152.83/22.57  | 
% 152.83/22.57  | Case 1:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (29)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 152.83/22.57  | |           e1)
% 152.83/22.57  | | 
% 152.83/22.57  | | REF_CLOSE: (1), (8), (10), (25), (26), (29) are inconsistent by sub-proof
% 152.83/22.57  | |            #310.
% 152.83/22.57  | | 
% 152.83/22.57  | Case 2:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (30)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 152.83/22.57  | |           e1)
% 152.83/22.57  | | 
% 152.83/22.57  | | BETA: splitting (30) gives:
% 152.83/22.57  | | 
% 152.83/22.57  | | Case 1:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (31)  all_56_6 = e1 & op(e1, e3) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | ALPHA: (31) implies:
% 152.83/22.57  | | |   (32)  op(e1, e3) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 152.83/22.57  | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 152.83/22.57  | | |            (24), (25), (27), (28), (32) are inconsistent by sub-proof
% 152.83/22.57  | | |            #308.
% 152.83/22.57  | | | 
% 152.83/22.57  | | Case 2:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (33)  all_56_12 = e1 & op(e0, e3) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | ALPHA: (33) implies:
% 152.83/22.57  | | |   (34)  all_56_12 = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | REF_CLOSE: (2), (7), (11), (15), (19), (20), (34) are inconsistent by
% 152.83/22.57  | | |            sub-proof #1100.
% 152.83/22.57  | | | 
% 152.83/22.57  | | End of split
% 152.83/22.57  | | 
% 152.83/22.57  | End of split
% 152.83/22.57  | 
% 152.83/22.57  End of proof
% 152.83/22.57  
% 152.83/22.57  Sub-proof #308 shows that the following formulas are inconsistent:
% 152.83/22.57  ----------------------------------------------------------------
% 152.83/22.57    (1)   ~ (e3 = e1)
% 152.83/22.57    (2)  op(e3, e0) = e3
% 152.83/22.57    (3)  all_56_11 = e2
% 152.83/22.57    (4)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.57         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.83/22.57    (5)   ~ (e2 = e0)
% 152.83/22.57    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.57    (7)  op(e0, e0) = e3
% 152.83/22.57    (8)  op(e3, e3) = e2
% 152.83/22.57    (9)  all_56_14 = e2
% 152.83/22.57    (10)  op(e1, e3) = e1
% 152.83/22.57    (11)  op(e0, e0) = e1
% 152.83/22.57    (12)  all_56_10 = e1
% 152.83/22.57    (13)  op(e3, e0) = all_52_12
% 152.83/22.57    (14)   ~ (e3 = e0)
% 152.83/22.57    (15)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.83/22.57          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.57    (16)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.83/22.57          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.83/22.57    (17)  op(e2, e2) = e2
% 152.83/22.57    (18)   ~ (e1 = e0)
% 152.83/22.57    (19)  all_56_13 = e3
% 152.83/22.57    (20)  op(e1, e1) = e3
% 152.83/22.57    (21)   ~ (e3 = e2)
% 152.83/22.57    (22)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.83/22.57          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.57    (23)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.57          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.57    (24)   ~ (e2 = e1)
% 152.83/22.57    (25)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.57          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.57    (26)  op(e1, e3) = all_52_2
% 152.83/22.57  
% 152.83/22.57  Begin of proof
% 152.83/22.57  | 
% 152.83/22.57  | BETA: splitting (25) gives:
% 152.83/22.57  | 
% 152.83/22.57  | Case 1:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (27)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 152.83/22.57  | |           e1)
% 152.83/22.57  | | 
% 152.83/22.57  | | BETA: splitting (27) gives:
% 152.83/22.57  | | 
% 152.83/22.57  | | Case 1:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (28)  all_56_1 = e1 & op(e3, e2) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | ALPHA: (28) implies:
% 152.83/22.57  | | |   (29)  all_56_1 = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | BETA: splitting (15) gives:
% 152.83/22.57  | | | 
% 152.83/22.57  | | | Case 1:
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | |   (30)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2)
% 152.83/22.57  | | | |           = e0)
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | REF_CLOSE: (5), (6), (8), (18), (29), (30) are inconsistent by sub-proof
% 152.83/22.57  | | | |            #1071.
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | Case 2:
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | |   (31)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0)
% 152.83/22.57  | | | |           = e0)
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | BETA: splitting (31) gives:
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | Case 1:
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | |   (32)  all_56_4 = e0 & op(e3, e1) = e0
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | ALPHA: (32) implies:
% 152.83/22.57  | | | | |   (33)  all_56_4 = e0
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | BETA: splitting (22) gives:
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | Case 1:
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | |   (34)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2,
% 152.83/22.57  | | | | | |             e1) = e1)
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | | BETA: splitting (34) gives:
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | | Case 1:
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | |   (35)  all_56_4 = e1 & op(e3, e1) = e1
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | | REF_CLOSE: (18), (33), (35) are inconsistent by sub-proof #309.
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | Case 2:
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | |   (36)  all_56_5 = e1 & op(e2, e1) = e1
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | | ALPHA: (36) implies:
% 152.83/22.57  | | | | | | |   (37)  all_56_5 = e1
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | | REF_CLOSE: (1), (4), (5), (6), (12), (14), (16), (17), (18), (21),
% 152.83/22.57  | | | | | | |            (37) are inconsistent by sub-proof #681.
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | End of split
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | Case 2:
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | |   (38)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0,
% 152.83/22.57  | | | | | |             e1) = e1)
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | | REF_CLOSE: (1), (6), (9), (20), (24), (38) are inconsistent by
% 152.83/22.57  | | | | | |            sub-proof #326.
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | End of split
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | Case 2:
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | |   (39)  all_56_9 = e0 & op(e3, e0) = e0
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | REF_CLOSE: (2), (6), (7), (11), (13), (18), (39) are inconsistent by
% 152.83/22.57  | | | | |            sub-proof #323.
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | End of split
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | End of split
% 152.83/22.57  | | | 
% 152.83/22.57  | | Case 2:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (40)  all_56_3 = e1 & op(e2, e2) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | ALPHA: (40) implies:
% 152.83/22.57  | | |   (41)  op(e2, e2) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | REF_CLOSE: (6), (17), (24), (41) are inconsistent by sub-proof #1158.
% 152.83/22.57  | | | 
% 152.83/22.57  | | End of split
% 152.83/22.57  | | 
% 152.83/22.57  | Case 2:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (42)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 152.83/22.57  | |           e1)
% 152.83/22.57  | | 
% 152.83/22.57  | | BETA: splitting (42) gives:
% 152.83/22.57  | | 
% 152.83/22.57  | | Case 1:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (43)  all_56_7 = e1 & op(e1, e2) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | REF_CLOSE: (3), (5), (6), (7), (10), (11), (18), (20), (23), (26), (43)
% 152.83/22.57  | | |            are inconsistent by sub-proof #329.
% 152.83/22.57  | | | 
% 152.83/22.57  | | Case 2:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (44)  all_56_13 = e1 & op(e0, e2) = e1
% 152.83/22.57  | | | 
% 152.83/22.57  | | | REF_CLOSE: (1), (19), (44) are inconsistent by sub-proof #878.
% 152.83/22.57  | | | 
% 152.83/22.57  | | End of split
% 152.83/22.57  | | 
% 152.83/22.57  | End of split
% 152.83/22.57  | 
% 152.83/22.57  End of proof
% 152.83/22.57  
% 152.83/22.57  Sub-proof #309 shows that the following formulas are inconsistent:
% 152.83/22.57  ----------------------------------------------------------------
% 152.83/22.57    (1)  all_56_4 = e1 & op(e3, e1) = e1
% 152.83/22.57    (2)  all_56_4 = e0
% 152.83/22.57    (3)   ~ (e1 = e0)
% 152.83/22.57  
% 152.83/22.57  Begin of proof
% 152.83/22.57  | 
% 152.83/22.57  | ALPHA: (1) implies:
% 152.83/22.57  |   (4)  all_56_4 = e1
% 152.83/22.57  | 
% 152.83/22.57  | COMBINE_EQS: (2), (4) imply:
% 152.83/22.57  |   (5)  e1 = e0
% 152.83/22.57  | 
% 152.83/22.57  | REDUCE: (3), (5) imply:
% 152.83/22.57  |   (6)  $false
% 152.83/22.57  | 
% 152.83/22.57  | CLOSE: (6) is inconsistent.
% 152.83/22.57  | 
% 152.83/22.57  End of proof
% 152.83/22.57  
% 152.83/22.57  Sub-proof #310 shows that the following formulas are inconsistent:
% 152.83/22.57  ----------------------------------------------------------------
% 152.83/22.57    (1)   ~ (e3 = e1)
% 152.83/22.57    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.57    (3)  op(e3, e3) = e2
% 152.83/22.57    (4)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 152.83/22.57    (5)   ~ (e2 = e1)
% 152.83/22.57    (6)  all_56_2 = e3
% 152.83/22.57  
% 152.83/22.57  Begin of proof
% 152.83/22.57  | 
% 152.83/22.57  | BETA: splitting (4) gives:
% 152.83/22.57  | 
% 152.83/22.57  | Case 1:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 152.83/22.57  | | 
% 152.83/22.57  | | ALPHA: (7) implies:
% 152.83/22.57  | |   (8)  op(e3, e3) = e1
% 152.83/22.57  | | 
% 152.83/22.57  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1074.
% 152.83/22.57  | | 
% 152.83/22.57  | Case 2:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (9)  all_56_2 = e1 & op(e2, e3) = e1
% 152.83/22.57  | | 
% 152.83/22.57  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #791.
% 152.83/22.57  | | 
% 152.83/22.57  | End of split
% 152.83/22.57  | 
% 152.83/22.57  End of proof
% 152.83/22.57  
% 152.83/22.57  Sub-proof #311 shows that the following formulas are inconsistent:
% 152.83/22.57  ----------------------------------------------------------------
% 152.83/22.57    (1)   ~ (e2 = e0)
% 152.83/22.57    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.57    (3)  op(e0, e0) = e3
% 152.83/22.57    (4)  all_56_14 = e2
% 152.83/22.57    (5)  all_56_12 = e1
% 152.83/22.57    (6)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.57             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 152.83/22.57               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.83/22.57               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.83/22.57    (7)   ~ (e3 = e0)
% 152.83/22.57    (8)   ~ (e1 = e0)
% 152.83/22.57    (9)  all_56_13 = e3
% 152.83/22.57  
% 152.83/22.57  Begin of proof
% 152.83/22.57  | 
% 152.83/22.57  | BETA: splitting (6) gives:
% 152.83/22.57  | 
% 152.83/22.57  | Case 1:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (10)  all_56_15 = e0 & op(e0, e0) = e0
% 152.83/22.57  | | 
% 152.83/22.57  | | ALPHA: (10) implies:
% 152.83/22.57  | |   (11)  op(e0, e0) = e0
% 152.83/22.57  | | 
% 152.83/22.57  | | REF_CLOSE: (2), (3), (7), (11) are inconsistent by sub-proof #1143.
% 152.83/22.57  | | 
% 152.83/22.57  | Case 2:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (12)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 152.83/22.57  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 152.83/22.57  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.83/22.57  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 152.83/22.57  | | 
% 152.83/22.57  | | ALPHA: (12) implies:
% 152.83/22.57  | |   (13)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 152.83/22.57  | |           e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.57  | | 
% 152.83/22.57  | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (13) are inconsistent by sub-proof
% 152.83/22.57  | |            #1100.
% 152.83/22.57  | | 
% 152.83/22.57  | End of split
% 152.83/22.57  | 
% 152.83/22.57  End of proof
% 152.83/22.57  
% 152.83/22.57  Sub-proof #312 shows that the following formulas are inconsistent:
% 152.83/22.57  ----------------------------------------------------------------
% 152.83/22.57    (1)  all_56_8 = e3
% 152.83/22.57    (2)   ~ (e3 = e1)
% 152.83/22.57    (3)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.57         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.83/22.57    (4)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.83/22.57         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.57    (5)   ~ (e2 = e0)
% 152.83/22.57    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.57           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.57    (7)  all_56_14 = e2
% 152.83/22.57    (8)   ~ (e3 = e0)
% 152.83/22.57    (9)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.83/22.57         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.83/22.57    (10)  op(e2, e2) = e2
% 152.83/22.57    (11)   ~ (e1 = e0)
% 152.83/22.57    (12)   ~ (e3 = e2)
% 152.83/22.57    (13)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.57          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.83/22.57    (14)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.83/22.57          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.57    (15)   ~ (e2 = e1)
% 152.83/22.57    (16)  all_56_2 = e3
% 152.83/22.57    (17)  all_56_4 = e3
% 152.83/22.57  
% 152.83/22.57  Begin of proof
% 152.83/22.57  | 
% 152.83/22.57  | BETA: splitting (4) gives:
% 152.83/22.57  | 
% 152.83/22.57  | Case 1:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (18)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 152.83/22.57  | |           e0)
% 152.83/22.57  | | 
% 152.83/22.57  | | BETA: splitting (18) gives:
% 152.83/22.57  | | 
% 152.83/22.57  | | Case 1:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (19)  all_56_4 = e0 & op(e3, e1) = e0
% 152.83/22.57  | | | 
% 152.83/22.57  | | | REF_CLOSE: (8), (17), (19) are inconsistent by sub-proof #361.
% 152.83/22.57  | | | 
% 152.83/22.57  | | Case 2:
% 152.83/22.57  | | | 
% 152.83/22.57  | | |   (20)  all_56_5 = e0 & op(e2, e1) = e0
% 152.83/22.57  | | | 
% 152.83/22.57  | | | ALPHA: (20) implies:
% 152.83/22.57  | | |   (21)  all_56_5 = e0
% 152.83/22.57  | | | 
% 152.83/22.57  | | | BETA: splitting (13) gives:
% 152.83/22.57  | | | 
% 152.83/22.57  | | | Case 1:
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | |   (22)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2)
% 152.83/22.57  | | | |           = e1)
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | REF_CLOSE: (2), (6), (10), (15), (16), (22) are inconsistent by
% 152.83/22.57  | | | |            sub-proof #364.
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | Case 2:
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | |   (23)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0)
% 152.83/22.57  | | | |           = e1)
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | BETA: splitting (23) gives:
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | | Case 1:
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | |   (24)  all_56_5 = e1 & op(e2, e1) = e1
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | ALPHA: (24) implies:
% 152.83/22.57  | | | | |   (25)  all_56_5 = e1
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | REF_CLOSE: (11), (21), (25) are inconsistent by sub-proof #682.
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | Case 2:
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | |   (26)  all_56_10 = e1 & op(e2, e0) = e1
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | ALPHA: (26) implies:
% 152.83/22.57  | | | | |   (27)  all_56_10 = e1
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | BETA: splitting (14) gives:
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | | Case 1:
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | |   (28)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2,
% 152.83/22.57  | | | | | |             e1) = e1)
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | | BETA: splitting (28) gives:
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | | Case 1:
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | |   (29)  all_56_4 = e1 & op(e3, e1) = e1
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | | REF_CLOSE: (2), (17), (29) are inconsistent by sub-proof #358.
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | Case 2:
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | |   (30)  all_56_5 = e1 & op(e2, e1) = e1
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | | ALPHA: (30) implies:
% 152.83/22.57  | | | | | | |   (31)  all_56_5 = e1
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (10), (11), (12), (27),
% 152.83/22.57  | | | | | | |            (31) are inconsistent by sub-proof #681.
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | End of split
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | Case 2:
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | |   (32)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0,
% 152.83/22.57  | | | | | |             e1) = e1)
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | | BETA: splitting (32) gives:
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | | Case 1:
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | |   (33)  all_56_8 = e1 & op(e1, e1) = e1
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | | REF_CLOSE: (1), (2), (33) are inconsistent by sub-proof #645.
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | Case 2:
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | |   (34)  all_56_14 = e1 & op(e0, e1) = e1
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | | REF_CLOSE: (7), (15), (34) are inconsistent by sub-proof #357.
% 152.83/22.57  | | | | | | | 
% 152.83/22.57  | | | | | | End of split
% 152.83/22.57  | | | | | | 
% 152.83/22.57  | | | | | End of split
% 152.83/22.57  | | | | | 
% 152.83/22.57  | | | | End of split
% 152.83/22.57  | | | | 
% 152.83/22.57  | | | End of split
% 152.83/22.57  | | | 
% 152.83/22.57  | | End of split
% 152.83/22.57  | | 
% 152.83/22.57  | Case 2:
% 152.83/22.57  | | 
% 152.83/22.57  | |   (35)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 152.83/22.57  | |           e0)
% 152.83/22.57  | | 
% 152.83/22.57  | | BETA: splitting (35) gives:
% 152.83/22.57  | | 
% 152.83/22.57  | | Case 1:
% 152.83/22.57  | | | 
% 152.83/22.58  | | |   (36)  all_56_8 = e0 & op(e1, e1) = e0
% 152.83/22.58  | | | 
% 152.83/22.58  | | | REF_CLOSE: (1), (8), (36) are inconsistent by sub-proof #1150.
% 152.83/22.58  | | | 
% 152.83/22.58  | | Case 2:
% 152.83/22.58  | | | 
% 152.83/22.58  | | |   (37)  all_56_14 = e0 & op(e0, e1) = e0
% 152.83/22.58  | | | 
% 152.83/22.58  | | | REF_CLOSE: (5), (7), (37) are inconsistent by sub-proof #1101.
% 152.83/22.58  | | | 
% 152.83/22.58  | | End of split
% 152.83/22.58  | | 
% 152.83/22.58  | End of split
% 152.83/22.58  | 
% 152.83/22.58  End of proof
% 152.83/22.58  
% 152.83/22.58  Sub-proof #313 shows that the following formulas are inconsistent:
% 152.83/22.58  ----------------------------------------------------------------
% 152.83/22.58    (1)  op(e0, e2) = all_52_7
% 152.83/22.58    (2)   ~ (all_52_3 = all_52_7)
% 152.83/22.58    (3)   ~ (e2 = e0)
% 152.83/22.58    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.58    (5)  op(e0, e0) = e3
% 152.83/22.58    (6)  all_57_5 = e0 & op(e0, e2) = e0
% 152.83/22.58    (7)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.58             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 152.83/22.58               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.83/22.58               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.83/22.58    (8)   ~ (e3 = e0)
% 152.83/22.58    (9)  op(e0, e1) = e2
% 152.83/22.58    (10)  op(e0, e3) = all_52_3
% 152.83/22.58    (11)  all_56_13 = e3
% 152.83/22.58  
% 152.83/22.58  Begin of proof
% 152.83/22.58  | 
% 152.83/22.58  | ALPHA: (6) implies:
% 152.83/22.58  |   (12)  op(e0, e2) = e0
% 152.83/22.58  | 
% 152.83/22.58  | BETA: splitting (7) gives:
% 152.83/22.58  | 
% 152.83/22.58  | Case 1:
% 152.83/22.58  | | 
% 152.83/22.58  | |   (13)  all_56_15 = e0 & op(e0, e0) = e0
% 152.83/22.58  | | 
% 152.83/22.58  | | ALPHA: (13) implies:
% 152.83/22.58  | |   (14)  op(e0, e0) = e0
% 152.83/22.58  | | 
% 152.83/22.58  | | REF_CLOSE: (4), (5), (8), (14) are inconsistent by sub-proof #1143.
% 152.83/22.58  | | 
% 152.83/22.58  | Case 2:
% 152.83/22.58  | | 
% 152.83/22.58  | |   (15)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 152.83/22.58  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 152.83/22.58  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.83/22.58  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 152.83/22.58  | | 
% 152.83/22.58  | | ALPHA: (15) implies:
% 152.83/22.58  | |   (16)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 152.83/22.58  | |           e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.58  | | 
% 152.83/22.58  | | REF_CLOSE: (1), (2), (3), (4), (8), (9), (10), (11), (12), (16) are
% 152.83/22.58  | |            inconsistent by sub-proof #314.
% 152.83/22.58  | | 
% 152.83/22.58  | End of split
% 152.83/22.58  | 
% 152.83/22.58  End of proof
% 152.83/22.58  
% 152.83/22.58  Sub-proof #314 shows that the following formulas are inconsistent:
% 152.83/22.58  ----------------------------------------------------------------
% 152.83/22.58    (1)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.83/22.58         (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.58    (2)  op(e0, e2) = all_52_7
% 152.83/22.58    (3)   ~ (all_52_3 = all_52_7)
% 152.83/22.58    (4)   ~ (e2 = e0)
% 152.83/22.58    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.58    (6)   ~ (e3 = e0)
% 152.83/22.58    (7)  op(e0, e1) = e2
% 152.83/22.58    (8)  op(e0, e3) = all_52_3
% 152.83/22.58    (9)  all_56_13 = e3
% 152.83/22.58    (10)  op(e0, e2) = e0
% 152.83/22.58  
% 152.83/22.58  Begin of proof
% 152.83/22.58  | 
% 152.83/22.58  | BETA: splitting (1) gives:
% 152.83/22.58  | 
% 152.83/22.58  | Case 1:
% 152.83/22.58  | | 
% 152.83/22.58  | |   (11)  all_56_12 = e0 & op(e0, e3) = e0
% 152.83/22.58  | | 
% 152.83/22.58  | | ALPHA: (11) implies:
% 152.83/22.58  | |   (12)  op(e0, e3) = e0
% 152.83/22.58  | | 
% 152.83/22.58  | | REF_CLOSE: (2), (3), (5), (8), (10), (12) are inconsistent by sub-proof
% 152.83/22.58  | |            #1123.
% 152.83/22.58  | | 
% 152.83/22.58  | Case 2:
% 152.83/22.58  | | 
% 152.83/22.58  | |   (13)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 152.83/22.58  | |           e0)
% 152.83/22.58  | | 
% 152.83/22.58  | | REF_CLOSE: (4), (5), (6), (7), (9), (13) are inconsistent by sub-proof #315.
% 152.83/22.58  | | 
% 152.83/22.58  | End of split
% 152.83/22.58  | 
% 152.83/22.58  End of proof
% 152.83/22.58  
% 152.83/22.58  Sub-proof #315 shows that the following formulas are inconsistent:
% 152.83/22.58  ----------------------------------------------------------------
% 152.83/22.58    (1)   ~ (e2 = e0)
% 152.83/22.58    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.58    (3)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.58    (4)   ~ (e3 = e0)
% 152.83/22.58    (5)  op(e0, e1) = e2
% 152.83/22.58    (6)  all_56_13 = e3
% 152.83/22.58  
% 152.83/22.58  Begin of proof
% 152.83/22.58  | 
% 152.83/22.58  | BETA: splitting (3) gives:
% 152.83/22.58  | 
% 152.83/22.58  | Case 1:
% 152.83/22.58  | | 
% 152.83/22.58  | |   (7)  all_56_13 = e0 & op(e0, e2) = e0
% 152.83/22.58  | | 
% 152.83/22.58  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #1102.
% 152.83/22.58  | | 
% 152.83/22.58  | Case 2:
% 152.83/22.58  | | 
% 152.83/22.58  | |   (8)  all_56_14 = e0 & op(e0, e1) = e0
% 152.83/22.58  | | 
% 152.83/22.58  | | ALPHA: (8) implies:
% 152.83/22.58  | |   (9)  op(e0, e1) = e0
% 152.83/22.58  | | 
% 152.83/22.58  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #1008.
% 152.83/22.58  | | 
% 152.83/22.58  | End of split
% 152.83/22.58  | 
% 152.83/22.58  End of proof
% 152.83/22.58  
% 152.83/22.58  Sub-proof #316 shows that the following formulas are inconsistent:
% 152.83/22.58  ----------------------------------------------------------------
% 152.83/22.58    (1)  all_56_8 = e3
% 152.83/22.58    (2)   ~ (e3 = e1)
% 152.83/22.58    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.83/22.58         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.83/22.58    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 152.83/22.58         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 152.83/22.58    (5)  all_56_11 = e2
% 152.83/22.58    (6)  op(e0, e0) = all_10_2
% 152.83/22.58    (7)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.58         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.83/22.58    (8)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.83/22.58         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.58    (9)   ~ (e2 = e0)
% 152.83/22.58    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.58    (11)  op(e0, e0) = e3
% 152.83/22.58    (12)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.83/22.58          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.83/22.58    (13)  op(e3, e3) = e2
% 152.83/22.58    (14)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 152.83/22.58            all_57_14 & $i(all_57_14))
% 152.83/22.58    (15)  all_56_14 = e2
% 152.83/22.58    (16)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.58              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.83/22.58                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.83/22.58                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.83/22.58    (17)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.83/22.58          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.83/22.58    (18)  all_57_3 = e3
% 152.83/22.58    (19)  op(e3, e0) = all_52_12
% 152.83/22.58    (20)   ~ (e3 = e0)
% 152.83/22.58    (21)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.83/22.58          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.58    (22)   ~ (all_52_9 = e2)
% 152.83/22.58    (23)  op(e0, e1) = e2
% 152.83/22.58    (24)  op(e0, e3) = all_52_3
% 152.83/22.58    (25)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.83/22.58          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.83/22.58    (26)  op(e2, e2) = e2
% 152.83/22.58    (27)  op(e2, e1) = all_52_9
% 152.83/22.58    (28)   ~ (e1 = e0)
% 152.83/22.58    (29)  op(e1, e1) = e3
% 152.83/22.58    (30)  all_57_12 = e2
% 152.83/22.58    (31)  op(e1, e0) = e2
% 152.83/22.58    (32)   ~ (e3 = e2)
% 152.83/22.58    (33)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.58          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.83/22.58    (34)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.58          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.83/22.58    (35)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.83/22.58          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.58    (36)   ~ (all_10_2 = e2)
% 152.83/22.58    (37)  op(e3, e1) = all_52_8
% 152.83/22.58    (38)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 152.83/22.58          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 152.83/22.58    (39)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.58          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.58    (40)   ~ (e2 = e1)
% 152.83/22.58    (41)  all_56_1 = e3
% 152.83/22.58    (42)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.58          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.58    (43)  op(e1, e3) = all_52_2
% 152.83/22.58    (44)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.83/22.58              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.83/22.58            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.83/22.58            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.83/22.58            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.83/22.58            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.83/22.58            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.83/22.58            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.83/22.58            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.83/22.58            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.83/22.58            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.83/22.58            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.83/22.58            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.83/22.58            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.83/22.58            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.83/22.58            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.83/22.58            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.83/22.58            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.83/22.58            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.83/22.58            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.83/22.58            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.83/22.58            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.83/22.58            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.83/22.58            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.83/22.58            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.58            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.83/22.58            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.83/22.58            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.58            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.58            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.83/22.58            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.83/22.58            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.83/22.58            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.83/22.58            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.83/22.58            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.58            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.83/22.58            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.58            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.83/22.58            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.83/22.58            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.58            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.83/22.58            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.83/22.58            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.58            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.83/22.58            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.83/22.58            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.58            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.83/22.58            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.83/22.58              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.83/22.58            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.83/22.58            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.83/22.58              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.83/22.58            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.83/22.58            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.83/22.58                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.83/22.58                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.83/22.58                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.83/22.58                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.83/22.58                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.83/22.58                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.83/22.58                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.83/22.58              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.83/22.58                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.83/22.58                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.58                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.83/22.58                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.83/22.58                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.83/22.58                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.58                $i(all_57_7))))
% 152.83/22.58    (45)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.83/22.58          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.83/22.58    (46)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.58          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 152.83/22.58            e1)
% 152.83/22.58    (47)  op(e2, e3) = all_52_1
% 152.83/22.58  
% 152.83/22.58  Begin of proof
% 152.83/22.58  | 
% 152.83/22.58  | BETA: splitting (4) gives:
% 152.83/22.58  | 
% 152.83/22.58  | Case 1:
% 152.83/22.58  | | 
% 152.83/22.58  | |   (48)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 152.83/22.58  | |           e3)
% 152.83/22.58  | | 
% 152.83/22.58  | | BETA: splitting (48) gives:
% 152.83/22.58  | | 
% 152.83/22.58  | | Case 1:
% 152.83/22.58  | | | 
% 152.83/22.58  | | |   (49)  all_56_0 = e3 & op(e3, e3) = e3
% 152.83/22.58  | | | 
% 152.83/22.58  | | | ALPHA: (49) implies:
% 152.83/22.58  | | |   (50)  op(e3, e3) = e3
% 152.83/22.58  | | | 
% 152.83/22.58  | | | REF_CLOSE: (10), (13), (32), (50) are inconsistent by sub-proof #1085.
% 152.83/22.58  | | | 
% 152.83/22.58  | | Case 2:
% 152.83/22.58  | | | 
% 152.83/22.58  | | |   (51)  all_56_2 = e3 & op(e2, e3) = e3
% 152.83/22.58  | | | 
% 152.83/22.58  | | | ALPHA: (51) implies:
% 152.83/22.58  | | |   (52)  all_56_2 = e3
% 152.83/22.58  | | | 
% 152.83/22.58  | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (12), (13), (14), (17),
% 152.83/22.58  | | |            (18), (20), (21), (22), (23), (25), (26), (27), (28), (29),
% 152.83/22.58  | | |            (30), (31), (32), (33), (34), (36), (38), (39), (40), (41),
% 152.83/22.58  | | |            (42), (44), (45), (47), (51), (52) are inconsistent by
% 152.83/22.58  | | |            sub-proof #336.
% 152.83/22.58  | | | 
% 152.83/22.58  | | End of split
% 152.83/22.58  | | 
% 152.83/22.58  | Case 2:
% 152.83/22.58  | | 
% 152.83/22.58  | |   (53)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 152.83/22.58  | |           e3)
% 152.83/22.58  | | 
% 152.83/22.58  | | BETA: splitting (53) gives:
% 152.83/22.58  | | 
% 152.83/22.58  | | Case 1:
% 152.83/22.58  | | | 
% 152.83/22.58  | | |   (54)  all_56_6 = e3 & op(e1, e3) = e3
% 152.83/22.58  | | | 
% 152.83/22.58  | | | ALPHA: (54) implies:
% 152.83/22.58  | | |   (55)  all_56_6 = e3
% 152.83/22.58  | | | 
% 152.83/22.58  | | | REF_CLOSE: (1), (2), (5), (9), (12), (20), (28), (39), (40), (55) are
% 152.83/22.58  | | |            inconsistent by sub-proof #608.
% 152.83/22.58  | | | 
% 152.83/22.58  | | Case 2:
% 152.83/22.58  | | | 
% 152.83/22.58  | | |   (56)  all_56_12 = e3 & op(e0, e3) = e3
% 152.83/22.58  | | | 
% 152.83/22.58  | | | ALPHA: (56) implies:
% 152.83/22.58  | | |   (57)  all_56_12 = e3
% 152.83/22.58  | | |   (58)  op(e0, e3) = e3
% 152.83/22.58  | | | 
% 152.83/22.58  | | | BETA: splitting (46) gives:
% 152.83/22.58  | | | 
% 152.83/22.58  | | | Case 1:
% 152.83/22.58  | | | | 
% 152.83/22.58  | | | |   (59)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0,
% 152.83/22.58  | | | |             e2) = e1)
% 152.83/22.58  | | | | 
% 152.83/22.58  | | | | BETA: splitting (59) gives:
% 152.83/22.58  | | | | 
% 152.83/22.58  | | | | Case 1:
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | |   (60)  all_56_12 = e1 & op(e0, e3) = e1
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | | REF_CLOSE: (2), (57), (60) are inconsistent by sub-proof #992.
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | Case 2:
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | |   (61)  all_56_13 = e1 & op(e0, e2) = e1
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | | ALPHA: (61) implies:
% 152.83/22.58  | | | | |   (62)  all_56_13 = e1
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | | REF_CLOSE: (9), (10), (11), (16), (20), (23), (28), (57), (62) are
% 152.83/22.58  | | | | |            inconsistent by sub-proof #335.
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | End of split
% 152.83/22.58  | | | | 
% 152.83/22.58  | | | Case 2:
% 152.83/22.58  | | | | 
% 152.83/22.58  | | | |   (63)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0,
% 152.83/22.58  | | | |             e0) = e1)
% 152.83/22.58  | | | | 
% 152.83/22.58  | | | | BETA: splitting (63) gives:
% 152.83/22.58  | | | | 
% 152.83/22.58  | | | | Case 1:
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | |   (64)  all_56_14 = e1 & op(e0, e1) = e1
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | | REF_CLOSE: (15), (40), (64) are inconsistent by sub-proof #357.
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | Case 2:
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | |   (65)  all_56_15 = e1 & op(e0, e0) = e1
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | | ALPHA: (65) implies:
% 152.83/22.58  | | | | |   (66)  all_56_15 = e1
% 152.83/22.58  | | | | |   (67)  op(e0, e0) = e1
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | | BETA: splitting (38) gives:
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | | Case 1:
% 152.83/22.58  | | | | | | 
% 152.83/22.58  | | | | | |   (68)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2,
% 152.83/22.58  | | | | | |             e0) = e3)
% 152.83/22.58  | | | | | | 
% 152.83/22.58  | | | | | | BETA: splitting (68) gives:
% 152.83/22.58  | | | | | | 
% 152.83/22.58  | | | | | | Case 1:
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | |   (69)  all_56_9 = e3 & op(e3, e0) = e3
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | | ALPHA: (69) implies:
% 152.83/22.58  | | | | | | |   (70)  all_56_9 = e3
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | | REF_CLOSE: (2), (9), (10), (13), (17), (20), (21), (28), (40),
% 152.83/22.58  | | | | | | |            (41), (70) are inconsistent by sub-proof #345.
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | Case 2:
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | |   (71)  all_56_10 = e3 & op(e2, e0) = e3
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | | ALPHA: (71) implies:
% 152.83/22.58  | | | | | | |   (72)  all_56_10 = e3
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11),
% 152.83/22.58  | | | | | | |            (13), (14), (15), (16), (17), (18), (19), (20), (22),
% 152.83/22.58  | | | | | | |            (23), (24), (26), (27), (28), (29), (30), (31), (33),
% 152.83/22.58  | | | | | | |            (35), (36), (37), (39), (40), (41), (42), (43), (44),
% 152.83/22.58  | | | | | | |            (47), (57), (58), (66), (67), (72) are inconsistent by
% 152.83/22.58  | | | | | | |            sub-proof #318.
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | End of split
% 152.83/22.58  | | | | | | 
% 152.83/22.58  | | | | | Case 2:
% 152.83/22.58  | | | | | | 
% 152.83/22.58  | | | | | |   (73)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 &
% 152.83/22.58  | | | | | |           op(e0, e0) = e3)
% 152.83/22.58  | | | | | | 
% 152.83/22.58  | | | | | | BETA: splitting (73) gives:
% 152.83/22.58  | | | | | | 
% 152.83/22.58  | | | | | | Case 1:
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | |   (74)  all_56_11 = e3 & op(e1, e0) = e3
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | | REF_CLOSE: (1), (2), (5), (9), (10), (12), (20), (26), (28), (32),
% 152.83/22.58  | | | | | | |            (34), (39), (40), (41), (42), (45), (74) are
% 152.83/22.58  | | | | | | |            inconsistent by sub-proof #317.
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | Case 2:
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | |   (75)  all_56_15 = e3 & op(e0, e0) = e3
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | | REF_CLOSE: (2), (66), (75) are inconsistent by sub-proof #338.
% 152.83/22.58  | | | | | | | 
% 152.83/22.58  | | | | | | End of split
% 152.83/22.58  | | | | | | 
% 152.83/22.58  | | | | | End of split
% 152.83/22.58  | | | | | 
% 152.83/22.58  | | | | End of split
% 152.83/22.58  | | | | 
% 152.83/22.58  | | | End of split
% 152.83/22.58  | | | 
% 152.83/22.58  | | End of split
% 152.83/22.58  | | 
% 152.83/22.58  | End of split
% 152.83/22.58  | 
% 152.83/22.58  End of proof
% 152.83/22.58  
% 152.83/22.58  Sub-proof #317 shows that the following formulas are inconsistent:
% 152.83/22.58  ----------------------------------------------------------------
% 152.83/22.58    (1)  all_56_8 = e3
% 152.83/22.58    (2)   ~ (e3 = e1)
% 152.83/22.58    (3)  all_56_11 = e2
% 152.83/22.58    (4)  all_56_11 = e3 & op(e1, e0) = e3
% 152.83/22.58    (5)   ~ (e2 = e0)
% 152.83/22.58    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.58           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.58    (7)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.83/22.58         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.83/22.58    (8)   ~ (e3 = e0)
% 152.83/22.58    (9)  op(e2, e2) = e2
% 152.83/22.58    (10)   ~ (e1 = e0)
% 152.83/22.58    (11)   ~ (e3 = e2)
% 152.83/22.58    (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.58          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.83/22.58    (13)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.58          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.58    (14)   ~ (e2 = e1)
% 152.83/22.58    (15)  all_56_1 = e3
% 152.83/22.58    (16)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.58          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.58    (17)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.83/22.58          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.83/22.58  
% 152.83/22.58  Begin of proof
% 152.83/22.58  | 
% 152.83/22.58  | ALPHA: (4) implies:
% 152.83/22.58  |   (18)  all_56_11 = e3
% 152.83/22.58  | 
% 152.83/22.58  | COMBINE_EQS: (3), (18) imply:
% 152.83/22.58  |   (19)  e3 = e2
% 152.83/22.58  | 
% 152.83/22.58  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 152.83/22.58  |            (14), (15), (16), (17), (19) are inconsistent by sub-proof #343.
% 152.83/22.58  | 
% 152.83/22.58  End of proof
% 152.83/22.58  
% 152.83/22.58  Sub-proof #318 shows that the following formulas are inconsistent:
% 152.83/22.58  ----------------------------------------------------------------
% 152.83/22.58    (1)  all_56_8 = e3
% 152.83/22.58    (2)  all_56_15 = e1
% 152.83/22.58    (3)   ~ (e3 = e1)
% 152.83/22.58    (4)  all_56_10 = e3
% 152.83/22.58    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.83/22.58         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.83/22.58    (6)  all_56_11 = e2
% 152.83/22.58    (7)  op(e0, e0) = all_10_2
% 152.83/22.58    (8)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.58         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.83/22.58    (9)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.83/22.58         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.58    (10)   ~ (e2 = e0)
% 152.83/22.58    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.58            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.58    (12)  op(e0, e0) = e3
% 152.83/22.58    (13)  op(e3, e3) = e2
% 152.83/22.58    (14)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 152.83/22.58            all_57_14 & $i(all_57_14))
% 152.83/22.58    (15)  all_56_14 = e2
% 152.83/22.58    (16)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.58              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 152.83/22.58                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.83/22.58                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.83/22.58    (17)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.83/22.58          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.83/22.58    (18)  all_57_3 = e3
% 152.83/22.58    (19)  op(e0, e0) = e1
% 152.83/22.58    (20)  op(e3, e0) = all_52_12
% 152.83/22.58    (21)   ~ (e3 = e0)
% 152.83/22.58    (22)   ~ (all_52_9 = e2)
% 152.83/22.58    (23)  op(e0, e1) = e2
% 152.83/22.58    (24)  op(e0, e3) = all_52_3
% 152.83/22.58    (25)  op(e2, e2) = e2
% 152.83/22.58    (26)  op(e2, e1) = all_52_9
% 152.83/22.58    (27)   ~ (e1 = e0)
% 152.83/22.58    (28)  op(e1, e1) = e3
% 152.83/22.58    (29)  all_57_12 = e2
% 152.83/22.58    (30)  op(e1, e0) = e2
% 152.83/22.58    (31)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.58          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.83/22.58    (32)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.83/22.58          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.58    (33)   ~ (all_10_2 = e2)
% 152.83/22.58    (34)  op(e3, e1) = all_52_8
% 152.83/22.58    (35)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.58          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.58    (36)   ~ (e2 = e1)
% 152.83/22.58    (37)  op(e0, e3) = e3
% 152.83/22.58    (38)  all_56_12 = e3
% 152.83/22.58    (39)  all_56_1 = e3
% 152.83/22.58    (40)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.58          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.58    (41)  op(e1, e3) = all_52_2
% 152.83/22.59    (42)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.83/22.59              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.83/22.59            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.83/22.59            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.83/22.59            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.83/22.59            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.83/22.59            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.83/22.59            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.83/22.59            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.83/22.59            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.83/22.59            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.83/22.59            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.83/22.59            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.83/22.59            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.83/22.59            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.83/22.59            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.83/22.59            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.83/22.59            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.83/22.59            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.83/22.59            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.83/22.59            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.83/22.59            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.83/22.59            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.83/22.59            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.83/22.59            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.59            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.83/22.59            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.83/22.59            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.59            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.59            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.83/22.59            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.83/22.59            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.83/22.59            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.83/22.59            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.83/22.59            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.59            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.83/22.59            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.59            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.83/22.59            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.83/22.59            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.59            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.83/22.59            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.83/22.59            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.59            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.83/22.59            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.83/22.59            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.59            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.83/22.59            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.83/22.59              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.83/22.59            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.83/22.59            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.83/22.59              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.83/22.59            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.83/22.59            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.83/22.59                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.83/22.59                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.83/22.59                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.83/22.59                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.83/22.59                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.83/22.59                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.83/22.59                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.83/22.59              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.83/22.59                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.83/22.59                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.59                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.83/22.59                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.83/22.59                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.83/22.59                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.59                $i(all_57_7))))
% 152.83/22.59    (43)  op(e2, e3) = all_52_1
% 152.83/22.59  
% 152.83/22.59  Begin of proof
% 152.83/22.59  | 
% 152.83/22.59  | BETA: splitting (16) gives:
% 152.83/22.59  | 
% 152.83/22.59  | Case 1:
% 152.83/22.59  | | 
% 152.83/22.59  | |   (44)  all_56_15 = e0 & op(e0, e0) = e0
% 152.83/22.59  | | 
% 152.83/22.59  | | ALPHA: (44) implies:
% 152.83/22.59  | |   (45)  op(e0, e0) = e0
% 152.83/22.59  | | 
% 152.83/22.59  | | REF_CLOSE: (11), (12), (21), (45) are inconsistent by sub-proof #1143.
% 152.83/22.59  | | 
% 152.83/22.59  | Case 2:
% 152.83/22.59  | | 
% 152.83/22.59  | |   (46)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 152.83/22.59  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 152.83/22.59  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.83/22.59  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 152.83/22.59  | | 
% 152.83/22.59  | | ALPHA: (46) implies:
% 152.83/22.59  | |   (47)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 152.83/22.59  | |           e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.59  | |   (48)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 152.83/22.59  | |           e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.59  | | 
% 152.83/22.59  | | BETA: splitting (42) gives:
% 152.83/22.59  | | 
% 152.83/22.59  | | Case 1:
% 152.83/22.59  | | | 
% 152.83/22.59  | | |   (49)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.59  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.83/22.59  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 152.83/22.59  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 152.83/22.59  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.83/22.59  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.83/22.59  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 152.83/22.59  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 152.83/22.59  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.83/22.59  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 152.83/22.59  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 152.83/22.59  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 152.83/22.59  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) | (all_57_3 =
% 152.83/22.59  | | |           e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 = e2) &
% 152.83/22.59  | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) = all_57_4
% 152.83/22.59  | | |           & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3 =
% 152.83/22.59  | | |           e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 152.83/22.59  | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5
% 152.83/22.59  | | |           & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 =
% 152.83/22.59  | | |           e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 152.83/22.59  | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 152.83/22.59  | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.83/22.59  | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 152.83/22.59  | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.83/22.59  | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.83/22.59  | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7
% 152.83/22.59  | | |             = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 152.83/22.59  | | |             e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.83/22.59  | | |           $i(all_57_7) & $i(all_57_10))
% 152.83/22.59  | | | 
% 152.83/22.59  | | | BETA: splitting (49) gives:
% 152.83/22.59  | | | 
% 152.83/22.59  | | | Case 1:
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | |   (50)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.59  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.83/22.59  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 152.83/22.59  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 152.83/22.59  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.83/22.59  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 152.83/22.59  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.83/22.59  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 152.83/22.59  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.83/22.59  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.83/22.59  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 152.83/22.59  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.83/22.59  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 152.83/22.59  | | | |           $i(all_57_14))
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | | BETA: splitting (50) gives:
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | | Case 1:
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | |   (51)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.59  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 152.83/22.59  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 152.83/22.59  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 152.83/22.59  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.83/22.59  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 152.83/22.59  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12))
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | | BETA: splitting (51) gives:
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | | Case 1:
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | |   (52)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.59  | | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 152.83/22.59  | | | | | |         & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 152.83/22.59  | | | | | |         $i(all_57_12)
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | ALPHA: (52) implies:
% 152.83/22.59  | | | | | |   (53)  op(e2, e2) = all_57_12
% 152.83/22.59  | | | | | |   (54)  op(e2, e3) = e2
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | REF_CLOSE: (1), (3), (4), (6), (9), (10), (11), (13), (17), (21),
% 152.83/22.59  | | | | | |            (23), (25), (27), (31), (36), (39), (43), (48), (54) are
% 152.83/22.59  | | | | | |            inconsistent by sub-proof #332.
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | Case 2:
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | |   (55)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 152.83/22.59  | | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 152.83/22.59  | | | | | |         & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 152.83/22.59  | | | | | |         $i(all_57_12)
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | ALPHA: (55) implies:
% 152.83/22.59  | | | | | |   (56)  op(e2, e3) = e2
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | REF_CLOSE: (1), (3), (4), (6), (9), (10), (11), (13), (17), (21),
% 152.83/22.59  | | | | | |            (23), (25), (27), (31), (36), (39), (43), (48), (56) are
% 152.83/22.59  | | | | | |            inconsistent by sub-proof #332.
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | End of split
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | Case 2:
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | |   (57)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.83/22.59  | | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.83/22.59  | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 152.83/22.59  | | | | |           $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 152.83/22.59  | | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.83/22.59  | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0)
% 152.83/22.59  | | | | |           = e3 & $i(all_57_2) & $i(all_57_14))
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | | REF_CLOSE: (3), (6), (10), (11), (12), (19), (21), (23), (25), (27),
% 152.83/22.59  | | | | |            (28), (35), (36), (38), (39), (40), (41), (47), (57) are
% 152.83/22.59  | | | | |            inconsistent by sub-proof #327.
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | End of split
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | Case 2:
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | |   (58)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.83/22.59  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 152.83/22.59  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 152.83/22.59  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.83/22.59  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 152.83/22.59  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.83/22.59  | | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 =
% 152.83/22.59  | | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) =
% 152.83/22.59  | | | |           e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 152.83/22.59  | | | |           all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 152.83/22.59  | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 152.83/22.59  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 152.83/22.59  | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 152.83/22.59  | | | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.83/22.59  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.59  | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.83/22.59  | | | |           $i(all_57_10))
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | | REF_CLOSE: (7), (11), (14), (18), (25), (33), (36), (58) are
% 152.83/22.59  | | | |            inconsistent by sub-proof #339.
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | End of split
% 152.83/22.59  | | | 
% 152.83/22.59  | | Case 2:
% 152.83/22.59  | | | 
% 152.83/22.59  | | |   (59)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.83/22.59  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.59  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.59  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 152.83/22.59  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.83/22.59  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.83/22.59  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 152.83/22.59  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 152.83/22.59  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 152.83/22.59  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 152.83/22.59  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 152.83/22.59  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 152.83/22.59  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 152.83/22.59  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.83/22.59  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.59  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.83/22.59  | | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9
% 152.83/22.59  | | |             = e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 152.83/22.59  | | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 152.83/22.59  | | |           $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1
% 152.83/22.59  | | |           &  ~ (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.83/22.59  | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 152.83/22.59  | | |           & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 152.83/22.59  | | |           e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.83/22.59  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 152.83/22.59  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 152.83/22.59  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.83/22.59  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 152.83/22.59  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 152.83/22.59  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.83/22.59  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.83/22.59  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.83/22.59  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.83/22.59  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.83/22.59  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 152.83/22.59  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.83/22.59  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.83/22.59  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 152.83/22.59  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 152.83/22.59  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.83/22.59  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.59  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 152.83/22.59  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 152.83/22.59  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.83/22.59  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.83/22.59  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 152.83/22.59  | | | 
% 152.83/22.59  | | | BETA: splitting (59) gives:
% 152.83/22.59  | | | 
% 152.83/22.59  | | | Case 1:
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | |   (60)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.83/22.59  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.59  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.59  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 152.83/22.59  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 152.83/22.59  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 152.83/22.59  | | | |           e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.83/22.59  | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 152.83/22.59  | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.83/22.59  | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.83/22.59  | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.83/22.59  | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.59  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.83/22.59  | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 152.83/22.59  | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 152.83/22.59  | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.83/22.59  | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | | BETA: splitting (60) gives:
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | | Case 1:
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | |   (61)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.83/22.59  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.83/22.59  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.59  | | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 152.83/22.59  | | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 152.83/22.59  | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 152.83/22.59  | | | | |           = e2 & $i(all_57_6) & $i(all_57_12))
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | | REF_CLOSE: (3), (4), (5), (6), (8), (10), (11), (12), (13), (15),
% 152.83/22.59  | | | | |            (21), (22), (23), (25), (26), (27), (28), (32), (34), (35),
% 152.83/22.59  | | | | |            (36), (38), (39), (40), (41), (47), (61) are inconsistent
% 152.83/22.59  | | | | |            by sub-proof #324.
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | Case 2:
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | |   (62)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.83/22.59  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 152.83/22.59  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.59  | | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 152.83/22.59  | | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 152.83/22.59  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 152.83/22.59  | | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 152.83/22.59  | | | | |           & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1)
% 152.83/22.59  | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 152.83/22.59  | | | | |           & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | | BETA: splitting (62) gives:
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | | Case 1:
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | |   (63)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.83/22.59  | | | | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 152.83/22.59  | | | | | |         & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.59  | | | | | |         $i(all_57_12)
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | ALPHA: (63) implies:
% 152.83/22.59  | | | | | |   (64)  op(e2, e1) = e2
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | REF_CLOSE: (11), (22), (26), (64) are inconsistent by sub-proof
% 152.83/22.59  | | | | | |            #1157.
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | Case 2:
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | |   (65)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.83/22.59  | | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 152.83/22.59  | | | | | |           e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.83/22.59  | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 152.83/22.59  | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1)
% 152.83/22.59  | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 152.83/22.59  | | | | | |           e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.83/22.59  | | | | | |           $i(all_57_13))
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | BETA: splitting (65) gives:
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | Case 1:
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | |   (66)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.83/22.59  | | | | | | |         (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 152.83/22.59  | | | | | | |         e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.83/22.59  | | | | | | |         $i(all_57_10) & $i(all_57_11)
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | | ALPHA: (66) implies:
% 152.83/22.59  | | | | | | |   (67)  op(e3, e0) = e3
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (16), (19), (20),
% 152.83/22.59  | | | | | | |            (21), (27), (67) are inconsistent by sub-proof #320.
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | Case 2:
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | |   (68)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.83/22.59  | | | | | | |         (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 152.83/22.59  | | | | | | |         e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.83/22.59  | | | | | | |         $i(all_57_10) & $i(all_57_13)
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | | ALPHA: (68) implies:
% 152.83/22.59  | | | | | | |   (69)  op(e3, e0) = e3
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | | REF_CLOSE: (2), (4), (6), (10), (11), (12), (16), (19), (20),
% 152.83/22.59  | | | | | | |            (21), (27), (69) are inconsistent by sub-proof #320.
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | End of split
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | End of split
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | End of split
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | Case 2:
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | |   (70)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 152.83/22.59  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.59  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.83/22.59  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 152.83/22.59  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.83/22.59  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 152.83/22.59  | | | |           e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 152.83/22.59  | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 152.83/22.59  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.83/22.59  | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 152.83/22.59  | | | |         (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 152.83/22.59  | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 152.83/22.59  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.83/22.59  | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.83/22.59  | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.83/22.59  | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 152.83/22.59  | | | |               & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 152.83/22.59  | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 152.83/22.59  | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 152.83/22.59  | | | |               e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.83/22.59  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 152.83/22.59  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.83/22.59  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.83/22.59  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 152.83/22.59  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.83/22.59  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 152.83/22.59  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 152.83/22.59  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.83/22.59  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 152.83/22.59  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | | BETA: splitting (70) gives:
% 152.83/22.59  | | | | 
% 152.83/22.59  | | | | Case 1:
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | |   (71)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 152.83/22.59  | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.59  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.83/22.59  | | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 152.83/22.59  | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.83/22.59  | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 152.83/22.59  | | | | |           = e1 & $i(all_57_9) & $i(all_57_14))
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | | REF_CLOSE: (10), (11), (13), (71) are inconsistent by sub-proof #1037.
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | Case 2:
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | |   (72)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 152.83/22.59  | | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.83/22.59  | | | | |           & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.83/22.59  | | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 152.83/22.59  | | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 152.83/22.59  | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0)
% 152.83/22.59  | | | | |           = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 152.83/22.59  | | | | |           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 152.83/22.59  | | | | |               &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3)
% 152.83/22.59  | | | | |               = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.83/22.59  | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.83/22.59  | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.83/22.59  | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.83/22.59  | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.83/22.59  | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.83/22.59  | | | | |               & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.83/22.59  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 152.83/22.59  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.83/22.59  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.83/22.59  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.59  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 152.83/22.59  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.83/22.59  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.83/22.59  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 152.83/22.59  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.59  | | | | |               $i(all_57_7))))
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | | BETA: splitting (72) gives:
% 152.83/22.59  | | | | | 
% 152.83/22.59  | | | | | Case 1:
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | |   (73)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 152.83/22.59  | | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.83/22.59  | | | | | |         & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.83/22.59  | | | | | |         $i(all_57_13)
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | ALPHA: (73) implies:
% 152.83/22.59  | | | | | |   (74)  op(e1, e1) = e0
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | REF_CLOSE: (11), (12), (19), (27), (28), (74) are inconsistent by
% 152.83/22.59  | | | | | |            sub-proof #331.
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | Case 2:
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | |   (75)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 152.83/22.59  | | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 152.83/22.59  | | | | | |           all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.83/22.59  | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 152.83/22.59  | | | | | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 152.83/22.59  | | | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.83/22.59  | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.83/22.59  | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.83/22.59  | | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.83/22.59  | | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.83/22.59  | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.83/22.59  | | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 152.83/22.59  | | | | | |               e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.83/22.59  | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 152.83/22.59  | | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.83/22.59  | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.83/22.59  | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.59  | | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 152.83/22.59  | | | | | |               e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.83/22.59  | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.83/22.59  | | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 152.83/22.59  | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.59  | | | | | |               $i(all_57_7))))
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | BETA: splitting (75) gives:
% 152.83/22.59  | | | | | | 
% 152.83/22.59  | | | | | | Case 1:
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | |   (76)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 152.83/22.59  | | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 152.83/22.59  | | | | | | |         all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.83/22.59  | | | | | | |         $i(all_57_11) & $i(all_57_14)
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | | ALPHA: (76) implies:
% 152.83/22.59  | | | | | | |   (77)  op(e1, e0) = e1
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | | REF_CLOSE: (11), (30), (36), (77) are inconsistent by sub-proof
% 152.83/22.59  | | | | | | |            #1125.
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | Case 2:
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | |   (78)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.83/22.59  | | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 152.83/22.59  | | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 152.83/22.59  | | | | | | |             op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 152.83/22.59  | | | | | | |             all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.83/22.59  | | | | | | |               e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.83/22.59  | | | | | | |             op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 152.83/22.59  | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 152.83/22.59  | | | | | | |               e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 152.83/22.59  | | | | | | |             op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 152.83/22.59  | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 152.83/22.59  | | | | | | |               e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.83/22.59  | | | | | | |             op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.83/22.59  | | | | | | |             all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 152.83/22.59  | | | | | | |               e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.83/22.59  | | | | | | |             op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 152.83/22.59  | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 152.83/22.59  | | | | | | |               e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.83/22.59  | | | | | | |             op(e0, e1) = e0 & $i(all_57_7)))
% 152.83/22.59  | | | | | | | 
% 152.83/22.59  | | | | | | | ALPHA: (78) implies:
% 152.83/22.59  | | | | | | |   (79)  op(e0, e0) = all_57_15
% 152.83/22.60  | | | | | | |   (80)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.83/22.60  | | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 152.83/22.60  | | | | | | |           e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 152.83/22.60  | | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.83/22.60  | | | | | | |             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.83/22.60  | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.83/22.60  | | | | | | |           = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 152.83/22.60  | | | | | | |             e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.83/22.60  | | | | | | |           $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 152.83/22.60  | | | | | | |           (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.83/22.60  | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.83/22.60  | | | | | | |           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.60  | | | | | | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 152.83/22.60  | | | | | | |           & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.83/22.60  | | | | | | |           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.83/22.60  | | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 152.83/22.60  | | | | | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.60  | | | | | | |           $i(all_57_7))
% 152.83/22.60  | | | | | | | 
% 152.83/22.60  | | | | | | | BETA: splitting (80) gives:
% 152.83/22.60  | | | | | | | 
% 152.83/22.60  | | | | | | | Case 1:
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | |   (81)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 152.83/22.60  | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 152.83/22.60  | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 152.83/22.60  | | | | | | | |         (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 152.83/22.60  | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 152.83/22.60  | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.83/22.60  | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 152.83/22.60  | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.83/22.60  | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | BETA: splitting (81) gives:
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | Case 1:
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | |   (82)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 152.83/22.60  | | | | | | | | |         ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 152.83/22.60  | | | | | | | | |           e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | ALPHA: (82) implies:
% 152.83/22.60  | | | | | | | | |   (83)  op(e0, e3) = e0
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | REF_CLOSE: (11), (12), (19), (24), (27), (37), (79), (83) are
% 152.83/22.60  | | | | | | | | |            inconsistent by sub-proof #319.
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | Case 2:
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | |   (84)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 152.83/22.60  | | | | | | | | |            ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 152.83/22.60  | | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 152.83/22.60  | | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &
% 152.83/22.60  | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.83/22.60  | | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | BETA: splitting (84) gives:
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | Case 1:
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | |   (85)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 152.83/22.60  | | | | | | | | | |         &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 152.83/22.60  | | | | | | | | | |         op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | ALPHA: (85) implies:
% 152.83/22.60  | | | | | | | | | |   (86)  op(e0, e3) = e0
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | REF_CLOSE: (11), (12), (19), (24), (27), (37), (79), (86) are
% 152.83/22.60  | | | | | | | | | |            inconsistent by sub-proof #319.
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | Case 2:
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | |   (87)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3)
% 152.83/22.60  | | | | | | | | | |         &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 152.83/22.60  | | | | | | | | | |         = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | ALPHA: (87) implies:
% 152.83/22.60  | | | | | | | | | |   (88)   ~ (all_57_3 = e3)
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | REDUCE: (18), (88) imply:
% 152.83/22.60  | | | | | | | | | |   (89)  $false
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | CLOSE: (89) is inconsistent.
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | End of split
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | End of split
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | Case 2:
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | |   (90)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) & 
% 152.83/22.60  | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 152.83/22.60  | | | | | | | |             e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 152.83/22.60  | | | | | | | |         (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 152.83/22.60  | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.83/22.60  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 152.83/22.60  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.83/22.60  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.83/22.60  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | REF_CLOSE: (10), (11), (14), (23), (25), (36), (90) are
% 152.83/22.60  | | | | | | | |            inconsistent by sub-proof #1004.
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | End of split
% 152.83/22.60  | | | | | | | 
% 152.83/22.60  | | | | | | End of split
% 152.83/22.60  | | | | | | 
% 152.83/22.60  | | | | | End of split
% 152.83/22.60  | | | | | 
% 152.83/22.60  | | | | End of split
% 152.83/22.60  | | | | 
% 152.83/22.60  | | | End of split
% 152.83/22.60  | | | 
% 152.83/22.60  | | End of split
% 152.83/22.60  | | 
% 152.83/22.60  | End of split
% 152.83/22.60  | 
% 152.83/22.60  End of proof
% 152.83/22.60  
% 152.83/22.60  Sub-proof #319 shows that the following formulas are inconsistent:
% 152.83/22.60  ----------------------------------------------------------------
% 152.83/22.60    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.60    (2)  op(e0, e0) = e3
% 152.83/22.60    (3)  op(e0, e3) = e0
% 152.83/22.60    (4)  op(e0, e0) = e1
% 152.83/22.60    (5)  op(e0, e3) = all_52_3
% 152.83/22.60    (6)   ~ (e1 = e0)
% 152.83/22.60    (7)  op(e0, e0) = all_57_15
% 152.83/22.60    (8)  op(e0, e3) = e3
% 152.83/22.60  
% 152.83/22.60  Begin of proof
% 152.83/22.60  | 
% 152.83/22.60  | GROUND_INST: instantiating (1) with e3, all_57_15, e0, e0, simplifying with
% 152.83/22.60  |              (2), (7) gives:
% 152.83/22.60  |   (9)  all_57_15 = e3
% 152.83/22.60  | 
% 152.83/22.60  | GROUND_INST: instantiating (1) with e1, all_57_15, e0, e0, simplifying with
% 152.83/22.60  |              (4), (7) gives:
% 152.83/22.60  |   (10)  all_57_15 = e1
% 152.83/22.60  | 
% 152.83/22.60  | GROUND_INST: instantiating (1) with all_52_3, e0, e3, e0, simplifying with
% 152.83/22.60  |              (3), (5) gives:
% 152.83/22.60  |   (11)  all_52_3 = e0
% 152.83/22.60  | 
% 152.83/22.60  | GROUND_INST: instantiating (1) with all_52_3, e3, e3, e0, simplifying with
% 152.83/22.60  |              (5), (8) gives:
% 152.83/22.60  |   (12)  all_52_3 = e3
% 152.83/22.60  | 
% 152.83/22.60  | COMBINE_EQS: (9), (10) imply:
% 152.83/22.60  |   (13)  e3 = e1
% 152.83/22.60  | 
% 152.83/22.60  | SIMP: (13) implies:
% 152.83/22.60  |   (14)  e3 = e1
% 152.83/22.60  | 
% 152.83/22.60  | COMBINE_EQS: (11), (12) imply:
% 152.83/22.60  |   (15)  e3 = e0
% 152.83/22.60  | 
% 152.83/22.60  | SIMP: (15) implies:
% 152.83/22.60  |   (16)  e3 = e0
% 152.83/22.60  | 
% 152.83/22.60  | COMBINE_EQS: (14), (16) imply:
% 152.83/22.60  |   (17)  e1 = e0
% 152.83/22.60  | 
% 152.83/22.60  | REDUCE: (6), (17) imply:
% 152.83/22.60  |   (18)  $false
% 152.83/22.60  | 
% 152.83/22.60  | CLOSE: (18) is inconsistent.
% 152.83/22.60  | 
% 152.83/22.60  End of proof
% 152.83/22.60  
% 152.83/22.60  Sub-proof #320 shows that the following formulas are inconsistent:
% 152.83/22.60  ----------------------------------------------------------------
% 152.83/22.60    (1)  all_56_15 = e1
% 152.83/22.60    (2)  all_56_10 = e3
% 152.83/22.60    (3)  op(e3, e0) = e3
% 152.83/22.60    (4)  all_56_11 = e2
% 152.83/22.60    (5)   ~ (e2 = e0)
% 152.83/22.60    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.60    (7)  op(e0, e0) = e3
% 152.83/22.60    (8)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.60             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 152.83/22.60               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.83/22.60               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.83/22.60    (9)  op(e0, e0) = e1
% 152.83/22.60    (10)  op(e3, e0) = all_52_12
% 152.83/22.60    (11)   ~ (e3 = e0)
% 152.83/22.60    (12)   ~ (e1 = e0)
% 152.83/22.60  
% 152.83/22.60  Begin of proof
% 152.83/22.60  | 
% 152.83/22.60  | BETA: splitting (8) gives:
% 152.83/22.60  | 
% 152.83/22.60  | Case 1:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (13)  all_56_15 = e0 & op(e0, e0) = e0
% 152.83/22.60  | | 
% 152.83/22.60  | | REF_CLOSE: (1), (12), (13) are inconsistent by sub-proof #409.
% 152.83/22.60  | | 
% 152.83/22.60  | Case 2:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (14)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 152.83/22.60  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 152.83/22.60  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.83/22.60  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 152.83/22.60  | | 
% 152.83/22.60  | | ALPHA: (14) implies:
% 152.83/22.60  | |   (15)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 152.83/22.60  | |           e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.60  | | 
% 152.83/22.60  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (15) are
% 152.83/22.60  | |            inconsistent by sub-proof #321.
% 152.83/22.60  | | 
% 152.83/22.60  | End of split
% 152.83/22.60  | 
% 152.83/22.60  End of proof
% 152.83/22.60  
% 152.83/22.60  Sub-proof #321 shows that the following formulas are inconsistent:
% 152.83/22.60  ----------------------------------------------------------------
% 152.83/22.60    (1)  all_56_10 = e3
% 152.83/22.60    (2)  op(e3, e0) = e3
% 152.83/22.60    (3)  all_56_11 = e2
% 152.83/22.60    (4)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 152.83/22.60         (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.60    (5)   ~ (e2 = e0)
% 152.83/22.60    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.60    (7)  op(e0, e0) = e3
% 152.83/22.60    (8)  op(e0, e0) = e1
% 152.83/22.60    (9)  op(e3, e0) = all_52_12
% 152.83/22.60    (10)   ~ (e3 = e0)
% 152.83/22.60    (11)   ~ (e1 = e0)
% 152.83/22.60  
% 152.83/22.60  Begin of proof
% 152.83/22.60  | 
% 152.83/22.60  | BETA: splitting (4) gives:
% 152.83/22.60  | 
% 152.83/22.60  | Case 1:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (12)  all_56_9 = e0 & op(e3, e0) = e0
% 152.83/22.60  | | 
% 152.83/22.60  | | REF_CLOSE: (2), (6), (7), (8), (9), (11), (12) are inconsistent by sub-proof
% 152.83/22.60  | |            #323.
% 152.83/22.60  | | 
% 152.83/22.60  | Case 2:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (13)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 152.83/22.60  | |           e0)
% 152.83/22.60  | | 
% 152.83/22.60  | | BETA: splitting (13) gives:
% 152.83/22.60  | | 
% 152.83/22.60  | | Case 1:
% 152.83/22.60  | | | 
% 152.83/22.60  | | |   (14)  all_56_10 = e0 & op(e2, e0) = e0
% 152.83/22.60  | | | 
% 152.83/22.60  | | | ALPHA: (14) implies:
% 152.83/22.60  | | |   (15)  all_56_10 = e0
% 152.83/22.60  | | | 
% 152.83/22.60  | | | REF_CLOSE: (1), (10), (15) are inconsistent by sub-proof #1134.
% 152.83/22.60  | | | 
% 152.83/22.60  | | Case 2:
% 152.83/22.60  | | | 
% 152.83/22.60  | | |   (16)  all_56_11 = e0 & op(e1, e0) = e0
% 152.83/22.60  | | | 
% 152.83/22.60  | | | REF_CLOSE: (3), (5), (16) are inconsistent by sub-proof #322.
% 152.83/22.60  | | | 
% 152.83/22.60  | | End of split
% 152.83/22.60  | | 
% 152.83/22.60  | End of split
% 152.83/22.60  | 
% 152.83/22.60  End of proof
% 152.83/22.60  
% 152.83/22.60  Sub-proof #322 shows that the following formulas are inconsistent:
% 152.83/22.60  ----------------------------------------------------------------
% 152.83/22.60    (1)  all_56_11 = e0 & op(e1, e0) = e0
% 152.83/22.60    (2)  all_56_11 = e2
% 152.83/22.60    (3)   ~ (e2 = e0)
% 152.83/22.60  
% 152.83/22.60  Begin of proof
% 152.83/22.60  | 
% 152.83/22.60  | ALPHA: (1) implies:
% 152.83/22.60  |   (4)  all_56_11 = e0
% 152.83/22.60  | 
% 152.83/22.60  | COMBINE_EQS: (2), (4) imply:
% 152.83/22.60  |   (5)  e2 = e0
% 152.83/22.60  | 
% 152.83/22.60  | SIMP: (5) implies:
% 152.83/22.60  |   (6)  e2 = e0
% 152.83/22.60  | 
% 152.83/22.60  | REDUCE: (3), (6) imply:
% 152.83/22.60  |   (7)  $false
% 152.83/22.60  | 
% 152.83/22.60  | CLOSE: (7) is inconsistent.
% 152.83/22.60  | 
% 152.83/22.60  End of proof
% 152.83/22.60  
% 152.83/22.60  Sub-proof #323 shows that the following formulas are inconsistent:
% 152.83/22.60  ----------------------------------------------------------------
% 152.83/22.60    (1)  op(e3, e0) = e3
% 152.83/22.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.60    (3)  op(e0, e0) = e3
% 152.83/22.60    (4)  all_56_9 = e0 & op(e3, e0) = e0
% 152.83/22.60    (5)  op(e0, e0) = e1
% 152.83/22.60    (6)  op(e3, e0) = all_52_12
% 152.83/22.60    (7)   ~ (e1 = e0)
% 152.83/22.60  
% 152.83/22.60  Begin of proof
% 152.83/22.60  | 
% 152.83/22.60  | ALPHA: (4) implies:
% 152.83/22.60  |   (8)  op(e3, e0) = e0
% 152.83/22.60  | 
% 152.83/22.60  | GROUND_INST: instantiating (2) with e1, e3, e0, e0, simplifying with (3), (5)
% 152.83/22.60  |              gives:
% 152.83/22.60  |   (9)  e3 = e1
% 152.83/22.60  | 
% 152.83/22.60  | GROUND_INST: instantiating (2) with all_52_12, e0, e0, e3, simplifying with
% 152.83/22.60  |              (6), (8) gives:
% 152.83/22.60  |   (10)  all_52_12 = e0
% 152.83/22.60  | 
% 152.83/22.60  | GROUND_INST: instantiating (2) with all_52_12, e3, e0, e3, simplifying with
% 152.83/22.60  |              (1), (6) gives:
% 152.83/22.60  |   (11)  all_52_12 = e3
% 152.83/22.60  | 
% 152.83/22.60  | COMBINE_EQS: (10), (11) imply:
% 152.83/22.60  |   (12)  e3 = e0
% 152.83/22.60  | 
% 152.83/22.60  | SIMP: (12) implies:
% 152.83/22.60  |   (13)  e3 = e0
% 152.83/22.60  | 
% 152.83/22.60  | COMBINE_EQS: (9), (13) imply:
% 152.83/22.60  |   (14)  e1 = e0
% 152.83/22.60  | 
% 152.83/22.60  | SIMP: (14) implies:
% 152.83/22.60  |   (15)  e1 = e0
% 152.83/22.60  | 
% 152.83/22.60  | REDUCE: (7), (15) imply:
% 152.83/22.60  |   (16)  $false
% 152.83/22.60  | 
% 152.83/22.60  | CLOSE: (16) is inconsistent.
% 152.83/22.60  | 
% 152.83/22.60  End of proof
% 152.83/22.60  
% 152.83/22.60  Sub-proof #324 shows that the following formulas are inconsistent:
% 152.83/22.60  ----------------------------------------------------------------
% 152.83/22.60    (1)   ~ (e3 = e1)
% 152.83/22.60    (2)  all_56_10 = e3
% 152.83/22.60    (3)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.83/22.60         (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.60    (4)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 152.83/22.60         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 152.83/22.60    (5)  all_56_11 = e2
% 152.83/22.60    (6)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.60         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.83/22.60    (7)   ~ (e2 = e0)
% 152.83/22.60    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.60    (9)  op(e0, e0) = e3
% 152.83/22.60    (10)  op(e3, e3) = e2
% 152.83/22.60    (11)  all_56_14 = e2
% 152.83/22.60    (12)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 152.83/22.60              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.83/22.60            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 152.83/22.60            = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 152.83/22.60            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 152.83/22.60            op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 152.83/22.60    (13)   ~ (e3 = e0)
% 152.83/22.60    (14)   ~ (all_52_9 = e2)
% 152.83/22.60    (15)  op(e0, e1) = e2
% 152.83/22.60    (16)  op(e2, e2) = e2
% 152.83/22.60    (17)  op(e2, e1) = all_52_9
% 152.83/22.60    (18)   ~ (e1 = e0)
% 152.83/22.60    (19)  op(e1, e1) = e3
% 152.83/22.60    (20)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.83/22.60          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.60    (21)  op(e3, e1) = all_52_8
% 152.83/22.60    (22)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.60          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.60    (23)   ~ (e2 = e1)
% 152.83/22.60    (24)  all_56_12 = e3
% 152.83/22.60    (25)  all_56_1 = e3
% 152.83/22.60    (26)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.60          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.60    (27)  op(e1, e3) = all_52_2
% 152.83/22.60  
% 152.83/22.60  Begin of proof
% 152.83/22.60  | 
% 152.83/22.60  | BETA: splitting (12) gives:
% 152.83/22.60  | 
% 152.83/22.60  | Case 1:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (28)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 152.83/22.60  | |           = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 152.83/22.60  | |         all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 152.83/22.60  | | 
% 152.83/22.60  | | ALPHA: (28) implies:
% 152.83/22.60  | |   (29)  op(e0, e0) = e1
% 152.83/22.60  | |   (30)  op(e3, e1) = e3
% 152.83/22.60  | | 
% 152.83/22.60  | | BETA: splitting (26) gives:
% 152.83/22.60  | | 
% 152.83/22.60  | | Case 1:
% 152.83/22.60  | | | 
% 152.83/22.60  | | |   (31)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 152.83/22.60  | | |           e1)
% 152.83/22.60  | | | 
% 152.83/22.60  | | | REF_CLOSE: (1), (8), (16), (23), (25), (31) are inconsistent by sub-proof
% 152.83/22.60  | | |            #935.
% 152.83/22.60  | | | 
% 152.83/22.60  | | Case 2:
% 152.83/22.60  | | | 
% 152.83/22.60  | | |   (32)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 152.83/22.60  | | |           e1)
% 152.83/22.60  | | | 
% 152.83/22.60  | | | BETA: splitting (32) gives:
% 152.83/22.60  | | | 
% 152.83/22.60  | | | Case 1:
% 152.83/22.60  | | | | 
% 152.83/22.60  | | | |   (33)  all_56_7 = e1 & op(e1, e2) = e1
% 152.83/22.60  | | | | 
% 152.83/22.60  | | | | ALPHA: (33) implies:
% 152.83/22.60  | | | |   (34)  all_56_7 = e1
% 152.83/22.60  | | | | 
% 152.83/22.60  | | | | BETA: splitting (22) gives:
% 152.83/22.60  | | | | 
% 152.83/22.60  | | | | Case 1:
% 152.83/22.60  | | | | | 
% 152.83/22.60  | | | | |   (35)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1,
% 152.83/22.60  | | | | |             e2) = e0)
% 152.83/22.60  | | | | | 
% 152.83/22.60  | | | | | BETA: splitting (35) gives:
% 152.83/22.60  | | | | | 
% 152.83/22.60  | | | | | Case 1:
% 152.83/22.60  | | | | | | 
% 152.83/22.60  | | | | | |   (36)  all_56_6 = e0 & op(e1, e3) = e0
% 152.83/22.60  | | | | | | 
% 152.83/22.60  | | | | | | ALPHA: (36) implies:
% 152.83/22.60  | | | | | |   (37)  op(e1, e3) = e0
% 152.83/22.60  | | | | | | 
% 152.83/22.60  | | | | | | BETA: splitting (4) gives:
% 152.83/22.60  | | | | | | 
% 152.83/22.60  | | | | | | Case 1:
% 152.83/22.60  | | | | | | | 
% 152.83/22.60  | | | | | | |   (38)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 &
% 152.83/22.60  | | | | | | |           op(e2, e3) = e1)
% 152.83/22.60  | | | | | | | 
% 152.83/22.60  | | | | | | | BETA: splitting (38) gives:
% 152.83/22.60  | | | | | | | 
% 152.83/22.60  | | | | | | | Case 1:
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | |   (39)  all_56_0 = e1 & op(e3, e3) = e1
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | ALPHA: (39) implies:
% 152.83/22.60  | | | | | | | |   (40)  op(e3, e3) = e1
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | REF_CLOSE: (8), (10), (23), (40) are inconsistent by sub-proof
% 152.83/22.60  | | | | | | | |            #1074.
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | Case 2:
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | |   (41)  all_56_2 = e1 & op(e2, e3) = e1
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | ALPHA: (41) implies:
% 152.83/22.60  | | | | | | | |   (42)  all_56_2 = e1
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | BETA: splitting (6) gives:
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | Case 1:
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | |   (43)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 &
% 152.83/22.60  | | | | | | | | |           op(e2, e2) = e0)
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | BETA: splitting (43) gives:
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | Case 1:
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | |   (44)  all_56_2 = e0 & op(e2, e3) = e0
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | ALPHA: (44) implies:
% 152.83/22.60  | | | | | | | | | |   (45)  all_56_2 = e0
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | REF_CLOSE: (18), (42), (45) are inconsistent by sub-proof
% 152.83/22.60  | | | | | | | | | |            #1060.
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | Case 2:
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | |   (46)  all_56_3 = e0 & op(e2, e2) = e0
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | ALPHA: (46) implies:
% 152.83/22.60  | | | | | | | | | |   (47)  op(e2, e2) = e0
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | REF_CLOSE: (7), (8), (16), (47) are inconsistent by sub-proof
% 152.83/22.60  | | | | | | | | | |            #1145.
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | End of split
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | Case 2:
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | |   (48)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 &
% 152.83/22.60  | | | | | | | | |           op(e2, e0) = e0)
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | BETA: splitting (48) gives:
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | Case 1:
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | |   (49)  all_56_5 = e0 & op(e2, e1) = e0
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | ALPHA: (49) implies:
% 152.83/22.60  | | | | | | | | | |   (50)  all_56_5 = e0
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | REF_CLOSE: (1), (8), (11), (18), (19), (20), (21), (23),
% 152.83/22.60  | | | | | | | | | |            (30), (50) are inconsistent by sub-proof #325.
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | Case 2:
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | |   (51)  all_56_10 = e0 & op(e2, e0) = e0
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | ALPHA: (51) implies:
% 152.83/22.60  | | | | | | | | | |   (52)  all_56_10 = e0
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | | REF_CLOSE: (2), (13), (52) are inconsistent by sub-proof
% 152.83/22.60  | | | | | | | | | |            #1134.
% 152.83/22.60  | | | | | | | | | | 
% 152.83/22.60  | | | | | | | | | End of split
% 152.83/22.60  | | | | | | | | | 
% 152.83/22.60  | | | | | | | | End of split
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | End of split
% 152.83/22.60  | | | | | | | 
% 152.83/22.60  | | | | | | Case 2:
% 152.83/22.60  | | | | | | | 
% 152.83/22.60  | | | | | | |   (53)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 &
% 152.83/22.60  | | | | | | |           op(e0, e3) = e1)
% 152.83/22.60  | | | | | | | 
% 152.83/22.60  | | | | | | | BETA: splitting (53) gives:
% 152.83/22.60  | | | | | | | 
% 152.83/22.60  | | | | | | | Case 1:
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | |   (54)  all_56_6 = e1 & op(e1, e3) = e1
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | ALPHA: (54) implies:
% 152.83/22.60  | | | | | | | |   (55)  op(e1, e3) = e1
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | REF_CLOSE: (8), (18), (27), (37), (55) are inconsistent by
% 152.83/22.60  | | | | | | | |            sub-proof #1127.
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | Case 2:
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | |   (56)  all_56_12 = e1 & op(e0, e3) = e1
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | ALPHA: (56) implies:
% 152.83/22.60  | | | | | | | |   (57)  all_56_12 = e1
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | | REF_CLOSE: (1), (24), (57) are inconsistent by sub-proof #1056.
% 152.83/22.60  | | | | | | | | 
% 152.83/22.60  | | | | | | | End of split
% 152.83/22.60  | | | | | | | 
% 152.83/22.60  | | | | | | End of split
% 152.83/22.60  | | | | | | 
% 152.83/22.60  | | | | | Case 2:
% 152.83/22.60  | | | | | | 
% 152.83/22.60  | | | | | |   (58)  all_56_7 = e0 & op(e1, e2) = e0
% 152.83/22.60  | | | | | | 
% 152.83/22.60  | | | | | | REF_CLOSE: (18), (34), (58) are inconsistent by sub-proof #880.
% 152.83/22.60  | | | | | | 
% 152.83/22.60  | | | | | End of split
% 152.83/22.60  | | | | | 
% 152.83/22.60  | | | | Case 2:
% 152.83/22.60  | | | | | 
% 152.83/22.60  | | | | |   (59)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1,
% 152.83/22.60  | | | | |             e0) = e0)
% 152.83/22.60  | | | | | 
% 152.83/22.60  | | | | | REF_CLOSE: (5), (7), (8), (9), (18), (19), (29), (59) are inconsistent
% 152.83/22.60  | | | | |            by sub-proof #330.
% 152.83/22.60  | | | | | 
% 152.83/22.60  | | | | End of split
% 152.83/22.60  | | | | 
% 152.83/22.60  | | | Case 2:
% 152.83/22.60  | | | | 
% 152.83/22.60  | | | |   (60)  all_56_13 = e1 & op(e0, e2) = e1
% 152.83/22.60  | | | | 
% 152.83/22.60  | | | | ALPHA: (60) implies:
% 152.83/22.60  | | | |   (61)  all_56_13 = e1
% 152.83/22.60  | | | | 
% 152.83/22.60  | | | | REF_CLOSE: (3), (7), (8), (13), (15), (18), (24), (61) are inconsistent
% 152.83/22.60  | | | |            by sub-proof #633.
% 152.83/22.60  | | | | 
% 152.83/22.60  | | | End of split
% 152.83/22.60  | | | 
% 152.83/22.60  | | End of split
% 152.83/22.60  | | 
% 152.83/22.60  | Case 2:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (62)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 152.83/22.60  | |           = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 152.83/22.60  | |         all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 152.83/22.60  | | 
% 152.83/22.60  | | ALPHA: (62) implies:
% 152.83/22.60  | |   (63)  op(e2, e1) = e2
% 152.83/22.60  | | 
% 152.83/22.60  | | REF_CLOSE: (8), (14), (17), (63) are inconsistent by sub-proof #1157.
% 152.83/22.60  | | 
% 152.83/22.60  | End of split
% 152.83/22.60  | 
% 152.83/22.60  End of proof
% 152.83/22.60  
% 152.83/22.60  Sub-proof #325 shows that the following formulas are inconsistent:
% 152.83/22.60  ----------------------------------------------------------------
% 152.83/22.60    (1)   ~ (e3 = e1)
% 152.83/22.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.60    (3)  op(e3, e1) = e3
% 152.83/22.60    (4)  all_56_14 = e2
% 152.83/22.60    (5)  all_56_5 = e0
% 152.83/22.60    (6)   ~ (e1 = e0)
% 152.83/22.60    (7)  op(e1, e1) = e3
% 152.83/22.60    (8)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 152.83/22.60         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.60    (9)  op(e3, e1) = all_52_8
% 152.83/22.60    (10)   ~ (e2 = e1)
% 152.83/22.60  
% 152.83/22.60  Begin of proof
% 152.83/22.60  | 
% 152.83/22.60  | BETA: splitting (8) gives:
% 152.83/22.60  | 
% 152.83/22.60  | Case 1:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (11)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) =
% 152.83/22.60  | |           e1)
% 152.83/22.60  | | 
% 152.83/22.60  | | BETA: splitting (11) gives:
% 152.83/22.60  | | 
% 152.83/22.60  | | Case 1:
% 152.83/22.60  | | | 
% 152.83/22.60  | | |   (12)  all_56_4 = e1 & op(e3, e1) = e1
% 152.83/22.60  | | | 
% 152.83/22.60  | | | ALPHA: (12) implies:
% 152.83/22.60  | | |   (13)  op(e3, e1) = e1
% 152.83/22.60  | | | 
% 152.83/22.60  | | | REF_CLOSE: (1), (2), (3), (9), (13) are inconsistent by sub-proof #439.
% 152.83/22.60  | | | 
% 152.83/22.60  | | Case 2:
% 152.83/22.60  | | | 
% 152.83/22.60  | | |   (14)  all_56_5 = e1 & op(e2, e1) = e1
% 152.83/22.60  | | | 
% 152.83/22.60  | | | REF_CLOSE: (5), (6), (14) are inconsistent by sub-proof #334.
% 152.83/22.60  | | | 
% 152.83/22.60  | | End of split
% 152.83/22.60  | | 
% 152.83/22.60  | Case 2:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (15)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) =
% 152.83/22.60  | |           e1)
% 152.83/22.60  | | 
% 152.83/22.60  | | REF_CLOSE: (1), (2), (4), (7), (10), (15) are inconsistent by sub-proof
% 152.83/22.60  | |            #326.
% 152.83/22.60  | | 
% 152.83/22.60  | End of split
% 152.83/22.60  | 
% 152.83/22.60  End of proof
% 152.83/22.60  
% 152.83/22.60  Sub-proof #326 shows that the following formulas are inconsistent:
% 152.83/22.60  ----------------------------------------------------------------
% 152.83/22.60    (1)   ~ (e3 = e1)
% 152.83/22.60    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.60    (3)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 152.83/22.60    (4)  all_56_14 = e2
% 152.83/22.60    (5)  op(e1, e1) = e3
% 152.83/22.60    (6)   ~ (e2 = e1)
% 152.83/22.60  
% 152.83/22.60  Begin of proof
% 152.83/22.60  | 
% 152.83/22.60  | BETA: splitting (3) gives:
% 152.83/22.60  | 
% 152.83/22.60  | Case 1:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (7)  all_56_8 = e1 & op(e1, e1) = e1
% 152.83/22.60  | | 
% 152.83/22.60  | | ALPHA: (7) implies:
% 152.83/22.60  | |   (8)  op(e1, e1) = e1
% 152.83/22.60  | | 
% 152.83/22.60  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #734.
% 152.83/22.60  | | 
% 152.83/22.60  | Case 2:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (9)  all_56_14 = e1 & op(e0, e1) = e1
% 152.83/22.60  | | 
% 152.83/22.60  | | ALPHA: (9) implies:
% 152.83/22.60  | |   (10)  all_56_14 = e1
% 152.83/22.60  | | 
% 152.83/22.60  | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #1099.
% 152.83/22.60  | | 
% 152.83/22.60  | End of split
% 152.83/22.60  | 
% 152.83/22.60  End of proof
% 152.83/22.60  
% 152.83/22.60  Sub-proof #327 shows that the following formulas are inconsistent:
% 152.83/22.60  ----------------------------------------------------------------
% 152.83/22.60    (1)   ~ (e3 = e1)
% 152.83/22.60    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.83/22.60         (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.60    (3)  all_56_11 = e2
% 152.83/22.60    (4)   ~ (e2 = e0)
% 152.83/22.60    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.60    (6)  op(e0, e0) = e3
% 152.83/22.60    (7)  op(e0, e0) = e1
% 152.83/22.60    (8)   ~ (e3 = e0)
% 152.83/22.60    (9)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 152.83/22.60             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.83/22.60           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 152.83/22.60           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 152.83/22.60             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 152.83/22.60             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 152.83/22.60    (10)  op(e0, e1) = e2
% 152.83/22.60    (11)  op(e2, e2) = e2
% 152.83/22.60    (12)   ~ (e1 = e0)
% 152.83/22.60    (13)  op(e1, e1) = e3
% 152.83/22.60    (14)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.60          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.60    (15)   ~ (e2 = e1)
% 152.83/22.60    (16)  all_56_12 = e3
% 152.83/22.60    (17)  all_56_1 = e3
% 152.83/22.60    (18)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.60          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.60    (19)  op(e1, e3) = all_52_2
% 152.83/22.60  
% 152.83/22.60  Begin of proof
% 152.83/22.60  | 
% 152.83/22.60  | BETA: splitting (9) gives:
% 152.83/22.60  | 
% 152.83/22.60  | Case 1:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (20)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 152.83/22.60  | |           = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1
% 152.83/22.60  | |         & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 152.83/22.60  | | 
% 152.83/22.60  | | ALPHA: (20) implies:
% 152.83/22.60  | |   (21)  op(e1, e3) = e1
% 152.83/22.60  | | 
% 152.83/22.60  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 152.83/22.60  | |            (14), (15), (16), (17), (18), (19), (21) are inconsistent by
% 152.83/22.60  | |            sub-proof #328.
% 152.83/22.60  | | 
% 152.83/22.60  | Case 2:
% 152.83/22.60  | | 
% 152.83/22.60  | |   (22)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 152.83/22.60  | |           = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 152.83/22.60  | |         all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 152.83/22.60  | | 
% 152.83/22.60  | | ALPHA: (22) implies:
% 152.83/22.60  | |   (23)  op(e1, e3) = e1
% 152.83/22.60  | | 
% 152.83/22.60  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 152.83/22.60  | |            (14), (15), (16), (17), (18), (19), (23) are inconsistent by
% 152.83/22.60  | |            sub-proof #328.
% 152.83/22.60  | | 
% 152.83/22.60  | End of split
% 152.83/22.60  | 
% 152.83/22.60  End of proof
% 152.83/22.60  
% 152.83/22.60  Sub-proof #328 shows that the following formulas are inconsistent:
% 152.83/22.60  ----------------------------------------------------------------
% 152.83/22.60    (1)   ~ (e3 = e1)
% 152.83/22.60    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.83/22.60         (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.60    (3)  all_56_11 = e2
% 152.83/22.60    (4)   ~ (e2 = e0)
% 152.83/22.60    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.60           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.60    (6)  op(e0, e0) = e3
% 152.83/22.60    (7)  op(e1, e3) = e1
% 152.83/22.60    (8)  op(e0, e0) = e1
% 152.83/22.60    (9)   ~ (e3 = e0)
% 152.83/22.60    (10)  op(e0, e1) = e2
% 152.83/22.60    (11)  op(e2, e2) = e2
% 152.83/22.60    (12)   ~ (e1 = e0)
% 152.83/22.60    (13)  op(e1, e1) = e3
% 152.83/22.60    (14)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.60          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.60    (15)   ~ (e2 = e1)
% 152.83/22.60    (16)  all_56_12 = e3
% 152.83/22.60    (17)  all_56_1 = e3
% 152.83/22.61    (18)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.61          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.61    (19)  op(e1, e3) = all_52_2
% 152.83/22.61  
% 152.83/22.61  Begin of proof
% 152.83/22.61  | 
% 152.83/22.61  | BETA: splitting (18) gives:
% 152.83/22.61  | 
% 152.83/22.61  | Case 1:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (20)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 152.83/22.61  | |           e1)
% 152.83/22.61  | | 
% 152.83/22.61  | | REF_CLOSE: (1), (5), (11), (15), (17), (20) are inconsistent by sub-proof
% 152.83/22.61  | |            #935.
% 152.83/22.61  | | 
% 152.83/22.61  | Case 2:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (21)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 152.83/22.61  | |           e1)
% 152.83/22.61  | | 
% 152.83/22.61  | | BETA: splitting (21) gives:
% 152.83/22.61  | | 
% 152.83/22.61  | | Case 1:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (22)  all_56_7 = e1 & op(e1, e2) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (12), (13), (14), (19), (22) are
% 152.83/22.61  | | |            inconsistent by sub-proof #329.
% 152.83/22.61  | | | 
% 152.83/22.61  | | Case 2:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (23)  all_56_13 = e1 & op(e0, e2) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | ALPHA: (23) implies:
% 152.83/22.61  | | |   (24)  all_56_13 = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (2), (4), (5), (9), (10), (12), (16), (24) are inconsistent by
% 152.83/22.61  | | |            sub-proof #633.
% 152.83/22.61  | | | 
% 152.83/22.61  | | End of split
% 152.83/22.61  | | 
% 152.83/22.61  | End of split
% 152.83/22.61  | 
% 152.83/22.61  End of proof
% 152.83/22.61  
% 152.83/22.61  Sub-proof #329 shows that the following formulas are inconsistent:
% 152.83/22.61  ----------------------------------------------------------------
% 152.83/22.61    (1)  all_56_11 = e2
% 152.83/22.61    (2)   ~ (e2 = e0)
% 152.83/22.61    (3)  all_56_7 = e1 & op(e1, e2) = e1
% 152.83/22.61    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.61    (5)  op(e0, e0) = e3
% 152.83/22.61    (6)  op(e1, e3) = e1
% 152.83/22.61    (7)  op(e0, e0) = e1
% 152.83/22.61    (8)   ~ (e1 = e0)
% 152.83/22.61    (9)  op(e1, e1) = e3
% 152.83/22.61    (10)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.61          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.61    (11)  op(e1, e3) = all_52_2
% 152.83/22.61  
% 152.83/22.61  Begin of proof
% 152.83/22.61  | 
% 152.83/22.61  | ALPHA: (3) implies:
% 152.83/22.61  |   (12)  all_56_7 = e1
% 152.83/22.61  | 
% 152.83/22.61  | BETA: splitting (10) gives:
% 152.83/22.61  | 
% 152.83/22.61  | Case 1:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (13)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) =
% 152.83/22.61  | |           e0)
% 152.83/22.61  | | 
% 152.83/22.61  | | BETA: splitting (13) gives:
% 152.83/22.61  | | 
% 152.83/22.61  | | Case 1:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (14)  all_56_6 = e0 & op(e1, e3) = e0
% 152.83/22.61  | | | 
% 152.83/22.61  | | | ALPHA: (14) implies:
% 152.83/22.61  | | |   (15)  op(e1, e3) = e0
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (4), (6), (8), (11), (15) are inconsistent by sub-proof #1127.
% 152.83/22.61  | | | 
% 152.83/22.61  | | Case 2:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (16)  all_56_7 = e0 & op(e1, e2) = e0
% 152.83/22.61  | | | 
% 152.83/22.61  | | | ALPHA: (16) implies:
% 152.83/22.61  | | |   (17)  all_56_7 = e0
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (8), (12), (17) are inconsistent by sub-proof #987.
% 152.83/22.61  | | | 
% 152.83/22.61  | | End of split
% 152.83/22.61  | | 
% 152.83/22.61  | Case 2:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (18)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 152.83/22.61  | |           e0)
% 152.83/22.61  | | 
% 152.83/22.61  | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (18) are inconsistent by
% 152.83/22.61  | |            sub-proof #330.
% 152.83/22.61  | | 
% 152.83/22.61  | End of split
% 152.83/22.61  | 
% 152.83/22.61  End of proof
% 152.83/22.61  
% 152.83/22.61  Sub-proof #330 shows that the following formulas are inconsistent:
% 152.83/22.61  ----------------------------------------------------------------
% 152.83/22.61    (1)  all_56_11 = e2
% 152.83/22.61    (2)   ~ (e2 = e0)
% 152.83/22.61    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.61    (4)  op(e0, e0) = e3
% 152.83/22.61    (5)  op(e0, e0) = e1
% 152.83/22.61    (6)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.61    (7)   ~ (e1 = e0)
% 152.83/22.61    (8)  op(e1, e1) = e3
% 152.83/22.61  
% 152.83/22.61  Begin of proof
% 152.83/22.61  | 
% 152.83/22.61  | BETA: splitting (6) gives:
% 152.83/22.61  | 
% 152.83/22.61  | Case 1:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (9)  all_56_8 = e0 & op(e1, e1) = e0
% 152.83/22.61  | | 
% 152.83/22.61  | | ALPHA: (9) implies:
% 152.83/22.61  | |   (10)  op(e1, e1) = e0
% 152.83/22.61  | | 
% 152.83/22.61  | | REF_CLOSE: (3), (4), (5), (7), (8), (10) are inconsistent by sub-proof #331.
% 152.83/22.61  | | 
% 152.83/22.61  | Case 2:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (11)  all_56_11 = e0 & op(e1, e0) = e0
% 152.83/22.61  | | 
% 152.83/22.61  | | REF_CLOSE: (1), (2), (11) are inconsistent by sub-proof #1149.
% 152.83/22.61  | | 
% 152.83/22.61  | End of split
% 152.83/22.61  | 
% 152.83/22.61  End of proof
% 152.83/22.61  
% 152.83/22.61  Sub-proof #331 shows that the following formulas are inconsistent:
% 152.83/22.61  ----------------------------------------------------------------
% 152.83/22.61    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.61    (2)  op(e0, e0) = e3
% 152.83/22.61    (3)  op(e1, e1) = e0
% 152.83/22.61    (4)  op(e0, e0) = e1
% 152.83/22.61    (5)   ~ (e1 = e0)
% 152.83/22.61    (6)  op(e1, e1) = e3
% 152.83/22.61  
% 152.83/22.61  Begin of proof
% 152.83/22.61  | 
% 152.83/22.61  | GROUND_INST: instantiating (1) with e1, e3, e0, e0, simplifying with (2), (4)
% 152.83/22.61  |              gives:
% 152.83/22.61  |   (7)  e3 = e1
% 152.83/22.61  | 
% 152.83/22.61  | GROUND_INST: instantiating (1) with e3, e0, e1, e1, simplifying with (3), (6)
% 152.83/22.61  |              gives:
% 152.83/22.61  |   (8)  e3 = e0
% 152.83/22.61  | 
% 152.83/22.61  | COMBINE_EQS: (7), (8) imply:
% 152.83/22.61  |   (9)  e1 = e0
% 152.83/22.61  | 
% 152.83/22.61  | REDUCE: (5), (9) imply:
% 152.83/22.61  |   (10)  $false
% 152.83/22.61  | 
% 152.83/22.61  | CLOSE: (10) is inconsistent.
% 152.83/22.61  | 
% 152.83/22.61  End of proof
% 152.83/22.61  
% 152.83/22.61  Sub-proof #332 shows that the following formulas are inconsistent:
% 152.83/22.61  ----------------------------------------------------------------
% 152.83/22.61    (1)  all_56_8 = e3
% 152.83/22.61    (2)   ~ (e3 = e1)
% 152.83/22.61    (3)  all_56_10 = e3
% 152.83/22.61    (4)  all_56_11 = e2
% 152.83/22.61    (5)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 152.83/22.61         (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.61    (6)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 152.83/22.61         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.61    (7)   ~ (e2 = e0)
% 152.83/22.61    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.61    (9)  op(e2, e3) = e2
% 152.83/22.61    (10)  op(e3, e3) = e2
% 152.83/22.61    (11)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.83/22.61          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.83/22.61    (12)   ~ (e3 = e0)
% 152.83/22.61    (13)  op(e0, e1) = e2
% 152.83/22.61    (14)  op(e2, e2) = e2
% 152.83/22.61    (15)   ~ (e1 = e0)
% 152.83/22.61    (16)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.61          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.83/22.61    (17)   ~ (e2 = e1)
% 152.83/22.61    (18)  all_56_1 = e3
% 152.83/22.61    (19)  op(e2, e3) = all_52_1
% 152.83/22.61  
% 152.83/22.61  Begin of proof
% 152.83/22.61  | 
% 152.83/22.61  | BETA: splitting (11) gives:
% 152.83/22.61  | 
% 152.83/22.61  | Case 1:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (20)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 152.83/22.61  | |           e1)
% 152.83/22.61  | | 
% 152.83/22.61  | | BETA: splitting (20) gives:
% 152.83/22.61  | | 
% 152.83/22.61  | | Case 1:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (21)  all_56_0 = e1 & op(e3, e3) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | ALPHA: (21) implies:
% 152.83/22.61  | | |   (22)  op(e3, e3) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (8), (10), (17), (22) are inconsistent by sub-proof #1074.
% 152.83/22.61  | | | 
% 152.83/22.61  | | Case 2:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (23)  all_56_1 = e1 & op(e3, e2) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | ALPHA: (23) implies:
% 152.83/22.61  | | |   (24)  all_56_1 = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (2), (18), (24) are inconsistent by sub-proof #1069.
% 152.83/22.61  | | | 
% 152.83/22.61  | | End of split
% 152.83/22.61  | | 
% 152.83/22.61  | Case 2:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (25)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 152.83/22.61  | |           e1)
% 152.83/22.61  | | 
% 152.83/22.61  | | BETA: splitting (25) gives:
% 152.83/22.61  | | 
% 152.83/22.61  | | Case 1:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (26)  all_56_4 = e1 & op(e3, e1) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | ALPHA: (26) implies:
% 152.83/22.61  | | |   (27)  all_56_4 = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | BETA: splitting (6) gives:
% 152.83/22.61  | | | 
% 152.83/22.61  | | | Case 1:
% 152.83/22.61  | | | | 
% 152.83/22.61  | | | |   (28)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1)
% 152.83/22.61  | | | |           = e0)
% 152.83/22.61  | | | | 
% 152.83/22.61  | | | | BETA: splitting (28) gives:
% 152.83/22.61  | | | | 
% 152.83/22.61  | | | | Case 1:
% 152.83/22.61  | | | | | 
% 152.83/22.61  | | | | |   (29)  all_56_4 = e0 & op(e3, e1) = e0
% 152.83/22.61  | | | | | 
% 152.83/22.61  | | | | | REF_CLOSE: (15), (27), (29) are inconsistent by sub-proof #347.
% 152.83/22.61  | | | | | 
% 152.83/22.61  | | | | Case 2:
% 152.83/22.61  | | | | | 
% 152.83/22.61  | | | | |   (30)  all_56_5 = e0 & op(e2, e1) = e0
% 152.83/22.61  | | | | | 
% 152.83/22.61  | | | | | ALPHA: (30) implies:
% 152.83/22.61  | | | | |   (31)  all_56_5 = e0
% 152.83/22.61  | | | | | 
% 152.83/22.61  | | | | | REF_CLOSE: (2), (3), (8), (9), (14), (15), (16), (17), (19), (31) are
% 152.83/22.61  | | | | |            inconsistent by sub-proof #333.
% 152.83/22.61  | | | | | 
% 152.83/22.61  | | | | End of split
% 152.83/22.61  | | | | 
% 152.83/22.61  | | | Case 2:
% 152.83/22.61  | | | | 
% 152.83/22.61  | | | |   (32)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1)
% 152.83/22.61  | | | |           = e0)
% 152.83/22.61  | | | | 
% 152.83/22.61  | | | | REF_CLOSE: (1), (7), (8), (12), (13), (32) are inconsistent by sub-proof
% 152.83/22.61  | | | |            #355.
% 152.83/22.61  | | | | 
% 152.83/22.61  | | | End of split
% 152.83/22.61  | | | 
% 152.83/22.61  | | Case 2:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (33)  all_56_9 = e1 & op(e3, e0) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | ALPHA: (33) implies:
% 152.83/22.61  | | |   (34)  all_56_9 = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (3), (4), (5), (7), (12), (15), (34) are inconsistent by
% 152.83/22.61  | | |            sub-proof #748.
% 152.83/22.61  | | | 
% 152.83/22.61  | | End of split
% 152.83/22.61  | | 
% 152.83/22.61  | End of split
% 152.83/22.61  | 
% 152.83/22.61  End of proof
% 152.83/22.61  
% 152.83/22.61  Sub-proof #333 shows that the following formulas are inconsistent:
% 152.83/22.61  ----------------------------------------------------------------
% 152.83/22.61    (1)   ~ (e3 = e1)
% 152.83/22.61    (2)  all_56_10 = e3
% 152.83/22.61    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.61    (4)  op(e2, e3) = e2
% 152.83/22.61    (5)  all_56_5 = e0
% 152.83/22.61    (6)  op(e2, e2) = e2
% 152.83/22.61    (7)   ~ (e1 = e0)
% 152.83/22.61    (8)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.61         (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.83/22.61    (9)   ~ (e2 = e1)
% 152.83/22.61    (10)  op(e2, e3) = all_52_1
% 152.83/22.61  
% 152.83/22.61  Begin of proof
% 152.83/22.61  | 
% 152.83/22.61  | BETA: splitting (8) gives:
% 152.83/22.61  | 
% 152.83/22.61  | Case 1:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (11)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 152.83/22.61  | |           e1)
% 152.83/22.61  | | 
% 152.83/22.61  | | BETA: splitting (11) gives:
% 152.83/22.61  | | 
% 152.83/22.61  | | Case 1:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (12)  all_56_2 = e1 & op(e2, e3) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | ALPHA: (12) implies:
% 152.83/22.61  | | |   (13)  op(e2, e3) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (3), (4), (9), (10), (13) are inconsistent by sub-proof #842.
% 152.83/22.61  | | | 
% 152.83/22.61  | | Case 2:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (14)  all_56_3 = e1 & op(e2, e2) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | ALPHA: (14) implies:
% 152.83/22.61  | | |   (15)  op(e2, e2) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (3), (6), (9), (15) are inconsistent by sub-proof #1158.
% 152.83/22.61  | | | 
% 152.83/22.61  | | End of split
% 152.83/22.61  | | 
% 152.83/22.61  | Case 2:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (16)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 152.83/22.61  | |           e1)
% 152.83/22.61  | | 
% 152.83/22.61  | | BETA: splitting (16) gives:
% 152.83/22.61  | | 
% 152.83/22.61  | | Case 1:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (17)  all_56_5 = e1 & op(e2, e1) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (5), (7), (17) are inconsistent by sub-proof #334.
% 152.83/22.61  | | | 
% 152.83/22.61  | | Case 2:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (18)  all_56_10 = e1 & op(e2, e0) = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | ALPHA: (18) implies:
% 152.83/22.61  | | |   (19)  all_56_10 = e1
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (1), (2), (19) are inconsistent by sub-proof #677.
% 152.83/22.61  | | | 
% 152.83/22.61  | | End of split
% 152.83/22.61  | | 
% 152.83/22.61  | End of split
% 152.83/22.61  | 
% 152.83/22.61  End of proof
% 152.83/22.61  
% 152.83/22.61  Sub-proof #334 shows that the following formulas are inconsistent:
% 152.83/22.61  ----------------------------------------------------------------
% 152.83/22.61    (1)  all_56_5 = e1 & op(e2, e1) = e1
% 152.83/22.61    (2)  all_56_5 = e0
% 152.83/22.61    (3)   ~ (e1 = e0)
% 152.83/22.61  
% 152.83/22.61  Begin of proof
% 152.83/22.61  | 
% 152.83/22.61  | ALPHA: (1) implies:
% 152.83/22.61  |   (4)  all_56_5 = e1
% 152.83/22.61  | 
% 152.83/22.61  | COMBINE_EQS: (2), (4) imply:
% 152.83/22.61  |   (5)  e1 = e0
% 152.83/22.61  | 
% 152.83/22.61  | REDUCE: (3), (5) imply:
% 152.83/22.61  |   (6)  $false
% 152.83/22.61  | 
% 152.83/22.61  | CLOSE: (6) is inconsistent.
% 152.83/22.61  | 
% 152.83/22.61  End of proof
% 152.83/22.61  
% 152.83/22.61  Sub-proof #335 shows that the following formulas are inconsistent:
% 152.83/22.61  ----------------------------------------------------------------
% 152.83/22.61    (1)   ~ (e2 = e0)
% 152.83/22.61    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.61    (3)  op(e0, e0) = e3
% 152.83/22.61    (4)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.61             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 152.83/22.61               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 152.83/22.61               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 152.83/22.61    (5)  all_56_13 = e1
% 152.83/22.61    (6)   ~ (e3 = e0)
% 152.83/22.61    (7)  op(e0, e1) = e2
% 152.83/22.61    (8)   ~ (e1 = e0)
% 152.83/22.61    (9)  all_56_12 = e3
% 152.83/22.61  
% 152.83/22.61  Begin of proof
% 152.83/22.61  | 
% 152.83/22.61  | BETA: splitting (4) gives:
% 152.83/22.61  | 
% 152.83/22.61  | Case 1:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (10)  all_56_15 = e0 & op(e0, e0) = e0
% 152.83/22.61  | | 
% 152.83/22.61  | | ALPHA: (10) implies:
% 152.83/22.61  | |   (11)  op(e0, e0) = e0
% 152.83/22.61  | | 
% 152.83/22.61  | | REF_CLOSE: (2), (3), (6), (11) are inconsistent by sub-proof #1143.
% 152.83/22.61  | | 
% 152.83/22.61  | Case 2:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (12)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 152.83/22.61  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 152.83/22.61  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 152.83/22.61  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 152.83/22.61  | | 
% 152.83/22.61  | | ALPHA: (12) implies:
% 152.83/22.61  | |   (13)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 152.83/22.61  | |           e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 152.83/22.61  | | 
% 152.83/22.61  | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (13) are inconsistent by
% 152.83/22.61  | |            sub-proof #633.
% 152.83/22.61  | | 
% 152.83/22.61  | End of split
% 152.83/22.61  | 
% 152.83/22.61  End of proof
% 152.83/22.61  
% 152.83/22.61  Sub-proof #336 shows that the following formulas are inconsistent:
% 152.83/22.61  ----------------------------------------------------------------
% 152.83/22.61    (1)  all_56_8 = e3
% 152.83/22.61    (2)   ~ (e3 = e1)
% 152.83/22.61    (3)  all_56_11 = e2
% 152.83/22.61    (4)  op(e0, e0) = all_10_2
% 152.83/22.61    (5)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.61         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 152.83/22.61    (6)   ~ (e2 = e0)
% 152.83/22.61    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 152.83/22.61           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 152.83/22.61    (8)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 152.83/22.61         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 152.83/22.61    (9)  op(e3, e3) = e2
% 152.83/22.61    (10)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 152.83/22.61            all_57_14 & $i(all_57_14))
% 152.83/22.61    (11)  all_56_2 = e3 & op(e2, e3) = e3
% 152.83/22.61    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 152.83/22.61          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 152.83/22.61    (13)  all_57_3 = e3
% 152.83/22.61    (14)   ~ (e3 = e0)
% 152.83/22.61    (15)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 152.83/22.61          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 152.83/22.61    (16)   ~ (all_52_9 = e2)
% 152.83/22.61    (17)  op(e0, e1) = e2
% 152.83/22.61    (18)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.83/22.61          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 152.83/22.61    (19)  op(e2, e2) = e2
% 152.83/22.61    (20)  op(e2, e1) = all_52_9
% 152.83/22.61    (21)   ~ (e1 = e0)
% 152.83/22.61    (22)  op(e1, e1) = e3
% 152.83/22.61    (23)  all_57_12 = e2
% 152.83/22.61    (24)  op(e1, e0) = e2
% 152.83/22.61    (25)   ~ (e3 = e2)
% 152.83/22.61    (26)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.61          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 152.83/22.61    (27)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 152.83/22.61          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 152.83/22.61    (28)   ~ (all_10_2 = e2)
% 152.83/22.61    (29)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 152.83/22.61          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 152.83/22.61    (30)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 152.83/22.61          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 152.83/22.61    (31)   ~ (e2 = e1)
% 152.83/22.61    (32)  all_56_2 = e3
% 152.83/22.61    (33)  all_56_1 = e3
% 152.83/22.61    (34)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 152.83/22.61          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 152.83/22.61    (35)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 152.83/22.61              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 152.83/22.61            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 152.83/22.61            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 152.83/22.61            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 152.83/22.61            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.83/22.61            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 152.83/22.61            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 152.83/22.61            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 152.83/22.61            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.83/22.61            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.83/22.61            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.83/22.61            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.83/22.61            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.83/22.61            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.83/22.61            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 152.83/22.61            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 152.83/22.61            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 152.83/22.61            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.83/22.61            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 152.83/22.61            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 152.83/22.61            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.83/22.61            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.83/22.61            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 152.83/22.61            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.61            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 152.83/22.61            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.83/22.61            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.61            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.61            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 152.83/22.61            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 152.83/22.61            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 152.83/22.61            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 152.83/22.61            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 152.83/22.61            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.61            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 152.83/22.61            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.61            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.83/22.61            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 152.83/22.61            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.61            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 152.83/22.61            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 152.83/22.61            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.61            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.83/22.61            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 152.83/22.61            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.61            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.83/22.61            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 152.83/22.61              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 152.83/22.61            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 152.83/22.61            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 152.83/22.61              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.83/22.61            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.83/22.61            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 152.83/22.61                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 152.83/22.61                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.83/22.61                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 152.83/22.61                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 152.83/22.61                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.83/22.61                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 152.83/22.61                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.83/22.61              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 152.83/22.61                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 152.83/22.61                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.61                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 152.83/22.61                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 152.83/22.61                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 152.83/22.61                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.61                $i(all_57_7))))
% 152.83/22.61    (36)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 152.83/22.61          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 152.83/22.61    (37)  op(e2, e3) = all_52_1
% 152.83/22.61  
% 152.83/22.61  Begin of proof
% 152.83/22.61  | 
% 152.83/22.61  | BETA: splitting (29) gives:
% 152.83/22.61  | 
% 152.83/22.61  | Case 1:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (38)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 152.83/22.61  | |           e3)
% 152.83/22.61  | | 
% 152.83/22.61  | | REF_CLOSE: (2), (5), (6), (7), (9), (12), (14), (15), (19), (21), (26),
% 152.83/22.61  | |            (31), (32), (33), (38) are inconsistent by sub-proof #344.
% 152.83/22.61  | | 
% 152.83/22.61  | Case 2:
% 152.83/22.61  | | 
% 152.83/22.61  | |   (39)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 152.83/22.61  | |           e3)
% 152.83/22.61  | | 
% 152.83/22.61  | | BETA: splitting (39) gives:
% 152.83/22.61  | | 
% 152.83/22.61  | | Case 1:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (40)  all_56_11 = e3 & op(e1, e0) = e3
% 152.83/22.61  | | | 
% 152.83/22.61  | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (14), (19), (21), (25), (27),
% 152.83/22.61  | | |            (30), (31), (33), (34), (36), (40) are inconsistent by
% 152.83/22.61  | | |            sub-proof #342.
% 152.83/22.61  | | | 
% 152.83/22.61  | | Case 2:
% 152.83/22.61  | | | 
% 152.83/22.61  | | |   (41)  all_56_15 = e3 & op(e0, e0) = e3
% 152.83/22.61  | | | 
% 152.83/22.61  | | | ALPHA: (41) implies:
% 152.83/22.61  | | |   (42)  all_56_15 = e3
% 152.83/22.61  | | |   (43)  op(e0, e0) = e3
% 152.83/22.61  | | | 
% 152.83/22.61  | | | BETA: splitting (35) gives:
% 152.83/22.61  | | | 
% 152.83/22.61  | | | Case 1:
% 152.83/22.61  | | | | 
% 152.83/22.61  | | | |   (44)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.61  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 152.83/22.61  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 152.83/22.61  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 152.83/22.61  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.83/22.61  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 152.83/22.61  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.83/22.61  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 152.83/22.61  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.83/22.61  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.83/22.61  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 152.83/22.61  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 152.83/22.61  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 152.83/22.61  | | | |           $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 152.83/22.61  | | | |           (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 152.83/22.61  | | | |           & op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 152.83/22.61  | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 =
% 152.83/22.61  | | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.83/22.61  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 152.83/22.61  | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 152.83/22.61  | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 152.83/22.61  | | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 152.83/22.61  | | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.83/22.61  | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 152.83/22.61  | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 152.83/22.61  | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.83/22.61  | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 152.83/22.61  | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 152.83/22.61  | | | |           & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 152.83/22.61  | | | |           $i(all_57_7) & $i(all_57_10))
% 152.83/22.61  | | | | 
% 152.83/22.61  | | | | BETA: splitting (44) gives:
% 152.83/22.61  | | | | 
% 152.83/22.61  | | | | Case 1:
% 152.83/22.61  | | | | | 
% 152.83/22.61  | | | | |   (45)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.61  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 152.83/22.61  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 152.83/22.61  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 152.83/22.61  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 152.83/22.61  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 152.83/22.61  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 152.83/22.61  | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 152.83/22.61  | | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 152.83/22.61  | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 152.83/22.61  | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 152.83/22.61  | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 152.83/22.61  | | | | |           & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 152.83/22.61  | | | | |           $i(all_57_14))
% 152.83/22.61  | | | | | 
% 152.83/22.61  | | | | | BETA: splitting (45) gives:
% 152.83/22.61  | | | | | 
% 152.83/22.61  | | | | | Case 1:
% 152.83/22.61  | | | | | | 
% 152.83/22.61  | | | | | |   (46)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.61  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.83/22.61  | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.83/22.61  | | | | | |           $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 & all_57_15
% 152.83/22.61  | | | | | |           = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2,
% 152.83/22.61  | | | | | |             e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 152.83/22.61  | | | | | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 152.83/22.61  | | | | | | 
% 152.83/22.61  | | | | | | BETA: splitting (46) gives:
% 152.83/22.61  | | | | | | 
% 152.83/22.61  | | | | | | Case 1:
% 152.83/22.61  | | | | | | | 
% 152.83/22.61  | | | | | | |   (47)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.61  | | | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.83/22.61  | | | | | | |         all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 152.83/22.61  | | | | | | |         $i(all_57_1) & $i(all_57_12)
% 152.83/22.61  | | | | | | | 
% 152.83/22.61  | | | | | | | ALPHA: (47) implies:
% 152.83/22.61  | | | | | | |   (48)   ~ (all_57_12 = e3)
% 152.83/22.61  | | | | | | |   (49)  op(e2, e2) = all_57_12
% 152.83/22.61  | | | | | | |   (50)  op(e2, e3) = e2
% 152.83/22.61  | | | | | | | 
% 152.83/22.61  | | | | | | | REDUCE: (23), (48) imply:
% 152.83/22.61  | | | | | | |   (51)   ~ (e3 = e2)
% 152.83/22.61  | | | | | | | 
% 152.83/22.61  | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (14), (18), (19),
% 152.83/22.61  | | | | | | |            (21), (25), (26), (27), (30), (31), (32), (33), (34),
% 152.83/22.61  | | | | | | |            (36), (37), (50) are inconsistent by sub-proof #340.
% 152.83/22.61  | | | | | | | 
% 152.83/22.61  | | | | | | Case 2:
% 152.83/22.61  | | | | | | | 
% 152.83/22.61  | | | | | | |   (52)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 152.83/22.61  | | | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 152.83/22.61  | | | | | | |         all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.83/22.61  | | | | | | |         $i(all_57_2) & $i(all_57_12)
% 152.83/22.61  | | | | | | | 
% 152.83/22.61  | | | | | | | ALPHA: (52) implies:
% 152.83/22.61  | | | | | | |   (53)   ~ (all_57_12 = e3)
% 152.83/22.62  | | | | | | |   (54)  op(e2, e2) = all_57_12
% 152.83/22.62  | | | | | | |   (55)  op(e2, e3) = e2
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | | REDUCE: (23), (53) imply:
% 152.83/22.62  | | | | | | |   (56)   ~ (e3 = e2)
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | | ALPHA: (11) implies:
% 152.83/22.62  | | | | | | |   (57)  op(e2, e3) = e3
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (14), (19), (21), (25),
% 152.83/22.62  | | | | | | |            (27), (30), (31), (33), (34), (36), (37), (55), (57)
% 152.83/22.62  | | | | | | |            are inconsistent by sub-proof #341.
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | End of split
% 152.83/22.62  | | | | | | 
% 152.83/22.62  | | | | | Case 2:
% 152.83/22.62  | | | | | | 
% 152.83/22.62  | | | | | |   (58)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.83/22.62  | | | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 152.83/22.62  | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0)
% 152.83/22.62  | | | | | |           & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 152.83/22.62  | | | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 152.83/22.62  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 152.83/22.62  | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 152.83/22.62  | | | | | | 
% 152.83/22.62  | | | | | | BETA: splitting (58) gives:
% 152.83/22.62  | | | | | | 
% 152.83/22.62  | | | | | | Case 1:
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | |   (59)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.83/22.62  | | | | | | |         (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 152.83/22.62  | | | | | | |         & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0)
% 152.83/22.62  | | | | | | |         & $i(all_57_14)
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | | ALPHA: (59) implies:
% 152.83/22.62  | | | | | | |   (60)  op(e2, e2) = e3
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | | REF_CLOSE: (7), (19), (25), (60) are inconsistent by sub-proof
% 152.83/22.62  | | | | | | |            #1179.
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | Case 2:
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | |   (61)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 152.83/22.62  | | | | | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 152.83/22.62  | | | | | | |         all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 152.83/22.62  | | | | | | |         $i(all_57_2) & $i(all_57_14)
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | | ALPHA: (61) implies:
% 152.83/22.62  | | | | | | |   (62)   ~ (all_57_14 = e3)
% 152.83/22.62  | | | | | | |   (63)  op(e1, e1) = all_57_14
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | | REF_CLOSE: (7), (22), (62), (63) are inconsistent by sub-proof
% 152.83/22.62  | | | | | | |            #816.
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | End of split
% 152.83/22.62  | | | | | | 
% 152.83/22.62  | | | | | End of split
% 152.83/22.62  | | | | | 
% 152.83/22.62  | | | | Case 2:
% 152.83/22.62  | | | | | 
% 152.83/22.62  | | | | |   (64)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.83/22.62  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 152.83/22.62  | | | | |           & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 152.83/22.62  | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 152.83/22.62  | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 152.83/22.62  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 152.83/22.62  | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1
% 152.83/22.62  | | | | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2)
% 152.83/22.62  | | | | |           & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1
% 152.83/22.62  | | | | |           & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 152.83/22.62  | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 152.83/22.62  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 152.83/22.62  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 152.83/22.62  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 152.83/22.62  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 152.83/22.62  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 152.83/22.62  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 152.83/22.62  | | | | | 
% 152.83/22.62  | | | | | REF_CLOSE: (4), (7), (10), (13), (19), (28), (31), (64) are
% 152.83/22.62  | | | | |            inconsistent by sub-proof #339.
% 152.83/22.62  | | | | | 
% 152.83/22.62  | | | | End of split
% 152.83/22.62  | | | | 
% 152.83/22.62  | | | Case 2:
% 152.83/22.62  | | | | 
% 152.83/22.62  | | | |   (65)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.83/22.62  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 152.83/22.62  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.62  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 152.83/22.62  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 152.83/22.62  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 152.83/22.62  | | | |           e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.83/22.62  | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 152.83/22.62  | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.83/22.62  | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.83/22.62  | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.83/22.62  | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 152.83/22.62  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.83/22.62  | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 152.83/22.62  | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 152.83/22.62  | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.83/22.62  | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0 &
% 152.83/22.62  | | | |           all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 = e0) &
% 152.83/22.62  | | | |           op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 152.83/22.62  | | | |           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 152.83/22.62  | | | |         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 152.83/22.62  | | | |           (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.62  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 152.83/22.62  | | | |           $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 152.83/22.62  | | | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 152.83/22.62  | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 152.83/22.62  | | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 152.83/22.62  | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 152.83/22.62  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 152.83/22.62  | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 152.83/22.62  | | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 152.83/22.62  | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3)
% 152.83/22.62  | | | |               & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 152.83/22.62  | | | |               e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.83/22.62  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.83/22.62  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.83/22.62  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.83/22.62  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 152.83/22.62  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 152.83/22.62  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.83/22.62  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 152.83/22.62  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 152.83/22.62  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 152.83/22.62  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 152.83/22.62  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.83/22.62  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 152.83/22.62  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.83/22.62  | | | | 
% 152.83/22.62  | | | | BETA: splitting (65) gives:
% 152.83/22.62  | | | | 
% 152.83/22.62  | | | | Case 1:
% 152.83/22.62  | | | | | 
% 152.83/22.62  | | | | |   (66)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 152.83/22.62  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 152.83/22.62  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 152.83/22.62  | | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 152.83/22.62  | | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 152.83/22.62  | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 152.83/22.62  | | | | |           = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 152.83/22.62  | | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 152.83/22.62  | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 152.83/22.62  | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 152.83/22.62  | | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 152.83/22.62  | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 152.83/22.62  | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 152.83/22.62  | | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 152.83/22.62  | | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 152.83/22.62  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 152.83/22.62  | | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 152.83/22.62  | | | | | 
% 152.83/22.62  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (14),
% 152.83/22.62  | | | | |            (15), (16), (19), (20), (21), (22), (25), (26), (27), (29),
% 152.83/22.62  | | | | |            (30), (31), (33), (34), (36), (42), (43), (66) are
% 152.83/22.62  | | | | |            inconsistent by sub-proof #337.
% 152.83/22.62  | | | | | 
% 152.83/22.62  | | | | Case 2:
% 152.83/22.62  | | | | | 
% 152.83/22.62  | | | | |   (67)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 152.83/22.62  | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 152.83/22.62  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 152.83/22.62  | | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 152.83/22.62  | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.83/22.62  | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 152.83/22.62  | | | | |           = e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 152.83/22.62  | | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 152.83/22.62  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 152.83/22.62  | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 152.83/22.62  | | | | |         (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 152.83/22.62  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 152.83/22.62  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.83/22.62  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.83/22.62  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.83/22.62  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 152.83/22.62  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 152.83/22.62  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 152.83/22.62  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 152.83/22.62  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 152.83/22.62  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 152.83/22.62  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.83/22.62  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 152.83/22.62  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.83/22.62  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.83/22.62  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.62  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 152.83/22.62  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.83/22.62  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.83/22.62  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 152.83/22.62  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.62  | | | | |               $i(all_57_7))))
% 152.83/22.62  | | | | | 
% 152.83/22.62  | | | | | BETA: splitting (67) gives:
% 152.83/22.62  | | | | | 
% 152.83/22.62  | | | | | Case 1:
% 152.83/22.62  | | | | | | 
% 152.83/22.62  | | | | | |   (68)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 152.83/22.62  | | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9
% 152.83/22.62  | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 152.83/22.62  | | | | | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 152.83/22.62  | | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 152.83/22.62  | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1,
% 152.83/22.62  | | | | | |             e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 152.83/22.62  | | | | | | 
% 152.83/22.62  | | | | | | REF_CLOSE: (6), (7), (9), (68) are inconsistent by sub-proof #1037.
% 152.83/22.62  | | | | | | 
% 152.83/22.62  | | | | | Case 2:
% 152.83/22.62  | | | | | | 
% 152.83/22.62  | | | | | |   (69)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 152.83/22.62  | | | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.83/22.62  | | | | | |           e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.83/22.62  | | | | | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 152.83/22.62  | | | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0)
% 152.83/22.62  | | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 152.83/22.62  | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 152.83/22.62  | | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 152.83/22.62  | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 152.83/22.62  | | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2)
% 152.83/22.62  | | | | | |               = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 =
% 152.83/22.62  | | | | | |               e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 152.83/22.62  | | | | | |               (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1)
% 152.83/22.62  | | | | | |               = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 152.83/22.62  | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 152.83/22.62  | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 152.83/22.62  | | | | | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5
% 152.83/22.62  | | | | | |               = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 152.83/22.62  | | | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1)
% 152.83/22.62  | | | | | |               = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 152.83/22.62  | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 152.83/22.62  | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 152.83/22.62  | | | | | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 152.83/22.62  | | | | | |               = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 152.83/22.62  | | | | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 152.83/22.62  | | | | | |               all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 152.83/22.62  | | | | | | 
% 152.83/22.62  | | | | | | BETA: splitting (69) gives:
% 152.83/22.62  | | | | | | 
% 152.83/22.62  | | | | | | Case 1:
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | |   (70)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 152.83/22.62  | | | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 152.83/22.62  | | | | | | |         e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 152.83/22.62  | | | | | | |         $i(all_57_12) & $i(all_57_13)
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | | ALPHA: (70) implies:
% 152.83/22.62  | | | | | | |   (71)  op(e1, e1) = e0
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | | REF_CLOSE: (7), (14), (22), (71) are inconsistent by sub-proof
% 152.83/22.62  | | | | | | |            #896.
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | Case 2:
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | |   (72)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 152.83/22.62  | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 152.83/22.62  | | | | | | |           all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.83/22.62  | | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 152.83/22.62  | | | | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 152.83/22.62  | | | | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 152.83/22.62  | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 152.83/22.62  | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 152.83/22.62  | | | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 152.83/22.62  | | | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 152.83/22.62  | | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 152.83/22.62  | | | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 152.83/22.62  | | | | | | |               e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 152.83/22.62  | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 152.83/22.62  | | | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 152.83/22.62  | | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 152.83/22.62  | | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 152.83/22.62  | | | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 152.83/22.62  | | | | | | |               e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 152.83/22.62  | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 152.83/22.62  | | | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 152.83/22.62  | | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 152.83/22.62  | | | | | | |               $i(all_57_7))))
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | | BETA: splitting (72) gives:
% 152.83/22.62  | | | | | | | 
% 152.83/22.62  | | | | | | | Case 1:
% 152.83/22.62  | | | | | | | | 
% 152.83/22.62  | | | | | | | |   (73)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 152.83/22.62  | | | | | | | |         ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 152.83/22.62  | | | | | | | |         all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 152.83/22.62  | | | | | | | |         $i(all_57_11) & $i(all_57_14)
% 152.83/22.62  | | | | | | | | 
% 152.83/22.62  | | | | | | | | ALPHA: (73) implies:
% 152.83/22.62  | | | | | | | |   (74)  op(e1, e0) = e1
% 153.05/22.62  | | | | | | | | 
% 153.05/22.62  | | | | | | | | REF_CLOSE: (7), (24), (31), (74) are inconsistent by sub-proof
% 153.05/22.62  | | | | | | | |            #1125.
% 153.05/22.62  | | | | | | | | 
% 153.05/22.62  | | | | | | | Case 2:
% 153.05/22.62  | | | | | | | | 
% 153.05/22.62  | | | | | | | |   (75)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0
% 153.05/22.62  | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.05/22.62  | | | | | | | |             (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.05/22.62  | | | | | | | |               e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.05/22.62  | | | | | | | |           (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 153.05/22.62  | | | | | | | |              ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.05/22.62  | | | | | | | |               e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.05/22.62  | | | | | | | |           (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &
% 153.05/22.62  | | | | | | | |              ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.05/22.62  | | | | | | | |             all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.05/22.62  | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &
% 153.05/22.62  | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.05/22.62  | | | | | | | |               e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.05/22.62  | | | | | | | |           (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &
% 153.05/22.62  | | | | | | | |              ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.05/22.62  | | | | | | | |             all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.05/22.62  | | | | | | | |           (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 153.05/22.62  | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.05/22.62  | | | | | | | |             all_57_7 & op(e0, e1) = e0 & $i(all_57_7)))
% 153.05/22.62  | | | | | | | | 
% 153.05/22.62  | | | | | | | | ALPHA: (75) implies:
% 153.05/22.62  | | | | | | | |   (76)  op(e0, e0) = all_57_15
% 153.05/22.62  | | | | | | | |   (77)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 153.05/22.62  | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.05/22.62  | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.05/22.62  | | | | | | | |         (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.05/22.62  | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.05/22.62  | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.05/22.62  | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.05/22.62  | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.05/22.62  | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5
% 153.05/22.62  | | | | | | | |           = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.05/22.62  | | | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1)
% 153.05/22.62  | | | | | | | |           = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 153.05/22.62  | | | | | | | |           e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.05/22.62  | | | | | | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.05/22.62  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 153.05/22.62  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.05/22.62  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.05/22.62  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.05/22.62  | | | | | | | | 
% 153.05/22.62  | | | | | | | | REF_CLOSE: (6), (7), (10), (13), (17), (19), (25), (31), (43),
% 153.05/22.62  | | | | | | | |            (76), (77) are inconsistent by sub-proof #1003.
% 153.05/22.62  | | | | | | | | 
% 153.05/22.62  | | | | | | | End of split
% 153.05/22.62  | | | | | | | 
% 153.05/22.62  | | | | | | End of split
% 153.05/22.62  | | | | | | 
% 153.05/22.62  | | | | | End of split
% 153.05/22.62  | | | | | 
% 153.05/22.62  | | | | End of split
% 153.05/22.62  | | | | 
% 153.05/22.62  | | | End of split
% 153.05/22.62  | | | 
% 153.05/22.62  | | End of split
% 153.05/22.62  | | 
% 153.05/22.62  | End of split
% 153.05/22.62  | 
% 153.05/22.62  End of proof
% 153.05/22.62  
% 153.05/22.62  Sub-proof #337 shows that the following formulas are inconsistent:
% 153.05/22.62  ----------------------------------------------------------------
% 153.05/22.62    (1)  all_56_8 = e3
% 153.05/22.62    (2)   ~ (e3 = e1)
% 153.05/22.62    (3)  all_56_11 = e2
% 153.05/22.62    (4)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.62         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.05/22.62    (5)   ~ (e2 = e0)
% 153.05/22.62    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.62    (7)  op(e0, e0) = e3
% 153.05/22.62    (8)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.05/22.62         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.05/22.62    (9)  op(e3, e3) = e2
% 153.05/22.62    (10)  all_56_2 = e3 & op(e2, e3) = e3
% 153.05/22.62    (11)  all_56_15 = e3
% 153.05/22.62    (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.05/22.62          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.05/22.62    (13)   ~ (e3 = e0)
% 153.05/22.62    (14)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.05/22.62          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.05/22.62    (15)   ~ (all_52_9 = e2)
% 153.05/22.62    (16)  op(e2, e2) = e2
% 153.05/22.62    (17)  op(e2, e1) = all_52_9
% 153.05/22.62    (18)   ~ (e1 = e0)
% 153.05/22.62    (19)  op(e1, e1) = e3
% 153.05/22.62    (20)   ~ (e3 = e2)
% 153.05/22.62    (21)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.05/22.62          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.05/22.62    (22)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.62          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.05/22.62    (23)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.05/22.62          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.05/22.62    (24)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.05/22.62              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.05/22.62            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.05/22.62            = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.05/22.62            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.05/22.62            op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.05/22.62            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2)
% 153.05/22.62            = all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0) =
% 153.05/22.62            e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &
% 153.05/22.62             ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 153.05/22.62            op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.05/22.62            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.05/22.62            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 153.05/22.62            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.05/22.62            $i(all_57_10) & $i(all_57_13))
% 153.05/22.62    (25)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.05/22.62          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.05/22.62    (26)   ~ (e2 = e1)
% 153.05/22.62    (27)  all_56_1 = e3
% 153.05/22.62    (28)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.05/22.62          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.05/22.62    (29)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.05/22.62          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.05/22.62  
% 153.05/22.62  Begin of proof
% 153.05/22.62  | 
% 153.05/22.62  | BETA: splitting (24) gives:
% 153.05/22.62  | 
% 153.05/22.62  | Case 1:
% 153.05/22.62  | | 
% 153.05/22.62  | |   (30)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 153.05/22.62  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.05/22.62  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 153.05/22.62  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 153.05/22.62  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.05/22.62  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 153.05/22.62  | | 
% 153.05/22.62  | | BETA: splitting (30) gives:
% 153.05/22.62  | | 
% 153.05/22.62  | | Case 1:
% 153.05/22.62  | | | 
% 153.05/22.62  | | |   (31)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.05/22.62  | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.05/22.62  | | |         op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.05/22.62  | | |         $i(all_57_10)
% 153.05/22.62  | | | 
% 153.05/22.62  | | | ALPHA: (31) implies:
% 153.05/22.62  | | |   (32)  op(e0, e0) = e1
% 153.05/22.62  | | | 
% 153.05/22.62  | | | ALPHA: (10) implies:
% 153.05/22.62  | | |   (33)  all_56_2 = e3
% 153.05/22.62  | | | 
% 153.05/22.62  | | | GROUND_INST: instantiating (6) with e1, e3, e0, e0, simplifying with (7),
% 153.05/22.62  | | |              (32) gives:
% 153.05/22.62  | | |   (34)  e3 = e1
% 153.05/22.62  | | | 
% 153.05/22.62  | | | COMBINE_EQS: (11), (34) imply:
% 153.05/22.62  | | |   (35)  all_56_15 = e1
% 153.05/22.62  | | | 
% 153.05/22.62  | | | BETA: splitting (23) gives:
% 153.05/22.62  | | | 
% 153.05/22.62  | | | Case 1:
% 153.05/22.62  | | | | 
% 153.05/22.62  | | | |   (36)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0)
% 153.05/22.62  | | | |           = e3)
% 153.05/22.62  | | | | 
% 153.05/22.62  | | | | REF_CLOSE: (2), (4), (5), (6), (9), (12), (13), (14), (16), (18), (21),
% 153.05/22.62  | | | |            (26), (27), (33), (36) are inconsistent by sub-proof #344.
% 153.05/22.62  | | | | 
% 153.05/22.62  | | | Case 2:
% 153.05/22.62  | | | | 
% 153.05/22.62  | | | |   (37)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0,
% 153.05/22.62  | | | |             e0) = e3)
% 153.05/22.62  | | | | 
% 153.05/22.62  | | | | BETA: splitting (37) gives:
% 153.05/22.62  | | | | 
% 153.05/22.62  | | | | Case 1:
% 153.05/22.62  | | | | | 
% 153.05/22.62  | | | | |   (38)  all_56_11 = e3 & op(e1, e0) = e3
% 153.05/22.62  | | | | | 
% 153.05/22.62  | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (13), (16), (18), (20), (22),
% 153.05/22.62  | | | | |            (25), (26), (27), (28), (29), (38) are inconsistent by
% 153.05/22.62  | | | | |            sub-proof #342.
% 153.05/22.62  | | | | | 
% 153.05/22.62  | | | | Case 2:
% 153.05/22.62  | | | | | 
% 153.05/22.62  | | | | |   (39)  all_56_15 = e3 & op(e0, e0) = e3
% 153.05/22.62  | | | | | 
% 153.05/22.62  | | | | | REF_CLOSE: (2), (35), (39) are inconsistent by sub-proof #338.
% 153.05/22.62  | | | | | 
% 153.05/22.62  | | | | End of split
% 153.05/22.62  | | | | 
% 153.05/22.62  | | | End of split
% 153.05/22.62  | | | 
% 153.05/22.62  | | Case 2:
% 153.05/22.62  | | | 
% 153.05/22.62  | | |   (40)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.05/22.62  | | |         (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.05/22.62  | | |         op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.05/22.62  | | |         $i(all_57_12)
% 153.05/22.62  | | | 
% 153.05/22.62  | | | ALPHA: (40) implies:
% 153.05/22.62  | | |   (41)  op(e2, e1) = e2
% 153.05/22.62  | | | 
% 153.05/22.62  | | | REF_CLOSE: (6), (15), (17), (41) are inconsistent by sub-proof #1157.
% 153.05/22.62  | | | 
% 153.05/22.62  | | End of split
% 153.05/22.62  | | 
% 153.05/22.62  | Case 2:
% 153.05/22.62  | | 
% 153.05/22.62  | |   (42)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 153.05/22.62  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.05/22.62  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.05/22.62  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.05/22.62  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.05/22.62  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.05/22.62  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 153.05/22.62  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 153.05/22.62  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.05/22.62  | |           $i(all_57_13))
% 153.05/22.62  | | 
% 153.05/22.62  | | REF_CLOSE: (5), (6), (13), (15), (16), (17), (19), (42) are inconsistent by
% 153.05/22.62  | |            sub-proof #433.
% 153.05/22.62  | | 
% 153.05/22.62  | End of split
% 153.05/22.62  | 
% 153.05/22.62  End of proof
% 153.05/22.62  
% 153.05/22.62  Sub-proof #338 shows that the following formulas are inconsistent:
% 153.05/22.62  ----------------------------------------------------------------
% 153.05/22.62    (1)  all_56_15 = e3 & op(e0, e0) = e3
% 153.05/22.62    (2)  all_56_15 = e1
% 153.05/22.62    (3)   ~ (e3 = e1)
% 153.05/22.62  
% 153.05/22.62  Begin of proof
% 153.05/22.62  | 
% 153.05/22.62  | ALPHA: (1) implies:
% 153.05/22.62  |   (4)  all_56_15 = e3
% 153.05/22.62  | 
% 153.05/22.62  | COMBINE_EQS: (2), (4) imply:
% 153.05/22.62  |   (5)  e3 = e1
% 153.05/22.62  | 
% 153.05/22.62  | SIMP: (5) implies:
% 153.05/22.62  |   (6)  e3 = e1
% 153.05/22.62  | 
% 153.05/22.62  | REDUCE: (3), (6) imply:
% 153.05/22.62  |   (7)  $false
% 153.05/22.62  | 
% 153.05/22.62  | CLOSE: (7) is inconsistent.
% 153.05/22.62  | 
% 153.05/22.62  End of proof
% 153.05/22.62  
% 153.05/22.62  Sub-proof #339 shows that the following formulas are inconsistent:
% 153.05/22.62  ----------------------------------------------------------------
% 153.05/22.62    (1)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.05/22.62             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.05/22.62           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 153.05/22.62           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.05/22.62           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.05/22.62           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 153.05/22.62           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3)
% 153.05/22.62           = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.05/22.62           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.05/22.62           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.05/22.62           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.05/22.62           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 153.05/22.62            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 153.05/22.62             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.05/22.62    (2)  op(e0, e0) = all_10_2
% 153.05/22.62    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.62           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.62    (4)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 153.05/22.62           all_57_14 & $i(all_57_14))
% 153.05/22.62    (5)  all_57_3 = e3
% 153.05/22.62    (6)  op(e2, e2) = e2
% 153.05/22.62    (7)   ~ (all_10_2 = e2)
% 153.05/22.62    (8)   ~ (e2 = e1)
% 153.05/22.62  
% 153.05/22.62  Begin of proof
% 153.05/22.62  | 
% 153.05/22.62  | BETA: splitting (1) gives:
% 153.05/22.62  | 
% 153.05/22.62  | Case 1:
% 153.05/22.62  | | 
% 153.05/22.62  | |   (9)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 153.05/22.62  | |            = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.05/22.62  | |          all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 153.05/22.62  | |        (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 153.05/22.62  | |            = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.05/22.62  | |          all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.05/22.62  | | 
% 153.05/22.62  | | BETA: splitting (9) gives:
% 153.05/22.62  | | 
% 153.05/22.62  | | Case 1:
% 153.05/22.62  | | | 
% 153.05/22.62  | | |   (10)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.05/22.62  | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.05/22.62  | | |         op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.05/22.62  | | |         $i(all_57_10)
% 153.05/22.62  | | | 
% 153.05/22.62  | | | ALPHA: (10) implies:
% 153.05/22.62  | | |   (11)  all_57_14 = e2
% 153.05/22.62  | | |   (12)   ~ (all_57_4 = e1)
% 153.05/22.62  | | | 
% 153.05/22.62  | | | REF_CLOSE: (4), (11), (12) are inconsistent by sub-proof #1005.
% 153.05/22.62  | | | 
% 153.05/22.62  | | Case 2:
% 153.05/22.62  | | | 
% 153.05/22.62  | | |   (13)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.05/22.62  | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.05/22.62  | | |         op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.05/22.62  | | |         $i(all_57_10)
% 153.05/22.62  | | | 
% 153.05/22.62  | | | ALPHA: (13) implies:
% 153.05/22.62  | | |   (14)  op(e0, e0) = e2
% 153.05/22.62  | | | 
% 153.05/22.62  | | | REF_CLOSE: (2), (3), (7), (14) are inconsistent by sub-proof #1097.
% 153.05/22.62  | | | 
% 153.05/22.62  | | End of split
% 153.05/22.62  | | 
% 153.05/22.62  | Case 2:
% 153.05/22.62  | | 
% 153.05/22.63  | |   (15)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 153.05/22.63  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 153.05/22.63  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.05/22.63  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.05/22.63  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.05/22.63  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.05/22.63  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.05/22.63  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.05/22.63  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.05/22.63  | | 
% 153.05/22.63  | | BETA: splitting (15) gives:
% 153.05/22.63  | | 
% 153.05/22.63  | | Case 1:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (16)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.05/22.63  | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.05/22.63  | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.05/22.63  | | |         $i(all_57_14)
% 153.05/22.63  | | | 
% 153.05/22.63  | | | ALPHA: (16) implies:
% 153.05/22.63  | | |   (17)   ~ (all_57_3 = e3)
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REDUCE: (5), (17) imply:
% 153.05/22.63  | | |   (18)  $false
% 153.05/22.63  | | | 
% 153.05/22.63  | | | CLOSE: (18) is inconsistent.
% 153.05/22.63  | | | 
% 153.05/22.63  | | Case 2:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (19)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.05/22.63  | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.05/22.63  | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.05/22.63  | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7
% 153.05/22.63  | | |             = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 153.05/22.63  | | |             e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.05/22.63  | | |           $i(all_57_7) & $i(all_57_10))
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REF_CLOSE: (2), (3), (6), (7), (8), (19) are inconsistent by sub-proof
% 153.05/22.63  | | |            #1084.
% 153.05/22.63  | | | 
% 153.05/22.63  | | End of split
% 153.05/22.63  | | 
% 153.05/22.63  | End of split
% 153.05/22.63  | 
% 153.05/22.63  End of proof
% 153.05/22.63  
% 153.05/22.63  Sub-proof #340 shows that the following formulas are inconsistent:
% 153.05/22.63  ----------------------------------------------------------------
% 153.05/22.63    (1)  all_56_8 = e3
% 153.05/22.63    (2)   ~ (e3 = e1)
% 153.05/22.63    (3)  all_56_11 = e2
% 153.05/22.63    (4)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.63         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.05/22.63    (5)   ~ (e2 = e0)
% 153.05/22.63    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.63    (7)  op(e2, e3) = e2
% 153.05/22.63    (8)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.05/22.63         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.05/22.63    (9)   ~ (e3 = e0)
% 153.05/22.63    (10)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.05/22.63          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.05/22.63    (11)  op(e2, e2) = e2
% 153.05/22.63    (12)   ~ (e1 = e0)
% 153.05/22.63    (13)   ~ (e3 = e2)
% 153.05/22.63    (14)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.05/22.63          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.05/22.63    (15)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.63          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.05/22.63    (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.05/22.63          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.05/22.63    (17)   ~ (e2 = e1)
% 153.05/22.63    (18)  all_56_2 = e3
% 153.05/22.63    (19)  all_56_1 = e3
% 153.05/22.63    (20)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.05/22.63          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.05/22.63    (21)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.05/22.63          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.05/22.63    (22)  op(e2, e3) = all_52_1
% 153.05/22.63  
% 153.05/22.63  Begin of proof
% 153.05/22.63  | 
% 153.05/22.63  | BETA: splitting (10) gives:
% 153.05/22.63  | 
% 153.05/22.63  | Case 1:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (23)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 153.05/22.63  | |           e3)
% 153.05/22.63  | | 
% 153.05/22.63  | | BETA: splitting (23) gives:
% 153.05/22.63  | | 
% 153.05/22.63  | | Case 1:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (24)  all_56_2 = e3 & op(e2, e3) = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | ALPHA: (24) implies:
% 153.05/22.63  | | |   (25)  op(e2, e3) = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (15),
% 153.05/22.63  | | |            (16), (17), (19), (20), (21), (22), (25) are inconsistent by
% 153.05/22.63  | | |            sub-proof #341.
% 153.05/22.63  | | | 
% 153.05/22.63  | | Case 2:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (26)  all_56_3 = e3 & op(e2, e2) = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | ALPHA: (26) implies:
% 153.05/22.63  | | |   (27)  op(e2, e2) = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REF_CLOSE: (6), (11), (13), (27) are inconsistent by sub-proof #1179.
% 153.05/22.63  | | | 
% 153.05/22.63  | | End of split
% 153.05/22.63  | | 
% 153.05/22.63  | Case 2:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (28)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 153.05/22.63  | |           e3)
% 153.05/22.63  | | 
% 153.05/22.63  | | BETA: splitting (28) gives:
% 153.05/22.63  | | 
% 153.05/22.63  | | Case 1:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (29)  all_56_5 = e3 & op(e2, e1) = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | ALPHA: (29) implies:
% 153.05/22.63  | | |   (30)  all_56_5 = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | BETA: splitting (4) gives:
% 153.05/22.63  | | | 
% 153.05/22.63  | | | Case 1:
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | |   (31)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2)
% 153.05/22.63  | | | |           = e0)
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | | BETA: splitting (31) gives:
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | | Case 1:
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | |   (32)  all_56_2 = e0 & op(e2, e3) = e0
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | | REF_CLOSE: (9), (18), (32) are inconsistent by sub-proof #932.
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | Case 2:
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | |   (33)  all_56_3 = e0 & op(e2, e2) = e0
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | | ALPHA: (33) implies:
% 153.05/22.63  | | | | |   (34)  op(e2, e2) = e0
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | | REF_CLOSE: (5), (6), (11), (34) are inconsistent by sub-proof #1145.
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | End of split
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | Case 2:
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | |   (35)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0)
% 153.05/22.63  | | | |           = e0)
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | | BETA: splitting (35) gives:
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | | Case 1:
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | |   (36)  all_56_5 = e0 & op(e2, e1) = e0
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | | REF_CLOSE: (9), (30), (36) are inconsistent by sub-proof #910.
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | Case 2:
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | |   (37)  all_56_10 = e0 & op(e2, e0) = e0
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | | ALPHA: (37) implies:
% 153.05/22.63  | | | | |   (38)  all_56_10 = e0
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | | BETA: splitting (14) gives:
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | | Case 1:
% 153.05/22.63  | | | | | | 
% 153.05/22.63  | | | | | |   (39)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2,
% 153.05/22.63  | | | | | |             e2) = e1)
% 153.05/22.63  | | | | | | 
% 153.05/22.63  | | | | | | REF_CLOSE: (2), (6), (11), (17), (18), (39) are inconsistent by
% 153.05/22.63  | | | | | |            sub-proof #364.
% 153.05/22.63  | | | | | | 
% 153.05/22.63  | | | | | Case 2:
% 153.05/22.63  | | | | | | 
% 153.05/22.63  | | | | | |   (40)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2,
% 153.05/22.63  | | | | | |             e0) = e1)
% 153.05/22.63  | | | | | | 
% 153.05/22.63  | | | | | | BETA: splitting (40) gives:
% 153.05/22.63  | | | | | | 
% 153.05/22.63  | | | | | | Case 1:
% 153.05/22.63  | | | | | | | 
% 153.05/22.63  | | | | | | |   (41)  all_56_5 = e1 & op(e2, e1) = e1
% 153.05/22.63  | | | | | | | 
% 153.05/22.63  | | | | | | | ALPHA: (41) implies:
% 153.05/22.63  | | | | | | |   (42)  all_56_5 = e1
% 153.05/22.63  | | | | | | | 
% 153.05/22.63  | | | | | | | REF_CLOSE: (2), (30), (42) are inconsistent by sub-proof #416.
% 153.05/22.63  | | | | | | | 
% 153.05/22.63  | | | | | | Case 2:
% 153.05/22.63  | | | | | | | 
% 153.05/22.63  | | | | | | |   (43)  all_56_10 = e1 & op(e2, e0) = e1
% 153.05/22.63  | | | | | | | 
% 153.05/22.63  | | | | | | | REF_CLOSE: (12), (38), (43) are inconsistent by sub-proof #1131.
% 153.05/22.63  | | | | | | | 
% 153.05/22.63  | | | | | | End of split
% 153.05/22.63  | | | | | | 
% 153.05/22.63  | | | | | End of split
% 153.05/22.63  | | | | | 
% 153.05/22.63  | | | | End of split
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | End of split
% 153.05/22.63  | | | 
% 153.05/22.63  | | Case 2:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (44)  all_56_10 = e3 & op(e2, e0) = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | ALPHA: (44) implies:
% 153.05/22.63  | | |   (45)  all_56_10 = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REF_CLOSE: (2), (4), (5), (6), (9), (11), (12), (14), (17), (18), (45) are
% 153.05/22.63  | | |            inconsistent by sub-proof #363.
% 153.05/22.63  | | | 
% 153.05/22.63  | | End of split
% 153.05/22.63  | | 
% 153.05/22.63  | End of split
% 153.05/22.63  | 
% 153.05/22.63  End of proof
% 153.05/22.63  
% 153.05/22.63  Sub-proof #341 shows that the following formulas are inconsistent:
% 153.05/22.63  ----------------------------------------------------------------
% 153.05/22.63    (1)  all_56_8 = e3
% 153.05/22.63    (2)   ~ (e3 = e1)
% 153.05/22.63    (3)  all_56_11 = e2
% 153.05/22.63    (4)   ~ (e2 = e0)
% 153.05/22.63    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.63    (6)  op(e2, e3) = e2
% 153.05/22.63    (7)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.05/22.63         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.05/22.63    (8)   ~ (e3 = e0)
% 153.05/22.63    (9)  op(e2, e2) = e2
% 153.05/22.63    (10)   ~ (e1 = e0)
% 153.05/22.63    (11)   ~ (e3 = e2)
% 153.05/22.63    (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.63          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.05/22.63    (13)  op(e2, e3) = e3
% 153.05/22.63    (14)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.05/22.63          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.05/22.63    (15)   ~ (e2 = e1)
% 153.05/22.63    (16)  all_56_1 = e3
% 153.05/22.63    (17)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.05/22.63          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.05/22.63    (18)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.05/22.63          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.05/22.63    (19)  op(e2, e3) = all_52_1
% 153.05/22.63  
% 153.05/22.63  Begin of proof
% 153.05/22.63  | 
% 153.05/22.63  | GROUND_INST: instantiating (5) with all_52_1, e2, e3, e2, simplifying with
% 153.05/22.63  |              (6), (19) gives:
% 153.05/22.63  |   (20)  all_52_1 = e2
% 153.05/22.63  | 
% 153.05/22.63  | GROUND_INST: instantiating (5) with all_52_1, e3, e3, e2, simplifying with
% 153.05/22.63  |              (13), (19) gives:
% 153.05/22.63  |   (21)  all_52_1 = e3
% 153.05/22.63  | 
% 153.05/22.63  | COMBINE_EQS: (20), (21) imply:
% 153.05/22.63  |   (22)  e3 = e2
% 153.05/22.63  | 
% 153.05/22.63  | SIMP: (22) implies:
% 153.05/22.63  |   (23)  e3 = e2
% 153.05/22.63  | 
% 153.05/22.63  | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14),
% 153.05/22.63  |            (15), (16), (17), (18), (23) are inconsistent by sub-proof #343.
% 153.05/22.63  | 
% 153.05/22.63  End of proof
% 153.05/22.63  
% 153.05/22.63  Sub-proof #342 shows that the following formulas are inconsistent:
% 153.05/22.63  ----------------------------------------------------------------
% 153.05/22.63    (1)  all_56_8 = e3
% 153.05/22.63    (2)   ~ (e3 = e1)
% 153.05/22.63    (3)  all_56_11 = e2
% 153.05/22.63    (4)  all_56_11 = e3 & op(e1, e0) = e3
% 153.05/22.63    (5)   ~ (e2 = e0)
% 153.05/22.63    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.63    (7)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.05/22.63         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.05/22.63    (8)   ~ (e3 = e0)
% 153.05/22.63    (9)  op(e2, e2) = e2
% 153.05/22.63    (10)   ~ (e1 = e0)
% 153.05/22.63    (11)   ~ (e3 = e2)
% 153.05/22.63    (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.63          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.05/22.63    (13)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.05/22.63          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.05/22.63    (14)   ~ (e2 = e1)
% 153.05/22.63    (15)  all_56_1 = e3
% 153.05/22.63    (16)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.05/22.63          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.05/22.63    (17)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.05/22.63          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.05/22.63  
% 153.05/22.63  Begin of proof
% 153.05/22.63  | 
% 153.05/22.63  | ALPHA: (4) implies:
% 153.05/22.63  |   (18)  all_56_11 = e3
% 153.05/22.63  | 
% 153.05/22.63  | COMBINE_EQS: (3), (18) imply:
% 153.05/22.63  |   (19)  e3 = e2
% 153.05/22.63  | 
% 153.05/22.63  | SIMP: (19) implies:
% 153.05/22.63  |   (20)  e3 = e2
% 153.05/22.63  | 
% 153.05/22.63  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 153.05/22.63  |            (14), (15), (16), (17), (20) are inconsistent by sub-proof #343.
% 153.05/22.63  | 
% 153.05/22.63  End of proof
% 153.05/22.63  
% 153.05/22.63  Sub-proof #343 shows that the following formulas are inconsistent:
% 153.05/22.63  ----------------------------------------------------------------
% 153.05/22.63    (1)  all_56_8 = e3
% 153.05/22.63    (2)   ~ (e3 = e1)
% 153.05/22.63    (3)  all_56_11 = e2
% 153.05/22.63    (4)   ~ (e2 = e0)
% 153.05/22.63    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.63    (6)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.05/22.63         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.05/22.63    (7)   ~ (e3 = e0)
% 153.05/22.63    (8)  op(e2, e2) = e2
% 153.05/22.63    (9)   ~ (e1 = e0)
% 153.05/22.63    (10)   ~ (e3 = e2)
% 153.05/22.63    (11)  e3 = e2
% 153.05/22.63    (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.63          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.05/22.63    (13)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.05/22.63          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.05/22.63    (14)   ~ (e2 = e1)
% 153.05/22.63    (15)  all_56_1 = e3
% 153.05/22.63    (16)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.05/22.63          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.05/22.63    (17)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.05/22.63          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.05/22.63  
% 153.05/22.63  Begin of proof
% 153.05/22.63  | 
% 153.05/22.63  | COMBINE_EQS: (11), (15) imply:
% 153.05/22.63  |   (18)  all_56_1 = e2
% 153.05/22.63  | 
% 153.05/22.63  | BETA: splitting (17) gives:
% 153.05/22.63  | 
% 153.05/22.63  | Case 1:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (19)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 153.05/22.63  | |           e3)
% 153.05/22.63  | | 
% 153.05/22.63  | | REF_CLOSE: (5), (8), (10), (18), (19) are inconsistent by sub-proof #926.
% 153.05/22.63  | | 
% 153.05/22.63  | Case 2:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (20)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 153.05/22.63  | |           e3)
% 153.05/22.63  | | 
% 153.05/22.63  | | BETA: splitting (20) gives:
% 153.05/22.63  | | 
% 153.05/22.63  | | Case 1:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (21)  all_56_7 = e3 & op(e1, e2) = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | ALPHA: (21) implies:
% 153.05/22.63  | | |   (22)  all_56_7 = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (13), (14), (22) are
% 153.05/22.63  | | |            inconsistent by sub-proof #643.
% 153.05/22.63  | | | 
% 153.05/22.63  | | Case 2:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (23)  all_56_13 = e3 & op(e0, e2) = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | ALPHA: (23) implies:
% 153.05/22.63  | | |   (24)  all_56_13 = e3
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (12), (14), (16), (18), (24) are
% 153.05/22.63  | | |            inconsistent by sub-proof #922.
% 153.05/22.63  | | | 
% 153.05/22.63  | | End of split
% 153.05/22.63  | | 
% 153.05/22.63  | End of split
% 153.05/22.63  | 
% 153.05/22.63  End of proof
% 153.05/22.63  
% 153.05/22.63  Sub-proof #344 shows that the following formulas are inconsistent:
% 153.05/22.63  ----------------------------------------------------------------
% 153.05/22.63    (1)   ~ (e3 = e1)
% 153.05/22.63    (2)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.63         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.05/22.63    (3)   ~ (e2 = e0)
% 153.05/22.63    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.63    (5)  op(e3, e3) = e2
% 153.05/22.63    (6)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.05/22.63         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.05/22.63    (7)   ~ (e3 = e0)
% 153.05/22.63    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.05/22.63         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.05/22.63    (9)  op(e2, e2) = e2
% 153.05/22.63    (10)   ~ (e1 = e0)
% 153.05/22.63    (11)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.05/22.63          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.05/22.63    (12)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.05/22.63    (13)   ~ (e2 = e1)
% 153.05/22.63    (14)  all_56_2 = e3
% 153.05/22.63    (15)  all_56_1 = e3
% 153.05/22.63  
% 153.05/22.63  Begin of proof
% 153.05/22.63  | 
% 153.05/22.63  | BETA: splitting (12) gives:
% 153.05/22.63  | 
% 153.05/22.63  | Case 1:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (16)  all_56_9 = e3 & op(e3, e0) = e3
% 153.05/22.63  | | 
% 153.05/22.63  | | ALPHA: (16) implies:
% 153.05/22.63  | |   (17)  all_56_9 = e3
% 153.05/22.63  | | 
% 153.05/22.63  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (13), (15), (17) are
% 153.05/22.63  | |            inconsistent by sub-proof #345.
% 153.05/22.63  | | 
% 153.05/22.63  | Case 2:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (18)  all_56_10 = e3 & op(e2, e0) = e3
% 153.05/22.63  | | 
% 153.05/22.63  | | ALPHA: (18) implies:
% 153.05/22.63  | |   (19)  all_56_10 = e3
% 153.05/22.63  | | 
% 153.05/22.63  | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (13), (14), (19) are
% 153.05/22.63  | |            inconsistent by sub-proof #363.
% 153.05/22.63  | | 
% 153.05/22.63  | End of split
% 153.05/22.63  | 
% 153.05/22.63  End of proof
% 153.05/22.63  
% 153.05/22.63  Sub-proof #345 shows that the following formulas are inconsistent:
% 153.05/22.63  ----------------------------------------------------------------
% 153.05/22.63    (1)   ~ (e3 = e1)
% 153.05/22.63    (2)  all_56_9 = e3
% 153.05/22.63    (3)   ~ (e2 = e0)
% 153.05/22.63    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.63    (5)  op(e3, e3) = e2
% 153.05/22.63    (6)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.05/22.63         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.05/22.63    (7)   ~ (e3 = e0)
% 153.05/22.63    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.05/22.63         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.05/22.63    (9)   ~ (e1 = e0)
% 153.05/22.63    (10)   ~ (e2 = e1)
% 153.05/22.63    (11)  all_56_1 = e3
% 153.05/22.63  
% 153.05/22.63  Begin of proof
% 153.05/22.63  | 
% 153.05/22.63  | BETA: splitting (6) gives:
% 153.05/22.63  | 
% 153.05/22.63  | Case 1:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 153.05/22.63  | |           e1)
% 153.05/22.63  | | 
% 153.05/22.63  | | REF_CLOSE: (1), (4), (5), (10), (11), (12) are inconsistent by sub-proof
% 153.05/22.63  | |            #658.
% 153.05/22.63  | | 
% 153.05/22.63  | Case 2:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (13)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 153.05/22.63  | |           e1)
% 153.05/22.63  | | 
% 153.05/22.63  | | BETA: splitting (13) gives:
% 153.05/22.63  | | 
% 153.05/22.63  | | Case 1:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (14)  all_56_4 = e1 & op(e3, e1) = e1
% 153.05/22.63  | | | 
% 153.05/22.63  | | | ALPHA: (14) implies:
% 153.05/22.63  | | |   (15)  all_56_4 = e1
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (11), (15) are inconsistent
% 153.05/22.63  | | |            by sub-proof #346.
% 153.05/22.63  | | | 
% 153.05/22.63  | | Case 2:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (16)  all_56_9 = e1 & op(e3, e0) = e1
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REF_CLOSE: (1), (2), (16) are inconsistent by sub-proof #493.
% 153.05/22.63  | | | 
% 153.05/22.63  | | End of split
% 153.05/22.63  | | 
% 153.05/22.63  | End of split
% 153.05/22.63  | 
% 153.05/22.63  End of proof
% 153.05/22.63  
% 153.05/22.63  Sub-proof #346 shows that the following formulas are inconsistent:
% 153.05/22.63  ----------------------------------------------------------------
% 153.05/22.63    (1)  all_56_9 = e3
% 153.05/22.63    (2)   ~ (e2 = e0)
% 153.05/22.63    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.63    (4)  op(e3, e3) = e2
% 153.05/22.63    (5)   ~ (e3 = e0)
% 153.05/22.63    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.05/22.63         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.05/22.63    (7)  all_56_4 = e1
% 153.05/22.63    (8)   ~ (e1 = e0)
% 153.05/22.63    (9)  all_56_1 = e3
% 153.05/22.63  
% 153.05/22.63  Begin of proof
% 153.05/22.63  | 
% 153.05/22.63  | BETA: splitting (6) gives:
% 153.05/22.63  | 
% 153.05/22.63  | Case 1:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 153.05/22.63  | |           e0)
% 153.05/22.63  | | 
% 153.05/22.63  | | REF_CLOSE: (2), (3), (4), (5), (9), (10) are inconsistent by sub-proof #659.
% 153.05/22.63  | | 
% 153.05/22.63  | Case 2:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (11)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 153.05/22.63  | |           e0)
% 153.05/22.63  | | 
% 153.05/22.63  | | BETA: splitting (11) gives:
% 153.05/22.63  | | 
% 153.05/22.63  | | Case 1:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (12)  all_56_4 = e0 & op(e3, e1) = e0
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REF_CLOSE: (7), (8), (12) are inconsistent by sub-proof #347.
% 153.05/22.63  | | | 
% 153.05/22.63  | | Case 2:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (13)  all_56_9 = e0 & op(e3, e0) = e0
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REF_CLOSE: (1), (5), (13) are inconsistent by sub-proof #446.
% 153.05/22.63  | | | 
% 153.05/22.63  | | End of split
% 153.05/22.63  | | 
% 153.05/22.63  | End of split
% 153.05/22.63  | 
% 153.05/22.63  End of proof
% 153.05/22.63  
% 153.05/22.63  Sub-proof #347 shows that the following formulas are inconsistent:
% 153.05/22.63  ----------------------------------------------------------------
% 153.05/22.63    (1)  all_56_4 = e0 & op(e3, e1) = e0
% 153.05/22.63    (2)  all_56_4 = e1
% 153.05/22.63    (3)   ~ (e1 = e0)
% 153.05/22.63  
% 153.05/22.63  Begin of proof
% 153.05/22.63  | 
% 153.05/22.63  | ALPHA: (1) implies:
% 153.05/22.63  |   (4)  all_56_4 = e0
% 153.05/22.63  | 
% 153.05/22.63  | COMBINE_EQS: (2), (4) imply:
% 153.05/22.63  |   (5)  e1 = e0
% 153.05/22.63  | 
% 153.05/22.63  | REDUCE: (3), (5) imply:
% 153.05/22.63  |   (6)  $false
% 153.05/22.63  | 
% 153.05/22.63  | CLOSE: (6) is inconsistent.
% 153.05/22.63  | 
% 153.05/22.63  End of proof
% 153.05/22.63  
% 153.05/22.63  Sub-proof #348 shows that the following formulas are inconsistent:
% 153.05/22.63  ----------------------------------------------------------------
% 153.05/22.63    (1)  op(e0, e2) = all_52_7
% 153.05/22.63    (2)   ~ (e2 = e0)
% 153.05/22.63    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.63    (4)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.05/22.63             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.05/22.63           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.05/22.63           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.05/22.63             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.05/22.63           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.05/22.63           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.05/22.63           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.05/22.63           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.05/22.63           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 153.05/22.63           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.05/22.63         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.05/22.63             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.05/22.63           $i(all_57_7))
% 153.05/22.63    (5)  op(e0, e1) = e2
% 153.05/22.63    (6)  op(e0, e3) = all_52_3
% 153.05/22.63    (7)  op(e2, e2) = e2
% 153.05/22.63    (8)   ~ (all_52_7 = e0)
% 153.05/22.63    (9)  op(e1, e1) = e3
% 153.05/22.63    (10)   ~ (e3 = e2)
% 153.05/22.63    (11)   ~ (all_52_3 = e0)
% 153.05/22.63    (12)   ~ (e2 = e1)
% 153.05/22.63  
% 153.05/22.63  Begin of proof
% 153.05/22.63  | 
% 153.05/22.63  | BETA: splitting (4) gives:
% 153.05/22.63  | 
% 153.05/22.63  | Case 1:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (13)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 153.05/22.63  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.05/22.63  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.05/22.63  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.05/22.63  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.05/22.63  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.05/22.63  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.05/22.63  | |           $i(all_57_3))
% 153.05/22.63  | | 
% 153.05/22.63  | | BETA: splitting (13) gives:
% 153.05/22.63  | | 
% 153.05/22.63  | | Case 1:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (14)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.05/22.63  | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.05/22.63  | | |         op(e0, e3) = e0 & $i(all_57_0)
% 153.05/22.63  | | | 
% 153.05/22.63  | | | ALPHA: (14) implies:
% 153.05/22.63  | | |   (15)  op(e0, e3) = e0
% 153.05/22.63  | | | 
% 153.05/22.63  | | | REF_CLOSE: (3), (6), (11), (15) are inconsistent by sub-proof #1142.
% 153.05/22.63  | | | 
% 153.05/22.63  | | Case 2:
% 153.05/22.63  | | | 
% 153.05/22.63  | | |   (16)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.05/22.63  | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.05/22.63  | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 153.05/22.63  | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.05/22.63  | | |           & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.05/22.63  | | | 
% 153.05/22.63  | | | BETA: splitting (16) gives:
% 153.05/22.63  | | | 
% 153.05/22.63  | | | Case 1:
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | |   (17)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.05/22.63  | | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.05/22.63  | | | |         op(e0, e3) = e0 & $i(all_57_1)
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | | ALPHA: (17) implies:
% 153.05/22.63  | | | |   (18)  op(e0, e3) = e0
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | | GROUND_INST: instantiating (3) with all_52_3, e0, e3, e0, simplifying
% 153.05/22.63  | | | |              with (6), (18) gives:
% 153.05/22.63  | | | |   (19)  all_52_3 = e0
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | | REDUCE: (11), (19) imply:
% 153.05/22.63  | | | |   (20)  $false
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | | CLOSE: (20) is inconsistent.
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | Case 2:
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | |   (21)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.05/22.63  | | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.05/22.63  | | | |         op(e0, e2) = e0 & $i(all_57_3)
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | | ALPHA: (21) implies:
% 153.05/22.63  | | | |   (22)  op(e0, e2) = e0
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | | REF_CLOSE: (1), (3), (8), (22) are inconsistent by sub-proof #1036.
% 153.05/22.63  | | | | 
% 153.05/22.63  | | | End of split
% 153.05/22.63  | | | 
% 153.05/22.63  | | End of split
% 153.05/22.63  | | 
% 153.05/22.63  | Case 2:
% 153.05/22.63  | | 
% 153.05/22.63  | |   (23)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.05/22.63  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.05/22.63  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.05/22.63  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.05/22.63  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.05/22.63  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.05/22.63  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.05/22.63  | |           $i(all_57_7))
% 153.05/22.63  | | 
% 153.05/22.63  | | REF_CLOSE: (2), (3), (5), (7), (9), (10), (12), (23) are inconsistent by
% 153.05/22.63  | |            sub-proof #431.
% 153.05/22.63  | | 
% 153.05/22.63  | End of split
% 153.05/22.63  | 
% 153.05/22.63  End of proof
% 153.05/22.63  
% 153.05/22.63  Sub-proof #349 shows that the following formulas are inconsistent:
% 153.05/22.63  ----------------------------------------------------------------
% 153.05/22.63    (1)   ~ (e3 = e1)
% 153.05/22.63    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.63           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.63    (3)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.05/22.63         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.05/22.63    (4)  op(e1, e3) = e0
% 153.05/22.63    (5)   ~ (e1 = e0)
% 153.05/22.63    (6)  op(e1, e1) = e3
% 153.05/22.63    (7)  op(e1, e0) = e2
% 153.05/22.63    (8)  all_56_7 = e0
% 153.05/22.63    (9)   ~ (e2 = e1)
% 153.05/22.63    (10)  op(e1, e3) = all_52_2
% 153.05/22.63  
% 153.05/22.63  Begin of proof
% 153.05/22.63  | 
% 153.05/22.64  | BETA: splitting (3) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (11)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 153.05/22.64  | |           e1)
% 153.05/22.64  | | 
% 153.05/22.64  | | BETA: splitting (11) gives:
% 153.05/22.64  | | 
% 153.05/22.64  | | Case 1:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (12)  all_56_6 = e1 & op(e1, e3) = e1
% 153.05/22.64  | | | 
% 153.05/22.64  | | | ALPHA: (12) implies:
% 153.05/22.64  | | |   (13)  op(e1, e3) = e1
% 153.05/22.64  | | | 
% 153.05/22.64  | | | REF_CLOSE: (2), (4), (5), (10), (13) are inconsistent by sub-proof #1127.
% 153.05/22.64  | | | 
% 153.05/22.64  | | Case 2:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (14)  all_56_7 = e1 & op(e1, e2) = e1
% 153.05/22.64  | | | 
% 153.05/22.64  | | | REF_CLOSE: (5), (8), (14) are inconsistent by sub-proof #1111.
% 153.05/22.64  | | | 
% 153.05/22.64  | | End of split
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (15)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 153.05/22.64  | |           e1)
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (1), (2), (6), (7), (9), (15) are inconsistent by sub-proof #350.
% 153.05/22.64  | | 
% 153.05/22.64  | End of split
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #350 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)   ~ (e3 = e1)
% 153.05/22.64    (2)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.05/22.64    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.64    (4)  op(e1, e1) = e3
% 153.05/22.64    (5)  op(e1, e0) = e2
% 153.05/22.64    (6)   ~ (e2 = e1)
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | BETA: splitting (2) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (7)  all_56_8 = e1 & op(e1, e1) = e1
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (7) implies:
% 153.05/22.64  | |   (8)  op(e1, e1) = e1
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #734.
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (9)  all_56_11 = e1 & op(e1, e0) = e1
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (9) implies:
% 153.05/22.64  | |   (10)  op(e1, e0) = e1
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1125.
% 153.05/22.64  | | 
% 153.05/22.64  | End of split
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #351 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)  all_56_8 = e3
% 153.05/22.64    (2)   ~ (e3 = e1)
% 153.05/22.64    (3)  all_56_11 = e2
% 153.05/22.64    (4)   ~ (e2 = e0)
% 153.05/22.64    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.64    (6)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.05/22.64         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.05/22.64    (7)  all_56_13 = e1
% 153.05/22.64    (8)   ~ (e3 = e0)
% 153.05/22.64    (9)  op(e2, e2) = e2
% 153.05/22.64    (10)   ~ (e1 = e0)
% 153.05/22.64    (11)   ~ (e3 = e2)
% 153.05/22.64    (12)  all_56_1 = e0
% 153.05/22.64    (13)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.05/22.64          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.05/22.64    (14)   ~ (e2 = e1)
% 153.05/22.64    (15)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.05/22.64          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | BETA: splitting (15) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 153.05/22.64  | |           e3)
% 153.05/22.64  | | 
% 153.05/22.64  | | BETA: splitting (16) gives:
% 153.05/22.64  | | 
% 153.05/22.64  | | Case 1:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (17)  all_56_1 = e3 & op(e3, e2) = e3
% 153.05/22.64  | | | 
% 153.05/22.64  | | | ALPHA: (17) implies:
% 153.05/22.64  | | |   (18)  all_56_1 = e3
% 153.05/22.64  | | | 
% 153.05/22.64  | | | REF_CLOSE: (8), (12), (18) are inconsistent by sub-proof #1065.
% 153.05/22.64  | | | 
% 153.05/22.64  | | Case 2:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (19)  all_56_3 = e3 & op(e2, e2) = e3
% 153.05/22.64  | | | 
% 153.05/22.64  | | | ALPHA: (19) implies:
% 153.05/22.64  | | |   (20)  op(e2, e2) = e3
% 153.05/22.64  | | | 
% 153.05/22.64  | | | REF_CLOSE: (5), (9), (11), (20) are inconsistent by sub-proof #1179.
% 153.05/22.64  | | | 
% 153.05/22.64  | | End of split
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (21)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 153.05/22.64  | |           e3)
% 153.05/22.64  | | 
% 153.05/22.64  | | BETA: splitting (21) gives:
% 153.05/22.64  | | 
% 153.05/22.64  | | Case 1:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (22)  all_56_7 = e3 & op(e1, e2) = e3
% 153.05/22.64  | | | 
% 153.05/22.64  | | | ALPHA: (22) implies:
% 153.05/22.64  | | |   (23)  all_56_7 = e3
% 153.05/22.64  | | | 
% 153.05/22.64  | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (13), (14), (23) are
% 153.05/22.64  | | |            inconsistent by sub-proof #643.
% 153.05/22.64  | | | 
% 153.05/22.64  | | Case 2:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (24)  all_56_13 = e3 & op(e0, e2) = e3
% 153.05/22.64  | | | 
% 153.05/22.64  | | | REF_CLOSE: (2), (7), (24) are inconsistent by sub-proof #585.
% 153.05/22.64  | | | 
% 153.05/22.64  | | End of split
% 153.05/22.64  | | 
% 153.05/22.64  | End of split
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #352 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.64    (2)   ~ (e3 = e0)
% 153.05/22.64    (3)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.05/22.64             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.05/22.64           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 153.05/22.64           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 153.05/22.64             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 153.05/22.64             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.05/22.64    (4)  op(e1, e1) = e3
% 153.05/22.64    (5)  op(e0, e0) = e0
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | BETA: splitting (3) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (6)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.05/22.64  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.05/22.64  | |        op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (6) implies:
% 153.05/22.64  | |   (7)   ~ (all_57_14 = e3)
% 153.05/22.64  | |   (8)  op(e1, e1) = all_57_14
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (1), (4), (7), (8) are inconsistent by sub-proof #816.
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (9)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 153.05/22.64  | |          e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.05/22.64  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (9) implies:
% 153.05/22.64  | |   (10)  op(e0, e0) = e3
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1143.
% 153.05/22.64  | | 
% 153.05/22.64  | End of split
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #353 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)  all_56_8 = e3
% 153.05/22.64    (2)   ~ (e3 = e1)
% 153.05/22.64    (3)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 153.05/22.64         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.05/22.64    (4)   ~ (e2 = e0)
% 153.05/22.64    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.64    (6)  all_56_14 = e2
% 153.05/22.64    (7)   ~ (e3 = e0)
% 153.05/22.64    (8)  op(e0, e1) = e2
% 153.05/22.64    (9)   ~ (e1 = e0)
% 153.05/22.64    (10)  op(e1, e1) = e3
% 153.05/22.64    (11)   ~ (e3 = e2)
% 153.05/22.64    (12)  all_56_9 = e2
% 153.05/22.64    (13)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.05/22.64    (14)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 153.05/22.64          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 153.05/22.64    (15)   ~ (e2 = e1)
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | BETA: splitting (13) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (16)  all_56_4 = e3 & op(e3, e1) = e3
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (16) implies:
% 153.05/22.64  | |   (17)  all_56_4 = e3
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (14), (15),
% 153.05/22.64  | |            (17) are inconsistent by sub-proof #354.
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (18)  all_56_9 = e3 & op(e3, e0) = e3
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (18) implies:
% 153.05/22.64  | |   (19)  all_56_9 = e3
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (11), (12), (19) are inconsistent by sub-proof #964.
% 153.05/22.64  | | 
% 153.05/22.64  | End of split
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #354 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)  all_56_8 = e3
% 153.05/22.64    (2)   ~ (e3 = e1)
% 153.05/22.64    (3)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 153.05/22.64         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.05/22.64    (4)   ~ (e2 = e0)
% 153.05/22.64    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.64    (6)  all_56_14 = e2
% 153.05/22.64    (7)   ~ (e3 = e0)
% 153.05/22.64    (8)  op(e0, e1) = e2
% 153.05/22.64    (9)   ~ (e1 = e0)
% 153.05/22.64    (10)  op(e1, e1) = e3
% 153.05/22.64    (11)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 153.05/22.64          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 153.05/22.64    (12)   ~ (e2 = e1)
% 153.05/22.64    (13)  all_56_4 = e3
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | BETA: splitting (3) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (14)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 153.05/22.64  | |           e0)
% 153.05/22.64  | | 
% 153.05/22.64  | | BETA: splitting (14) gives:
% 153.05/22.64  | | 
% 153.05/22.64  | | Case 1:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (15)  all_56_4 = e0 & op(e3, e1) = e0
% 153.05/22.64  | | | 
% 153.05/22.64  | | | REF_CLOSE: (7), (13), (15) are inconsistent by sub-proof #361.
% 153.05/22.64  | | | 
% 153.05/22.64  | | Case 2:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (16)  all_56_5 = e0 & op(e2, e1) = e0
% 153.05/22.64  | | | 
% 153.05/22.64  | | | ALPHA: (16) implies:
% 153.05/22.64  | | |   (17)  all_56_5 = e0
% 153.05/22.64  | | | 
% 153.05/22.64  | | | BETA: splitting (11) gives:
% 153.05/22.64  | | | 
% 153.05/22.64  | | | Case 1:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | |   (18)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1)
% 153.05/22.64  | | | |           = e1)
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | BETA: splitting (18) gives:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | Case 1:
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | |   (19)  all_56_4 = e1 & op(e3, e1) = e1
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | REF_CLOSE: (2), (13), (19) are inconsistent by sub-proof #358.
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | Case 2:
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | |   (20)  all_56_5 = e1 & op(e2, e1) = e1
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | ALPHA: (20) implies:
% 153.05/22.64  | | | | |   (21)  all_56_5 = e1
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | REF_CLOSE: (9), (17), (21) are inconsistent by sub-proof #682.
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | End of split
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | Case 2:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | |   (22)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1)
% 153.05/22.64  | | | |           = e1)
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | REF_CLOSE: (2), (5), (6), (10), (12), (22) are inconsistent by sub-proof
% 153.05/22.64  | | | |            #356.
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | End of split
% 153.05/22.64  | | | 
% 153.05/22.64  | | End of split
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (23)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 153.05/22.64  | |           e0)
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (1), (4), (5), (7), (8), (23) are inconsistent by sub-proof #355.
% 153.05/22.64  | | 
% 153.05/22.64  | End of split
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #355 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)  all_56_8 = e3
% 153.05/22.64    (2)   ~ (e2 = e0)
% 153.05/22.64    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.64    (4)   ~ (e3 = e0)
% 153.05/22.64    (5)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.05/22.64    (6)  op(e0, e1) = e2
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | BETA: splitting (5) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (7)  all_56_8 = e0 & op(e1, e1) = e0
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #360.
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (8)  all_56_14 = e0 & op(e0, e1) = e0
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (8) implies:
% 153.05/22.64  | |   (9)  op(e0, e1) = e0
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #1008.
% 153.05/22.64  | | 
% 153.05/22.64  | End of split
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #356 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)   ~ (e3 = e1)
% 153.05/22.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.64    (3)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 153.05/22.64    (4)  all_56_14 = e2
% 153.05/22.64    (5)  op(e1, e1) = e3
% 153.05/22.64    (6)   ~ (e2 = e1)
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | BETA: splitting (3) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (7)  all_56_8 = e1 & op(e1, e1) = e1
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (7) implies:
% 153.05/22.64  | |   (8)  op(e1, e1) = e1
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #734.
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (9)  all_56_14 = e1 & op(e0, e1) = e1
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #357.
% 153.05/22.64  | | 
% 153.05/22.64  | End of split
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #357 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)  all_56_14 = e1 & op(e0, e1) = e1
% 153.05/22.64    (2)  all_56_14 = e2
% 153.05/22.64    (3)   ~ (e2 = e1)
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | ALPHA: (1) implies:
% 153.05/22.64  |   (4)  all_56_14 = e1
% 153.05/22.64  | 
% 153.05/22.64  | COMBINE_EQS: (2), (4) imply:
% 153.05/22.64  |   (5)  e2 = e1
% 153.05/22.64  | 
% 153.05/22.64  | REDUCE: (3), (5) imply:
% 153.05/22.64  |   (6)  $false
% 153.05/22.64  | 
% 153.05/22.64  | CLOSE: (6) is inconsistent.
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #358 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)  all_56_4 = e1 & op(e3, e1) = e1
% 153.05/22.64    (2)  all_56_4 = e3
% 153.05/22.64    (3)   ~ (e3 = e1)
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | ALPHA: (1) implies:
% 153.05/22.64  |   (4)  all_56_4 = e1
% 153.05/22.64  | 
% 153.05/22.64  | COMBINE_EQS: (2), (4) imply:
% 153.05/22.64  |   (5)  e3 = e1
% 153.05/22.64  | 
% 153.05/22.64  | REDUCE: (3), (5) imply:
% 153.05/22.64  |   (6)  $false
% 153.05/22.64  | 
% 153.05/22.64  | CLOSE: (6) is inconsistent.
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #359 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)   ~ (e3 = e1)
% 153.05/22.64    (2)   ~ (e2 = e0)
% 153.05/22.64    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.64    (4)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 153.05/22.64         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 153.05/22.64    (5)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.05/22.64             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.05/22.64               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.05/22.64               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.05/22.64    (6)  op(e0, e0) = e1
% 153.05/22.64    (7)   ~ (e3 = e0)
% 153.05/22.64    (8)   ~ (all_52_9 = e2)
% 153.05/22.64    (9)  op(e2, e2) = e2
% 153.05/22.64    (10)  op(e2, e1) = all_52_9
% 153.05/22.64    (11)   ~ (e1 = e0)
% 153.05/22.64    (12)  all_56_13 = e3
% 153.05/22.64    (13)  op(e1, e1) = e3
% 153.05/22.64    (14)   ~ (e3 = e2)
% 153.05/22.64    (15)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.64          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.05/22.64    (16)  all_56_12 = e2
% 153.05/22.64    (17)   ~ (e2 = e1)
% 153.05/22.64    (18)  all_56_4 = e3
% 153.05/22.64    (19)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.05/22.64          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.05/22.64    (20)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.05/22.64          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | BETA: splitting (5) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (21)  all_56_15 = e0 & op(e0, e0) = e0
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (21) implies:
% 153.05/22.64  | |   (22)  op(e0, e0) = e0
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (3), (6), (11), (22) are inconsistent by sub-proof #1040.
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (23)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.05/22.64  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 153.05/22.64  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.05/22.64  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (23) implies:
% 153.05/22.64  | |   (24)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 153.05/22.64  | |           e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.05/22.64  | | 
% 153.05/22.64  | | BETA: splitting (4) gives:
% 153.05/22.64  | | 
% 153.05/22.64  | | Case 1:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (25)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) =
% 153.05/22.64  | | |           e2)
% 153.05/22.64  | | | 
% 153.05/22.64  | | | BETA: splitting (25) gives:
% 153.05/22.64  | | | 
% 153.05/22.64  | | | Case 1:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | |   (26)  all_56_4 = e2 & op(e3, e1) = e2
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | ALPHA: (26) implies:
% 153.05/22.64  | | | |   (27)  all_56_4 = e2
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | COMBINE_EQS: (18), (27) imply:
% 153.05/22.64  | | | |   (28)  e3 = e2
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | SIMP: (28) implies:
% 153.05/22.64  | | | |   (29)  e3 = e2
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | COMBINE_EQS: (12), (29) imply:
% 153.05/22.64  | | | |   (30)  all_56_13 = e2
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | REF_CLOSE: (1), (2), (3), (7), (9), (11), (14), (15), (17), (19), (20),
% 153.05/22.64  | | | |            (30) are inconsistent by sub-proof #1104.
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | Case 2:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | |   (31)  all_56_5 = e2 & op(e2, e1) = e2
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | ALPHA: (31) implies:
% 153.05/22.64  | | | |   (32)  op(e2, e1) = e2
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | REF_CLOSE: (3), (8), (10), (32) are inconsistent by sub-proof #1157.
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | End of split
% 153.05/22.64  | | | 
% 153.05/22.64  | | Case 2:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (33)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) =
% 153.05/22.64  | | |           e2)
% 153.05/22.64  | | | 
% 153.05/22.64  | | | BETA: splitting (33) gives:
% 153.05/22.64  | | | 
% 153.05/22.64  | | | Case 1:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | |   (34)  all_56_8 = e2 & op(e1, e1) = e2
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | ALPHA: (34) implies:
% 153.05/22.64  | | | |   (35)  op(e1, e1) = e2
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | REF_CLOSE: (3), (13), (14), (35) are inconsistent by sub-proof #834.
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | Case 2:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | |   (36)  all_56_14 = e2 & op(e0, e1) = e2
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | ALPHA: (36) implies:
% 153.05/22.64  | | | |   (37)  all_56_14 = e2
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | BETA: splitting (24) gives:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | Case 1:
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | |   (38)  all_56_12 = e0 & op(e0, e3) = e0
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | ALPHA: (38) implies:
% 153.05/22.64  | | | | |   (39)  all_56_12 = e0
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | REF_CLOSE: (2), (16), (39) are inconsistent by sub-proof #1119.
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | Case 2:
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | |   (40)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 153.05/22.64  | | | | |             e1) = e0)
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | BETA: splitting (40) gives:
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | Case 1:
% 153.05/22.64  | | | | | | 
% 153.05/22.64  | | | | | |   (41)  all_56_13 = e0 & op(e0, e2) = e0
% 153.05/22.64  | | | | | | 
% 153.05/22.64  | | | | | | ALPHA: (41) implies:
% 153.05/22.64  | | | | | |   (42)  all_56_13 = e0
% 153.05/22.64  | | | | | | 
% 153.05/22.64  | | | | | | REF_CLOSE: (7), (12), (42) are inconsistent by sub-proof #1094.
% 153.05/22.64  | | | | | | 
% 153.05/22.64  | | | | | Case 2:
% 153.05/22.64  | | | | | | 
% 153.05/22.64  | | | | | |   (43)  all_56_14 = e0 & op(e0, e1) = e0
% 153.05/22.64  | | | | | | 
% 153.05/22.64  | | | | | | ALPHA: (43) implies:
% 153.05/22.64  | | | | | |   (44)  all_56_14 = e0
% 153.05/22.64  | | | | | | 
% 153.05/22.64  | | | | | | COMBINE_EQS: (37), (44) imply:
% 153.05/22.64  | | | | | |   (45)  e2 = e0
% 153.05/22.64  | | | | | | 
% 153.05/22.64  | | | | | | SIMP: (45) implies:
% 153.05/22.64  | | | | | |   (46)  e2 = e0
% 153.05/22.64  | | | | | | 
% 153.05/22.64  | | | | | | REDUCE: (2), (46) imply:
% 153.05/22.64  | | | | | |   (47)  $false
% 153.05/22.64  | | | | | | 
% 153.05/22.64  | | | | | | CLOSE: (47) is inconsistent.
% 153.05/22.64  | | | | | | 
% 153.05/22.64  | | | | | End of split
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | End of split
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | End of split
% 153.05/22.64  | | | 
% 153.05/22.64  | | End of split
% 153.05/22.64  | | 
% 153.05/22.64  | End of split
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #360 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)  all_56_8 = e0 & op(e1, e1) = e0
% 153.05/22.64    (2)  all_56_8 = e3
% 153.05/22.64    (3)   ~ (e3 = e0)
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | ALPHA: (1) implies:
% 153.05/22.64  |   (4)  all_56_8 = e0
% 153.05/22.64  | 
% 153.05/22.64  | COMBINE_EQS: (2), (4) imply:
% 153.05/22.64  |   (5)  e3 = e0
% 153.05/22.64  | 
% 153.05/22.64  | SIMP: (5) implies:
% 153.05/22.64  |   (6)  e3 = e0
% 153.05/22.64  | 
% 153.05/22.64  | REDUCE: (3), (6) imply:
% 153.05/22.64  |   (7)  $false
% 153.05/22.64  | 
% 153.05/22.64  | CLOSE: (7) is inconsistent.
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #361 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)  all_56_4 = e0 & op(e3, e1) = e0
% 153.05/22.64    (2)  all_56_4 = e3
% 153.05/22.64    (3)   ~ (e3 = e0)
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | ALPHA: (1) implies:
% 153.05/22.64  |   (4)  all_56_4 = e0
% 153.05/22.64  | 
% 153.05/22.64  | COMBINE_EQS: (2), (4) imply:
% 153.05/22.64  |   (5)  e3 = e0
% 153.05/22.64  | 
% 153.05/22.64  | REDUCE: (3), (5) imply:
% 153.05/22.64  |   (6)  $false
% 153.05/22.64  | 
% 153.05/22.64  | CLOSE: (6) is inconsistent.
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #362 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)  all_56_11 = e1
% 153.05/22.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.64    (3)   ~ (e3 = e0)
% 153.05/22.64    (4)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.05/22.64    (5)   ~ (e1 = e0)
% 153.05/22.64    (6)  op(e1, e1) = e3
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | BETA: splitting (4) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (7)  all_56_8 = e0 & op(e1, e1) = e0
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (7) implies:
% 153.05/22.64  | |   (8)  op(e1, e1) = e0
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #896.
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (9)  all_56_11 = e0 & op(e1, e0) = e0
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (9) implies:
% 153.05/22.64  | |   (10)  all_56_11 = e0
% 153.05/22.64  | | 
% 153.05/22.64  | | COMBINE_EQS: (1), (10) imply:
% 153.05/22.64  | |   (11)  e1 = e0
% 153.05/22.64  | | 
% 153.05/22.64  | | REDUCE: (5), (11) imply:
% 153.05/22.64  | |   (12)  $false
% 153.05/22.64  | | 
% 153.05/22.64  | | CLOSE: (12) is inconsistent.
% 153.05/22.64  | | 
% 153.05/22.64  | End of split
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #363 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)   ~ (e3 = e1)
% 153.05/22.64    (2)  all_56_10 = e3
% 153.05/22.64    (3)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.64         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.05/22.64    (4)   ~ (e2 = e0)
% 153.05/22.64    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.64    (6)   ~ (e3 = e0)
% 153.05/22.64    (7)  op(e2, e2) = e2
% 153.05/22.64    (8)   ~ (e1 = e0)
% 153.05/22.64    (9)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.05/22.64         (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.05/22.64    (10)   ~ (e2 = e1)
% 153.05/22.64    (11)  all_56_2 = e3
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | BETA: splitting (9) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (12)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 153.05/22.64  | |           e1)
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (1), (5), (7), (10), (11), (12) are inconsistent by sub-proof
% 153.05/22.64  | |            #364.
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (13)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 153.05/22.64  | |           e1)
% 153.05/22.64  | | 
% 153.05/22.64  | | BETA: splitting (13) gives:
% 153.05/22.64  | | 
% 153.05/22.64  | | Case 1:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (14)  all_56_5 = e1 & op(e2, e1) = e1
% 153.05/22.64  | | | 
% 153.05/22.64  | | | ALPHA: (14) implies:
% 153.05/22.64  | | |   (15)  all_56_5 = e1
% 153.05/22.64  | | | 
% 153.05/22.64  | | | BETA: splitting (3) gives:
% 153.05/22.64  | | | 
% 153.05/22.64  | | | Case 1:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | |   (16)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2)
% 153.05/22.64  | | | |           = e0)
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | BETA: splitting (16) gives:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | Case 1:
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | |   (17)  all_56_2 = e0 & op(e2, e3) = e0
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | ALPHA: (17) implies:
% 153.05/22.64  | | | | |   (18)  all_56_2 = e0
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | REF_CLOSE: (6), (11), (18) are inconsistent by sub-proof #1137.
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | Case 2:
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | |   (19)  all_56_3 = e0 & op(e2, e2) = e0
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | ALPHA: (19) implies:
% 153.05/22.64  | | | | |   (20)  op(e2, e2) = e0
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | REF_CLOSE: (4), (5), (7), (20) are inconsistent by sub-proof #1145.
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | End of split
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | Case 2:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | |   (21)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0)
% 153.05/22.64  | | | |           = e0)
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | BETA: splitting (21) gives:
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | | Case 1:
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | |   (22)  all_56_5 = e0 & op(e2, e1) = e0
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | ALPHA: (22) implies:
% 153.05/22.64  | | | | |   (23)  all_56_5 = e0
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | REF_CLOSE: (8), (15), (23) are inconsistent by sub-proof #682.
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | Case 2:
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | |   (24)  all_56_10 = e0 & op(e2, e0) = e0
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | ALPHA: (24) implies:
% 153.05/22.64  | | | | |   (25)  all_56_10 = e0
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | | REF_CLOSE: (2), (6), (25) are inconsistent by sub-proof #1134.
% 153.05/22.64  | | | | | 
% 153.05/22.64  | | | | End of split
% 153.05/22.64  | | | | 
% 153.05/22.64  | | | End of split
% 153.05/22.64  | | | 
% 153.05/22.64  | | Case 2:
% 153.05/22.64  | | | 
% 153.05/22.64  | | |   (26)  all_56_10 = e1 & op(e2, e0) = e1
% 153.05/22.64  | | | 
% 153.05/22.64  | | | REF_CLOSE: (1), (2), (26) are inconsistent by sub-proof #584.
% 153.05/22.64  | | | 
% 153.05/22.64  | | End of split
% 153.05/22.64  | | 
% 153.05/22.64  | End of split
% 153.05/22.64  | 
% 153.05/22.64  End of proof
% 153.05/22.64  
% 153.05/22.64  Sub-proof #364 shows that the following formulas are inconsistent:
% 153.05/22.64  ----------------------------------------------------------------
% 153.05/22.64    (1)   ~ (e3 = e1)
% 153.05/22.64    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.64           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.64    (3)  op(e2, e2) = e2
% 153.05/22.64    (4)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 153.05/22.64    (5)   ~ (e2 = e1)
% 153.05/22.64    (6)  all_56_2 = e3
% 153.05/22.64  
% 153.05/22.64  Begin of proof
% 153.05/22.64  | 
% 153.05/22.64  | BETA: splitting (4) gives:
% 153.05/22.64  | 
% 153.05/22.64  | Case 1:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (7)  all_56_2 = e1 & op(e2, e3) = e1
% 153.05/22.64  | | 
% 153.05/22.64  | | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #791.
% 153.05/22.64  | | 
% 153.05/22.64  | Case 2:
% 153.05/22.64  | | 
% 153.05/22.64  | |   (8)  all_56_3 = e1 & op(e2, e2) = e1
% 153.05/22.64  | | 
% 153.05/22.64  | | ALPHA: (8) implies:
% 153.05/22.65  | |   (9)  op(e2, e2) = e1
% 153.05/22.65  | | 
% 153.05/22.65  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1158.
% 153.05/22.65  | | 
% 153.05/22.65  | End of split
% 153.05/22.65  | 
% 153.05/22.65  End of proof
% 153.05/22.65  
% 153.05/22.65  Sub-proof #365 shows that the following formulas are inconsistent:
% 153.05/22.65  ----------------------------------------------------------------
% 153.05/22.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.65    (2)   ~ (all_52_1 = e3)
% 153.05/22.65    (3)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 153.05/22.65    (4)  op(e2, e2) = e2
% 153.05/22.65    (5)   ~ (e3 = e2)
% 153.05/22.65    (6)  op(e2, e3) = all_52_1
% 153.05/22.65  
% 153.05/22.65  Begin of proof
% 153.05/22.65  | 
% 153.05/22.65  | BETA: splitting (3) gives:
% 153.05/22.65  | 
% 153.05/22.65  | Case 1:
% 153.05/22.65  | | 
% 153.05/22.65  | |   (7)  all_56_2 = e3 & op(e2, e3) = e3
% 153.05/22.65  | | 
% 153.05/22.65  | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #917.
% 153.05/22.65  | | 
% 153.05/22.65  | Case 2:
% 153.05/22.65  | | 
% 153.05/22.65  | |   (8)  all_56_3 = e3 & op(e2, e2) = e3
% 153.05/22.65  | | 
% 153.05/22.65  | | ALPHA: (8) implies:
% 153.05/22.65  | |   (9)  op(e2, e2) = e3
% 153.05/22.65  | | 
% 153.05/22.65  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1179.
% 153.05/22.65  | | 
% 153.05/22.65  | End of split
% 153.05/22.65  | 
% 153.05/22.65  End of proof
% 153.05/22.65  
% 153.05/22.65  Sub-proof #366 shows that the following formulas are inconsistent:
% 153.05/22.65  ----------------------------------------------------------------
% 153.05/22.65    (1)   ~ (all_14_2 = e0)
% 153.05/22.65    (2)  op(e3, e3) = all_14_2
% 153.05/22.65    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.65    (4)  op(e3, e3) = e2
% 153.05/22.65    (5)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.05/22.65    (6)  all_54_0 = all_14_2
% 153.05/22.65    (7)   ~ (all_14_2 = e2)
% 153.05/22.65    (8)   ~ (all_14_2 = e1)
% 153.05/22.65  
% 153.05/22.65  Begin of proof
% 153.05/22.65  | 
% 153.05/22.65  | BETA: splitting (5) gives:
% 153.05/22.65  | 
% 153.05/22.65  | Case 1:
% 153.05/22.65  | | 
% 153.05/22.65  | |   (9)  all_54_0 = e3
% 153.05/22.65  | | 
% 153.05/22.65  | | COMBINE_EQS: (6), (9) imply:
% 153.05/22.65  | |   (10)  all_14_2 = e3
% 153.05/22.65  | | 
% 153.05/22.65  | | REDUCE: (7), (10) imply:
% 153.05/22.65  | |   (11)   ~ (e3 = e2)
% 153.05/22.65  | | 
% 153.05/22.65  | | REDUCE: (2), (10) imply:
% 153.05/22.65  | |   (12)  op(e3, e3) = e3
% 153.05/22.65  | | 
% 153.05/22.65  | | REF_CLOSE: (3), (4), (11), (12) are inconsistent by sub-proof #1085.
% 153.05/22.65  | | 
% 153.05/22.65  | Case 2:
% 153.05/22.65  | | 
% 153.05/22.65  | |   (13)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.05/22.65  | | 
% 153.05/22.65  | | REF_CLOSE: (1), (6), (7), (8), (13) are inconsistent by sub-proof #1140.
% 153.05/22.65  | | 
% 153.05/22.65  | End of split
% 153.05/22.65  | 
% 153.05/22.65  End of proof
% 153.05/22.65  
% 153.05/22.65  Sub-proof #367 shows that the following formulas are inconsistent:
% 153.05/22.65  ----------------------------------------------------------------
% 153.05/22.65    (1)  op(e0, e0) = all_10_2
% 153.05/22.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.65    (3)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.05/22.65             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.05/22.65           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 153.05/22.65           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.05/22.65           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.05/22.65           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.05/22.65    (4)  op(e1, e1) = e3
% 153.05/22.65    (5)   ~ (e3 = e2)
% 153.05/22.65    (6)   ~ (all_10_2 = e2)
% 153.05/22.65  
% 153.05/22.65  Begin of proof
% 153.05/22.65  | 
% 153.05/22.65  | BETA: splitting (3) gives:
% 153.05/22.65  | 
% 153.05/22.65  | Case 1:
% 153.05/22.65  | | 
% 153.05/22.65  | |   (7)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.05/22.65  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.05/22.65  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 153.05/22.65  | | 
% 153.05/22.65  | | ALPHA: (7) implies:
% 153.05/22.65  | |   (8)  op(e1, e1) = e2
% 153.05/22.65  | | 
% 153.05/22.65  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #834.
% 153.05/22.65  | | 
% 153.05/22.65  | Case 2:
% 153.05/22.65  | | 
% 153.05/22.65  | |   (9)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 153.05/22.65  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.05/22.65  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 153.05/22.65  | | 
% 153.05/22.65  | | ALPHA: (9) implies:
% 153.05/22.65  | |   (10)  op(e0, e0) = e2
% 153.05/22.65  | | 
% 153.05/22.65  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #1097.
% 153.05/22.65  | | 
% 153.05/22.65  | End of split
% 153.05/22.65  | 
% 153.05/22.65  End of proof
% 153.05/22.65  
% 153.05/22.65  Sub-proof #368 shows that the following formulas are inconsistent:
% 153.05/22.65  ----------------------------------------------------------------
% 153.05/22.65    (1)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.05/22.65             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.05/22.65           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 153.05/22.65           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 153.05/22.65             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 153.05/22.65             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.05/22.65    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.65    (3)  op(e1, e1) = e3
% 153.05/22.65  
% 153.05/22.65  Begin of proof
% 153.05/22.65  | 
% 153.05/22.65  | BETA: splitting (1) gives:
% 153.05/22.65  | 
% 153.05/22.65  | Case 1:
% 153.05/22.65  | | 
% 153.05/22.65  | |   (4)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.05/22.65  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.05/22.65  | |        op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 153.05/22.65  | | 
% 153.05/22.65  | | ALPHA: (4) implies:
% 153.05/22.65  | |   (5)   ~ (all_57_14 = e3)
% 153.05/22.65  | |   (6)  op(e1, e1) = all_57_14
% 153.05/22.65  | | 
% 153.05/22.65  | | REF_CLOSE: (2), (3), (5), (6) are inconsistent by sub-proof #816.
% 153.05/22.65  | | 
% 153.05/22.65  | Case 2:
% 153.05/22.65  | | 
% 153.05/22.65  | |   (7)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 153.05/22.65  | |          e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.05/22.65  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 153.05/22.65  | | 
% 153.05/22.65  | | ALPHA: (7) implies:
% 153.05/22.65  | |   (8)   ~ (all_57_14 = e3)
% 153.05/22.65  | |   (9)  op(e1, e1) = all_57_14
% 153.05/22.65  | | 
% 153.05/22.65  | | REF_CLOSE: (2), (3), (8), (9) are inconsistent by sub-proof #816.
% 153.05/22.65  | | 
% 153.05/22.65  | End of split
% 153.05/22.65  | 
% 153.05/22.65  End of proof
% 153.05/22.65  
% 153.05/22.65  Sub-proof #369 shows that the following formulas are inconsistent:
% 153.05/22.65  ----------------------------------------------------------------
% 153.05/22.65    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.65    (2)   ~ (all_52_9 = e3)
% 153.05/22.65    (3)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3)
% 153.05/22.65    (4)  op(e2, e1) = all_52_9
% 153.05/22.65    (5)   ~ (all_52_8 = e3)
% 153.05/22.65    (6)  op(e3, e1) = all_52_8
% 153.05/22.65  
% 153.05/22.65  Begin of proof
% 153.05/22.65  | 
% 153.05/22.65  | BETA: splitting (3) gives:
% 153.05/22.65  | 
% 153.05/22.65  | Case 1:
% 153.05/22.65  | | 
% 153.05/22.65  | |   (7)  all_56_4 = e3 & op(e3, e1) = e3
% 153.05/22.65  | | 
% 153.05/22.65  | | ALPHA: (7) implies:
% 153.05/22.65  | |   (8)  op(e3, e1) = e3
% 153.05/22.65  | | 
% 153.05/22.65  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #1164.
% 153.05/22.65  | | 
% 153.05/22.65  | Case 2:
% 153.05/22.65  | | 
% 153.05/22.65  | |   (9)  all_56_5 = e3 & op(e2, e1) = e3
% 153.05/22.65  | | 
% 153.05/22.65  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #647.
% 153.05/22.65  | | 
% 153.05/22.65  | End of split
% 153.05/22.65  | 
% 153.05/22.65  End of proof
% 153.05/22.65  
% 153.05/22.65  Sub-proof #370 shows that the following formulas are inconsistent:
% 153.05/22.65  ----------------------------------------------------------------
% 153.05/22.65    (1)  op(e3, e3) = e0
% 153.05/22.65    (2)   ~ (e3 = e1)
% 153.05/22.65    (3)  op(e2, e2) = e1
% 153.05/22.65    (4)   ~ (all_52_9 = all_52_13)
% 153.05/22.65    (5)  op(e1, e1) = all_4_2
% 153.05/22.65    (6)   ~ (e2 = e0)
% 153.05/22.65    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.65           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.65    (8)   ~ (all_52_14 = e1)
% 153.05/22.65    (9)  op(e1, e0) = all_52_14
% 153.05/22.65    (10)  op(e0, e0) = e1
% 153.05/22.65    (11)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.05/22.65            all_57_10 & $i(all_57_10))
% 153.05/22.65    (12)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 153.05/22.65            all_57_15 & $i(all_57_15))
% 153.05/22.65    (13)  op(e2, e0) = all_52_13
% 153.05/22.65    (14)  op(e0, e3) = all_52_3
% 153.05/22.65    (15)  op(e1, e1) = e1
% 153.05/22.65    (16)  op(e2, e1) = all_52_9
% 153.05/22.65    (17)   ~ (e1 = e0)
% 153.05/22.65    (18)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.05/22.65            all_57_12 & $i(all_57_12))
% 153.05/22.65    (19)   ~ (all_52_3 = e0)
% 153.05/22.65    (20)   ~ (e2 = e1)
% 153.05/22.65    (21)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.05/22.65              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.05/22.65            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.05/22.65            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.05/22.65            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.05/22.65            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.05/22.65            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.05/22.65            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.05/22.65            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.05/22.65            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.05/22.65            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.05/22.65            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.05/22.65            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.05/22.65            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.05/22.65            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.05/22.65            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.05/22.65            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.05/22.65            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.05/22.65            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.05/22.65            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.05/22.65            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.05/22.65            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.05/22.65            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.05/22.65            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.05/22.65            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.05/22.65            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.05/22.65            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.05/22.65            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.05/22.65            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.05/22.65            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.05/22.65            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.05/22.65            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.05/22.65            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.05/22.65            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.05/22.65            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.05/22.65            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.05/22.65            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.05/22.65            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.05/22.65            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.05/22.65            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.05/22.65            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.05/22.65            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.05/22.65            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.05/22.65            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.05/22.65            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.05/22.65            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.05/22.65            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.05/22.65            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.05/22.65              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.05/22.65            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.05/22.65            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.05/22.65              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.05/22.65            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.05/22.65            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.05/22.65                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.05/22.65                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.05/22.65                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.05/22.65                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.05/22.65                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.05/22.65                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.05/22.65                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.05/22.65              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.05/22.65                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.05/22.65                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.05/22.65                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.05/22.65                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.05/22.65                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.05/22.65                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.05/22.65                $i(all_57_7))))
% 153.05/22.65  
% 153.05/22.65  Begin of proof
% 153.05/22.65  | 
% 153.05/22.65  | BETA: splitting (18) gives:
% 153.05/22.65  | 
% 153.05/22.65  | Case 1:
% 153.05/22.65  | | 
% 153.05/22.65  | |   (22)  all_57_7 = e2 & op(e2, e1) = e2
% 153.05/22.65  | | 
% 153.05/22.65  | | ALPHA: (22) implies:
% 153.05/22.65  | |   (23)  op(e2, e1) = e2
% 153.05/22.65  | | 
% 153.05/22.65  | | BETA: splitting (12) gives:
% 153.05/22.65  | | 
% 153.05/22.65  | | Case 1:
% 153.05/22.65  | | | 
% 153.05/22.65  | | |   (24)  all_57_8 = e0 & op(e0, e1) = e0
% 153.05/22.65  | | | 
% 153.05/22.65  | | | ALPHA: (24) implies:
% 153.05/22.65  | | |   (25)  all_57_8 = e0
% 153.05/22.65  | | | 
% 153.05/22.65  | | | BETA: splitting (21) gives:
% 153.05/22.65  | | | 
% 153.05/22.65  | | | Case 1:
% 153.05/22.65  | | | | 
% 153.05/22.65  | | | |   (26)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.05/22.65  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.05/22.65  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.05/22.65  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.05/22.65  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.05/22.65  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.05/22.65  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.05/22.65  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.05/22.65  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.05/22.65  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.05/22.65  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.05/22.65  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.05/22.65  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.05/22.65  | | | |           $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.05/22.65  | | | |           (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 153.05/22.65  | | | |           & op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.05/22.65  | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 =
% 153.05/22.65  | | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.05/22.65  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.05/22.65  | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 153.05/22.65  | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 153.05/22.65  | | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.05/22.65  | | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.05/22.65  | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.05/22.65  | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.05/22.65  | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.05/22.65  | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.05/22.65  | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 153.05/22.65  | | | |           & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.05/22.65  | | | |           $i(all_57_7) & $i(all_57_10))
% 153.05/22.65  | | | | 
% 153.05/22.65  | | | | BETA: splitting (26) gives:
% 153.05/22.65  | | | | 
% 153.05/22.65  | | | | Case 1:
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | |   (27)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.05/22.65  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 153.05/22.65  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.05/22.65  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.05/22.65  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.05/22.65  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 153.05/22.65  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.05/22.65  | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.05/22.65  | | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.05/22.65  | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.05/22.65  | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.05/22.65  | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.05/22.65  | | | | |           & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.05/22.65  | | | | |           $i(all_57_14))
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | | BETA: splitting (27) gives:
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | | Case 1:
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | |   (28)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.05/22.65  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.05/22.65  | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.05/22.65  | | | | | |           $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 & all_57_15
% 153.05/22.65  | | | | | |           = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2,
% 153.05/22.65  | | | | | |             e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.05/22.65  | | | | | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | | REF_CLOSE: (2), (7), (10), (15), (28) are inconsistent by sub-proof
% 153.05/22.65  | | | | | |            #404.
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | Case 2:
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | |   (29)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.05/22.65  | | | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 153.05/22.65  | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0)
% 153.05/22.65  | | | | | |           & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.05/22.65  | | | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.05/22.65  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 153.05/22.65  | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | | BETA: splitting (29) gives:
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | | Case 1:
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | |   (30)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.05/22.65  | | | | | | |         (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 153.05/22.65  | | | | | | |         & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0)
% 153.05/22.65  | | | | | | |         & $i(all_57_14)
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | | ALPHA: (30) implies:
% 153.05/22.65  | | | | | | |   (31)  op(e2, e2) = e3
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | | REF_CLOSE: (2), (3), (7), (31) are inconsistent by sub-proof
% 153.05/22.65  | | | | | | |            #1136.
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | Case 2:
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | |   (32)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.05/22.65  | | | | | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 153.05/22.65  | | | | | | |         all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.05/22.65  | | | | | | |         $i(all_57_2) & $i(all_57_14)
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | | ALPHA: (32) implies:
% 153.05/22.65  | | | | | | |   (33)  op(e0, e0) = e3
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | | REF_CLOSE: (2), (7), (10), (33) are inconsistent by sub-proof
% 153.05/22.65  | | | | | | |            #1022.
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | End of split
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | End of split
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | Case 2:
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | |   (34)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.05/22.65  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.05/22.65  | | | | |           & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.05/22.65  | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.05/22.65  | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.05/22.65  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.05/22.65  | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1
% 153.05/22.65  | | | | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2)
% 153.05/22.65  | | | | |           & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1
% 153.05/22.65  | | | | |           & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.05/22.65  | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.05/22.65  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.05/22.65  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.05/22.65  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.05/22.65  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.05/22.65  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.05/22.65  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | | REF_CLOSE: (1), (5), (6), (7), (10), (15), (18), (20), (34) are
% 153.05/22.65  | | | | |            inconsistent by sub-proof #374.
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | End of split
% 153.05/22.65  | | | | 
% 153.05/22.65  | | | Case 2:
% 153.05/22.65  | | | | 
% 153.05/22.65  | | | |   (35)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.05/22.65  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.05/22.65  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.05/22.65  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.05/22.65  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.05/22.65  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.05/22.65  | | | |           e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.05/22.65  | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.05/22.65  | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.05/22.65  | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.05/22.65  | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.05/22.65  | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.05/22.65  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.05/22.65  | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.05/22.65  | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.05/22.65  | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.05/22.65  | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0 &
% 153.05/22.65  | | | |           all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 = e0) &
% 153.05/22.65  | | | |           op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.05/22.65  | | | |           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 153.05/22.65  | | | |         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 153.05/22.65  | | | |           (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.05/22.65  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.05/22.65  | | | |           $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.05/22.65  | | | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.05/22.65  | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.05/22.65  | | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.05/22.65  | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.05/22.65  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.05/22.65  | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.05/22.65  | | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.05/22.65  | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3)
% 153.05/22.65  | | | |               & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.05/22.65  | | | |               e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.05/22.65  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.05/22.65  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.05/22.65  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.05/22.65  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.05/22.65  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.05/22.65  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.05/22.65  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.05/22.65  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.05/22.65  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.05/22.65  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.05/22.65  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.05/22.65  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.05/22.65  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.05/22.65  | | | | 
% 153.05/22.65  | | | | BETA: splitting (35) gives:
% 153.05/22.65  | | | | 
% 153.05/22.65  | | | | Case 1:
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | |   (36)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.05/22.65  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.05/22.65  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.05/22.65  | | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.05/22.65  | | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.05/22.65  | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 153.05/22.65  | | | | |           = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.05/22.65  | | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.05/22.65  | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.05/22.65  | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.05/22.65  | | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.05/22.65  | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.05/22.65  | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.05/22.65  | | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.05/22.65  | | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.05/22.65  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.05/22.65  | | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | | BETA: splitting (36) gives:
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | | Case 1:
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | |   (37)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.05/22.65  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 153.05/22.65  | | | | | |           e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.05/22.65  | | | | | |           $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 & all_57_10
% 153.05/22.65  | | | | | |           = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3,
% 153.05/22.65  | | | | | |             e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.05/22.65  | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.05/22.65  | | | | | |           $i(all_57_12))
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | | REF_CLOSE: (7), (11), (25), (37) are inconsistent by sub-proof #373.
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | Case 2:
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | |   (38)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.05/22.65  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.05/22.65  | | | | | |           e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.05/22.65  | | | | | |           $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12
% 153.05/22.65  | | | | | |           = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3,
% 153.05/22.65  | | | | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.05/22.65  | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 153.05/22.65  | | | | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.05/22.65  | | | | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 153.05/22.65  | | | | | |           e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.05/22.65  | | | | | |           $i(all_57_10) & $i(all_57_13))
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | | BETA: splitting (38) gives:
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | | Case 1:
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | |   (39)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.05/22.65  | | | | | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.05/22.65  | | | | | | |         e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.05/22.65  | | | | | | |         $i(all_57_8) & $i(all_57_12)
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | | ALPHA: (39) implies:
% 153.05/22.65  | | | | | | |   (40)   ~ (all_57_12 = e1)
% 153.05/22.65  | | | | | | |   (41)  op(e2, e2) = all_57_12
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | | REF_CLOSE: (3), (7), (40), (41) are inconsistent by sub-proof
% 153.05/22.65  | | | | | | |            #1014.
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | Case 2:
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | |   (42)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.05/22.65  | | | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 153.05/22.65  | | | | | | |           e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.05/22.65  | | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.05/22.65  | | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 =
% 153.05/22.65  | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.05/22.65  | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10)
% 153.05/22.65  | | | | | | |           & $i(all_57_13))
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | | REF_CLOSE: (1), (7), (15), (17), (42) are inconsistent by
% 153.05/22.65  | | | | | | |            sub-proof #519.
% 153.05/22.65  | | | | | | | 
% 153.05/22.65  | | | | | | End of split
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | End of split
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | Case 2:
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | |   (43)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.05/22.65  | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.05/22.65  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.05/22.65  | | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.05/22.65  | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.05/22.65  | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.05/22.65  | | | | |           = e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 153.05/22.65  | | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 153.05/22.65  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.05/22.65  | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 153.05/22.65  | | | | |         (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.05/22.65  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.05/22.65  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.05/22.65  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.05/22.65  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.05/22.65  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 153.05/22.65  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.05/22.65  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.05/22.65  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.05/22.65  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.05/22.65  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 153.05/22.65  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.05/22.65  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.05/22.65  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.05/22.65  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.05/22.65  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.05/22.65  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.05/22.65  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.05/22.65  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.05/22.65  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.05/22.65  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.05/22.65  | | | | |               $i(all_57_7))))
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | | BETA: splitting (43) gives:
% 153.05/22.65  | | | | | 
% 153.05/22.65  | | | | | Case 1:
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | |   (44)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.05/22.65  | | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9
% 153.05/22.65  | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 153.05/22.65  | | | | | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.05/22.65  | | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.05/22.65  | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1,
% 153.05/22.65  | | | | | |             e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | | BETA: splitting (44) gives:
% 153.05/22.65  | | | | | | 
% 153.05/22.65  | | | | | | Case 1:
% 153.05/22.65  | | | | | | | 
% 153.05/22.66  | | | | | | |   (45)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.05/22.66  | | | | | | |         (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9
% 153.05/22.66  | | | | | | |         & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 153.05/22.66  | | | | | | |         & $i(all_57_12)
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | | ALPHA: (45) implies:
% 153.05/22.66  | | | | | | |   (46)  op(e2, e0) = e2
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | | REF_CLOSE: (4), (7), (13), (16), (23), (46) are inconsistent by
% 153.05/22.66  | | | | | | |            sub-proof #400.
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | Case 2:
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | |   (47)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 153.05/22.66  | | | | | | |         (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9
% 153.05/22.66  | | | | | | |         & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 153.05/22.66  | | | | | | |         & $i(all_57_14)
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | | ALPHA: (47) implies:
% 153.05/22.66  | | | | | | |   (48)  op(e1, e0) = e1
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | | REF_CLOSE: (7), (8), (9), (48) are inconsistent by sub-proof #961.
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | End of split
% 153.05/22.66  | | | | | | 
% 153.05/22.66  | | | | | Case 2:
% 153.05/22.66  | | | | | | 
% 153.05/22.66  | | | | | |   (49)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.05/22.66  | | | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.05/22.66  | | | | | |           e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.05/22.66  | | | | | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.05/22.66  | | | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0)
% 153.05/22.66  | | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.05/22.66  | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.05/22.66  | | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.05/22.66  | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.05/22.66  | | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2)
% 153.05/22.66  | | | | | |               = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 =
% 153.05/22.66  | | | | | |               e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.05/22.66  | | | | | |               (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1)
% 153.05/22.66  | | | | | |               = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 153.05/22.66  | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.05/22.66  | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.05/22.66  | | | | | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5
% 153.05/22.66  | | | | | |               = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.05/22.66  | | | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1)
% 153.05/22.66  | | | | | |               = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 153.05/22.66  | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.05/22.66  | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.05/22.66  | | | | | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 153.05/22.66  | | | | | |               = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.05/22.66  | | | | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.05/22.66  | | | | | |               all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.05/22.66  | | | | | | 
% 153.05/22.66  | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (9), (11), (14), (15), (17),
% 153.05/22.66  | | | | | |            (18), (19), (20), (49) are inconsistent by sub-proof
% 153.05/22.66  | | | | | |            #371.
% 153.05/22.66  | | | | | | 
% 153.05/22.66  | | | | | End of split
% 153.05/22.66  | | | | | 
% 153.05/22.66  | | | | End of split
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | End of split
% 153.05/22.66  | | | 
% 153.05/22.66  | | Case 2:
% 153.05/22.66  | | | 
% 153.05/22.66  | | |   (50)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)
% 153.05/22.66  | | | 
% 153.05/22.66  | | | ALPHA: (50) implies:
% 153.05/22.66  | | |   (51)   ~ (all_57_15 = e1)
% 153.05/22.66  | | |   (52)  op(e0, e0) = all_57_15
% 153.05/22.66  | | | 
% 153.05/22.66  | | | REF_CLOSE: (7), (10), (51), (52) are inconsistent by sub-proof #940.
% 153.05/22.66  | | | 
% 153.05/22.66  | | End of split
% 153.05/22.66  | | 
% 153.05/22.66  | Case 2:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (53)   ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12)
% 153.05/22.66  | | 
% 153.05/22.66  | | ALPHA: (53) implies:
% 153.05/22.66  | |   (54)   ~ (all_57_12 = e1)
% 153.05/22.66  | |   (55)  op(e2, e2) = all_57_12
% 153.05/22.66  | | 
% 153.05/22.66  | | REF_CLOSE: (3), (7), (54), (55) are inconsistent by sub-proof #1014.
% 153.05/22.66  | | 
% 153.05/22.66  | End of split
% 153.05/22.66  | 
% 153.05/22.66  End of proof
% 153.05/22.66  
% 153.05/22.66  Sub-proof #371 shows that the following formulas are inconsistent:
% 153.05/22.66  ----------------------------------------------------------------
% 153.05/22.66    (1)  op(e3, e3) = e0
% 153.05/22.66    (2)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 =
% 153.05/22.66             e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.05/22.66           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 =
% 153.05/22.66           e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.05/22.66           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 153.05/22.66           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.05/22.66           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 153.05/22.66               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.05/22.66               op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 153.05/22.66               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.05/22.66               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.05/22.66               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 153.05/22.66                 e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.05/22.66               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.05/22.66               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1,
% 153.05/22.66                 e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.05/22.66               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 153.05/22.66                 e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.05/22.66               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.05/22.66               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 153.05/22.66                 e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.05/22.66               $i(all_57_7))))
% 153.05/22.66    (3)  op(e1, e1) = all_4_2
% 153.05/22.66    (4)   ~ (e2 = e0)
% 153.05/22.66    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.66    (6)   ~ (all_52_14 = e1)
% 153.05/22.66    (7)  op(e1, e0) = all_52_14
% 153.05/22.66    (8)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.05/22.66           all_57_10 & $i(all_57_10))
% 153.05/22.66    (9)  op(e0, e3) = all_52_3
% 153.05/22.66    (10)  op(e1, e1) = e1
% 153.05/22.66    (11)   ~ (e1 = e0)
% 153.05/22.66    (12)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.05/22.66            all_57_12 & $i(all_57_12))
% 153.05/22.66    (13)   ~ (all_52_3 = e0)
% 153.05/22.66    (14)   ~ (e2 = e1)
% 153.05/22.66  
% 153.05/22.66  Begin of proof
% 153.05/22.66  | 
% 153.05/22.66  | BETA: splitting (2) gives:
% 153.05/22.66  | 
% 153.05/22.66  | Case 1:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (15)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.05/22.66  | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 153.05/22.66  | |           e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)
% 153.05/22.66  | | 
% 153.05/22.66  | | ALPHA: (15) implies:
% 153.05/22.66  | |   (16)  op(e1, e1) = e0
% 153.05/22.66  | | 
% 153.05/22.66  | | REF_CLOSE: (5), (10), (11), (16) are inconsistent by sub-proof #1038.
% 153.05/22.66  | | 
% 153.05/22.66  | Case 2:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (17)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.05/22.66  | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.05/22.66  | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.05/22.66  | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.05/22.66  | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.05/22.66  | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.05/22.66  | |               op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 153.05/22.66  | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.05/22.66  | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.05/22.66  | |             (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.05/22.66  | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.05/22.66  | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 153.05/22.66  | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.05/22.66  | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.05/22.66  | |             (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.05/22.66  | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.05/22.66  | |               op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 153.05/22.66  | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 153.05/22.66  | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.05/22.66  | | 
% 153.05/22.66  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14),
% 153.05/22.66  | |            (17) are inconsistent by sub-proof #372.
% 153.05/22.66  | | 
% 153.05/22.66  | End of split
% 153.05/22.66  | 
% 153.05/22.66  End of proof
% 153.05/22.66  
% 153.05/22.66  Sub-proof #372 shows that the following formulas are inconsistent:
% 153.05/22.66  ----------------------------------------------------------------
% 153.05/22.66    (1)  op(e3, e3) = e0
% 153.05/22.66    (2)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 =
% 153.05/22.66             e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.05/22.66           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0,
% 153.05/22.66             e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 & 
% 153.05/22.66               ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.05/22.66               op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 153.05/22.66               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.05/22.66               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.05/22.66               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 153.05/22.66                 e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.05/22.66               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.05/22.66               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1,
% 153.05/22.66                 e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.05/22.66               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 153.05/22.66                 e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.05/22.66               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.05/22.66               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 153.05/22.66                 e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.05/22.66               $i(all_57_7))))
% 153.05/22.66    (3)  op(e1, e1) = all_4_2
% 153.05/22.66    (4)   ~ (e2 = e0)
% 153.05/22.66    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.66    (6)   ~ (all_52_14 = e1)
% 153.05/22.66    (7)  op(e1, e0) = all_52_14
% 153.05/22.66    (8)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.05/22.66           all_57_10 & $i(all_57_10))
% 153.05/22.66    (9)  op(e0, e3) = all_52_3
% 153.05/22.66    (10)  op(e1, e1) = e1
% 153.05/22.66    (11)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.05/22.66            all_57_12 & $i(all_57_12))
% 153.05/22.66    (12)   ~ (all_52_3 = e0)
% 153.05/22.66    (13)   ~ (e2 = e1)
% 153.05/22.66  
% 153.05/22.66  Begin of proof
% 153.05/22.66  | 
% 153.05/22.66  | BETA: splitting (2) gives:
% 153.05/22.66  | 
% 153.05/22.66  | Case 1:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (14)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.05/22.66  | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1,
% 153.05/22.66  | |           e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 153.05/22.66  | | 
% 153.05/22.66  | | ALPHA: (14) implies:
% 153.05/22.66  | |   (15)  op(e1, e0) = e1
% 153.05/22.66  | | 
% 153.05/22.66  | | REF_CLOSE: (5), (6), (7), (15) are inconsistent by sub-proof #961.
% 153.05/22.66  | | 
% 153.05/22.66  | Case 2:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (16)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12
% 153.05/22.66  | |             = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.05/22.66  | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.05/22.66  | |           (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.05/22.66  | |             (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.05/22.66  | |             op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 153.05/22.66  | |             e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.05/22.66  | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.05/22.66  | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.05/22.66  | |             (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.05/22.66  | |             op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 =
% 153.05/22.66  | |             e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.05/22.66  | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.05/22.66  | |           (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.05/22.66  | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.05/22.66  | |             op(e0, e1) = e0 & $i(all_57_7)))
% 153.05/22.66  | | 
% 153.05/22.66  | | ALPHA: (16) implies:
% 153.05/22.66  | |   (17)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 153.05/22.66  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.05/22.66  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.05/22.66  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.05/22.66  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.05/22.66  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.05/22.66  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.05/22.66  | |           $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.05/22.66  | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.05/22.66  | |           e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 153.05/22.66  | |           = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.05/22.66  | |           & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.05/22.66  | |         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15
% 153.05/22.66  | |             = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) =
% 153.05/22.66  | |           e0 & $i(all_57_7))
% 153.05/22.66  | | 
% 153.05/22.66  | | BETA: splitting (17) gives:
% 153.05/22.66  | | 
% 153.05/22.66  | | Case 1:
% 153.05/22.66  | | | 
% 153.05/22.66  | | |   (18)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.05/22.66  | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.05/22.66  | | |           op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 153.05/22.66  | | |           e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.05/22.66  | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.05/22.66  | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.05/22.66  | | |           (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.05/22.66  | | |           op(e0, e2) = e0 & $i(all_57_3))
% 153.05/22.66  | | | 
% 153.05/22.66  | | | REF_CLOSE: (1), (4), (5), (9), (12), (18) are inconsistent by sub-proof
% 153.05/22.66  | | |            #538.
% 153.05/22.66  | | | 
% 153.05/22.66  | | Case 2:
% 153.05/22.66  | | | 
% 153.05/22.66  | | |   (19)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.05/22.66  | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.05/22.66  | | |           op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 =
% 153.05/22.66  | | |           e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.05/22.66  | | |           & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.05/22.66  | | |         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.05/22.66  | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.05/22.66  | | |           op(e0, e1) = e0 & $i(all_57_7))
% 153.05/22.66  | | | 
% 153.05/22.66  | | | REF_CLOSE: (3), (5), (8), (10), (11), (13), (19) are inconsistent by
% 153.05/22.66  | | |            sub-proof #454.
% 153.05/22.66  | | | 
% 153.05/22.66  | | End of split
% 153.05/22.66  | | 
% 153.05/22.66  | End of split
% 153.05/22.66  | 
% 153.05/22.66  End of proof
% 153.05/22.66  
% 153.05/22.66  Sub-proof #373 shows that the following formulas are inconsistent:
% 153.05/22.66  ----------------------------------------------------------------
% 153.05/22.66    (1)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.05/22.66             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.05/22.66           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.05/22.66           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.05/22.66           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.05/22.66           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 153.05/22.66    (2)  all_57_8 = e0
% 153.05/22.66    (3)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.05/22.66           all_57_10 & $i(all_57_10))
% 153.05/22.66    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.66  
% 153.05/22.66  Begin of proof
% 153.05/22.66  | 
% 153.05/22.66  | BETA: splitting (1) gives:
% 153.05/22.66  | 
% 153.05/22.66  | Case 1:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (5)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.05/22.66  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.05/22.66  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 153.05/22.66  | | 
% 153.05/22.66  | | ALPHA: (5) implies:
% 153.05/22.66  | |   (6)   ~ (all_57_8 = e0)
% 153.05/22.66  | | 
% 153.05/22.66  | | REDUCE: (2), (6) imply:
% 153.05/22.66  | |   (7)  $false
% 153.05/22.66  | | 
% 153.05/22.66  | | CLOSE: (7) is inconsistent.
% 153.05/22.66  | | 
% 153.05/22.66  | Case 2:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (8)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 153.05/22.66  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.05/22.66  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 153.05/22.66  | | 
% 153.05/22.66  | | ALPHA: (8) implies:
% 153.05/22.66  | |   (9)   ~ (all_57_6 = e3)
% 153.05/22.66  | |   (10)  op(e3, e3) = e1
% 153.05/22.66  | | 
% 153.05/22.66  | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #456.
% 153.05/22.66  | | 
% 153.05/22.66  | End of split
% 153.05/22.66  | 
% 153.05/22.66  End of proof
% 153.05/22.66  
% 153.05/22.66  Sub-proof #374 shows that the following formulas are inconsistent:
% 153.05/22.66  ----------------------------------------------------------------
% 153.05/22.66    (1)  op(e3, e3) = e0
% 153.05/22.66    (2)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.05/22.66             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.05/22.66           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 153.05/22.66           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.05/22.66           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.05/22.66           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 153.05/22.66           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3)
% 153.05/22.66           = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.05/22.66           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.05/22.66           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.05/22.66           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.05/22.66           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 153.05/22.66            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 153.05/22.66             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.05/22.66    (3)  op(e1, e1) = all_4_2
% 153.05/22.66    (4)   ~ (e2 = e0)
% 153.05/22.66    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.66    (6)  op(e0, e0) = e1
% 153.05/22.66    (7)  op(e1, e1) = e1
% 153.05/22.66    (8)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.05/22.66           all_57_12 & $i(all_57_12))
% 153.05/22.66    (9)   ~ (e2 = e1)
% 153.05/22.66  
% 153.05/22.66  Begin of proof
% 153.05/22.66  | 
% 153.05/22.66  | BETA: splitting (2) gives:
% 153.05/22.66  | 
% 153.05/22.66  | Case 1:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (10)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 153.05/22.66  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.05/22.66  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 153.05/22.66  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 153.05/22.66  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.05/22.66  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.05/22.66  | | 
% 153.05/22.66  | | REF_CLOSE: (3), (5), (6), (7), (9), (10) are inconsistent by sub-proof #402.
% 153.05/22.66  | | 
% 153.05/22.66  | Case 2:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (11)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 153.05/22.66  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 153.05/22.66  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.05/22.66  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.05/22.66  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.05/22.66  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.05/22.66  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.05/22.66  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.05/22.66  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.05/22.66  | | 
% 153.05/22.66  | | BETA: splitting (11) gives:
% 153.05/22.66  | | 
% 153.05/22.66  | | Case 1:
% 153.05/22.66  | | | 
% 153.05/22.66  | | |   (12)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.05/22.66  | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.05/22.66  | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.05/22.66  | | |         $i(all_57_14)
% 153.05/22.66  | | | 
% 153.05/22.66  | | | ALPHA: (12) implies:
% 153.05/22.66  | | |   (13)  op(e3, e3) = e2
% 153.05/22.66  | | | 
% 153.05/22.66  | | | REF_CLOSE: (1), (4), (5), (13) are inconsistent by sub-proof #1073.
% 153.05/22.66  | | | 
% 153.05/22.66  | | Case 2:
% 153.05/22.66  | | | 
% 153.05/22.66  | | |   (14)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.05/22.66  | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.05/22.66  | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.05/22.66  | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7
% 153.05/22.66  | | |             = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 153.05/22.66  | | |             e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.05/22.66  | | |           $i(all_57_7) & $i(all_57_10))
% 153.05/22.66  | | | 
% 153.05/22.66  | | | REF_CLOSE: (5), (6), (8), (9), (14) are inconsistent by sub-proof #401.
% 153.05/22.66  | | | 
% 153.05/22.66  | | End of split
% 153.05/22.66  | | 
% 153.05/22.66  | End of split
% 153.05/22.66  | 
% 153.05/22.66  End of proof
% 153.05/22.66  
% 153.05/22.66  Sub-proof #375 shows that the following formulas are inconsistent:
% 153.05/22.66  ----------------------------------------------------------------
% 153.05/22.66    (1)  all_54_14 = e1 | all_54_14 = e0
% 153.05/22.66    (2)  all_54_14 = all_52_11
% 153.05/22.66    (3)   ~ (all_52_11 = e1)
% 153.05/22.66    (4)   ~ (all_52_11 = e0)
% 153.05/22.66  
% 153.05/22.66  Begin of proof
% 153.05/22.66  | 
% 153.05/22.66  | BETA: splitting (1) gives:
% 153.05/22.66  | 
% 153.05/22.66  | Case 1:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (5)  all_54_14 = e1
% 153.05/22.66  | | 
% 153.05/22.66  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #753.
% 153.05/22.66  | | 
% 153.05/22.66  | Case 2:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (6)  all_54_14 = e0
% 153.05/22.66  | | 
% 153.05/22.66  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #886.
% 153.05/22.66  | | 
% 153.05/22.66  | End of split
% 153.05/22.66  | 
% 153.05/22.66  End of proof
% 153.05/22.66  
% 153.05/22.66  Sub-proof #376 shows that the following formulas are inconsistent:
% 153.05/22.66  ----------------------------------------------------------------
% 153.05/22.66    (1)  all_54_6 = all_52_9
% 153.05/22.66    (2)   ~ (all_52_1 = e0)
% 153.05/22.66    (3)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 153.05/22.66    (4)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 153.05/22.66    (5)   ~ (all_52_9 = all_52_13)
% 153.05/22.66    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.66    (7)   ~ (all_52_1 = all_52_13)
% 153.05/22.66    (8)   ~ (all_52_9 = e3)
% 153.05/22.66    (9)   ~ (all_52_1 = all_52_9)
% 153.05/22.66    (10)   ~ (all_52_1 = e3)
% 153.05/22.66    (11)   ~ (all_52_13 = e2)
% 153.05/22.66    (12)  op(e0, e1) = all_30_1
% 153.05/22.66    (13)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.05/22.66    (14)  op(e2, e0) = all_52_13
% 153.05/22.66    (15)   ~ (all_52_9 = e2)
% 153.05/22.66    (16)  op(e0, e1) = e2
% 153.05/22.66    (17)   ~ (all_52_2 = e3)
% 153.05/22.66    (18)   ~ (all_52_2 = e0)
% 153.05/22.66    (19)  all_54_8 = all_52_2
% 153.05/22.66    (20)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 153.05/22.66    (21)  all_54_4 = all_52_1
% 153.05/22.66    (22)   ~ (all_52_1 = all_52_2)
% 153.05/22.66    (23)  all_54_7 = all_52_13
% 153.05/22.66    (24)  ( ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 & op(e0, e1) =
% 153.05/22.66            all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e2) & op(e0,
% 153.05/22.66              e1) = all_10_1 & $i(all_10_1))
% 153.05/22.66    (25)  op(e2, e3) = all_52_1
% 153.05/22.66    (26)   ~ (all_52_1 = e2)
% 153.05/22.66  
% 153.05/22.66  Begin of proof
% 153.05/22.66  | 
% 153.05/22.66  | BETA: splitting (3) gives:
% 153.05/22.66  | 
% 153.05/22.66  | Case 1:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (27)  all_54_4 = e3
% 153.05/22.66  | | 
% 153.05/22.66  | | COMBINE_EQS: (21), (27) imply:
% 153.05/22.66  | |   (28)  all_52_1 = e3
% 153.05/22.66  | | 
% 153.05/22.66  | | REDUCE: (10), (28) imply:
% 153.05/22.66  | |   (29)  $false
% 153.05/22.66  | | 
% 153.05/22.66  | | CLOSE: (29) is inconsistent.
% 153.05/22.66  | | 
% 153.05/22.66  | Case 2:
% 153.05/22.66  | | 
% 153.05/22.66  | |   (30)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 153.05/22.66  | | 
% 153.05/22.66  | | BETA: splitting (30) gives:
% 153.05/22.66  | | 
% 153.05/22.66  | | Case 1:
% 153.05/22.66  | | | 
% 153.05/22.66  | | |   (31)  all_54_4 = e2
% 153.05/22.66  | | | 
% 153.05/22.66  | | | COMBINE_EQS: (21), (31) imply:
% 153.05/22.66  | | |   (32)  all_52_1 = e2
% 153.05/22.66  | | | 
% 153.05/22.66  | | | REDUCE: (26), (32) imply:
% 153.05/22.66  | | |   (33)  $false
% 153.05/22.66  | | | 
% 153.05/22.66  | | | CLOSE: (33) is inconsistent.
% 153.05/22.66  | | | 
% 153.05/22.66  | | Case 2:
% 153.05/22.66  | | | 
% 153.05/22.66  | | |   (34)  all_54_4 = e1 | all_54_4 = e0
% 153.05/22.66  | | | 
% 153.05/22.66  | | | BETA: splitting (34) gives:
% 153.05/22.66  | | | 
% 153.05/22.66  | | | Case 1:
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | |   (35)  all_54_4 = e1
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | | COMBINE_EQS: (21), (35) imply:
% 153.05/22.66  | | | |   (36)  all_52_1 = e1
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | | REDUCE: (22), (36) imply:
% 153.05/22.66  | | | |   (37)   ~ (all_52_2 = e1)
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | | SIMP: (37) implies:
% 153.05/22.66  | | | |   (38)   ~ (all_52_2 = e1)
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | | REDUCE: (9), (36) imply:
% 153.05/22.66  | | | |   (39)   ~ (all_52_9 = e1)
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | | SIMP: (39) implies:
% 153.05/22.66  | | | |   (40)   ~ (all_52_9 = e1)
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | | REDUCE: (25), (36) imply:
% 153.05/22.66  | | | |   (41)  op(e2, e3) = e1
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | | BETA: splitting (20) gives:
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | | Case 1:
% 153.05/22.66  | | | | | 
% 153.05/22.66  | | | | |   (42)  all_54_6 = e3
% 153.05/22.66  | | | | | 
% 153.05/22.66  | | | | | REF_CLOSE: (1), (8), (42) are inconsistent by sub-proof #650.
% 153.05/22.66  | | | | | 
% 153.05/22.66  | | | | Case 2:
% 153.05/22.66  | | | | | 
% 153.05/22.66  | | | | |   (43)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 153.05/22.66  | | | | | 
% 153.05/22.66  | | | | | BETA: splitting (43) gives:
% 153.05/22.66  | | | | | 
% 153.05/22.66  | | | | | Case 1:
% 153.05/22.66  | | | | | | 
% 153.05/22.66  | | | | | |   (44)  all_54_6 = e2
% 153.05/22.66  | | | | | | 
% 153.05/22.66  | | | | | | REF_CLOSE: (1), (15), (44) are inconsistent by sub-proof #379.
% 153.05/22.66  | | | | | | 
% 153.05/22.66  | | | | | Case 2:
% 153.05/22.66  | | | | | | 
% 153.05/22.66  | | | | | |   (45)  all_54_6 = e1 | all_54_6 = e0
% 153.05/22.66  | | | | | | 
% 153.05/22.66  | | | | | | BETA: splitting (45) gives:
% 153.05/22.66  | | | | | | 
% 153.05/22.66  | | | | | | Case 1:
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | |   (46)  all_54_6 = e1
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | | REF_CLOSE: (1), (40), (46) are inconsistent by sub-proof #378.
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | Case 2:
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | |   (47)  all_54_6 = e0
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | | COMBINE_EQS: (1), (47) imply:
% 153.05/22.66  | | | | | | |   (48)  all_52_9 = e0
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | | SIMP: (48) implies:
% 153.05/22.66  | | | | | | |   (49)  all_52_9 = e0
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | | REDUCE: (5), (49) imply:
% 153.05/22.66  | | | | | | |   (50)   ~ (all_52_13 = e0)
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | | SIMP: (50) implies:
% 153.05/22.66  | | | | | | |   (51)   ~ (all_52_13 = e0)
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | | BETA: splitting (4) gives:
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | | Case 1:
% 153.05/22.66  | | | | | | | | 
% 153.05/22.66  | | | | | | | |   (52)  all_54_7 = e3
% 153.05/22.66  | | | | | | | | 
% 153.05/22.66  | | | | | | | | COMBINE_EQS: (23), (52) imply:
% 153.05/22.66  | | | | | | | |   (53)  all_52_13 = e3
% 153.05/22.66  | | | | | | | | 
% 153.05/22.66  | | | | | | | | SIMP: (53) implies:
% 153.05/22.66  | | | | | | | |   (54)  all_52_13 = e3
% 153.05/22.66  | | | | | | | | 
% 153.05/22.66  | | | | | | | | REDUCE: (14), (54) imply:
% 153.05/22.66  | | | | | | | |   (55)  op(e2, e0) = e3
% 153.05/22.66  | | | | | | | | 
% 153.05/22.66  | | | | | | | | BETA: splitting (13) gives:
% 153.05/22.66  | | | | | | | | 
% 153.05/22.66  | | | | | | | | Case 1:
% 153.05/22.66  | | | | | | | | | 
% 153.05/22.66  | | | | | | | | |   (56)  all_54_8 = e3
% 153.05/22.66  | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | REF_CLOSE: (17), (19), (56) are inconsistent by sub-proof
% 153.05/22.66  | | | | | | | | |            #394.
% 153.05/22.66  | | | | | | | | | 
% 153.05/22.66  | | | | | | | | Case 2:
% 153.05/22.66  | | | | | | | | | 
% 153.05/22.66  | | | | | | | | |   (57)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.05/22.66  | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | BETA: splitting (24) gives:
% 153.05/22.66  | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | Case 1:
% 153.05/22.66  | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | |   (58)   ~ (all_10_0 = e3) & op(all_10_1, e0) = all_10_0 &
% 153.05/22.66  | | | | | | | | | |         op(e0, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)
% 153.05/22.66  | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | ALPHA: (58) implies:
% 153.05/22.66  | | | | | | | | | |   (59)   ~ (all_10_0 = e3)
% 153.05/22.66  | | | | | | | | | |   (60)  op(e0, e1) = all_10_1
% 153.05/22.66  | | | | | | | | | |   (61)  op(all_10_1, e0) = all_10_0
% 153.05/22.66  | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | BETA: splitting (57) gives:
% 153.05/22.66  | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | Case 1:
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | GROUND_INST: instantiating (6) with all_10_1, all_30_1, e1, e0,
% 153.05/22.66  | | | | | | | | | | |              simplifying with (12), (60) gives:
% 153.05/22.66  | | | | | | | | | | |   (62)  all_30_1 = all_10_1
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | GROUND_INST: instantiating (6) with e2, all_30_1, e1, e0,
% 153.05/22.66  | | | | | | | | | | |              simplifying with (12), (16) gives:
% 153.05/22.66  | | | | | | | | | | |   (63)  all_30_1 = e2
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | GROUND_INST: instantiating (6) with e3, all_10_0, e0, e2,
% 153.05/22.66  | | | | | | | | | | |              simplifying with (55) gives:
% 153.05/22.66  | | | | | | | | | | |   (64)  all_10_0 = e3 |  ~ (op(e2, e0) = all_10_0)
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | COMBINE_EQS: (62), (63) imply:
% 153.05/22.66  | | | | | | | | | | |   (65)  all_10_1 = e2
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | REDUCE: (61), (65) imply:
% 153.05/22.66  | | | | | | | | | | |   (66)  op(e2, e0) = all_10_0
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | BETA: splitting (64) gives:
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | Case 1:
% 153.05/22.66  | | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | |   (67)   ~ (op(e2, e0) = all_10_0)
% 153.05/22.66  | | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | | PRED_UNIFY: (66), (67) imply:
% 153.05/22.66  | | | | | | | | | | | |   (68)  $false
% 153.05/22.66  | | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | | CLOSE: (68) is inconsistent.
% 153.05/22.66  | | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | Case 2:
% 153.05/22.66  | | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | |   (69)  all_10_0 = e3
% 153.05/22.66  | | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | | REDUCE: (59), (69) imply:
% 153.05/22.66  | | | | | | | | | | | |   (70)  $false
% 153.05/22.66  | | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | | CLOSE: (70) is inconsistent.
% 153.05/22.66  | | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | End of split
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | Case 2:
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | |   (71)  all_54_8 = e1 | all_54_8 = e0
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | | REF_CLOSE: (18), (19), (38), (71) are inconsistent by
% 153.05/22.66  | | | | | | | | | | |            sub-proof #461.
% 153.05/22.66  | | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | End of split
% 153.05/22.66  | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | Case 2:
% 153.05/22.66  | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | |   (72)   ~ (all_10_1 = e2) & op(e0, e1) = all_10_1 &
% 153.05/22.66  | | | | | | | | | |         $i(all_10_1)
% 153.05/22.66  | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | ALPHA: (72) implies:
% 153.05/22.66  | | | | | | | | | |   (73)   ~ (all_10_1 = e2)
% 153.05/22.66  | | | | | | | | | |   (74)  op(e0, e1) = all_10_1
% 153.05/22.66  | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | | REF_CLOSE: (6), (12), (16), (73), (74) are inconsistent by
% 153.05/22.66  | | | | | | | | | |            sub-proof #377.
% 153.05/22.66  | | | | | | | | | | 
% 153.05/22.66  | | | | | | | | | End of split
% 153.05/22.66  | | | | | | | | | 
% 153.05/22.66  | | | | | | | | End of split
% 153.05/22.66  | | | | | | | | 
% 153.05/22.66  | | | | | | | Case 2:
% 153.05/22.66  | | | | | | | | 
% 153.05/22.66  | | | | | | | |   (75)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 153.05/22.66  | | | | | | | | 
% 153.05/22.66  | | | | | | | | REF_CLOSE: (6), (7), (11), (23), (25), (41), (51), (75) are
% 153.05/22.66  | | | | | | | |            inconsistent by sub-proof #1160.
% 153.05/22.66  | | | | | | | | 
% 153.05/22.66  | | | | | | | End of split
% 153.05/22.66  | | | | | | | 
% 153.05/22.66  | | | | | | End of split
% 153.05/22.66  | | | | | | 
% 153.05/22.66  | | | | | End of split
% 153.05/22.66  | | | | | 
% 153.05/22.66  | | | | End of split
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | Case 2:
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | |   (76)  all_54_4 = e0
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | | COMBINE_EQS: (21), (76) imply:
% 153.05/22.66  | | | |   (77)  all_52_1 = e0
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | | REDUCE: (2), (77) imply:
% 153.05/22.66  | | | |   (78)  $false
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | | CLOSE: (78) is inconsistent.
% 153.05/22.66  | | | | 
% 153.05/22.66  | | | End of split
% 153.05/22.66  | | | 
% 153.05/22.66  | | End of split
% 153.05/22.66  | | 
% 153.05/22.66  | End of split
% 153.05/22.66  | 
% 153.05/22.66  End of proof
% 153.05/22.66  
% 153.05/22.66  Sub-proof #377 shows that the following formulas are inconsistent:
% 153.05/22.66  ----------------------------------------------------------------
% 153.05/22.66    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.66           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.66    (2)  op(e0, e1) = all_10_1
% 153.05/22.66    (3)  op(e0, e1) = all_30_1
% 153.05/22.67    (4)  op(e0, e1) = e2
% 153.05/22.67    (5)   ~ (all_10_1 = e2)
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | GROUND_INST: instantiating (1) with all_10_1, all_30_1, e1, e0, simplifying
% 153.05/22.67  |              with (2), (3) gives:
% 153.05/22.67  |   (6)  all_30_1 = all_10_1
% 153.05/22.67  | 
% 153.05/22.67  | GROUND_INST: instantiating (1) with e2, all_30_1, e1, e0, simplifying with
% 153.05/22.67  |              (3), (4) gives:
% 153.05/22.67  |   (7)  all_30_1 = e2
% 153.05/22.67  | 
% 153.05/22.67  | COMBINE_EQS: (6), (7) imply:
% 153.05/22.67  |   (8)  all_10_1 = e2
% 153.05/22.67  | 
% 153.05/22.67  | REDUCE: (5), (8) imply:
% 153.05/22.67  |   (9)  $false
% 153.05/22.67  | 
% 153.05/22.67  | CLOSE: (9) is inconsistent.
% 153.05/22.67  | 
% 153.05/22.67  End of proof
% 153.05/22.67  
% 153.05/22.67  Sub-proof #378 shows that the following formulas are inconsistent:
% 153.05/22.67  ----------------------------------------------------------------
% 153.05/22.67    (1)  all_54_6 = all_52_9
% 153.05/22.67    (2)  all_54_6 = e1
% 153.05/22.67    (3)   ~ (all_52_9 = e1)
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | COMBINE_EQS: (1), (2) imply:
% 153.05/22.67  |   (4)  all_52_9 = e1
% 153.05/22.67  | 
% 153.05/22.67  | SIMP: (4) implies:
% 153.05/22.67  |   (5)  all_52_9 = e1
% 153.05/22.67  | 
% 153.05/22.67  | REDUCE: (3), (5) imply:
% 153.05/22.67  |   (6)  $false
% 153.05/22.67  | 
% 153.05/22.67  | CLOSE: (6) is inconsistent.
% 153.05/22.67  | 
% 153.05/22.67  End of proof
% 153.05/22.67  
% 153.05/22.67  Sub-proof #379 shows that the following formulas are inconsistent:
% 153.05/22.67  ----------------------------------------------------------------
% 153.05/22.67    (1)  all_54_6 = all_52_9
% 153.05/22.67    (2)  all_54_6 = e2
% 153.05/22.67    (3)   ~ (all_52_9 = e2)
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | COMBINE_EQS: (1), (2) imply:
% 153.05/22.67  |   (4)  all_52_9 = e2
% 153.05/22.67  | 
% 153.05/22.67  | SIMP: (4) implies:
% 153.05/22.67  |   (5)  all_52_9 = e2
% 153.05/22.67  | 
% 153.05/22.67  | REDUCE: (3), (5) imply:
% 153.05/22.67  |   (6)  $false
% 153.05/22.67  | 
% 153.05/22.67  | CLOSE: (6) is inconsistent.
% 153.05/22.67  | 
% 153.05/22.67  End of proof
% 153.05/22.67  
% 153.05/22.67  Sub-proof #380 shows that the following formulas are inconsistent:
% 153.05/22.67  ----------------------------------------------------------------
% 153.05/22.67    (1)  op(e3, e3) = e0
% 153.05/22.67    (2)   ~ (e2 = e0)
% 153.05/22.67    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.67    (4)  op(e0, e0) = e1
% 153.05/22.67    (5)  op(e2, e2) = e2
% 153.05/22.67    (6)   ~ (e2 = e1)
% 153.05/22.67    (7)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.05/22.67             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.05/22.67           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 153.05/22.67           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 153.05/22.67             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.05/22.67             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.05/22.67           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.05/22.67           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.05/22.67           $i(all_57_7) & $i(all_57_10))
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | BETA: splitting (7) gives:
% 153.05/22.67  | 
% 153.05/22.67  | Case 1:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (8)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.05/22.67  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.05/22.67  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 153.05/22.67  | | 
% 153.05/22.67  | | ALPHA: (8) implies:
% 153.05/22.67  | |   (9)  op(e3, e3) = e2
% 153.05/22.67  | | 
% 153.05/22.67  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #1073.
% 153.05/22.67  | | 
% 153.05/22.67  | Case 2:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (10)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.05/22.67  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.05/22.67  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.05/22.67  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.05/22.67  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.05/22.67  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.05/22.67  | | 
% 153.05/22.67  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #441.
% 153.05/22.67  | | 
% 153.05/22.67  | End of split
% 153.05/22.67  | 
% 153.05/22.67  End of proof
% 153.05/22.67  
% 153.05/22.67  Sub-proof #381 shows that the following formulas are inconsistent:
% 153.05/22.67  ----------------------------------------------------------------
% 153.05/22.67    (1)  op(e0, e1) = all_52_11
% 153.05/22.67    (2)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.05/22.67         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.05/22.67    (3)   ~ (e3 = e1)
% 153.05/22.67    (4)   ~ (all_52_2 = all_52_14)
% 153.05/22.67    (5)   ~ (all_52_11 = all_10_2)
% 153.05/22.67    (6)  op(e0, e0) = all_10_2
% 153.05/22.67    (7)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.05/22.67    (8)   ~ (all_52_9 = all_52_13)
% 153.05/22.67    (9)  op(e1, e1) = all_4_2
% 153.05/22.67    (10)   ~ (e2 = e0)
% 153.05/22.67    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.67            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.67    (12)  all_54_10 = all_4_2
% 153.05/22.67    (13)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.05/22.67              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.05/22.67                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.05/22.67                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.05/22.67    (14)  op(e1, e0) = all_52_14
% 153.05/22.67    (15)  op(e0, e0) = e1
% 153.05/22.67    (16)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.05/22.67            all_57_10 & $i(all_57_10))
% 153.05/22.67    (17)   ~ (e3 = e0)
% 153.05/22.67    (18)  op(e3, e3) = e1
% 153.05/22.67    (19)  op(e2, e0) = all_52_13
% 153.05/22.67    (20)   ~ (all_52_14 = all_4_2)
% 153.05/22.67    (21)   ~ (all_4_2 = e2)
% 153.05/22.67    (22)  op(e1, e1) = e1
% 153.05/22.67    (23)  op(e2, e1) = all_52_9
% 153.05/22.67    (24)   ~ (e1 = e0)
% 153.05/22.67    (25)   ~ (all_52_1 = e1)
% 153.05/22.67    (26)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.05/22.67              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.05/22.67            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.05/22.67                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.05/22.67              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.05/22.67          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.05/22.67              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.05/22.67            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.05/22.67                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.05/22.67              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.05/22.67          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.05/22.67              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.05/22.67            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.05/22.67                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.05/22.67              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.05/22.67          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.05/22.67              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.05/22.67            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.05/22.67                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.05/22.67                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.05/22.67                $i(all_57_14))))
% 153.05/22.67    (27)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.05/22.67            all_57_12 & $i(all_57_12))
% 153.05/22.67    (28)   ~ (all_4_2 = e3)
% 153.05/22.67    (29)   ~ (e3 = e2)
% 153.05/22.67    (30)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.05/22.67          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.05/22.67    (31)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.05/22.67          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.05/22.67    (32)   ~ (all_52_2 = e1)
% 153.05/22.67    (33)   ~ (all_52_9 = all_4_2)
% 153.05/22.67    (34)   ~ (e2 = e1)
% 153.05/22.67    (35)  op(e1, e3) = all_52_2
% 153.05/22.67    (36)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.05/22.67              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.05/22.67            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.05/22.67            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.05/22.67            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.05/22.67            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.05/22.67            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.05/22.67            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.05/22.67            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.05/22.67            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.05/22.67            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.05/22.67            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.05/22.67            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.05/22.67            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.05/22.67            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.05/22.67            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.05/22.67            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.05/22.67            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.05/22.67            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.05/22.67            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.05/22.67            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.05/22.67            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.05/22.67            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.05/22.67            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.05/22.67            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.05/22.67            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.05/22.67            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.05/22.67            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.05/22.67            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.05/22.67            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.05/22.67            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.05/22.67            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.05/22.67            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.05/22.67            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.05/22.67            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.05/22.67            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.05/22.67            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.05/22.67            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.05/22.67            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.05/22.67            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.05/22.67            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.05/22.67            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.05/22.67            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.05/22.67            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.05/22.67            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.05/22.67            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.05/22.67            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.05/22.67            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.05/22.67              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.05/22.67            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.05/22.67            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.05/22.67              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.05/22.67            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.05/22.67            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.05/22.67                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.05/22.67                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.05/22.67                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.05/22.67                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.05/22.67                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.05/22.67                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.05/22.67                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.05/22.67              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.05/22.67                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.05/22.67                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.05/22.67                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.05/22.67                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.05/22.67                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.05/22.67                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.05/22.67                $i(all_57_7))))
% 153.05/22.67    (37)  op(e2, e3) = all_52_1
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | BETA: splitting (30) gives:
% 153.05/22.67  | 
% 153.05/22.67  | Case 1:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (38)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 153.05/22.67  | |           e1)
% 153.05/22.67  | | 
% 153.05/22.67  | | BETA: splitting (38) gives:
% 153.05/22.67  | | 
% 153.05/22.67  | | Case 1:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (39)  all_56_2 = e1 & op(e2, e3) = e1
% 153.05/22.67  | | | 
% 153.05/22.67  | | | ALPHA: (39) implies:
% 153.05/22.67  | | |   (40)  op(e2, e3) = e1
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (11), (25), (37), (40) are inconsistent by sub-proof #1177.
% 153.05/22.67  | | | 
% 153.05/22.67  | | Case 2:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (41)  all_56_3 = e1 & op(e2, e2) = e1
% 153.05/22.67  | | | 
% 153.05/22.67  | | | ALPHA: (41) implies:
% 153.05/22.67  | | |   (42)  op(e2, e2) = e1
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15),
% 153.05/22.67  | | |            (16), (18), (19), (20), (21), (22), (23), (24), (26), (27),
% 153.05/22.67  | | |            (28), (32), (34), (35), (36), (42) are inconsistent by
% 153.05/22.67  | | |            sub-proof #398.
% 153.05/22.67  | | | 
% 153.05/22.67  | | End of split
% 153.05/22.67  | | 
% 153.05/22.67  | Case 2:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (43)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 153.05/22.67  | |           e1)
% 153.05/22.67  | | 
% 153.05/22.67  | | BETA: splitting (43) gives:
% 153.05/22.67  | | 
% 153.05/22.67  | | Case 1:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (44)  all_56_5 = e1 & op(e2, e1) = e1
% 153.05/22.67  | | | 
% 153.05/22.67  | | | ALPHA: (44) implies:
% 153.05/22.67  | | |   (45)  op(e2, e1) = e1
% 153.05/22.67  | | | 
% 153.05/22.67  | | | GROUND_INST: instantiating (11) with all_4_2, e1, e1, e1, simplifying with
% 153.05/22.67  | | |              (9), (22) gives:
% 153.05/22.67  | | |   (46)  all_4_2 = e1
% 153.05/22.67  | | | 
% 153.05/22.67  | | | GROUND_INST: instantiating (11) with all_52_9, e1, e1, e2, simplifying
% 153.05/22.67  | | |              with (23), (45) gives:
% 153.05/22.67  | | |   (47)  all_52_9 = e1
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REDUCE: (33), (46), (47) imply:
% 153.05/22.67  | | |   (48)  $false
% 153.05/22.67  | | | 
% 153.05/22.67  | | | CLOSE: (48) is inconsistent.
% 153.05/22.67  | | | 
% 153.05/22.67  | | Case 2:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (49)  all_56_10 = e1 & op(e2, e0) = e1
% 153.05/22.67  | | | 
% 153.05/22.67  | | | ALPHA: (49) implies:
% 153.05/22.67  | | |   (50)  all_56_10 = e1
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (2), (3), (10), (11), (13), (15), (17), (24), (29), (31), (34),
% 153.05/22.67  | | |            (50) are inconsistent by sub-proof #445.
% 153.05/22.67  | | | 
% 153.05/22.67  | | End of split
% 153.05/22.67  | | 
% 153.05/22.67  | End of split
% 153.05/22.67  | 
% 153.05/22.67  End of proof
% 153.05/22.67  
% 153.05/22.67  Sub-proof #382 shows that the following formulas are inconsistent:
% 153.05/22.67  ----------------------------------------------------------------
% 153.05/22.67    (1)  all_54_2 = all_52_8
% 153.05/22.67    (2)   ~ (all_52_8 = e1)
% 153.05/22.67    (3)  all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 153.05/22.67    (4)   ~ (all_52_8 = e0)
% 153.05/22.67    (5)   ~ (all_52_8 = e2)
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | BETA: splitting (3) gives:
% 153.05/22.67  | 
% 153.05/22.67  | Case 1:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (6)  all_54_2 = e2
% 153.05/22.67  | | 
% 153.05/22.67  | | COMBINE_EQS: (1), (6) imply:
% 153.05/22.67  | |   (7)  all_52_8 = e2
% 153.05/22.67  | | 
% 153.05/22.67  | | REDUCE: (5), (7) imply:
% 153.05/22.67  | |   (8)  $false
% 153.05/22.67  | | 
% 153.05/22.67  | | CLOSE: (8) is inconsistent.
% 153.05/22.67  | | 
% 153.05/22.67  | Case 2:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (9)  all_54_2 = e1 | all_54_2 = e0
% 153.05/22.67  | | 
% 153.05/22.67  | | BETA: splitting (9) gives:
% 153.05/22.67  | | 
% 153.05/22.67  | | Case 1:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (10)  all_54_2 = e1
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #384.
% 153.05/22.67  | | | 
% 153.05/22.67  | | Case 2:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (11)  all_54_2 = e0
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (1), (4), (11) are inconsistent by sub-proof #383.
% 153.05/22.67  | | | 
% 153.05/22.67  | | End of split
% 153.05/22.67  | | 
% 153.05/22.67  | End of split
% 153.05/22.67  | 
% 153.05/22.67  End of proof
% 153.05/22.67  
% 153.05/22.67  Sub-proof #383 shows that the following formulas are inconsistent:
% 153.05/22.67  ----------------------------------------------------------------
% 153.05/22.67    (1)  all_54_2 = all_52_8
% 153.05/22.67    (2)  all_54_2 = e0
% 153.05/22.67    (3)   ~ (all_52_8 = e0)
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | COMBINE_EQS: (1), (2) imply:
% 153.05/22.67  |   (4)  all_52_8 = e0
% 153.05/22.67  | 
% 153.05/22.67  | SIMP: (4) implies:
% 153.05/22.67  |   (5)  all_52_8 = e0
% 153.05/22.67  | 
% 153.05/22.67  | REDUCE: (3), (5) imply:
% 153.05/22.67  |   (6)  $false
% 153.05/22.67  | 
% 153.05/22.67  | CLOSE: (6) is inconsistent.
% 153.05/22.67  | 
% 153.05/22.67  End of proof
% 153.05/22.67  
% 153.05/22.67  Sub-proof #384 shows that the following formulas are inconsistent:
% 153.05/22.67  ----------------------------------------------------------------
% 153.05/22.67    (1)  all_54_2 = all_52_8
% 153.05/22.67    (2)  all_54_2 = e1
% 153.05/22.67    (3)   ~ (all_52_8 = e1)
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | COMBINE_EQS: (1), (2) imply:
% 153.05/22.67  |   (4)  all_52_8 = e1
% 153.05/22.67  | 
% 153.05/22.67  | SIMP: (4) implies:
% 153.05/22.67  |   (5)  all_52_8 = e1
% 153.05/22.67  | 
% 153.05/22.67  | REDUCE: (3), (5) imply:
% 153.05/22.67  |   (6)  $false
% 153.05/22.67  | 
% 153.05/22.67  | CLOSE: (6) is inconsistent.
% 153.05/22.67  | 
% 153.05/22.67  End of proof
% 153.05/22.67  
% 153.05/22.67  Sub-proof #385 shows that the following formulas are inconsistent:
% 153.05/22.67  ----------------------------------------------------------------
% 153.05/22.67    (1)  op(e3, e2) = all_52_4
% 153.05/22.67    (2)  op(e0, e2) = all_52_7
% 153.05/22.67    (3)   ~ (e2 = e0)
% 153.05/22.67    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.67    (5)  op(e3, e3) = e2
% 153.05/22.67    (6)   ~ (e3 = e0)
% 153.05/22.67    (7)   ~ (all_52_6 = e0)
% 153.05/22.67    (8)  op(e1, e2) = all_52_6
% 153.05/22.67    (9)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.05/22.67             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.05/22.67           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.05/22.67               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.05/22.67             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.05/22.67         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.05/22.67             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.05/22.67           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.05/22.67               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.05/22.67             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 153.05/22.67    (10)   ~ (all_52_7 = e0)
% 153.05/22.67    (11)   ~ (e3 = e2)
% 153.05/22.67    (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.67          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | BETA: splitting (9) gives:
% 153.05/22.67  | 
% 153.05/22.67  | Case 1:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (13)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.05/22.67  | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.05/22.67  | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.05/22.67  | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.05/22.67  | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.05/22.67  | |               e0) = all_57_15 & $i(all_57_15)))
% 153.05/22.67  | | 
% 153.05/22.67  | | ALPHA: (13) implies:
% 153.05/22.67  | |   (14)  op(e3, e3) = e3
% 153.05/22.67  | | 
% 153.05/22.67  | | REF_CLOSE: (4), (5), (11), (14) are inconsistent by sub-proof #1085.
% 153.05/22.67  | | 
% 153.05/22.67  | Case 2:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (15)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 153.05/22.67  | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.05/22.67  | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 153.05/22.67  | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.05/22.67  | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 153.05/22.67  | |               e0) = all_57_15 & $i(all_57_15)))
% 153.05/22.67  | | 
% 153.05/22.67  | | ALPHA: (15) implies:
% 153.05/22.67  | |   (16)  op(e2, e2) = e2
% 153.05/22.67  | |   (17)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3,
% 153.05/22.67  | |             e3) = all_57_10 & $i(all_57_10))
% 153.05/22.67  | | 
% 153.05/22.67  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (12), (16), (17)
% 153.05/22.67  | |            are inconsistent by sub-proof #1027.
% 153.05/22.67  | | 
% 153.05/22.67  | End of split
% 153.05/22.67  | 
% 153.05/22.67  End of proof
% 153.05/22.67  
% 153.05/22.67  Sub-proof #386 shows that the following formulas are inconsistent:
% 153.05/22.67  ----------------------------------------------------------------
% 153.05/22.67    (1)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.05/22.67         (all_56_14 = e0 & op(e0, e1) = e0)
% 153.05/22.67    (2)   ~ (e2 = e0)
% 153.05/22.67    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.67    (4)  all_56_13 = e1
% 153.05/22.67    (5)  op(e0, e0) = e1
% 153.05/22.67    (6)   ~ (e3 = e0)
% 153.05/22.67    (7)  all_56_14 = e3
% 153.05/22.67    (8)   ~ (e1 = e0)
% 153.05/22.67    (9)   ~ (e3 = e2)
% 153.05/22.67    (10)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.05/22.67          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 153.05/22.67            e2)
% 153.05/22.67    (11)   ~ (e2 = e1)
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | BETA: splitting (10) gives:
% 153.05/22.67  | 
% 153.05/22.67  | Case 1:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (12)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 153.05/22.67  | |           e2)
% 153.05/22.67  | | 
% 153.05/22.67  | | BETA: splitting (12) gives:
% 153.05/22.67  | | 
% 153.05/22.67  | | Case 1:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (13)  all_56_12 = e2 & op(e0, e3) = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | ALPHA: (13) implies:
% 153.05/22.67  | | |   (14)  all_56_12 = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (14) are inconsistent by
% 153.05/22.67  | | |            sub-proof #580.
% 153.05/22.67  | | | 
% 153.05/22.67  | | Case 2:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (15)  all_56_13 = e2 & op(e0, e2) = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (4), (11), (15) are inconsistent by sub-proof #739.
% 153.05/22.67  | | | 
% 153.05/22.67  | | End of split
% 153.05/22.67  | | 
% 153.05/22.67  | Case 2:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (16)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 153.05/22.67  | |           e2)
% 153.05/22.67  | | 
% 153.05/22.67  | | BETA: splitting (16) gives:
% 153.05/22.67  | | 
% 153.05/22.67  | | Case 1:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (17)  all_56_14 = e2 & op(e0, e1) = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | ALPHA: (17) implies:
% 153.05/22.67  | | |   (18)  all_56_14 = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | COMBINE_EQS: (7), (18) imply:
% 153.05/22.67  | | |   (19)  e3 = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | SIMP: (19) implies:
% 153.05/22.67  | | |   (20)  e3 = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REDUCE: (9), (20) imply:
% 153.05/22.67  | | |   (21)  $false
% 153.05/22.67  | | | 
% 153.05/22.67  | | | CLOSE: (21) is inconsistent.
% 153.05/22.67  | | | 
% 153.05/22.67  | | Case 2:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (22)  all_56_15 = e2 & op(e0, e0) = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | ALPHA: (22) implies:
% 153.05/22.67  | | |   (23)  op(e0, e0) = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (3), (5), (11), (23) are inconsistent by sub-proof #978.
% 153.05/22.67  | | | 
% 153.05/22.67  | | End of split
% 153.05/22.67  | | 
% 153.05/22.67  | End of split
% 153.05/22.67  | 
% 153.05/22.67  End of proof
% 153.05/22.67  
% 153.05/22.67  Sub-proof #387 shows that the following formulas are inconsistent:
% 153.05/22.67  ----------------------------------------------------------------
% 153.05/22.67    (1)  all_56_10 = e3
% 153.05/22.67    (2)  op(e2, e2) = e1
% 153.05/22.67    (3)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.05/22.67         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.05/22.67    (4)   ~ (e2 = e0)
% 153.05/22.67    (5)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.05/22.67         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.05/22.67    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.67    (7)  op(e2, e3) = e1
% 153.05/22.67    (8)   ~ (e3 = e0)
% 153.05/22.67    (9)  all_56_3 = e1
% 153.05/22.67    (10)  all_56_2 = e1
% 153.05/22.67    (11)   ~ (e1 = e0)
% 153.05/22.67    (12)   ~ (e3 = e2)
% 153.05/22.67    (13)   ~ (e2 = e1)
% 153.05/22.67    (14)  op(e2, e3) = all_52_1
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | BETA: splitting (3) gives:
% 153.05/22.67  | 
% 153.05/22.67  | Case 1:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (15)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 153.05/22.67  | |           e0)
% 153.05/22.67  | | 
% 153.05/22.67  | | BETA: splitting (15) gives:
% 153.05/22.67  | | 
% 153.05/22.67  | | Case 1:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (16)  all_56_2 = e0 & op(e2, e3) = e0
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (10), (11), (16) are inconsistent by sub-proof #996.
% 153.05/22.67  | | | 
% 153.05/22.67  | | Case 2:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (17)  all_56_3 = e0 & op(e2, e2) = e0
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (9), (11), (17) are inconsistent by sub-proof #741.
% 153.05/22.67  | | | 
% 153.05/22.67  | | End of split
% 153.05/22.67  | | 
% 153.05/22.67  | Case 2:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (18)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.05/22.67  | |           e0)
% 153.05/22.67  | | 
% 153.05/22.67  | | BETA: splitting (18) gives:
% 153.05/22.67  | | 
% 153.05/22.67  | | Case 1:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (19)  all_56_5 = e0 & op(e2, e1) = e0
% 153.05/22.67  | | | 
% 153.05/22.67  | | | ALPHA: (19) implies:
% 153.05/22.67  | | |   (20)  all_56_5 = e0
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (12), (13), (14), (20) are
% 153.05/22.67  | | |            inconsistent by sub-proof #388.
% 153.05/22.67  | | | 
% 153.05/22.67  | | Case 2:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (21)  all_56_10 = e0 & op(e2, e0) = e0
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (1), (8), (21) are inconsistent by sub-proof #749.
% 153.05/22.67  | | | 
% 153.05/22.67  | | End of split
% 153.05/22.67  | | 
% 153.05/22.67  | End of split
% 153.05/22.67  | 
% 153.05/22.67  End of proof
% 153.05/22.67  
% 153.05/22.67  Sub-proof #388 shows that the following formulas are inconsistent:
% 153.05/22.67  ----------------------------------------------------------------
% 153.05/22.67    (1)  all_56_10 = e3
% 153.05/22.67    (2)  op(e2, e2) = e1
% 153.05/22.67    (3)   ~ (e2 = e0)
% 153.05/22.67    (4)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.05/22.67         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.05/22.67    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.67           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.67    (6)  op(e2, e3) = e1
% 153.05/22.67    (7)  all_56_5 = e0
% 153.05/22.67    (8)   ~ (e3 = e2)
% 153.05/22.67    (9)   ~ (e2 = e1)
% 153.05/22.67    (10)  op(e2, e3) = all_52_1
% 153.05/22.67  
% 153.05/22.67  Begin of proof
% 153.05/22.67  | 
% 153.05/22.67  | BETA: splitting (4) gives:
% 153.05/22.67  | 
% 153.05/22.67  | Case 1:
% 153.05/22.67  | | 
% 153.05/22.67  | |   (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 153.05/22.67  | |           e2)
% 153.05/22.67  | | 
% 153.05/22.67  | | BETA: splitting (11) gives:
% 153.05/22.67  | | 
% 153.05/22.67  | | Case 1:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (12)  all_56_2 = e2 & op(e2, e3) = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | ALPHA: (12) implies:
% 153.05/22.67  | | |   (13)  op(e2, e3) = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (5), (6), (9), (10), (13) are inconsistent by sub-proof #842.
% 153.05/22.67  | | | 
% 153.05/22.67  | | Case 2:
% 153.05/22.67  | | | 
% 153.05/22.67  | | |   (14)  all_56_3 = e2 & op(e2, e2) = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | ALPHA: (14) implies:
% 153.05/22.67  | | |   (15)  op(e2, e2) = e2
% 153.05/22.67  | | | 
% 153.05/22.67  | | | REF_CLOSE: (2), (5), (9), (15) are inconsistent by sub-proof #1158.
% 153.05/22.67  | | | 
% 153.05/22.67  | | End of split
% 153.05/22.67  | | 
% 153.05/22.68  | Case 2:
% 153.05/22.68  | | 
% 153.05/22.68  | |   (16)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 153.05/22.68  | |           e2)
% 153.05/22.68  | | 
% 153.05/22.68  | | BETA: splitting (16) gives:
% 153.05/22.68  | | 
% 153.05/22.68  | | Case 1:
% 153.05/22.68  | | | 
% 153.05/22.68  | | |   (17)  all_56_5 = e2 & op(e2, e1) = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | REF_CLOSE: (3), (7), (17) are inconsistent by sub-proof #389.
% 153.05/22.68  | | | 
% 153.05/22.68  | | Case 2:
% 153.05/22.68  | | | 
% 153.05/22.68  | | |   (18)  all_56_10 = e2 & op(e2, e0) = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | ALPHA: (18) implies:
% 153.05/22.68  | | |   (19)  all_56_10 = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | COMBINE_EQS: (1), (19) imply:
% 153.05/22.68  | | |   (20)  e3 = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | REDUCE: (8), (20) imply:
% 153.05/22.68  | | |   (21)  $false
% 153.05/22.68  | | | 
% 153.05/22.68  | | | CLOSE: (21) is inconsistent.
% 153.05/22.68  | | | 
% 153.05/22.68  | | End of split
% 153.05/22.68  | | 
% 153.05/22.68  | End of split
% 153.05/22.68  | 
% 153.05/22.68  End of proof
% 153.05/22.68  
% 153.05/22.68  Sub-proof #389 shows that the following formulas are inconsistent:
% 153.05/22.68  ----------------------------------------------------------------
% 153.05/22.68    (1)  all_56_5 = e2 & op(e2, e1) = e2
% 153.05/22.68    (2)  all_56_5 = e0
% 153.05/22.68    (3)   ~ (e2 = e0)
% 153.05/22.68  
% 153.05/22.68  Begin of proof
% 153.05/22.68  | 
% 153.05/22.68  | ALPHA: (1) implies:
% 153.05/22.68  |   (4)  all_56_5 = e2
% 153.05/22.68  | 
% 153.05/22.68  | COMBINE_EQS: (2), (4) imply:
% 153.05/22.68  |   (5)  e2 = e0
% 153.05/22.68  | 
% 153.05/22.68  | REDUCE: (3), (5) imply:
% 153.05/22.68  |   (6)  $false
% 153.05/22.68  | 
% 153.05/22.68  | CLOSE: (6) is inconsistent.
% 153.05/22.68  | 
% 153.05/22.68  End of proof
% 153.05/22.68  
% 153.05/22.68  Sub-proof #390 shows that the following formulas are inconsistent:
% 153.05/22.68  ----------------------------------------------------------------
% 153.05/22.68    (1)   ~ (all_52_1 = e0)
% 153.05/22.68    (2)  op(e0, e1) = e3
% 153.05/22.68    (3)  all_56_1 = e1
% 153.05/22.68    (4)   ~ (e3 = e1)
% 153.05/22.68    (5)   ~ (all_52_2 = all_52_14)
% 153.05/22.68    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.05/22.68         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.05/22.68    (7)  all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 153.05/22.68    (8)   ~ (all_52_3 = all_52_7)
% 153.05/22.68    (9)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 153.05/22.68         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.05/22.68    (10)   ~ (e2 = e0)
% 153.05/22.68    (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.05/22.68          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.05/22.68    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.05/22.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.05/22.68    (13)  op(e2, e3) = e1
% 153.05/22.68    (14)  all_56_5 = e2
% 153.05/22.68    (15)  op(e2, e0) = e3
% 153.05/22.68    (16)   ~ (all_52_7 = e1)
% 153.05/22.68    (17)  op(e0, e1) = all_10_1
% 153.05/22.68    (18)   ~ (all_52_14 = e1)
% 153.05/22.68    (19)   ~ (e3 = e0)
% 153.05/22.68    (20)  all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.05/22.68    (21)   ~ (all_52_3 = e3)
% 153.05/22.68    (22)   ~ (all_52_1 = all_52_3)
% 153.05/22.68    (23)   ~ (all_52_2 = e3)
% 153.05/22.68    (24)  all_56_14 = e3
% 153.05/22.68    (25)  all_54_12 = all_52_3
% 153.05/22.68    (26)  op(e2, e1) = all_52_9
% 153.05/22.68    (27)   ~ (all_52_7 = e0)
% 153.05/22.68    (28)   ~ (e1 = e0)
% 153.05/22.68    (29)  all_54_8 = all_52_2
% 153.05/22.68    (30)   ~ (e3 = e2)
% 153.05/22.68    (31)  all_54_4 = all_52_1
% 153.05/22.68    (32)   ~ (all_52_14 = e3)
% 153.05/22.68    (33)   ~ (all_52_1 = all_52_2)
% 153.05/22.68    (34)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.05/22.68    (35)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 153.05/22.68          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 153.05/22.68    (36)  all_54_13 = all_52_7
% 153.05/22.68    (37)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 153.05/22.68            all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0,
% 153.05/22.68              e1) = all_30_1 & $i(all_30_1))
% 153.05/22.68    (38)   ~ (all_52_9 = e0)
% 153.05/22.68    (39)   ~ (all_52_2 = all_52_3)
% 153.05/22.68    (40)  op(e3, e3) = e3
% 153.05/22.68    (41)  all_54_4 = e1 | all_54_4 = e0
% 153.05/22.68    (42)   ~ (e2 = e1)
% 153.05/22.68    (43)  all_54_11 = all_52_14
% 153.05/22.68    (44)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 153.05/22.68    (45)  op(e2, e2) = e0
% 153.05/22.68    (46)  op(e2, e3) = all_52_1
% 153.05/22.68  
% 153.05/22.68  Begin of proof
% 153.05/22.68  | 
% 153.05/22.68  | BETA: splitting (6) gives:
% 153.05/22.68  | 
% 153.05/22.68  | Case 1:
% 153.05/22.68  | | 
% 153.05/22.68  | |   (47)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) =
% 153.05/22.68  | |           e2)
% 153.05/22.68  | | 
% 153.05/22.68  | | BETA: splitting (47) gives:
% 153.05/22.68  | | 
% 153.05/22.68  | | Case 1:
% 153.05/22.68  | | | 
% 153.05/22.68  | | |   (48)  all_56_0 = e2 & op(e3, e3) = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | ALPHA: (48) implies:
% 153.05/22.68  | | |   (49)  op(e3, e3) = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | REF_CLOSE: (12), (30), (40), (49) are inconsistent by sub-proof #1085.
% 153.05/22.68  | | | 
% 153.05/22.68  | | Case 2:
% 153.05/22.68  | | | 
% 153.05/22.68  | | |   (50)  all_56_1 = e2 & op(e3, e2) = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | ALPHA: (50) implies:
% 153.05/22.68  | | |   (51)  all_56_1 = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | COMBINE_EQS: (3), (51) imply:
% 153.05/22.68  | | |   (52)  e2 = e1
% 153.05/22.68  | | | 
% 153.05/22.68  | | | COMBINE_EQS: (14), (52) imply:
% 153.05/22.68  | | |   (53)  all_56_5 = e1
% 153.05/22.68  | | | 
% 153.05/22.68  | | | BETA: splitting (11) gives:
% 153.05/22.68  | | | 
% 153.05/22.68  | | | Case 1:
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | |   (54)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2)
% 153.05/22.68  | | | |           = e2)
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | | REF_CLOSE: (10), (12), (13), (42), (45), (46), (54) are inconsistent by
% 153.05/22.68  | | | |            sub-proof #624.
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | Case 2:
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | |   (55)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0)
% 153.05/22.68  | | | |           = e2)
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | | BETA: splitting (55) gives:
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | | Case 1:
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | |   (56)  all_56_5 = e2 & op(e2, e1) = e2
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | | REF_CLOSE: (42), (53), (56) are inconsistent by sub-proof #680.
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | Case 2:
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | |   (57)  all_56_10 = e2 & op(e2, e0) = e2
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | | ALPHA: (57) implies:
% 153.05/22.68  | | | | |   (58)  op(e2, e0) = e2
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | | REF_CLOSE: (12), (15), (30), (58) are inconsistent by sub-proof #854.
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | End of split
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | End of split
% 153.05/22.68  | | | 
% 153.05/22.68  | | End of split
% 153.05/22.68  | | 
% 153.05/22.68  | Case 2:
% 153.05/22.68  | | 
% 153.05/22.68  | |   (59)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 153.05/22.68  | |           e2)
% 153.05/22.68  | | 
% 153.05/22.68  | | BETA: splitting (59) gives:
% 153.05/22.68  | | 
% 153.05/22.68  | | Case 1:
% 153.05/22.68  | | | 
% 153.05/22.68  | | |   (60)  all_56_4 = e2 & op(e3, e1) = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | ALPHA: (60) implies:
% 153.05/22.68  | | |   (61)  all_56_4 = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | REF_CLOSE: (4), (9), (10), (12), (14), (19), (24), (26), (28), (35), (38),
% 153.05/22.68  | | |            (42), (61) are inconsistent by sub-proof #468.
% 153.05/22.68  | | | 
% 153.05/22.68  | | Case 2:
% 153.05/22.68  | | | 
% 153.05/22.68  | | |   (62)  all_56_9 = e2 & op(e3, e0) = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | ALPHA: (62) implies:
% 153.05/22.68  | | |   (63)  op(e3, e0) = e2
% 153.05/22.68  | | | 
% 153.05/22.68  | | | BETA: splitting (34) gives:
% 153.05/22.68  | | | 
% 153.05/22.68  | | | Case 1:
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | |   (64)  all_54_13 = e2
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | | COMBINE_EQS: (36), (64) imply:
% 153.05/22.68  | | | |   (65)  all_52_7 = e2
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | | SIMP: (65) implies:
% 153.05/22.68  | | | |   (66)  all_52_7 = e2
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | | REDUCE: (8), (66) imply:
% 153.05/22.68  | | | |   (67)   ~ (all_52_3 = e2)
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | | BETA: splitting (44) gives:
% 153.05/22.68  | | | | 
% 153.05/22.68  | | | | Case 1:
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | |   (68)  all_54_12 = e3
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | | REF_CLOSE: (21), (25), (68) are inconsistent by sub-proof #1093.
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | Case 2:
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | |   (69)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | | BETA: splitting (69) gives:
% 153.05/22.68  | | | | | 
% 153.05/22.68  | | | | | Case 1:
% 153.05/22.68  | | | | | | 
% 153.05/22.68  | | | | | |   (70)  all_54_12 = e2
% 153.05/22.68  | | | | | | 
% 153.05/22.68  | | | | | | REF_CLOSE: (25), (67), (70) are inconsistent by sub-proof #882.
% 153.05/22.68  | | | | | | 
% 153.05/22.68  | | | | | Case 2:
% 153.05/22.68  | | | | | | 
% 153.05/22.68  | | | | | |   (71)  all_54_12 = e1 | all_54_12 = e0
% 153.05/22.68  | | | | | | 
% 153.05/22.68  | | | | | | BETA: splitting (41) gives:
% 153.05/22.68  | | | | | | 
% 153.05/22.68  | | | | | | Case 1:
% 153.05/22.68  | | | | | | | 
% 153.05/22.68  | | | | | | |   (72)  all_54_4 = e1
% 153.05/22.68  | | | | | | | 
% 153.05/22.68  | | | | | | | COMBINE_EQS: (31), (72) imply:
% 153.05/22.68  | | | | | | |   (73)  all_52_1 = e1
% 153.05/22.68  | | | | | | | 
% 153.05/22.68  | | | | | | | SIMP: (73) implies:
% 153.05/22.68  | | | | | | |   (74)  all_52_1 = e1
% 153.05/22.68  | | | | | | | 
% 153.05/22.68  | | | | | | | REDUCE: (33), (74) imply:
% 153.05/22.68  | | | | | | |   (75)   ~ (all_52_2 = e1)
% 153.05/22.68  | | | | | | | 
% 153.05/22.68  | | | | | | | SIMP: (75) implies:
% 153.05/22.68  | | | | | | |   (76)   ~ (all_52_2 = e1)
% 153.05/22.68  | | | | | | | 
% 153.05/22.68  | | | | | | | REDUCE: (22), (74) imply:
% 153.05/22.68  | | | | | | |   (77)   ~ (all_52_3 = e1)
% 153.05/22.68  | | | | | | | 
% 153.05/22.68  | | | | | | | SIMP: (77) implies:
% 153.05/22.68  | | | | | | |   (78)   ~ (all_52_3 = e1)
% 153.05/22.68  | | | | | | | 
% 153.05/22.68  | | | | | | | BETA: splitting (71) gives:
% 153.05/22.68  | | | | | | | 
% 153.05/22.68  | | | | | | | Case 1:
% 153.05/22.68  | | | | | | | | 
% 153.05/22.68  | | | | | | | |   (79)  all_54_12 = e1
% 153.05/22.68  | | | | | | | | 
% 153.05/22.68  | | | | | | | | REF_CLOSE: (25), (78), (79) are inconsistent by sub-proof #1091.
% 153.05/22.68  | | | | | | | | 
% 153.05/22.68  | | | | | | | Case 2:
% 153.05/22.68  | | | | | | | | 
% 153.05/22.68  | | | | | | | |   (80)  all_54_12 = e0
% 153.05/22.68  | | | | | | | | 
% 153.05/22.68  | | | | | | | | COMBINE_EQS: (25), (80) imply:
% 153.05/22.68  | | | | | | | |   (81)  all_52_3 = e0
% 153.05/22.68  | | | | | | | | 
% 153.05/22.68  | | | | | | | | SIMP: (81) implies:
% 153.14/22.68  | | | | | | | |   (82)  all_52_3 = e0
% 153.14/22.68  | | | | | | | | 
% 153.14/22.68  | | | | | | | | REDUCE: (39), (82) imply:
% 153.14/22.68  | | | | | | | |   (83)   ~ (all_52_2 = e0)
% 153.14/22.68  | | | | | | | | 
% 153.14/22.68  | | | | | | | | BETA: splitting (20) gives:
% 153.14/22.68  | | | | | | | | 
% 153.14/22.68  | | | | | | | | Case 1:
% 153.14/22.68  | | | | | | | | | 
% 153.14/22.68  | | | | | | | | |   (84)  all_54_8 = e3
% 153.14/22.68  | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | REF_CLOSE: (23), (29), (84) are inconsistent by sub-proof
% 153.14/22.68  | | | | | | | | |            #394.
% 153.14/22.68  | | | | | | | | | 
% 153.14/22.68  | | | | | | | | Case 2:
% 153.14/22.68  | | | | | | | | | 
% 153.14/22.68  | | | | | | | | |   (85)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.14/22.68  | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | BETA: splitting (85) gives:
% 153.14/22.68  | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | Case 1:
% 153.14/22.68  | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | |   (86)  all_54_8 = e2
% 153.14/22.68  | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | COMBINE_EQS: (29), (86) imply:
% 153.14/22.68  | | | | | | | | | |   (87)  all_52_2 = e2
% 153.14/22.68  | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | SIMP: (87) implies:
% 153.14/22.68  | | | | | | | | | |   (88)  all_52_2 = e2
% 153.14/22.68  | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | REDUCE: (5), (88) imply:
% 153.14/22.68  | | | | | | | | | |   (89)   ~ (all_52_14 = e2)
% 153.14/22.68  | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | SIMP: (89) implies:
% 153.14/22.68  | | | | | | | | | |   (90)   ~ (all_52_14 = e2)
% 153.14/22.68  | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | BETA: splitting (7) gives:
% 153.14/22.68  | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | Case 1:
% 153.14/22.68  | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | |   (91)  all_54_11 = e3
% 153.14/22.68  | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | | REF_CLOSE: (32), (43), (91) are inconsistent by sub-proof
% 153.14/22.68  | | | | | | | | | | |            #661.
% 153.14/22.68  | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | Case 2:
% 153.14/22.68  | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | |   (92)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 153.14/22.68  | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | | BETA: splitting (37) gives:
% 153.14/22.68  | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | | Case 1:
% 153.14/22.68  | | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | | |   (93)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 &
% 153.14/22.68  | | | | | | | | | | | |         op(e0, e1) = all_30_1 & $i(all_30_0) &
% 153.14/22.68  | | | | | | | | | | | |         $i(all_30_1)
% 153.14/22.68  | | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | | | ALPHA: (93) implies:
% 153.14/22.68  | | | | | | | | | | | |   (94)   ~ (all_30_0 = e2)
% 153.14/22.68  | | | | | | | | | | | |   (95)  op(e0, e1) = all_30_1
% 153.14/22.68  | | | | | | | | | | | |   (96)  op(all_30_1, e0) = all_30_0
% 153.14/22.68  | | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | | | REF_CLOSE: (2), (12), (17), (18), (43), (63), (90), (92),
% 153.14/22.68  | | | | | | | | | | | |            (94), (95), (96) are inconsistent by sub-proof
% 153.14/22.68  | | | | | | | | | | | |            #392.
% 153.14/22.68  | | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | | Case 2:
% 153.14/22.68  | | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | | |   (97)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 &
% 153.14/22.68  | | | | | | | | | | | |         $i(all_30_1)
% 153.14/22.68  | | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | | | ALPHA: (97) implies:
% 153.14/22.68  | | | | | | | | | | | |   (98)   ~ (all_30_1 = e3)
% 153.14/22.68  | | | | | | | | | | | |   (99)  op(e0, e1) = all_30_1
% 153.14/22.68  | | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | | | REF_CLOSE: (2), (12), (17), (98), (99) are inconsistent by
% 153.14/22.68  | | | | | | | | | | | |            sub-proof #391.
% 153.14/22.68  | | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | | End of split
% 153.14/22.68  | | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | End of split
% 153.14/22.68  | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | Case 2:
% 153.14/22.68  | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | |   (100)  all_54_8 = e1 | all_54_8 = e0
% 153.14/22.68  | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | | REF_CLOSE: (29), (76), (83), (100) are inconsistent by
% 153.14/22.68  | | | | | | | | | |            sub-proof #461.
% 153.14/22.68  | | | | | | | | | | 
% 153.14/22.68  | | | | | | | | | End of split
% 153.14/22.68  | | | | | | | | | 
% 153.14/22.68  | | | | | | | | End of split
% 153.14/22.68  | | | | | | | | 
% 153.14/22.68  | | | | | | | End of split
% 153.14/22.68  | | | | | | | 
% 153.14/22.68  | | | | | | Case 2:
% 153.14/22.68  | | | | | | | 
% 153.14/22.68  | | | | | | |   (101)  all_54_4 = e0
% 153.14/22.68  | | | | | | | 
% 153.14/22.68  | | | | | | | REF_CLOSE: (1), (31), (101) are inconsistent by sub-proof #796.
% 153.14/22.68  | | | | | | | 
% 153.14/22.68  | | | | | | End of split
% 153.14/22.68  | | | | | | 
% 153.14/22.68  | | | | | End of split
% 153.14/22.68  | | | | | 
% 153.14/22.68  | | | | End of split
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | Case 2:
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | |   (102)  all_54_13 = e1 | all_54_13 = e0
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | | REF_CLOSE: (16), (27), (36), (102) are inconsistent by sub-proof #983.
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | End of split
% 153.14/22.68  | | | 
% 153.14/22.68  | | End of split
% 153.14/22.68  | | 
% 153.14/22.68  | End of split
% 153.14/22.68  | 
% 153.14/22.68  End of proof
% 153.14/22.68  
% 153.14/22.68  Sub-proof #391 shows that the following formulas are inconsistent:
% 153.14/22.68  ----------------------------------------------------------------
% 153.14/22.68    (1)  op(e0, e1) = e3
% 153.14/22.68    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.68    (3)  op(e0, e1) = all_10_1
% 153.14/22.68    (4)  op(e0, e1) = all_30_1
% 153.14/22.68    (5)   ~ (all_30_1 = e3)
% 153.14/22.68  
% 153.14/22.68  Begin of proof
% 153.14/22.68  | 
% 153.14/22.68  | GROUND_INST: instantiating (2) with all_10_1, all_30_1, e1, e0, simplifying
% 153.14/22.68  |              with (3), (4) gives:
% 153.14/22.68  |   (6)  all_30_1 = all_10_1
% 153.14/22.68  | 
% 153.14/22.68  | GROUND_INST: instantiating (2) with e3, all_30_1, e1, e0, simplifying with
% 153.14/22.68  |              (1), (4) gives:
% 153.14/22.68  |   (7)  all_30_1 = e3
% 153.14/22.68  | 
% 153.14/22.68  | COMBINE_EQS: (6), (7) imply:
% 153.14/22.68  |   (8)  all_10_1 = e3
% 153.14/22.68  | 
% 153.14/22.68  | REDUCE: (5), (7) imply:
% 153.14/22.68  |   (9)  $false
% 153.14/22.68  | 
% 153.14/22.68  | CLOSE: (9) is inconsistent.
% 153.14/22.68  | 
% 153.14/22.68  End of proof
% 153.14/22.68  
% 153.14/22.68  Sub-proof #392 shows that the following formulas are inconsistent:
% 153.14/22.68  ----------------------------------------------------------------
% 153.14/22.68    (1)  op(e0, e1) = e3
% 153.14/22.68    (2)   ~ (all_52_14 = e2)
% 153.14/22.68    (3)  op(e3, e0) = e2
% 153.14/22.68    (4)   ~ (all_30_0 = e2)
% 153.14/22.68    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.68    (6)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 153.14/22.68    (7)  op(e0, e1) = all_10_1
% 153.14/22.68    (8)   ~ (all_52_14 = e1)
% 153.14/22.68    (9)  op(e0, e1) = all_30_1
% 153.14/22.68    (10)  op(all_30_1, e0) = all_30_0
% 153.14/22.68    (11)  all_54_11 = all_52_14
% 153.14/22.68  
% 153.14/22.68  Begin of proof
% 153.14/22.68  | 
% 153.14/22.68  | BETA: splitting (6) gives:
% 153.14/22.68  | 
% 153.14/22.68  | Case 1:
% 153.14/22.68  | | 
% 153.14/22.68  | |   (12)  all_54_11 = e2
% 153.14/22.68  | | 
% 153.14/22.68  | | REF_CLOSE: (2), (11), (12) are inconsistent by sub-proof #393.
% 153.14/22.68  | | 
% 153.14/22.68  | Case 2:
% 153.14/22.68  | | 
% 153.14/22.68  | |   (13)  all_54_11 = e1 | all_54_11 = e0
% 153.14/22.68  | | 
% 153.14/22.68  | | BETA: splitting (13) gives:
% 153.14/22.68  | | 
% 153.14/22.68  | | Case 1:
% 153.14/22.68  | | | 
% 153.14/22.68  | | |   (14)  all_54_11 = e1
% 153.14/22.68  | | | 
% 153.14/22.68  | | | COMBINE_EQS: (11), (14) imply:
% 153.14/22.68  | | |   (15)  all_52_14 = e1
% 153.14/22.68  | | | 
% 153.14/22.68  | | | SIMP: (15) implies:
% 153.14/22.68  | | |   (16)  all_52_14 = e1
% 153.14/22.68  | | | 
% 153.14/22.68  | | | REDUCE: (8), (16) imply:
% 153.14/22.68  | | |   (17)  $false
% 153.14/22.68  | | | 
% 153.14/22.68  | | | CLOSE: (17) is inconsistent.
% 153.14/22.68  | | | 
% 153.14/22.68  | | Case 2:
% 153.14/22.68  | | | 
% 153.14/22.68  | | | 
% 153.14/22.68  | | | GROUND_INST: instantiating (5) with all_10_1, all_30_1, e1, e0,
% 153.14/22.68  | | |              simplifying with (7), (9) gives:
% 153.14/22.68  | | |   (18)  all_30_1 = all_10_1
% 153.14/22.68  | | | 
% 153.14/22.68  | | | GROUND_INST: instantiating (5) with e3, all_30_1, e1, e0, simplifying with
% 153.14/22.68  | | |              (1), (9) gives:
% 153.14/22.68  | | |   (19)  all_30_1 = e3
% 153.14/22.68  | | | 
% 153.14/22.68  | | | GROUND_INST: instantiating (5) with e2, all_30_0, e0, e3, simplifying with
% 153.14/22.68  | | |              (3) gives:
% 153.14/22.68  | | |   (20)  all_30_0 = e2 |  ~ (op(e3, e0) = all_30_0)
% 153.14/22.68  | | | 
% 153.14/22.68  | | | COMBINE_EQS: (18), (19) imply:
% 153.14/22.68  | | |   (21)  all_10_1 = e3
% 153.14/22.68  | | | 
% 153.14/22.68  | | | REDUCE: (10), (19) imply:
% 153.14/22.68  | | |   (22)  op(e3, e0) = all_30_0
% 153.14/22.68  | | | 
% 153.14/22.68  | | | BETA: splitting (20) gives:
% 153.14/22.68  | | | 
% 153.14/22.68  | | | Case 1:
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | |   (23)   ~ (op(e3, e0) = all_30_0)
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | | PRED_UNIFY: (22), (23) imply:
% 153.14/22.68  | | | |   (24)  $false
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | | CLOSE: (24) is inconsistent.
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | Case 2:
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | |   (25)  all_30_0 = e2
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | | REDUCE: (4), (25) imply:
% 153.14/22.68  | | | |   (26)  $false
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | | CLOSE: (26) is inconsistent.
% 153.14/22.68  | | | | 
% 153.14/22.68  | | | End of split
% 153.14/22.68  | | | 
% 153.14/22.68  | | End of split
% 153.14/22.68  | | 
% 153.14/22.68  | End of split
% 153.14/22.68  | 
% 153.14/22.68  End of proof
% 153.14/22.68  
% 153.14/22.68  Sub-proof #393 shows that the following formulas are inconsistent:
% 153.14/22.68  ----------------------------------------------------------------
% 153.14/22.68    (1)  all_54_11 = all_52_14
% 153.14/22.68    (2)  all_54_11 = e2
% 153.14/22.68    (3)   ~ (all_52_14 = e2)
% 153.14/22.68  
% 153.14/22.68  Begin of proof
% 153.14/22.68  | 
% 153.14/22.68  | COMBINE_EQS: (1), (2) imply:
% 153.14/22.68  |   (4)  all_52_14 = e2
% 153.14/22.68  | 
% 153.14/22.68  | SIMP: (4) implies:
% 153.14/22.68  |   (5)  all_52_14 = e2
% 153.14/22.68  | 
% 153.14/22.68  | REDUCE: (3), (5) imply:
% 153.14/22.68  |   (6)  $false
% 153.14/22.68  | 
% 153.14/22.68  | CLOSE: (6) is inconsistent.
% 153.14/22.68  | 
% 153.14/22.68  End of proof
% 153.14/22.68  
% 153.14/22.68  Sub-proof #394 shows that the following formulas are inconsistent:
% 153.14/22.68  ----------------------------------------------------------------
% 153.14/22.68    (1)  all_54_8 = all_52_2
% 153.14/22.68    (2)  all_54_8 = e3
% 153.14/22.68    (3)   ~ (all_52_2 = e3)
% 153.14/22.68  
% 153.14/22.68  Begin of proof
% 153.14/22.68  | 
% 153.14/22.68  | COMBINE_EQS: (1), (2) imply:
% 153.14/22.68  |   (4)  all_52_2 = e3
% 153.14/22.68  | 
% 153.14/22.68  | SIMP: (4) implies:
% 153.14/22.68  |   (5)  all_52_2 = e3
% 153.14/22.68  | 
% 153.14/22.68  | REDUCE: (3), (5) imply:
% 153.14/22.68  |   (6)  $false
% 153.14/22.68  | 
% 153.14/22.68  | CLOSE: (6) is inconsistent.
% 153.14/22.68  | 
% 153.14/22.68  End of proof
% 153.14/22.68  
% 153.14/22.68  Sub-proof #395 shows that the following formulas are inconsistent:
% 153.14/22.68  ----------------------------------------------------------------
% 153.14/22.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.68    (2)  op(e0, e0) = e1
% 153.14/22.68    (3)   ~ (e1 = e0)
% 153.14/22.68    (4)   ~ (e3 = e2)
% 153.14/22.68    (5)  op(e3, e3) = e3
% 153.14/22.68    (6)   ~ (e2 = e1)
% 153.14/22.68    (7)  op(e2, e2) = e0
% 153.14/22.68    (8)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.14/22.68             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.14/22.68           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 153.14/22.68           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 153.14/22.68             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.14/22.68             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.14/22.68           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.14/22.68           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.14/22.68           $i(all_57_7) & $i(all_57_10))
% 153.14/22.68  
% 153.14/22.68  Begin of proof
% 153.14/22.68  | 
% 153.14/22.68  | BETA: splitting (8) gives:
% 153.14/22.68  | 
% 153.14/22.68  | Case 1:
% 153.14/22.68  | | 
% 153.14/22.68  | |   (9)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.14/22.68  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.14/22.68  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 153.14/22.68  | | 
% 153.14/22.68  | | ALPHA: (9) implies:
% 153.14/22.68  | |   (10)  op(e3, e3) = e2
% 153.14/22.68  | | 
% 153.14/22.68  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #1085.
% 153.14/22.68  | | 
% 153.14/22.68  | Case 2:
% 153.14/22.68  | | 
% 153.14/22.68  | |   (11)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.14/22.68  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.14/22.68  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.14/22.68  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.14/22.68  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.14/22.68  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.14/22.68  | | 
% 153.14/22.68  | | REF_CLOSE: (1), (2), (3), (6), (7), (11) are inconsistent by sub-proof #396.
% 153.14/22.68  | | 
% 153.14/22.68  | End of split
% 153.14/22.68  | 
% 153.14/22.68  End of proof
% 153.14/22.68  
% 153.14/22.68  Sub-proof #396 shows that the following formulas are inconsistent:
% 153.14/22.68  ----------------------------------------------------------------
% 153.14/22.68    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.68    (2)  op(e0, e0) = e1
% 153.14/22.68    (3)   ~ (e1 = e0)
% 153.14/22.68    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.14/22.68             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.14/22.68           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.14/22.68           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.14/22.68           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 153.14/22.68           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.14/22.68    (5)   ~ (e2 = e1)
% 153.14/22.68    (6)  op(e2, e2) = e0
% 153.14/22.68  
% 153.14/22.68  Begin of proof
% 153.14/22.68  | 
% 153.14/22.68  | BETA: splitting (4) gives:
% 153.14/22.68  | 
% 153.14/22.68  | Case 1:
% 153.14/22.68  | | 
% 153.14/22.68  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.14/22.68  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.14/22.68  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 153.14/22.68  | | 
% 153.14/22.68  | | ALPHA: (7) implies:
% 153.14/22.68  | |   (8)  op(e0, e0) = e2
% 153.14/22.68  | | 
% 153.14/22.68  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #978.
% 153.14/22.68  | | 
% 153.14/22.68  | Case 2:
% 153.14/22.68  | | 
% 153.14/22.68  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.14/22.68  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.14/22.68  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 153.14/22.68  | | 
% 153.14/22.68  | | ALPHA: (9) implies:
% 153.14/22.68  | |   (10)  op(e2, e2) = e1
% 153.14/22.68  | | 
% 153.14/22.68  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #853.
% 153.14/22.68  | | 
% 153.14/22.68  | End of split
% 153.14/22.68  | 
% 153.14/22.68  End of proof
% 153.14/22.68  
% 153.14/22.68  Sub-proof #397 shows that the following formulas are inconsistent:
% 153.14/22.68  ----------------------------------------------------------------
% 153.14/22.68    (1)   ~ (e3 = e1)
% 153.14/22.68    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.68           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.68    (3)  op(e0, e0) = e1
% 153.14/22.68    (4)   ~ (e3 = e0)
% 153.14/22.68    (5)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.14/22.68             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.14/22.68           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 153.14/22.68           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 153.14/22.68             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 153.14/22.68             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.14/22.68    (6)  op(e2, e2) = e0
% 153.14/22.68  
% 153.14/22.68  Begin of proof
% 153.14/22.68  | 
% 153.14/22.68  | BETA: splitting (5) gives:
% 153.14/22.68  | 
% 153.14/22.68  | Case 1:
% 153.14/22.68  | | 
% 153.14/22.68  | |   (7)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.14/22.68  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.14/22.68  | |        op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 153.14/22.68  | | 
% 153.14/22.68  | | ALPHA: (7) implies:
% 153.14/22.68  | |   (8)  op(e2, e2) = e3
% 153.14/22.68  | | 
% 153.14/22.68  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #719.
% 153.14/22.68  | | 
% 153.14/22.68  | Case 2:
% 153.14/22.68  | | 
% 153.14/22.68  | |   (9)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 153.14/22.68  | |          e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.14/22.68  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 153.14/22.68  | | 
% 153.14/22.68  | | ALPHA: (9) implies:
% 153.14/22.68  | |   (10)  op(e0, e0) = e3
% 153.14/22.68  | | 
% 153.14/22.68  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #1022.
% 153.14/22.68  | | 
% 153.14/22.68  | End of split
% 153.14/22.68  | 
% 153.14/22.68  End of proof
% 153.14/22.68  
% 153.14/22.68  Sub-proof #398 shows that the following formulas are inconsistent:
% 153.14/22.68  ----------------------------------------------------------------
% 153.14/22.68    (1)  op(e0, e1) = all_52_11
% 153.14/22.68    (2)   ~ (e3 = e1)
% 153.14/22.68    (3)   ~ (all_52_2 = all_52_14)
% 153.14/22.68    (4)   ~ (all_52_11 = all_10_2)
% 153.14/22.68    (5)  op(e2, e2) = e1
% 153.14/22.68    (6)  op(e0, e0) = all_10_2
% 153.14/22.68    (7)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.14/22.68    (8)   ~ (all_52_9 = all_52_13)
% 153.14/22.68    (9)  op(e1, e1) = all_4_2
% 153.14/22.68    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.68            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.68    (11)  all_54_10 = all_4_2
% 153.14/22.68    (12)  op(e1, e0) = all_52_14
% 153.14/22.68    (13)  op(e0, e0) = e1
% 153.14/22.68    (14)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.14/22.68            all_57_10 & $i(all_57_10))
% 153.14/22.68    (15)  op(e3, e3) = e1
% 153.14/22.68    (16)  op(e2, e0) = all_52_13
% 153.14/22.68    (17)   ~ (all_52_14 = all_4_2)
% 153.14/22.68    (18)   ~ (all_4_2 = e2)
% 153.14/22.68    (19)  op(e1, e1) = e1
% 153.14/22.68    (20)  op(e2, e1) = all_52_9
% 153.14/22.68    (21)   ~ (e1 = e0)
% 153.14/22.68    (22)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.14/22.68              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.14/22.68            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.14/22.68                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.14/22.68              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.68          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.14/22.68              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.68            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.14/22.68                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.14/22.68              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.68          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.14/22.68              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.68            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.14/22.68                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.14/22.68              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.68          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.14/22.68              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.68            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.14/22.68                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.14/22.68                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.14/22.68                $i(all_57_14))))
% 153.14/22.68    (23)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.14/22.68            all_57_12 & $i(all_57_12))
% 153.14/22.68    (24)   ~ (all_4_2 = e3)
% 153.14/22.68    (25)   ~ (all_52_2 = e1)
% 153.14/22.68    (26)   ~ (e2 = e1)
% 153.14/22.68    (27)  op(e1, e3) = all_52_2
% 153.14/22.69    (28)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.14/22.69              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.69            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.14/22.69            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.14/22.69            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.14/22.69            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.69            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.14/22.69            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.14/22.69            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.14/22.69            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.14/22.69            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.14/22.69            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.14/22.69            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.69            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.14/22.69            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.14/22.69            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.69            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.14/22.69            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.14/22.69            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.69            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.14/22.69            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.14/22.69            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.69            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.14/22.69            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.14/22.69            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.69            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.14/22.69            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.69            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.69            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.69            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.14/22.69            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.14/22.69            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.14/22.69            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.69            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.14/22.69            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.69            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.69            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.69            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.14/22.69            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.69            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.69            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.14/22.69            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.14/22.69            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.69            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.14/22.69            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.14/22.69            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.69            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.14/22.69            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.14/22.69              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.14/22.69            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.14/22.69            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.14/22.69              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.14/22.69            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.14/22.69            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.14/22.69                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.14/22.69                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.69                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.14/22.69                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.14/22.69                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.14/22.69                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.14/22.69                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.14/22.69              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.14/22.69                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.14/22.69                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.69                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.14/22.69                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.14/22.69                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.14/22.69                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.69                $i(all_57_7))))
% 153.14/22.69  
% 153.14/22.69  Begin of proof
% 153.14/22.69  | 
% 153.14/22.69  | BETA: splitting (23) gives:
% 153.14/22.69  | 
% 153.14/22.69  | Case 1:
% 153.14/22.69  | | 
% 153.14/22.69  | |   (29)  all_57_7 = e2 & op(e2, e1) = e2
% 153.14/22.69  | | 
% 153.14/22.69  | | ALPHA: (29) implies:
% 153.14/22.69  | |   (30)  op(e2, e1) = e2
% 153.14/22.69  | | 
% 153.14/22.69  | | BETA: splitting (28) gives:
% 153.14/22.69  | | 
% 153.14/22.69  | | Case 1:
% 153.14/22.69  | | | 
% 153.14/22.69  | | |   (31)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.14/22.69  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.14/22.69  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.14/22.69  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 153.14/22.69  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.14/22.69  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.14/22.69  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 153.14/22.69  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.14/22.69  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.14/22.69  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 153.14/22.69  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.14/22.69  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 153.14/22.69  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) | (all_57_3 =
% 153.14/22.69  | | |           e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 = e2) &
% 153.14/22.69  | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) = all_57_4
% 153.14/22.69  | | |           & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3 =
% 153.14/22.69  | | |           e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.14/22.69  | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5
% 153.14/22.69  | | |           & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 =
% 153.14/22.69  | | |           e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 153.14/22.69  | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.14/22.69  | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.14/22.69  | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.14/22.69  | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.69  | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.14/22.69  | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7
% 153.14/22.69  | | |             = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 153.14/22.69  | | |             e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.14/22.69  | | |           $i(all_57_7) & $i(all_57_10))
% 153.14/22.69  | | | 
% 153.14/22.69  | | | BETA: splitting (31) gives:
% 153.14/22.69  | | | 
% 153.14/22.69  | | | Case 1:
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | |   (32)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.14/22.69  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.14/22.69  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.14/22.69  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.14/22.69  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.14/22.69  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.14/22.69  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.69  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.14/22.69  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.14/22.69  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.14/22.69  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.14/22.69  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.69  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.14/22.69  | | | |           $i(all_57_14))
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | | BETA: splitting (32) gives:
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | | Case 1:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | |   (33)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.14/22.69  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 153.14/22.69  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.14/22.69  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.14/22.69  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.14/22.69  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 153.14/22.69  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12))
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | REF_CLOSE: (2), (10), (13), (19), (33) are inconsistent by sub-proof
% 153.14/22.69  | | | | |            #404.
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | Case 2:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | |   (34)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.14/22.69  | | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.14/22.69  | | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.14/22.69  | | | | |           $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.14/22.69  | | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.14/22.69  | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0)
% 153.14/22.69  | | | | |           = e3 & $i(all_57_2) & $i(all_57_14))
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | REF_CLOSE: (2), (10), (13), (25), (27), (34) are inconsistent by
% 153.14/22.69  | | | | |            sub-proof #403.
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | End of split
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | Case 2:
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | |   (35)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.14/22.69  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.14/22.69  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.14/22.69  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.14/22.69  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 153.14/22.69  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.14/22.69  | | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 =
% 153.14/22.69  | | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) =
% 153.14/22.69  | | | |           e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.14/22.69  | | | |           all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 153.14/22.69  | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 153.14/22.69  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.14/22.69  | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.14/22.69  | | | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.14/22.69  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.69  | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.14/22.69  | | | |           $i(all_57_10))
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | | BETA: splitting (35) gives:
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | | Case 1:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | |   (36)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.14/22.69  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.14/22.69  | | | | |           & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.14/22.69  | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.14/22.69  | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.14/22.69  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.14/22.69  | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | REF_CLOSE: (9), (10), (13), (19), (26), (36) are inconsistent by
% 153.14/22.69  | | | | |            sub-proof #402.
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | Case 2:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | |   (37)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.14/22.69  | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.14/22.69  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.14/22.69  | | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.14/22.69  | | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.14/22.69  | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 153.14/22.69  | | | | |           = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 153.14/22.69  | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.14/22.69  | | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.14/22.69  | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | BETA: splitting (37) gives:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | Case 1:
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | |   (38)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.14/22.69  | | | | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.14/22.69  | | | | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.14/22.69  | | | | | |         $i(all_57_14)
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | ALPHA: (38) implies:
% 153.14/22.69  | | | | | |   (39)  op(e3, e3) = e2
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | REF_CLOSE: (10), (15), (26), (39) are inconsistent by sub-proof
% 153.14/22.69  | | | | | |            #1074.
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | Case 2:
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | |   (40)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.14/22.69  | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.14/22.69  | | | | | |           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.14/22.69  | | | | | |           $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.14/22.69  | | | | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3,
% 153.14/22.69  | | | | | |             e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.14/22.69  | | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | REF_CLOSE: (10), (13), (23), (26), (40) are inconsistent by
% 153.14/22.69  | | | | | |            sub-proof #401.
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | End of split
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | End of split
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | End of split
% 153.14/22.69  | | | 
% 153.14/22.69  | | Case 2:
% 153.14/22.69  | | | 
% 153.14/22.69  | | |   (41)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.69  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.69  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.69  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 153.14/22.69  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.14/22.69  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.14/22.69  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 153.14/22.69  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 153.14/22.69  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 153.14/22.69  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 153.14/22.69  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 153.14/22.69  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.14/22.69  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 153.14/22.69  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.14/22.69  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.69  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.14/22.69  | | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9
% 153.14/22.69  | | |             = e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.14/22.69  | | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.14/22.69  | | |           $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1
% 153.14/22.69  | | |           &  ~ (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.14/22.69  | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.14/22.69  | | |           & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 153.14/22.69  | | |           e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.14/22.69  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.14/22.69  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.14/22.69  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.14/22.69  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.14/22.69  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.14/22.69  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.14/22.69  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.14/22.69  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.69  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.14/22.69  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.14/22.69  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 153.14/22.69  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.14/22.69  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.14/22.69  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.14/22.69  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 153.14/22.69  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.69  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.69  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.14/22.69  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.14/22.69  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.14/22.69  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.14/22.69  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 153.14/22.69  | | | 
% 153.14/22.69  | | | BETA: splitting (41) gives:
% 153.14/22.69  | | | 
% 153.14/22.69  | | | Case 1:
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | |   (42)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.69  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.69  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.69  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.14/22.69  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.14/22.69  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.14/22.69  | | | |           e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.14/22.69  | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.14/22.69  | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.14/22.69  | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.14/22.69  | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.14/22.69  | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.69  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.14/22.69  | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.14/22.69  | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.14/22.69  | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.14/22.69  | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | | BETA: splitting (42) gives:
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | | Case 1:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | |   (43)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.69  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.14/22.69  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.69  | | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.14/22.69  | | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.14/22.69  | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 153.14/22.69  | | | | |           = e2 & $i(all_57_6) & $i(all_57_12))
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | BETA: splitting (43) gives:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | Case 1:
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | |   (44)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.69  | | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.14/22.69  | | | | | |         & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.69  | | | | | |         $i(all_57_10)
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | ALPHA: (44) implies:
% 153.14/22.69  | | | | | |   (45)   ~ (all_57_10 = e1)
% 153.14/22.69  | | | | | |   (46)  op(e3, e3) = all_57_10
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | REF_CLOSE: (10), (15), (45), (46) are inconsistent by sub-proof
% 153.14/22.69  | | | | | |            #893.
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | Case 2:
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | |   (47)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.14/22.69  | | | | | |         (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.14/22.69  | | | | | |         op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.14/22.69  | | | | | |         $i(all_57_12)
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | ALPHA: (47) implies:
% 153.14/22.69  | | | | | |   (48)   ~ (all_57_6 = e3)
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | REF_CLOSE: (10), (14), (15), (48) are inconsistent by sub-proof
% 153.14/22.69  | | | | | |            #456.
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | End of split
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | Case 2:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | |   (49)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.69  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 153.14/22.69  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.69  | | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 153.14/22.69  | | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 153.14/22.69  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 153.14/22.69  | | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 153.14/22.69  | | | | |           & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1)
% 153.14/22.69  | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 153.14/22.69  | | | | |           & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | BETA: splitting (49) gives:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | Case 1:
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | |   (50)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.69  | | | | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 153.14/22.69  | | | | | |         & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.69  | | | | | |         $i(all_57_12)
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | ALPHA: (50) implies:
% 153.14/22.69  | | | | | |   (51)   ~ (all_57_12 = e1)
% 153.14/22.69  | | | | | |   (52)  op(e2, e2) = all_57_12
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | REF_CLOSE: (5), (10), (51), (52) are inconsistent by sub-proof
% 153.14/22.69  | | | | | |            #1014.
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | Case 2:
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | |   (53)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.14/22.69  | | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 153.14/22.69  | | | | | |           e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.14/22.69  | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.14/22.69  | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1)
% 153.14/22.69  | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 153.14/22.69  | | | | | |           e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.14/22.69  | | | | | |           $i(all_57_13))
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | REF_CLOSE: (5), (10), (19), (21), (53) are inconsistent by sub-proof
% 153.14/22.69  | | | | | |            #765.
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | End of split
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | End of split
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | Case 2:
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | |   (54)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.14/22.69  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.69  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.14/22.69  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.14/22.69  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.14/22.69  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.14/22.69  | | | |           e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 153.14/22.69  | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 153.14/22.69  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.14/22.69  | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 153.14/22.69  | | | |         (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.14/22.69  | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.14/22.69  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.14/22.69  | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.14/22.69  | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.14/22.69  | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 153.14/22.69  | | | |               & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.14/22.69  | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 153.14/22.69  | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 153.14/22.69  | | | |               e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.14/22.69  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.14/22.69  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.14/22.69  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.14/22.69  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.14/22.69  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.14/22.69  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.14/22.69  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.14/22.69  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.69  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.14/22.69  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | | BETA: splitting (54) gives:
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | | Case 1:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | |   (55)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.14/22.69  | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.69  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.14/22.69  | | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.14/22.69  | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.14/22.69  | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.14/22.69  | | | | |           = e1 & $i(all_57_9) & $i(all_57_14))
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | REF_CLOSE: (10), (15), (21), (55) are inconsistent by sub-proof #956.
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | Case 2:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | |   (56)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.14/22.69  | | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.14/22.69  | | | | |           & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.14/22.69  | | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 153.14/22.69  | | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.14/22.69  | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.14/22.69  | | | | |           = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.14/22.69  | | | | |           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 153.14/22.69  | | | | |               &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3)
% 153.14/22.69  | | | | |               = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.69  | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.14/22.69  | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.14/22.69  | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.14/22.69  | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.14/22.69  | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.14/22.69  | | | | |               & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.14/22.69  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.14/22.69  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.14/22.69  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.69  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.69  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.14/22.69  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.14/22.69  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.69  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.14/22.69  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.69  | | | | |               $i(all_57_7))))
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | BETA: splitting (56) gives:
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | | Case 1:
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | |   (57)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.14/22.69  | | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.14/22.69  | | | | | |         & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.14/22.69  | | | | | |         $i(all_57_13)
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | ALPHA: (57) implies:
% 153.14/22.69  | | | | | |   (58)  op(e2, e0) = e2
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | REF_CLOSE: (8), (10), (16), (20), (30), (58) are inconsistent by
% 153.14/22.69  | | | | | |            sub-proof #400.
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | Case 2:
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | |   (59)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.14/22.69  | | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.14/22.69  | | | | | |           all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.14/22.69  | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.14/22.69  | | | | | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 153.14/22.69  | | | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.14/22.69  | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.69  | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.14/22.69  | | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.14/22.69  | | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.14/22.69  | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.14/22.69  | | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.14/22.69  | | | | | |               e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.14/22.69  | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.14/22.69  | | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.14/22.69  | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.69  | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.69  | | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.14/22.69  | | | | | |               e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.14/22.69  | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.69  | | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 153.14/22.69  | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.69  | | | | | |               $i(all_57_7))))
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | BETA: splitting (59) gives:
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | | Case 1:
% 153.14/22.69  | | | | | | | 
% 153.14/22.69  | | | | | | |   (60)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.14/22.69  | | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.14/22.69  | | | | | | |         all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.14/22.69  | | | | | | |         $i(all_57_11) & $i(all_57_14)
% 153.14/22.69  | | | | | | | 
% 153.14/22.69  | | | | | | | ALPHA: (60) implies:
% 153.14/22.69  | | | | | | |   (61)  op(e1, e0) = e1
% 153.14/22.69  | | | | | | | 
% 153.14/22.69  | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11),
% 153.14/22.69  | | | | | | |            (12), (15), (17), (18), (22), (24), (26), (27), (28),
% 153.14/22.69  | | | | | | |            (61) are inconsistent by sub-proof #757.
% 153.14/22.69  | | | | | | | 
% 153.14/22.69  | | | | | | Case 2:
% 153.14/22.69  | | | | | | | 
% 153.14/22.69  | | | | | | |   (62)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.14/22.69  | | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.14/22.69  | | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.14/22.69  | | | | | | |             op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.14/22.69  | | | | | | |             all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.14/22.69  | | | | | | |               e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.14/22.69  | | | | | | |             op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 153.14/22.69  | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 153.14/22.69  | | | | | | |               e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.14/22.69  | | | | | | |             op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.14/22.69  | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.14/22.69  | | | | | | |               e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.14/22.69  | | | | | | |             op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.14/22.69  | | | | | | |             all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.14/22.69  | | | | | | |               e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.14/22.69  | | | | | | |             op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.14/22.69  | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.14/22.69  | | | | | | |               e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.14/22.69  | | | | | | |             op(e0, e1) = e0 & $i(all_57_7)))
% 153.14/22.69  | | | | | | | 
% 153.14/22.69  | | | | | | | ALPHA: (62) implies:
% 153.14/22.69  | | | | | | |   (63)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.14/22.69  | | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 153.14/22.69  | | | | | | |           e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.14/22.69  | | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.14/22.69  | | | | | | |             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.14/22.69  | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.14/22.69  | | | | | | |           = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 153.14/22.69  | | | | | | |             e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.14/22.69  | | | | | | |           $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.14/22.69  | | | | | | |           (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.14/22.69  | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.69  | | | | | | |           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.69  | | | | | | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.14/22.69  | | | | | | |           & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.14/22.69  | | | | | | |           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.69  | | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.14/22.69  | | | | | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.69  | | | | | | |           $i(all_57_7))
% 153.14/22.69  | | | | | | | 
% 153.14/22.69  | | | | | | | REF_CLOSE: (2), (5), (9), (10), (14), (15), (19), (23), (26), (63)
% 153.14/22.69  | | | | | | |            are inconsistent by sub-proof #399.
% 153.14/22.69  | | | | | | | 
% 153.14/22.69  | | | | | | End of split
% 153.14/22.69  | | | | | | 
% 153.14/22.69  | | | | | End of split
% 153.14/22.69  | | | | | 
% 153.14/22.69  | | | | End of split
% 153.14/22.69  | | | | 
% 153.14/22.69  | | | End of split
% 153.14/22.69  | | | 
% 153.14/22.69  | | End of split
% 153.14/22.69  | | 
% 153.14/22.69  | Case 2:
% 153.14/22.69  | | 
% 153.14/22.69  | |   (64)   ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12)
% 153.14/22.69  | | 
% 153.14/22.69  | | ALPHA: (64) implies:
% 153.14/22.69  | |   (65)   ~ (all_57_12 = e1)
% 153.14/22.69  | |   (66)  op(e2, e2) = all_57_12
% 153.14/22.69  | | 
% 153.14/22.69  | | REF_CLOSE: (5), (10), (65), (66) are inconsistent by sub-proof #1014.
% 153.14/22.69  | | 
% 153.14/22.69  | End of split
% 153.14/22.69  | 
% 153.14/22.69  End of proof
% 153.14/22.69  
% 153.14/22.69  Sub-proof #399 shows that the following formulas are inconsistent:
% 153.14/22.69  ----------------------------------------------------------------
% 153.14/22.69    (1)   ~ (e3 = e1)
% 153.14/22.69    (2)  op(e2, e2) = e1
% 153.14/22.69    (3)  op(e1, e1) = all_4_2
% 153.14/22.69    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.69           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.69    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.14/22.69             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.69           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.14/22.69           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.14/22.69             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.14/22.69           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.69           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.14/22.69           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.14/22.69           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.14/22.69           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 153.14/22.69           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.14/22.69         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.14/22.69             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.69           $i(all_57_7))
% 153.14/22.69    (6)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.14/22.69           all_57_10 & $i(all_57_10))
% 153.14/22.69    (7)  op(e3, e3) = e1
% 153.14/22.69    (8)  op(e1, e1) = e1
% 153.14/22.69    (9)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.14/22.69           all_57_12 & $i(all_57_12))
% 153.14/22.69    (10)   ~ (e2 = e1)
% 153.14/22.69  
% 153.14/22.69  Begin of proof
% 153.14/22.69  | 
% 153.14/22.69  | BETA: splitting (5) gives:
% 153.14/22.69  | 
% 153.14/22.69  | Case 1:
% 153.14/22.69  | | 
% 153.14/22.69  | |   (11)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 153.14/22.69  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.14/22.69  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.14/22.69  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.14/22.69  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.14/22.69  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.14/22.69  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.14/22.69  | |           $i(all_57_3))
% 153.14/22.69  | | 
% 153.14/22.69  | | BETA: splitting (11) gives:
% 153.14/22.69  | | 
% 153.14/22.69  | | Case 1:
% 153.14/22.69  | | | 
% 153.14/22.69  | | |   (12)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.14/22.69  | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.14/22.69  | | |         op(e0, e3) = e0 & $i(all_57_0)
% 153.14/22.69  | | | 
% 153.14/22.69  | | | ALPHA: (12) implies:
% 153.14/22.69  | | |   (13)  op(e2, e2) = e3
% 153.14/22.69  | | | 
% 153.14/22.69  | | | REF_CLOSE: (1), (2), (4), (13) are inconsistent by sub-proof #1136.
% 153.14/22.69  | | | 
% 153.14/22.69  | | Case 2:
% 153.14/22.69  | | | 
% 153.14/22.70  | | |   (14)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.14/22.70  | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.14/22.70  | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 153.14/22.70  | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.14/22.70  | | |           & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.14/22.70  | | | 
% 153.14/22.70  | | | BETA: splitting (14) gives:
% 153.14/22.70  | | | 
% 153.14/22.70  | | | Case 1:
% 153.14/22.70  | | | | 
% 153.14/22.70  | | | |   (15)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.14/22.70  | | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.14/22.70  | | | |         op(e0, e3) = e0 & $i(all_57_1)
% 153.14/22.70  | | | | 
% 153.14/22.70  | | | | ALPHA: (15) implies:
% 153.14/22.70  | | | |   (16)  op(e1, e1) = e3
% 153.14/22.70  | | | | 
% 153.14/22.70  | | | | REF_CLOSE: (1), (4), (8), (16) are inconsistent by sub-proof #734.
% 153.14/22.70  | | | | 
% 153.14/22.70  | | | Case 2:
% 153.14/22.70  | | | | 
% 153.14/22.70  | | | |   (17)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.14/22.70  | | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.14/22.70  | | | |         op(e0, e2) = e0 & $i(all_57_3)
% 153.14/22.70  | | | | 
% 153.14/22.70  | | | | ALPHA: (17) implies:
% 153.14/22.70  | | | |   (18)  op(e3, e3) = e2
% 153.14/22.70  | | | | 
% 153.14/22.70  | | | | REF_CLOSE: (4), (7), (10), (18) are inconsistent by sub-proof #1074.
% 153.14/22.70  | | | | 
% 153.14/22.70  | | | End of split
% 153.14/22.70  | | | 
% 153.14/22.70  | | End of split
% 153.14/22.70  | | 
% 153.14/22.70  | Case 2:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (19)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.14/22.70  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.14/22.70  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.70  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.14/22.70  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.14/22.70  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.14/22.70  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.70  | |           $i(all_57_7))
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (3), (4), (6), (8), (9), (10), (19) are inconsistent by sub-proof
% 153.14/22.70  | |            #454.
% 153.14/22.70  | | 
% 153.14/22.70  | End of split
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #400 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)   ~ (all_52_9 = all_52_13)
% 153.14/22.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (3)  op(e2, e0) = e2
% 153.14/22.70    (4)  op(e2, e1) = e2
% 153.14/22.70    (5)  op(e2, e0) = all_52_13
% 153.14/22.70    (6)  op(e2, e1) = all_52_9
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | GROUND_INST: instantiating (2) with all_52_13, e2, e0, e2, simplifying with
% 153.14/22.70  |              (3), (5) gives:
% 153.14/22.70  |   (7)  all_52_13 = e2
% 153.14/22.70  | 
% 153.14/22.70  | GROUND_INST: instantiating (2) with all_52_9, e2, e1, e2, simplifying with
% 153.14/22.70  |              (4), (6) gives:
% 153.14/22.70  |   (8)  all_52_9 = e2
% 153.14/22.70  | 
% 153.14/22.70  | REDUCE: (1), (7), (8) imply:
% 153.14/22.70  |   (9)  $false
% 153.14/22.70  | 
% 153.14/22.70  | CLOSE: (9) is inconsistent.
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #401 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (2)  op(e0, e0) = e1
% 153.14/22.70    (3)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.14/22.70           all_57_12 & $i(all_57_12))
% 153.14/22.70    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.14/22.70             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.14/22.70           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.14/22.70           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.14/22.70           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 153.14/22.70           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.14/22.70    (5)   ~ (e2 = e1)
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | BETA: splitting (4) gives:
% 153.14/22.70  | 
% 153.14/22.70  | Case 1:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (6)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.14/22.70  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.14/22.70  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (6) implies:
% 153.14/22.70  | |   (7)  op(e0, e0) = e2
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #978.
% 153.14/22.70  | | 
% 153.14/22.70  | Case 2:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (8)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.14/22.70  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.14/22.70  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (8) implies:
% 153.14/22.70  | |   (9)   ~ (all_57_7 = e2)
% 153.14/22.70  | |   (10)  op(e2, e2) = e1
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (1), (3), (9), (10) are inconsistent by sub-proof #713.
% 153.14/22.70  | | 
% 153.14/22.70  | End of split
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #402 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)  op(e1, e1) = all_4_2
% 153.14/22.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (3)  op(e0, e0) = e1
% 153.14/22.70    (4)  op(e1, e1) = e1
% 153.14/22.70    (5)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.14/22.70             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.14/22.70           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 153.14/22.70           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.14/22.70           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.14/22.70           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.14/22.70    (6)   ~ (e2 = e1)
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | BETA: splitting (5) gives:
% 153.14/22.70  | 
% 153.14/22.70  | Case 1:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (7)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.14/22.70  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.14/22.70  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (7) implies:
% 153.14/22.70  | |   (8)  op(e1, e1) = e2
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (1), (2), (4), (6), (8) are inconsistent by sub-proof #1044.
% 153.14/22.70  | | 
% 153.14/22.70  | Case 2:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (9)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 153.14/22.70  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.14/22.70  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (9) implies:
% 153.14/22.70  | |   (10)  op(e0, e0) = e2
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #978.
% 153.14/22.70  | | 
% 153.14/22.70  | End of split
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #403 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)   ~ (e3 = e1)
% 153.14/22.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (3)  op(e0, e0) = e1
% 153.14/22.70    (4)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.14/22.70             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.14/22.70           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 153.14/22.70           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 153.14/22.70             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 153.14/22.70             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.14/22.70    (5)   ~ (all_52_2 = e1)
% 153.14/22.70    (6)  op(e1, e3) = all_52_2
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | BETA: splitting (4) gives:
% 153.14/22.70  | 
% 153.14/22.70  | Case 1:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (7)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.14/22.70  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.14/22.70  | |        op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (7) implies:
% 153.14/22.70  | |   (8)  op(e1, e3) = e1
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #1046.
% 153.14/22.70  | | 
% 153.14/22.70  | Case 2:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (9)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 153.14/22.70  | |          e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.14/22.70  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (9) implies:
% 153.14/22.70  | |   (10)  op(e0, e0) = e3
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #1022.
% 153.14/22.70  | | 
% 153.14/22.70  | End of split
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #404 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)   ~ (e3 = e1)
% 153.14/22.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (3)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.14/22.70             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.70           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.14/22.70           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.14/22.70           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.14/22.70           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.14/22.70    (4)  op(e0, e0) = e1
% 153.14/22.70    (5)  op(e1, e1) = e1
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | BETA: splitting (3) gives:
% 153.14/22.70  | 
% 153.14/22.70  | Case 1:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (6)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.14/22.70  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.70  | |        all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (6) implies:
% 153.14/22.70  | |   (7)  op(e1, e1) = e3
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #734.
% 153.14/22.70  | | 
% 153.14/22.70  | Case 2:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (8)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 153.14/22.70  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.14/22.70  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (8) implies:
% 153.14/22.70  | |   (9)  op(e0, e0) = e3
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #1022.
% 153.14/22.70  | | 
% 153.14/22.70  | End of split
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #405 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (2)  op(e0, e3) = all_52_3
% 153.14/22.70    (3)  op(e0, e3) = e1
% 153.14/22.70    (4)   ~ (all_52_3 = e1)
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | GROUND_INST: instantiating (1) with all_52_3, e1, e3, e0, simplifying with
% 153.14/22.70  |              (2), (3) gives:
% 153.14/22.70  |   (5)  all_52_3 = e1
% 153.14/22.70  | 
% 153.14/22.70  | REDUCE: (4), (5) imply:
% 153.14/22.70  |   (6)  $false
% 153.14/22.70  | 
% 153.14/22.70  | CLOSE: (6) is inconsistent.
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #406 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (2)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.14/22.70             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.70           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.14/22.70           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.14/22.70             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.14/22.70           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.70           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.14/22.70    (3)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 153.14/22.70           all_57_14 & $i(all_57_14))
% 153.14/22.70    (4)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 153.14/22.70           all_57_12 & $i(all_57_12))
% 153.14/22.70    (5)   ~ (e3 = e2)
% 153.14/22.70    (6)  op(e3, e3) = e3
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | BETA: splitting (2) gives:
% 153.14/22.70  | 
% 153.14/22.70  | Case 1:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (7)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.14/22.70  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.70  | |        $i(all_57_0)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (7) implies:
% 153.14/22.70  | |   (8)  all_57_12 = e3
% 153.14/22.70  | |   (9)   ~ (all_57_0 = e2)
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (4), (8), (9) are inconsistent by sub-proof #832.
% 153.14/22.70  | | 
% 153.14/22.70  | Case 2:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (10)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 153.14/22.70  | |             = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 153.14/22.70  | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.14/22.70  | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 153.14/22.70  | |             e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.14/22.70  | | 
% 153.14/22.70  | | BETA: splitting (10) gives:
% 153.14/22.70  | | 
% 153.14/22.70  | | Case 1:
% 153.14/22.70  | | | 
% 153.14/22.70  | | |   (11)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.14/22.70  | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.14/22.70  | | |         op(e0, e3) = e0 & $i(all_57_1)
% 153.14/22.70  | | | 
% 153.14/22.70  | | | ALPHA: (11) implies:
% 153.14/22.70  | | |   (12)   ~ (all_57_1 = e1)
% 153.14/22.70  | | |   (13)  op(e1, e1) = e3
% 153.14/22.70  | | | 
% 153.14/22.70  | | | REF_CLOSE: (1), (3), (12), (13) are inconsistent by sub-proof #815.
% 153.14/22.70  | | | 
% 153.14/22.70  | | Case 2:
% 153.14/22.70  | | | 
% 153.14/22.70  | | |   (14)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.14/22.70  | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.14/22.70  | | |         op(e0, e2) = e0 & $i(all_57_3)
% 153.14/22.70  | | | 
% 153.14/22.70  | | | ALPHA: (14) implies:
% 153.14/22.70  | | |   (15)  op(e3, e3) = e2
% 153.14/22.70  | | | 
% 153.14/22.70  | | | REF_CLOSE: (1), (5), (6), (15) are inconsistent by sub-proof #1085.
% 153.14/22.70  | | | 
% 153.14/22.70  | | End of split
% 153.14/22.70  | | 
% 153.14/22.70  | End of split
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #407 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)   ~ (e3 = e1)
% 153.14/22.70    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.14/22.70         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.14/22.70    (3)   ~ (e2 = e0)
% 153.14/22.70    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (5)   ~ (e3 = e0)
% 153.14/22.70    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.14/22.70         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.14/22.70    (7)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.14/22.70         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.14/22.70    (8)   ~ (e1 = e0)
% 153.14/22.70    (9)   ~ (all_52_1 = e1)
% 153.14/22.70    (10)   ~ (e3 = e2)
% 153.14/22.70    (11)  op(e3, e3) = e3
% 153.14/22.70    (12)   ~ (e2 = e1)
% 153.14/22.70    (13)  all_56_12 = e3
% 153.14/22.70    (14)  op(e1, e3) = all_52_2
% 153.14/22.70    (15)  op(e2, e3) = all_52_1
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | BETA: splitting (2) gives:
% 153.14/22.70  | 
% 153.14/22.70  | Case 1:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (16)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 153.14/22.70  | |           e1)
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (1), (4), (9), (11), (15), (16) are inconsistent by sub-proof
% 153.14/22.70  | |            #1176.
% 153.14/22.70  | | 
% 153.14/22.70  | Case 2:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (17)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 153.14/22.70  | |           e1)
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13), (14),
% 153.14/22.70  | |            (17) are inconsistent by sub-proof #991.
% 153.14/22.70  | | 
% 153.14/22.70  | End of split
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #408 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)  all_56_13 = e3 & op(e0, e2) = e3
% 153.14/22.70    (2)  all_56_13 = e0
% 153.14/22.70    (3)   ~ (e3 = e0)
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | ALPHA: (1) implies:
% 153.14/22.70  |   (4)  all_56_13 = e3
% 153.14/22.70  | 
% 153.14/22.70  | COMBINE_EQS: (2), (4) imply:
% 153.14/22.70  |   (5)  e3 = e0
% 153.14/22.70  | 
% 153.14/22.70  | REDUCE: (3), (5) imply:
% 153.14/22.70  |   (6)  $false
% 153.14/22.70  | 
% 153.14/22.70  | CLOSE: (6) is inconsistent.
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #409 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)  all_56_15 = e0 & op(e0, e0) = e0
% 153.14/22.70    (2)  all_56_15 = e1
% 153.14/22.70    (3)   ~ (e1 = e0)
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | ALPHA: (1) implies:
% 153.14/22.70  |   (4)  all_56_15 = e0
% 153.14/22.70  | 
% 153.14/22.70  | COMBINE_EQS: (2), (4) imply:
% 153.14/22.70  |   (5)  e1 = e0
% 153.14/22.70  | 
% 153.14/22.70  | REDUCE: (3), (5) imply:
% 153.14/22.70  |   (6)  $false
% 153.14/22.70  | 
% 153.14/22.70  | CLOSE: (6) is inconsistent.
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #410 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 153.14/22.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (3)   ~ (e3 = e2)
% 153.14/22.70    (4)  op(e3, e3) = e3
% 153.14/22.70    (5)  op(e2, e3) = all_52_1
% 153.14/22.70    (6)   ~ (all_52_1 = e2)
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | BETA: splitting (1) gives:
% 153.14/22.70  | 
% 153.14/22.70  | Case 1:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (7) implies:
% 153.14/22.70  | |   (8)  op(e3, e3) = e2
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1085.
% 153.14/22.70  | | 
% 153.14/22.70  | Case 2:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (9)  all_56_2 = e2 & op(e2, e3) = e2
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (9) implies:
% 153.14/22.70  | |   (10)  op(e2, e3) = e2
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1181.
% 153.14/22.70  | | 
% 153.14/22.70  | End of split
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #411 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)   ~ (e3 = e1)
% 153.14/22.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (3)  op(e0, e0) = e1
% 153.14/22.70    (4)  op(e3, e1) = e1
% 153.14/22.70    (5)   ~ (e3 = e2)
% 153.14/22.70    (6)  op(e3, e1) = all_52_8
% 153.14/22.70    (7)  op(e3, e3) = e3
% 153.14/22.70    (8)   ~ (e2 = e1)
% 153.14/22.70    (9)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.14/22.70             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.14/22.70           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 153.14/22.70           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 153.14/22.70             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.14/22.70             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.14/22.70           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.14/22.70           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.14/22.70           $i(all_57_7) & $i(all_57_10))
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | BETA: splitting (9) gives:
% 153.14/22.70  | 
% 153.14/22.70  | Case 1:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (10)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 153.14/22.70  | |           = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1
% 153.14/22.70  | |         & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (10) implies:
% 153.14/22.70  | |   (11)  op(e3, e3) = e2
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (2), (5), (7), (11) are inconsistent by sub-proof #1085.
% 153.14/22.70  | | 
% 153.14/22.70  | Case 2:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (12)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.14/22.70  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.14/22.70  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.14/22.70  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.14/22.70  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.14/22.70  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.14/22.70  | | 
% 153.14/22.70  | | BETA: splitting (12) gives:
% 153.14/22.70  | | 
% 153.14/22.70  | | Case 1:
% 153.14/22.70  | | | 
% 153.14/22.70  | | |   (13)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.14/22.70  | | |         (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.70  | | |         op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.14/22.70  | | |         $i(all_57_14)
% 153.14/22.70  | | | 
% 153.14/22.70  | | | ALPHA: (13) implies:
% 153.14/22.70  | | |   (14)  op(e0, e0) = e2
% 153.14/22.70  | | | 
% 153.14/22.70  | | | REF_CLOSE: (2), (3), (8), (14) are inconsistent by sub-proof #978.
% 153.14/22.70  | | | 
% 153.14/22.70  | | Case 2:
% 153.14/22.70  | | | 
% 153.14/22.70  | | |   (15)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.14/22.70  | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.70  | | |         op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.14/22.70  | | |         $i(all_57_10)
% 153.14/22.70  | | | 
% 153.14/22.70  | | | ALPHA: (15) implies:
% 153.14/22.70  | | |   (16)  op(e3, e1) = e3
% 153.14/22.70  | | | 
% 153.14/22.70  | | | REF_CLOSE: (1), (2), (4), (6), (16) are inconsistent by sub-proof #439.
% 153.14/22.70  | | | 
% 153.14/22.70  | | End of split
% 153.14/22.70  | | 
% 153.14/22.70  | End of split
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #412 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)  op(e3, e2) = all_52_4
% 153.14/22.70    (2)   ~ (e2 = e0)
% 153.14/22.70    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (4)  op(e1, e1) = e0
% 153.14/22.70    (5)   ~ (all_52_4 = e3)
% 153.14/22.70    (6)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.14/22.70             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.14/22.70           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 153.14/22.70           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.14/22.70           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.14/22.70           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | BETA: splitting (6) gives:
% 153.14/22.70  | 
% 153.14/22.70  | Case 1:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (7)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.14/22.70  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.14/22.70  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (7) implies:
% 153.14/22.70  | |   (8)  op(e1, e1) = e2
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1006.
% 153.14/22.70  | | 
% 153.14/22.70  | Case 2:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (9)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 153.14/22.70  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.14/22.70  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (9) implies:
% 153.14/22.70  | |   (10)  op(e3, e2) = e3
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #1166.
% 153.14/22.70  | | 
% 153.14/22.70  | End of split
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #413 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (2)  op(e3, e3) = all_14_2
% 153.14/22.70    (3)  op(e3, e3) = e1
% 153.14/22.70    (4)   ~ (all_14_2 = e1)
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | GROUND_INST: instantiating (1) with all_14_2, e1, e3, e3, simplifying with
% 153.14/22.70  |              (2), (3) gives:
% 153.14/22.70  |   (5)  all_14_2 = e1
% 153.14/22.70  | 
% 153.14/22.70  | REDUCE: (4), (5) imply:
% 153.14/22.70  |   (6)  $false
% 153.14/22.70  | 
% 153.14/22.70  | CLOSE: (6) is inconsistent.
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #414 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)  all_56_13 = e1 & op(e0, e2) = e1
% 153.14/22.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (3)  op(e0, e2) = all_52_7
% 153.14/22.70    (4)   ~ (all_52_7 = e1)
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | ALPHA: (1) implies:
% 153.14/22.70  |   (5)  op(e0, e2) = e1
% 153.14/22.70  | 
% 153.14/22.70  | GROUND_INST: instantiating (2) with all_52_7, e1, e2, e0, simplifying with
% 153.14/22.70  |              (3), (5) gives:
% 153.14/22.70  |   (6)  all_52_7 = e1
% 153.14/22.70  | 
% 153.14/22.70  | REDUCE: (4), (6) imply:
% 153.14/22.70  |   (7)  $false
% 153.14/22.70  | 
% 153.14/22.70  | CLOSE: (7) is inconsistent.
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #415 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.14/22.70             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.14/22.70           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 153.14/22.70           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 153.14/22.70             e1) = e0 & $i(all_57_7))
% 153.14/22.70    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.70    (3)  op(e0, e0) = e1
% 153.14/22.70    (4)  op(e2, e2) = e2
% 153.14/22.70    (5)  op(e0, e0) = all_57_15
% 153.14/22.70    (6)   ~ (e2 = e1)
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | BETA: splitting (1) gives:
% 153.14/22.70  | 
% 153.14/22.70  | Case 1:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (7)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.14/22.70  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.14/22.70  | |        $i(all_57_6)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (7) implies:
% 153.14/22.70  | |   (8)   ~ (all_57_15 = e1)
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #940.
% 153.14/22.70  | | 
% 153.14/22.70  | Case 2:
% 153.14/22.70  | | 
% 153.14/22.70  | |   (9)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.14/22.70  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.70  | |        $i(all_57_7)
% 153.14/22.70  | | 
% 153.14/22.70  | | ALPHA: (9) implies:
% 153.14/22.70  | |   (10)  op(e2, e2) = e1
% 153.14/22.70  | | 
% 153.14/22.70  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #1158.
% 153.14/22.70  | | 
% 153.14/22.70  | End of split
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #416 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)  all_56_5 = e3
% 153.14/22.70    (2)  all_56_5 = e1
% 153.14/22.70    (3)   ~ (e3 = e1)
% 153.14/22.70  
% 153.14/22.70  Begin of proof
% 153.14/22.70  | 
% 153.14/22.70  | COMBINE_EQS: (1), (2) imply:
% 153.14/22.70  |   (4)  e3 = e1
% 153.14/22.70  | 
% 153.14/22.70  | SIMP: (4) implies:
% 153.14/22.70  |   (5)  e3 = e1
% 153.14/22.70  | 
% 153.14/22.70  | REDUCE: (3), (5) imply:
% 153.14/22.70  |   (6)  $false
% 153.14/22.70  | 
% 153.14/22.70  | CLOSE: (6) is inconsistent.
% 153.14/22.70  | 
% 153.14/22.70  End of proof
% 153.14/22.70  
% 153.14/22.70  Sub-proof #417 shows that the following formulas are inconsistent:
% 153.14/22.70  ----------------------------------------------------------------
% 153.14/22.70    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.70           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.71    (2)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.14/22.71             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.14/22.71           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.14/22.71           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.14/22.71           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.14/22.71           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 153.14/22.71    (3)  op(e3, e3) = e1
% 153.14/22.71    (4)   ~ (all_52_9 = e2)
% 153.14/22.71    (5)  op(e2, e1) = all_52_9
% 153.14/22.71  
% 153.14/22.71  Begin of proof
% 153.14/22.71  | 
% 153.14/22.71  | BETA: splitting (2) gives:
% 153.14/22.71  | 
% 153.14/22.71  | Case 1:
% 153.14/22.71  | | 
% 153.14/22.71  | |   (6)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.14/22.71  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.14/22.71  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 153.14/22.71  | | 
% 153.14/22.71  | | ALPHA: (6) implies:
% 153.14/22.71  | |   (7)   ~ (all_57_10 = e1)
% 153.14/22.71  | |   (8)  op(e3, e3) = all_57_10
% 153.14/22.71  | | 
% 153.14/22.71  | | REF_CLOSE: (1), (3), (7), (8) are inconsistent by sub-proof #893.
% 153.14/22.71  | | 
% 153.14/22.71  | Case 2:
% 153.14/22.71  | | 
% 153.14/22.71  | |   (9)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 153.14/22.71  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.14/22.71  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 153.14/22.71  | | 
% 153.14/22.71  | | ALPHA: (9) implies:
% 153.14/22.71  | |   (10)  op(e2, e1) = e2
% 153.14/22.71  | | 
% 153.14/22.71  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #1157.
% 153.14/22.71  | | 
% 153.14/22.71  | End of split
% 153.14/22.71  | 
% 153.14/22.71  End of proof
% 153.14/22.71  
% 153.14/22.71  Sub-proof #418 shows that the following formulas are inconsistent:
% 153.14/22.71  ----------------------------------------------------------------
% 153.14/22.71    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.71    (2)  op(e0, e0) = e1
% 153.14/22.71    (3)  op(e3, e3) = e1
% 153.14/22.71    (4)  op(e2, e2) = e2
% 153.14/22.71    (5)   ~ (e2 = e1)
% 153.14/22.71    (6)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.14/22.71             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.14/22.71           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 153.14/22.71           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 153.14/22.71             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.14/22.71             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.14/22.71           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.14/22.71           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.14/22.71           $i(all_57_7) & $i(all_57_10))
% 153.14/22.71  
% 153.14/22.71  Begin of proof
% 153.14/22.71  | 
% 153.14/22.71  | BETA: splitting (6) gives:
% 153.14/22.71  | 
% 153.14/22.71  | Case 1:
% 153.14/22.71  | | 
% 153.14/22.71  | |   (7)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.14/22.71  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.14/22.71  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 153.14/22.71  | | 
% 153.14/22.71  | | ALPHA: (7) implies:
% 153.14/22.71  | |   (8)  op(e3, e3) = e2
% 153.14/22.71  | | 
% 153.14/22.71  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1074.
% 153.14/22.71  | | 
% 153.14/22.71  | Case 2:
% 153.14/22.71  | | 
% 153.14/22.71  | |   (9)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.14/22.71  | |            = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.14/22.71  | |          all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.14/22.71  | |        (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.14/22.71  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.14/22.71  | |          e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.14/22.71  | | 
% 153.14/22.71  | | REF_CLOSE: (1), (2), (4), (5), (9) are inconsistent by sub-proof #441.
% 153.14/22.71  | | 
% 153.14/22.71  | End of split
% 153.14/22.71  | 
% 153.14/22.71  End of proof
% 153.14/22.71  
% 153.14/22.71  Sub-proof #419 shows that the following formulas are inconsistent:
% 153.14/22.71  ----------------------------------------------------------------
% 153.14/22.71    (1)   ~ (e3 = e1)
% 153.14/22.71    (2)   ~ (all_52_2 = all_52_6)
% 153.14/22.71    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.71    (4)  op(e0, e0) = e1
% 153.14/22.71    (5)  op(e1, e2) = all_52_6
% 153.14/22.71    (6)  op(e1, e2) = e1
% 153.14/22.71    (7)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.14/22.71             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.71           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.14/22.71           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.14/22.71           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.14/22.71           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.71           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.14/22.71           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.14/22.71           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.14/22.71           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 153.14/22.71           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.14/22.71           $i(all_57_14))
% 153.14/22.71    (8)  op(e1, e3) = all_52_2
% 153.14/22.71    (9)  op(e2, e3) = all_52_1
% 153.14/22.71    (10)   ~ (all_52_1 = e2)
% 153.14/22.71  
% 153.14/22.71  Begin of proof
% 153.14/22.71  | 
% 153.14/22.71  | BETA: splitting (7) gives:
% 153.14/22.71  | 
% 153.14/22.71  | Case 1:
% 153.14/22.71  | | 
% 153.14/22.71  | |   (11)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 153.14/22.71  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.71  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 153.14/22.71  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 153.14/22.71  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.14/22.71  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.14/22.71  | | 
% 153.14/22.71  | | REF_CLOSE: (3), (9), (10), (11) are inconsistent by sub-proof #1180.
% 153.14/22.71  | | 
% 153.14/22.71  | Case 2:
% 153.14/22.71  | | 
% 153.14/22.71  | |   (12)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 153.14/22.71  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 153.14/22.71  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.14/22.71  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 153.14/22.71  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.14/22.71  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.14/22.71  | | 
% 153.14/22.71  | | BETA: splitting (12) gives:
% 153.14/22.71  | | 
% 153.14/22.71  | | Case 1:
% 153.14/22.71  | | | 
% 153.14/22.71  | | |   (13)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.14/22.71  | | |         (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.14/22.71  | | |         op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.14/22.71  | | |         $i(all_57_14)
% 153.14/22.71  | | | 
% 153.14/22.71  | | | ALPHA: (13) implies:
% 153.14/22.71  | | |   (14)  op(e1, e3) = e1
% 153.14/22.71  | | | 
% 153.14/22.71  | | | REF_CLOSE: (2), (3), (5), (6), (8), (14) are inconsistent by sub-proof
% 153.14/22.71  | | |            #911.
% 153.14/22.71  | | | 
% 153.14/22.71  | | Case 2:
% 153.14/22.71  | | | 
% 153.14/22.71  | | |   (15)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.14/22.71  | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.71  | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.14/22.71  | | |         $i(all_57_14)
% 153.14/22.71  | | | 
% 153.14/22.71  | | | ALPHA: (15) implies:
% 153.14/22.71  | | |   (16)  op(e0, e0) = e3
% 153.14/22.71  | | | 
% 153.14/22.71  | | | REF_CLOSE: (1), (3), (4), (16) are inconsistent by sub-proof #1022.
% 153.14/22.71  | | | 
% 153.14/22.71  | | End of split
% 153.14/22.71  | | 
% 153.14/22.71  | End of split
% 153.14/22.71  | 
% 153.14/22.71  End of proof
% 153.14/22.71  
% 153.14/22.71  Sub-proof #420 shows that the following formulas are inconsistent:
% 153.14/22.71  ----------------------------------------------------------------
% 153.14/22.71    (1)  all_56_1 = e1 & op(e3, e2) = e1
% 153.14/22.71    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.71    (3)  op(e3, e2) = all_52_4
% 153.14/22.71    (4)   ~ (all_52_4 = e1)
% 153.14/22.71  
% 153.14/22.71  Begin of proof
% 153.14/22.71  | 
% 153.14/22.71  | ALPHA: (1) implies:
% 153.14/22.71  |   (5)  op(e3, e2) = e1
% 153.14/22.71  | 
% 153.14/22.71  | GROUND_INST: instantiating (2) with all_52_4, e1, e2, e3, simplifying with
% 153.14/22.71  |              (3), (5) gives:
% 153.14/22.71  |   (6)  all_52_4 = e1
% 153.14/22.71  | 
% 153.14/22.71  | REDUCE: (4), (6) imply:
% 153.14/22.71  |   (7)  $false
% 153.14/22.71  | 
% 153.14/22.71  | CLOSE: (7) is inconsistent.
% 153.14/22.71  | 
% 153.14/22.71  End of proof
% 153.14/22.71  
% 153.14/22.71  Sub-proof #421 shows that the following formulas are inconsistent:
% 153.14/22.71  ----------------------------------------------------------------
% 153.14/22.71    (1)  op(e0, e1) = all_52_11
% 153.14/22.71    (2)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 153.14/22.71         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.14/22.71    (3)   ~ (all_52_7 = all_52_11)
% 153.14/22.71    (4)   ~ (e3 = e1)
% 153.14/22.71    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.14/22.71         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.14/22.71    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.14/22.71         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.14/22.71    (7)  op(e3, e2) = all_52_4
% 153.14/22.71    (8)   ~ (all_52_4 = all_52_7)
% 153.14/22.71    (9)   ~ (all_52_3 = all_52_7)
% 153.14/22.71    (10)   ~ (all_52_4 = e2)
% 153.14/22.71    (11)  op(e1, e1) = all_4_2
% 153.14/22.71    (12)   ~ (all_52_4 = all_52_12)
% 153.14/22.71    (13)   ~ (e2 = e0)
% 153.14/22.71    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.71            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.71    (15)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.14/22.71          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.14/22.71    (16)   ~ (all_52_7 = e1)
% 153.14/22.71    (17)  op(e0, e1) = all_10_1
% 153.14/22.71    (18)  op(e3, e3) = e2
% 153.14/22.71    (19)  all_56_14 = e2
% 153.14/22.71    (20)   ~ (all_52_13 = e2)
% 153.14/22.71    (21)  op(e0, e0) = e1
% 153.14/22.71    (22)  op(e3, e0) = all_52_12
% 153.14/22.71    (23)   ~ (e3 = e0)
% 153.14/22.71    (24)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.14/22.71          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.14/22.71    (25)  op(e2, e0) = all_52_13
% 153.14/22.71    (26)   ~ (all_52_9 = e2)
% 153.14/22.71    (27)  op(e0, e1) = e2
% 153.14/22.71    (28)   ~ (all_52_4 = all_52_8)
% 153.14/22.71    (29)  op(e0, e3) = all_52_3
% 153.14/22.71    (30)   ~ (all_4_2 = e2)
% 153.14/22.71    (31)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.14/22.71    (32)  op(e2, e1) = all_52_9
% 153.14/22.71    (33)   ~ (e1 = e0)
% 153.14/22.71    (34)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.14/22.71          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.14/22.71    (35)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.14/22.71              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.14/22.71            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.14/22.71                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.14/22.71              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.71          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.14/22.71              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.71            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.14/22.71                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.14/22.71              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.71          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.14/22.71              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.71            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.14/22.71                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.14/22.71              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.71          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.14/22.71              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.71            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.14/22.71                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.14/22.71                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.14/22.71                $i(all_57_14))))
% 153.14/22.71    (36)  op(e1, e0) = e2
% 153.14/22.71    (37)   ~ (e3 = e2)
% 153.14/22.71    (38)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.14/22.71          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 153.14/22.71            e2)
% 153.14/22.71    (39)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.14/22.71          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.14/22.71    (40)  all_54_13 = all_52_7
% 153.14/22.71    (41)  op(e3, e1) = all_52_8
% 153.14/22.71    (42)  ( ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 153.14/22.71            all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e3) & op(e0,
% 153.14/22.71              e1) = all_30_1 & $i(all_30_1))
% 153.14/22.71    (43)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.14/22.71          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.14/22.71    (44)   ~ (e2 = e1)
% 153.14/22.71    (45)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.14/22.71          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.14/22.71    (46)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.14/22.71              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.71            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.14/22.71            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.14/22.71            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.14/22.71            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.71            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.14/22.71            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.14/22.71            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.14/22.71            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.14/22.71            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.14/22.71            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.14/22.71            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.71            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.14/22.71            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.14/22.71            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.71            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.14/22.71            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.14/22.71            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.71            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.14/22.71            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.14/22.71            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.71            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.14/22.71            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.14/22.71            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.71            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.14/22.71            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.71            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.71            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.71            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.14/22.71            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.14/22.71            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.14/22.71            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.71            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.14/22.71            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.71            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.71            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.71            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.14/22.71            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.71            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.71            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.14/22.71            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.14/22.71            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.71            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.14/22.71            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.14/22.71            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.71            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.14/22.71            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.14/22.71              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.14/22.71            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.14/22.71            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.14/22.71              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.14/22.71            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.14/22.71            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.14/22.71                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.14/22.71                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.71                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.14/22.71                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.14/22.71                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.14/22.71                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.14/22.71                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.14/22.71              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.14/22.71                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.14/22.71                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.71                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.14/22.71                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.14/22.71                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.14/22.71                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.71                $i(all_57_7))))
% 153.14/22.71    (47)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.14/22.71          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.14/22.71    (48)  op(e2, e3) = all_52_1
% 153.14/22.71    (49)   ~ (all_52_1 = e2)
% 153.14/22.71  
% 153.14/22.71  Begin of proof
% 153.14/22.71  | 
% 153.14/22.71  | BETA: splitting (35) gives:
% 153.14/22.71  | 
% 153.14/22.71  | Case 1:
% 153.14/22.71  | | 
% 153.14/22.71  | |   (50)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.14/22.71  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.14/22.71  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.14/22.71  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.14/22.71  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.14/22.71  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 153.14/22.71  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 153.14/22.71  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.71  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.14/22.71  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.14/22.71  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.14/22.71  | |               $i(all_57_15))))
% 153.14/22.71  | | 
% 153.14/22.71  | | BETA: splitting (50) gives:
% 153.14/22.71  | | 
% 153.14/22.71  | | Case 1:
% 153.14/22.71  | | | 
% 153.14/22.71  | | |   (51)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.14/22.71  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.14/22.71  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.14/22.71  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.14/22.71  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.14/22.71  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.14/22.71  | | | 
% 153.14/22.71  | | | ALPHA: (51) implies:
% 153.14/22.71  | | |   (52)  op(e3, e3) = e3
% 153.14/22.71  | | | 
% 153.14/22.71  | | | REF_CLOSE: (14), (18), (37), (52) are inconsistent by sub-proof #1085.
% 153.14/22.71  | | | 
% 153.14/22.71  | | Case 2:
% 153.14/22.71  | | | 
% 153.14/22.71  | | |   (53)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 153.14/22.71  | | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.71  | | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 153.14/22.71  | | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.14/22.71  | | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 153.14/22.71  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.14/22.71  | | | 
% 153.14/22.71  | | | ALPHA: (53) implies:
% 153.14/22.71  | | |   (54)  op(e2, e2) = e2
% 153.14/22.71  | | |   (55)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3,
% 153.14/22.71  | | |             e3) = all_57_10 & $i(all_57_10))
% 153.14/22.71  | | | 
% 153.14/22.71  | | | BETA: splitting (42) gives:
% 153.14/22.71  | | | 
% 153.14/22.71  | | | Case 1:
% 153.14/22.71  | | | | 
% 153.14/22.71  | | | |   (56)   ~ (all_30_0 = e2) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 153.14/22.71  | | | |         all_30_1 & $i(all_30_0) & $i(all_30_1)
% 153.14/22.71  | | | | 
% 153.14/22.71  | | | | ALPHA: (56) implies:
% 153.14/22.71  | | | |   (57)  op(e0, e1) = all_30_1
% 153.14/22.71  | | | | 
% 153.14/22.71  | | | | BETA: splitting (55) gives:
% 153.14/22.71  | | | | 
% 153.14/22.71  | | | | Case 1:
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | |   (58)  all_57_3 = e3 & op(e3, e2) = e3
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | ALPHA: (58) implies:
% 153.14/22.71  | | | | |   (59)  op(e3, e2) = e3
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | GROUND_INST: instantiating (14) with e2, all_30_1, e1, e0, simplifying
% 153.14/22.71  | | | | |              with (27), (57) gives:
% 153.14/22.71  | | | | |   (60)  all_30_1 = e2
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | GROUND_INST: instantiating (14) with all_10_1, all_30_1, e1, e0,
% 153.14/22.71  | | | | |              simplifying with (17), (57) gives:
% 153.14/22.71  | | | | |   (61)  all_30_1 = all_10_1
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | GROUND_INST: instantiating (14) with all_52_4, e3, e2, e3, simplifying
% 153.14/22.71  | | | | |              with (7), (59) gives:
% 153.14/22.71  | | | | |   (62)  all_52_4 = e3
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | COMBINE_EQS: (60), (61) imply:
% 153.14/22.71  | | | | |   (63)  all_10_1 = e2
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | SIMP: (63) implies:
% 153.14/22.71  | | | | |   (64)  all_10_1 = e2
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | REDUCE: (28), (62) imply:
% 153.14/22.71  | | | | |   (65)   ~ (all_52_8 = e3)
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | SIMP: (65) implies:
% 153.14/22.71  | | | | |   (66)   ~ (all_52_8 = e3)
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | REDUCE: (12), (62) imply:
% 153.14/22.71  | | | | |   (67)   ~ (all_52_12 = e3)
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | SIMP: (67) implies:
% 153.14/22.71  | | | | |   (68)   ~ (all_52_12 = e3)
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13),
% 153.14/22.71  | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 153.14/22.71  | | | | |            (24), (25), (26), (29), (30), (31), (32), (33), (34), (35),
% 153.14/22.71  | | | | |            (36), (37), (38), (39), (40), (41), (43), (44), (45), (46),
% 153.14/22.71  | | | | |            (47), (48), (49), (54), (55), (64), (66), (68) are
% 153.14/22.71  | | | | |            inconsistent by sub-proof #423.
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | Case 2:
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | |   (69)   ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10)
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | ALPHA: (69) implies:
% 153.14/22.71  | | | | |   (70)   ~ (all_57_10 = e2)
% 153.14/22.71  | | | | |   (71)  op(e3, e3) = all_57_10
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | REF_CLOSE: (14), (18), (70), (71) are inconsistent by sub-proof #1031.
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | End of split
% 153.14/22.71  | | | | 
% 153.14/22.71  | | | Case 2:
% 153.14/22.71  | | | | 
% 153.14/22.71  | | | |   (72)   ~ (all_30_1 = e3) & op(e0, e1) = all_30_1 & $i(all_30_1)
% 153.14/22.71  | | | | 
% 153.14/22.71  | | | | ALPHA: (72) implies:
% 153.14/22.71  | | | |   (73)   ~ (all_30_1 = e3)
% 153.14/22.71  | | | |   (74)  op(e0, e1) = all_30_1
% 153.14/22.71  | | | | 
% 153.14/22.71  | | | | BETA: splitting (55) gives:
% 153.14/22.71  | | | | 
% 153.14/22.71  | | | | Case 1:
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | |   (75)  all_57_3 = e3 & op(e3, e2) = e3
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | ALPHA: (75) implies:
% 153.14/22.71  | | | | |   (76)  op(e3, e2) = e3
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | GROUND_INST: instantiating (14) with e2, all_30_1, e1, e0, simplifying
% 153.14/22.71  | | | | |              with (27), (74) gives:
% 153.14/22.71  | | | | |   (77)  all_30_1 = e2
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | GROUND_INST: instantiating (14) with all_10_1, all_30_1, e1, e0,
% 153.14/22.71  | | | | |              simplifying with (17), (74) gives:
% 153.14/22.71  | | | | |   (78)  all_30_1 = all_10_1
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | GROUND_INST: instantiating (14) with all_52_4, e3, e2, e3, simplifying
% 153.14/22.71  | | | | |              with (7), (76) gives:
% 153.14/22.71  | | | | |   (79)  all_52_4 = e3
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | COMBINE_EQS: (77), (78) imply:
% 153.14/22.71  | | | | |   (80)  all_10_1 = e2
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | REDUCE: (28), (79) imply:
% 153.14/22.71  | | | | |   (81)   ~ (all_52_8 = e3)
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | SIMP: (81) implies:
% 153.14/22.71  | | | | |   (82)   ~ (all_52_8 = e3)
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | REDUCE: (12), (79) imply:
% 153.14/22.71  | | | | |   (83)   ~ (all_52_12 = e3)
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | SIMP: (83) implies:
% 153.14/22.71  | | | | |   (84)   ~ (all_52_12 = e3)
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | REDUCE: (73), (77) imply:
% 153.14/22.71  | | | | |   (85)   ~ (e3 = e2)
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13),
% 153.14/22.71  | | | | |            (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 153.14/22.71  | | | | |            (24), (25), (26), (29), (30), (31), (32), (33), (34), (35),
% 153.14/22.71  | | | | |            (36), (37), (38), (39), (40), (41), (43), (44), (45), (46),
% 153.14/22.71  | | | | |            (47), (48), (49), (54), (55), (80), (82), (84) are
% 153.14/22.71  | | | | |            inconsistent by sub-proof #423.
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | Case 2:
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | |   (86)   ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10)
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | ALPHA: (86) implies:
% 153.14/22.71  | | | | |   (87)   ~ (all_57_10 = e2)
% 153.14/22.71  | | | | |   (88)  op(e3, e3) = all_57_10
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | | REF_CLOSE: (14), (18), (87), (88) are inconsistent by sub-proof #1031.
% 153.14/22.71  | | | | | 
% 153.14/22.71  | | | | End of split
% 153.14/22.71  | | | | 
% 153.14/22.71  | | | End of split
% 153.14/22.71  | | | 
% 153.14/22.71  | | End of split
% 153.14/22.71  | | 
% 153.14/22.71  | Case 2:
% 153.14/22.71  | | 
% 153.14/22.71  | |   (89)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.14/22.71  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.14/22.71  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.14/22.71  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.14/22.71  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.14/22.71  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 153.14/22.71  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 153.14/22.71  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.71  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 153.14/22.71  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 153.14/22.71  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 153.14/22.71  | |               all_57_14 & $i(all_57_14))))
% 153.14/22.71  | | 
% 153.14/22.71  | | BETA: splitting (89) gives:
% 153.14/22.71  | | 
% 153.14/22.71  | | Case 1:
% 153.14/22.71  | | | 
% 153.14/22.71  | | |   (90)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.14/22.71  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.14/22.71  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.14/22.71  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.14/22.71  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.14/22.71  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.14/22.71  | | | 
% 153.14/22.71  | | | ALPHA: (90) implies:
% 153.14/22.71  | | |   (91)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.14/22.71  | | |             e0) = all_57_15 & $i(all_57_15))
% 153.14/22.71  | | | 
% 153.14/22.71  | | | REF_CLOSE: (13), (14), (21), (27), (91) are inconsistent by sub-proof
% 153.14/22.71  | | |            #422.
% 153.14/22.71  | | | 
% 153.14/22.71  | | Case 2:
% 153.14/22.71  | | | 
% 153.14/22.71  | | |   (92)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 153.14/22.71  | | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.14/22.71  | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 153.14/22.71  | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.14/22.71  | | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 153.14/22.71  | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 153.14/22.71  | | | 
% 153.14/22.71  | | | ALPHA: (92) implies:
% 153.14/22.71  | | |   (93)  op(e0, e0) = e0
% 153.14/22.71  | | | 
% 153.14/22.71  | | | REF_CLOSE: (14), (21), (33), (93) are inconsistent by sub-proof #1040.
% 153.14/22.71  | | | 
% 153.14/22.71  | | End of split
% 153.14/22.71  | | 
% 153.14/22.71  | End of split
% 153.14/22.71  | 
% 153.14/22.71  End of proof
% 153.14/22.71  
% 153.14/22.71  Sub-proof #422 shows that the following formulas are inconsistent:
% 153.14/22.71  ----------------------------------------------------------------
% 153.14/22.71    (1)   ~ (e2 = e0)
% 153.14/22.71    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.71           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.71    (3)  op(e0, e0) = e1
% 153.14/22.71    (4)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 153.14/22.71           all_57_15 & $i(all_57_15))
% 153.14/22.71    (5)  op(e0, e1) = e2
% 153.14/22.71  
% 153.14/22.71  Begin of proof
% 153.14/22.71  | 
% 153.14/22.71  | BETA: splitting (4) gives:
% 153.14/22.71  | 
% 153.14/22.71  | Case 1:
% 153.14/22.71  | | 
% 153.14/22.71  | |   (6)  all_57_8 = e0 & op(e0, e1) = e0
% 153.14/22.71  | | 
% 153.14/22.71  | | ALPHA: (6) implies:
% 153.14/22.71  | |   (7)  op(e0, e1) = e0
% 153.14/22.71  | | 
% 153.14/22.71  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #1008.
% 153.14/22.71  | | 
% 153.14/22.71  | Case 2:
% 153.14/22.71  | | 
% 153.14/22.71  | |   (8)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)
% 153.14/22.71  | | 
% 153.14/22.71  | | ALPHA: (8) implies:
% 153.14/22.72  | |   (9)   ~ (all_57_15 = e1)
% 153.14/22.72  | |   (10)  op(e0, e0) = all_57_15
% 153.14/22.72  | | 
% 153.14/22.72  | | REF_CLOSE: (2), (3), (9), (10) are inconsistent by sub-proof #940.
% 153.14/22.72  | | 
% 153.14/22.72  | End of split
% 153.14/22.72  | 
% 153.14/22.72  End of proof
% 153.14/22.72  
% 153.14/22.72  Sub-proof #423 shows that the following formulas are inconsistent:
% 153.14/22.72  ----------------------------------------------------------------
% 153.14/22.72    (1)  op(e0, e1) = all_52_11
% 153.14/22.72    (2)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 153.14/22.72         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.14/22.72    (3)   ~ (all_52_7 = all_52_11)
% 153.14/22.72    (4)   ~ (e3 = e1)
% 153.14/22.72    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.14/22.72         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.14/22.72    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.14/22.72         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.14/22.72    (7)  op(e3, e2) = all_52_4
% 153.14/22.72    (8)   ~ (all_52_4 = all_52_7)
% 153.14/22.72    (9)   ~ (all_52_3 = all_52_7)
% 153.14/22.72    (10)  op(e1, e1) = all_4_2
% 153.14/22.72    (11)   ~ (e2 = e0)
% 153.14/22.72    (12)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.72            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.72    (13)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.14/22.72          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.14/22.72    (14)   ~ (all_52_7 = e1)
% 153.14/22.72    (15)  op(e0, e1) = all_10_1
% 153.14/22.72    (16)  op(e3, e3) = e2
% 153.14/22.72    (17)  all_56_14 = e2
% 153.14/22.72    (18)   ~ (all_52_13 = e2)
% 153.14/22.72    (19)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3, e3) =
% 153.14/22.72            all_57_10 & $i(all_57_10))
% 153.14/22.72    (20)  op(e0, e0) = e1
% 153.14/22.72    (21)  op(e3, e0) = all_52_12
% 153.14/22.72    (22)   ~ (e3 = e0)
% 153.14/22.72    (23)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.14/22.72          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.14/22.72    (24)   ~ (all_52_12 = e3)
% 153.14/22.72    (25)  op(e2, e0) = all_52_13
% 153.14/22.72    (26)   ~ (all_52_9 = e2)
% 153.14/22.72    (27)  op(e0, e3) = all_52_3
% 153.14/22.72    (28)   ~ (all_4_2 = e2)
% 153.14/22.72    (29)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.14/22.72    (30)  op(e2, e2) = e2
% 153.14/22.72    (31)  op(e2, e1) = all_52_9
% 153.14/22.72    (32)   ~ (e1 = e0)
% 153.14/22.72    (33)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.14/22.72          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.14/22.72    (34)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.14/22.72              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.14/22.72            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.14/22.72                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.14/22.72              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.72          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.14/22.72              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.72            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.14/22.72                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.14/22.72              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.72          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.14/22.72              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.72            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.14/22.72                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.14/22.72              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.72          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.14/22.72              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.72            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.14/22.72                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.14/22.72                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.14/22.72                $i(all_57_14))))
% 153.14/22.72    (35)  op(e1, e0) = e2
% 153.14/22.72    (36)   ~ (e3 = e2)
% 153.14/22.72    (37)  all_10_1 = e2
% 153.14/22.72    (38)   ~ (all_52_8 = e3)
% 153.14/22.72    (39)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.14/22.72          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 153.14/22.72            e2)
% 153.14/22.72    (40)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.14/22.72          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.14/22.72    (41)  all_54_13 = all_52_7
% 153.14/22.72    (42)  op(e3, e1) = all_52_8
% 153.14/22.72    (43)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.14/22.72          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.14/22.72    (44)   ~ (e2 = e1)
% 153.14/22.72    (45)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.14/22.72          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.14/22.72    (46)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.14/22.72              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.72            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.14/22.72            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.14/22.72            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.14/22.72            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.72            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.14/22.72            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.14/22.72            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.14/22.72            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.14/22.72            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.14/22.72            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.14/22.72            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.72            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.14/22.72            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.14/22.72            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.72            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.14/22.72            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.14/22.72            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.72            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.14/22.72            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.14/22.72            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.72            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.14/22.72            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.14/22.72            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.72            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.14/22.72            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.72            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.72            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.72            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.14/22.72            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.14/22.72            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.14/22.72            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.72            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.14/22.72            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.72            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.72            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.72            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.14/22.72            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.72            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.72            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.14/22.72            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.14/22.72            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.72            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.14/22.72            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.14/22.72            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.72            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.14/22.72            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.14/22.72              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.14/22.72            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.14/22.72            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.14/22.72              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.14/22.72            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.14/22.72            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.14/22.72                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.14/22.72                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.72                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.14/22.72                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.14/22.72                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.14/22.72                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.14/22.72                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.14/22.72              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.14/22.72                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.14/22.72                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.72                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.14/22.72                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.14/22.72                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.14/22.72                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.72                $i(all_57_7))))
% 153.14/22.72    (47)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.14/22.72          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.14/22.72    (48)  op(e2, e3) = all_52_1
% 153.14/22.72    (49)   ~ (all_52_1 = e2)
% 153.14/22.72  
% 153.14/22.72  Begin of proof
% 153.14/22.72  | 
% 153.14/22.72  | REDUCE: (15), (37) imply:
% 153.14/22.72  |   (50)  op(e0, e1) = e2
% 153.14/22.72  | 
% 153.14/22.72  | BETA: splitting (2) gives:
% 153.14/22.72  | 
% 153.14/22.72  | Case 1:
% 153.14/22.72  | | 
% 153.14/22.72  | |   (51)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) =
% 153.14/22.72  | |           e3)
% 153.14/22.72  | | 
% 153.14/22.72  | | BETA: splitting (51) gives:
% 153.14/22.72  | | 
% 153.14/22.72  | | Case 1:
% 153.14/22.72  | | | 
% 153.14/22.72  | | |   (52)  all_56_4 = e3 & op(e3, e1) = e3
% 153.14/22.72  | | | 
% 153.14/22.72  | | | ALPHA: (52) implies:
% 153.14/22.72  | | |   (53)  op(e3, e1) = e3
% 153.14/22.72  | | | 
% 153.14/22.72  | | | REF_CLOSE: (12), (38), (42), (53) are inconsistent by sub-proof #1164.
% 153.14/22.72  | | | 
% 153.14/22.72  | | Case 2:
% 153.14/22.72  | | | 
% 153.14/22.72  | | |   (54)  all_56_5 = e3 & op(e2, e1) = e3
% 153.14/22.72  | | | 
% 153.14/22.72  | | | ALPHA: (54) implies:
% 153.14/22.72  | | |   (55)  op(e2, e1) = e3
% 153.14/22.72  | | | 
% 153.14/22.72  | | | BETA: splitting (46) gives:
% 153.14/22.72  | | | 
% 153.14/22.72  | | | Case 1:
% 153.14/22.72  | | | | 
% 153.14/22.72  | | | |   (56)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.14/22.72  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.14/22.72  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.14/22.72  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.14/22.72  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.14/22.72  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.14/22.72  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.72  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.14/22.72  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.14/22.72  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.14/22.72  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.14/22.72  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.72  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.14/22.72  | | | |           $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.14/22.72  | | | |           (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 153.14/22.72  | | | |           & op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.14/22.72  | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 =
% 153.14/22.72  | | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.14/22.72  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.14/22.72  | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 153.14/22.72  | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 153.14/22.72  | | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.14/22.72  | | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.14/22.72  | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.14/22.72  | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.72  | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.14/22.72  | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.14/22.72  | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 153.14/22.72  | | | |           & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.14/22.72  | | | |           $i(all_57_7) & $i(all_57_10))
% 153.14/22.72  | | | | 
% 153.14/22.72  | | | | BETA: splitting (56) gives:
% 153.14/22.72  | | | | 
% 153.14/22.72  | | | | Case 1:
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | |   (57)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.14/22.72  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 153.14/22.72  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.14/22.72  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.14/22.72  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.14/22.72  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 153.14/22.72  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.72  | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.14/22.72  | | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.14/22.72  | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.14/22.72  | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.14/22.72  | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.14/22.72  | | | | |           & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.14/22.72  | | | | |           $i(all_57_14))
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | | REF_CLOSE: (4), (12), (20), (30), (36), (48), (49), (57) are
% 153.14/22.72  | | | | |            inconsistent by sub-proof #442.
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | Case 2:
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | |   (58)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.14/22.72  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.14/22.72  | | | | |           & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.14/22.72  | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.14/22.72  | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.14/22.72  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.14/22.72  | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1
% 153.14/22.72  | | | | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2)
% 153.14/22.72  | | | | |           & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1
% 153.14/22.72  | | | | |           & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.14/22.72  | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.14/22.72  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.14/22.72  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.14/22.72  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.14/22.72  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.14/22.72  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.14/22.72  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | | BETA: splitting (58) gives:
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | | Case 1:
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | |   (59)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.14/22.72  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 153.14/22.72  | | | | | |           e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.14/22.72  | | | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15
% 153.14/22.72  | | | | | |           = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3,
% 153.14/22.72  | | | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.14/22.72  | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | | REF_CLOSE: (10), (12), (20), (28), (44), (59) are inconsistent by
% 153.14/22.72  | | | | | |            sub-proof #438.
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | Case 2:
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | |   (60)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.14/22.72  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3
% 153.14/22.72  | | | | | |           & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3)
% 153.14/22.72  | | | | | |           & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.14/22.72  | | | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.14/22.72  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.14/22.72  | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 =
% 153.14/22.72  | | | | | |           e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.14/22.72  | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 153.14/22.72  | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.14/22.72  | | | | | |           $i(all_57_10))
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | | REF_CLOSE: (12), (19), (20), (30), (44), (60) are inconsistent by
% 153.14/22.72  | | | | | |            sub-proof #437.
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | End of split
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | End of split
% 153.14/22.72  | | | | 
% 153.14/22.72  | | | Case 2:
% 153.14/22.72  | | | | 
% 153.14/22.72  | | | |   (61)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.72  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.72  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.72  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.14/22.72  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.14/22.72  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.14/22.72  | | | |           e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.14/22.72  | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.14/22.72  | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.14/22.72  | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.14/22.72  | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.14/22.72  | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.72  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.14/22.72  | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.14/22.72  | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.14/22.72  | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.14/22.72  | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0 &
% 153.14/22.72  | | | |           all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 = e0) &
% 153.14/22.72  | | | |           op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.14/22.72  | | | |           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 153.14/22.72  | | | |         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 153.14/22.72  | | | |           (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.72  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.14/22.72  | | | |           $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.14/22.72  | | | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.14/22.72  | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.14/22.72  | | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.14/22.72  | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.14/22.72  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.14/22.72  | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.14/22.72  | | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.14/22.72  | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3)
% 153.14/22.72  | | | |               & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.14/22.72  | | | |               e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.14/22.72  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.14/22.72  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.14/22.72  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.14/22.72  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.14/22.72  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.14/22.72  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.14/22.72  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.14/22.72  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.14/22.72  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.14/22.72  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.14/22.72  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.72  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.14/22.72  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.14/22.72  | | | | 
% 153.14/22.72  | | | | BETA: splitting (61) gives:
% 153.14/22.72  | | | | 
% 153.14/22.72  | | | | Case 1:
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | |   (62)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.72  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.14/22.72  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.72  | | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.14/22.72  | | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.14/22.72  | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 153.14/22.72  | | | | |           = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.14/22.72  | | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.14/22.72  | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.14/22.72  | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.14/22.72  | | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.14/22.72  | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.14/22.72  | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.14/22.72  | | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.14/22.72  | | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.14/22.72  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.14/22.72  | | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | | BETA: splitting (62) gives:
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | | Case 1:
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | |   (63)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.72  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 153.14/22.72  | | | | | |           e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.14/22.72  | | | | | |           $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 & all_57_10
% 153.14/22.72  | | | | | |           = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3,
% 153.14/22.72  | | | | | |             e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.14/22.72  | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.14/22.72  | | | | | |           $i(all_57_12))
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | | REF_CLOSE: (12), (36), (38), (42), (55), (63) are inconsistent by
% 153.14/22.72  | | | | | |            sub-proof #828.
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | Case 2:
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | |   (64)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.72  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.14/22.72  | | | | | |           e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.14/22.72  | | | | | |           $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12
% 153.14/22.72  | | | | | |           = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3,
% 153.14/22.72  | | | | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.14/22.72  | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 153.14/22.72  | | | | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.14/22.72  | | | | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 153.14/22.72  | | | | | |           e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.14/22.72  | | | | | |           $i(all_57_10) & $i(all_57_13))
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | | BETA: splitting (64) gives:
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | | Case 1:
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | |   (65)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.72  | | | | | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.14/22.72  | | | | | | |         e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.14/22.72  | | | | | | |         $i(all_57_8) & $i(all_57_12)
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | | ALPHA: (65) implies:
% 153.14/22.72  | | | | | | |   (66)  op(e2, e1) = e2
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | | REF_CLOSE: (12), (36), (55), (66) are inconsistent by sub-proof
% 153.14/22.72  | | | | | | |            #1135.
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | Case 2:
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | |   (67)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.14/22.72  | | | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 153.14/22.72  | | | | | | |           e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.14/22.72  | | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.14/22.72  | | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 =
% 153.14/22.72  | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.72  | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10)
% 153.14/22.72  | | | | | | |           & $i(all_57_13))
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | | REF_CLOSE: (12), (21), (24), (67) are inconsistent by sub-proof
% 153.14/22.72  | | | | | | |            #1081.
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | End of split
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | End of split
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | Case 2:
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | |   (68)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.14/22.72  | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.72  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.14/22.72  | | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.14/22.72  | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.14/22.72  | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.14/22.72  | | | | |           = e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 153.14/22.72  | | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 153.14/22.72  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.14/22.72  | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 153.14/22.72  | | | | |         (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.14/22.72  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.14/22.72  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.14/22.72  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.14/22.72  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.14/22.72  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 153.14/22.72  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.14/22.72  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.14/22.72  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.14/22.72  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.14/22.72  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 153.14/22.72  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.14/22.72  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.14/22.72  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.14/22.72  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.72  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.72  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.14/22.72  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.14/22.72  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.72  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.14/22.72  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.72  | | | | |               $i(all_57_7))))
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | | BETA: splitting (68) gives:
% 153.14/22.72  | | | | | 
% 153.14/22.72  | | | | | Case 1:
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | |   (69)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.14/22.72  | | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9
% 153.14/22.72  | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 153.14/22.72  | | | | | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.14/22.72  | | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.14/22.72  | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1,
% 153.14/22.72  | | | | | |             e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | | REF_CLOSE: (11), (12), (16), (69) are inconsistent by sub-proof
% 153.14/22.72  | | | | | |            #1037.
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | Case 2:
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | |   (70)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.14/22.72  | | | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.14/22.72  | | | | | |           e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.14/22.72  | | | | | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.14/22.72  | | | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0)
% 153.14/22.72  | | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.14/22.72  | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.14/22.72  | | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.14/22.72  | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.14/22.72  | | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2)
% 153.14/22.72  | | | | | |               = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 =
% 153.14/22.72  | | | | | |               e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.14/22.72  | | | | | |               (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1)
% 153.14/22.72  | | | | | |               = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 153.14/22.72  | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.14/22.72  | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.72  | | | | | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5
% 153.14/22.72  | | | | | |               = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.14/22.72  | | | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1)
% 153.14/22.72  | | | | | |               = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 153.14/22.72  | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.14/22.72  | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.14/22.72  | | | | | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 153.14/22.72  | | | | | |               = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.14/22.72  | | | | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.14/22.72  | | | | | |               all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | | BETA: splitting (70) gives:
% 153.14/22.72  | | | | | | 
% 153.14/22.72  | | | | | | Case 1:
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | |   (71)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.14/22.72  | | | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.14/22.72  | | | | | | |         e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.14/22.72  | | | | | | |         $i(all_57_12) & $i(all_57_13)
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | | ALPHA: (71) implies:
% 153.14/22.72  | | | | | | |   (72)  op(e2, e0) = e2
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | | REF_CLOSE: (12), (18), (25), (72) are inconsistent by sub-proof
% 153.14/22.72  | | | | | | |            #1156.
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | Case 2:
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | |   (73)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 153.14/22.72  | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.14/22.72  | | | | | | |           all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.14/22.72  | | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 153.14/22.72  | | | | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 153.14/22.72  | | | | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.14/22.72  | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.72  | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.14/22.72  | | | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.14/22.72  | | | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.14/22.72  | | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.14/22.72  | | | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.14/22.72  | | | | | | |               e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.14/22.72  | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.14/22.72  | | | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.14/22.72  | | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.72  | | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.72  | | | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.14/22.72  | | | | | | |               e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.14/22.72  | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.72  | | | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 153.14/22.72  | | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.72  | | | | | | |               $i(all_57_7))))
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | | BETA: splitting (73) gives:
% 153.14/22.72  | | | | | | | 
% 153.14/22.72  | | | | | | | Case 1:
% 153.14/22.72  | | | | | | | | 
% 153.14/22.72  | | | | | | | |   (74)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 153.14/22.72  | | | | | | | |         ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.14/22.72  | | | | | | | |         all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.14/22.72  | | | | | | | |         $i(all_57_11) & $i(all_57_14)
% 153.14/22.72  | | | | | | | | 
% 153.14/22.72  | | | | | | | | ALPHA: (74) implies:
% 153.14/22.72  | | | | | | | |   (75)  op(e1, e0) = e1
% 153.14/22.72  | | | | | | | | 
% 153.14/22.72  | | | | | | | | REF_CLOSE: (12), (35), (44), (75) are inconsistent by sub-proof
% 153.14/22.72  | | | | | | | |            #1125.
% 153.14/22.72  | | | | | | | | 
% 153.14/22.72  | | | | | | | Case 2:
% 153.14/22.72  | | | | | | | | 
% 153.14/22.72  | | | | | | | |   (76)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0
% 153.14/22.72  | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.14/22.72  | | | | | | | |             (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.14/22.72  | | | | | | | |               e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.14/22.72  | | | | | | | |           (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 153.14/22.72  | | | | | | | |              ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.14/22.72  | | | | | | | |               e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.14/22.72  | | | | | | | |           (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &
% 153.14/22.72  | | | | | | | |              ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.72  | | | | | | | |             all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.14/22.72  | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &
% 153.14/22.72  | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.14/22.72  | | | | | | | |               e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.14/22.72  | | | | | | | |           (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &
% 153.14/22.72  | | | | | | | |              ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.14/22.72  | | | | | | | |             all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.14/22.72  | | | | | | | |           (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 153.14/22.72  | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.14/22.73  | | | | | | | |             all_57_7 & op(e0, e1) = e0 & $i(all_57_7)))
% 153.14/22.73  | | | | | | | | 
% 153.14/22.73  | | | | | | | | ALPHA: (76) implies:
% 153.14/22.73  | | | | | | | |   (77)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 153.14/22.73  | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.14/22.73  | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.14/22.73  | | | | | | | |         (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.14/22.73  | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.14/22.73  | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.14/22.73  | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.14/22.73  | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.73  | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5
% 153.14/22.73  | | | | | | | |           = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.14/22.73  | | | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1)
% 153.14/22.73  | | | | | | | |           = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 153.14/22.73  | | | | | | | |           e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.14/22.73  | | | | | | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.14/22.73  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 153.14/22.73  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.14/22.73  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.14/22.73  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.14/22.73  | | | | | | | | 
% 153.14/22.73  | | | | | | | | BETA: splitting (77) gives:
% 153.14/22.73  | | | | | | | | 
% 153.14/22.73  | | | | | | | | Case 1:
% 153.14/22.73  | | | | | | | | | 
% 153.14/22.73  | | | | | | | | |   (78)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &
% 153.14/22.73  | | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.14/22.73  | | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.14/22.73  | | | | | | | | |         (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 153.14/22.73  | | | | | | | | |            ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.14/22.73  | | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.14/22.73  | | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &
% 153.14/22.73  | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.73  | | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.14/22.73  | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | BETA: splitting (78) gives:
% 153.14/22.73  | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | Case 1:
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | |   (79)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2)
% 153.14/22.73  | | | | | | | | | |         &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.14/22.73  | | | | | | | | | |         op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | ALPHA: (79) implies:
% 153.14/22.73  | | | | | | | | | |   (80)  op(e2, e2) = e3
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | REF_CLOSE: (12), (30), (36), (80) are inconsistent by
% 153.14/22.73  | | | | | | | | | |            sub-proof #1179.
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | Case 2:
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | |   (81)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 153.14/22.73  | | | | | | | | | |           &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.14/22.73  | | | | | | | | | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 153.14/22.73  | | | | | | | | | |         | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 153.14/22.73  | | | | | | | | | |             e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.14/22.73  | | | | | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.14/22.73  | | | | | | | | | |           $i(all_57_3))
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | BETA: splitting (81) gives:
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | Case 1:
% 153.14/22.73  | | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | |   (82)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.14/22.73  | | | | | | | | | | |           e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.14/22.73  | | | | | | | | | | |         all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.14/22.73  | | | | | | | | | | |         $i(all_57_1)
% 153.14/22.73  | | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | | ALPHA: (82) implies:
% 153.14/22.73  | | | | | | | | | | |   (83)  op(e1, e1) = e3
% 153.14/22.73  | | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (11), (12), (14),
% 153.14/22.73  | | | | | | | | | | |            (16), (18), (20), (22), (25), (26), (27), (29),
% 153.14/22.73  | | | | | | | | | | |            (31), (32), (34), (35), (36), (38), (41), (42),
% 153.14/22.73  | | | | | | | | | | |            (44), (46), (48), (49), (50), (83) are
% 153.14/22.73  | | | | | | | | | | |            inconsistent by sub-proof #428.
% 153.14/22.73  | | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | Case 2:
% 153.14/22.73  | | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | |   (84)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 153.14/22.73  | | | | | | | | | | |           e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.14/22.73  | | | | | | | | | | |         op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.14/22.73  | | | | | | | | | | |         $i(all_57_3)
% 153.14/22.73  | | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | | ALPHA: (84) implies:
% 153.14/22.73  | | | | | | | | | | |   (85)  all_57_10 = e2
% 153.14/22.73  | | | | | | | | | | |   (86)   ~ (all_57_3 = e3)
% 153.14/22.73  | | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | | REF_CLOSE: (19), (85), (86) are inconsistent by sub-proof
% 153.14/22.73  | | | | | | | | | | |            #1018.
% 153.14/22.73  | | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | End of split
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | End of split
% 153.14/22.73  | | | | | | | | | 
% 153.14/22.73  | | | | | | | | Case 2:
% 153.14/22.73  | | | | | | | | | 
% 153.14/22.73  | | | | | | | | |   (87)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &
% 153.14/22.73  | | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.14/22.73  | | | | | | | | |             e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.14/22.73  | | | | | | | | |         (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &
% 153.14/22.73  | | | | | | | | |            ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.14/22.73  | | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.14/22.73  | | | | | | | | |         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 153.14/22.73  | | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.14/22.73  | | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.14/22.73  | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | BETA: splitting (87) gives:
% 153.14/22.73  | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | Case 1:
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | |   (88)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1)
% 153.14/22.73  | | | | | | | | | |         &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 &
% 153.14/22.73  | | | | | | | | | |         op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | ALPHA: (88) implies:
% 153.14/22.73  | | | | | | | | | |   (89)  op(e1, e1) = e2
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | REF_CLOSE: (10), (12), (28), (89) are inconsistent by
% 153.14/22.73  | | | | | | | | | |            sub-proof #1169.
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | Case 2:
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | |   (90)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.14/22.73  | | | | | | | | | |           &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.14/22.73  | | | | | | | | | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6))
% 153.14/22.73  | | | | | | | | | |         | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 153.14/22.73  | | | | | | | | | |             e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.14/22.73  | | | | | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.73  | | | | | | | | | |           $i(all_57_7))
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | | REF_CLOSE: (11), (12), (30), (44), (50), (90) are
% 153.14/22.73  | | | | | | | | | |            inconsistent by sub-proof #1007.
% 153.14/22.73  | | | | | | | | | | 
% 153.14/22.73  | | | | | | | | | End of split
% 153.14/22.73  | | | | | | | | | 
% 153.14/22.73  | | | | | | | | End of split
% 153.14/22.73  | | | | | | | | 
% 153.14/22.73  | | | | | | | End of split
% 153.14/22.73  | | | | | | | 
% 153.14/22.73  | | | | | | End of split
% 153.14/22.73  | | | | | | 
% 153.14/22.73  | | | | | End of split
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | End of split
% 153.14/22.73  | | | | 
% 153.14/22.73  | | | End of split
% 153.14/22.73  | | | 
% 153.14/22.73  | | End of split
% 153.14/22.73  | | 
% 153.14/22.73  | Case 2:
% 153.14/22.73  | | 
% 153.14/22.73  | |   (91)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 153.14/22.73  | |           e3)
% 153.14/22.73  | | 
% 153.14/22.73  | | BETA: splitting (91) gives:
% 153.14/22.73  | | 
% 153.14/22.73  | | Case 1:
% 153.14/22.73  | | | 
% 153.14/22.73  | | |   (92)  all_56_8 = e3 & op(e1, e1) = e3
% 153.14/22.73  | | | 
% 153.14/22.73  | | | ALPHA: (92) implies:
% 153.14/22.73  | | |   (93)  all_56_8 = e3
% 153.14/22.73  | | |   (94)  op(e1, e1) = e3
% 153.14/22.73  | | | 
% 153.14/22.73  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (11), (12), (13), (14),
% 153.14/22.73  | | |            (16), (18), (20), (22), (23), (25), (26), (27), (29), (31),
% 153.14/22.73  | | |            (32), (33), (34), (35), (36), (38), (39), (40), (41), (42),
% 153.14/22.73  | | |            (43), (44), (45), (46), (47), (48), (49), (93), (94) are
% 153.14/22.73  | | |            inconsistent by sub-proof #425.
% 153.14/22.73  | | | 
% 153.14/22.73  | | Case 2:
% 153.14/22.73  | | | 
% 153.14/22.73  | | |   (95)  all_56_14 = e3 & op(e0, e1) = e3
% 153.14/22.73  | | | 
% 153.14/22.73  | | | REF_CLOSE: (17), (36), (95) are inconsistent by sub-proof #424.
% 153.14/22.73  | | | 
% 153.14/22.73  | | End of split
% 153.14/22.73  | | 
% 153.14/22.73  | End of split
% 153.14/22.73  | 
% 153.14/22.73  End of proof
% 153.14/22.73  
% 153.14/22.73  Sub-proof #424 shows that the following formulas are inconsistent:
% 153.14/22.73  ----------------------------------------------------------------
% 153.14/22.73    (1)  all_56_14 = e3 & op(e0, e1) = e3
% 153.14/22.73    (2)  all_56_14 = e2
% 153.14/22.73    (3)   ~ (e3 = e2)
% 153.14/22.73  
% 153.14/22.73  Begin of proof
% 153.14/22.73  | 
% 153.14/22.73  | ALPHA: (1) implies:
% 153.14/22.73  |   (4)  all_56_14 = e3
% 153.14/22.73  | 
% 153.14/22.73  | COMBINE_EQS: (2), (4) imply:
% 153.14/22.73  |   (5)  e3 = e2
% 153.14/22.73  | 
% 153.14/22.73  | REDUCE: (3), (5) imply:
% 153.14/22.73  |   (6)  $false
% 153.14/22.73  | 
% 153.14/22.73  | CLOSE: (6) is inconsistent.
% 153.14/22.73  | 
% 153.14/22.73  End of proof
% 153.14/22.73  
% 153.14/22.73  Sub-proof #425 shows that the following formulas are inconsistent:
% 153.14/22.73  ----------------------------------------------------------------
% 153.14/22.73    (1)  op(e0, e1) = all_52_11
% 153.14/22.73    (2)  all_56_8 = e3
% 153.14/22.73    (3)   ~ (all_52_7 = all_52_11)
% 153.14/22.73    (4)   ~ (e3 = e1)
% 153.14/22.73    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.14/22.73         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.14/22.73    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.14/22.73         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.14/22.73    (7)  op(e3, e2) = all_52_4
% 153.14/22.73    (8)   ~ (all_52_4 = all_52_7)
% 153.14/22.73    (9)   ~ (all_52_3 = all_52_7)
% 153.14/22.73    (10)   ~ (e2 = e0)
% 153.14/22.73    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.73            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.73    (12)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.14/22.73          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.14/22.73    (13)   ~ (all_52_7 = e1)
% 153.14/22.73    (14)  op(e3, e3) = e2
% 153.14/22.73    (15)   ~ (all_52_13 = e2)
% 153.14/22.73    (16)  op(e0, e0) = e1
% 153.14/22.73    (17)   ~ (e3 = e0)
% 153.14/22.73    (18)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.14/22.73          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.14/22.73    (19)  op(e2, e0) = all_52_13
% 153.14/22.73    (20)   ~ (all_52_9 = e2)
% 153.14/22.73    (21)  op(e0, e3) = all_52_3
% 153.14/22.73    (22)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.14/22.73    (23)  op(e2, e1) = all_52_9
% 153.14/22.73    (24)   ~ (e1 = e0)
% 153.14/22.73    (25)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.14/22.73          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.14/22.73    (26)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.14/22.73              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.14/22.73            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.14/22.73                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.14/22.73              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.73          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.14/22.73              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.73            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.14/22.73                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.14/22.73              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.73          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.14/22.73              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.73            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.14/22.73                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.14/22.73              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.73          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.14/22.73              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.73            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.14/22.73                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.14/22.73                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.14/22.73                $i(all_57_14))))
% 153.14/22.73    (27)  op(e1, e1) = e3
% 153.14/22.73    (28)  op(e1, e0) = e2
% 153.14/22.73    (29)   ~ (e3 = e2)
% 153.14/22.73    (30)   ~ (all_52_8 = e3)
% 153.14/22.73    (31)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.14/22.73          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 153.14/22.73            e2)
% 153.14/22.73    (32)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.14/22.73          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.14/22.73    (33)  all_54_13 = all_52_7
% 153.14/22.73    (34)  op(e3, e1) = all_52_8
% 153.14/22.73    (35)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.14/22.73          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.14/22.73    (36)   ~ (e2 = e1)
% 153.14/22.73    (37)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.14/22.73          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.14/22.73    (38)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.14/22.73              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.73            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.14/22.73            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.14/22.73            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.14/22.73            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.73            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.14/22.73            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.14/22.73            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.14/22.73            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.14/22.73            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.14/22.73            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.14/22.73            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.73            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.14/22.73            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.14/22.73            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.73            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.14/22.73            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.14/22.73            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.73            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.14/22.73            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.14/22.73            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.73            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.14/22.73            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.14/22.73            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.73            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.14/22.73            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.73            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.73            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.73            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.14/22.73            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.14/22.73            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.14/22.73            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.73            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.14/22.73            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.73            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.73            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.73            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.14/22.73            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.73            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.73            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.14/22.73            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.14/22.73            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.73            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.14/22.73            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.14/22.73            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.73            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.14/22.73            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.14/22.73              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.14/22.73            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.14/22.73            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.14/22.73              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.14/22.73            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.14/22.73            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.14/22.73                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.14/22.73                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.73                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.14/22.73                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.14/22.73                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.14/22.73                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.14/22.73                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.14/22.73              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.14/22.73                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.14/22.73                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.73                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.14/22.73                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.14/22.73                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.14/22.73                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.73                $i(all_57_7))))
% 153.14/22.73    (39)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.14/22.73          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.14/22.73    (40)  op(e2, e3) = all_52_1
% 153.14/22.73    (41)   ~ (all_52_1 = e2)
% 153.14/22.73  
% 153.14/22.73  Begin of proof
% 153.14/22.73  | 
% 153.14/22.73  | BETA: splitting (26) gives:
% 153.14/22.73  | 
% 153.14/22.73  | Case 1:
% 153.14/22.73  | | 
% 153.14/22.73  | |   (42)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.14/22.73  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.14/22.73  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.14/22.73  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.14/22.73  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.14/22.73  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 153.14/22.73  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 153.14/22.73  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.73  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.14/22.73  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.14/22.73  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.14/22.73  | |               $i(all_57_15))))
% 153.14/22.73  | | 
% 153.14/22.73  | | BETA: splitting (42) gives:
% 153.14/22.73  | | 
% 153.14/22.73  | | Case 1:
% 153.14/22.73  | | | 
% 153.14/22.73  | | |   (43)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.14/22.73  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.14/22.73  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.14/22.73  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.14/22.73  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.14/22.73  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.14/22.73  | | | 
% 153.14/22.73  | | | ALPHA: (43) implies:
% 153.14/22.73  | | |   (44)  op(e3, e3) = e3
% 153.14/22.73  | | | 
% 153.14/22.73  | | | REF_CLOSE: (11), (14), (29), (44) are inconsistent by sub-proof #1085.
% 153.14/22.73  | | | 
% 153.14/22.73  | | Case 2:
% 153.14/22.73  | | | 
% 153.14/22.73  | | |   (45)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 153.14/22.73  | | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.73  | | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 153.14/22.73  | | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.14/22.73  | | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 153.14/22.73  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.14/22.73  | | | 
% 153.14/22.73  | | | ALPHA: (45) implies:
% 153.14/22.73  | | |   (46)  op(e2, e2) = e2
% 153.14/22.73  | | |   (47)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3,
% 153.14/22.73  | | |             e3) = all_57_10 & $i(all_57_10))
% 153.14/22.73  | | | 
% 153.14/22.73  | | | BETA: splitting (31) gives:
% 153.14/22.73  | | | 
% 153.14/22.73  | | | Case 1:
% 153.14/22.73  | | | | 
% 153.14/22.73  | | | |   (48)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0,
% 153.14/22.73  | | | |             e2) = e2)
% 153.14/22.73  | | | | 
% 153.14/22.73  | | | | BETA: splitting (48) gives:
% 153.14/22.73  | | | | 
% 153.14/22.73  | | | | Case 1:
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | |   (49)  all_56_12 = e2 & op(e0, e3) = e2
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | | REF_CLOSE: (2), (4), (5), (6), (10), (11), (12), (14), (17), (18),
% 153.14/22.73  | | | | |            (24), (25), (27), (29), (35), (36), (49) are inconsistent
% 153.14/22.73  | | | | |            by sub-proof #426.
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | Case 2:
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | |   (50)  all_56_13 = e2 & op(e0, e2) = e2
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | | ALPHA: (50) implies:
% 153.14/22.73  | | | | |   (51)  all_56_13 = e2
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | | REF_CLOSE: (4), (10), (11), (17), (24), (29), (32), (36), (37), (39),
% 153.14/22.73  | | | | |            (46), (51) are inconsistent by sub-proof #1104.
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | End of split
% 153.14/22.73  | | | | 
% 153.14/22.73  | | | Case 2:
% 153.14/22.73  | | | | 
% 153.14/22.73  | | | |   (52)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0,
% 153.14/22.73  | | | |             e0) = e2)
% 153.14/22.73  | | | | 
% 153.14/22.73  | | | | BETA: splitting (52) gives:
% 153.14/22.73  | | | | 
% 153.14/22.73  | | | | Case 1:
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | |   (53)  all_56_14 = e2 & op(e0, e1) = e2
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | | ALPHA: (53) implies:
% 153.14/22.73  | | | | |   (54)  op(e0, e1) = e2
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | | REF_CLOSE: (1), (3), (4), (7), (8), (9), (10), (11), (13), (14), (15),
% 153.14/22.73  | | | | |            (16), (17), (19), (20), (21), (22), (23), (27), (28), (29),
% 153.14/22.73  | | | | |            (30), (33), (34), (36), (38), (40), (41), (46), (47), (54)
% 153.14/22.73  | | | | |            are inconsistent by sub-proof #430.
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | Case 2:
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | |   (55)  all_56_15 = e2 & op(e0, e0) = e2
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | | ALPHA: (55) implies:
% 153.14/22.73  | | | | |   (56)  op(e0, e0) = e2
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | | REF_CLOSE: (11), (16), (36), (56) are inconsistent by sub-proof #978.
% 153.14/22.73  | | | | | 
% 153.14/22.73  | | | | End of split
% 153.14/22.73  | | | | 
% 153.14/22.73  | | | End of split
% 153.14/22.73  | | | 
% 153.14/22.73  | | End of split
% 153.14/22.73  | | 
% 153.14/22.73  | Case 2:
% 153.14/22.73  | | 
% 153.14/22.73  | |   (57)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.14/22.73  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.14/22.73  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.14/22.73  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.14/22.73  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.14/22.73  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 153.14/22.73  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 153.14/22.73  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.73  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 153.14/22.73  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 153.14/22.73  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 153.14/22.73  | |               all_57_14 & $i(all_57_14))))
% 153.14/22.73  | | 
% 153.14/22.73  | | REF_CLOSE: (4), (11), (16), (24), (27), (57) are inconsistent by sub-proof
% 153.14/22.73  | |            #429.
% 153.14/22.73  | | 
% 153.14/22.73  | End of split
% 153.14/22.73  | 
% 153.14/22.73  End of proof
% 153.14/22.73  
% 153.14/22.73  Sub-proof #426 shows that the following formulas are inconsistent:
% 153.14/22.73  ----------------------------------------------------------------
% 153.14/22.73    (1)  all_56_8 = e3
% 153.14/22.73    (2)   ~ (e3 = e1)
% 153.14/22.73    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.14/22.73         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.14/22.73    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.14/22.73         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.14/22.73    (5)   ~ (e2 = e0)
% 153.14/22.73    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.73    (7)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.14/22.73         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.14/22.73    (8)  op(e3, e3) = e2
% 153.14/22.73    (9)   ~ (e3 = e0)
% 153.14/22.73    (10)  all_56_12 = e2 & op(e0, e3) = e2
% 153.14/22.73    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.14/22.73          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.14/22.73    (12)   ~ (e1 = e0)
% 153.14/22.73    (13)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.14/22.73          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.14/22.73    (14)  op(e1, e1) = e3
% 153.14/22.73    (15)   ~ (e3 = e2)
% 153.14/22.73    (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.14/22.73          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.14/22.73    (17)   ~ (e2 = e1)
% 153.14/22.73  
% 153.14/22.73  Begin of proof
% 153.14/22.73  | 
% 153.14/22.73  | ALPHA: (10) implies:
% 153.14/22.73  |   (18)  all_56_12 = e2
% 153.14/22.73  | 
% 153.14/22.73  | BETA: splitting (4) gives:
% 153.14/22.73  | 
% 153.14/22.73  | Case 1:
% 153.14/22.73  | | 
% 153.14/22.73  | |   (19)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 153.14/22.73  | |           e3)
% 153.14/22.73  | | 
% 153.14/22.73  | | REF_CLOSE: (2), (3), (5), (6), (8), (9), (11), (12), (15), (17), (18), (19)
% 153.14/22.73  | |            are inconsistent by sub-proof #786.
% 153.14/22.73  | | 
% 153.14/22.73  | Case 2:
% 153.14/22.73  | | 
% 153.14/22.73  | |   (20)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 153.14/22.73  | |           e3)
% 153.14/22.73  | | 
% 153.14/22.73  | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (12), (13), (14), (15), (16), (17),
% 153.14/22.73  | |            (18), (20) are inconsistent by sub-proof #427.
% 153.14/22.73  | | 
% 153.14/22.73  | End of split
% 153.14/22.73  | 
% 153.14/22.73  End of proof
% 153.14/22.73  
% 153.14/22.73  Sub-proof #427 shows that the following formulas are inconsistent:
% 153.14/22.73  ----------------------------------------------------------------
% 153.14/22.73    (1)  all_56_8 = e3
% 153.14/22.73    (2)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.14/22.73    (3)   ~ (e3 = e1)
% 153.14/22.73    (4)   ~ (e2 = e0)
% 153.14/22.73    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.73    (6)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.14/22.73         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.14/22.73    (7)   ~ (e3 = e0)
% 153.14/22.73    (8)   ~ (e1 = e0)
% 153.14/22.73    (9)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.14/22.73         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.14/22.73    (10)  op(e1, e1) = e3
% 153.14/22.73    (11)   ~ (e3 = e2)
% 153.14/22.73    (12)  all_56_12 = e2
% 153.14/22.73    (13)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.14/22.73          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.14/22.73    (14)   ~ (e2 = e1)
% 153.14/22.73  
% 153.14/22.73  Begin of proof
% 153.14/22.73  | 
% 153.14/22.73  | BETA: splitting (2) gives:
% 153.14/22.73  | 
% 153.14/22.73  | Case 1:
% 153.14/22.73  | | 
% 153.14/22.73  | |   (15)  all_56_6 = e3 & op(e1, e3) = e3
% 153.14/22.73  | | 
% 153.14/22.73  | | ALPHA: (15) implies:
% 153.14/22.73  | |   (16)  all_56_6 = e3
% 153.14/22.73  | | 
% 153.14/22.73  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 153.14/22.73  | |            (16) are inconsistent by sub-proof #607.
% 153.14/22.73  | | 
% 153.14/22.73  | Case 2:
% 153.14/22.73  | | 
% 153.14/22.73  | |   (17)  all_56_12 = e3 & op(e0, e3) = e3
% 153.14/22.73  | | 
% 153.14/22.73  | | ALPHA: (17) implies:
% 153.14/22.73  | |   (18)  all_56_12 = e3
% 153.14/22.73  | | 
% 153.14/22.73  | | REF_CLOSE: (11), (12), (18) are inconsistent by sub-proof #869.
% 153.14/22.73  | | 
% 153.14/22.73  | End of split
% 153.14/22.73  | 
% 153.14/22.73  End of proof
% 153.14/22.73  
% 153.14/22.73  Sub-proof #428 shows that the following formulas are inconsistent:
% 153.14/22.73  ----------------------------------------------------------------
% 153.14/22.73    (1)  op(e0, e1) = all_52_11
% 153.14/22.73    (2)   ~ (all_52_7 = all_52_11)
% 153.14/22.73    (3)   ~ (e3 = e1)
% 153.14/22.73    (4)  op(e3, e2) = all_52_4
% 153.14/22.73    (5)   ~ (all_52_4 = all_52_7)
% 153.14/22.73    (6)   ~ (all_52_3 = all_52_7)
% 153.14/22.73    (7)   ~ (e2 = e0)
% 153.14/22.73    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.73           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.73    (9)   ~ (all_52_7 = e1)
% 153.14/22.73    (10)  op(e3, e3) = e2
% 153.14/22.73    (11)   ~ (all_52_13 = e2)
% 153.14/22.73    (12)  op(e0, e0) = e1
% 153.14/22.73    (13)   ~ (e3 = e0)
% 153.14/22.73    (14)  op(e2, e0) = all_52_13
% 153.14/22.73    (15)   ~ (all_52_9 = e2)
% 153.14/22.73    (16)  op(e0, e1) = e2
% 153.14/22.73    (17)  op(e0, e3) = all_52_3
% 153.14/22.73    (18)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.14/22.73    (19)  op(e2, e1) = all_52_9
% 153.14/22.73    (20)   ~ (e1 = e0)
% 153.14/22.74    (21)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.14/22.74              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.14/22.74            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.14/22.74                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.14/22.74              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.74          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.14/22.74              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.74            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.14/22.74                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.14/22.74              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.74          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.14/22.74              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.74            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.14/22.74                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.14/22.74              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.74          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.14/22.74              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.74            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.14/22.74                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.14/22.74                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.14/22.74                $i(all_57_14))))
% 153.14/22.74    (22)  op(e1, e1) = e3
% 153.14/22.74    (23)  op(e1, e0) = e2
% 153.14/22.74    (24)   ~ (e3 = e2)
% 153.14/22.74    (25)   ~ (all_52_8 = e3)
% 153.14/22.74    (26)  all_54_13 = all_52_7
% 153.14/22.74    (27)  op(e3, e1) = all_52_8
% 153.14/22.74    (28)   ~ (e2 = e1)
% 153.14/22.74    (29)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.14/22.74              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.74            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.14/22.74            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.14/22.74            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.14/22.74            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.74            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.14/22.74            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.14/22.74            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.14/22.74            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.14/22.74            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.14/22.74            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.14/22.74            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.74            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.14/22.74            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.14/22.74            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.74            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.14/22.74            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.14/22.74            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.74            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.14/22.74            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.14/22.74            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.74            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.14/22.74            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.14/22.74            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.74            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.14/22.74            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.74            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.74            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.74            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.14/22.74            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.14/22.74            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.14/22.74            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.74            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.14/22.74            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.74            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.74            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.74            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.14/22.74            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.74            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.74            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.14/22.74            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.14/22.74            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.74            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.14/22.74            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.14/22.74            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.74            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.14/22.74            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.14/22.74              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.14/22.74            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.14/22.74            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.14/22.74              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.14/22.74            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.14/22.74            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.14/22.74                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.14/22.74                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.74                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.14/22.74                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.14/22.74                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.14/22.74                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.14/22.74                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.14/22.74              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.14/22.74                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.14/22.74                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.74                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.14/22.74                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.14/22.74                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.14/22.74                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.74                $i(all_57_7))))
% 153.14/22.74    (30)  op(e2, e3) = all_52_1
% 153.14/22.74    (31)   ~ (all_52_1 = e2)
% 153.14/22.74  
% 153.14/22.74  Begin of proof
% 153.14/22.74  | 
% 153.14/22.74  | BETA: splitting (21) gives:
% 153.14/22.74  | 
% 153.14/22.74  | Case 1:
% 153.14/22.74  | | 
% 153.14/22.74  | |   (32)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.14/22.74  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.14/22.74  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.14/22.74  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.14/22.74  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.14/22.74  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 153.14/22.74  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 153.14/22.74  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.74  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.14/22.74  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.14/22.74  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.14/22.74  | |               $i(all_57_15))))
% 153.14/22.74  | | 
% 153.14/22.74  | | BETA: splitting (32) gives:
% 153.14/22.74  | | 
% 153.14/22.74  | | Case 1:
% 153.14/22.74  | | | 
% 153.14/22.74  | | |   (33)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.14/22.74  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.14/22.74  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.14/22.74  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.14/22.74  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.14/22.74  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.14/22.74  | | | 
% 153.14/22.74  | | | ALPHA: (33) implies:
% 153.14/22.74  | | |   (34)  op(e3, e3) = e3
% 153.14/22.74  | | | 
% 153.14/22.74  | | | REF_CLOSE: (8), (10), (24), (34) are inconsistent by sub-proof #1085.
% 153.14/22.74  | | | 
% 153.14/22.74  | | Case 2:
% 153.14/22.74  | | | 
% 153.14/22.74  | | |   (35)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 153.14/22.74  | | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.74  | | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 153.14/22.74  | | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.14/22.74  | | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 153.14/22.74  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.14/22.74  | | | 
% 153.14/22.74  | | | ALPHA: (35) implies:
% 153.14/22.74  | | |   (36)  op(e2, e2) = e2
% 153.14/22.74  | | |   (37)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3,
% 153.14/22.74  | | |             e3) = all_57_10 & $i(all_57_10))
% 153.14/22.74  | | | 
% 153.14/22.74  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 153.14/22.74  | | |            (13), (14), (15), (16), (17), (18), (19), (22), (23), (24),
% 153.14/22.74  | | |            (25), (26), (27), (28), (29), (30), (31), (36), (37) are
% 153.14/22.74  | | |            inconsistent by sub-proof #430.
% 153.14/22.74  | | | 
% 153.14/22.74  | | End of split
% 153.14/22.74  | | 
% 153.14/22.74  | Case 2:
% 153.14/22.74  | | 
% 153.14/22.74  | |   (38)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.14/22.74  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.14/22.74  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.14/22.74  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.14/22.74  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.14/22.74  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 153.14/22.74  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 153.14/22.74  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.74  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 153.14/22.74  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 153.14/22.74  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 153.14/22.74  | |               all_57_14 & $i(all_57_14))))
% 153.14/22.74  | | 
% 153.14/22.74  | | REF_CLOSE: (3), (8), (12), (20), (22), (38) are inconsistent by sub-proof
% 153.14/22.74  | |            #429.
% 153.14/22.74  | | 
% 153.14/22.74  | End of split
% 153.14/22.74  | 
% 153.14/22.74  End of proof
% 153.14/22.74  
% 153.14/22.74  Sub-proof #429 shows that the following formulas are inconsistent:
% 153.14/22.74  ----------------------------------------------------------------
% 153.14/22.74    (1)   ~ (e3 = e1)
% 153.14/22.74    (2)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.14/22.74             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.74           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.14/22.74               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.14/22.74             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.14/22.74         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.14/22.74             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.74           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 153.14/22.74               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 153.14/22.74             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 153.14/22.74    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.74    (4)  op(e0, e0) = e1
% 153.14/22.74    (5)   ~ (e1 = e0)
% 153.14/22.74    (6)  op(e1, e1) = e3
% 153.14/22.74  
% 153.14/22.74  Begin of proof
% 153.14/22.74  | 
% 153.14/22.74  | BETA: splitting (2) gives:
% 153.14/22.74  | 
% 153.14/22.74  | Case 1:
% 153.14/22.74  | | 
% 153.14/22.74  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3)
% 153.14/22.74  | |          | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.74  | |        ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 153.14/22.74  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 153.14/22.74  | |              e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 153.14/22.74  | |            $i(all_57_15)))
% 153.14/22.74  | | 
% 153.14/22.74  | | ALPHA: (7) implies:
% 153.14/22.74  | |   (8)  op(e1, e1) = e1
% 153.14/22.74  | | 
% 153.14/22.74  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #734.
% 153.14/22.74  | | 
% 153.14/22.74  | Case 2:
% 153.14/22.74  | | 
% 153.14/22.74  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3)
% 153.14/22.74  | |          | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.14/22.74  | |        ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.14/22.74  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.14/22.74  | |              e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.14/22.74  | |            $i(all_57_14)))
% 153.14/22.74  | | 
% 153.14/22.74  | | ALPHA: (9) implies:
% 153.14/22.74  | |   (10)  op(e0, e0) = e0
% 153.14/22.74  | | 
% 153.14/22.74  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #1040.
% 153.14/22.74  | | 
% 153.14/22.74  | End of split
% 153.14/22.74  | 
% 153.14/22.74  End of proof
% 153.14/22.74  
% 153.14/22.74  Sub-proof #430 shows that the following formulas are inconsistent:
% 153.14/22.74  ----------------------------------------------------------------
% 153.14/22.74    (1)  op(e0, e1) = all_52_11
% 153.14/22.74    (2)   ~ (all_52_7 = all_52_11)
% 153.14/22.74    (3)   ~ (e3 = e1)
% 153.14/22.74    (4)  op(e3, e2) = all_52_4
% 153.14/22.74    (5)   ~ (all_52_4 = all_52_7)
% 153.14/22.74    (6)   ~ (all_52_3 = all_52_7)
% 153.14/22.74    (7)   ~ (e2 = e0)
% 153.14/22.74    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.74           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.74    (9)   ~ (all_52_7 = e1)
% 153.14/22.74    (10)  op(e3, e3) = e2
% 153.14/22.74    (11)   ~ (all_52_13 = e2)
% 153.14/22.74    (12)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3, e3) =
% 153.14/22.74            all_57_10 & $i(all_57_10))
% 153.14/22.74    (13)  op(e0, e0) = e1
% 153.14/22.74    (14)   ~ (e3 = e0)
% 153.14/22.74    (15)  op(e2, e0) = all_52_13
% 153.14/22.74    (16)   ~ (all_52_9 = e2)
% 153.14/22.74    (17)  op(e0, e1) = e2
% 153.14/22.74    (18)  op(e0, e3) = all_52_3
% 153.14/22.74    (19)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.14/22.74    (20)  op(e2, e2) = e2
% 153.14/22.74    (21)  op(e2, e1) = all_52_9
% 153.14/22.74    (22)  op(e1, e1) = e3
% 153.14/22.74    (23)  op(e1, e0) = e2
% 153.14/22.74    (24)   ~ (e3 = e2)
% 153.14/22.74    (25)   ~ (all_52_8 = e3)
% 153.14/22.74    (26)  all_54_13 = all_52_7
% 153.14/22.74    (27)  op(e3, e1) = all_52_8
% 153.14/22.74    (28)   ~ (e2 = e1)
% 153.14/22.74    (29)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.14/22.74              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.74            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.14/22.74            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.14/22.74            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.14/22.74            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.74            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.14/22.74            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.14/22.74            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.14/22.74            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.14/22.74            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.14/22.74            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.14/22.74            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.74            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.14/22.74            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.14/22.74            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.14/22.74            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.14/22.74            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.14/22.74            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.74            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.14/22.74            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.14/22.74            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.74            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.14/22.74            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.14/22.74            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.74            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.14/22.74            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.74            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.74            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.74            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.14/22.74            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.14/22.74            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.14/22.74            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.14/22.74            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.14/22.74            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.74            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.74            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.74            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.14/22.74            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.14/22.74            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.74            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.14/22.74            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.14/22.74            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.74            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.14/22.74            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.14/22.74            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.74            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.14/22.74            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.14/22.74              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.14/22.74            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.14/22.74            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.14/22.74              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.14/22.74            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.14/22.74            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.14/22.74                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.14/22.74                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.74                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.14/22.74                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.14/22.74                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.14/22.74                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.14/22.74                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.14/22.74              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.14/22.74                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.14/22.74                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.74                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.14/22.74                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.14/22.74                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.14/22.74                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.74                $i(all_57_7))))
% 153.14/22.74    (30)  op(e2, e3) = all_52_1
% 153.14/22.74    (31)   ~ (all_52_1 = e2)
% 153.14/22.74  
% 153.14/22.74  Begin of proof
% 153.14/22.74  | 
% 153.14/22.74  | BETA: splitting (12) gives:
% 153.14/22.74  | 
% 153.14/22.74  | Case 1:
% 153.14/22.74  | | 
% 153.14/22.74  | |   (32)  all_57_3 = e3 & op(e3, e2) = e3
% 153.14/22.74  | | 
% 153.14/22.74  | | ALPHA: (32) implies:
% 153.14/22.74  | |   (33)  op(e3, e2) = e3
% 153.14/22.74  | | 
% 153.14/22.74  | | BETA: splitting (29) gives:
% 153.14/22.74  | | 
% 153.14/22.74  | | Case 1:
% 153.14/22.74  | | | 
% 153.14/22.74  | | |   (34)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.14/22.74  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.14/22.74  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.14/22.74  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 153.14/22.74  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.14/22.74  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.14/22.74  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 153.14/22.74  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.14/22.74  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.14/22.74  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 153.14/22.74  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.14/22.74  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 153.14/22.74  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) | (all_57_3 =
% 153.14/22.74  | | |           e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 = e2) &
% 153.14/22.74  | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) = all_57_4
% 153.14/22.74  | | |           & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3 =
% 153.14/22.74  | | |           e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.14/22.74  | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5
% 153.14/22.74  | | |           & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 =
% 153.14/22.74  | | |           e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 153.14/22.74  | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.14/22.74  | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.14/22.74  | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.14/22.74  | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.74  | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.14/22.74  | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7
% 153.14/22.74  | | |             = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 153.14/22.74  | | |             e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.14/22.74  | | |           $i(all_57_7) & $i(all_57_10))
% 153.14/22.74  | | | 
% 153.14/22.74  | | | BETA: splitting (34) gives:
% 153.14/22.74  | | | 
% 153.14/22.74  | | | Case 1:
% 153.14/22.74  | | | | 
% 153.14/22.74  | | | |   (35)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.14/22.74  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.14/22.74  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.14/22.74  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.14/22.74  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.14/22.74  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.14/22.74  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.74  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.14/22.74  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.14/22.74  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.14/22.74  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.14/22.74  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.74  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.14/22.74  | | | |           $i(all_57_14))
% 153.14/22.74  | | | | 
% 153.14/22.74  | | | | REF_CLOSE: (3), (8), (13), (22), (30), (31), (35) are inconsistent by
% 153.14/22.74  | | | |            sub-proof #436.
% 153.14/22.74  | | | | 
% 153.14/22.74  | | | Case 2:
% 153.14/22.74  | | | | 
% 153.14/22.74  | | | |   (36)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.14/22.74  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.14/22.74  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.14/22.74  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.14/22.74  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 153.14/22.74  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.14/22.74  | | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 =
% 153.14/22.74  | | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) =
% 153.14/22.74  | | | |           e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.14/22.74  | | | |           all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 153.14/22.74  | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 153.14/22.74  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.14/22.74  | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.14/22.74  | | | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.14/22.74  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.74  | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.14/22.74  | | | |           $i(all_57_10))
% 153.14/22.74  | | | | 
% 153.14/22.74  | | | | BETA: splitting (36) gives:
% 153.14/22.74  | | | | 
% 153.14/22.74  | | | | Case 1:
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | |   (37)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.14/22.74  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.14/22.74  | | | | |           & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.14/22.74  | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.14/22.74  | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.14/22.74  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.14/22.74  | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | | REF_CLOSE: (8), (13), (22), (24), (28), (37) are inconsistent by
% 153.14/22.74  | | | | |            sub-proof #435.
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | Case 2:
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | |   (38)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.14/22.74  | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.14/22.74  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.14/22.74  | | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.14/22.74  | | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.14/22.74  | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 153.14/22.74  | | | | |           = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 153.14/22.74  | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.14/22.74  | | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.14/22.74  | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | | REF_CLOSE: (8), (12), (13), (20), (28), (38) are inconsistent by
% 153.14/22.74  | | | | |            sub-proof #437.
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | End of split
% 153.14/22.74  | | | | 
% 153.14/22.74  | | | End of split
% 153.14/22.74  | | | 
% 153.14/22.74  | | Case 2:
% 153.14/22.74  | | | 
% 153.14/22.74  | | |   (39)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.74  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.74  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.74  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 153.14/22.74  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.14/22.74  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.14/22.74  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 153.14/22.74  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 153.14/22.74  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 153.14/22.74  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 153.14/22.74  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 153.14/22.74  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.14/22.74  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 153.14/22.74  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.14/22.74  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.74  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.14/22.74  | | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9
% 153.14/22.74  | | |             = e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.14/22.74  | | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.14/22.74  | | |           $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1
% 153.14/22.74  | | |           &  ~ (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.14/22.74  | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.14/22.74  | | |           & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 153.14/22.74  | | |           e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.14/22.74  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.14/22.74  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.14/22.74  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.14/22.74  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.14/22.74  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.14/22.74  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.14/22.74  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.14/22.74  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.74  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.14/22.74  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.14/22.74  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 153.14/22.74  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.14/22.74  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.14/22.74  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.14/22.74  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 153.14/22.74  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.74  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.74  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.14/22.74  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.14/22.74  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.14/22.74  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.14/22.74  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 153.14/22.74  | | | 
% 153.14/22.74  | | | BETA: splitting (39) gives:
% 153.14/22.74  | | | 
% 153.14/22.74  | | | Case 1:
% 153.14/22.74  | | | | 
% 153.14/22.74  | | | |   (40)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.74  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.14/22.74  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.74  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.14/22.74  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.14/22.74  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.14/22.74  | | | |           e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.14/22.74  | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.14/22.74  | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.14/22.74  | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.14/22.74  | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.14/22.74  | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.74  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.14/22.74  | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.14/22.74  | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.14/22.74  | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.14/22.74  | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.14/22.74  | | | | 
% 153.14/22.74  | | | | BETA: splitting (40) gives:
% 153.14/22.74  | | | | 
% 153.14/22.74  | | | | Case 1:
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | |   (41)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.74  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.14/22.74  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.74  | | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.14/22.74  | | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.14/22.74  | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 153.14/22.74  | | | | |           = e2 & $i(all_57_6) & $i(all_57_12))
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | | REF_CLOSE: (8), (16), (21), (25), (27), (41) are inconsistent by
% 153.14/22.74  | | | | |            sub-proof #1083.
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | Case 2:
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | |   (42)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.14/22.74  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 153.14/22.74  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.14/22.74  | | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 153.14/22.74  | | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 153.14/22.74  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 153.14/22.74  | | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 153.14/22.74  | | | | |           & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1)
% 153.14/22.74  | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 153.14/22.74  | | | | |           & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | | REF_CLOSE: (7), (8), (14), (16), (20), (21), (22), (42) are
% 153.14/22.74  | | | | |            inconsistent by sub-proof #433.
% 153.14/22.74  | | | | | 
% 153.14/22.74  | | | | End of split
% 153.14/22.74  | | | | 
% 153.14/22.74  | | | Case 2:
% 153.14/22.74  | | | | 
% 153.14/22.75  | | | |   (43)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.14/22.75  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.75  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.14/22.75  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.14/22.75  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.14/22.75  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.14/22.75  | | | |           e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 153.14/22.75  | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 153.14/22.75  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.14/22.75  | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 153.14/22.75  | | | |         (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.14/22.75  | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.14/22.75  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.14/22.75  | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.14/22.75  | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.14/22.75  | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 153.14/22.75  | | | |               & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.14/22.75  | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 153.14/22.75  | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 153.14/22.75  | | | |               e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.14/22.75  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.14/22.75  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.14/22.75  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.14/22.75  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.14/22.75  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.14/22.75  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.14/22.75  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.14/22.75  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.75  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.14/22.75  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.14/22.75  | | | | 
% 153.14/22.75  | | | | BETA: splitting (43) gives:
% 153.14/22.75  | | | | 
% 153.14/22.75  | | | | Case 1:
% 153.14/22.75  | | | | | 
% 153.14/22.75  | | | | |   (44)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.14/22.75  | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.14/22.75  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.14/22.75  | | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.14/22.75  | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.14/22.75  | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.14/22.75  | | | | |           = e1 & $i(all_57_9) & $i(all_57_14))
% 153.14/22.75  | | | | | 
% 153.14/22.75  | | | | | REF_CLOSE: (7), (8), (10), (44) are inconsistent by sub-proof #1037.
% 153.14/22.75  | | | | | 
% 153.14/22.75  | | | | Case 2:
% 153.14/22.75  | | | | | 
% 153.14/22.75  | | | | |   (45)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.14/22.75  | | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.14/22.75  | | | | |           & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.14/22.75  | | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 153.14/22.75  | | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.14/22.75  | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.14/22.75  | | | | |           = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.14/22.75  | | | | |           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 153.14/22.75  | | | | |               &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3)
% 153.14/22.75  | | | | |               = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.75  | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.14/22.75  | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.14/22.75  | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.14/22.75  | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.14/22.75  | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.14/22.75  | | | | |               & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.14/22.75  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.14/22.75  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.14/22.75  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.75  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.75  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.14/22.75  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.14/22.75  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.75  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.14/22.75  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.75  | | | | |               $i(all_57_7))))
% 153.14/22.75  | | | | | 
% 153.14/22.75  | | | | | BETA: splitting (45) gives:
% 153.14/22.75  | | | | | 
% 153.14/22.75  | | | | | Case 1:
% 153.14/22.75  | | | | | | 
% 153.14/22.75  | | | | | |   (46)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.14/22.75  | | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.14/22.75  | | | | | |         & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.14/22.75  | | | | | |         $i(all_57_13)
% 153.14/22.75  | | | | | | 
% 153.14/22.75  | | | | | | ALPHA: (46) implies:
% 153.14/22.75  | | | | | |   (47)  op(e2, e0) = e2
% 153.14/22.75  | | | | | | 
% 153.14/22.75  | | | | | | REF_CLOSE: (8), (11), (15), (47) are inconsistent by sub-proof
% 153.14/22.75  | | | | | |            #1156.
% 153.14/22.75  | | | | | | 
% 153.14/22.75  | | | | | Case 2:
% 153.14/22.75  | | | | | | 
% 153.14/22.75  | | | | | |   (48)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.14/22.75  | | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.14/22.75  | | | | | |           all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.14/22.75  | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.14/22.75  | | | | | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 153.14/22.75  | | | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.14/22.75  | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.14/22.75  | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.14/22.75  | | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.14/22.75  | | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.14/22.75  | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.14/22.75  | | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.14/22.75  | | | | | |               e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.14/22.75  | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.14/22.75  | | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.14/22.75  | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.75  | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.75  | | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.14/22.75  | | | | | |               e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.14/22.75  | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.75  | | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 153.14/22.75  | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.75  | | | | | |               $i(all_57_7))))
% 153.14/22.75  | | | | | | 
% 153.14/22.75  | | | | | | BETA: splitting (48) gives:
% 153.14/22.75  | | | | | | 
% 153.14/22.75  | | | | | | Case 1:
% 153.14/22.75  | | | | | | | 
% 153.14/22.75  | | | | | | |   (49)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.14/22.75  | | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.14/22.75  | | | | | | |         all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.14/22.75  | | | | | | |         $i(all_57_11) & $i(all_57_14)
% 153.14/22.75  | | | | | | | 
% 153.14/22.75  | | | | | | | ALPHA: (49) implies:
% 153.14/22.75  | | | | | | |   (50)  op(e1, e0) = e1
% 153.14/22.75  | | | | | | | 
% 153.14/22.75  | | | | | | | REF_CLOSE: (8), (23), (28), (50) are inconsistent by sub-proof
% 153.14/22.75  | | | | | | |            #1125.
% 153.14/22.75  | | | | | | | 
% 153.14/22.75  | | | | | | Case 2:
% 153.14/22.75  | | | | | | | 
% 153.14/22.75  | | | | | | |   (51)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.14/22.75  | | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.14/22.75  | | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.14/22.75  | | | | | | |             op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.14/22.75  | | | | | | |             all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.14/22.75  | | | | | | |               e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.14/22.75  | | | | | | |             op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 153.14/22.75  | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 153.14/22.75  | | | | | | |               e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.14/22.75  | | | | | | |             op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.14/22.75  | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.14/22.75  | | | | | | |               e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.14/22.75  | | | | | | |             op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.14/22.75  | | | | | | |             all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.14/22.75  | | | | | | |               e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.14/22.75  | | | | | | |             op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.14/22.75  | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.14/22.75  | | | | | | |               e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.14/22.75  | | | | | | |             op(e0, e1) = e0 & $i(all_57_7)))
% 153.14/22.75  | | | | | | | 
% 153.14/22.75  | | | | | | | ALPHA: (51) implies:
% 153.14/22.75  | | | | | | |   (52)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.14/22.75  | | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 153.14/22.75  | | | | | | |           e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.14/22.75  | | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.14/22.75  | | | | | | |             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.14/22.75  | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.14/22.75  | | | | | | |           = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 153.14/22.75  | | | | | | |             e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.14/22.75  | | | | | | |           $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.14/22.75  | | | | | | |           (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.14/22.75  | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.75  | | | | | | |           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.14/22.75  | | | | | | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.14/22.75  | | | | | | |           & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.14/22.75  | | | | | | |           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.75  | | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.14/22.75  | | | | | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.14/22.75  | | | | | | |           $i(all_57_7))
% 153.14/22.75  | | | | | | | 
% 153.14/22.75  | | | | | | | BETA: splitting (52) gives:
% 153.14/22.75  | | | | | | | 
% 153.14/22.75  | | | | | | | Case 1:
% 153.14/22.75  | | | | | | | | 
% 153.14/22.75  | | | | | | | |   (53)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 153.14/22.75  | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.14/22.75  | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.14/22.75  | | | | | | | |         (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.14/22.75  | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.14/22.75  | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.14/22.75  | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.14/22.75  | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.75  | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.14/22.75  | | | | | | | | 
% 153.14/22.75  | | | | | | | | BETA: splitting (53) gives:
% 153.14/22.75  | | | | | | | | 
% 153.14/22.75  | | | | | | | | Case 1:
% 153.14/22.75  | | | | | | | | | 
% 153.14/22.75  | | | | | | | | |   (54)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 153.14/22.75  | | | | | | | | |         ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.14/22.75  | | | | | | | | |           e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)
% 153.14/22.75  | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | ALPHA: (54) implies:
% 153.14/22.75  | | | | | | | | |   (55)  op(e2, e2) = e3
% 153.14/22.75  | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | REF_CLOSE: (8), (20), (24), (55) are inconsistent by sub-proof
% 153.14/22.75  | | | | | | | | |            #1179.
% 153.14/22.75  | | | | | | | | | 
% 153.14/22.75  | | | | | | | | Case 2:
% 153.14/22.75  | | | | | | | | | 
% 153.14/22.75  | | | | | | | | |   (56)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 153.14/22.75  | | | | | | | | |            ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.14/22.75  | | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.14/22.75  | | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &
% 153.14/22.75  | | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.14/22.75  | | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.14/22.75  | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | BETA: splitting (56) gives:
% 153.14/22.75  | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | Case 1:
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | |   (57)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 153.14/22.75  | | | | | | | | | |         &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.14/22.75  | | | | | | | | | |         op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | ALPHA: (57) implies:
% 153.14/22.75  | | | | | | | | | |   (58)  op(e0, e3) = e0
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_11, e2, e1, e0,
% 153.14/22.75  | | | | | | | | | |              simplifying with (1), (17) gives:
% 153.14/22.75  | | | | | | | | | |   (59)  all_52_11 = e2
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_3, e0, e3, e0,
% 153.14/22.75  | | | | | | | | | |              simplifying with (18), (58) gives:
% 153.14/22.75  | | | | | | | | | |   (60)  all_52_3 = e0
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | GROUND_INST: instantiating (8) with all_52_4, e3, e2, e3,
% 153.14/22.75  | | | | | | | | | |              simplifying with (4), (33) gives:
% 153.14/22.75  | | | | | | | | | |   (61)  all_52_4 = e3
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | REDUCE: (6), (60) imply:
% 153.14/22.75  | | | | | | | | | |   (62)   ~ (all_52_7 = e0)
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | SIMP: (62) implies:
% 153.14/22.75  | | | | | | | | | |   (63)   ~ (all_52_7 = e0)
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | REDUCE: (5), (61) imply:
% 153.14/22.75  | | | | | | | | | |   (64)   ~ (all_52_7 = e3)
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | SIMP: (64) implies:
% 153.14/22.75  | | | | | | | | | |   (65)   ~ (all_52_7 = e3)
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | REDUCE: (2), (59) imply:
% 153.14/22.75  | | | | | | | | | |   (66)   ~ (all_52_7 = e2)
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | REF_CLOSE: (9), (19), (26), (63), (65), (66) are inconsistent
% 153.14/22.75  | | | | | | | | | |            by sub-proof #432.
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | Case 2:
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | |   (67)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3)
% 153.14/22.75  | | | | | | | | | |         &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 153.14/22.75  | | | | | | | | | |         = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | ALPHA: (67) implies:
% 153.14/22.75  | | | | | | | | | |   (68)  all_57_10 = e2
% 153.14/22.75  | | | | | | | | | |   (69)   ~ (all_57_3 = e3)
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | | REF_CLOSE: (12), (68), (69) are inconsistent by sub-proof
% 153.14/22.75  | | | | | | | | | |            #1018.
% 153.14/22.75  | | | | | | | | | | 
% 153.14/22.75  | | | | | | | | | End of split
% 153.14/22.75  | | | | | | | | | 
% 153.14/22.75  | | | | | | | | End of split
% 153.14/22.75  | | | | | | | | 
% 153.14/22.75  | | | | | | | Case 2:
% 153.14/22.75  | | | | | | | | 
% 153.14/22.75  | | | | | | | |   (70)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) & 
% 153.14/22.75  | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.14/22.75  | | | | | | | |             e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.14/22.75  | | | | | | | |         (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.14/22.75  | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.14/22.75  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 153.14/22.75  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.14/22.75  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.14/22.75  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.14/22.75  | | | | | | | | 
% 153.14/22.75  | | | | | | | | REF_CLOSE: (7), (8), (17), (20), (22), (24), (28), (70) are
% 153.14/22.75  | | | | | | | |            inconsistent by sub-proof #431.
% 153.14/22.75  | | | | | | | | 
% 153.14/22.75  | | | | | | | End of split
% 153.14/22.75  | | | | | | | 
% 153.14/22.75  | | | | | | End of split
% 153.14/22.75  | | | | | | 
% 153.14/22.75  | | | | | End of split
% 153.14/22.75  | | | | | 
% 153.14/22.75  | | | | End of split
% 153.14/22.75  | | | | 
% 153.14/22.75  | | | End of split
% 153.14/22.75  | | | 
% 153.14/22.75  | | End of split
% 153.14/22.75  | | 
% 153.14/22.75  | Case 2:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (71)   ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10)
% 153.14/22.75  | | 
% 153.14/22.75  | | ALPHA: (71) implies:
% 153.14/22.75  | |   (72)   ~ (all_57_10 = e2)
% 153.14/22.75  | |   (73)  op(e3, e3) = all_57_10
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (8), (10), (72), (73) are inconsistent by sub-proof #1031.
% 153.14/22.75  | | 
% 153.14/22.75  | End of split
% 153.14/22.75  | 
% 153.14/22.75  End of proof
% 153.14/22.75  
% 153.14/22.75  Sub-proof #431 shows that the following formulas are inconsistent:
% 153.14/22.75  ----------------------------------------------------------------
% 153.14/22.75    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.14/22.75             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.75           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.14/22.75           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.14/22.75             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.75           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.14/22.75           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.14/22.75    (2)   ~ (e2 = e0)
% 153.14/22.75    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.75    (4)  op(e0, e1) = e2
% 153.14/22.75    (5)  op(e2, e2) = e2
% 153.14/22.75    (6)  op(e1, e1) = e3
% 153.14/22.75    (7)   ~ (e3 = e2)
% 153.14/22.75    (8)   ~ (e2 = e1)
% 153.14/22.75  
% 153.14/22.75  Begin of proof
% 153.14/22.75  | 
% 153.14/22.75  | BETA: splitting (1) gives:
% 153.14/22.75  | 
% 153.14/22.75  | Case 1:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (9)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.14/22.75  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.14/22.75  | |        $i(all_57_4)
% 153.14/22.75  | | 
% 153.14/22.75  | | ALPHA: (9) implies:
% 153.14/22.75  | |   (10)  op(e1, e1) = e2
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (3), (6), (7), (10) are inconsistent by sub-proof #834.
% 153.14/22.75  | | 
% 153.14/22.75  | Case 2:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (11)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 153.14/22.75  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.14/22.75  | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.14/22.75  | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2,
% 153.14/22.75  | |             e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (2), (3), (4), (5), (8), (11) are inconsistent by sub-proof
% 153.14/22.75  | |            #1007.
% 153.14/22.75  | | 
% 153.14/22.75  | End of split
% 153.14/22.75  | 
% 153.14/22.75  End of proof
% 153.14/22.75  
% 153.14/22.75  Sub-proof #432 shows that the following formulas are inconsistent:
% 153.14/22.75  ----------------------------------------------------------------
% 153.14/22.75    (1)   ~ (all_52_7 = e1)
% 153.14/22.75    (2)   ~ (all_52_7 = e3)
% 153.14/22.75    (3)   ~ (all_52_7 = e2)
% 153.14/22.75    (4)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.14/22.75    (5)   ~ (all_52_7 = e0)
% 153.14/22.75    (6)  all_54_13 = all_52_7
% 153.14/22.75  
% 153.14/22.75  Begin of proof
% 153.14/22.75  | 
% 153.14/22.75  | BETA: splitting (4) gives:
% 153.14/22.75  | 
% 153.14/22.75  | Case 1:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (7)  all_54_13 = e3
% 153.14/22.75  | | 
% 153.14/22.75  | | COMBINE_EQS: (6), (7) imply:
% 153.14/22.75  | |   (8)  all_52_7 = e3
% 153.14/22.75  | | 
% 153.14/22.75  | | REDUCE: (2), (8) imply:
% 153.14/22.75  | |   (9)  $false
% 153.14/22.75  | | 
% 153.14/22.75  | | CLOSE: (9) is inconsistent.
% 153.14/22.75  | | 
% 153.14/22.75  | Case 2:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (10)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #982.
% 153.14/22.75  | | 
% 153.14/22.75  | End of split
% 153.14/22.75  | 
% 153.14/22.75  End of proof
% 153.14/22.75  
% 153.14/22.75  Sub-proof #433 shows that the following formulas are inconsistent:
% 153.14/22.75  ----------------------------------------------------------------
% 153.14/22.75    (1)   ~ (e2 = e0)
% 153.14/22.75    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.75    (3)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 153.14/22.75             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.14/22.75           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 153.14/22.75           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 153.14/22.75           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 153.14/22.75           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.14/22.75           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 153.14/22.75           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.14/22.75           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.14/22.75    (4)   ~ (e3 = e0)
% 153.14/22.75    (5)   ~ (all_52_9 = e2)
% 153.14/22.75    (6)  op(e2, e2) = e2
% 153.14/22.75    (7)  op(e2, e1) = all_52_9
% 153.14/22.75    (8)  op(e1, e1) = e3
% 153.14/22.75  
% 153.14/22.75  Begin of proof
% 153.14/22.75  | 
% 153.14/22.75  | BETA: splitting (3) gives:
% 153.14/22.75  | 
% 153.14/22.75  | Case 1:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (9)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 153.14/22.75  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.14/22.75  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 153.14/22.75  | | 
% 153.14/22.75  | | ALPHA: (9) implies:
% 153.14/22.75  | |   (10)  op(e2, e1) = e2
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (2), (5), (7), (10) are inconsistent by sub-proof #1157.
% 153.14/22.75  | | 
% 153.14/22.75  | Case 2:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (11)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.14/22.75  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.14/22.75  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.14/22.75  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 153.14/22.75  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 153.14/22.75  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.14/22.75  | |           $i(all_57_13))
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (1), (2), (4), (6), (8), (11) are inconsistent by sub-proof #434.
% 153.14/22.75  | | 
% 153.14/22.75  | End of split
% 153.14/22.75  | 
% 153.14/22.75  End of proof
% 153.14/22.75  
% 153.14/22.75  Sub-proof #434 shows that the following formulas are inconsistent:
% 153.14/22.75  ----------------------------------------------------------------
% 153.14/22.75    (1)   ~ (e2 = e0)
% 153.14/22.75    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.75    (3)   ~ (e3 = e0)
% 153.14/22.75    (4)  op(e2, e2) = e2
% 153.14/22.75    (5)  op(e1, e1) = e3
% 153.14/22.75    (6)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 153.14/22.75             e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.14/22.75           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 =
% 153.14/22.75           e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 153.14/22.75           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 153.14/22.75           = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.14/22.75  
% 153.14/22.75  Begin of proof
% 153.14/22.75  | 
% 153.14/22.75  | BETA: splitting (6) gives:
% 153.14/22.75  | 
% 153.14/22.75  | Case 1:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (7)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 153.14/22.75  | |          = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0
% 153.14/22.75  | |        & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)
% 153.14/22.75  | | 
% 153.14/22.75  | | ALPHA: (7) implies:
% 153.14/22.75  | |   (8)  op(e2, e2) = e0
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #1145.
% 153.14/22.75  | | 
% 153.14/22.75  | Case 2:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (9)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 153.14/22.75  | |          = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 153.14/22.75  | |        & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)
% 153.14/22.75  | | 
% 153.14/22.75  | | ALPHA: (9) implies:
% 153.14/22.75  | |   (10)  op(e1, e1) = e0
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #896.
% 153.14/22.75  | | 
% 153.14/22.75  | End of split
% 153.14/22.75  | 
% 153.14/22.75  End of proof
% 153.14/22.75  
% 153.14/22.75  Sub-proof #435 shows that the following formulas are inconsistent:
% 153.14/22.75  ----------------------------------------------------------------
% 153.14/22.75    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.75    (2)  op(e0, e0) = e1
% 153.14/22.75    (3)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.14/22.75             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.14/22.75           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 153.14/22.75           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.14/22.75           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.14/22.75           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.14/22.75    (4)  op(e1, e1) = e3
% 153.14/22.75    (5)   ~ (e3 = e2)
% 153.14/22.75    (6)   ~ (e2 = e1)
% 153.14/22.75  
% 153.14/22.75  Begin of proof
% 153.14/22.75  | 
% 153.14/22.75  | BETA: splitting (3) gives:
% 153.14/22.75  | 
% 153.14/22.75  | Case 1:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (7)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.14/22.75  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.14/22.75  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 153.14/22.75  | | 
% 153.14/22.75  | | ALPHA: (7) implies:
% 153.14/22.75  | |   (8)  op(e1, e1) = e2
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #834.
% 153.14/22.75  | | 
% 153.14/22.75  | Case 2:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (9)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 153.14/22.75  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.14/22.75  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 153.14/22.75  | | 
% 153.14/22.75  | | ALPHA: (9) implies:
% 153.14/22.75  | |   (10)  op(e0, e0) = e2
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #978.
% 153.14/22.75  | | 
% 153.14/22.75  | End of split
% 153.14/22.75  | 
% 153.14/22.75  End of proof
% 153.14/22.75  
% 153.14/22.75  Sub-proof #436 shows that the following formulas are inconsistent:
% 153.14/22.75  ----------------------------------------------------------------
% 153.14/22.75    (1)   ~ (e3 = e1)
% 153.14/22.75    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.75    (3)  op(e0, e0) = e1
% 153.14/22.75    (4)  op(e1, e1) = e3
% 153.14/22.75    (5)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.14/22.75             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.75           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.14/22.75           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.14/22.75           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.14/22.75           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.14/22.75           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.14/22.75           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.14/22.75           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.14/22.75           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 153.14/22.75           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.14/22.75           $i(all_57_14))
% 153.14/22.75    (6)  op(e2, e3) = all_52_1
% 153.14/22.75    (7)   ~ (all_52_1 = e2)
% 153.14/22.75  
% 153.14/22.75  Begin of proof
% 153.14/22.75  | 
% 153.14/22.75  | BETA: splitting (5) gives:
% 153.14/22.75  | 
% 153.14/22.75  | Case 1:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (8)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 153.14/22.75  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.14/22.75  | |          all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 153.14/22.75  | |        (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 153.14/22.75  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.14/22.75  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (2), (6), (7), (8) are inconsistent by sub-proof #1180.
% 153.14/22.75  | | 
% 153.14/22.75  | Case 2:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (9)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 153.14/22.75  | |            = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1
% 153.14/22.75  | |          & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.14/22.75  | |        (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 153.14/22.75  | |            = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.14/22.75  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.14/22.75  | | 
% 153.14/22.75  | | BETA: splitting (9) gives:
% 153.14/22.75  | | 
% 153.14/22.75  | | Case 1:
% 153.14/22.75  | | | 
% 153.14/22.75  | | |   (10)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.14/22.75  | | |         (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.14/22.75  | | |         op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.14/22.75  | | |         $i(all_57_14)
% 153.14/22.75  | | | 
% 153.14/22.75  | | | ALPHA: (10) implies:
% 153.14/22.75  | | |   (11)   ~ (all_57_14 = e3)
% 153.14/22.75  | | |   (12)  op(e1, e1) = all_57_14
% 153.14/22.75  | | | 
% 153.14/22.75  | | | REF_CLOSE: (2), (4), (11), (12) are inconsistent by sub-proof #816.
% 153.14/22.75  | | | 
% 153.14/22.75  | | Case 2:
% 153.14/22.75  | | | 
% 153.14/22.75  | | |   (13)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.14/22.75  | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.14/22.75  | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.14/22.75  | | |         $i(all_57_14)
% 153.14/22.75  | | | 
% 153.14/22.75  | | | ALPHA: (13) implies:
% 153.14/22.75  | | |   (14)  op(e0, e0) = e3
% 153.14/22.75  | | | 
% 153.14/22.75  | | | REF_CLOSE: (1), (2), (3), (14) are inconsistent by sub-proof #1022.
% 153.14/22.75  | | | 
% 153.14/22.75  | | End of split
% 153.14/22.75  | | 
% 153.14/22.75  | End of split
% 153.14/22.75  | 
% 153.14/22.75  End of proof
% 153.14/22.75  
% 153.14/22.75  Sub-proof #437 shows that the following formulas are inconsistent:
% 153.14/22.75  ----------------------------------------------------------------
% 153.14/22.75    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.75    (2)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3, e3) =
% 153.14/22.75           all_57_10 & $i(all_57_10))
% 153.14/22.75    (3)  op(e0, e0) = e1
% 153.14/22.75    (4)  op(e2, e2) = e2
% 153.14/22.75    (5)   ~ (e2 = e1)
% 153.14/22.75    (6)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.14/22.75             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.14/22.75           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 153.14/22.75           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 153.14/22.75             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.14/22.75             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.14/22.75           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.14/22.75           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.14/22.75           $i(all_57_7) & $i(all_57_10))
% 153.14/22.75  
% 153.14/22.75  Begin of proof
% 153.14/22.75  | 
% 153.14/22.75  | BETA: splitting (6) gives:
% 153.14/22.75  | 
% 153.14/22.75  | Case 1:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (7)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.14/22.75  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.14/22.75  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 153.14/22.75  | | 
% 153.14/22.75  | | ALPHA: (7) implies:
% 153.14/22.75  | |   (8)  all_57_10 = e2
% 153.14/22.75  | |   (9)   ~ (all_57_3 = e3)
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (2), (8), (9) are inconsistent by sub-proof #1018.
% 153.14/22.75  | | 
% 153.14/22.75  | Case 2:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (10)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.14/22.75  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.14/22.75  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.14/22.75  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.14/22.75  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.14/22.75  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (1), (3), (4), (5), (10) are inconsistent by sub-proof #441.
% 153.14/22.75  | | 
% 153.14/22.75  | End of split
% 153.14/22.75  | 
% 153.14/22.75  End of proof
% 153.14/22.75  
% 153.14/22.75  Sub-proof #438 shows that the following formulas are inconsistent:
% 153.14/22.75  ----------------------------------------------------------------
% 153.14/22.75    (1)  op(e1, e1) = all_4_2
% 153.14/22.75    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.75    (3)  op(e0, e0) = e1
% 153.14/22.75    (4)   ~ (all_4_2 = e2)
% 153.14/22.75    (5)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.14/22.75             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.14/22.75           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 153.14/22.75           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.14/22.75           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.14/22.75           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.14/22.75    (6)   ~ (e2 = e1)
% 153.14/22.75  
% 153.14/22.75  Begin of proof
% 153.14/22.75  | 
% 153.14/22.75  | BETA: splitting (5) gives:
% 153.14/22.75  | 
% 153.14/22.75  | Case 1:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (7)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.14/22.75  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.14/22.75  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 153.14/22.75  | | 
% 153.14/22.75  | | ALPHA: (7) implies:
% 153.14/22.75  | |   (8)  op(e1, e1) = e2
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #1169.
% 153.14/22.75  | | 
% 153.14/22.75  | Case 2:
% 153.14/22.75  | | 
% 153.14/22.75  | |   (9)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 153.14/22.75  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.14/22.75  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 153.14/22.75  | | 
% 153.14/22.75  | | ALPHA: (9) implies:
% 153.14/22.75  | |   (10)  op(e0, e0) = e2
% 153.14/22.75  | | 
% 153.14/22.75  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #978.
% 153.14/22.75  | | 
% 153.14/22.75  | End of split
% 153.14/22.75  | 
% 153.14/22.75  End of proof
% 153.14/22.75  
% 153.14/22.75  Sub-proof #439 shows that the following formulas are inconsistent:
% 153.14/22.75  ----------------------------------------------------------------
% 153.14/22.75    (1)   ~ (e3 = e1)
% 153.14/22.75    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.75           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.75    (3)  op(e3, e1) = e3
% 153.14/22.75    (4)  op(e3, e1) = e1
% 153.14/22.75    (5)  op(e3, e1) = all_52_8
% 153.14/22.75  
% 153.14/22.75  Begin of proof
% 153.14/22.75  | 
% 153.14/22.75  | GROUND_INST: instantiating (2) with all_52_8, e1, e1, e3, simplifying with
% 153.14/22.75  |              (4), (5) gives:
% 153.14/22.75  |   (6)  all_52_8 = e1
% 153.14/22.75  | 
% 153.14/22.75  | GROUND_INST: instantiating (2) with all_52_8, e3, e1, e3, simplifying with
% 153.14/22.75  |              (3), (5) gives:
% 153.14/22.75  |   (7)  all_52_8 = e3
% 153.14/22.75  | 
% 153.14/22.75  | COMBINE_EQS: (6), (7) imply:
% 153.14/22.75  |   (8)  e3 = e1
% 153.14/22.75  | 
% 153.14/22.75  | REDUCE: (1), (8) imply:
% 153.14/22.75  |   (9)  $false
% 153.14/22.75  | 
% 153.14/22.75  | CLOSE: (9) is inconsistent.
% 153.14/22.75  | 
% 153.14/22.75  End of proof
% 153.14/22.75  
% 153.14/22.75  Sub-proof #440 shows that the following formulas are inconsistent:
% 153.14/22.75  ----------------------------------------------------------------
% 153.14/22.75    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.14/22.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.14/22.76    (2)  op(e3, e0) = all_52_12
% 153.14/22.76    (3)   ~ (all_52_12 = e3)
% 153.14/22.76    (4)   ~ (all_52_9 = e2)
% 153.14/22.76    (5)  op(e2, e1) = all_52_9
% 153.14/22.76    (6)   ~ (all_52_8 = e3)
% 153.14/22.76    (7)  op(e3, e1) = all_52_8
% 153.14/22.76    (8)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.14/22.76             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.14/22.76           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.14/22.76           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.14/22.76           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.14/22.76           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.14/22.76           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2)
% 153.14/22.76           = all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1
% 153.23/22.76           & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 153.23/22.76           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 153.23/22.76           op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.23/22.76           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.23/22.76           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 153.23/22.76           op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.23/22.76           $i(all_57_10) & $i(all_57_13))
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | BETA: splitting (8) gives:
% 153.23/22.76  | 
% 153.23/22.76  | Case 1:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (9)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 153.23/22.76  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.23/22.76  | |          all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 153.23/22.76  | |        (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 153.23/22.76  | |            = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.23/22.76  | |          all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 153.23/22.76  | | 
% 153.23/22.76  | | REF_CLOSE: (1), (4), (5), (6), (7), (9) are inconsistent by sub-proof #1083.
% 153.23/22.76  | | 
% 153.23/22.76  | Case 2:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (10)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 153.23/22.76  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.23/22.76  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.23/22.76  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.23/22.76  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.23/22.76  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.23/22.76  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 153.23/22.76  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 153.23/22.76  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.23/22.76  | |           $i(all_57_13))
% 153.23/22.76  | | 
% 153.23/22.76  | | BETA: splitting (10) gives:
% 153.23/22.76  | | 
% 153.23/22.76  | | Case 1:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (11)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.23/22.76  | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.23/22.76  | | |         op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.23/22.76  | | |         $i(all_57_12)
% 153.23/22.76  | | | 
% 153.23/22.76  | | | ALPHA: (11) implies:
% 153.23/22.76  | | |   (12)  op(e2, e1) = e2
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (1), (4), (5), (12) are inconsistent by sub-proof #1157.
% 153.23/22.76  | | | 
% 153.23/22.76  | | Case 2:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (13)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.23/22.76  | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.23/22.76  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.23/22.76  | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10
% 153.23/22.76  | | |             = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 153.23/22.76  | | |             e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.23/22.76  | | |           $i(all_57_10) & $i(all_57_13))
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (1), (2), (3), (13) are inconsistent by sub-proof #1081.
% 153.23/22.76  | | | 
% 153.23/22.76  | | End of split
% 153.23/22.76  | | 
% 153.23/22.76  | End of split
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #441 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.76    (2)  op(e0, e0) = e1
% 153.23/22.76    (3)  op(e2, e2) = e2
% 153.23/22.76    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.23/22.76             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.23/22.76           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.23/22.76           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.23/22.76           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 153.23/22.76           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.23/22.76    (5)   ~ (e2 = e1)
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | BETA: splitting (4) gives:
% 153.23/22.76  | 
% 153.23/22.76  | Case 1:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (6)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.23/22.76  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.23/22.76  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 153.23/22.76  | | 
% 153.23/22.76  | | ALPHA: (6) implies:
% 153.23/22.76  | |   (7)  op(e0, e0) = e2
% 153.23/22.76  | | 
% 153.23/22.76  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #978.
% 153.23/22.76  | | 
% 153.23/22.76  | Case 2:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (8)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.23/22.76  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.23/22.76  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 153.23/22.76  | | 
% 153.23/22.76  | | ALPHA: (8) implies:
% 153.23/22.76  | |   (9)  op(e2, e2) = e1
% 153.23/22.76  | | 
% 153.23/22.76  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1158.
% 153.23/22.76  | | 
% 153.23/22.76  | End of split
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #442 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)   ~ (e3 = e1)
% 153.23/22.76    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.76    (3)  op(e0, e0) = e1
% 153.23/22.76    (4)  op(e2, e2) = e2
% 153.23/22.76    (5)   ~ (e3 = e2)
% 153.23/22.76    (6)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.23/22.76             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.23/22.76           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.23/22.76           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.23/22.76           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.23/22.76           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.23/22.76           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.23/22.76           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.23/22.76           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.23/22.76           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 153.23/22.76           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.23/22.76           $i(all_57_14))
% 153.23/22.76    (7)  op(e2, e3) = all_52_1
% 153.23/22.76    (8)   ~ (all_52_1 = e2)
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | BETA: splitting (6) gives:
% 153.23/22.76  | 
% 153.23/22.76  | Case 1:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (9)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 153.23/22.76  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.23/22.76  | |          all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 153.23/22.76  | |        (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 153.23/22.76  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.23/22.76  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.23/22.76  | | 
% 153.23/22.76  | | REF_CLOSE: (2), (7), (8), (9) are inconsistent by sub-proof #1180.
% 153.23/22.76  | | 
% 153.23/22.76  | Case 2:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (10)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 153.23/22.76  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 153.23/22.76  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.23/22.76  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 153.23/22.76  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.23/22.76  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.23/22.76  | | 
% 153.23/22.76  | | BETA: splitting (10) gives:
% 153.23/22.76  | | 
% 153.23/22.76  | | Case 1:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (11)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.23/22.76  | | |         (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.23/22.76  | | |         op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.23/22.76  | | |         $i(all_57_14)
% 153.23/22.76  | | | 
% 153.23/22.76  | | | ALPHA: (11) implies:
% 153.23/22.76  | | |   (12)  op(e2, e2) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (2), (4), (5), (12) are inconsistent by sub-proof #1179.
% 153.23/22.76  | | | 
% 153.23/22.76  | | Case 2:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (13)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.23/22.76  | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.23/22.76  | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.23/22.76  | | |         $i(all_57_14)
% 153.23/22.76  | | | 
% 153.23/22.76  | | | ALPHA: (13) implies:
% 153.23/22.76  | | |   (14)  op(e0, e0) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (1), (2), (3), (14) are inconsistent by sub-proof #1022.
% 153.23/22.76  | | | 
% 153.23/22.76  | | End of split
% 153.23/22.76  | | 
% 153.23/22.76  | End of split
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #443 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)  all_54_5 = all_6_2
% 153.23/22.76    (2)  all_54_5 = e3
% 153.23/22.76    (3)   ~ (all_6_2 = e3)
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | COMBINE_EQS: (1), (2) imply:
% 153.23/22.76  |   (4)  all_6_2 = e3
% 153.23/22.76  | 
% 153.23/22.76  | SIMP: (4) implies:
% 153.23/22.76  |   (5)  all_6_2 = e3
% 153.23/22.76  | 
% 153.23/22.76  | REDUCE: (3), (5) imply:
% 153.23/22.76  |   (6)  $false
% 153.23/22.76  | 
% 153.23/22.76  | CLOSE: (6) is inconsistent.
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #444 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.23/22.76         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.23/22.76    (2)   ~ (e3 = e1)
% 153.23/22.76    (3)   ~ (e2 = e0)
% 153.23/22.76    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.76    (5)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.23/22.76             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.23/22.76               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.23/22.76               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.23/22.76    (6)  op(e0, e0) = e1
% 153.23/22.76    (7)   ~ (e3 = e0)
% 153.23/22.76    (8)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.23/22.76    (9)   ~ (e1 = e0)
% 153.23/22.76    (10)   ~ (e3 = e2)
% 153.23/22.76    (11)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.23/22.76          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.23/22.76    (12)   ~ (e2 = e1)
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | BETA: splitting (8) gives:
% 153.23/22.76  | 
% 153.23/22.76  | Case 1:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (13)  all_56_9 = e1 & op(e3, e0) = e1
% 153.23/22.76  | | 
% 153.23/22.76  | | ALPHA: (13) implies:
% 153.23/22.76  | |   (14)  all_56_9 = e1
% 153.23/22.76  | | 
% 153.23/22.76  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14)
% 153.23/22.76  | |            are inconsistent by sub-proof #496.
% 153.23/22.76  | | 
% 153.23/22.76  | Case 2:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (15)  all_56_10 = e1 & op(e2, e0) = e1
% 153.23/22.76  | | 
% 153.23/22.76  | | ALPHA: (15) implies:
% 153.23/22.76  | |   (16)  all_56_10 = e1
% 153.23/22.76  | | 
% 153.23/22.76  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (16)
% 153.23/22.76  | |            are inconsistent by sub-proof #445.
% 153.23/22.76  | | 
% 153.23/22.76  | End of split
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #445 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.23/22.76         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.23/22.76    (2)   ~ (e3 = e1)
% 153.23/22.76    (3)   ~ (e2 = e0)
% 153.23/22.76    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.76    (5)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.23/22.76             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.23/22.76               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.23/22.76               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.23/22.76    (6)  op(e0, e0) = e1
% 153.23/22.76    (7)  all_56_10 = e1
% 153.23/22.76    (8)   ~ (e3 = e0)
% 153.23/22.76    (9)   ~ (e1 = e0)
% 153.23/22.76    (10)   ~ (e3 = e2)
% 153.23/22.76    (11)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.23/22.76          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.23/22.76    (12)   ~ (e2 = e1)
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | BETA: splitting (11) gives:
% 153.23/22.76  | 
% 153.23/22.76  | Case 1:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (13)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 153.23/22.76  | |           e3)
% 153.23/22.76  | | 
% 153.23/22.76  | | BETA: splitting (13) gives:
% 153.23/22.76  | | 
% 153.23/22.76  | | Case 1:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (14)  all_56_9 = e3 & op(e3, e0) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | ALPHA: (14) implies:
% 153.23/22.76  | | |   (15)  all_56_9 = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | BETA: splitting (5) gives:
% 153.23/22.76  | | | 
% 153.23/22.76  | | | Case 1:
% 153.23/22.76  | | | | 
% 153.23/22.76  | | | |   (16)  all_56_15 = e0 & op(e0, e0) = e0
% 153.23/22.76  | | | | 
% 153.23/22.76  | | | | ALPHA: (16) implies:
% 153.23/22.76  | | | |   (17)  op(e0, e0) = e0
% 153.23/22.76  | | | | 
% 153.23/22.76  | | | | REF_CLOSE: (4), (6), (9), (17) are inconsistent by sub-proof #1040.
% 153.23/22.76  | | | | 
% 153.23/22.76  | | | Case 2:
% 153.23/22.76  | | | | 
% 153.23/22.76  | | | |   (18)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 153.23/22.76  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 153.23/22.76  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 153.23/22.76  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 153.23/22.76  | | | | 
% 153.23/22.76  | | | | ALPHA: (18) implies:
% 153.23/22.76  | | | |   (19)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0)
% 153.23/22.76  | | | |           = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.23/22.76  | | | | 
% 153.23/22.76  | | | | BETA: splitting (19) gives:
% 153.23/22.76  | | | | 
% 153.23/22.76  | | | | Case 1:
% 153.23/22.76  | | | | | 
% 153.23/22.76  | | | | |   (20)  all_56_9 = e0 & op(e3, e0) = e0
% 153.23/22.76  | | | | | 
% 153.23/22.76  | | | | | REF_CLOSE: (8), (15), (20) are inconsistent by sub-proof #446.
% 153.23/22.76  | | | | | 
% 153.23/22.76  | | | | Case 2:
% 153.23/22.76  | | | | | 
% 153.23/22.76  | | | | |   (21)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1,
% 153.23/22.76  | | | | |             e0) = e0)
% 153.23/22.76  | | | | | 
% 153.23/22.76  | | | | | BETA: splitting (21) gives:
% 153.23/22.76  | | | | | 
% 153.23/22.76  | | | | | Case 1:
% 153.23/22.76  | | | | | | 
% 153.23/22.76  | | | | | |   (22)  all_56_10 = e0 & op(e2, e0) = e0
% 153.23/22.76  | | | | | | 
% 153.23/22.76  | | | | | | ALPHA: (22) implies:
% 153.23/22.76  | | | | | |   (23)  all_56_10 = e0
% 153.23/22.76  | | | | | | 
% 153.23/22.76  | | | | | | REF_CLOSE: (7), (9), (23) are inconsistent by sub-proof #963.
% 153.23/22.76  | | | | | | 
% 153.23/22.76  | | | | | Case 2:
% 153.23/22.76  | | | | | | 
% 153.23/22.76  | | | | | |   (24)  all_56_11 = e0 & op(e1, e0) = e0
% 153.23/22.76  | | | | | | 
% 153.23/22.76  | | | | | | ALPHA: (24) implies:
% 153.23/22.76  | | | | | |   (25)  all_56_11 = e0
% 153.23/22.76  | | | | | | 
% 153.23/22.76  | | | | | | BETA: splitting (1) gives:
% 153.23/22.76  | | | | | | 
% 153.23/22.76  | | | | | | Case 1:
% 153.23/22.76  | | | | | | | 
% 153.23/22.76  | | | | | | |   (26)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 &
% 153.23/22.76  | | | | | | |           op(e2, e0) = e2)
% 153.23/22.76  | | | | | | | 
% 153.23/22.76  | | | | | | | BETA: splitting (26) gives:
% 153.23/22.76  | | | | | | | 
% 153.23/22.76  | | | | | | | Case 1:
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | |   (27)  all_56_9 = e2 & op(e3, e0) = e2
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | | ALPHA: (27) implies:
% 153.23/22.76  | | | | | | | |   (28)  all_56_9 = e2
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | | REF_CLOSE: (10), (15), (28) are inconsistent by sub-proof #964.
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | Case 2:
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | |   (29)  all_56_10 = e2 & op(e2, e0) = e2
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | | REF_CLOSE: (7), (12), (29) are inconsistent by sub-proof #679.
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | End of split
% 153.23/22.76  | | | | | | | 
% 153.23/22.76  | | | | | | Case 2:
% 153.23/22.76  | | | | | | | 
% 153.23/22.76  | | | | | | |   (30)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 &
% 153.23/22.76  | | | | | | |           op(e0, e0) = e2)
% 153.23/22.76  | | | | | | | 
% 153.23/22.76  | | | | | | | BETA: splitting (30) gives:
% 153.23/22.76  | | | | | | | 
% 153.23/22.76  | | | | | | | Case 1:
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | |   (31)  all_56_11 = e2 & op(e1, e0) = e2
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | | REF_CLOSE: (3), (25), (31) are inconsistent by sub-proof #459.
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | Case 2:
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | |   (32)  all_56_15 = e2 & op(e0, e0) = e2
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | | ALPHA: (32) implies:
% 153.23/22.76  | | | | | | | |   (33)  op(e0, e0) = e2
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | | REF_CLOSE: (4), (6), (12), (33) are inconsistent by sub-proof
% 153.23/22.76  | | | | | | | |            #978.
% 153.23/22.76  | | | | | | | | 
% 153.23/22.76  | | | | | | | End of split
% 153.23/22.76  | | | | | | | 
% 153.23/22.76  | | | | | | End of split
% 153.23/22.76  | | | | | | 
% 153.23/22.76  | | | | | End of split
% 153.23/22.76  | | | | | 
% 153.23/22.76  | | | | End of split
% 153.23/22.76  | | | | 
% 153.23/22.76  | | | End of split
% 153.23/22.76  | | | 
% 153.23/22.76  | | Case 2:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (34)  all_56_10 = e3 & op(e2, e0) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | ALPHA: (34) implies:
% 153.23/22.76  | | |   (35)  all_56_10 = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (2), (7), (35) are inconsistent by sub-proof #677.
% 153.23/22.76  | | | 
% 153.23/22.76  | | End of split
% 153.23/22.76  | | 
% 153.23/22.76  | Case 2:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (36)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 153.23/22.76  | |           e3)
% 153.23/22.76  | | 
% 153.23/22.76  | | BETA: splitting (36) gives:
% 153.23/22.76  | | 
% 153.23/22.76  | | Case 1:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (37)  all_56_11 = e3 & op(e1, e0) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | ALPHA: (37) implies:
% 153.23/22.76  | | |   (38)  all_56_11 = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (38) are
% 153.23/22.76  | | |            inconsistent by sub-proof #588.
% 153.23/22.76  | | | 
% 153.23/22.76  | | Case 2:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (39)  all_56_15 = e3 & op(e0, e0) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | ALPHA: (39) implies:
% 153.23/22.76  | | |   (40)  op(e0, e0) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (2), (4), (6), (40) are inconsistent by sub-proof #1022.
% 153.23/22.76  | | | 
% 153.23/22.76  | | End of split
% 153.23/22.76  | | 
% 153.23/22.76  | End of split
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #446 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)  all_56_9 = e0 & op(e3, e0) = e0
% 153.23/22.76    (2)  all_56_9 = e3
% 153.23/22.76    (3)   ~ (e3 = e0)
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | ALPHA: (1) implies:
% 153.23/22.76  |   (4)  all_56_9 = e0
% 153.23/22.76  | 
% 153.23/22.76  | COMBINE_EQS: (2), (4) imply:
% 153.23/22.76  |   (5)  e3 = e0
% 153.23/22.76  | 
% 153.23/22.76  | REDUCE: (3), (5) imply:
% 153.23/22.76  |   (6)  $false
% 153.23/22.76  | 
% 153.23/22.76  | CLOSE: (6) is inconsistent.
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #447 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.76    (2)  op(e0, e0) = e2
% 153.23/22.76    (3)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.23/22.76             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.23/22.76           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.23/22.76           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.23/22.76           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.23/22.76           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 153.23/22.76    (4)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.23/22.76           all_57_10 & $i(all_57_10))
% 153.23/22.76    (5)   ~ (e2 = e1)
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | BETA: splitting (3) gives:
% 153.23/22.76  | 
% 153.23/22.76  | Case 1:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (6)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.23/22.76  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.23/22.76  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 153.23/22.76  | | 
% 153.23/22.76  | | ALPHA: (6) implies:
% 153.23/22.76  | |   (7)  op(e0, e0) = e1
% 153.23/22.76  | | 
% 153.23/22.76  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #978.
% 153.23/22.76  | | 
% 153.23/22.76  | Case 2:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (8)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 153.23/22.76  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.23/22.76  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 153.23/22.76  | | 
% 153.23/22.76  | | ALPHA: (8) implies:
% 153.23/22.76  | |   (9)   ~ (all_57_6 = e3)
% 153.23/22.76  | |   (10)  op(e3, e3) = e1
% 153.23/22.76  | | 
% 153.23/22.76  | | REF_CLOSE: (1), (4), (9), (10) are inconsistent by sub-proof #456.
% 153.23/22.76  | | 
% 153.23/22.76  | End of split
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #448 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)   ~ (all_52_6 = e1)
% 153.23/22.76    (2)  op(e3, e3) = e0
% 153.23/22.76    (3)   ~ (e2 = e0)
% 153.23/22.76    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.76    (5)  op(e1, e2) = all_52_6
% 153.23/22.76    (6)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.23/22.76           all_57_12 & $i(all_57_12))
% 153.23/22.76    (7)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.23/22.76             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.23/22.76           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 153.23/22.76           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 153.23/22.76             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.23/22.76             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.23/22.76           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.23/22.76           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.23/22.76           $i(all_57_7) & $i(all_57_10))
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | BETA: splitting (7) gives:
% 153.23/22.76  | 
% 153.23/22.76  | Case 1:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (8)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.23/22.76  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.23/22.76  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 153.23/22.76  | | 
% 153.23/22.76  | | ALPHA: (8) implies:
% 153.23/22.76  | |   (9)  op(e3, e3) = e2
% 153.23/22.76  | | 
% 153.23/22.76  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1073.
% 153.23/22.76  | | 
% 153.23/22.76  | Case 2:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (10)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.23/22.76  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.23/22.76  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.23/22.76  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.23/22.76  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.23/22.76  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.23/22.76  | | 
% 153.23/22.76  | | REF_CLOSE: (1), (4), (5), (6), (10) are inconsistent by sub-proof #485.
% 153.23/22.76  | | 
% 153.23/22.76  | End of split
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #449 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)   ~ (all_52_13 = e1)
% 153.23/22.76    (2)   ~ (all_52_13 = e0)
% 153.23/22.76    (3)   ~ (all_52_13 = e2)
% 153.23/22.76    (4)  all_54_7 = all_52_13
% 153.23/22.76    (5)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | BETA: splitting (5) gives:
% 153.23/22.76  | 
% 153.23/22.76  | Case 1:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (6)  all_54_7 = e2
% 153.23/22.76  | | 
% 153.23/22.76  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #1162.
% 153.23/22.76  | | 
% 153.23/22.76  | Case 2:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (7)  all_54_7 = e1 | all_54_7 = e0
% 153.23/22.76  | | 
% 153.23/22.76  | | BETA: splitting (7) gives:
% 153.23/22.76  | | 
% 153.23/22.76  | | Case 1:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (8)  all_54_7 = e1
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #495.
% 153.23/22.76  | | | 
% 153.23/22.76  | | Case 2:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (9)  all_54_7 = e0
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #1161.
% 153.23/22.76  | | | 
% 153.23/22.76  | | End of split
% 153.23/22.76  | | 
% 153.23/22.76  | End of split
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #450 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)   ~ (e3 = e1)
% 153.23/22.76    (2)   ~ (e2 = e0)
% 153.23/22.76    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.23/22.76         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.23/22.76    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.76    (5)   ~ (all_52_9 = e3)
% 153.23/22.76    (6)  all_56_10 = e0
% 153.23/22.76    (7)   ~ (e3 = e0)
% 153.23/22.76    (8)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.23/22.76         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.23/22.76    (9)  op(e2, e1) = all_52_9
% 153.23/22.76    (10)   ~ (e1 = e0)
% 153.23/22.76    (11)   ~ (e3 = e2)
% 153.23/22.76    (12)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.23/22.76          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.23/22.76    (13)   ~ (e2 = e1)
% 153.23/22.76    (14)  op(e2, e2) = e0
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | BETA: splitting (8) gives:
% 153.23/22.76  | 
% 153.23/22.76  | Case 1:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (15)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 153.23/22.76  | |           e3)
% 153.23/22.76  | | 
% 153.23/22.76  | | BETA: splitting (15) gives:
% 153.23/22.76  | | 
% 153.23/22.76  | | Case 1:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (16)  all_56_2 = e3 & op(e2, e3) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | ALPHA: (16) implies:
% 153.23/22.76  | | |   (17)  all_56_2 = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (1), (2), (3), (4), (6), (10), (11), (12), (13), (14), (17) are
% 153.23/22.76  | | |            inconsistent by sub-proof #554.
% 153.23/22.76  | | | 
% 153.23/22.76  | | Case 2:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (18)  all_56_3 = e3 & op(e2, e2) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | ALPHA: (18) implies:
% 153.23/22.76  | | |   (19)  op(e2, e2) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (4), (7), (14), (19) are inconsistent by sub-proof #719.
% 153.23/22.76  | | | 
% 153.23/22.76  | | End of split
% 153.23/22.76  | | 
% 153.23/22.76  | Case 2:
% 153.23/22.76  | | 
% 153.23/22.76  | |   (20)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 153.23/22.76  | |           e3)
% 153.23/22.76  | | 
% 153.23/22.76  | | BETA: splitting (20) gives:
% 153.23/22.76  | | 
% 153.23/22.76  | | Case 1:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (21)  all_56_5 = e3 & op(e2, e1) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (4), (5), (9), (21) are inconsistent by sub-proof #647.
% 153.23/22.76  | | | 
% 153.23/22.76  | | Case 2:
% 153.23/22.76  | | | 
% 153.23/22.76  | | |   (22)  all_56_10 = e3 & op(e2, e0) = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | ALPHA: (22) implies:
% 153.23/22.76  | | |   (23)  all_56_10 = e3
% 153.23/22.76  | | | 
% 153.23/22.76  | | | REF_CLOSE: (6), (7), (23) are inconsistent by sub-proof #1134.
% 153.23/22.76  | | | 
% 153.23/22.76  | | End of split
% 153.23/22.76  | | 
% 153.23/22.76  | End of split
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #451 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)  all_54_3 = all_52_12
% 153.23/22.76    (2)  all_54_3 = e3
% 153.23/22.76    (3)   ~ (all_52_12 = e3)
% 153.23/22.76  
% 153.23/22.76  Begin of proof
% 153.23/22.76  | 
% 153.23/22.76  | COMBINE_EQS: (1), (2) imply:
% 153.23/22.76  |   (4)  all_52_12 = e3
% 153.23/22.76  | 
% 153.23/22.76  | SIMP: (4) implies:
% 153.23/22.76  |   (5)  all_52_12 = e3
% 153.23/22.76  | 
% 153.23/22.76  | REDUCE: (3), (5) imply:
% 153.23/22.76  |   (6)  $false
% 153.23/22.76  | 
% 153.23/22.76  | CLOSE: (6) is inconsistent.
% 153.23/22.76  | 
% 153.23/22.76  End of proof
% 153.23/22.76  
% 153.23/22.76  Sub-proof #452 shows that the following formulas are inconsistent:
% 153.23/22.76  ----------------------------------------------------------------
% 153.23/22.76    (1)  op(e3, e3) = e0
% 153.23/22.76    (2)   ~ (e3 = e1)
% 153.23/22.76    (3)  op(e0, e0) = all_10_2
% 153.23/22.76    (4)  op(e1, e0) = e0
% 153.23/22.76    (5)   ~ (e2 = e0)
% 153.23/22.76    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.76           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.76    (7)  op(e1, e0) = all_52_14
% 153.23/22.76    (8)   ~ (e3 = e0)
% 153.23/22.76    (9)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.23/22.76             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.23/22.76           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.23/22.76               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.23/22.76             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.23/22.76         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.23/22.76             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.23/22.76           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.23/22.77               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.23/22.77             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.23/22.77         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.23/22.77             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.23/22.77           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.23/22.77               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.23/22.77             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.23/22.77         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.23/22.77             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.23/22.77           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 153.23/22.77               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 153.23/22.77             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 153.23/22.77    (10)  op(e1, e1) = e3
% 153.23/22.77    (11)   ~ (all_52_14 = all_10_2)
% 153.23/22.77    (12)  op(e2, e2) = e0
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | BETA: splitting (9) gives:
% 153.23/22.77  | 
% 153.23/22.77  | Case 1:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (13)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.23/22.77  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.23/22.77  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.23/22.77  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.23/22.77  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.23/22.77  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 153.23/22.77  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 153.23/22.77  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.23/22.77  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.23/22.77  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.23/22.77  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.23/22.77  | |               $i(all_57_15))))
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (1), (5), (6), (8), (12), (13) are inconsistent by sub-proof
% 153.23/22.77  | |            #477.
% 153.23/22.77  | | 
% 153.23/22.77  | Case 2:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (14)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.23/22.77  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.23/22.77  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.23/22.77  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.23/22.77  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.23/22.77  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 153.23/22.77  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 153.23/22.77  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.23/22.77  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 153.23/22.77  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 153.23/22.77  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 153.23/22.77  | |               all_57_14 & $i(all_57_14))))
% 153.23/22.77  | | 
% 153.23/22.77  | | BETA: splitting (14) gives:
% 153.23/22.77  | | 
% 153.23/22.77  | | Case 1:
% 153.23/22.77  | | | 
% 153.23/22.77  | | |   (15)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.23/22.77  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.23/22.77  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.23/22.77  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.23/22.77  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.23/22.77  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.23/22.77  | | | 
% 153.23/22.77  | | | ALPHA: (15) implies:
% 153.23/22.77  | | |   (16)  op(e1, e1) = e1
% 153.23/22.77  | | | 
% 153.23/22.77  | | | REF_CLOSE: (2), (6), (10), (16) are inconsistent by sub-proof #734.
% 153.23/22.77  | | | 
% 153.23/22.77  | | Case 2:
% 153.23/22.77  | | | 
% 153.23/22.77  | | |   (17)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 153.23/22.77  | | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.23/22.77  | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 153.23/22.77  | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.23/22.77  | | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 153.23/22.77  | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 153.23/22.77  | | | 
% 153.23/22.77  | | | ALPHA: (17) implies:
% 153.23/22.77  | | |   (18)  op(e0, e0) = e0
% 153.23/22.77  | | | 
% 153.23/22.77  | | | REF_CLOSE: (3), (4), (6), (7), (11), (18) are inconsistent by sub-proof
% 153.23/22.77  | | |            #453.
% 153.23/22.77  | | | 
% 153.23/22.77  | | End of split
% 153.23/22.77  | | 
% 153.23/22.77  | End of split
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #453 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)  op(e0, e0) = all_10_2
% 153.23/22.77    (2)  op(e1, e0) = e0
% 153.23/22.77    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.77    (4)  op(e1, e0) = all_52_14
% 153.23/22.77    (5)   ~ (all_52_14 = all_10_2)
% 153.23/22.77    (6)  op(e0, e0) = e0
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | GROUND_INST: instantiating (3) with all_10_2, e0, e0, e0, simplifying with
% 153.23/22.77  |              (1), (6) gives:
% 153.23/22.77  |   (7)  all_10_2 = e0
% 153.23/22.77  | 
% 153.23/22.77  | GROUND_INST: instantiating (3) with all_52_14, e0, e0, e1, simplifying with
% 153.23/22.77  |              (2), (4) gives:
% 153.23/22.77  |   (8)  all_52_14 = e0
% 153.23/22.77  | 
% 153.23/22.77  | REDUCE: (5), (7), (8) imply:
% 153.23/22.77  |   (9)  $false
% 153.23/22.77  | 
% 153.23/22.77  | CLOSE: (9) is inconsistent.
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #454 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.23/22.77             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.23/22.77           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.23/22.77           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.23/22.77             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.23/22.77           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.23/22.77           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.23/22.77    (2)  op(e1, e1) = all_4_2
% 153.23/22.77    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.77    (4)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.23/22.77           all_57_10 & $i(all_57_10))
% 153.23/22.77    (5)  op(e1, e1) = e1
% 153.23/22.77    (6)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.23/22.77           all_57_12 & $i(all_57_12))
% 153.23/22.77    (7)   ~ (e2 = e1)
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | BETA: splitting (1) gives:
% 153.23/22.77  | 
% 153.23/22.77  | Case 1:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (8)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.23/22.77  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.23/22.77  | |        $i(all_57_4)
% 153.23/22.77  | | 
% 153.23/22.77  | | ALPHA: (8) implies:
% 153.23/22.77  | |   (9)  op(e1, e1) = e2
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (2), (3), (5), (7), (9) are inconsistent by sub-proof #1044.
% 153.23/22.77  | | 
% 153.23/22.77  | Case 2:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (10)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 153.23/22.77  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.23/22.77  | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.23/22.77  | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2,
% 153.23/22.77  | |             e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.23/22.77  | | 
% 153.23/22.77  | | BETA: splitting (10) gives:
% 153.23/22.77  | | 
% 153.23/22.77  | | Case 1:
% 153.23/22.77  | | | 
% 153.23/22.77  | | |   (11)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.23/22.77  | | |         (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.23/22.77  | | |         op(e0, e1) = e0 & $i(all_57_6)
% 153.23/22.77  | | | 
% 153.23/22.77  | | | ALPHA: (11) implies:
% 153.23/22.77  | | |   (12)   ~ (all_57_6 = e3)
% 153.23/22.77  | | |   (13)  op(e3, e3) = e1
% 153.23/22.77  | | | 
% 153.23/22.77  | | | REF_CLOSE: (3), (4), (12), (13) are inconsistent by sub-proof #456.
% 153.23/22.77  | | | 
% 153.23/22.77  | | Case 2:
% 153.23/22.77  | | | 
% 153.23/22.77  | | |   (14)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.23/22.77  | | |         (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.23/22.77  | | |         op(e0, e1) = e0 & $i(all_57_7)
% 153.23/22.77  | | | 
% 153.23/22.77  | | | ALPHA: (14) implies:
% 153.23/22.77  | | |   (15)   ~ (all_57_7 = e2)
% 153.23/22.77  | | |   (16)  op(e2, e2) = e1
% 153.23/22.77  | | | 
% 153.23/22.77  | | | REF_CLOSE: (3), (6), (15), (16) are inconsistent by sub-proof #713.
% 153.23/22.77  | | | 
% 153.23/22.77  | | End of split
% 153.23/22.77  | | 
% 153.23/22.77  | End of split
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #455 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)   ~ (e3 = e1)
% 153.23/22.77    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.77    (3)  op(e0, e0) = e3
% 153.23/22.77    (4)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.23/22.77           all_57_10 & $i(all_57_10))
% 153.23/22.77    (5)  op(e3, e0) = all_52_12
% 153.23/22.77    (6)   ~ (all_52_12 = e3)
% 153.23/22.77    (7)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.23/22.77             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.23/22.77           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.23/22.77           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.23/22.77           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.23/22.77           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.23/22.77           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2)
% 153.23/22.77           = all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1
% 153.23/22.77           & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 153.23/22.77           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 153.23/22.77           op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.23/22.77           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.23/22.77           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 153.23/22.77           op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.23/22.77           $i(all_57_10) & $i(all_57_13))
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | BETA: splitting (7) gives:
% 153.23/22.77  | 
% 153.23/22.77  | Case 1:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (8)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 153.23/22.77  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.23/22.77  | |          all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 153.23/22.77  | |        (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 153.23/22.77  | |            = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.23/22.77  | |          all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 153.23/22.77  | | 
% 153.23/22.77  | | BETA: splitting (8) gives:
% 153.23/22.77  | | 
% 153.23/22.77  | | Case 1:
% 153.23/22.77  | | | 
% 153.23/22.77  | | |   (9)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 153.23/22.77  | | |          = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.23/22.77  | | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 153.23/22.77  | | | 
% 153.23/22.77  | | | ALPHA: (9) implies:
% 153.23/22.77  | | |   (10)  op(e0, e0) = e1
% 153.23/22.77  | | | 
% 153.23/22.77  | | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #1022.
% 153.23/22.77  | | | 
% 153.23/22.77  | | Case 2:
% 153.23/22.77  | | | 
% 153.23/22.77  | | |   (11)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.23/22.77  | | |         (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.23/22.77  | | |         op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.23/22.77  | | |         $i(all_57_12)
% 153.23/22.77  | | | 
% 153.23/22.77  | | | ALPHA: (11) implies:
% 153.23/22.77  | | |   (12)   ~ (all_57_6 = e3)
% 153.23/22.77  | | |   (13)  op(e3, e3) = e1
% 153.23/22.77  | | | 
% 153.23/22.77  | | | REF_CLOSE: (2), (4), (12), (13) are inconsistent by sub-proof #456.
% 153.23/22.77  | | | 
% 153.23/22.77  | | End of split
% 153.23/22.77  | | 
% 153.23/22.77  | Case 2:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (14)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 153.23/22.77  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.23/22.77  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.23/22.77  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.23/22.77  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.23/22.77  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.23/22.77  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 153.23/22.77  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 153.23/22.77  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.23/22.77  | |           $i(all_57_13))
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (1), (2), (3), (5), (6), (14) are inconsistent by sub-proof
% 153.23/22.77  | |            #1020.
% 153.23/22.77  | | 
% 153.23/22.77  | End of split
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #456 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.23/22.77           all_57_10 & $i(all_57_10))
% 153.23/22.77    (2)   ~ (all_57_6 = e3)
% 153.23/22.77    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.77    (4)  op(e3, e3) = e1
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | BETA: splitting (1) gives:
% 153.23/22.77  | 
% 153.23/22.77  | Case 1:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (5)  all_57_6 = e3 & op(e3, e1) = e3
% 153.23/22.77  | | 
% 153.23/22.77  | | ALPHA: (5) implies:
% 153.23/22.77  | |   (6)  all_57_6 = e3
% 153.23/22.77  | | 
% 153.23/22.77  | | REDUCE: (2), (6) imply:
% 153.23/22.77  | |   (7)  $false
% 153.23/22.77  | | 
% 153.23/22.77  | | CLOSE: (7) is inconsistent.
% 153.23/22.77  | | 
% 153.23/22.77  | Case 2:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (8)   ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10)
% 153.23/22.77  | | 
% 153.23/22.77  | | ALPHA: (8) implies:
% 153.23/22.77  | |   (9)   ~ (all_57_10 = e1)
% 153.23/22.77  | |   (10)  op(e3, e3) = all_57_10
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #893.
% 153.23/22.77  | | 
% 153.23/22.77  | End of split
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #457 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)  op(e3, e3) = e0
% 153.23/22.77    (2)   ~ (e2 = e0)
% 153.23/22.77    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.77    (4)  op(e0, e0) = e3
% 153.23/22.77    (5)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.23/22.77           all_57_12 & $i(all_57_12))
% 153.23/22.77    (6)   ~ (e3 = e2)
% 153.23/22.77    (7)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.23/22.77             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.23/22.77           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 153.23/22.77           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 153.23/22.77             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.23/22.77             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.23/22.77           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.23/22.77           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.23/22.77           $i(all_57_7) & $i(all_57_10))
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | BETA: splitting (7) gives:
% 153.23/22.77  | 
% 153.23/22.77  | Case 1:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (8)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.23/22.77  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.23/22.77  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 153.23/22.77  | | 
% 153.23/22.77  | | ALPHA: (8) implies:
% 153.23/22.77  | |   (9)  op(e3, e3) = e2
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #1073.
% 153.23/22.77  | | 
% 153.23/22.77  | Case 2:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (10)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.23/22.77  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.23/22.77  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.23/22.77  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.23/22.77  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.23/22.77  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #458.
% 153.23/22.77  | | 
% 153.23/22.77  | End of split
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #458 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.77    (2)  op(e0, e0) = e3
% 153.23/22.77    (3)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.23/22.77           all_57_12 & $i(all_57_12))
% 153.23/22.77    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.23/22.77             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.23/22.77           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.23/22.77           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.23/22.77           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 153.23/22.77           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.23/22.77    (5)   ~ (e3 = e2)
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | BETA: splitting (4) gives:
% 153.23/22.77  | 
% 153.23/22.77  | Case 1:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (6)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.23/22.77  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.23/22.77  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 153.23/22.77  | | 
% 153.23/22.77  | | ALPHA: (6) implies:
% 153.23/22.77  | |   (7)  op(e0, e0) = e2
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #1087.
% 153.23/22.77  | | 
% 153.23/22.77  | Case 2:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (8)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.23/22.77  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.23/22.77  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 153.23/22.77  | | 
% 153.23/22.77  | | ALPHA: (8) implies:
% 153.23/22.77  | |   (9)   ~ (all_57_7 = e2)
% 153.23/22.77  | |   (10)  op(e2, e2) = e1
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (1), (3), (9), (10) are inconsistent by sub-proof #713.
% 153.23/22.77  | | 
% 153.23/22.77  | End of split
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #459 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)  all_56_11 = e2 & op(e1, e0) = e2
% 153.23/22.77    (2)  all_56_11 = e0
% 153.23/22.77    (3)   ~ (e2 = e0)
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | ALPHA: (1) implies:
% 153.23/22.77  |   (4)  all_56_11 = e2
% 153.23/22.77  | 
% 153.23/22.77  | COMBINE_EQS: (2), (4) imply:
% 153.23/22.77  |   (5)  e2 = e0
% 153.23/22.77  | 
% 153.23/22.77  | REDUCE: (3), (5) imply:
% 153.23/22.77  |   (6)  $false
% 153.23/22.77  | 
% 153.23/22.77  | CLOSE: (6) is inconsistent.
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #460 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)   ~ (all_52_2 = e2)
% 153.23/22.77    (2)   ~ (all_52_2 = e0)
% 153.23/22.77    (3)  all_54_8 = all_52_2
% 153.23/22.77    (4)  all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 153.23/22.77    (5)   ~ (all_52_2 = e1)
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | BETA: splitting (4) gives:
% 153.23/22.77  | 
% 153.23/22.77  | Case 1:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (6)  all_54_8 = e2
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #463.
% 153.23/22.77  | | 
% 153.23/22.77  | Case 2:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (7)  all_54_8 = e1 | all_54_8 = e0
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #461.
% 153.23/22.77  | | 
% 153.23/22.77  | End of split
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #461 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)  all_54_8 = e1 | all_54_8 = e0
% 153.23/22.77    (2)  all_54_8 = all_52_2
% 153.23/22.77    (3)   ~ (all_52_2 = e1)
% 153.23/22.77    (4)   ~ (all_52_2 = e0)
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | BETA: splitting (1) gives:
% 153.23/22.77  | 
% 153.23/22.77  | Case 1:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (5)  all_54_8 = e1
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #462.
% 153.23/22.77  | | 
% 153.23/22.77  | Case 2:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (6)  all_54_8 = e0
% 153.23/22.77  | | 
% 153.23/22.77  | | COMBINE_EQS: (2), (6) imply:
% 153.23/22.77  | |   (7)  all_52_2 = e0
% 153.23/22.77  | | 
% 153.23/22.77  | | SIMP: (7) implies:
% 153.23/22.77  | |   (8)  all_52_2 = e0
% 153.23/22.77  | | 
% 153.23/22.77  | | REDUCE: (4), (8) imply:
% 153.23/22.77  | |   (9)  $false
% 153.23/22.77  | | 
% 153.23/22.77  | | CLOSE: (9) is inconsistent.
% 153.23/22.77  | | 
% 153.23/22.77  | End of split
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #462 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)  all_54_8 = all_52_2
% 153.23/22.77    (2)  all_54_8 = e1
% 153.23/22.77    (3)   ~ (all_52_2 = e1)
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | COMBINE_EQS: (1), (2) imply:
% 153.23/22.77  |   (4)  all_52_2 = e1
% 153.23/22.77  | 
% 153.23/22.77  | SIMP: (4) implies:
% 153.23/22.77  |   (5)  all_52_2 = e1
% 153.23/22.77  | 
% 153.23/22.77  | REDUCE: (3), (5) imply:
% 153.23/22.77  |   (6)  $false
% 153.23/22.77  | 
% 153.23/22.77  | CLOSE: (6) is inconsistent.
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #463 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)  all_54_8 = all_52_2
% 153.23/22.77    (2)  all_54_8 = e2
% 153.23/22.77    (3)   ~ (all_52_2 = e2)
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | COMBINE_EQS: (1), (2) imply:
% 153.23/22.77  |   (4)  all_52_2 = e2
% 153.23/22.77  | 
% 153.23/22.77  | SIMP: (4) implies:
% 153.23/22.77  |   (5)  all_52_2 = e2
% 153.23/22.77  | 
% 153.23/22.77  | REDUCE: (3), (5) imply:
% 153.23/22.77  |   (6)  $false
% 153.23/22.77  | 
% 153.23/22.77  | CLOSE: (6) is inconsistent.
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #464 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)  all_56_13 = e2
% 153.23/22.77    (2)  all_56_1 = e1
% 153.23/22.77    (3)   ~ (e3 = e1)
% 153.23/22.77    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.77    (5)   ~ (e3 = e0)
% 153.23/22.77    (6)   ~ (all_52_6 = e3)
% 153.23/22.77    (7)  op(e1, e2) = all_52_6
% 153.23/22.77    (8)   ~ (e3 = e2)
% 153.23/22.77    (9)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.23/22.77         (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.23/22.77    (10)  op(e2, e2) = e0
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | BETA: splitting (9) gives:
% 153.23/22.77  | 
% 153.23/22.77  | Case 1:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (11)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 153.23/22.77  | |           e3)
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (2), (3), (4), (5), (10), (11) are inconsistent by sub-proof
% 153.23/22.77  | |            #465.
% 153.23/22.77  | | 
% 153.23/22.77  | Case 2:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (12)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 153.23/22.77  | |           e3)
% 153.23/22.77  | | 
% 153.23/22.77  | | BETA: splitting (12) gives:
% 153.23/22.77  | | 
% 153.23/22.77  | | Case 1:
% 153.23/22.77  | | | 
% 153.23/22.77  | | |   (13)  all_56_7 = e3 & op(e1, e2) = e3
% 153.23/22.77  | | | 
% 153.23/22.77  | | | REF_CLOSE: (4), (6), (7), (13) are inconsistent by sub-proof #925.
% 153.23/22.77  | | | 
% 153.23/22.77  | | Case 2:
% 153.23/22.77  | | | 
% 153.23/22.77  | | |   (14)  all_56_13 = e3 & op(e0, e2) = e3
% 153.23/22.77  | | | 
% 153.23/22.77  | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #563.
% 153.23/22.77  | | | 
% 153.23/22.77  | | End of split
% 153.23/22.77  | | 
% 153.23/22.77  | End of split
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #465 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)  all_56_1 = e1
% 153.23/22.77    (2)   ~ (e3 = e1)
% 153.23/22.77    (3)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 153.23/22.77    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.77    (5)   ~ (e3 = e0)
% 153.23/22.77    (6)  op(e2, e2) = e0
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | BETA: splitting (3) gives:
% 153.23/22.77  | 
% 153.23/22.77  | Case 1:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (7)  all_56_1 = e3 & op(e3, e2) = e3
% 153.23/22.77  | | 
% 153.23/22.77  | | ALPHA: (7) implies:
% 153.23/22.77  | |   (8)  all_56_1 = e3
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #1069.
% 153.23/22.77  | | 
% 153.23/22.77  | Case 2:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (9)  all_56_3 = e3 & op(e2, e2) = e3
% 153.23/22.77  | | 
% 153.23/22.77  | | ALPHA: (9) implies:
% 153.23/22.77  | |   (10)  op(e2, e2) = e3
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #719.
% 153.23/22.77  | | 
% 153.23/22.77  | End of split
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #466 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 153.23/22.77    (2)  op(e1, e1) = all_4_2
% 153.23/22.77    (3)   ~ (e2 = e0)
% 153.23/22.77    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.77    (5)  op(e0, e1) = e0
% 153.23/22.77    (6)  op(e1, e1) = e1
% 153.23/22.77    (7)   ~ (e2 = e1)
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | BETA: splitting (1) gives:
% 153.23/22.77  | 
% 153.23/22.77  | Case 1:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (8)  all_56_8 = e2 & op(e1, e1) = e2
% 153.23/22.77  | | 
% 153.23/22.77  | | ALPHA: (8) implies:
% 153.23/22.77  | |   (9)  op(e1, e1) = e2
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (2), (4), (6), (7), (9) are inconsistent by sub-proof #1044.
% 153.23/22.77  | | 
% 153.23/22.77  | Case 2:
% 153.23/22.77  | | 
% 153.23/22.77  | |   (10)  all_56_14 = e2 & op(e0, e1) = e2
% 153.23/22.77  | | 
% 153.23/22.77  | | ALPHA: (10) implies:
% 153.23/22.77  | |   (11)  op(e0, e1) = e2
% 153.23/22.77  | | 
% 153.23/22.77  | | REF_CLOSE: (3), (4), (5), (11) are inconsistent by sub-proof #1008.
% 153.23/22.77  | | 
% 153.23/22.77  | End of split
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #467 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.77    (2)  op(e1, e0) = e1
% 153.23/22.77    (3)  op(e1, e0) = e0
% 153.23/22.77    (4)   ~ (e1 = e0)
% 153.23/22.77  
% 153.23/22.77  Begin of proof
% 153.23/22.77  | 
% 153.23/22.77  | GROUND_INST: instantiating (1) with e0, e1, e0, e1, simplifying with (2), (3)
% 153.23/22.77  |              gives:
% 153.23/22.77  |   (5)  e1 = e0
% 153.23/22.77  | 
% 153.23/22.77  | REDUCE: (4), (5) imply:
% 153.23/22.77  |   (6)  $false
% 153.23/22.77  | 
% 153.23/22.77  | CLOSE: (6) is inconsistent.
% 153.23/22.77  | 
% 153.23/22.77  End of proof
% 153.23/22.77  
% 153.23/22.77  Sub-proof #468 shows that the following formulas are inconsistent:
% 153.23/22.77  ----------------------------------------------------------------
% 153.23/22.77    (1)   ~ (e3 = e1)
% 153.23/22.77    (2)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 153.23/22.77         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.23/22.77    (3)   ~ (e2 = e0)
% 153.23/22.77    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.23/22.77           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.23/22.77    (5)  all_56_4 = e2
% 153.23/22.77    (6)  all_56_5 = e2
% 153.23/22.77    (7)   ~ (e3 = e0)
% 153.23/22.77    (8)  all_56_14 = e3
% 153.23/22.77    (9)  op(e2, e1) = all_52_9
% 153.23/22.77    (10)   ~ (e1 = e0)
% 153.25/22.77    (11)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 153.25/22.77          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 153.25/22.77    (12)   ~ (all_52_9 = e0)
% 153.25/22.77    (13)   ~ (e2 = e1)
% 153.25/22.77  
% 153.25/22.77  Begin of proof
% 153.25/22.77  | 
% 153.25/22.77  | BETA: splitting (2) gives:
% 153.25/22.77  | 
% 153.25/22.77  | Case 1:
% 153.25/22.77  | | 
% 153.25/22.77  | |   (14)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 153.25/22.77  | |           e0)
% 153.25/22.77  | | 
% 153.25/22.77  | | BETA: splitting (14) gives:
% 153.25/22.77  | | 
% 153.25/22.77  | | Case 1:
% 153.25/22.77  | | | 
% 153.25/22.77  | | |   (15)  all_56_4 = e0 & op(e3, e1) = e0
% 153.25/22.77  | | | 
% 153.25/22.77  | | | REF_CLOSE: (3), (5), (15) are inconsistent by sub-proof #1070.
% 153.25/22.77  | | | 
% 153.25/22.77  | | Case 2:
% 153.25/22.77  | | | 
% 153.25/22.77  | | |   (16)  all_56_5 = e0 & op(e2, e1) = e0
% 153.25/22.77  | | | 
% 153.25/22.77  | | | REF_CLOSE: (4), (9), (12), (16) are inconsistent by sub-proof #1144.
% 153.25/22.77  | | | 
% 153.25/22.77  | | End of split
% 153.25/22.77  | | 
% 153.25/22.77  | Case 2:
% 153.25/22.77  | | 
% 153.25/22.77  | |   (17)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 153.25/22.77  | |           e0)
% 153.25/22.77  | | 
% 153.25/22.77  | | BETA: splitting (17) gives:
% 153.25/22.77  | | 
% 153.25/22.77  | | Case 1:
% 153.25/22.77  | | | 
% 153.25/22.77  | | |   (18)  all_56_8 = e0 & op(e1, e1) = e0
% 153.25/22.77  | | | 
% 153.25/22.77  | | | ALPHA: (18) implies:
% 153.25/22.77  | | |   (19)  op(e1, e1) = e0
% 153.25/22.77  | | | 
% 153.25/22.77  | | | REF_CLOSE: (1), (4), (5), (6), (8), (10), (11), (13), (19) are
% 153.25/22.77  | | |            inconsistent by sub-proof #480.
% 153.25/22.77  | | | 
% 153.25/22.77  | | Case 2:
% 153.25/22.77  | | | 
% 153.25/22.77  | | |   (20)  all_56_14 = e0 & op(e0, e1) = e0
% 153.25/22.77  | | | 
% 153.25/22.77  | | | REF_CLOSE: (7), (8), (20) are inconsistent by sub-proof #469.
% 153.25/22.77  | | | 
% 153.25/22.77  | | End of split
% 153.25/22.77  | | 
% 153.25/22.77  | End of split
% 153.25/22.77  | 
% 153.25/22.77  End of proof
% 153.25/22.77  
% 153.25/22.77  Sub-proof #469 shows that the following formulas are inconsistent:
% 153.25/22.77  ----------------------------------------------------------------
% 153.25/22.77    (1)  all_56_14 = e0 & op(e0, e1) = e0
% 153.25/22.77    (2)  all_56_14 = e3
% 153.25/22.77    (3)   ~ (e3 = e0)
% 153.25/22.77  
% 153.25/22.77  Begin of proof
% 153.25/22.77  | 
% 153.25/22.77  | ALPHA: (1) implies:
% 153.25/22.77  |   (4)  all_56_14 = e0
% 153.25/22.77  | 
% 153.25/22.77  | COMBINE_EQS: (2), (4) imply:
% 153.25/22.77  |   (5)  e3 = e0
% 153.25/22.77  | 
% 153.25/22.77  | REDUCE: (3), (5) imply:
% 153.25/22.77  |   (6)  $false
% 153.25/22.77  | 
% 153.25/22.77  | CLOSE: (6) is inconsistent.
% 153.25/22.77  | 
% 153.25/22.77  End of proof
% 153.25/22.77  
% 153.25/22.77  Sub-proof #470 shows that the following formulas are inconsistent:
% 153.25/22.77  ----------------------------------------------------------------
% 153.25/22.77    (1)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 =
% 153.25/22.77             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.25/22.77           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 153.25/22.77         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 153.25/22.77             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 153.25/22.77           all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 153.25/22.77    (2)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) & op(e3, e3) =
% 153.25/22.77           all_57_10 & $i(all_57_10))
% 153.25/22.77  
% 153.25/22.77  Begin of proof
% 153.25/22.77  | 
% 153.25/22.77  | BETA: splitting (1) gives:
% 153.25/22.77  | 
% 153.25/22.77  | Case 1:
% 153.25/22.77  | | 
% 153.25/22.78  | |   (3)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12
% 153.25/22.78  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.25/22.78  | |        all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 153.25/22.78  | | 
% 153.25/22.78  | | ALPHA: (3) implies:
% 153.25/22.78  | |   (4)  all_57_10 = e0
% 153.25/22.78  | |   (5)   ~ (all_57_9 = e3)
% 153.25/22.78  | | 
% 153.25/22.78  | | REF_CLOSE: (2), (4), (5) are inconsistent by sub-proof #471.
% 153.25/22.78  | | 
% 153.25/22.78  | Case 2:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (6)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14
% 153.25/22.78  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 153.25/22.78  | |        all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 153.25/22.78  | | 
% 153.25/22.78  | | ALPHA: (6) implies:
% 153.25/22.78  | |   (7)  all_57_10 = e0
% 153.25/22.78  | |   (8)   ~ (all_57_9 = e3)
% 153.25/22.78  | | 
% 153.25/22.78  | | REF_CLOSE: (2), (7), (8) are inconsistent by sub-proof #471.
% 153.25/22.78  | | 
% 153.25/22.78  | End of split
% 153.25/22.78  | 
% 153.25/22.78  End of proof
% 153.25/22.78  
% 153.25/22.78  Sub-proof #471 shows that the following formulas are inconsistent:
% 153.25/22.78  ----------------------------------------------------------------
% 153.25/22.78    (1)  (all_57_9 = e3 & op(e3, e0) = e3) | ( ~ (all_57_10 = e0) & op(e3, e3) =
% 153.25/22.78           all_57_10 & $i(all_57_10))
% 153.25/22.78    (2)   ~ (all_57_9 = e3)
% 153.25/22.78    (3)  all_57_10 = e0
% 153.25/22.78  
% 153.25/22.78  Begin of proof
% 153.25/22.78  | 
% 153.25/22.78  | BETA: splitting (1) gives:
% 153.25/22.78  | 
% 153.25/22.78  | Case 1:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (4)  all_57_9 = e3 & op(e3, e0) = e3
% 153.25/22.78  | | 
% 153.25/22.78  | | ALPHA: (4) implies:
% 153.25/22.78  | |   (5)  all_57_9 = e3
% 153.25/22.78  | | 
% 153.25/22.78  | | REDUCE: (2), (5) imply:
% 153.25/22.78  | |   (6)  $false
% 153.25/22.78  | | 
% 153.25/22.78  | | CLOSE: (6) is inconsistent.
% 153.25/22.78  | | 
% 153.25/22.78  | Case 2:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (7)   ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10)
% 153.25/22.78  | | 
% 153.25/22.78  | | ALPHA: (7) implies:
% 153.25/22.78  | |   (8)   ~ (all_57_10 = e0)
% 153.25/22.78  | | 
% 153.25/22.78  | | REDUCE: (3), (8) imply:
% 153.25/22.78  | |   (9)  $false
% 153.25/22.78  | | 
% 153.25/22.78  | | CLOSE: (9) is inconsistent.
% 153.25/22.78  | | 
% 153.25/22.78  | End of split
% 153.25/22.78  | 
% 153.25/22.78  End of proof
% 153.25/22.78  
% 153.25/22.78  Sub-proof #472 shows that the following formulas are inconsistent:
% 153.25/22.78  ----------------------------------------------------------------
% 153.25/22.78    (1)  op(e3, e3) = e0
% 153.25/22.78    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.78    (3)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 153.25/22.78             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.25/22.78           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 153.25/22.78           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 153.25/22.78           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 153.25/22.78           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.25/22.78           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 153.25/22.78           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.25/22.78           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.25/22.78    (4)   ~ (e1 = e0)
% 153.25/22.78    (5)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 153.25/22.78           all_57_14 & $i(all_57_14))
% 153.25/22.78    (6)  op(e0, e0) = e0
% 153.25/22.78  
% 153.25/22.78  Begin of proof
% 153.25/22.78  | 
% 153.25/22.78  | BETA: splitting (3) gives:
% 153.25/22.78  | 
% 153.25/22.78  | Case 1:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (7)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 153.25/22.78  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.25/22.78  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 153.25/22.78  | | 
% 153.25/22.78  | | ALPHA: (7) implies:
% 153.25/22.78  | |   (8)  op(e0, e0) = e1
% 153.25/22.78  | | 
% 153.25/22.78  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1040.
% 153.25/22.78  | | 
% 153.25/22.78  | Case 2:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (9)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 153.25/22.78  | |            = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) =
% 153.25/22.78  | |          e0 & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 153.25/22.78  | |        (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 153.25/22.78  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 153.25/22.78  | |          e0 & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.25/22.78  | | 
% 153.25/22.78  | | BETA: splitting (9) gives:
% 153.25/22.78  | | 
% 153.25/22.78  | | Case 1:
% 153.25/22.78  | | | 
% 153.25/22.78  | | |   (10)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.25/22.78  | | |         (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.25/22.78  | | |         op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.25/22.78  | | |         $i(all_57_11)
% 153.25/22.78  | | | 
% 153.25/22.78  | | | ALPHA: (10) implies:
% 153.25/22.78  | | |   (11)   ~ (all_57_10 = e0)
% 153.25/22.78  | | |   (12)  op(e3, e3) = all_57_10
% 153.25/22.78  | | | 
% 153.25/22.78  | | | REF_CLOSE: (1), (2), (11), (12) are inconsistent by sub-proof #543.
% 153.25/22.78  | | | 
% 153.25/22.78  | | Case 2:
% 153.25/22.78  | | | 
% 153.25/22.78  | | |   (13)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.25/22.78  | | |         (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.25/22.78  | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.25/22.78  | | |         $i(all_57_13)
% 153.25/22.78  | | | 
% 153.25/22.78  | | | ALPHA: (13) implies:
% 153.25/22.78  | | |   (14)   ~ (all_57_13 = e1)
% 153.25/22.78  | | |   (15)  op(e1, e1) = e0
% 153.25/22.78  | | | 
% 153.25/22.78  | | | REF_CLOSE: (2), (5), (14), (15) are inconsistent by sub-proof #959.
% 153.25/22.78  | | | 
% 153.25/22.78  | | End of split
% 153.25/22.78  | | 
% 153.25/22.78  | End of split
% 153.25/22.78  | 
% 153.25/22.78  End of proof
% 153.25/22.78  
% 153.25/22.78  Sub-proof #473 shows that the following formulas are inconsistent:
% 153.25/22.78  ----------------------------------------------------------------
% 153.25/22.78    (1)  op(e3, e3) = e0
% 153.25/22.78    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.78    (3)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.25/22.78             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.25/22.78           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.25/22.78           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.25/22.78           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.25/22.78           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 153.25/22.78    (4)   ~ (e1 = e0)
% 153.25/22.78    (5)  op(e0, e0) = e0
% 153.25/22.78  
% 153.25/22.78  Begin of proof
% 153.25/22.78  | 
% 153.25/22.78  | BETA: splitting (3) gives:
% 153.25/22.78  | 
% 153.25/22.78  | Case 1:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (6)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.25/22.78  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.25/22.78  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 153.25/22.78  | | 
% 153.25/22.78  | | ALPHA: (6) implies:
% 153.25/22.78  | |   (7)  op(e0, e0) = e1
% 153.25/22.78  | | 
% 153.25/22.78  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #1040.
% 153.25/22.78  | | 
% 153.25/22.78  | Case 2:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (8)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 153.25/22.78  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.25/22.78  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 153.25/22.78  | | 
% 153.25/22.78  | | ALPHA: (8) implies:
% 153.25/22.78  | |   (9)  op(e3, e3) = e1
% 153.25/22.78  | | 
% 153.25/22.78  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #957.
% 153.25/22.78  | | 
% 153.25/22.78  | End of split
% 153.25/22.78  | 
% 153.25/22.78  End of proof
% 153.25/22.78  
% 153.25/22.78  Sub-proof #474 shows that the following formulas are inconsistent:
% 153.25/22.78  ----------------------------------------------------------------
% 153.25/22.78    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.78    (2)   ~ (e3 = e0)
% 153.25/22.78    (3)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.25/22.78             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.25/22.78           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 153.25/22.78           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 153.25/22.78             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 153.25/22.78             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.25/22.78    (4)  op(e0, e0) = e0
% 153.25/22.78    (5)  op(e2, e2) = e0
% 153.25/22.78  
% 153.25/22.78  Begin of proof
% 153.25/22.78  | 
% 153.25/22.78  | BETA: splitting (3) gives:
% 153.25/22.78  | 
% 153.25/22.78  | Case 1:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (6)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.25/22.78  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.25/22.78  | |        op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 153.25/22.78  | | 
% 153.25/22.78  | | ALPHA: (6) implies:
% 153.25/22.78  | |   (7)  op(e2, e2) = e3
% 153.25/22.78  | | 
% 153.25/22.78  | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #719.
% 153.25/22.78  | | 
% 153.25/22.78  | Case 2:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (8)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 153.25/22.78  | |          e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.25/22.78  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 153.25/22.78  | | 
% 153.25/22.78  | | ALPHA: (8) implies:
% 153.25/22.78  | |   (9)  op(e0, e0) = e3
% 153.25/22.78  | | 
% 153.25/22.78  | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #1143.
% 153.25/22.78  | | 
% 153.25/22.78  | End of split
% 153.25/22.78  | 
% 153.25/22.78  End of proof
% 153.25/22.78  
% 153.25/22.78  Sub-proof #475 shows that the following formulas are inconsistent:
% 153.25/22.78  ----------------------------------------------------------------
% 153.25/22.78    (1)  op(e0, e1) = all_52_11
% 153.25/22.78    (2)  op(e3, e3) = e0
% 153.25/22.78    (3)   ~ (e3 = e1)
% 153.25/22.78    (4)   ~ (all_52_11 = all_10_2)
% 153.25/22.78    (5)  op(e0, e0) = all_10_2
% 153.25/22.78    (6)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 153.25/22.78         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.25/22.78    (7)   ~ (e2 = e0)
% 153.25/22.78    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.78    (9)   ~ (e3 = e0)
% 153.25/22.78    (10)   ~ (all_52_8 = e0)
% 153.25/22.78    (11)  op(e2, e1) = all_52_9
% 153.25/22.78    (12)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.25/22.78              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.25/22.78            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.25/22.78                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.25/22.78              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.25/22.78          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.25/22.78              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.78            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.25/22.78                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.25/22.78              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.25/22.78          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.25/22.78              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.78            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.25/22.78                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.25/22.78              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.25/22.78          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.25/22.78              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.78            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.25/22.78                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.25/22.78                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.25/22.78                $i(all_57_14))))
% 153.25/22.78    (13)  op(e1, e1) = e3
% 153.25/22.78    (14)  op(e3, e1) = all_52_8
% 153.25/22.78    (15)   ~ (all_52_9 = e0)
% 153.25/22.78    (16)  op(e2, e2) = e0
% 153.25/22.78  
% 153.25/22.78  Begin of proof
% 153.25/22.78  | 
% 153.25/22.78  | BETA: splitting (6) gives:
% 153.25/22.78  | 
% 153.25/22.78  | Case 1:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (17)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 153.25/22.78  | |           e0)
% 153.25/22.78  | | 
% 153.25/22.78  | | BETA: splitting (17) gives:
% 153.25/22.78  | | 
% 153.25/22.78  | | Case 1:
% 153.25/22.78  | | | 
% 153.25/22.78  | | |   (18)  all_56_4 = e0 & op(e3, e1) = e0
% 153.25/22.78  | | | 
% 153.25/22.78  | | | REF_CLOSE: (8), (10), (14), (18) are inconsistent by sub-proof #1130.
% 153.25/22.78  | | | 
% 153.25/22.78  | | Case 2:
% 153.25/22.78  | | | 
% 153.25/22.78  | | |   (19)  all_56_5 = e0 & op(e2, e1) = e0
% 153.25/22.78  | | | 
% 153.25/22.78  | | | REF_CLOSE: (8), (11), (15), (19) are inconsistent by sub-proof #1144.
% 153.25/22.78  | | | 
% 153.25/22.78  | | End of split
% 153.25/22.78  | | 
% 153.25/22.78  | Case 2:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (20)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 153.25/22.78  | |           e0)
% 153.25/22.78  | | 
% 153.25/22.78  | | BETA: splitting (20) gives:
% 153.25/22.78  | | 
% 153.25/22.78  | | Case 1:
% 153.25/22.78  | | | 
% 153.25/22.78  | | |   (21)  all_56_8 = e0 & op(e1, e1) = e0
% 153.25/22.78  | | | 
% 153.25/22.78  | | | ALPHA: (21) implies:
% 153.25/22.78  | | |   (22)  op(e1, e1) = e0
% 153.25/22.78  | | | 
% 153.25/22.78  | | | REF_CLOSE: (8), (9), (13), (22) are inconsistent by sub-proof #896.
% 153.25/22.78  | | | 
% 153.25/22.78  | | Case 2:
% 153.25/22.78  | | | 
% 153.25/22.78  | | |   (23)  all_56_14 = e0 & op(e0, e1) = e0
% 153.25/22.78  | | | 
% 153.25/22.78  | | | ALPHA: (23) implies:
% 153.25/22.78  | | |   (24)  op(e0, e1) = e0
% 153.25/22.78  | | | 
% 153.25/22.78  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (12), (13), (16), (24)
% 153.25/22.78  | | |            are inconsistent by sub-proof #476.
% 153.25/22.78  | | | 
% 153.25/22.78  | | End of split
% 153.25/22.78  | | 
% 153.25/22.78  | End of split
% 153.25/22.78  | 
% 153.25/22.78  End of proof
% 153.25/22.78  
% 153.25/22.78  Sub-proof #476 shows that the following formulas are inconsistent:
% 153.25/22.78  ----------------------------------------------------------------
% 153.25/22.78    (1)  op(e0, e1) = all_52_11
% 153.25/22.78    (2)  op(e3, e3) = e0
% 153.25/22.78    (3)   ~ (e3 = e1)
% 153.25/22.78    (4)   ~ (all_52_11 = all_10_2)
% 153.25/22.78    (5)  op(e0, e0) = all_10_2
% 153.25/22.78    (6)   ~ (e2 = e0)
% 153.25/22.78    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.78    (8)  op(e0, e1) = e0
% 153.25/22.78    (9)   ~ (e3 = e0)
% 153.25/22.78    (10)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.25/22.78              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.25/22.78            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.25/22.78                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.25/22.78              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.25/22.78          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.25/22.78              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.78            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.25/22.78                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.25/22.78              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.25/22.78          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.25/22.78              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.78            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.25/22.78                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.25/22.78              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.25/22.78          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.25/22.78              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.78            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.25/22.78                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.25/22.78                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.25/22.78                $i(all_57_14))))
% 153.25/22.78    (11)  op(e1, e1) = e3
% 153.25/22.78    (12)  op(e2, e2) = e0
% 153.25/22.78  
% 153.25/22.78  Begin of proof
% 153.25/22.78  | 
% 153.25/22.78  | BETA: splitting (10) gives:
% 153.25/22.78  | 
% 153.25/22.78  | Case 1:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (13)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.25/22.78  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.25/22.78  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.25/22.78  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.25/22.78  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.25/22.78  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 153.25/22.78  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 153.25/22.78  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.78  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.25/22.78  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.25/22.78  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.25/22.78  | |               $i(all_57_15))))
% 153.25/22.78  | | 
% 153.25/22.78  | | REF_CLOSE: (2), (6), (7), (9), (12), (13) are inconsistent by sub-proof
% 153.25/22.78  | |            #477.
% 153.25/22.78  | | 
% 153.25/22.78  | Case 2:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (14)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.25/22.78  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.25/22.78  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.25/22.78  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.25/22.78  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.25/22.78  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 153.25/22.78  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 153.25/22.78  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.78  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 153.25/22.78  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 153.25/22.78  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 153.25/22.78  | |               all_57_14 & $i(all_57_14))))
% 153.25/22.78  | | 
% 153.25/22.78  | | BETA: splitting (14) gives:
% 153.25/22.78  | | 
% 153.25/22.78  | | Case 1:
% 153.25/22.78  | | | 
% 153.25/22.78  | | |   (15)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.25/22.78  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.25/22.78  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.25/22.78  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.25/22.78  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.25/22.78  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.25/22.78  | | | 
% 153.25/22.78  | | | ALPHA: (15) implies:
% 153.25/22.78  | | |   (16)  op(e1, e1) = e1
% 153.25/22.78  | | | 
% 153.25/22.78  | | | REF_CLOSE: (3), (7), (11), (16) are inconsistent by sub-proof #734.
% 153.25/22.78  | | | 
% 153.25/22.78  | | Case 2:
% 153.25/22.78  | | | 
% 153.25/22.78  | | |   (17)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 153.25/22.78  | | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.25/22.78  | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 153.25/22.78  | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.25/22.78  | | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 153.25/22.78  | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 153.25/22.78  | | | 
% 153.25/22.78  | | | ALPHA: (17) implies:
% 153.25/22.78  | | |   (18)  op(e0, e0) = e0
% 153.25/22.78  | | | 
% 153.25/22.78  | | | REF_CLOSE: (1), (4), (5), (7), (8), (18) are inconsistent by sub-proof
% 153.25/22.78  | | |            #1034.
% 153.25/22.78  | | | 
% 153.25/22.78  | | End of split
% 153.25/22.78  | | 
% 153.25/22.78  | End of split
% 153.25/22.78  | 
% 153.25/22.78  End of proof
% 153.25/22.78  
% 153.25/22.78  Sub-proof #477 shows that the following formulas are inconsistent:
% 153.25/22.78  ----------------------------------------------------------------
% 153.25/22.78    (1)  op(e3, e3) = e0
% 153.25/22.78    (2)   ~ (e2 = e0)
% 153.25/22.78    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.78           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.78    (4)   ~ (e3 = e0)
% 153.25/22.78    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.25/22.78             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.25/22.78           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.25/22.78               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.25/22.78             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.25/22.78         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.25/22.78             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.78           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.25/22.78               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.25/22.78             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 153.25/22.78    (6)  op(e2, e2) = e0
% 153.25/22.78  
% 153.25/22.78  Begin of proof
% 153.25/22.78  | 
% 153.25/22.78  | BETA: splitting (5) gives:
% 153.25/22.78  | 
% 153.25/22.78  | Case 1:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2)
% 153.25/22.78  | |          | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.25/22.78  | |        ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 153.25/22.78  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 153.25/22.78  | |              e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 153.25/22.78  | |            $i(all_57_15)))
% 153.25/22.78  | | 
% 153.25/22.78  | | ALPHA: (7) implies:
% 153.25/22.78  | |   (8)  op(e3, e3) = e3
% 153.25/22.78  | | 
% 153.25/22.78  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1141.
% 153.25/22.78  | | 
% 153.25/22.78  | Case 2:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3)
% 153.25/22.78  | |          | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.78  | |        ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.25/22.78  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.25/22.78  | |              e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.25/22.78  | |            $i(all_57_15)))
% 153.25/22.78  | | 
% 153.25/22.78  | | ALPHA: (9) implies:
% 153.25/22.78  | |   (10)  op(e2, e2) = e2
% 153.25/22.78  | | 
% 153.25/22.78  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #1145.
% 153.25/22.78  | | 
% 153.25/22.78  | End of split
% 153.25/22.78  | 
% 153.25/22.78  End of proof
% 153.25/22.78  
% 153.25/22.78  Sub-proof #478 shows that the following formulas are inconsistent:
% 153.25/22.78  ----------------------------------------------------------------
% 153.25/22.78    (1)   ~ (all_52_14 = e0)
% 153.25/22.78    (2)   ~ (all_52_14 = e2)
% 153.25/22.78    (3)  all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 153.25/22.78    (4)   ~ (all_52_14 = e1)
% 153.25/22.78    (5)  all_54_11 = all_52_14
% 153.25/22.78  
% 153.25/22.78  Begin of proof
% 153.25/22.78  | 
% 153.25/22.78  | BETA: splitting (3) gives:
% 153.25/22.78  | 
% 153.25/22.78  | Case 1:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (6)  all_54_11 = e2
% 153.25/22.78  | | 
% 153.25/22.78  | | COMBINE_EQS: (5), (6) imply:
% 153.25/22.78  | |   (7)  all_52_14 = e2
% 153.25/22.78  | | 
% 153.25/22.78  | | REDUCE: (2), (7) imply:
% 153.25/22.78  | |   (8)  $false
% 153.25/22.78  | | 
% 153.25/22.78  | | CLOSE: (8) is inconsistent.
% 153.25/22.78  | | 
% 153.25/22.78  | Case 2:
% 153.25/22.78  | | 
% 153.25/22.78  | |   (9)  all_54_11 = e1 | all_54_11 = e0
% 153.25/22.78  | | 
% 153.25/22.78  | | BETA: splitting (9) gives:
% 153.25/22.78  | | 
% 153.25/22.78  | | Case 1:
% 153.25/22.78  | | | 
% 153.25/22.78  | | |   (10)  all_54_11 = e1
% 153.25/22.78  | | | 
% 153.25/22.78  | | | COMBINE_EQS: (5), (10) imply:
% 153.25/22.78  | | |   (11)  all_52_14 = e1
% 153.25/22.78  | | | 
% 153.25/22.78  | | | REDUCE: (4), (11) imply:
% 153.25/22.78  | | |   (12)  $false
% 153.25/22.78  | | | 
% 153.25/22.78  | | | CLOSE: (12) is inconsistent.
% 153.25/22.78  | | | 
% 153.25/22.78  | | Case 2:
% 153.25/22.78  | | | 
% 153.25/22.78  | | |   (13)  all_54_11 = e0
% 153.25/22.78  | | | 
% 153.25/22.78  | | | COMBINE_EQS: (5), (13) imply:
% 153.25/22.78  | | |   (14)  all_52_14 = e0
% 153.25/22.78  | | | 
% 153.25/22.78  | | | REDUCE: (1), (14) imply:
% 153.25/22.78  | | |   (15)  $false
% 153.25/22.78  | | | 
% 153.25/22.78  | | | CLOSE: (15) is inconsistent.
% 153.25/22.78  | | | 
% 153.25/22.78  | | End of split
% 153.25/22.78  | | 
% 153.25/22.78  | End of split
% 153.25/22.78  | 
% 153.25/22.78  End of proof
% 153.25/22.78  
% 153.25/22.78  Sub-proof #479 shows that the following formulas are inconsistent:
% 153.25/22.78  ----------------------------------------------------------------
% 153.25/22.78    (1)  op(e3, e0) = e1
% 153.25/22.78    (2)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.25/22.78         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.25/22.78    (3)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 153.25/22.78         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.25/22.78    (4)   ~ (all_52_6 = e1)
% 153.25/22.78    (5)  op(e3, e3) = e0
% 153.25/22.78    (6)   ~ (e3 = e1)
% 153.25/22.78    (7)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.25/22.78         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.25/22.78    (8)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.25/22.78         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.25/22.78    (9)  all_56_11 = e3
% 153.25/22.78    (10)  all_56_9 = e1
% 153.25/22.78    (11)  op(e2, e2) = e1
% 153.25/22.78    (12)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.25/22.78          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.25/22.78    (13)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.25/22.78          (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.25/22.78    (14)   ~ (all_52_14 = e2)
% 153.25/22.78    (15)  op(e1, e1) = all_4_2
% 153.25/22.78    (16)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 153.25/22.78          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.25/22.78    (17)   ~ (e2 = e0)
% 153.25/22.78    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.78            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.78    (19)  all_40_2 = e2
% 153.25/22.78    (20)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.25/22.78          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.25/22.78    (21)  all_56_5 = e2
% 153.25/22.78    (22)  ( ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 153.25/22.78            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e2,
% 153.25/22.78              e1) = all_20_1 & $i(all_20_1))
% 153.25/22.78    (23)   ~ (all_52_14 = e1)
% 153.25/22.78    (24)  op(e0, e0) = e2
% 153.25/22.78    (25)  all_56_10 = e0
% 153.25/22.78    (26)  all_56_12 = e1
% 153.25/22.78    (27)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.25/22.78              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.25/22.78                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.25/22.78                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.25/22.78    (28)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0 &
% 153.25/22.78            op(e0, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 153.25/22.78              e3) & op(e0, e2) = all_40_1 & $i(all_40_1))
% 153.25/22.78    (29)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.25/22.78          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.25/22.78    (30)  op(e1, e0) = all_52_14
% 153.25/22.78    (31)   ~ (all_52_13 = e2)
% 153.25/22.78    (32)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.25/22.78          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 153.25/22.78            e3)
% 153.25/22.78    (33)  op(e3, e0) = all_52_12
% 153.25/22.78    (34)   ~ (e3 = e0)
% 153.25/22.78    (35)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.25/22.78          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.25/22.78    (36)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.25/22.78          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.25/22.78    (37)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.25/22.78          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.25/22.78    (38)   ~ (all_52_6 = e3)
% 153.25/22.78    (39)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.25/22.78          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.25/22.78    (40)  op(e1, e2) = all_52_6
% 153.25/22.78    (41)   ~ (all_52_12 = e3)
% 153.25/22.78    (42)  op(e2, e0) = all_52_13
% 153.25/22.78    (43)   ~ (all_52_8 = e0)
% 153.25/22.78    (44)  op(e0, e3) = all_52_3
% 153.25/22.78    (45)   ~ (all_4_2 = e2)
% 153.25/22.78    (46)  op(e1, e1) = e1
% 153.25/22.78    (47)  ( ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0 & op(e2, e1) =
% 153.25/22.78            all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e2,
% 153.25/22.78              e1) = all_38_1 & $i(all_38_1))
% 153.25/22.78    (48)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.25/22.78          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.25/22.78    (49)   ~ (e1 = e0)
% 153.25/22.78    (50)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.25/22.78          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.25/22.79    (51)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.25/22.79              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.25/22.79            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.25/22.79                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.25/22.79              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.25/22.79          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.25/22.79              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.79            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.25/22.79                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.25/22.79              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.25/22.79          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.25/22.79              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.79            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.25/22.79                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.25/22.79              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.25/22.79          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.25/22.79              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.25/22.79            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.25/22.79                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.25/22.79                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.25/22.79                $i(all_57_14))))
% 153.25/22.79    (52)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.25/22.79            all_57_12 & $i(all_57_12))
% 153.25/22.79    (53)   ~ (e3 = e2)
% 153.25/22.79    (54)   ~ (all_52_8 = e3)
% 153.25/22.79    (55)   ~ (all_52_3 = e0)
% 153.25/22.79    (56)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 153.25/22.79          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 153.25/22.79    (57)  op(e3, e1) = all_52_8
% 153.25/22.79    (58)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.25/22.79          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.25/22.79    (59)   ~ (all_52_2 = e1)
% 153.25/22.79    (60)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.25/22.79          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.25/22.79    (61)   ~ (e2 = e1)
% 153.25/22.79    (62)  op(e1, e3) = all_52_2
% 153.25/22.79    (63)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.25/22.79              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.25/22.79            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.25/22.79            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.25/22.79            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.25/22.79            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.25/22.79            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.25/22.79            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.25/22.79            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.25/22.79            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.25/22.79            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.25/22.79            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.25/22.79            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.25/22.79            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.25/22.79            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.25/22.79            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.25/22.79            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.25/22.79            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.25/22.79            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.25/22.79            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.25/22.79            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.25/22.79            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.25/22.79            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.25/22.79            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.25/22.79            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.25/22.79            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.25/22.79            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.25/22.79            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.25/22.79            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.25/22.79            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.25/22.79            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.25/22.79            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.25/22.79            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.25/22.79            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.25/22.79            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.25/22.79            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.25/22.79            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.25/22.79            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.25/22.79            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.25/22.79            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.25/22.79            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.25/22.79            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.25/22.79            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.25/22.79            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.25/22.79            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.25/22.79            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.25/22.79            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.25/22.79            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.25/22.79              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.25/22.79            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.25/22.79            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.25/22.79              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.25/22.79            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.25/22.79            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.25/22.79                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.25/22.79                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.25/22.79                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.25/22.79                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.25/22.79                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.25/22.79                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.25/22.79                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.25/22.79              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.25/22.79                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.25/22.79                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.25/22.79                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.25/22.79                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.25/22.79                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.25/22.79                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.25/22.79                $i(all_57_7))))
% 153.25/22.79    (64)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.25/22.79          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.25/22.79    (65)  op(e2, e3) = all_52_1
% 153.25/22.79    (66)   ~ (all_52_1 = e2)
% 153.25/22.79  
% 153.25/22.79  Begin of proof
% 153.25/22.79  | 
% 153.25/22.79  | BETA: splitting (48) gives:
% 153.25/22.79  | 
% 153.25/22.79  | Case 1:
% 153.25/22.79  | | 
% 153.25/22.79  | |   (67)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 153.25/22.79  | |           e3)
% 153.25/22.79  | | 
% 153.25/22.79  | | BETA: splitting (67) gives:
% 153.25/22.79  | | 
% 153.25/22.79  | | Case 1:
% 153.25/22.79  | | | 
% 153.25/22.79  | | |   (68)  all_56_2 = e3 & op(e2, e3) = e3
% 153.25/22.79  | | | 
% 153.25/22.79  | | | ALPHA: (68) implies:
% 153.25/22.79  | | |   (69)  all_56_2 = e3
% 153.25/22.79  | | | 
% 153.25/22.79  | | | BETA: splitting (63) gives:
% 153.25/22.79  | | | 
% 153.25/22.79  | | | Case 1:
% 153.25/22.79  | | | | 
% 153.25/22.79  | | | |   (70)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.25/22.79  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.25/22.79  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.25/22.79  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.25/22.79  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.25/22.79  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.25/22.79  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.25/22.79  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.25/22.79  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.25/22.79  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.25/22.79  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.25/22.79  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.25/22.79  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.25/22.79  | | | |           $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.25/22.79  | | | |           (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 153.25/22.79  | | | |           & op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.25/22.79  | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 =
% 153.25/22.79  | | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.25/22.79  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.25/22.79  | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 153.25/22.79  | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 153.25/22.79  | | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.25/22.79  | | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.25/22.79  | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.25/22.79  | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.25/22.79  | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.25/22.79  | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.25/22.79  | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 153.25/22.79  | | | |           & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.25/22.79  | | | |           $i(all_57_7) & $i(all_57_10))
% 153.25/22.79  | | | | 
% 153.25/22.79  | | | | BETA: splitting (70) gives:
% 153.25/22.79  | | | | 
% 153.25/22.79  | | | | Case 1:
% 153.25/22.79  | | | | | 
% 153.25/22.79  | | | | |   (71)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.25/22.79  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 153.25/22.79  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.25/22.79  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.25/22.79  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.25/22.79  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 153.25/22.79  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.25/22.79  | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.25/22.79  | | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.25/22.79  | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.25/22.79  | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.25/22.79  | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.25/22.79  | | | | |           & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.25/22.79  | | | | |           $i(all_57_14))
% 153.25/22.79  | | | | | 
% 153.25/22.79  | | | | | BETA: splitting (71) gives:
% 153.25/22.79  | | | | | 
% 153.25/22.79  | | | | | Case 1:
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | |   (72)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.25/22.79  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.25/22.79  | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.25/22.79  | | | | | |           $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 & all_57_15
% 153.25/22.79  | | | | | |           = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2,
% 153.25/22.79  | | | | | |             e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.25/22.79  | | | | | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | | REF_CLOSE: (18), (65), (66), (72) are inconsistent by sub-proof
% 153.25/22.79  | | | | | |            #1180.
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | Case 2:
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | |   (73)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.25/22.79  | | | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 153.25/22.79  | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0)
% 153.25/22.79  | | | | | |           & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.25/22.79  | | | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.25/22.79  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 153.25/22.79  | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | | REF_CLOSE: (18), (24), (53), (59), (62), (73) are inconsistent by
% 153.25/22.79  | | | | | |            sub-proof #723.
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | End of split
% 153.25/22.79  | | | | | 
% 153.25/22.79  | | | | Case 2:
% 153.25/22.79  | | | | | 
% 153.25/22.79  | | | | |   (74)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.25/22.79  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.25/22.79  | | | | |           & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.25/22.79  | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.25/22.79  | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.25/22.79  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.25/22.79  | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1
% 153.25/22.79  | | | | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2)
% 153.25/22.79  | | | | |           & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1
% 153.25/22.79  | | | | |           & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.25/22.79  | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.25/22.79  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.25/22.79  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.25/22.79  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.25/22.79  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.25/22.79  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.25/22.79  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.25/22.79  | | | | | 
% 153.25/22.79  | | | | | BETA: splitting (74) gives:
% 153.25/22.79  | | | | | 
% 153.25/22.79  | | | | | Case 1:
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | |   (75)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.25/22.79  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 153.25/22.79  | | | | | |           e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.25/22.79  | | | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15
% 153.25/22.79  | | | | | |           = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3,
% 153.25/22.79  | | | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.25/22.79  | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | | BETA: splitting (75) gives:
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | | Case 1:
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | |   (76)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.25/22.79  | | | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 153.25/22.79  | | | | | | |         e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.25/22.79  | | | | | | |         $i(all_57_4) & $i(all_57_10)
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | ALPHA: (76) implies:
% 153.25/22.79  | | | | | | |   (77)  op(e1, e1) = e2
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | REF_CLOSE: (15), (18), (46), (61), (77) are inconsistent by
% 153.25/22.79  | | | | | | |            sub-proof #1044.
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | Case 2:
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | |   (78)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.25/22.79  | | | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 153.25/22.79  | | | | | | |         e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.25/22.79  | | | | | | |         $i(all_57_5) & $i(all_57_10)
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | ALPHA: (78) implies:
% 153.25/22.79  | | | | | | |   (79)   ~ (all_57_10 = e2)
% 153.25/22.79  | | | | | | |   (80)  op(e3, e3) = all_57_10
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | BETA: splitting (8) gives:
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | Case 1:
% 153.25/22.79  | | | | | | | | 
% 153.25/22.79  | | | | | | | |   (81)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 &
% 153.25/22.79  | | | | | | | |           op(e3, e2) = e2)
% 153.25/22.79  | | | | | | | | 
% 153.25/22.79  | | | | | | | | BETA: splitting (81) gives:
% 153.25/22.79  | | | | | | | | 
% 153.25/22.79  | | | | | | | | Case 1:
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | |   (82)  all_56_0 = e2 & op(e3, e3) = e2
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | ALPHA: (82) implies:
% 153.25/22.79  | | | | | | | | |   (83)  op(e3, e3) = e2
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | REF_CLOSE: (18), (79), (80), (83) are inconsistent by
% 153.25/22.79  | | | | | | | | |            sub-proof #1031.
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | Case 2:
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | |   (84)  all_56_1 = e2 & op(e3, e2) = e2
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | ALPHA: (84) implies:
% 153.25/22.79  | | | | | | | | |   (85)  all_56_1 = e2
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | REF_CLOSE: (1), (6), (11), (18), (19), (28), (38), (40), (53),
% 153.25/22.79  | | | | | | | | |            (64), (85) are inconsistent by sub-proof #494.
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | End of split
% 153.25/22.79  | | | | | | | | 
% 153.25/22.79  | | | | | | | Case 2:
% 153.25/22.79  | | | | | | | | 
% 153.25/22.79  | | | | | | | |   (86)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 &
% 153.25/22.79  | | | | | | | |           op(e3, e0) = e2)
% 153.25/22.79  | | | | | | | | 
% 153.25/22.79  | | | | | | | | BETA: splitting (86) gives:
% 153.25/22.79  | | | | | | | | 
% 153.25/22.79  | | | | | | | | Case 1:
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | |   (87)  all_56_4 = e2 & op(e3, e1) = e2
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | ALPHA: (87) implies:
% 153.25/22.79  | | | | | | | | |   (88)  all_56_4 = e2
% 153.25/22.79  | | | | | | | | |   (89)  op(e3, e1) = e2
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | BETA: splitting (20) gives:
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | Case 1:
% 153.25/22.79  | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | |   (90)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 &
% 153.25/22.79  | | | | | | | | | |           op(e3, e2) = e3)
% 153.25/22.79  | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | BETA: splitting (90) gives:
% 153.25/22.79  | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | Case 1:
% 153.25/22.79  | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | |   (91)  all_56_0 = e3 & op(e3, e3) = e3
% 153.25/22.79  | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | ALPHA: (91) implies:
% 153.25/22.79  | | | | | | | | | | |   (92)  op(e3, e3) = e3
% 153.25/22.79  | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | REF_CLOSE: (5), (18), (34), (92) are inconsistent by
% 153.25/22.79  | | | | | | | | | | |            sub-proof #1141.
% 153.25/22.79  | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | Case 2:
% 153.25/22.79  | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | |   (93)  all_56_1 = e3 & op(e3, e2) = e3
% 153.25/22.79  | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | ALPHA: (93) implies:
% 153.25/22.79  | | | | | | | | | | |   (94)  all_56_1 = e3
% 153.25/22.79  | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | BETA: splitting (16) gives:
% 153.25/22.79  | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | Case 1:
% 153.25/22.79  | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | |   (95)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 153.25/22.79  | | | | | | | | | | | |           & op(e2, e1) = e0)
% 153.25/22.79  | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | BETA: splitting (95) gives:
% 153.25/22.79  | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | Case 1:
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | |   (96)  all_56_4 = e0 & op(e3, e1) = e0
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | REF_CLOSE: (18), (43), (57), (96) are inconsistent by
% 153.25/22.79  | | | | | | | | | | | | |            sub-proof #1130.
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | Case 2:
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | |   (97)  all_56_5 = e0 & op(e2, e1) = e0
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | ALPHA: (97) implies:
% 153.25/22.79  | | | | | | | | | | | | |   (98)  op(e2, e1) = e0
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | REF_CLOSE: (11), (17), (18), (22), (47), (52), (98) are
% 153.25/22.79  | | | | | | | | | | | | |            inconsistent by sub-proof #513.
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | End of split
% 153.25/22.79  | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | Case 2:
% 153.25/22.79  | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | |   (99)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 153.25/22.79  | | | | | | | | | | | |           e0 & op(e0, e1) = e0)
% 153.25/22.79  | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | BETA: splitting (99) gives:
% 153.25/22.79  | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | Case 1:
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | |   (100)  all_56_8 = e0 & op(e1, e1) = e0
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | ALPHA: (100) implies:
% 153.25/22.79  | | | | | | | | | | | | |   (101)  op(e1, e1) = e0
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | REF_CLOSE: (18), (46), (49), (101) are inconsistent by
% 153.25/22.79  | | | | | | | | | | | | |            sub-proof #1038.
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | Case 2:
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | |   (102)  all_56_14 = e0 & op(e0, e1) = e0
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | ALPHA: (102) implies:
% 153.25/22.79  | | | | | | | | | | | | |   (103)  all_56_14 = e0
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | BETA: splitting (32) gives:
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | Case 1:
% 153.25/22.79  | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | |   (104)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 =
% 153.25/22.79  | | | | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 153.25/22.79  | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 153.25/22.79  | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | Case 1:
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | |   (105)  all_56_12 = e3 & op(e0, e3) = e3
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 153.25/22.79  | | | | | | | | | | | | | | |   (106)  all_56_12 = e3
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | COMBINE_EQS: (26), (106) imply:
% 153.25/22.79  | | | | | | | | | | | | | | |   (107)  e3 = e1
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | SIMP: (107) implies:
% 153.25/22.79  | | | | | | | | | | | | | | |   (108)  e3 = e1
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | COMBINE_EQS: (94), (108) imply:
% 153.25/22.79  | | | | | | | | | | | | | | |   (109)  all_56_1 = e1
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (18), (20), (33), (34), (41), (53),
% 153.25/22.79  | | | | | | | | | | | | | | |            (88), (109) are inconsistent by sub-proof #533.
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | Case 2:
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | |   (110)  all_56_13 = e3 & op(e0, e2) = e3
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | REF_CLOSE: (1), (18), (19), (28), (110) are inconsistent by
% 153.25/22.79  | | | | | | | | | | | | | | |            sub-proof #979.
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | End of split
% 153.25/22.79  | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | Case 2:
% 153.25/22.79  | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | |   (111)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 =
% 153.25/22.79  | | | | | | | | | | | | | |            e3 & op(e0, e0) = e3)
% 153.25/22.79  | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | BETA: splitting (111) gives:
% 153.25/22.79  | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | Case 1:
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | |   (112)  all_56_14 = e3 & op(e0, e1) = e3
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | ALPHA: (112) implies:
% 153.25/22.79  | | | | | | | | | | | | | | |   (113)  all_56_14 = e3
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | COMBINE_EQS: (103), (113) imply:
% 153.25/22.79  | | | | | | | | | | | | | | |   (114)  e3 = e0
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | SIMP: (114) implies:
% 153.25/22.79  | | | | | | | | | | | | | | |   (115)  e3 = e0
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | COMBINE_EQS: (94), (115) imply:
% 153.25/22.79  | | | | | | | | | | | | | | |   (116)  all_56_1 = e0
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (17), (18), (20), (29), (34), (49),
% 153.25/22.79  | | | | | | | | | | | | | | |            (53), (54), (57), (61), (116) are inconsistent by
% 153.25/22.79  | | | | | | | | | | | | | | |            sub-proof #492.
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | Case 2:
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | |   (117)  all_56_15 = e3 & op(e0, e0) = e3
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | ALPHA: (117) implies:
% 153.25/22.79  | | | | | | | | | | | | | | |   (118)  op(e0, e0) = e3
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | | REF_CLOSE: (18), (24), (53), (118) are inconsistent by
% 153.25/22.79  | | | | | | | | | | | | | | |            sub-proof #1087.
% 153.25/22.79  | | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | | End of split
% 153.25/22.79  | | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | | End of split
% 153.25/22.79  | | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | | End of split
% 153.25/22.79  | | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | | End of split
% 153.25/22.79  | | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | End of split
% 153.25/22.79  | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | Case 2:
% 153.25/22.79  | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | |   (119)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 153.25/22.79  | | | | | | | | | |            & op(e3, e0) = e3)
% 153.25/22.79  | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | | REF_CLOSE: (18), (33), (41), (53), (89), (119) are
% 153.25/22.79  | | | | | | | | | |            inconsistent by sub-proof #491.
% 153.25/22.79  | | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | End of split
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | Case 2:
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | |   (120)  all_56_9 = e2 & op(e3, e0) = e2
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | ALPHA: (120) implies:
% 153.25/22.79  | | | | | | | | |   (121)  all_56_9 = e2
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | | REF_CLOSE: (6), (17), (18), (24), (27), (34), (36), (49),
% 153.25/22.79  | | | | | | | | |            (53), (58), (61), (121) are inconsistent by
% 153.25/22.79  | | | | | | | | |            sub-proof #486.
% 153.25/22.79  | | | | | | | | | 
% 153.25/22.79  | | | | | | | | End of split
% 153.25/22.79  | | | | | | | | 
% 153.25/22.79  | | | | | | | End of split
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | End of split
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | Case 2:
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | |   (122)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.25/22.79  | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.25/22.79  | | | | | |            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.25/22.79  | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 153.25/22.79  | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2)
% 153.25/22.79  | | | | | |            & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.25/22.79  | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.25/22.79  | | | | | |            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.25/22.79  | | | | | |            (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.25/22.79  | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2,
% 153.25/22.79  | | | | | |              e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | | BETA: splitting (122) gives:
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | | Case 1:
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | |   (123)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.25/22.79  | | | | | | |          (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.25/22.79  | | | | | | |          all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.25/22.79  | | | | | | |          $i(all_57_3) & $i(all_57_14)
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | ALPHA: (123) implies:
% 153.25/22.79  | | | | | | |   (124)  op(e3, e3) = e2
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | REF_CLOSE: (6), (7), (11), (13), (14), (15), (17), (18), (24),
% 153.25/22.79  | | | | | | |            (30), (31), (34), (35), (42), (49), (50), (51), (53),
% 153.25/22.79  | | | | | | |            (61), (63), (65), (66), (124) are inconsistent by
% 153.25/22.79  | | | | | | |            sub-proof #705.
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | Case 2:
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | |   (125)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.25/22.79  | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.25/22.79  | | | | | | |            all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.25/22.79  | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 153.25/22.79  | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.25/22.79  | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.25/22.79  | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7)
% 153.25/22.79  | | | | | | |            & $i(all_57_10))
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | REF_CLOSE: (4), (18), (40), (52), (125) are inconsistent by
% 153.25/22.79  | | | | | | |            sub-proof #485.
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | End of split
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | End of split
% 153.25/22.79  | | | | | 
% 153.25/22.79  | | | | End of split
% 153.25/22.79  | | | | 
% 153.25/22.79  | | | Case 2:
% 153.25/22.79  | | | | 
% 153.25/22.79  | | | |   (126)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.25/22.79  | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.25/22.79  | | | |            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.25/22.79  | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.25/22.79  | | | |            (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.25/22.79  | | | |            op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.25/22.79  | | | |            e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.25/22.79  | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.25/22.79  | | | |            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.25/22.79  | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.25/22.79  | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.25/22.79  | | | |            (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.25/22.79  | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.25/22.79  | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.25/22.79  | | | |            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.25/22.79  | | | |            all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.25/22.79  | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 153.25/22.79  | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 = e0) &
% 153.25/22.79  | | | |            op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.25/22.79  | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 153.25/22.79  | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 153.25/22.79  | | | |            (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.25/22.79  | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.25/22.79  | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.25/22.79  | | | |            (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.25/22.79  | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.25/22.79  | | | |            all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 153.25/22.79  | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0)
% 153.25/22.79  | | | |            & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.25/22.79  | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14))
% 153.25/22.79  | | | |          | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.25/22.79  | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3)
% 153.25/22.79  | | | |                & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.25/22.79  | | | |                e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.25/22.79  | | | |                (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.25/22.79  | | | |                all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.25/22.79  | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.25/22.79  | | | |                (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.25/22.79  | | | |                op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.25/22.79  | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.25/22.79  | | | |                (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.25/22.79  | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.25/22.79  | | | |                all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.25/22.79  | | | |                & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.25/22.79  | | | |                e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.25/22.79  | | | |                (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.25/22.79  | | | |                op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.25/22.79  | | | | 
% 153.25/22.79  | | | | BETA: splitting (126) gives:
% 153.25/22.79  | | | | 
% 153.25/22.79  | | | | Case 1:
% 153.25/22.79  | | | | | 
% 153.25/22.79  | | | | |   (127)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.25/22.79  | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.25/22.79  | | | | |            & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.25/22.79  | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.25/22.79  | | | | |            (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.25/22.79  | | | | |            op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 153.25/22.79  | | | | |            = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.25/22.79  | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.25/22.79  | | | | |            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.25/22.79  | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12))
% 153.25/22.79  | | | | |          | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.25/22.79  | | | | |            (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.25/22.79  | | | | |            & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10)
% 153.25/22.79  | | | | |            & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.25/22.79  | | | | |            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.25/22.79  | | | | |            all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 153.25/22.79  | | | | |            = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.25/22.79  | | | | | 
% 153.25/22.79  | | | | | BETA: splitting (127) gives:
% 153.25/22.79  | | | | | 
% 153.25/22.79  | | | | | Case 1:
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | |   (128)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.25/22.79  | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 153.25/22.79  | | | | | |            e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.25/22.79  | | | | | |            $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 &
% 153.25/22.79  | | | | | |            all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1)
% 153.25/22.79  | | | | | |            & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.25/22.79  | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.25/22.79  | | | | | |            $i(all_57_12))
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | | BETA: splitting (128) gives:
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | | Case 1:
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | |   (129)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.25/22.79  | | | | | | |          (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 153.25/22.79  | | | | | | |          e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.25/22.79  | | | | | | |          $i(all_57_8) & $i(all_57_10)
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | ALPHA: (129) implies:
% 153.25/22.79  | | | | | | |   (130)  op(e3, e1) = e3
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | REF_CLOSE: (18), (54), (57), (130) are inconsistent by sub-proof
% 153.25/22.79  | | | | | | |            #1164.
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | Case 2:
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | |   (131)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.25/22.79  | | | | | | |          (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.25/22.79  | | | | | | |          all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.25/22.79  | | | | | | |          $i(all_57_6) & $i(all_57_12)
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | ALPHA: (131) implies:
% 153.25/22.79  | | | | | | |   (132)  op(e3, e3) = e1
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | REF_CLOSE: (17), (18), (26), (34), (35), (39), (49), (53), (61),
% 153.25/22.79  | | | | | | |            (69), (132) are inconsistent by sub-proof #928.
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | End of split
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | Case 2:
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | |   (133)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.25/22.79  | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.25/22.79  | | | | | |            e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.25/22.79  | | | | | |            $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 153.25/22.79  | | | | | |            all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 153.25/22.79  | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 153.25/22.79  | | | | | |              e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.25/22.79  | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.25/22.79  | | | | | |            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.25/22.79  | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1,
% 153.25/22.79  | | | | | |              e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | | BETA: splitting (133) gives:
% 153.25/22.79  | | | | | | 
% 153.25/22.79  | | | | | | Case 1:
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | |   (134)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.25/22.79  | | | | | | |          (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.25/22.79  | | | | | | |          e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.25/22.79  | | | | | | |          $i(all_57_8) & $i(all_57_12)
% 153.25/22.79  | | | | | | | 
% 153.25/22.79  | | | | | | | ALPHA: (134) implies:
% 153.25/22.79  | | | | | | |   (135)  op(e0, e0) = e1
% 153.25/22.79  | | | | | | | 
% 153.25/22.80  | | | | | | | REF_CLOSE: (2), (9), (10), (17), (18), (27), (34), (49), (53),
% 153.25/22.80  | | | | | | |            (61), (135) are inconsistent by sub-proof #497.
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | Case 2:
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | |   (136)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) & 
% 153.25/22.80  | | | | | | |            ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 153.25/22.80  | | | | | | |              e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.25/22.80  | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.25/22.80  | | | | | | |            all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 =
% 153.25/22.80  | | | | | | |              e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.25/22.80  | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.25/22.80  | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | | REF_CLOSE: (18), (33), (41), (136) are inconsistent by sub-proof
% 153.25/22.80  | | | | | | |            #1081.
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | End of split
% 153.25/22.80  | | | | | | 
% 153.25/22.80  | | | | | End of split
% 153.25/22.80  | | | | | 
% 153.25/22.80  | | | | Case 2:
% 153.25/22.80  | | | | | 
% 153.25/22.80  | | | | |   (137)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.25/22.80  | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9
% 153.25/22.80  | | | | |            & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.25/22.80  | | | | |            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.25/22.80  | | | | |            (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.25/22.80  | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.25/22.80  | | | | |            = e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 153.25/22.80  | | | | |            all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1)
% 153.25/22.80  | | | | |            & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) =
% 153.25/22.80  | | | | |            e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.25/22.80  | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 153.25/22.80  | | | | |            (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.25/22.80  | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 153.25/22.80  | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.25/22.80  | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 =
% 153.25/22.80  | | | | |                e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2,
% 153.25/22.80  | | | | |                  e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.25/22.80  | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.25/22.80  | | | | |                (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.25/22.80  | | | | |                all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.25/22.80  | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.25/22.80  | | | | |                (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.25/22.80  | | | | |                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.25/22.80  | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.25/22.80  | | | | |                (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.25/22.80  | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.25/22.80  | | | | |                $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.25/22.80  | | | | |                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.25/22.80  | | | | |                & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.25/22.80  | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.25/22.80  | | | | |                (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.25/22.80  | | | | |                & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.25/22.80  | | | | |                $i(all_57_7))))
% 153.25/22.80  | | | | | 
% 153.25/22.80  | | | | | BETA: splitting (137) gives:
% 153.25/22.80  | | | | | 
% 153.25/22.80  | | | | | Case 1:
% 153.25/22.80  | | | | | | 
% 153.25/22.80  | | | | | |   (138)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.25/22.80  | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.25/22.80  | | | | | |            all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.25/22.80  | | | | | |            $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 &
% 153.25/22.80  | | | | | |            all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 = e0)
% 153.25/22.80  | | | | | |            & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 153.25/22.80  | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.25/22.80  | | | | | |            $i(all_57_14))
% 153.25/22.80  | | | | | | 
% 153.25/22.80  | | | | | | REF_CLOSE: (18), (23), (30), (31), (42), (138) are inconsistent by
% 153.25/22.80  | | | | | |            sub-proof #535.
% 153.25/22.80  | | | | | | 
% 153.25/22.80  | | | | | Case 2:
% 153.25/22.80  | | | | | | 
% 153.25/22.80  | | | | | |   (139)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.25/22.80  | | | | | |            (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.25/22.80  | | | | | |            e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.25/22.80  | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.25/22.80  | | | | | |            all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 =
% 153.25/22.80  | | | | | |              e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1,
% 153.25/22.80  | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.25/22.80  | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15)
% 153.25/22.80  | | | | | |            & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &
% 153.25/22.80  | | | | | |                 ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.25/22.80  | | | | | |                  e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.25/22.80  | | | | | |              (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.25/22.80  | | | | | |                ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.25/22.80  | | | | | |                  e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.25/22.80  | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.25/22.80  | | | | | |                ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.25/22.80  | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.25/22.80  | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) & 
% 153.25/22.80  | | | | | |                ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.25/22.80  | | | | | |                  e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.25/22.80  | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.25/22.80  | | | | | |                ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.25/22.80  | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.25/22.80  | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 153.25/22.80  | | | | | |                ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.25/22.80  | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.25/22.80  | | | | | | 
% 153.25/22.80  | | | | | | BETA: splitting (139) gives:
% 153.25/22.80  | | | | | | 
% 153.25/22.80  | | | | | | Case 1:
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | |   (140)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) & 
% 153.25/22.80  | | | | | | |          ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0)
% 153.25/22.80  | | | | | | |          = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.25/22.80  | | | | | | |          $i(all_57_12) & $i(all_57_13)
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | | ALPHA: (140) implies:
% 153.25/22.80  | | | | | | |   (141)  op(e2, e0) = e2
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | | REF_CLOSE: (18), (31), (42), (141) are inconsistent by sub-proof
% 153.25/22.80  | | | | | | |            #1156.
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | Case 2:
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | |   (142)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 153.25/22.80  | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.25/22.80  | | | | | | |            all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.25/22.80  | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.25/22.80  | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12
% 153.25/22.80  | | | | | | |                = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.25/22.80  | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 153.25/22.80  | | | | | | |                  e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.25/22.80  | | | | | | |                all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 153.25/22.80  | | | | | | |                  = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.25/22.80  | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 153.25/22.80  | | | | | | |                all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15
% 153.25/22.80  | | | | | | |                  = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.25/22.80  | | | | | | |                op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.25/22.80  | | | | | | |                all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.25/22.80  | | | | | | |                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.25/22.80  | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.25/22.80  | | | | | | |                all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 153.25/22.80  | | | | | | |                  = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.25/22.80  | | | | | | |                op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.25/22.80  | | | | | | |                all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15
% 153.25/22.80  | | | | | | |                  = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.25/22.80  | | | | | | |                op(e0, e1) = e0 & $i(all_57_7))))
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | | BETA: splitting (142) gives:
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | 
% 153.25/22.80  | | | | | | | |   (143)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &
% 153.25/22.80  | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.25/22.80  | | | | | | | |          all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.25/22.80  | | | | | | | |          $i(all_57_11) & $i(all_57_14)
% 153.25/22.80  | | | | | | | | 
% 153.25/22.80  | | | | | | | | ALPHA: (143) implies:
% 153.25/22.80  | | | | | | | |   (144)  op(e1, e0) = e1
% 153.25/22.80  | | | | | | | | 
% 153.25/22.80  | | | | | | | | REF_CLOSE: (18), (23), (30), (144) are inconsistent by sub-proof
% 153.25/22.80  | | | | | | | |            #961.
% 153.25/22.80  | | | | | | | | 
% 153.25/22.80  | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | 
% 153.25/22.80  | | | | | | | |   (145)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 =
% 153.25/22.80  | | | | | | | |              e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.25/22.80  | | | | | | | |              (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.25/22.80  | | | | | | | |                e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.25/22.80  | | | | | | | |            (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 153.25/22.80  | | | | | | | |              &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.25/22.80  | | | | | | | |              op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.25/22.80  | | | | | | | |            (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3)
% 153.25/22.80  | | | | | | | |              &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 153.25/22.80  | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.25/22.80  | | | | | | | |            | (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.25/22.80  | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.25/22.80  | | | | | | | |              & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4))
% 153.25/22.80  | | | | | | | |            | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 153.25/22.80  | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.25/22.80  | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.25/22.80  | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 & 
% 153.25/22.80  | | | | | | | |              ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 153.25/22.80  | | | | | | | |                e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) =
% 153.25/22.80  | | | | | | | |              e0 & $i(all_57_7)))
% 153.25/22.80  | | | | | | | | 
% 153.25/22.80  | | | | | | | | ALPHA: (145) implies:
% 153.25/22.80  | | | | | | | |   (146)  op(e0, e0) = all_57_15
% 153.25/22.80  | | | | | | | |   (147)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 153.25/22.80  | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.25/22.80  | | | | | | | |              e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.25/22.80  | | | | | | | |          (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.25/22.80  | | | | | | | |            ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.25/22.80  | | | | | | | |              e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.25/22.80  | | | | | | | |          (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.25/22.80  | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.25/22.80  | | | | | | | |            all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.25/22.80  | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) & 
% 153.25/22.80  | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.25/22.80  | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.25/22.80  | | | | | | | |          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.25/22.80  | | | | | | | |            ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.25/22.80  | | | | | | | |            all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.25/22.80  | | | | | | | |          (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 153.25/22.80  | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.25/22.80  | | | | | | | |            all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.25/22.80  | | | | | | | | 
% 153.25/22.80  | | | | | | | | BETA: splitting (8) gives:
% 153.25/22.80  | | | | | | | | 
% 153.25/22.80  | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | 
% 153.25/22.80  | | | | | | | | |   (148)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 &
% 153.25/22.80  | | | | | | | | |            op(e3, e2) = e2)
% 153.25/22.80  | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | BETA: splitting (148) gives:
% 153.25/22.80  | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | |   (149)  all_56_0 = e2 & op(e3, e3) = e2
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | ALPHA: (149) implies:
% 153.25/22.80  | | | | | | | | | |   (150)  op(e3, e3) = e2
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | REF_CLOSE: (6), (11), (15), (18), (24), (46), (52), (61),
% 153.25/22.80  | | | | | | | | | |            (146), (147), (150) are inconsistent by sub-proof
% 153.25/22.80  | | | | | | | | | |            #709.
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | |   (151)  all_56_1 = e2 & op(e3, e2) = e2
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | ALPHA: (151) implies:
% 153.25/22.80  | | | | | | | | | |   (152)  all_56_1 = e2
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | REF_CLOSE: (1), (6), (11), (18), (19), (28), (38), (40),
% 153.25/22.80  | | | | | | | | | |            (53), (64), (152) are inconsistent by sub-proof
% 153.25/22.80  | | | | | | | | | |            #494.
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | 
% 153.25/22.80  | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | 
% 153.25/22.80  | | | | | | | | |   (153)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 &
% 153.25/22.80  | | | | | | | | |            op(e3, e0) = e2)
% 153.25/22.80  | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | BETA: splitting (153) gives:
% 153.25/22.80  | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | |   (154)  all_56_4 = e2 & op(e3, e1) = e2
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | ALPHA: (154) implies:
% 153.25/22.80  | | | | | | | | | |   (155)  all_56_4 = e2
% 153.25/22.80  | | | | | | | | | |   (156)  op(e3, e1) = e2
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | BETA: splitting (3) gives:
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | |   (157)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 153.25/22.80  | | | | | | | | | | |            & op(e2, e1) = e3)
% 153.25/22.80  | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | BETA: splitting (157) gives:
% 153.25/22.80  | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | |   (158)  all_56_4 = e3 & op(e3, e1) = e3
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | ALPHA: (158) implies:
% 153.25/22.80  | | | | | | | | | | | |   (159)  op(e3, e1) = e3
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | REF_CLOSE: (18), (53), (156), (159) are inconsistent by
% 153.25/22.80  | | | | | | | | | | | |            sub-proof #504.
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | |   (160)  all_56_5 = e3 & op(e2, e1) = e3
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | ALPHA: (160) implies:
% 153.25/22.80  | | | | | | | | | | | |   (161)  op(e2, e1) = e3
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | REF_CLOSE: (11), (18), (52), (53), (161) are inconsistent by
% 153.25/22.80  | | | | | | | | | | | |            sub-proof #844.
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | |   (162)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 153.25/22.80  | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 153.25/22.80  | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | BETA: splitting (162) gives:
% 153.25/22.80  | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | |   (163)  all_56_8 = e3 & op(e1, e1) = e3
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | ALPHA: (163) implies:
% 153.25/22.80  | | | | | | | | | | | |   (164)  op(e1, e1) = e3
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | REF_CLOSE: (6), (18), (46), (164) are inconsistent by
% 153.25/22.80  | | | | | | | | | | | |            sub-proof #734.
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | |   (165)  all_56_14 = e3 & op(e0, e1) = e3
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | ALPHA: (165) implies:
% 153.25/22.80  | | | | | | | | | | | |   (166)  all_56_14 = e3
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | BETA: splitting (20) gives:
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | |   (167)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3
% 153.25/22.80  | | | | | | | | | | | | |            & op(e3, e2) = e3)
% 153.25/22.80  | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | BETA: splitting (167) gives:
% 153.25/22.80  | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | |   (168)  all_56_0 = e3 & op(e3, e3) = e3
% 153.25/22.80  | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | ALPHA: (168) implies:
% 153.25/22.80  | | | | | | | | | | | | | |   (169)  op(e3, e3) = e3
% 153.25/22.80  | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | REF_CLOSE: (5), (18), (34), (169) are inconsistent by
% 153.25/22.80  | | | | | | | | | | | | | |            sub-proof #1141.
% 153.25/22.80  | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | |   (170)  all_56_1 = e3 & op(e3, e2) = e3
% 153.25/22.80  | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | ALPHA: (170) implies:
% 153.25/22.80  | | | | | | | | | | | | | |   (171)  all_56_1 = e3
% 153.25/22.80  | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 153.25/22.80  | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | |   (172)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 153.25/22.80  | | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 153.25/22.80  | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 153.25/22.80  | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | |   (173)  all_56_6 = e0 & op(e1, e3) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | |   (174)  all_56_6 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | |   (175)  op(e1, e3) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | |   (176)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | |            & op(e2, e3) = e2)
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | |   (177)  all_56_0 = e2 & op(e3, e3) = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | | |   (178)  op(e3, e3) = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10), (17), (18), (20), (34), (37), (49),
% 153.25/22.80  | | | | | | | | | | | | | | | | | |            (53), (54), (57), (155), (178) are inconsistent by
% 153.25/22.80  | | | | | | | | | | | | | | | | | |            sub-proof #484.
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | |   (179)  all_56_2 = e2 & op(e2, e3) = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | ALPHA: (179) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | | |   (180)  op(e2, e3) = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (65), (66), (180) are inconsistent by
% 153.25/22.80  | | | | | | | | | | | | | | | | | |            sub-proof #1181.
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | |   (181)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 153.25/22.80  | | | | | | | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | BETA: splitting (181) gives:
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | |   (182)  all_56_6 = e2 & op(e1, e3) = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | | |   (183)  all_56_6 = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (174), (183) are inconsistent by sub-proof
% 153.25/22.80  | | | | | | | | | | | | | | | | | |            #724.
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | |   (184)  all_56_12 = e2 & op(e0, e3) = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | | |   (185)  all_56_12 = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (13), (18), (34), (49), (53), (61),
% 153.25/22.80  | | | | | | | | | | | | | | | | | |            (62), (174), (175), (185) are inconsistent by
% 153.25/22.80  | | | | | | | | | | | | | | | | | |            sub-proof #619.
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | |   (186)  all_56_7 = e0 & op(e1, e2) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | |   (187)  all_56_7 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | BETA: splitting (27) gives:
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | |   (188)  all_56_15 = e0 & op(e0, e0) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | |   (189)  op(e0, e0) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (24), (189) are inconsistent by
% 153.25/22.80  | | | | | | | | | | | | | | | | |            sub-proof #1043.
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | |   (190)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 =
% 153.25/22.80  | | | | | | | | | | | | | | | | |              e0 & op(e2, e0) = e0) | (all_56_11 = e0 &
% 153.25/22.80  | | | | | | | | | | | | | | | | |              op(e1, e0) = e0)) & ((all_56_12 = e0 & op(e0,
% 153.25/22.80  | | | | | | | | | | | | | | | | |                e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 153.25/22.80  | | | | | | | | | | | | | | | | |              e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | |   (191)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 =
% 153.25/22.80  | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 153.25/22.80  | | | | | | | | | | | | | | | | |              e1) = e0)
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | |   (192)  all_56_12 = e0 & op(e0, e3) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | | |   (193)  op(e0, e3) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (44), (55), (193) are inconsistent by
% 153.25/22.80  | | | | | | | | | | | | | | | | | |            sub-proof #1142.
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | |   (194)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 =
% 153.25/22.80  | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | |   (195)  all_56_13 = e0 & op(e0, e2) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | |   (196)  all_56_13 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | |   (197)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |   (198)  all_56_1 = e2 & op(e3, e2) = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (171), (198) are inconsistent by sub-proof
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |            #907.
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |   (199)  all_56_3 = e2 & op(e2, e2) = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |   (200)  op(e2, e2) = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (15), (17), (18), (44), (45), (49), (55),
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |            (61), (147), (200) are inconsistent by sub-proof
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |            #536.
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | |   (201)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |   (202)  all_56_7 = e2 & op(e1, e2) = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |   (203)  all_56_7 = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (17), (187), (203) are inconsistent by sub-proof
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |            #483.
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |   (204)  all_56_13 = e2 & op(e0, e2) = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | ALPHA: (204) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |   (205)  all_56_13 = e2
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (196), (205) imply:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |   (206)  e2 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | SIMP: (206) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |   (207)  e2 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | REDUCE: (17), (207) imply:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | |   (208)  $false
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | CLOSE: (208) is inconsistent.
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | |   (209)  all_56_14 = e0 & op(e0, e1) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | ALPHA: (209) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | |   (210)  all_56_14 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (166), (210) imply:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | |   (211)  e3 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (171), (211) imply:
% 153.25/22.80  | | | | | | | | | | | | | | | | | | |   (212)  all_56_1 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (17), (18), (20), (29), (34), (49),
% 153.25/22.80  | | | | | | | | | | | | | | | | | | |            (53), (54), (57), (61), (212) are inconsistent by
% 153.25/22.80  | | | | | | | | | | | | | | | | | | |            sub-proof #492.
% 153.25/22.80  | | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | |   (213)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 153.25/22.80  | | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 153.25/22.80  | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 153.25/22.80  | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | Case 1:
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | |   (214)  all_56_8 = e0 & op(e1, e1) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | |   (215)  op(e1, e1) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | REF_CLOSE: (6), (18), (21), (49), (56), (61), (155), (166),
% 153.25/22.80  | | | | | | | | | | | | | | | |            (215) are inconsistent by sub-proof #480.
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | |   (216)  all_56_11 = e0 & op(e1, e0) = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | |   (217)  all_56_11 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | COMBINE_EQS: (9), (217) imply:
% 153.25/22.80  | | | | | | | | | | | | | | | |   (218)  e3 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | SIMP: (218) implies:
% 153.25/22.80  | | | | | | | | | | | | | | | |   (219)  e3 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | COMBINE_EQS: (171), (219) imply:
% 153.25/22.80  | | | | | | | | | | | | | | | |   (220)  all_56_1 = e0
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (17), (18), (20), (29), (34), (49),
% 153.25/22.80  | | | | | | | | | | | | | | | |            (53), (54), (57), (61), (220) are inconsistent by
% 153.25/22.80  | | | | | | | | | | | | | | | |            sub-proof #492.
% 153.25/22.80  | | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | |   (221)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3
% 153.25/22.80  | | | | | | | | | | | | |            & op(e3, e0) = e3)
% 153.25/22.80  | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | | REF_CLOSE: (18), (33), (41), (53), (156), (221) are
% 153.25/22.80  | | | | | | | | | | | | |            inconsistent by sub-proof #491.
% 153.25/22.80  | | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | Case 2:
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | |   (222)  all_56_9 = e2 & op(e3, e0) = e2
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | ALPHA: (222) implies:
% 153.25/22.80  | | | | | | | | | |   (223)  all_56_9 = e2
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | | REF_CLOSE: (6), (17), (18), (24), (27), (34), (36), (49),
% 153.25/22.80  | | | | | | | | | |            (53), (58), (61), (223) are inconsistent by
% 153.25/22.80  | | | | | | | | | |            sub-proof #486.
% 153.25/22.80  | | | | | | | | | | 
% 153.25/22.80  | | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | | 
% 153.25/22.80  | | | | | | | | End of split
% 153.25/22.80  | | | | | | | | 
% 153.25/22.80  | | | | | | | End of split
% 153.25/22.80  | | | | | | | 
% 153.25/22.80  | | | | | | End of split
% 153.25/22.80  | | | | | | 
% 153.25/22.80  | | | | | End of split
% 153.25/22.80  | | | | | 
% 153.25/22.80  | | | | End of split
% 153.25/22.80  | | | | 
% 153.25/22.80  | | | End of split
% 153.25/22.80  | | | 
% 153.25/22.80  | | Case 2:
% 153.25/22.80  | | | 
% 153.25/22.80  | | |   (224)  all_56_3 = e3 & op(e2, e2) = e3
% 153.25/22.80  | | | 
% 153.25/22.80  | | | ALPHA: (224) implies:
% 153.25/22.80  | | |   (225)  op(e2, e2) = e3
% 153.25/22.80  | | | 
% 153.25/22.80  | | | REF_CLOSE: (6), (11), (18), (225) are inconsistent by sub-proof #1136.
% 153.25/22.80  | | | 
% 153.25/22.80  | | End of split
% 153.25/22.80  | | 
% 153.25/22.80  | Case 2:
% 153.25/22.80  | | 
% 153.25/22.80  | |   (226)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 153.25/22.80  | |            e3)
% 153.25/22.80  | | 
% 153.25/22.80  | | BETA: splitting (226) gives:
% 153.25/22.80  | | 
% 153.25/22.80  | | Case 1:
% 153.25/22.80  | | | 
% 153.25/22.80  | | |   (227)  all_56_5 = e3 & op(e2, e1) = e3
% 153.25/22.80  | | | 
% 153.25/22.80  | | | ALPHA: (227) implies:
% 153.25/22.80  | | |   (228)  op(e2, e1) = e3
% 153.25/22.80  | | | 
% 153.25/22.80  | | | REF_CLOSE: (11), (18), (52), (53), (228) are inconsistent by sub-proof
% 153.25/22.80  | | |            #844.
% 153.25/22.80  | | | 
% 153.25/22.80  | | Case 2:
% 153.25/22.80  | | | 
% 153.25/22.80  | | |   (229)  all_56_10 = e3 & op(e2, e0) = e3
% 153.25/22.80  | | | 
% 153.25/22.80  | | | ALPHA: (229) implies:
% 153.25/22.80  | | |   (230)  all_56_10 = e3
% 153.25/22.80  | | | 
% 153.25/22.80  | | | REF_CLOSE: (25), (34), (230) are inconsistent by sub-proof #1134.
% 153.25/22.80  | | | 
% 153.25/22.80  | | End of split
% 153.25/22.80  | | 
% 153.25/22.80  | End of split
% 153.25/22.80  | 
% 153.25/22.80  End of proof
% 153.25/22.80  
% 153.25/22.80  Sub-proof #480 shows that the following formulas are inconsistent:
% 153.25/22.80  ----------------------------------------------------------------
% 153.25/22.80    (1)   ~ (e3 = e1)
% 153.25/22.80    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.80           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.80    (3)  all_56_4 = e2
% 153.25/22.80    (4)  all_56_5 = e2
% 153.25/22.80    (5)  op(e1, e1) = e0
% 153.25/22.80    (6)  all_56_14 = e3
% 153.25/22.80    (7)   ~ (e1 = e0)
% 153.25/22.80    (8)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 153.25/22.80         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 153.25/22.80    (9)   ~ (e2 = e1)
% 153.25/22.80  
% 153.25/22.80  Begin of proof
% 153.25/22.80  | 
% 153.25/22.80  | BETA: splitting (8) gives:
% 153.25/22.80  | 
% 153.25/22.80  | Case 1:
% 153.25/22.80  | | 
% 153.25/22.80  | |   (10)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) =
% 153.25/22.81  | |           e1)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (10) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (11)  all_56_4 = e1 & op(e3, e1) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (3), (9), (11) are inconsistent by sub-proof #1066.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (12)  all_56_5 = e1 & op(e2, e1) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (4), (9), (12) are inconsistent by sub-proof #482.
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | Case 2:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (13)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) =
% 153.25/22.81  | |           e1)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (13) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (14)  all_56_8 = e1 & op(e1, e1) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (14) implies:
% 153.25/22.81  | | |   (15)  op(e1, e1) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (2), (5), (7), (15) are inconsistent by sub-proof #1038.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (16)  all_56_14 = e1 & op(e0, e1) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (1), (6), (16) are inconsistent by sub-proof #481.
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | End of split
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #481 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)  all_56_14 = e1 & op(e0, e1) = e1
% 153.25/22.81    (2)  all_56_14 = e3
% 153.25/22.81    (3)   ~ (e3 = e1)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | ALPHA: (1) implies:
% 153.25/22.81  |   (4)  all_56_14 = e1
% 153.25/22.81  | 
% 153.25/22.81  | COMBINE_EQS: (2), (4) imply:
% 153.25/22.81  |   (5)  e3 = e1
% 153.25/22.81  | 
% 153.25/22.81  | REDUCE: (3), (5) imply:
% 153.25/22.81  |   (6)  $false
% 153.25/22.81  | 
% 153.25/22.81  | CLOSE: (6) is inconsistent.
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #482 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)  all_56_5 = e1 & op(e2, e1) = e1
% 153.25/22.81    (2)  all_56_5 = e2
% 153.25/22.81    (3)   ~ (e2 = e1)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | ALPHA: (1) implies:
% 153.25/22.81  |   (4)  all_56_5 = e1
% 153.25/22.81  | 
% 153.25/22.81  | COMBINE_EQS: (2), (4) imply:
% 153.25/22.81  |   (5)  e2 = e1
% 153.25/22.81  | 
% 153.25/22.81  | REDUCE: (3), (5) imply:
% 153.25/22.81  |   (6)  $false
% 153.25/22.81  | 
% 153.25/22.81  | CLOSE: (6) is inconsistent.
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #483 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)  all_56_7 = e2
% 153.25/22.81    (2)  all_56_7 = e0
% 153.25/22.81    (3)   ~ (e2 = e0)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | COMBINE_EQS: (1), (2) imply:
% 153.25/22.81  |   (4)  e2 = e0
% 153.25/22.81  | 
% 153.25/22.81  | SIMP: (4) implies:
% 153.25/22.81  |   (5)  e2 = e0
% 153.25/22.81  | 
% 153.25/22.81  | REDUCE: (3), (5) imply:
% 153.25/22.81  |   (6)  $false
% 153.25/22.81  | 
% 153.25/22.81  | CLOSE: (6) is inconsistent.
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #484 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)   ~ (e3 = e1)
% 153.25/22.81    (2)  all_56_9 = e1
% 153.25/22.81    (3)   ~ (e2 = e0)
% 153.25/22.81    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.81    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.25/22.81         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.25/22.81    (6)  all_56_4 = e2
% 153.25/22.81    (7)  op(e3, e3) = e2
% 153.25/22.81    (8)   ~ (e3 = e0)
% 153.25/22.81    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.25/22.81         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.25/22.81    (10)   ~ (e1 = e0)
% 153.25/22.81    (11)   ~ (e3 = e2)
% 153.25/22.81    (12)   ~ (all_52_8 = e3)
% 153.25/22.81    (13)  op(e3, e1) = all_52_8
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | BETA: splitting (9) gives:
% 153.25/22.81  | 
% 153.25/22.81  | Case 1:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (14)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 153.25/22.81  | |           e0)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (14) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (15)  all_56_0 = e0 & op(e3, e3) = e0
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (15) implies:
% 153.25/22.81  | | |   (16)  op(e3, e3) = e0
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (3), (4), (7), (16) are inconsistent by sub-proof #1073.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (17)  all_56_1 = e0 & op(e3, e2) = e0
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (17) implies:
% 153.25/22.81  | | |   (18)  all_56_1 = e0
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (11), (12), (13), (18) are
% 153.25/22.81  | | |            inconsistent by sub-proof #808.
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | Case 2:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (19)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 153.25/22.81  | |           e0)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (19) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (20)  all_56_4 = e0 & op(e3, e1) = e0
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (3), (6), (20) are inconsistent by sub-proof #1070.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (21)  all_56_9 = e0 & op(e3, e0) = e0
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (2), (10), (21) are inconsistent by sub-proof #1063.
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | End of split
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #485 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)   ~ (all_52_6 = e1)
% 153.25/22.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.81    (3)  op(e1, e2) = all_52_6
% 153.25/22.81    (4)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.25/22.81           all_57_12 & $i(all_57_12))
% 153.25/22.81    (5)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.25/22.81             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.25/22.81           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.25/22.81           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.25/22.81           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 153.25/22.81           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | BETA: splitting (5) gives:
% 153.25/22.81  | 
% 153.25/22.81  | Case 1:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (6)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.25/22.81  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.25/22.81  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 153.25/22.81  | | 
% 153.25/22.81  | | ALPHA: (6) implies:
% 153.25/22.81  | |   (7)  op(e1, e2) = e1
% 153.25/22.81  | | 
% 153.25/22.81  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #1042.
% 153.25/22.81  | | 
% 153.25/22.81  | Case 2:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (8)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.25/22.81  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.25/22.81  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 153.25/22.81  | | 
% 153.25/22.81  | | ALPHA: (8) implies:
% 153.25/22.81  | |   (9)   ~ (all_57_7 = e2)
% 153.25/22.81  | |   (10)  op(e2, e2) = e1
% 153.25/22.81  | | 
% 153.25/22.81  | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #713.
% 153.25/22.81  | | 
% 153.25/22.81  | End of split
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #486 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)   ~ (e3 = e1)
% 153.25/22.81    (2)   ~ (e2 = e0)
% 153.25/22.81    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.81    (4)  op(e0, e0) = e2
% 153.25/22.81    (5)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.25/22.81             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.25/22.81               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.25/22.81               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.25/22.81    (6)   ~ (e3 = e0)
% 153.25/22.81    (7)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.25/22.81         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.25/22.81    (8)   ~ (e1 = e0)
% 153.25/22.81    (9)   ~ (e3 = e2)
% 153.25/22.81    (10)  all_56_9 = e2
% 153.25/22.81    (11)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.25/22.81          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.25/22.81    (12)   ~ (e2 = e1)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | BETA: splitting (5) gives:
% 153.25/22.81  | 
% 153.25/22.81  | Case 1:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (13)  all_56_15 = e0 & op(e0, e0) = e0
% 153.25/22.81  | | 
% 153.25/22.81  | | ALPHA: (13) implies:
% 153.25/22.81  | |   (14)  op(e0, e0) = e0
% 153.25/22.81  | | 
% 153.25/22.81  | | REF_CLOSE: (2), (3), (4), (14) are inconsistent by sub-proof #1043.
% 153.25/22.81  | | 
% 153.25/22.81  | Case 2:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (15)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.25/22.81  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 153.25/22.81  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.25/22.81  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 153.25/22.81  | | 
% 153.25/22.81  | | ALPHA: (15) implies:
% 153.25/22.81  | |   (16)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.25/22.81  | |           e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (16) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (17)  all_56_9 = e0 & op(e3, e0) = e0
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (2), (10), (17) are inconsistent by sub-proof #746.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (18)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.25/22.81  | | |           = e0)
% 153.25/22.81  | | | 
% 153.25/22.81  | | | BETA: splitting (18) gives:
% 153.25/22.81  | | | 
% 153.25/22.81  | | | Case 1:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | |   (19)  all_56_10 = e0 & op(e2, e0) = e0
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | ALPHA: (19) implies:
% 153.25/22.81  | | | |   (20)  all_56_10 = e0
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12),
% 153.25/22.81  | | | |            (16), (20) are inconsistent by sub-proof #489.
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | Case 2:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | |   (21)  all_56_11 = e0 & op(e1, e0) = e0
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | ALPHA: (21) implies:
% 153.25/22.81  | | | |   (22)  all_56_11 = e0
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (22) are
% 153.25/22.81  | | | |            inconsistent by sub-proof #487.
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | End of split
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | End of split
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #487 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)   ~ (e3 = e1)
% 153.25/22.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.81    (3)  op(e0, e0) = e2
% 153.25/22.81    (4)   ~ (e3 = e0)
% 153.25/22.81    (5)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.25/22.81         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.25/22.81    (6)  all_56_11 = e0
% 153.25/22.81    (7)   ~ (e1 = e0)
% 153.25/22.81    (8)   ~ (e3 = e2)
% 153.25/22.81    (9)  all_56_9 = e2
% 153.25/22.81    (10)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.25/22.81          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.25/22.81    (11)   ~ (e2 = e1)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | BETA: splitting (5) gives:
% 153.25/22.81  | 
% 153.25/22.81  | Case 1:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (12)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 153.25/22.81  | |           e1)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (12) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (13)  all_56_9 = e1 & op(e3, e0) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (9), (11), (13) are inconsistent by sub-proof #656.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (14)  all_56_10 = e1 & op(e2, e0) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (14) implies:
% 153.25/22.81  | | |   (15)  all_56_10 = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | BETA: splitting (10) gives:
% 153.25/22.81  | | | 
% 153.25/22.81  | | | Case 1:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | |   (16)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0)
% 153.25/22.81  | | | |           = e3)
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | BETA: splitting (16) gives:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | Case 1:
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | |   (17)  all_56_9 = e3 & op(e3, e0) = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | ALPHA: (17) implies:
% 153.25/22.81  | | | | |   (18)  all_56_9 = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | REF_CLOSE: (8), (9), (18) are inconsistent by sub-proof #964.
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | Case 2:
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | |   (19)  all_56_10 = e3 & op(e2, e0) = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | ALPHA: (19) implies:
% 153.25/22.81  | | | | |   (20)  all_56_10 = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | REF_CLOSE: (1), (15), (20) are inconsistent by sub-proof #677.
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | End of split
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | Case 2:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | |   (21)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0,
% 153.25/22.81  | | | |             e0) = e3)
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | REF_CLOSE: (2), (3), (4), (6), (8), (21) are inconsistent by sub-proof
% 153.25/22.81  | | | |            #488.
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | End of split
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | Case 2:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (22)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 153.25/22.81  | |           e1)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (22) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (23)  all_56_11 = e1 & op(e1, e0) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (23) implies:
% 153.25/22.81  | | |   (24)  all_56_11 = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (6), (7), (24) are inconsistent by sub-proof #745.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (25)  all_56_15 = e1 & op(e0, e0) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (25) implies:
% 153.25/22.81  | | |   (26)  op(e0, e0) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (2), (3), (11), (26) are inconsistent by sub-proof #978.
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | End of split
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #488 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.25/22.81    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.81    (3)  op(e0, e0) = e2
% 153.25/22.81    (4)   ~ (e3 = e0)
% 153.25/22.81    (5)  all_56_11 = e0
% 153.25/22.81    (6)   ~ (e3 = e2)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | BETA: splitting (1) gives:
% 153.25/22.81  | 
% 153.25/22.81  | Case 1:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (7)  all_56_11 = e3 & op(e1, e0) = e3
% 153.25/22.81  | | 
% 153.25/22.81  | | ALPHA: (7) implies:
% 153.25/22.81  | |   (8)  all_56_11 = e3
% 153.25/22.81  | | 
% 153.25/22.81  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #772.
% 153.25/22.81  | | 
% 153.25/22.81  | Case 2:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (9)  all_56_15 = e3 & op(e0, e0) = e3
% 153.25/22.81  | | 
% 153.25/22.81  | | ALPHA: (9) implies:
% 153.25/22.81  | |   (10)  op(e0, e0) = e3
% 153.25/22.81  | | 
% 153.25/22.81  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #1087.
% 153.25/22.81  | | 
% 153.25/22.81  | End of split
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #489 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)   ~ (e3 = e1)
% 153.25/22.81    (2)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 153.25/22.81         (all_56_11 = e0 & op(e1, e0) = e0)
% 153.25/22.81    (3)   ~ (e2 = e0)
% 153.25/22.81    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.81    (5)  op(e0, e0) = e2
% 153.25/22.81    (6)  all_56_10 = e0
% 153.25/22.81    (7)   ~ (e3 = e0)
% 153.25/22.81    (8)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.25/22.81         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.25/22.81    (9)   ~ (e1 = e0)
% 153.25/22.81    (10)   ~ (e3 = e2)
% 153.25/22.81    (11)  all_56_9 = e2
% 153.25/22.81    (12)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.25/22.81          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.25/22.81    (13)   ~ (e2 = e1)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | BETA: splitting (8) gives:
% 153.25/22.81  | 
% 153.25/22.81  | Case 1:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (14)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 153.25/22.81  | |           e1)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (14) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (15)  all_56_9 = e1 & op(e3, e0) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (11), (13), (15) are inconsistent by sub-proof #656.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (16)  all_56_10 = e1 & op(e2, e0) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (16) implies:
% 153.25/22.81  | | |   (17)  all_56_10 = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (6), (9), (17) are inconsistent by sub-proof #963.
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | Case 2:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (18)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 153.25/22.81  | |           e1)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (18) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (19)  all_56_11 = e1 & op(e1, e0) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (19) implies:
% 153.25/22.81  | | |   (20)  all_56_11 = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | BETA: splitting (12) gives:
% 153.25/22.81  | | | 
% 153.25/22.81  | | | Case 1:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | |   (21)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0)
% 153.25/22.81  | | | |           = e3)
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | BETA: splitting (21) gives:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | Case 1:
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | |   (22)  all_56_9 = e3 & op(e3, e0) = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | ALPHA: (22) implies:
% 153.25/22.81  | | | | |   (23)  all_56_9 = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | REF_CLOSE: (10), (11), (23) are inconsistent by sub-proof #964.
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | Case 2:
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | |   (24)  all_56_10 = e3 & op(e2, e0) = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | ALPHA: (24) implies:
% 153.25/22.81  | | | | |   (25)  all_56_10 = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | REF_CLOSE: (2), (3), (7), (9), (11), (20), (25) are inconsistent by
% 153.25/22.81  | | | | |            sub-proof #744.
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | End of split
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | Case 2:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | |   (26)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0,
% 153.25/22.81  | | | |             e0) = e3)
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | BETA: splitting (26) gives:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | Case 1:
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | |   (27)  all_56_11 = e3 & op(e1, e0) = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | ALPHA: (27) implies:
% 153.25/22.81  | | | | |   (28)  all_56_11 = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | REF_CLOSE: (1), (20), (28) are inconsistent by sub-proof #490.
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | Case 2:
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | |   (29)  all_56_15 = e3 & op(e0, e0) = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | ALPHA: (29) implies:
% 153.25/22.81  | | | | |   (30)  op(e0, e0) = e3
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | REF_CLOSE: (4), (5), (10), (30) are inconsistent by sub-proof #1087.
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | End of split
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | End of split
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (31)  all_56_15 = e1 & op(e0, e0) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (31) implies:
% 153.25/22.81  | | |   (32)  op(e0, e0) = e1
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (4), (5), (13), (32) are inconsistent by sub-proof #978.
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | End of split
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #490 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)  all_56_11 = e3
% 153.25/22.81    (2)  all_56_11 = e1
% 153.25/22.81    (3)   ~ (e3 = e1)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | COMBINE_EQS: (1), (2) imply:
% 153.25/22.81  |   (4)  e3 = e1
% 153.25/22.81  | 
% 153.25/22.81  | SIMP: (4) implies:
% 153.25/22.81  |   (5)  e3 = e1
% 153.25/22.81  | 
% 153.25/22.81  | REDUCE: (3), (5) imply:
% 153.25/22.81  |   (6)  $false
% 153.25/22.81  | 
% 153.25/22.81  | CLOSE: (6) is inconsistent.
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #491 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.81    (2)  op(e3, e0) = all_52_12
% 153.25/22.81    (3)   ~ (all_52_12 = e3)
% 153.25/22.81    (4)  op(e3, e1) = e2
% 153.25/22.81    (5)   ~ (e3 = e2)
% 153.25/22.81    (6)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | BETA: splitting (6) gives:
% 153.25/22.81  | 
% 153.25/22.81  | Case 1:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (7)  all_56_4 = e3 & op(e3, e1) = e3
% 153.25/22.81  | | 
% 153.25/22.81  | | ALPHA: (7) implies:
% 153.25/22.81  | |   (8)  op(e3, e1) = e3
% 153.25/22.81  | | 
% 153.25/22.81  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #504.
% 153.25/22.81  | | 
% 153.25/22.81  | Case 2:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (9)  all_56_9 = e3 & op(e3, e0) = e3
% 153.25/22.81  | | 
% 153.25/22.81  | | ALPHA: (9) implies:
% 153.25/22.81  | |   (10)  op(e3, e0) = e3
% 153.25/22.81  | | 
% 153.25/22.81  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #1082.
% 153.25/22.81  | | 
% 153.25/22.81  | End of split
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #492 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)  op(e3, e3) = e0
% 153.25/22.81    (2)   ~ (e3 = e1)
% 153.25/22.81    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.25/22.81         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.25/22.81    (4)   ~ (e2 = e0)
% 153.25/22.81    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.81    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.25/22.81         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.25/22.81    (7)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.25/22.81         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.25/22.81    (8)   ~ (e3 = e0)
% 153.25/22.81    (9)   ~ (e1 = e0)
% 153.25/22.81    (10)   ~ (e3 = e2)
% 153.25/22.81    (11)   ~ (all_52_8 = e3)
% 153.25/22.81    (12)  all_56_1 = e0
% 153.25/22.81    (13)  op(e3, e1) = all_52_8
% 153.25/22.81    (14)   ~ (e2 = e1)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | BETA: splitting (6) gives:
% 153.25/22.81  | 
% 153.25/22.81  | Case 1:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (15)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 153.25/22.81  | |           e3)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (15) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (16)  all_56_0 = e3 & op(e3, e3) = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (16) implies:
% 153.25/22.81  | | |   (17)  op(e3, e3) = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (1), (5), (8), (17) are inconsistent by sub-proof #1141.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (18)  all_56_1 = e3 & op(e3, e2) = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (18) implies:
% 153.25/22.81  | | |   (19)  all_56_1 = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (8), (12), (19) are inconsistent by sub-proof #1065.
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | Case 2:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (20)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 153.25/22.81  | |           e3)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (20) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (21)  all_56_4 = e3 & op(e3, e1) = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (21) implies:
% 153.25/22.81  | | |   (22)  op(e3, e1) = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (5), (11), (13), (22) are inconsistent by sub-proof #1164.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (23)  all_56_9 = e3 & op(e3, e0) = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (23) implies:
% 153.25/22.81  | | |   (24)  all_56_9 = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | BETA: splitting (7) gives:
% 153.25/22.81  | | | 
% 153.25/22.81  | | | Case 1:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | |   (25)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2)
% 153.25/22.81  | | | |           = e1)
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | BETA: splitting (25) gives:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | Case 1:
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | |   (26)  all_56_0 = e1 & op(e3, e3) = e1
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | ALPHA: (26) implies:
% 153.25/22.81  | | | | |   (27)  op(e3, e3) = e1
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | REF_CLOSE: (1), (5), (9), (27) are inconsistent by sub-proof #957.
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | Case 2:
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | |   (28)  all_56_1 = e1 & op(e3, e2) = e1
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | ALPHA: (28) implies:
% 153.25/22.81  | | | | |   (29)  all_56_1 = e1
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | REF_CLOSE: (9), (12), (29) are inconsistent by sub-proof #1107.
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | End of split
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | Case 2:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | |   (30)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0)
% 153.25/22.81  | | | |           = e1)
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | BETA: splitting (30) gives:
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | | Case 1:
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | |   (31)  all_56_4 = e1 & op(e3, e1) = e1
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | ALPHA: (31) implies:
% 153.25/22.81  | | | | |   (32)  all_56_4 = e1
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | BETA: splitting (3) gives:
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | Case 1:
% 153.25/22.81  | | | | | | 
% 153.25/22.81  | | | | | |   (33)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3,
% 153.25/22.81  | | | | | |             e2) = e2)
% 153.25/22.81  | | | | | | 
% 153.25/22.81  | | | | | | BETA: splitting (33) gives:
% 153.25/22.81  | | | | | | 
% 153.25/22.81  | | | | | | Case 1:
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | |   (34)  all_56_0 = e2 & op(e3, e3) = e2
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | | ALPHA: (34) implies:
% 153.25/22.81  | | | | | | |   (35)  op(e3, e3) = e2
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | | REF_CLOSE: (1), (4), (5), (35) are inconsistent by sub-proof
% 153.25/22.81  | | | | | | |            #1073.
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | Case 2:
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | |   (36)  all_56_1 = e2 & op(e3, e2) = e2
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | | REF_CLOSE: (4), (12), (36) are inconsistent by sub-proof #848.
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | End of split
% 153.25/22.81  | | | | | | 
% 153.25/22.81  | | | | | Case 2:
% 153.25/22.81  | | | | | | 
% 153.25/22.81  | | | | | |   (37)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3,
% 153.25/22.81  | | | | | |             e0) = e2)
% 153.25/22.81  | | | | | | 
% 153.25/22.81  | | | | | | BETA: splitting (37) gives:
% 153.25/22.81  | | | | | | 
% 153.25/22.81  | | | | | | Case 1:
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | |   (38)  all_56_4 = e2 & op(e3, e1) = e2
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | | ALPHA: (38) implies:
% 153.25/22.81  | | | | | | |   (39)  all_56_4 = e2
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | | REF_CLOSE: (14), (32), (39) are inconsistent by sub-proof #980.
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | Case 2:
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | |   (40)  all_56_9 = e2 & op(e3, e0) = e2
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | | ALPHA: (40) implies:
% 153.25/22.81  | | | | | | |   (41)  all_56_9 = e2
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | | REF_CLOSE: (10), (24), (41) are inconsistent by sub-proof #964.
% 153.25/22.81  | | | | | | | 
% 153.25/22.81  | | | | | | End of split
% 153.25/22.81  | | | | | | 
% 153.25/22.81  | | | | | End of split
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | Case 2:
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | |   (42)  all_56_9 = e1 & op(e3, e0) = e1
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | | REF_CLOSE: (2), (24), (42) are inconsistent by sub-proof #493.
% 153.25/22.81  | | | | | 
% 153.25/22.81  | | | | End of split
% 153.25/22.81  | | | | 
% 153.25/22.81  | | | End of split
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | End of split
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #493 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)  all_56_9 = e1 & op(e3, e0) = e1
% 153.25/22.81    (2)  all_56_9 = e3
% 153.25/22.81    (3)   ~ (e3 = e1)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | ALPHA: (1) implies:
% 153.25/22.81  |   (4)  all_56_9 = e1
% 153.25/22.81  | 
% 153.25/22.81  | COMBINE_EQS: (2), (4) imply:
% 153.25/22.81  |   (5)  e3 = e1
% 153.25/22.81  | 
% 153.25/22.81  | REDUCE: (3), (5) imply:
% 153.25/22.81  |   (6)  $false
% 153.25/22.81  | 
% 153.25/22.81  | CLOSE: (6) is inconsistent.
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #494 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)  op(e3, e0) = e1
% 153.25/22.81    (2)   ~ (e3 = e1)
% 153.25/22.81    (3)  op(e2, e2) = e1
% 153.25/22.81    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.81           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.81    (5)  all_40_2 = e2
% 153.25/22.81    (6)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0 &
% 153.25/22.81           op(e0, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 153.25/22.81             e3) & op(e0, e2) = all_40_1 & $i(all_40_1))
% 153.25/22.81    (7)   ~ (all_52_6 = e3)
% 153.25/22.81    (8)  op(e1, e2) = all_52_6
% 153.25/22.81    (9)  all_56_1 = e2
% 153.25/22.81    (10)   ~ (e3 = e2)
% 153.25/22.81    (11)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.25/22.81          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | BETA: splitting (11) gives:
% 153.25/22.81  | 
% 153.25/22.81  | Case 1:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (12)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 153.25/22.81  | |           e3)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (12) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (13)  all_56_1 = e3 & op(e3, e2) = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (13) implies:
% 153.25/22.81  | | |   (14)  all_56_1 = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (9), (10), (14) are inconsistent by sub-proof #950.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (15)  all_56_3 = e3 & op(e2, e2) = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | ALPHA: (15) implies:
% 153.25/22.81  | | |   (16)  op(e2, e2) = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (2), (3), (4), (16) are inconsistent by sub-proof #1136.
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | Case 2:
% 153.25/22.81  | | 
% 153.25/22.81  | |   (17)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 153.25/22.81  | |           e3)
% 153.25/22.81  | | 
% 153.25/22.81  | | BETA: splitting (17) gives:
% 153.25/22.81  | | 
% 153.25/22.81  | | Case 1:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (18)  all_56_7 = e3 & op(e1, e2) = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (4), (7), (8), (18) are inconsistent by sub-proof #925.
% 153.25/22.81  | | | 
% 153.25/22.81  | | Case 2:
% 153.25/22.81  | | | 
% 153.25/22.81  | | |   (19)  all_56_13 = e3 & op(e0, e2) = e3
% 153.25/22.81  | | | 
% 153.25/22.81  | | | REF_CLOSE: (1), (4), (5), (6), (19) are inconsistent by sub-proof #979.
% 153.25/22.81  | | | 
% 153.25/22.81  | | End of split
% 153.25/22.81  | | 
% 153.25/22.81  | End of split
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #495 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)  all_54_7 = all_52_13
% 153.25/22.81    (2)  all_54_7 = e1
% 153.25/22.81    (3)   ~ (all_52_13 = e1)
% 153.25/22.81  
% 153.25/22.81  Begin of proof
% 153.25/22.81  | 
% 153.25/22.81  | COMBINE_EQS: (1), (2) imply:
% 153.25/22.81  |   (4)  all_52_13 = e1
% 153.25/22.81  | 
% 153.25/22.81  | SIMP: (4) implies:
% 153.25/22.81  |   (5)  all_52_13 = e1
% 153.25/22.81  | 
% 153.25/22.81  | REDUCE: (3), (5) imply:
% 153.25/22.81  |   (6)  $false
% 153.25/22.81  | 
% 153.25/22.81  | CLOSE: (6) is inconsistent.
% 153.25/22.81  | 
% 153.25/22.81  End of proof
% 153.25/22.81  
% 153.25/22.81  Sub-proof #496 shows that the following formulas are inconsistent:
% 153.25/22.81  ----------------------------------------------------------------
% 153.25/22.81    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.25/22.81         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.25/22.81    (2)   ~ (e3 = e1)
% 153.25/22.82    (3)  all_56_9 = e1
% 153.25/22.82    (4)   ~ (e2 = e0)
% 153.25/22.82    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.25/22.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.25/22.82    (6)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.25/22.82             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.25/22.82               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.25/22.82               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.25/22.82    (7)  op(e0, e0) = e1
% 153.25/22.82    (8)   ~ (e3 = e0)
% 153.25/22.82    (9)   ~ (e1 = e0)
% 153.25/22.82    (10)   ~ (e3 = e2)
% 153.29/22.82    (11)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.29/22.82          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.29/22.82    (12)   ~ (e2 = e1)
% 153.29/22.82  
% 153.29/22.82  Begin of proof
% 153.29/22.82  | 
% 153.29/22.82  | BETA: splitting (11) gives:
% 153.29/22.82  | 
% 153.29/22.82  | Case 1:
% 153.29/22.82  | | 
% 153.29/22.82  | |   (13)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 153.29/22.82  | |           e3)
% 153.29/22.82  | | 
% 153.29/22.82  | | BETA: splitting (13) gives:
% 153.29/22.82  | | 
% 153.29/22.82  | | Case 1:
% 153.29/22.82  | | | 
% 153.29/22.82  | | |   (14)  all_56_9 = e3 & op(e3, e0) = e3
% 153.29/22.82  | | | 
% 153.29/22.82  | | | ALPHA: (14) implies:
% 153.29/22.82  | | |   (15)  all_56_9 = e3
% 153.29/22.82  | | | 
% 153.29/22.82  | | | REF_CLOSE: (2), (3), (15) are inconsistent by sub-proof #1064.
% 153.29/22.82  | | | 
% 153.29/22.82  | | Case 2:
% 153.29/22.82  | | | 
% 153.29/22.82  | | |   (16)  all_56_10 = e3 & op(e2, e0) = e3
% 153.29/22.82  | | | 
% 153.29/22.82  | | | ALPHA: (16) implies:
% 153.29/22.82  | | |   (17)  all_56_10 = e3
% 153.29/22.82  | | |   (18)  op(e2, e0) = e3
% 153.29/22.82  | | | 
% 153.29/22.82  | | | BETA: splitting (6) gives:
% 153.29/22.82  | | | 
% 153.29/22.82  | | | Case 1:
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | |   (19)  all_56_15 = e0 & op(e0, e0) = e0
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | ALPHA: (19) implies:
% 153.29/22.82  | | | |   (20)  op(e0, e0) = e0
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | REF_CLOSE: (5), (7), (9), (20) are inconsistent by sub-proof #1040.
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | Case 2:
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | |   (21)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 153.29/22.82  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 153.29/22.82  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 153.29/22.82  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | ALPHA: (21) implies:
% 153.29/22.82  | | | |   (22)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0)
% 153.29/22.82  | | | |           = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | BETA: splitting (1) gives:
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | Case 1:
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | |   (23)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2,
% 153.29/22.82  | | | | |             e0) = e2)
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | BETA: splitting (23) gives:
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | Case 1:
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | |   (24)  all_56_9 = e2 & op(e3, e0) = e2
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | | ALPHA: (24) implies:
% 153.29/22.82  | | | | | |   (25)  all_56_9 = e2
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | | REF_CLOSE: (3), (12), (25) are inconsistent by sub-proof #948.
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | Case 2:
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | |   (26)  all_56_10 = e2 & op(e2, e0) = e2
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | | ALPHA: (26) implies:
% 153.29/22.82  | | | | | |   (27)  op(e2, e0) = e2
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | | REF_CLOSE: (5), (10), (18), (27) are inconsistent by sub-proof #854.
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | End of split
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | Case 2:
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | |   (28)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0,
% 153.29/22.82  | | | | |             e0) = e2)
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | BETA: splitting (28) gives:
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | Case 1:
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | |   (29)  all_56_11 = e2 & op(e1, e0) = e2
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | | ALPHA: (29) implies:
% 153.29/22.82  | | | | | |   (30)  all_56_11 = e2
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | | REF_CLOSE: (3), (4), (8), (9), (17), (22), (30) are inconsistent by
% 153.29/22.82  | | | | | |            sub-proof #748.
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | Case 2:
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | |   (31)  all_56_15 = e2 & op(e0, e0) = e2
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | | ALPHA: (31) implies:
% 153.29/22.82  | | | | | |   (32)  op(e0, e0) = e2
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | | REF_CLOSE: (5), (7), (12), (32) are inconsistent by sub-proof #978.
% 153.29/22.82  | | | | | | 
% 153.29/22.82  | | | | | End of split
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | End of split
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | End of split
% 153.29/22.82  | | | 
% 153.29/22.82  | | End of split
% 153.29/22.82  | | 
% 153.29/22.82  | Case 2:
% 153.29/22.82  | | 
% 153.29/22.82  | |   (33)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 153.29/22.82  | |           e3)
% 153.29/22.82  | | 
% 153.29/22.82  | | BETA: splitting (33) gives:
% 153.29/22.82  | | 
% 153.29/22.82  | | Case 1:
% 153.29/22.82  | | | 
% 153.29/22.82  | | |   (34)  all_56_11 = e3 & op(e1, e0) = e3
% 153.29/22.82  | | | 
% 153.29/22.82  | | | ALPHA: (34) implies:
% 153.29/22.82  | | |   (35)  all_56_11 = e3
% 153.29/22.82  | | | 
% 153.29/22.82  | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (35) are
% 153.29/22.82  | | |            inconsistent by sub-proof #497.
% 153.29/22.82  | | | 
% 153.29/22.82  | | Case 2:
% 153.29/22.82  | | | 
% 153.29/22.82  | | |   (36)  all_56_15 = e3 & op(e0, e0) = e3
% 153.29/22.82  | | | 
% 153.29/22.82  | | | ALPHA: (36) implies:
% 153.29/22.82  | | |   (37)  op(e0, e0) = e3
% 153.29/22.82  | | | 
% 153.29/22.82  | | | REF_CLOSE: (2), (5), (7), (37) are inconsistent by sub-proof #1022.
% 153.29/22.82  | | | 
% 153.29/22.82  | | End of split
% 153.29/22.82  | | 
% 153.29/22.82  | End of split
% 153.29/22.82  | 
% 153.29/22.82  End of proof
% 153.29/22.82  
% 153.29/22.82  Sub-proof #497 shows that the following formulas are inconsistent:
% 153.29/22.82  ----------------------------------------------------------------
% 153.29/22.82    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.29/22.82         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.29/22.82    (2)  all_56_11 = e3
% 153.29/22.82    (3)  all_56_9 = e1
% 153.29/22.82    (4)   ~ (e2 = e0)
% 153.29/22.82    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.82    (6)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.29/22.82             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.29/22.82               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.29/22.82               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.29/22.82    (7)  op(e0, e0) = e1
% 153.29/22.82    (8)   ~ (e3 = e0)
% 153.29/22.82    (9)   ~ (e1 = e0)
% 153.29/22.82    (10)   ~ (e3 = e2)
% 153.29/22.82    (11)   ~ (e2 = e1)
% 153.29/22.82  
% 153.29/22.82  Begin of proof
% 153.29/22.82  | 
% 153.29/22.82  | BETA: splitting (6) gives:
% 153.29/22.82  | 
% 153.29/22.82  | Case 1:
% 153.29/22.82  | | 
% 153.29/22.82  | |   (12)  all_56_15 = e0 & op(e0, e0) = e0
% 153.29/22.82  | | 
% 153.29/22.82  | | ALPHA: (12) implies:
% 153.29/22.82  | |   (13)  op(e0, e0) = e0
% 153.29/22.82  | | 
% 153.29/22.82  | | REF_CLOSE: (5), (7), (9), (13) are inconsistent by sub-proof #1040.
% 153.29/22.82  | | 
% 153.29/22.82  | Case 2:
% 153.29/22.82  | | 
% 153.29/22.82  | |   (14)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.29/22.82  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 153.29/22.82  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.29/22.82  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 153.29/22.82  | | 
% 153.29/22.82  | | ALPHA: (14) implies:
% 153.29/22.82  | |   (15)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.29/22.82  | |           e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.29/22.82  | | 
% 153.29/22.82  | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (15) are
% 153.29/22.82  | |            inconsistent by sub-proof #498.
% 153.29/22.82  | | 
% 153.29/22.82  | End of split
% 153.29/22.82  | 
% 153.29/22.82  End of proof
% 153.29/22.82  
% 153.29/22.82  Sub-proof #498 shows that the following formulas are inconsistent:
% 153.29/22.82  ----------------------------------------------------------------
% 153.29/22.82    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.29/22.82         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.29/22.82    (2)  all_56_11 = e3
% 153.29/22.82    (3)  all_56_9 = e1
% 153.29/22.82    (4)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 153.29/22.82         (all_56_11 = e0 & op(e1, e0) = e0)
% 153.29/22.82    (5)   ~ (e2 = e0)
% 153.29/22.82    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.82    (7)  op(e0, e0) = e1
% 153.29/22.82    (8)   ~ (e3 = e0)
% 153.29/22.82    (9)   ~ (e1 = e0)
% 153.29/22.82    (10)   ~ (e3 = e2)
% 153.29/22.82    (11)   ~ (e2 = e1)
% 153.29/22.82  
% 153.29/22.82  Begin of proof
% 153.29/22.82  | 
% 153.29/22.82  | BETA: splitting (4) gives:
% 153.29/22.82  | 
% 153.29/22.82  | Case 1:
% 153.29/22.82  | | 
% 153.29/22.82  | |   (12)  all_56_9 = e0 & op(e3, e0) = e0
% 153.29/22.82  | | 
% 153.29/22.82  | | REF_CLOSE: (3), (9), (12) are inconsistent by sub-proof #1063.
% 153.29/22.82  | | 
% 153.29/22.82  | Case 2:
% 153.29/22.82  | | 
% 153.29/22.82  | |   (13)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.29/22.82  | |           e0)
% 153.29/22.82  | | 
% 153.29/22.82  | | BETA: splitting (13) gives:
% 153.29/22.82  | | 
% 153.29/22.82  | | Case 1:
% 153.29/22.82  | | | 
% 153.29/22.82  | | |   (14)  all_56_10 = e0 & op(e2, e0) = e0
% 153.29/22.82  | | | 
% 153.29/22.82  | | | ALPHA: (14) implies:
% 153.29/22.82  | | |   (15)  all_56_10 = e0
% 153.29/22.82  | | | 
% 153.29/22.82  | | | BETA: splitting (1) gives:
% 153.29/22.82  | | | 
% 153.29/22.82  | | | Case 1:
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | |   (16)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0)
% 153.29/22.82  | | | |           = e2)
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | BETA: splitting (16) gives:
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | Case 1:
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | |   (17)  all_56_9 = e2 & op(e3, e0) = e2
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | REF_CLOSE: (3), (11), (17) are inconsistent by sub-proof #503.
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | Case 2:
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | |   (18)  all_56_10 = e2 & op(e2, e0) = e2
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | REF_CLOSE: (5), (15), (18) are inconsistent by sub-proof #1132.
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | End of split
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | Case 2:
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | |   (19)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0,
% 153.29/22.82  | | | |             e0) = e2)
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | REF_CLOSE: (2), (6), (7), (10), (11), (19) are inconsistent by sub-proof
% 153.29/22.82  | | | |            #590.
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | End of split
% 153.29/22.82  | | | 
% 153.29/22.82  | | Case 2:
% 153.29/22.82  | | | 
% 153.29/22.82  | | |   (20)  all_56_11 = e0 & op(e1, e0) = e0
% 153.29/22.82  | | | 
% 153.29/22.82  | | | ALPHA: (20) implies:
% 153.29/22.82  | | |   (21)  all_56_11 = e0
% 153.29/22.82  | | | 
% 153.29/22.82  | | | REF_CLOSE: (2), (8), (21) are inconsistent by sub-proof #772.
% 153.29/22.82  | | | 
% 153.29/22.82  | | End of split
% 153.29/22.82  | | 
% 153.29/22.82  | End of split
% 153.29/22.82  | 
% 153.29/22.82  End of proof
% 153.29/22.82  
% 153.29/22.82  Sub-proof #499 shows that the following formulas are inconsistent:
% 153.29/22.82  ----------------------------------------------------------------
% 153.29/22.82    (1)  all_56_13 = e1 & op(e0, e2) = e1
% 153.29/22.82    (2)   ~ (e3 = e1)
% 153.29/22.82    (3)  op(e2, e2) = e1
% 153.29/22.82    (4)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.29/22.82         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.29/22.82    (5)  op(e3, e2) = all_52_4
% 153.29/22.82    (6)   ~ (e2 = e0)
% 153.29/22.82    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.82    (8)   ~ (e3 = e0)
% 153.29/22.82    (9)   ~ (e1 = e0)
% 153.29/22.82    (10)   ~ (e3 = e2)
% 153.29/22.82    (11)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.29/22.82          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.29/22.82    (12)   ~ (e2 = e1)
% 153.29/22.82    (13)   ~ (all_52_4 = e0)
% 153.29/22.82    (14)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.29/22.82          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.29/22.82  
% 153.29/22.82  Begin of proof
% 153.29/22.82  | 
% 153.29/22.82  | ALPHA: (1) implies:
% 153.29/22.82  |   (15)  all_56_13 = e1
% 153.29/22.82  | 
% 153.29/22.82  | BETA: splitting (11) gives:
% 153.29/22.82  | 
% 153.29/22.82  | Case 1:
% 153.29/22.82  | | 
% 153.29/22.82  | |   (16)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 153.29/22.82  | |           e0)
% 153.29/22.82  | | 
% 153.29/22.82  | | BETA: splitting (16) gives:
% 153.29/22.82  | | 
% 153.29/22.82  | | Case 1:
% 153.29/22.82  | | | 
% 153.29/22.82  | | |   (17)  all_56_1 = e0 & op(e3, e2) = e0
% 153.29/22.82  | | | 
% 153.29/22.82  | | | REF_CLOSE: (5), (7), (13), (17) are inconsistent by sub-proof #1013.
% 153.29/22.82  | | | 
% 153.29/22.82  | | Case 2:
% 153.29/22.82  | | | 
% 153.29/22.82  | | |   (18)  all_56_3 = e0 & op(e2, e2) = e0
% 153.29/22.82  | | | 
% 153.29/22.82  | | | ALPHA: (18) implies:
% 153.29/22.82  | | |   (19)  op(e2, e2) = e0
% 153.29/22.82  | | | 
% 153.29/22.82  | | | REF_CLOSE: (3), (7), (9), (19) are inconsistent by sub-proof #853.
% 153.29/22.82  | | | 
% 153.29/22.82  | | End of split
% 153.29/22.82  | | 
% 153.29/22.82  | Case 2:
% 153.29/22.82  | | 
% 153.29/22.82  | |   (20)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 153.29/22.82  | |           e0)
% 153.29/22.82  | | 
% 153.29/22.82  | | BETA: splitting (20) gives:
% 153.29/22.82  | | 
% 153.29/22.82  | | Case 1:
% 153.29/22.82  | | | 
% 153.29/22.82  | | |   (21)  all_56_7 = e0 & op(e1, e2) = e0
% 153.29/22.82  | | | 
% 153.29/22.82  | | | ALPHA: (21) implies:
% 153.29/22.82  | | |   (22)  all_56_7 = e0
% 153.29/22.82  | | | 
% 153.29/22.82  | | | BETA: splitting (14) gives:
% 153.29/22.82  | | | 
% 153.29/22.82  | | | Case 1:
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | |   (23)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2)
% 153.29/22.82  | | | |           = e3)
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | BETA: splitting (23) gives:
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | Case 1:
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | |   (24)  all_56_1 = e3 & op(e3, e2) = e3
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | ALPHA: (24) implies:
% 153.29/22.82  | | | | |   (25)  all_56_1 = e3
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | REF_CLOSE: (3), (4), (6), (7), (10), (12), (15), (22), (25) are
% 153.29/22.82  | | | | |            inconsistent by sub-proof #738.
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | Case 2:
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | |   (26)  all_56_3 = e3 & op(e2, e2) = e3
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | ALPHA: (26) implies:
% 153.29/22.82  | | | | |   (27)  op(e2, e2) = e3
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | REF_CLOSE: (2), (3), (7), (27) are inconsistent by sub-proof #1136.
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | End of split
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | Case 2:
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | |   (28)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2)
% 153.29/22.82  | | | |           = e3)
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | BETA: splitting (28) gives:
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | | Case 1:
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | |   (29)  all_56_7 = e3 & op(e1, e2) = e3
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | REF_CLOSE: (8), (22), (29) are inconsistent by sub-proof #989.
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | Case 2:
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | |   (30)  all_56_13 = e3 & op(e0, e2) = e3
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | ALPHA: (30) implies:
% 153.29/22.82  | | | | |   (31)  all_56_13 = e3
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | | REF_CLOSE: (2), (15), (31) are inconsistent by sub-proof #1121.
% 153.29/22.82  | | | | | 
% 153.29/22.82  | | | | End of split
% 153.29/22.82  | | | | 
% 153.29/22.82  | | | End of split
% 153.29/22.82  | | | 
% 153.29/22.82  | | Case 2:
% 153.29/22.82  | | | 
% 153.29/22.82  | | |   (32)  all_56_13 = e0 & op(e0, e2) = e0
% 153.29/22.82  | | | 
% 153.29/22.82  | | | REF_CLOSE: (9), (15), (32) are inconsistent by sub-proof #737.
% 153.29/22.82  | | | 
% 153.29/22.82  | | End of split
% 153.29/22.82  | | 
% 153.29/22.82  | End of split
% 153.29/22.82  | 
% 153.29/22.82  End of proof
% 153.29/22.82  
% 153.29/22.82  Sub-proof #500 shows that the following formulas are inconsistent:
% 153.29/22.82  ----------------------------------------------------------------
% 153.29/22.82    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.29/22.82         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.29/22.82    (2)   ~ (e3 = e1)
% 153.29/22.82    (3)  op(e0, e0) = all_10_2
% 153.29/22.82    (4)   ~ (e2 = e0)
% 153.29/22.82    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.82           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.82    (6)  op(e0, e0) = e3
% 153.29/22.82    (7)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.29/22.82             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.29/22.82               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.29/22.82               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.29/22.82    (8)   ~ (e3 = e0)
% 153.29/22.82    (9)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.29/22.82         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.29/22.82    (10)  op(e2, e0) = all_52_13
% 153.29/22.82    (11)  op(e1, e1) = e1
% 153.29/22.82    (12)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 153.29/22.82    (13)   ~ (e1 = e0)
% 153.29/22.82    (14)   ~ (e3 = e2)
% 153.29/22.82    (15)   ~ (all_10_2 = e2)
% 153.29/22.82    (16)   ~ (e2 = e1)
% 153.29/22.82  
% 153.29/22.82  Begin of proof
% 153.29/22.82  | 
% 153.29/22.82  | BETA: splitting (12) gives:
% 153.29/22.82  | 
% 153.29/22.82  | Case 1:
% 153.29/22.82  | | 
% 153.29/22.82  | |   (17)  all_56_8 = e3 & op(e1, e1) = e3
% 153.29/22.82  | | 
% 153.29/22.82  | | ALPHA: (17) implies:
% 153.29/22.82  | |   (18)  op(e1, e1) = e3
% 153.29/22.82  | | 
% 153.29/22.82  | | REF_CLOSE: (2), (5), (11), (18) are inconsistent by sub-proof #734.
% 153.29/22.82  | | 
% 153.29/22.82  | Case 2:
% 153.29/22.82  | | 
% 153.29/22.82  | |   (19)  all_56_11 = e3 & op(e1, e0) = e3
% 153.29/22.82  | | 
% 153.29/22.82  | | ALPHA: (19) implies:
% 153.29/22.82  | |   (20)  all_56_11 = e3
% 153.29/22.82  | | 
% 153.29/22.82  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (13), (14),
% 153.29/22.82  | |            (15), (16), (20) are inconsistent by sub-proof #771.
% 153.29/22.82  | | 
% 153.29/22.82  | End of split
% 153.29/22.82  | 
% 153.29/22.82  End of proof
% 153.29/22.82  
% 153.29/22.82  Sub-proof #501 shows that the following formulas are inconsistent:
% 153.29/22.82  ----------------------------------------------------------------
% 153.29/22.82    (1)   ~ (all_52_1 = e0)
% 153.29/22.82    (2)  op(e0, e1) = all_52_11
% 153.29/22.82    (3)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.29/22.82         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.29/22.82    (4)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 153.29/22.82         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.29/22.82    (5)   ~ (all_52_7 = all_52_11)
% 153.29/22.82    (6)   ~ (all_52_6 = e1)
% 153.29/22.82    (7)  all_54_2 = all_52_8
% 153.29/22.82    (8)   ~ (e3 = e1)
% 153.29/22.82    (9)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.29/22.82         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.29/22.82    (10)  all_56_9 = e1
% 153.29/22.82    (11)  all_57_7 = e2
% 153.29/22.82    (12)  op(e2, e2) = e1
% 153.29/22.82    (13)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.29/22.82          (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.29/22.82    (14)  op(e0, e0) = all_10_2
% 153.29/22.82    (15)  op(e3, e2) = all_52_4
% 153.29/22.82    (16)  op(e0, e2) = all_52_7
% 153.29/22.82    (17)  all_54_14 = all_52_11
% 153.29/22.82    (18)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.29/22.82          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.29/22.82    (19)  op(e1, e1) = all_4_2
% 153.29/22.82    (20)   ~ (all_52_8 = e1)
% 153.29/22.82    (21)   ~ (e2 = e0)
% 153.29/22.82    (22)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.29/22.82          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.29/22.82    (23)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.82            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.82    (24)  op(e0, e0) = e3
% 153.29/22.82    (25)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.29/22.82          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.29/22.82    (26)  all_56_5 = e2
% 153.29/22.82    (27)   ~ (all_52_14 = e1)
% 153.29/22.82    (28)  all_56_12 = e1
% 153.29/22.82    (29)   ~ (all_52_11 = e3)
% 153.29/22.82    (30)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.29/22.82              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.29/22.82                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.29/22.82                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.29/22.82    (31)   ~ (all_52_8 = all_52_12)
% 153.29/22.82    (32)  op(e1, e0) = all_52_14
% 153.29/22.82    (33)   ~ (all_52_13 = e2)
% 153.29/22.82    (34)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.29/22.82    (35)  op(e3, e0) = all_52_12
% 153.29/22.82    (36)   ~ (e3 = e0)
% 153.29/22.82    (37)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.29/22.82          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.29/22.82    (38)  op(e2, e1) = e2
% 153.29/22.82    (39)  all_56_6 = e3 & op(e1, e3) = e3
% 153.29/22.82    (40)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.29/22.82          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.29/22.82    (41)  op(e1, e2) = all_52_6
% 153.29/22.82    (42)  op(e2, e0) = all_52_13
% 153.29/22.82    (43)   ~ (all_52_8 = e0)
% 153.29/22.82    (44)   ~ (all_52_4 = all_52_8)
% 153.29/22.82    (45)  op(e1, e1) = e1
% 153.29/22.82    (46)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.29/22.82          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.29/22.82    (47)   ~ (all_52_8 = all_52_11)
% 153.29/22.82    (48)   ~ (all_52_8 = e2)
% 153.29/22.82    (49)   ~ (e1 = e0)
% 153.29/22.82    (50)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.29/22.82          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.29/22.82    (51)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.29/22.82            all_57_12 & $i(all_57_12))
% 153.29/22.82    (52)   ~ (e3 = e2)
% 153.29/22.82    (53)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.29/22.82          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.29/22.82    (54)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.29/22.82          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.29/22.82    (55)  all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 153.29/22.82    (56)   ~ (all_10_2 = e2)
% 153.29/22.82    (57)  op(e3, e1) = all_52_8
% 153.29/22.82    (58)   ~ (all_52_2 = e1)
% 153.29/22.82    (59)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.29/22.82          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.29/22.82    (60)   ~ (e2 = e1)
% 153.29/22.82    (61)   ~ (all_52_11 = e1)
% 153.29/22.82    (62)   ~ (all_52_4 = e0)
% 153.29/22.82    (63)  op(e1, e3) = all_52_2
% 153.29/22.82    (64)   ~ (all_52_11 = e2)
% 153.29/22.82    (65)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.29/22.82              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.29/22.82            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.29/22.82            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.29/22.82            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.29/22.82            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.29/22.82            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.29/22.82            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.29/22.82            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.29/22.82            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.29/22.82            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.29/22.82            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.29/22.82            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.29/22.82            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.29/22.82            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.29/22.82            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.29/22.82            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.29/22.82            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.29/22.82            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.29/22.82            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.29/22.82            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.29/22.82            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.29/22.82            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.29/22.82            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.29/22.82            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.29/22.82            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.29/22.82            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.29/22.82            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.29/22.82            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.29/22.82            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.29/22.82            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.29/22.82            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.29/22.82            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.29/22.82            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.29/22.82            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.29/22.82            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.29/22.82            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.29/22.82            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.29/22.82            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.29/22.82            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.29/22.82            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.29/22.82            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.29/22.82            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.29/22.82            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.29/22.82            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.29/22.82            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.29/22.82            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.29/22.82            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.29/22.82              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.29/22.82            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.29/22.82            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.29/22.82              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.29/22.82            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.29/22.82            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.29/22.82                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.29/22.82                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.29/22.82                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.29/22.82                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.29/22.82                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.29/22.82                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.29/22.82                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.29/22.82              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.29/22.82                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.29/22.82                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.29/22.82                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.29/22.82                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.29/22.82                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.29/22.82                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.29/22.82                $i(all_57_7))))
% 153.29/22.82    (66)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.29/22.82          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.29/22.82    (67)  op(e2, e3) = all_52_1
% 153.29/22.82    (68)   ~ (all_52_1 = e2)
% 153.29/22.82  
% 153.29/22.82  Begin of proof
% 153.29/22.82  | 
% 153.29/22.82  | ALPHA: (39) implies:
% 153.29/22.82  |   (69)  all_56_6 = e3
% 153.29/22.82  | 
% 153.29/22.82  | BETA: splitting (55) gives:
% 153.29/22.82  | 
% 153.29/22.82  | Case 1:
% 153.29/22.82  | | 
% 153.29/22.82  | |   (70)  all_54_2 = e3
% 153.29/22.82  | | 
% 153.29/22.82  | | COMBINE_EQS: (7), (70) imply:
% 153.29/22.82  | |   (71)  all_52_8 = e3
% 153.29/22.82  | | 
% 153.29/22.82  | | SIMP: (71) implies:
% 153.29/22.82  | |   (72)  all_52_8 = e3
% 153.29/22.82  | | 
% 153.29/22.82  | | REDUCE: (44), (72) imply:
% 153.29/22.82  | |   (73)   ~ (all_52_4 = e3)
% 153.29/22.82  | | 
% 153.29/22.82  | | REDUCE: (47), (72) imply:
% 153.29/22.82  | |   (74)   ~ (all_52_11 = e3)
% 153.29/22.82  | | 
% 153.29/22.82  | | REDUCE: (31), (72) imply:
% 153.29/22.82  | |   (75)   ~ (all_52_12 = e3)
% 153.29/22.82  | | 
% 153.29/22.82  | | SIMP: (75) implies:
% 153.29/22.82  | |   (76)   ~ (all_52_12 = e3)
% 153.29/22.82  | | 
% 153.29/22.82  | | REDUCE: (57), (72) imply:
% 153.29/22.82  | |   (77)  op(e3, e1) = e3
% 153.29/22.82  | | 
% 153.29/22.82  | | BETA: splitting (18) gives:
% 153.29/22.82  | | 
% 153.29/22.82  | | Case 1:
% 153.29/22.82  | | | 
% 153.29/22.83  | | |   (78)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 153.29/22.83  | | |           e0)
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (1), (12), (23), (49), (67), (78) are inconsistent by sub-proof
% 153.29/22.83  | | |            #516.
% 153.29/22.83  | | | 
% 153.29/22.83  | | Case 2:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (79)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.29/22.83  | | |           e0)
% 153.29/22.83  | | | 
% 153.29/22.83  | | | BETA: splitting (79) gives:
% 153.29/22.83  | | | 
% 153.29/22.83  | | | Case 1:
% 153.29/22.83  | | | | 
% 153.29/22.83  | | | |   (80)  all_56_5 = e0 & op(e2, e1) = e0
% 153.29/22.83  | | | | 
% 153.29/22.83  | | | | ALPHA: (80) implies:
% 153.29/22.83  | | | |   (81)  all_56_5 = e0
% 153.29/22.83  | | | | 
% 153.29/22.83  | | | | REF_CLOSE: (21), (26), (81) are inconsistent by sub-proof #509.
% 153.29/22.83  | | | | 
% 153.29/22.83  | | | Case 2:
% 153.29/22.83  | | | | 
% 153.29/22.83  | | | |   (82)  all_56_10 = e0 & op(e2, e0) = e0
% 153.29/22.83  | | | | 
% 153.29/22.83  | | | | ALPHA: (82) implies:
% 153.29/22.83  | | | |   (83)  all_56_10 = e0
% 153.29/22.83  | | | | 
% 153.29/22.83  | | | | BETA: splitting (46) gives:
% 153.29/22.83  | | | | 
% 153.29/22.83  | | | | Case 1:
% 153.29/22.83  | | | | | 
% 153.29/22.83  | | | | |   (84)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2,
% 153.29/22.83  | | | | |             e2) = e3)
% 153.29/22.83  | | | | | 
% 153.29/22.83  | | | | | BETA: splitting (84) gives:
% 153.29/22.83  | | | | | 
% 153.29/22.83  | | | | | Case 1:
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | |   (85)  all_56_2 = e3 & op(e2, e3) = e3
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | | ALPHA: (85) implies:
% 153.29/22.83  | | | | | |   (86)  all_56_2 = e3
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | | BETA: splitting (9) gives:
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | | Case 1:
% 153.29/22.83  | | | | | | | 
% 153.29/22.83  | | | | | | |   (87)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 &
% 153.29/22.83  | | | | | | |           op(e3, e2) = e2)
% 153.29/22.83  | | | | | | | 
% 153.29/22.83  | | | | | | | BETA: splitting (87) gives:
% 153.29/22.83  | | | | | | | 
% 153.29/22.83  | | | | | | | Case 1:
% 153.29/22.83  | | | | | | | | 
% 153.29/22.83  | | | | | | | |   (88)  all_56_0 = e2 & op(e3, e3) = e2
% 153.29/22.83  | | | | | | | | 
% 153.29/22.83  | | | | | | | | ALPHA: (88) implies:
% 153.29/22.83  | | | | | | | |   (89)  op(e3, e3) = e2
% 153.29/22.83  | | | | | | | | 
% 153.29/22.83  | | | | | | | | REF_CLOSE: (5), (6), (8), (11), (16), (17), (19), (21), (23),
% 153.29/22.83  | | | | | | | |            (24), (27), (28), (29), (32), (33), (34), (35), (36),
% 153.29/22.83  | | | | | | | |            (37), (40), (41), (42), (45), (49), (52), (58), (60),
% 153.29/22.83  | | | | | | | |            (61), (63), (64), (65), (67), (68), (76), (86), (89)
% 153.29/22.83  | | | | | | | |            are inconsistent by sub-proof #750.
% 153.29/22.83  | | | | | | | | 
% 153.29/22.83  | | | | | | | Case 2:
% 153.29/22.83  | | | | | | | | 
% 153.29/22.83  | | | | | | | |   (90)  all_56_1 = e2 & op(e3, e2) = e2
% 153.29/22.83  | | | | | | | | 
% 153.29/22.83  | | | | | | | | ALPHA: (90) implies:
% 153.29/22.83  | | | | | | | |   (91)  all_56_1 = e2
% 153.29/22.83  | | | | | | | | 
% 153.29/22.83  | | | | | | | | BETA: splitting (66) gives:
% 153.29/22.83  | | | | | | | | 
% 153.29/22.83  | | | | | | | | Case 1:
% 153.29/22.83  | | | | | | | | | 
% 153.29/22.83  | | | | | | | | |   (92)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 &
% 153.29/22.83  | | | | | | | | |           op(e2, e2) = e3)
% 153.29/22.83  | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | REF_CLOSE: (8), (12), (15), (23), (73), (92) are inconsistent
% 153.29/22.83  | | | | | | | | |            by sub-proof #849.
% 153.29/22.83  | | | | | | | | | 
% 153.29/22.83  | | | | | | | | Case 2:
% 153.29/22.83  | | | | | | | | | 
% 153.29/22.83  | | | | | | | | |   (93)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 &
% 153.29/22.83  | | | | | | | | |           op(e0, e2) = e3)
% 153.29/22.83  | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | BETA: splitting (93) gives:
% 153.29/22.83  | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | Case 1:
% 153.29/22.83  | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | |   (94)  all_56_7 = e3 & op(e1, e2) = e3
% 153.29/22.83  | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | ALPHA: (94) implies:
% 153.29/22.83  | | | | | | | | | |   (95)  all_56_7 = e3
% 153.29/22.83  | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | REF_CLOSE: (5), (8), (12), (15), (16), (17), (21), (22),
% 153.29/22.83  | | | | | | | | | |            (23), (29), (34), (36), (38), (46), (49), (52),
% 153.29/22.83  | | | | | | | | | |            (53), (54), (60), (61), (62), (64), (83), (86),
% 153.29/22.83  | | | | | | | | | |            (95) are inconsistent by sub-proof #508.
% 153.29/22.83  | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | Case 2:
% 153.29/22.83  | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | |   (96)  all_56_13 = e3 & op(e0, e2) = e3
% 153.29/22.83  | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | ALPHA: (96) implies:
% 153.29/22.83  | | | | | | | | | |   (97)  all_56_13 = e3
% 153.29/22.83  | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | BETA: splitting (40) gives:
% 153.29/22.83  | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | Case 1:
% 153.29/22.83  | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | |   (98)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2
% 153.29/22.83  | | | | | | | | | | |           & op(e2, e3) = e2)
% 153.29/22.83  | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | BETA: splitting (98) gives:
% 153.29/22.83  | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | Case 1:
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | |   (99)  all_56_0 = e2 & op(e3, e3) = e2
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | | ALPHA: (99) implies:
% 153.29/22.83  | | | | | | | | | | | |   (100)  op(e3, e3) = e2
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (11), (16), (17), (19), (21), (23),
% 153.29/22.83  | | | | | | | | | | | |            (24), (27), (28), (29), (32), (33), (34), (35),
% 153.29/22.83  | | | | | | | | | | | |            (36), (37), (40), (41), (42), (45), (49), (52),
% 153.29/22.83  | | | | | | | | | | | |            (58), (60), (61), (63), (64), (65), (67), (68),
% 153.29/22.83  | | | | | | | | | | | |            (76), (86), (100) are inconsistent by sub-proof
% 153.29/22.83  | | | | | | | | | | | |            #750.
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | Case 2:
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | |   (101)  all_56_2 = e2 & op(e2, e3) = e2
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | | ALPHA: (101) implies:
% 153.29/22.83  | | | | | | | | | | | |   (102)  op(e2, e3) = e2
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | | REF_CLOSE: (23), (67), (68), (102) are inconsistent by
% 153.29/22.83  | | | | | | | | | | | |            sub-proof #1181.
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | End of split
% 153.29/22.83  | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | Case 2:
% 153.29/22.83  | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | |   (103)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 =
% 153.29/22.83  | | | | | | | | | | |            e2 & op(e0, e3) = e2)
% 153.29/22.83  | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | BETA: splitting (103) gives:
% 153.29/22.83  | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | Case 1:
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | |   (104)  all_56_6 = e2 & op(e1, e3) = e2
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | | REF_CLOSE: (52), (69), (104) are inconsistent by sub-proof
% 153.29/22.83  | | | | | | | | | | | |            #779.
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | Case 2:
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | |   (105)  all_56_12 = e2 & op(e0, e3) = e2
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | | ALPHA: (105) implies:
% 153.29/22.83  | | | | | | | | | | | |   (106)  all_56_12 = e2
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | | COMBINE_EQS: (28), (106) imply:
% 153.29/22.83  | | | | | | | | | | | |   (107)  e2 = e1
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | | COMBINE_EQS: (91), (107) imply:
% 153.29/22.83  | | | | | | | | | | | |   (108)  all_56_1 = e1
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | | REF_CLOSE: (12), (13), (21), (23), (36), (49), (52), (54),
% 153.29/22.83  | | | | | | | | | | | |            (60), (97), (108) are inconsistent by sub-proof
% 153.29/22.83  | | | | | | | | | | | |            #505.
% 153.29/22.83  | | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | | End of split
% 153.29/22.83  | | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | | End of split
% 153.29/22.83  | | | | | | | | | | 
% 153.29/22.83  | | | | | | | | | End of split
% 153.29/22.83  | | | | | | | | | 
% 153.29/22.83  | | | | | | | | End of split
% 153.29/22.83  | | | | | | | | 
% 153.29/22.83  | | | | | | | End of split
% 153.29/22.83  | | | | | | | 
% 153.29/22.83  | | | | | | Case 2:
% 153.29/22.83  | | | | | | | 
% 153.29/22.83  | | | | | | |   (109)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 &
% 153.29/22.83  | | | | | | |            op(e3, e0) = e2)
% 153.29/22.83  | | | | | | | 
% 153.29/22.83  | | | | | | | REF_CLOSE: (10), (23), (52), (60), (77), (109) are inconsistent by
% 153.29/22.83  | | | | | | |            sub-proof #502.
% 153.29/22.83  | | | | | | | 
% 153.29/22.83  | | | | | | End of split
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | Case 2:
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | |   (110)  all_56_3 = e3 & op(e2, e2) = e3
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | | ALPHA: (110) implies:
% 153.29/22.83  | | | | | |   (111)  op(e2, e2) = e3
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | | REF_CLOSE: (8), (12), (23), (111) are inconsistent by sub-proof
% 153.29/22.83  | | | | | |            #1136.
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | End of split
% 153.29/22.83  | | | | | 
% 153.29/22.83  | | | | Case 2:
% 153.29/22.83  | | | | | 
% 153.29/22.83  | | | | |   (112)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2,
% 153.29/22.83  | | | | |              e0) = e3)
% 153.29/22.83  | | | | | 
% 153.29/22.83  | | | | | BETA: splitting (112) gives:
% 153.29/22.83  | | | | | 
% 153.29/22.83  | | | | | Case 1:
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | |   (113)  all_56_5 = e3 & op(e2, e1) = e3
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | | ALPHA: (113) implies:
% 153.29/22.83  | | | | | |   (114)  op(e2, e1) = e3
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | | REF_CLOSE: (12), (23), (51), (52), (114) are inconsistent by
% 153.29/22.83  | | | | | |            sub-proof #844.
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | Case 2:
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | |   (115)  all_56_10 = e3 & op(e2, e0) = e3
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | | ALPHA: (115) implies:
% 153.29/22.83  | | | | | |   (116)  all_56_10 = e3
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | | REF_CLOSE: (3), (10), (14), (21), (23), (24), (30), (33), (36),
% 153.29/22.83  | | | | | |            (42), (49), (56), (60), (116) are inconsistent by
% 153.29/22.83  | | | | | |            sub-proof #747.
% 153.29/22.83  | | | | | | 
% 153.29/22.83  | | | | | End of split
% 153.29/22.83  | | | | | 
% 153.29/22.83  | | | | End of split
% 153.29/22.83  | | | | 
% 153.29/22.83  | | | End of split
% 153.29/22.83  | | | 
% 153.29/22.83  | | End of split
% 153.29/22.83  | | 
% 153.29/22.83  | Case 2:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (117)   ~ (all_54_2 = e3)
% 153.29/22.83  | | 
% 153.29/22.83  | | REDUCE: (7), (117) imply:
% 153.29/22.83  | |   (118)   ~ (all_52_8 = e3)
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (2), (4), (8), (21), (23), (25), (29), (36), (38), (49), (50),
% 153.29/22.83  | |            (52), (57), (59), (60), (69), (118) are inconsistent by sub-proof
% 153.29/22.83  | |            #605.
% 153.29/22.83  | | 
% 153.29/22.83  | End of split
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #502 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)  all_56_9 = e1
% 153.29/22.83    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.83    (3)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.29/22.83    (4)  op(e3, e1) = e3
% 153.29/22.83    (5)   ~ (e3 = e2)
% 153.29/22.83    (6)   ~ (e2 = e1)
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | BETA: splitting (3) gives:
% 153.29/22.83  | 
% 153.29/22.83  | Case 1:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (7)  all_56_4 = e2 & op(e3, e1) = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | ALPHA: (7) implies:
% 153.29/22.83  | |   (8)  op(e3, e1) = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #504.
% 153.29/22.83  | | 
% 153.29/22.83  | Case 2:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (9)  all_56_9 = e2 & op(e3, e0) = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #503.
% 153.29/22.83  | | 
% 153.29/22.83  | End of split
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #503 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)  all_56_9 = e2 & op(e3, e0) = e2
% 153.29/22.83    (2)  all_56_9 = e1
% 153.29/22.83    (3)   ~ (e2 = e1)
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | ALPHA: (1) implies:
% 153.29/22.83  |   (4)  all_56_9 = e2
% 153.29/22.83  | 
% 153.29/22.83  | COMBINE_EQS: (2), (4) imply:
% 153.29/22.83  |   (5)  e2 = e1
% 153.29/22.83  | 
% 153.29/22.83  | REDUCE: (3), (5) imply:
% 153.29/22.83  |   (6)  $false
% 153.29/22.83  | 
% 153.29/22.83  | CLOSE: (6) is inconsistent.
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #504 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.83    (2)  op(e3, e1) = e3
% 153.29/22.83    (3)  op(e3, e1) = e2
% 153.29/22.83    (4)   ~ (e3 = e2)
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | GROUND_INST: instantiating (1) with e2, e3, e1, e3, simplifying with (2), (3)
% 153.29/22.83  |              gives:
% 153.29/22.83  |   (5)  e3 = e2
% 153.29/22.83  | 
% 153.29/22.83  | REDUCE: (4), (5) imply:
% 153.29/22.83  |   (6)  $false
% 153.29/22.83  | 
% 153.29/22.83  | CLOSE: (6) is inconsistent.
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #505 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)  all_56_1 = e1
% 153.29/22.83    (2)  op(e2, e2) = e1
% 153.29/22.83    (3)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.29/22.83         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.29/22.83    (4)   ~ (e2 = e0)
% 153.29/22.83    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.83    (6)   ~ (e3 = e0)
% 153.29/22.83    (7)   ~ (e1 = e0)
% 153.29/22.83    (8)  all_56_13 = e3
% 153.29/22.83    (9)   ~ (e3 = e2)
% 153.29/22.83    (10)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.29/22.83          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.29/22.83    (11)   ~ (e2 = e1)
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | BETA: splitting (10) gives:
% 153.29/22.83  | 
% 153.29/22.83  | Case 1:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 153.29/22.83  | |           e0)
% 153.29/22.83  | | 
% 153.29/22.83  | | BETA: splitting (12) gives:
% 153.29/22.83  | | 
% 153.29/22.83  | | Case 1:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (13)  all_56_1 = e0 & op(e3, e2) = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (1), (7), (13) are inconsistent by sub-proof #1072.
% 153.29/22.83  | | | 
% 153.29/22.83  | | Case 2:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (14)  all_56_3 = e0 & op(e2, e2) = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | ALPHA: (14) implies:
% 153.29/22.83  | | |   (15)  op(e2, e2) = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (2), (5), (7), (15) are inconsistent by sub-proof #853.
% 153.29/22.83  | | | 
% 153.29/22.83  | | End of split
% 153.29/22.83  | | 
% 153.29/22.83  | Case 2:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (16)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 153.29/22.83  | |           e0)
% 153.29/22.83  | | 
% 153.29/22.83  | | BETA: splitting (16) gives:
% 153.29/22.83  | | 
% 153.29/22.83  | | Case 1:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (17)  all_56_7 = e0 & op(e1, e2) = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | ALPHA: (17) implies:
% 153.29/22.83  | | |   (18)  all_56_7 = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (11), (18) are inconsistent
% 153.29/22.83  | | |            by sub-proof #506.
% 153.29/22.83  | | | 
% 153.29/22.83  | | Case 2:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (19)  all_56_13 = e0 & op(e0, e2) = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (6), (8), (19) are inconsistent by sub-proof #1102.
% 153.29/22.83  | | | 
% 153.29/22.83  | | End of split
% 153.29/22.83  | | 
% 153.29/22.83  | End of split
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #506 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)  all_56_1 = e1
% 153.29/22.83    (2)  op(e2, e2) = e1
% 153.29/22.83    (3)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.29/22.83         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.29/22.83    (4)   ~ (e2 = e0)
% 153.29/22.83    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.83    (6)  all_56_13 = e3
% 153.29/22.83    (7)   ~ (e3 = e2)
% 153.29/22.83    (8)  all_56_7 = e0
% 153.29/22.83    (9)   ~ (e2 = e1)
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | BETA: splitting (3) gives:
% 153.29/22.83  | 
% 153.29/22.83  | Case 1:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (10)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 153.29/22.83  | |           e2)
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (1), (2), (5), (9), (10) are inconsistent by sub-proof #507.
% 153.29/22.83  | | 
% 153.29/22.83  | Case 2:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (11)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 153.29/22.83  | |           e2)
% 153.29/22.83  | | 
% 153.29/22.83  | | BETA: splitting (11) gives:
% 153.29/22.83  | | 
% 153.29/22.83  | | Case 1:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (12)  all_56_7 = e2 & op(e1, e2) = e2
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (4), (8), (12) are inconsistent by sub-proof #740.
% 153.29/22.83  | | | 
% 153.29/22.83  | | Case 2:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (13)  all_56_13 = e2 & op(e0, e2) = e2
% 153.29/22.83  | | | 
% 153.29/22.83  | | | ALPHA: (13) implies:
% 153.29/22.83  | | |   (14)  all_56_13 = e2
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (6), (7), (14) are inconsistent by sub-proof #1105.
% 153.29/22.83  | | | 
% 153.29/22.83  | | End of split
% 153.29/22.83  | | 
% 153.29/22.83  | End of split
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #507 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)  all_56_1 = e1
% 153.29/22.83    (2)  op(e2, e2) = e1
% 153.29/22.83    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.83    (4)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 153.29/22.83    (5)   ~ (e2 = e1)
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | BETA: splitting (4) gives:
% 153.29/22.83  | 
% 153.29/22.83  | Case 1:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (6)  all_56_1 = e2 & op(e3, e2) = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | ALPHA: (6) implies:
% 153.29/22.83  | |   (7)  all_56_1 = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #595.
% 153.29/22.83  | | 
% 153.29/22.83  | Case 2:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (8)  all_56_3 = e2 & op(e2, e2) = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | ALPHA: (8) implies:
% 153.29/22.83  | |   (9)  op(e2, e2) = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1158.
% 153.29/22.83  | | 
% 153.29/22.83  | End of split
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #508 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)   ~ (all_52_7 = all_52_11)
% 153.29/22.83    (2)   ~ (e3 = e1)
% 153.29/22.83    (3)  op(e2, e2) = e1
% 153.29/22.83    (4)  op(e3, e2) = all_52_4
% 153.29/22.83    (5)  op(e0, e2) = all_52_7
% 153.29/22.83    (6)  all_54_14 = all_52_11
% 153.29/22.83    (7)   ~ (e2 = e0)
% 153.29/22.83    (8)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.29/22.83         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.29/22.83    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.83    (10)  all_56_7 = e3
% 153.29/22.83    (11)  all_56_10 = e0
% 153.29/22.83    (12)   ~ (all_52_11 = e3)
% 153.29/22.83    (13)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.29/22.83    (14)   ~ (e3 = e0)
% 153.29/22.83    (15)  op(e2, e1) = e2
% 153.29/22.83    (16)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.29/22.83          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.29/22.83    (17)   ~ (e1 = e0)
% 153.29/22.83    (18)   ~ (e3 = e2)
% 153.29/22.83    (19)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.29/22.83          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.29/22.83    (20)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.29/22.83          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.29/22.83    (21)   ~ (e2 = e1)
% 153.29/22.83    (22)  all_56_2 = e3
% 153.29/22.83    (23)   ~ (all_52_11 = e1)
% 153.29/22.83    (24)   ~ (all_52_4 = e0)
% 153.29/22.83    (25)   ~ (all_52_11 = e2)
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | BETA: splitting (20) gives:
% 153.29/22.83  | 
% 153.29/22.83  | Case 1:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (26)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 153.29/22.83  | |           e0)
% 153.29/22.83  | | 
% 153.29/22.83  | | BETA: splitting (26) gives:
% 153.29/22.83  | | 
% 153.29/22.83  | | Case 1:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (27)  all_56_1 = e0 & op(e3, e2) = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (4), (9), (24), (27) are inconsistent by sub-proof #1013.
% 153.29/22.83  | | | 
% 153.29/22.83  | | Case 2:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (28)  all_56_3 = e0 & op(e2, e2) = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | ALPHA: (28) implies:
% 153.29/22.83  | | |   (29)  op(e2, e2) = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (2), (7), (8), (9), (11), (17), (18), (19), (21), (22), (29)
% 153.29/22.83  | | |            are inconsistent by sub-proof #554.
% 153.29/22.83  | | | 
% 153.29/22.83  | | End of split
% 153.29/22.83  | | 
% 153.29/22.83  | Case 2:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (30)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 153.29/22.83  | |           e0)
% 153.29/22.83  | | 
% 153.29/22.83  | | BETA: splitting (30) gives:
% 153.29/22.83  | | 
% 153.29/22.83  | | Case 1:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (31)  all_56_7 = e0 & op(e1, e2) = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | ALPHA: (31) implies:
% 153.29/22.83  | | |   (32)  all_56_7 = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | COMBINE_EQS: (10), (32) imply:
% 153.29/22.83  | | |   (33)  e3 = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | COMBINE_EQS: (22), (33) imply:
% 153.29/22.83  | | |   (34)  all_56_2 = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (2), (3), (9), (11), (14), (15), (16), (18), (34) are
% 153.29/22.83  | | |            inconsistent by sub-proof #1133.
% 153.29/22.83  | | | 
% 153.29/22.83  | | Case 2:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (35)  all_56_13 = e0 & op(e0, e2) = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | ALPHA: (35) implies:
% 153.29/22.83  | | |   (36)  op(e0, e2) = e0
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (1), (5), (6), (9), (12), (13), (23), (25), (36) are
% 153.29/22.83  | | |            inconsistent by sub-proof #751.
% 153.29/22.83  | | | 
% 153.29/22.83  | | End of split
% 153.29/22.83  | | 
% 153.29/22.83  | End of split
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #509 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)  all_56_5 = e2
% 153.29/22.83    (2)  all_56_5 = e0
% 153.29/22.83    (3)   ~ (e2 = e0)
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | COMBINE_EQS: (1), (2) imply:
% 153.29/22.83  |   (4)  e2 = e0
% 153.29/22.83  | 
% 153.29/22.83  | SIMP: (4) implies:
% 153.29/22.83  |   (5)  e2 = e0
% 153.29/22.83  | 
% 153.29/22.83  | REDUCE: (3), (5) imply:
% 153.29/22.83  |   (6)  $false
% 153.29/22.83  | 
% 153.29/22.83  | CLOSE: (6) is inconsistent.
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #510 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)   ~ (all_52_13 = e1)
% 153.29/22.83    (2)   ~ (e3 = e1)
% 153.29/22.83    (3)  op(e3, e0) = e3
% 153.29/22.83    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.83    (5)   ~ (all_52_14 = e1)
% 153.29/22.83    (6)  op(e1, e0) = all_52_14
% 153.29/22.83    (7)  op(e3, e0) = all_52_12
% 153.29/22.83    (8)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.29/22.83         (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.29/22.83    (9)  op(e2, e0) = all_52_13
% 153.29/22.83    (10)   ~ (e1 = e0)
% 153.29/22.83    (11)  op(e0, e0) = e0
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | BETA: splitting (8) gives:
% 153.29/22.83  | 
% 153.29/22.83  | Case 1:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (12)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 153.29/22.83  | |           e1)
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (12) are inconsistent by sub-proof
% 153.29/22.83  | |            #511.
% 153.29/22.83  | | 
% 153.29/22.83  | Case 2:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (13)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 153.29/22.83  | |           e1)
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (4), (5), (6), (10), (11), (13) are inconsistent by sub-proof
% 153.29/22.83  | |            #960.
% 153.29/22.83  | | 
% 153.29/22.83  | End of split
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #511 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)   ~ (all_52_13 = e1)
% 153.29/22.83    (2)   ~ (e3 = e1)
% 153.29/22.83    (3)  op(e3, e0) = e3
% 153.29/22.83    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.83    (5)  op(e3, e0) = all_52_12
% 153.29/22.83    (6)  op(e2, e0) = all_52_13
% 153.29/22.83    (7)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | BETA: splitting (7) gives:
% 153.29/22.83  | 
% 153.29/22.83  | Case 1:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (8)  all_56_9 = e1 & op(e3, e0) = e1
% 153.29/22.83  | | 
% 153.29/22.83  | | ALPHA: (8) implies:
% 153.29/22.83  | |   (9)  op(e3, e0) = e1
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (2), (3), (4), (5), (9) are inconsistent by sub-proof #512.
% 153.29/22.83  | | 
% 153.29/22.83  | Case 2:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (10)  all_56_10 = e1 & op(e2, e0) = e1
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #810.
% 153.29/22.83  | | 
% 153.29/22.83  | End of split
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #512 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)  op(e3, e0) = e1
% 153.29/22.83    (2)   ~ (e3 = e1)
% 153.29/22.83    (3)  op(e3, e0) = e3
% 153.29/22.83    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.83    (5)  op(e3, e0) = all_52_12
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | GROUND_INST: instantiating (4) with all_52_12, e1, e0, e3, simplifying with
% 153.29/22.83  |              (1), (5) gives:
% 153.29/22.83  |   (6)  all_52_12 = e1
% 153.29/22.83  | 
% 153.29/22.83  | GROUND_INST: instantiating (4) with all_52_12, e3, e0, e3, simplifying with
% 153.29/22.83  |              (3), (5) gives:
% 153.29/22.83  |   (7)  all_52_12 = e3
% 153.29/22.83  | 
% 153.29/22.83  | COMBINE_EQS: (6), (7) imply:
% 153.29/22.83  |   (8)  e3 = e1
% 153.29/22.83  | 
% 153.29/22.83  | SIMP: (8) implies:
% 153.29/22.83  |   (9)  e3 = e1
% 153.29/22.83  | 
% 153.29/22.83  | REDUCE: (2), (9) imply:
% 153.29/22.83  |   (10)  $false
% 153.29/22.83  | 
% 153.29/22.83  | CLOSE: (10) is inconsistent.
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #513 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)  op(e2, e2) = e1
% 153.29/22.83    (2)   ~ (e2 = e0)
% 153.29/22.83    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.83    (4)  ( ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 & op(e2, e1) = all_20_1
% 153.29/22.83           & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e2, e1) =
% 153.29/22.83           all_20_1 & $i(all_20_1))
% 153.29/22.83    (5)  op(e2, e1) = e0
% 153.29/22.83    (6)  ( ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0 & op(e2, e1) = all_38_1
% 153.29/22.83           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e2, e1) =
% 153.29/22.83           all_38_1 & $i(all_38_1))
% 153.29/22.83    (7)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.29/22.83           all_57_12 & $i(all_57_12))
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | BETA: splitting (7) gives:
% 153.29/22.83  | 
% 153.29/22.83  | Case 1:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (8)  all_57_7 = e2 & op(e2, e1) = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | ALPHA: (8) implies:
% 153.29/22.83  | |   (9)  op(e2, e1) = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | BETA: splitting (4) gives:
% 153.29/22.83  | | 
% 153.29/22.83  | | Case 1:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (10)   ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 153.29/22.83  | | |         all_20_1 & $i(all_20_0) & $i(all_20_1)
% 153.29/22.83  | | | 
% 153.29/22.83  | | | ALPHA: (10) implies:
% 153.29/22.83  | | |   (11)  op(e2, e1) = all_20_1
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (2), (3), (5), (6), (9), (11) are inconsistent by sub-proof
% 153.29/22.83  | | |            #514.
% 153.29/22.83  | | | 
% 153.29/22.83  | | Case 2:
% 153.29/22.83  | | | 
% 153.29/22.83  | | |   (12)   ~ (all_20_1 = e3) & op(e2, e1) = all_20_1 & $i(all_20_1)
% 153.29/22.83  | | | 
% 153.29/22.83  | | | ALPHA: (12) implies:
% 153.29/22.83  | | |   (13)  op(e2, e1) = all_20_1
% 153.29/22.83  | | | 
% 153.29/22.83  | | | REF_CLOSE: (2), (3), (5), (6), (9), (13) are inconsistent by sub-proof
% 153.29/22.83  | | |            #514.
% 153.29/22.83  | | | 
% 153.29/22.83  | | End of split
% 153.29/22.83  | | 
% 153.29/22.83  | Case 2:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (14)   ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12)
% 153.29/22.83  | | 
% 153.29/22.83  | | ALPHA: (14) implies:
% 153.29/22.83  | |   (15)   ~ (all_57_12 = e1)
% 153.29/22.83  | |   (16)  op(e2, e2) = all_57_12
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (1), (3), (15), (16) are inconsistent by sub-proof #1014.
% 153.29/22.83  | | 
% 153.29/22.83  | End of split
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #514 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)   ~ (e2 = e0)
% 153.29/22.83    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.83    (3)  op(e2, e1) = e0
% 153.29/22.83    (4)  op(e2, e1) = e2
% 153.29/22.83    (5)  ( ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0 & op(e2, e1) = all_38_1
% 153.29/22.83           & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e2, e1) =
% 153.29/22.83           all_38_1 & $i(all_38_1))
% 153.29/22.83    (6)  op(e2, e1) = all_20_1
% 153.29/22.83  
% 153.29/22.83  Begin of proof
% 153.29/22.83  | 
% 153.29/22.83  | BETA: splitting (5) gives:
% 153.29/22.83  | 
% 153.29/22.83  | Case 1:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (7)   ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0 & op(e2, e1) =
% 153.29/22.83  | |        all_38_1 & $i(all_38_0) & $i(all_38_1)
% 153.29/22.83  | | 
% 153.29/22.83  | | ALPHA: (7) implies:
% 153.29/22.83  | |   (8)  op(e2, e1) = all_38_1
% 153.29/22.83  | | 
% 153.29/22.83  | | GROUND_INST: instantiating (2) with e0, all_20_1, e1, e2, simplifying with
% 153.29/22.83  | |              (3), (6) gives:
% 153.29/22.83  | |   (9)  all_20_1 = e0
% 153.29/22.83  | | 
% 153.29/22.83  | | GROUND_INST: instantiating (2) with all_20_1, all_38_1, e1, e2, simplifying
% 153.29/22.83  | |              with (6), (8) gives:
% 153.29/22.83  | |   (10)  all_38_1 = all_20_1
% 153.29/22.83  | | 
% 153.29/22.83  | | GROUND_INST: instantiating (2) with e2, all_38_1, e1, e2, simplifying with
% 153.29/22.83  | |              (4), (8) gives:
% 153.29/22.83  | |   (11)  all_38_1 = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | COMBINE_EQS: (10), (11) imply:
% 153.29/22.83  | |   (12)  all_20_1 = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | SIMP: (12) implies:
% 153.29/22.83  | |   (13)  all_20_1 = e2
% 153.29/22.83  | | 
% 153.29/22.83  | | COMBINE_EQS: (9), (13) imply:
% 153.29/22.83  | |   (14)  e2 = e0
% 153.29/22.83  | | 
% 153.29/22.83  | | REDUCE: (1), (14) imply:
% 153.29/22.83  | |   (15)  $false
% 153.29/22.83  | | 
% 153.29/22.83  | | CLOSE: (15) is inconsistent.
% 153.29/22.83  | | 
% 153.29/22.83  | Case 2:
% 153.29/22.83  | | 
% 153.29/22.83  | |   (16)   ~ (all_38_1 = e0) & op(e2, e1) = all_38_1 & $i(all_38_1)
% 153.29/22.83  | | 
% 153.29/22.83  | | ALPHA: (16) implies:
% 153.29/22.83  | |   (17)   ~ (all_38_1 = e0)
% 153.29/22.83  | |   (18)  op(e2, e1) = all_38_1
% 153.29/22.83  | | 
% 153.29/22.83  | | REF_CLOSE: (2), (3), (17), (18) are inconsistent by sub-proof #801.
% 153.29/22.83  | | 
% 153.29/22.83  | End of split
% 153.29/22.83  | 
% 153.29/22.83  End of proof
% 153.29/22.83  
% 153.29/22.83  Sub-proof #515 shows that the following formulas are inconsistent:
% 153.29/22.83  ----------------------------------------------------------------
% 153.29/22.83    (1)  op(e3, e3) = e0
% 153.29/22.83    (2)  op(e2, e2) = e1
% 153.29/22.83    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.83           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.84    (4)   ~ (e3 = e0)
% 153.29/22.84    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.29/22.84             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.29/22.84           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.29/22.84               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.29/22.84             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.29/22.84         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.29/22.84             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.29/22.84           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.29/22.84               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.29/22.84             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 153.29/22.84    (6)   ~ (e2 = e1)
% 153.29/22.84  
% 153.29/22.84  Begin of proof
% 153.29/22.84  | 
% 153.29/22.84  | BETA: splitting (5) gives:
% 153.29/22.84  | 
% 153.29/22.84  | Case 1:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2)
% 153.29/22.84  | |          | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.29/22.84  | |        ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 153.29/22.84  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 153.29/22.84  | |              e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 153.29/22.84  | |            $i(all_57_15)))
% 153.29/22.84  | | 
% 153.29/22.84  | | ALPHA: (7) implies:
% 153.29/22.84  | |   (8)  op(e3, e3) = e3
% 153.29/22.84  | | 
% 153.29/22.84  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1141.
% 153.29/22.84  | | 
% 153.29/22.84  | Case 2:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3)
% 153.29/22.84  | |          | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.29/22.84  | |        ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.29/22.84  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.29/22.84  | |              e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.29/22.84  | |            $i(all_57_15)))
% 153.29/22.84  | | 
% 153.29/22.84  | | ALPHA: (9) implies:
% 153.29/22.84  | |   (10)  op(e2, e2) = e2
% 153.29/22.84  | | 
% 153.29/22.84  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #1158.
% 153.29/22.84  | | 
% 153.29/22.84  | End of split
% 153.29/22.84  | 
% 153.29/22.84  End of proof
% 153.29/22.84  
% 153.29/22.84  Sub-proof #516 shows that the following formulas are inconsistent:
% 153.29/22.84  ----------------------------------------------------------------
% 153.29/22.84    (1)   ~ (all_52_1 = e0)
% 153.29/22.84    (2)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 153.29/22.84    (3)  op(e2, e2) = e1
% 153.29/22.84    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.84    (5)   ~ (e1 = e0)
% 153.29/22.84    (6)  op(e2, e3) = all_52_1
% 153.29/22.84  
% 153.29/22.84  Begin of proof
% 153.29/22.84  | 
% 153.29/22.84  | BETA: splitting (2) gives:
% 153.29/22.84  | 
% 153.29/22.84  | Case 1:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (7)  all_56_2 = e0 & op(e2, e3) = e0
% 153.29/22.84  | | 
% 153.29/22.84  | | REF_CLOSE: (1), (4), (6), (7) are inconsistent by sub-proof #840.
% 153.29/22.84  | | 
% 153.29/22.84  | Case 2:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (8)  all_56_3 = e0 & op(e2, e2) = e0
% 153.29/22.84  | | 
% 153.29/22.84  | | ALPHA: (8) implies:
% 153.29/22.84  | |   (9)  op(e2, e2) = e0
% 153.29/22.84  | | 
% 153.29/22.84  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #853.
% 153.29/22.84  | | 
% 153.29/22.84  | End of split
% 153.29/22.84  | 
% 153.29/22.84  End of proof
% 153.29/22.84  
% 153.29/22.84  Sub-proof #517 shows that the following formulas are inconsistent:
% 153.29/22.84  ----------------------------------------------------------------
% 153.29/22.84    (1)  op(e3, e3) = e0
% 153.29/22.84    (2)   ~ (e3 = e1)
% 153.29/22.84    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.29/22.84         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.29/22.84    (4)  all_56_6 = e2
% 153.29/22.84    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.29/22.84         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.29/22.84    (6)   ~ (e2 = e0)
% 153.29/22.84    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.84    (8)   ~ (e3 = e0)
% 153.29/22.84    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.29/22.84         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.29/22.84    (10)   ~ (e1 = e0)
% 153.29/22.84    (11)   ~ (e3 = e2)
% 153.29/22.84    (12)  all_56_12 = e2
% 153.29/22.84    (13)   ~ (e2 = e1)
% 153.29/22.84  
% 153.29/22.84  Begin of proof
% 153.29/22.84  | 
% 153.29/22.84  | BETA: splitting (3) gives:
% 153.29/22.84  | 
% 153.29/22.84  | Case 1:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (14)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 153.29/22.84  | |           e1)
% 153.29/22.84  | | 
% 153.29/22.84  | | BETA: splitting (14) gives:
% 153.29/22.84  | | 
% 153.29/22.84  | | Case 1:
% 153.29/22.84  | | | 
% 153.29/22.84  | | |   (15)  all_56_0 = e1 & op(e3, e3) = e1
% 153.29/22.84  | | | 
% 153.29/22.84  | | | ALPHA: (15) implies:
% 153.29/22.84  | | |   (16)  op(e3, e3) = e1
% 153.29/22.84  | | | 
% 153.29/22.84  | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (16) are
% 153.29/22.84  | | |            inconsistent by sub-proof #867.
% 153.29/22.84  | | | 
% 153.29/22.84  | | Case 2:
% 153.29/22.84  | | | 
% 153.29/22.84  | | |   (17)  all_56_2 = e1 & op(e2, e3) = e1
% 153.29/22.84  | | | 
% 153.29/22.84  | | | ALPHA: (17) implies:
% 153.29/22.84  | | |   (18)  all_56_2 = e1
% 153.29/22.84  | | | 
% 153.29/22.84  | | | BETA: splitting (5) gives:
% 153.29/22.84  | | | 
% 153.29/22.84  | | | Case 1:
% 153.29/22.84  | | | | 
% 153.29/22.84  | | | |   (19)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3)
% 153.29/22.84  | | | |           = e3)
% 153.29/22.84  | | | | 
% 153.29/22.84  | | | | REF_CLOSE: (1), (2), (7), (8), (18), (19) are inconsistent by sub-proof
% 153.29/22.84  | | | |            #620.
% 153.29/22.84  | | | | 
% 153.29/22.84  | | | Case 2:
% 153.29/22.84  | | | | 
% 153.29/22.84  | | | |   (20)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3)
% 153.29/22.84  | | | |           = e3)
% 153.29/22.84  | | | | 
% 153.29/22.84  | | | | REF_CLOSE: (4), (11), (12), (20) are inconsistent by sub-proof #868.
% 153.29/22.84  | | | | 
% 153.29/22.84  | | | End of split
% 153.29/22.84  | | | 
% 153.29/22.84  | | End of split
% 153.29/22.84  | | 
% 153.29/22.84  | Case 2:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (21)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 153.29/22.84  | |           e1)
% 153.29/22.84  | | 
% 153.29/22.84  | | BETA: splitting (21) gives:
% 153.29/22.84  | | 
% 153.29/22.84  | | Case 1:
% 153.29/22.84  | | | 
% 153.29/22.84  | | |   (22)  all_56_6 = e1 & op(e1, e3) = e1
% 153.29/22.84  | | | 
% 153.29/22.84  | | | REF_CLOSE: (4), (13), (22) are inconsistent by sub-proof #1058.
% 153.29/22.84  | | | 
% 153.29/22.84  | | Case 2:
% 153.29/22.84  | | | 
% 153.29/22.84  | | |   (23)  all_56_12 = e1 & op(e0, e3) = e1
% 153.29/22.84  | | | 
% 153.29/22.84  | | | REF_CLOSE: (12), (13), (23) are inconsistent by sub-proof #789.
% 153.29/22.84  | | | 
% 153.29/22.84  | | End of split
% 153.29/22.84  | | 
% 153.29/22.84  | End of split
% 153.29/22.84  | 
% 153.29/22.84  End of proof
% 153.29/22.84  
% 153.29/22.84  Sub-proof #518 shows that the following formulas are inconsistent:
% 153.29/22.84  ----------------------------------------------------------------
% 153.29/22.84    (1)  op(e3, e3) = e0
% 153.29/22.84    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.84    (3)  op(e0, e0) = e2
% 153.29/22.84    (4)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 153.29/22.84             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.29/22.84           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 153.29/22.84           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 153.29/22.84           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 153.29/22.84           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.29/22.84           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 153.29/22.84           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.29/22.84           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.29/22.84    (5)  op(e1, e1) = e1
% 153.29/22.84    (6)   ~ (e1 = e0)
% 153.29/22.84    (7)   ~ (e2 = e1)
% 153.29/22.84  
% 153.29/22.84  Begin of proof
% 153.29/22.84  | 
% 153.29/22.84  | BETA: splitting (4) gives:
% 153.29/22.84  | 
% 153.29/22.84  | Case 1:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (8)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 153.29/22.84  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.29/22.84  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 153.29/22.84  | | 
% 153.29/22.84  | | ALPHA: (8) implies:
% 153.29/22.84  | |   (9)  op(e0, e0) = e1
% 153.29/22.84  | | 
% 153.29/22.84  | | REF_CLOSE: (2), (3), (7), (9) are inconsistent by sub-proof #978.
% 153.29/22.84  | | 
% 153.29/22.84  | Case 2:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (10)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.29/22.84  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.29/22.84  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.29/22.84  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 153.29/22.84  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 153.29/22.84  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.29/22.84  | |           $i(all_57_13))
% 153.29/22.84  | | 
% 153.29/22.84  | | REF_CLOSE: (1), (2), (5), (6), (10) are inconsistent by sub-proof #519.
% 153.29/22.84  | | 
% 153.29/22.84  | End of split
% 153.29/22.84  | 
% 153.29/22.84  End of proof
% 153.29/22.84  
% 153.29/22.84  Sub-proof #519 shows that the following formulas are inconsistent:
% 153.29/22.84  ----------------------------------------------------------------
% 153.29/22.84    (1)  op(e3, e3) = e0
% 153.29/22.84    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.84    (3)  op(e1, e1) = e1
% 153.29/22.84    (4)   ~ (e1 = e0)
% 153.29/22.84    (5)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 153.29/22.84             e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.29/22.84           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 =
% 153.29/22.84           e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 153.29/22.84           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 153.29/22.84           = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.29/22.84  
% 153.29/22.84  Begin of proof
% 153.29/22.84  | 
% 153.29/22.84  | BETA: splitting (5) gives:
% 153.29/22.84  | 
% 153.29/22.84  | Case 1:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (6)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 153.29/22.84  | |          = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0
% 153.29/22.84  | |        & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)
% 153.29/22.84  | | 
% 153.29/22.84  | | ALPHA: (6) implies:
% 153.29/22.84  | |   (7)   ~ (all_57_10 = e0)
% 153.29/22.84  | |   (8)  op(e3, e3) = all_57_10
% 153.29/22.84  | | 
% 153.29/22.84  | | REF_CLOSE: (1), (2), (7), (8) are inconsistent by sub-proof #543.
% 153.29/22.84  | | 
% 153.29/22.84  | Case 2:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (9)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 153.29/22.84  | |          = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 153.29/22.84  | |        & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)
% 153.29/22.84  | | 
% 153.29/22.84  | | ALPHA: (9) implies:
% 153.29/22.84  | |   (10)  op(e1, e1) = e0
% 153.29/22.84  | | 
% 153.29/22.84  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #1038.
% 153.29/22.84  | | 
% 153.29/22.84  | End of split
% 153.29/22.84  | 
% 153.29/22.84  End of proof
% 153.29/22.84  
% 153.29/22.84  Sub-proof #520 shows that the following formulas are inconsistent:
% 153.29/22.84  ----------------------------------------------------------------
% 153.29/22.84    (1)  op(e1, e0) = e3
% 153.29/22.84    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.29/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.29/22.84    (3)  ( ~ (all_24_0 = e3) & op(all_24_1, e0) = all_24_0 & op(e0, e2) = all_24_1
% 153.29/22.84           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0, e2) =
% 153.29/22.84           all_24_1 & $i(all_24_1))
% 153.29/22.84    (4)  op(e0, e2) = e1
% 153.29/22.84    (5)  ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0 & op(e0, e2) = all_40_1
% 153.29/22.84           & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) & op(e0, e2) =
% 153.29/22.84           all_40_1 & $i(all_40_1))
% 153.29/22.84  
% 153.29/22.84  Begin of proof
% 153.29/22.84  | 
% 153.29/22.84  | BETA: splitting (5) gives:
% 153.29/22.84  | 
% 153.29/22.84  | Case 1:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (6)   ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0 & op(e0, e2) =
% 153.29/22.84  | |        all_40_1 & $i(all_40_0) & $i(all_40_1)
% 153.29/22.84  | | 
% 153.29/22.84  | | ALPHA: (6) implies:
% 153.29/22.84  | |   (7)  op(e0, e2) = all_40_1
% 153.29/22.84  | | 
% 153.29/22.84  | | REF_CLOSE: (1), (2), (3), (4), (7) are inconsistent by sub-proof #521.
% 153.29/22.84  | | 
% 153.29/22.84  | Case 2:
% 153.29/22.84  | | 
% 153.29/22.84  | |   (8)   ~ (all_40_1 = e3) & op(e0, e2) = all_40_1 & $i(all_40_1)
% 153.29/22.84  | | 
% 153.29/22.84  | | ALPHA: (8) implies:
% 153.32/22.84  | |   (9)  op(e0, e2) = all_40_1
% 153.32/22.84  | | 
% 153.32/22.84  | | REF_CLOSE: (1), (2), (3), (4), (9) are inconsistent by sub-proof #521.
% 153.32/22.84  | | 
% 153.32/22.84  | End of split
% 153.32/22.84  | 
% 153.32/22.84  End of proof
% 153.32/22.84  
% 153.32/22.84  Sub-proof #521 shows that the following formulas are inconsistent:
% 153.32/22.84  ----------------------------------------------------------------
% 153.32/22.84    (1)  op(e1, e0) = e3
% 153.32/22.84    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.84    (3)  op(e0, e2) = all_40_1
% 153.32/22.84    (4)  ( ~ (all_24_0 = e3) & op(all_24_1, e0) = all_24_0 & op(e0, e2) = all_24_1
% 153.32/22.84           & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e1) & op(e0, e2) =
% 153.32/22.84           all_24_1 & $i(all_24_1))
% 153.32/22.84    (5)  op(e0, e2) = e1
% 153.32/22.84  
% 153.32/22.84  Begin of proof
% 153.32/22.84  | 
% 153.32/22.84  | BETA: splitting (4) gives:
% 153.32/22.84  | 
% 153.32/22.84  | Case 1:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (6)   ~ (all_24_0 = e3) & op(all_24_1, e0) = all_24_0 & op(e0, e2) =
% 153.32/22.84  | |        all_24_1 & $i(all_24_0) & $i(all_24_1)
% 153.32/22.84  | | 
% 153.32/22.84  | | ALPHA: (6) implies:
% 153.32/22.84  | |   (7)   ~ (all_24_0 = e3)
% 153.32/22.84  | |   (8)  op(e0, e2) = all_24_1
% 153.32/22.84  | |   (9)  op(all_24_1, e0) = all_24_0
% 153.32/22.84  | | 
% 153.32/22.84  | | GROUND_INST: instantiating (2) with all_24_1, all_40_1, e2, e0, simplifying
% 153.32/22.84  | |              with (3), (8) gives:
% 153.32/22.84  | |   (10)  all_40_1 = all_24_1
% 153.32/22.84  | | 
% 153.32/22.84  | | GROUND_INST: instantiating (2) with e1, all_40_1, e2, e0, simplifying with
% 153.32/22.84  | |              (3), (5) gives:
% 153.32/22.84  | |   (11)  all_40_1 = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | GROUND_INST: instantiating (2) with e3, all_24_0, e0, e1, simplifying with
% 153.32/22.84  | |              (1) gives:
% 153.32/22.84  | |   (12)  all_24_0 = e3 |  ~ (op(e1, e0) = all_24_0)
% 153.32/22.84  | | 
% 153.32/22.84  | | COMBINE_EQS: (10), (11) imply:
% 153.32/22.84  | |   (13)  all_24_1 = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | REDUCE: (9), (13) imply:
% 153.32/22.84  | |   (14)  op(e1, e0) = all_24_0
% 153.32/22.84  | | 
% 153.32/22.84  | | BETA: splitting (12) gives:
% 153.32/22.84  | | 
% 153.32/22.84  | | Case 1:
% 153.32/22.84  | | | 
% 153.32/22.84  | | |   (15)   ~ (op(e1, e0) = all_24_0)
% 153.32/22.84  | | | 
% 153.32/22.84  | | | PRED_UNIFY: (14), (15) imply:
% 153.32/22.84  | | |   (16)  $false
% 153.32/22.84  | | | 
% 153.32/22.84  | | | CLOSE: (16) is inconsistent.
% 153.32/22.84  | | | 
% 153.32/22.84  | | Case 2:
% 153.32/22.84  | | | 
% 153.32/22.84  | | |   (17)  all_24_0 = e3
% 153.32/22.84  | | | 
% 153.32/22.84  | | | REDUCE: (7), (17) imply:
% 153.32/22.84  | | |   (18)  $false
% 153.32/22.84  | | | 
% 153.32/22.84  | | | CLOSE: (18) is inconsistent.
% 153.32/22.84  | | | 
% 153.32/22.84  | | End of split
% 153.32/22.84  | | 
% 153.32/22.84  | Case 2:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (19)   ~ (all_24_1 = e1) & op(e0, e2) = all_24_1 & $i(all_24_1)
% 153.32/22.84  | | 
% 153.32/22.84  | | ALPHA: (19) implies:
% 153.32/22.84  | |   (20)   ~ (all_24_1 = e1)
% 153.32/22.84  | |   (21)  op(e0, e2) = all_24_1
% 153.32/22.84  | | 
% 153.32/22.84  | | GROUND_INST: instantiating (2) with all_24_1, all_40_1, e2, e0, simplifying
% 153.32/22.84  | |              with (3), (21) gives:
% 153.32/22.84  | |   (22)  all_40_1 = all_24_1
% 153.32/22.84  | | 
% 153.32/22.84  | | GROUND_INST: instantiating (2) with e1, all_40_1, e2, e0, simplifying with
% 153.32/22.84  | |              (3), (5) gives:
% 153.32/22.84  | |   (23)  all_40_1 = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | COMBINE_EQS: (22), (23) imply:
% 153.32/22.84  | |   (24)  all_24_1 = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | REDUCE: (20), (24) imply:
% 153.32/22.84  | |   (25)  $false
% 153.32/22.84  | | 
% 153.32/22.84  | | CLOSE: (25) is inconsistent.
% 153.32/22.84  | | 
% 153.32/22.84  | End of split
% 153.32/22.84  | 
% 153.32/22.84  End of proof
% 153.32/22.84  
% 153.32/22.84  Sub-proof #522 shows that the following formulas are inconsistent:
% 153.32/22.84  ----------------------------------------------------------------
% 153.32/22.84    (1)   ~ (all_52_6 = e1)
% 153.32/22.84    (2)   ~ (e3 = e1)
% 153.32/22.84    (3)  all_56_6 = e2
% 153.32/22.84    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.84    (5)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.32/22.84         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.32/22.84    (6)   ~ (all_52_14 = e1)
% 153.32/22.84    (7)  op(e1, e0) = all_52_14
% 153.32/22.84    (8)  op(e1, e2) = all_52_6
% 153.32/22.84    (9)  op(e1, e1) = e3
% 153.32/22.84    (10)   ~ (e2 = e1)
% 153.32/22.84  
% 153.32/22.84  Begin of proof
% 153.32/22.84  | 
% 153.32/22.84  | BETA: splitting (5) gives:
% 153.32/22.84  | 
% 153.32/22.84  | Case 1:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (11)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 153.32/22.84  | |           e1)
% 153.32/22.84  | | 
% 153.32/22.84  | | REF_CLOSE: (1), (3), (4), (8), (10), (11) are inconsistent by sub-proof
% 153.32/22.84  | |            #524.
% 153.32/22.84  | | 
% 153.32/22.84  | Case 2:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (12)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 153.32/22.84  | |           e1)
% 153.32/22.84  | | 
% 153.32/22.84  | | REF_CLOSE: (2), (4), (6), (7), (9), (12) are inconsistent by sub-proof #523.
% 153.32/22.84  | | 
% 153.32/22.84  | End of split
% 153.32/22.84  | 
% 153.32/22.84  End of proof
% 153.32/22.84  
% 153.32/22.84  Sub-proof #523 shows that the following formulas are inconsistent:
% 153.32/22.84  ----------------------------------------------------------------
% 153.32/22.84    (1)   ~ (e3 = e1)
% 153.32/22.84    (2)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.32/22.84    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.84    (4)   ~ (all_52_14 = e1)
% 153.32/22.84    (5)  op(e1, e0) = all_52_14
% 153.32/22.84    (6)  op(e1, e1) = e3
% 153.32/22.84  
% 153.32/22.84  Begin of proof
% 153.32/22.84  | 
% 153.32/22.84  | BETA: splitting (2) gives:
% 153.32/22.84  | 
% 153.32/22.84  | Case 1:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (7)  all_56_8 = e1 & op(e1, e1) = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | ALPHA: (7) implies:
% 153.32/22.84  | |   (8)  op(e1, e1) = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #734.
% 153.32/22.84  | | 
% 153.32/22.84  | Case 2:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (9)  all_56_11 = e1 & op(e1, e0) = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | ALPHA: (9) implies:
% 153.32/22.84  | |   (10)  op(e1, e0) = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #961.
% 153.32/22.84  | | 
% 153.32/22.84  | End of split
% 153.32/22.84  | 
% 153.32/22.84  End of proof
% 153.32/22.84  
% 153.32/22.84  Sub-proof #524 shows that the following formulas are inconsistent:
% 153.32/22.84  ----------------------------------------------------------------
% 153.32/22.84    (1)   ~ (all_52_6 = e1)
% 153.32/22.84    (2)  all_56_6 = e2
% 153.32/22.84    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.84    (4)  op(e1, e2) = all_52_6
% 153.32/22.84    (5)   ~ (e2 = e1)
% 153.32/22.84    (6)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1)
% 153.32/22.84  
% 153.32/22.84  Begin of proof
% 153.32/22.84  | 
% 153.32/22.84  | BETA: splitting (6) gives:
% 153.32/22.84  | 
% 153.32/22.84  | Case 1:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (7)  all_56_6 = e1 & op(e1, e3) = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | ALPHA: (7) implies:
% 153.32/22.84  | |   (8)  all_56_6 = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #1172.
% 153.32/22.84  | | 
% 153.32/22.84  | Case 2:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (9)  all_56_7 = e1 & op(e1, e2) = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | ALPHA: (9) implies:
% 153.32/22.84  | |   (10)  op(e1, e2) = e1
% 153.32/22.84  | | 
% 153.32/22.84  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1042.
% 153.32/22.84  | | 
% 153.32/22.84  | End of split
% 153.32/22.84  | 
% 153.32/22.84  End of proof
% 153.32/22.84  
% 153.32/22.84  Sub-proof #525 shows that the following formulas are inconsistent:
% 153.32/22.84  ----------------------------------------------------------------
% 153.32/22.84    (1)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 153.32/22.84           all_57_15 & $i(all_57_15))
% 153.32/22.84    (2)   ~ (all_57_5 = e0)
% 153.32/22.84    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.84    (4)  op(e0, e0) = e2
% 153.32/22.84  
% 153.32/22.84  Begin of proof
% 153.32/22.84  | 
% 153.32/22.84  | BETA: splitting (1) gives:
% 153.32/22.84  | 
% 153.32/22.84  | Case 1:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (5)  all_57_5 = e0 & op(e0, e2) = e0
% 153.32/22.84  | | 
% 153.32/22.84  | | ALPHA: (5) implies:
% 153.32/22.84  | |   (6)  all_57_5 = e0
% 153.32/22.84  | | 
% 153.32/22.84  | | REDUCE: (2), (6) imply:
% 153.32/22.84  | |   (7)  $false
% 153.32/22.84  | | 
% 153.32/22.84  | | CLOSE: (7) is inconsistent.
% 153.32/22.84  | | 
% 153.32/22.84  | Case 2:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (8)   ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)
% 153.32/22.84  | | 
% 153.32/22.84  | | ALPHA: (8) implies:
% 153.32/22.84  | |   (9)   ~ (all_57_15 = e2)
% 153.32/22.84  | |   (10)  op(e0, e0) = all_57_15
% 153.32/22.84  | | 
% 153.32/22.84  | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #901.
% 153.32/22.84  | | 
% 153.32/22.84  | End of split
% 153.32/22.84  | 
% 153.32/22.84  End of proof
% 153.32/22.84  
% 153.32/22.84  Sub-proof #526 shows that the following formulas are inconsistent:
% 153.32/22.84  ----------------------------------------------------------------
% 153.32/22.84    (1)  op(e3, e3) = e0
% 153.32/22.84    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 153.32/22.84    (3)   ~ (e2 = e0)
% 153.32/22.84    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.84    (5)  op(e2, e3) = all_52_1
% 153.32/22.84    (6)   ~ (all_52_1 = e2)
% 153.32/22.84  
% 153.32/22.84  Begin of proof
% 153.32/22.84  | 
% 153.32/22.84  | BETA: splitting (2) gives:
% 153.32/22.84  | 
% 153.32/22.84  | Case 1:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 153.32/22.84  | | 
% 153.32/22.84  | | ALPHA: (7) implies:
% 153.32/22.84  | |   (8)  op(e3, e3) = e2
% 153.32/22.84  | | 
% 153.32/22.84  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1073.
% 153.32/22.84  | | 
% 153.32/22.84  | Case 2:
% 153.32/22.84  | | 
% 153.32/22.84  | |   (9)  all_56_2 = e2 & op(e2, e3) = e2
% 153.32/22.84  | | 
% 153.32/22.84  | | ALPHA: (9) implies:
% 153.32/22.84  | |   (10)  op(e2, e3) = e2
% 153.32/22.84  | | 
% 153.32/22.84  | | REF_CLOSE: (4), (5), (6), (10) are inconsistent by sub-proof #1181.
% 153.32/22.84  | | 
% 153.32/22.84  | End of split
% 153.32/22.84  | 
% 153.32/22.84  End of proof
% 153.32/22.84  
% 153.32/22.84  Sub-proof #527 shows that the following formulas are inconsistent:
% 153.32/22.84  ----------------------------------------------------------------
% 153.32/22.84    (1)  op(e0, e1) = all_52_11
% 153.32/22.84    (2)  op(e3, e3) = e0
% 153.32/22.84    (3)  op(e0, e2) = all_52_7
% 153.32/22.84    (4)   ~ (all_52_3 = all_52_7)
% 153.32/22.84    (5)   ~ (e2 = e0)
% 153.32/22.84    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.84           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.84    (7)  op(e1, e1) = e0
% 153.32/22.84    (8)  op(e0, e0) = e2
% 153.32/22.84    (9)   ~ (all_52_13 = e2)
% 153.32/22.84    (10)   ~ (all_52_11 = e0)
% 153.32/22.84    (11)  op(e2, e0) = all_52_13
% 153.32/22.84    (12)   ~ (all_52_9 = e2)
% 153.32/22.84    (13)  op(e0, e3) = all_52_3
% 153.32/22.84    (14)  op(e2, e2) = e2
% 153.32/22.84    (15)  op(e2, e1) = all_52_9
% 153.32/22.84    (16)   ~ (e3 = e2)
% 153.32/22.84    (17)   ~ (e2 = e1)
% 153.32/22.84    (18)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 153.32/22.84            all_57_15 & $i(all_57_15))
% 153.32/22.84    (19)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.32/22.84              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.32/22.84            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.32/22.84            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.32/22.84            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.32/22.84            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.32/22.84            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.32/22.84            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.32/22.84            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.32/22.84            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.32/22.84            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.32/22.84            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.32/22.84            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.32/22.84            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.32/22.84            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.32/22.84            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.32/22.84            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.32/22.84            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.32/22.84            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.32/22.84            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.32/22.84            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.32/22.84            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.32/22.84            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.32/22.84            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.32/22.84            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.32/22.84            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.32/22.84            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.32/22.84            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.32/22.84            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.32/22.84            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.32/22.84            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.32/22.84            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.32/22.85            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.32/22.85            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.32/22.85            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.32/22.85            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.32/22.85            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.32/22.85            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.32/22.85            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.32/22.85            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.32/22.85            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.32/22.85            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.32/22.85            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.32/22.85            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.32/22.85            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.32/22.85            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.32/22.85            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.32/22.85            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.32/22.85              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.32/22.85            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.32/22.85            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.32/22.85              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.32/22.85            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.32/22.85            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.32/22.85                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.32/22.85                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.32/22.85                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.32/22.85                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.32/22.85                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.32/22.85                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.32/22.85                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.32/22.85              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.32/22.85                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.32/22.85                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.32/22.85                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.32/22.85                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.32/22.85                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.32/22.85                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.32/22.85                $i(all_57_7))))
% 153.32/22.85    (20)  op(e2, e3) = all_52_1
% 153.32/22.85    (21)   ~ (all_52_1 = e2)
% 153.32/22.85  
% 153.32/22.85  Begin of proof
% 153.32/22.85  | 
% 153.32/22.85  | BETA: splitting (18) gives:
% 153.32/22.85  | 
% 153.32/22.85  | Case 1:
% 153.32/22.85  | | 
% 153.32/22.85  | |   (22)  all_57_5 = e0 & op(e0, e2) = e0
% 153.32/22.85  | | 
% 153.32/22.85  | | ALPHA: (22) implies:
% 153.32/22.85  | |   (23)  all_57_5 = e0
% 153.32/22.85  | |   (24)  op(e0, e2) = e0
% 153.32/22.85  | | 
% 153.32/22.85  | | BETA: splitting (19) gives:
% 153.32/22.85  | | 
% 153.32/22.85  | | Case 1:
% 153.32/22.85  | | | 
% 153.32/22.85  | | |   (25)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.32/22.85  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.32/22.85  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.32/22.85  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 153.32/22.85  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.32/22.85  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.32/22.85  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 153.32/22.85  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.32/22.85  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.32/22.85  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 153.32/22.85  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.32/22.85  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 153.32/22.85  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) | (all_57_3 =
% 153.32/22.85  | | |           e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 = e2) &
% 153.32/22.85  | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) = all_57_4
% 153.32/22.85  | | |           & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3 =
% 153.32/22.85  | | |           e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.32/22.85  | | |           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5
% 153.32/22.85  | | |           & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 =
% 153.32/22.85  | | |           e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 153.32/22.85  | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.32/22.85  | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.32/22.85  | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.32/22.85  | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.32/22.85  | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.32/22.85  | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7
% 153.32/22.85  | | |             = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 153.32/22.85  | | |             e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.32/22.85  | | |           $i(all_57_7) & $i(all_57_10))
% 153.32/22.85  | | | 
% 153.32/22.85  | | | BETA: splitting (25) gives:
% 153.32/22.85  | | | 
% 153.32/22.85  | | | Case 1:
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | |   (26)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.32/22.85  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.32/22.85  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.32/22.85  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.32/22.85  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.32/22.85  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.32/22.85  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.32/22.85  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.32/22.85  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.32/22.85  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.32/22.85  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.32/22.85  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.32/22.85  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.32/22.85  | | | |           $i(all_57_14))
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | | REF_CLOSE: (6), (8), (14), (16), (20), (21), (26) are inconsistent by
% 153.32/22.85  | | | |            sub-proof #1000.
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | Case 2:
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | |   (27)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.32/22.85  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.32/22.85  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.32/22.85  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.32/22.85  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 153.32/22.85  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.32/22.85  | | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 =
% 153.32/22.85  | | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) =
% 153.32/22.85  | | | |           e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.32/22.85  | | | |           all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 153.32/22.85  | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 153.32/22.85  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.32/22.85  | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.32/22.85  | | | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.32/22.85  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.32/22.85  | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.32/22.85  | | | |           $i(all_57_10))
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | | BETA: splitting (27) gives:
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | | Case 1:
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | |   (28)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.32/22.85  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.32/22.85  | | | | |           & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.32/22.85  | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.32/22.85  | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.32/22.85  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.32/22.85  | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | | BETA: splitting (28) gives:
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | | Case 1:
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | |   (29)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.32/22.85  | | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.32/22.85  | | | | | |         & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.32/22.85  | | | | | |         $i(all_57_10)
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | ALPHA: (29) implies:
% 153.32/22.85  | | | | | |   (30)  op(e1, e1) = e2
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | REF_CLOSE: (5), (6), (7), (30) are inconsistent by sub-proof #1006.
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | Case 2:
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | |   (31)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.32/22.85  | | | | | |         (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.32/22.85  | | | | | |         & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.32/22.85  | | | | | |         $i(all_57_10)
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | ALPHA: (31) implies:
% 153.32/22.85  | | | | | |   (32)   ~ (all_57_5 = e0)
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | REDUCE: (23), (32) imply:
% 153.32/22.85  | | | | | |   (33)  $false
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | CLOSE: (33) is inconsistent.
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | End of split
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | Case 2:
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | |   (34)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.32/22.85  | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.32/22.85  | | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.32/22.85  | | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.32/22.85  | | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.32/22.85  | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 153.32/22.85  | | | | |           = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 153.32/22.85  | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.32/22.85  | | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.32/22.85  | | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | | REF_CLOSE: (2), (5), (6), (14), (17), (23), (34) are inconsistent by
% 153.32/22.85  | | | | |            sub-proof #531.
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | End of split
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | End of split
% 153.32/22.85  | | | 
% 153.32/22.85  | | Case 2:
% 153.32/22.85  | | | 
% 153.32/22.85  | | |   (35)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.32/22.85  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.32/22.85  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.32/22.85  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 153.32/22.85  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.32/22.85  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.32/22.85  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 153.32/22.85  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 153.32/22.85  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 153.32/22.85  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 153.32/22.85  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 153.32/22.85  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.32/22.85  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 153.32/22.85  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.32/22.85  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.32/22.85  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.32/22.85  | | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9
% 153.32/22.85  | | |             = e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.32/22.85  | | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.32/22.85  | | |           $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1
% 153.32/22.85  | | |           &  ~ (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.32/22.85  | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.32/22.85  | | |           & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 153.32/22.85  | | |           e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.32/22.85  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.32/22.85  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.32/22.85  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.32/22.85  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.32/22.85  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.32/22.85  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.32/22.85  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.32/22.85  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.32/22.85  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.32/22.85  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.32/22.85  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 153.32/22.85  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.32/22.85  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.32/22.85  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.32/22.85  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 153.32/22.85  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.32/22.85  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.32/22.85  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.32/22.85  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.32/22.85  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.32/22.85  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.32/22.85  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 153.32/22.85  | | | 
% 153.32/22.85  | | | BETA: splitting (35) gives:
% 153.32/22.85  | | | 
% 153.32/22.85  | | | Case 1:
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | |   (36)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.32/22.85  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.32/22.85  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.32/22.85  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.32/22.85  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.32/22.85  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.32/22.85  | | | |           e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.32/22.85  | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.32/22.85  | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.32/22.85  | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.32/22.85  | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.32/22.85  | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.32/22.85  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.32/22.85  | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.32/22.85  | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.32/22.85  | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.32/22.85  | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | | BETA: splitting (36) gives:
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | | Case 1:
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | |   (37)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.32/22.85  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.32/22.85  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.32/22.85  | | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.32/22.85  | | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.32/22.85  | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 153.32/22.85  | | | | |           = e2 & $i(all_57_6) & $i(all_57_12))
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | | REF_CLOSE: (6), (8), (12), (15), (17), (37) are inconsistent by
% 153.32/22.85  | | | | |            sub-proof #977.
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | Case 2:
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | |   (38)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.32/22.85  | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 153.32/22.85  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.32/22.85  | | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 153.32/22.85  | | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 153.32/22.85  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 153.32/22.85  | | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 153.32/22.85  | | | | |           & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1)
% 153.32/22.85  | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 153.32/22.85  | | | | |           & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | | BETA: splitting (38) gives:
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | | Case 1:
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | |   (39)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.32/22.85  | | | | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2
% 153.32/22.85  | | | | | |         & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.32/22.85  | | | | | |         $i(all_57_12)
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | ALPHA: (39) implies:
% 153.32/22.85  | | | | | |   (40)  op(e0, e0) = e1
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | REF_CLOSE: (6), (8), (17), (40) are inconsistent by sub-proof #978.
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | Case 2:
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | |   (41)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.32/22.85  | | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 153.32/22.85  | | | | | |           e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.32/22.85  | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.32/22.85  | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1)
% 153.32/22.85  | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 153.32/22.85  | | | | | |           e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.32/22.85  | | | | | |           $i(all_57_13))
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | REF_CLOSE: (2), (6), (41) are inconsistent by sub-proof #542.
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | End of split
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | End of split
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | Case 2:
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | |   (42)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.32/22.85  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.32/22.85  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.32/22.85  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.32/22.85  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.32/22.85  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.32/22.85  | | | |           e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 153.32/22.85  | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 153.32/22.85  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.32/22.85  | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 153.32/22.85  | | | |         (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.32/22.85  | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.32/22.85  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.32/22.85  | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.32/22.85  | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.32/22.85  | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 153.32/22.85  | | | |               & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.32/22.85  | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 153.32/22.85  | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 153.32/22.85  | | | |               e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.32/22.85  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.32/22.85  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.32/22.85  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.32/22.85  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.32/22.85  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.32/22.85  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.32/22.85  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.32/22.85  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.32/22.85  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.32/22.85  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | | BETA: splitting (42) gives:
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | | Case 1:
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | |   (43)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.32/22.85  | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.32/22.85  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.32/22.85  | | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.32/22.85  | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.32/22.85  | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.32/22.85  | | | | |           = e1 & $i(all_57_9) & $i(all_57_14))
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | | REF_CLOSE: (6), (7), (9), (11), (43) are inconsistent by sub-proof
% 153.32/22.85  | | | | |            #530.
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | Case 2:
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | |   (44)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.32/22.85  | | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.32/22.85  | | | | |           & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.32/22.85  | | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 153.32/22.85  | | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.32/22.85  | | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.32/22.85  | | | | |           = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.32/22.85  | | | | |           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 153.32/22.85  | | | | |               &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3)
% 153.32/22.85  | | | | |               = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.32/22.85  | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.32/22.85  | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.32/22.85  | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.32/22.85  | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.32/22.85  | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.32/22.85  | | | | |               & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.32/22.85  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.32/22.85  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.32/22.85  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.32/22.85  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.32/22.85  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.32/22.85  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.32/22.85  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.32/22.85  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.32/22.85  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.32/22.85  | | | | |               $i(all_57_7))))
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | | BETA: splitting (44) gives:
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | | Case 1:
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | |   (45)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.32/22.85  | | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.32/22.85  | | | | | |         & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.32/22.85  | | | | | |         $i(all_57_13)
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | ALPHA: (45) implies:
% 153.32/22.85  | | | | | |   (46)  op(e2, e0) = e2
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | REF_CLOSE: (6), (9), (11), (46) are inconsistent by sub-proof #1156.
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | Case 2:
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | |   (47)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.32/22.85  | | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.32/22.85  | | | | | |           all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.32/22.85  | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.32/22.85  | | | | | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 153.32/22.85  | | | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.32/22.85  | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.32/22.85  | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.32/22.85  | | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.32/22.85  | | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.32/22.85  | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.32/22.85  | | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.32/22.85  | | | | | |               e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.32/22.85  | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.32/22.85  | | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.32/22.85  | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.32/22.85  | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.32/22.85  | | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.32/22.85  | | | | | |               e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.32/22.85  | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.32/22.85  | | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 153.32/22.85  | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.32/22.85  | | | | | |               $i(all_57_7))))
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | BETA: splitting (47) gives:
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | | Case 1:
% 153.32/22.85  | | | | | | | 
% 153.32/22.85  | | | | | | |   (48)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.32/22.85  | | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.32/22.85  | | | | | | |         all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.32/22.85  | | | | | | |         $i(all_57_11) & $i(all_57_14)
% 153.32/22.85  | | | | | | | 
% 153.32/22.85  | | | | | | | ALPHA: (48) implies:
% 153.32/22.85  | | | | | | |   (49)   ~ (all_57_14 = e0)
% 153.32/22.85  | | | | | | |   (50)  op(e1, e1) = all_57_14
% 153.32/22.85  | | | | | | | 
% 153.32/22.85  | | | | | | | REF_CLOSE: (6), (7), (49), (50) are inconsistent by sub-proof
% 153.32/22.85  | | | | | | |            #1026.
% 153.32/22.85  | | | | | | | 
% 153.32/22.85  | | | | | | Case 2:
% 153.32/22.85  | | | | | | | 
% 153.32/22.85  | | | | | | |   (51)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.32/22.85  | | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.32/22.85  | | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.32/22.85  | | | | | | |             op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.32/22.85  | | | | | | |             all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.32/22.85  | | | | | | |               e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.32/22.85  | | | | | | |             op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 153.32/22.85  | | | | | | |             all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 153.32/22.85  | | | | | | |               e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.32/22.85  | | | | | | |             op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.32/22.85  | | | | | | |             all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.32/22.85  | | | | | | |               e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.32/22.85  | | | | | | |             op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.32/22.85  | | | | | | |             all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.32/22.85  | | | | | | |               e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.32/22.85  | | | | | | |             op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.32/22.85  | | | | | | |             all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.32/22.85  | | | | | | |               e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.32/22.85  | | | | | | |             op(e0, e1) = e0 & $i(all_57_7)))
% 153.32/22.85  | | | | | | | 
% 153.32/22.85  | | | | | | | ALPHA: (51) implies:
% 153.32/22.85  | | | | | | |   (52)  op(e0, e0) = all_57_15
% 153.32/22.85  | | | | | | |   (53)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.32/22.85  | | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 153.32/22.85  | | | | | | |           e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.32/22.85  | | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.32/22.85  | | | | | | |             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.32/22.85  | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.32/22.85  | | | | | | |           = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 153.32/22.85  | | | | | | |             e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.32/22.85  | | | | | | |           $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.32/22.85  | | | | | | |           (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.32/22.85  | | | | | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.32/22.85  | | | | | | |           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.32/22.85  | | | | | | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.32/22.85  | | | | | | |           & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.32/22.85  | | | | | | |           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.32/22.85  | | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.32/22.85  | | | | | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.32/22.85  | | | | | | |           $i(all_57_7))
% 153.32/22.85  | | | | | | | 
% 153.32/22.85  | | | | | | | BETA: splitting (53) gives:
% 153.32/22.85  | | | | | | | 
% 153.32/22.85  | | | | | | | Case 1:
% 153.32/22.85  | | | | | | | | 
% 153.32/22.85  | | | | | | | |   (54)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 153.32/22.85  | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.32/22.85  | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.32/22.85  | | | | | | | |         (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.32/22.85  | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.32/22.85  | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.32/22.85  | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.32/22.85  | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.32/22.85  | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.32/22.85  | | | | | | | | 
% 153.32/22.85  | | | | | | | | REF_CLOSE: (3), (4), (6), (8), (13), (24), (52), (54) are
% 153.32/22.85  | | | | | | | |            inconsistent by sub-proof #529.
% 153.32/22.85  | | | | | | | | 
% 153.32/22.85  | | | | | | | Case 2:
% 153.32/22.85  | | | | | | | | 
% 153.32/22.85  | | | | | | | |   (55)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) & 
% 153.32/22.85  | | | | | | | |           ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.32/22.85  | | | | | | | |             e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.32/22.85  | | | | | | | |         (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.32/22.85  | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.32/22.85  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 153.32/22.85  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.32/22.85  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.32/22.85  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.32/22.85  | | | | | | | | 
% 153.32/22.85  | | | | | | | | REF_CLOSE: (1), (5), (6), (7), (10), (14), (17), (55) are
% 153.32/22.85  | | | | | | | |            inconsistent by sub-proof #528.
% 153.32/22.85  | | | | | | | | 
% 153.32/22.85  | | | | | | | End of split
% 153.32/22.85  | | | | | | | 
% 153.32/22.85  | | | | | | End of split
% 153.32/22.85  | | | | | | 
% 153.32/22.85  | | | | | End of split
% 153.32/22.85  | | | | | 
% 153.32/22.85  | | | | End of split
% 153.32/22.85  | | | | 
% 153.32/22.85  | | | End of split
% 153.32/22.85  | | | 
% 153.32/22.85  | | End of split
% 153.32/22.85  | | 
% 153.32/22.85  | Case 2:
% 153.32/22.85  | | 
% 153.32/22.85  | |   (56)   ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)
% 153.32/22.85  | | 
% 153.32/22.85  | | ALPHA: (56) implies:
% 153.32/22.85  | |   (57)   ~ (all_57_15 = e2)
% 153.32/22.85  | |   (58)  op(e0, e0) = all_57_15
% 153.32/22.85  | | 
% 153.32/22.85  | | REF_CLOSE: (6), (8), (57), (58) are inconsistent by sub-proof #901.
% 153.32/22.85  | | 
% 153.32/22.85  | End of split
% 153.32/22.85  | 
% 153.32/22.85  End of proof
% 153.32/22.85  
% 153.32/22.85  Sub-proof #528 shows that the following formulas are inconsistent:
% 153.32/22.85  ----------------------------------------------------------------
% 153.32/22.85    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.32/22.85             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.32/22.85           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.32/22.85           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.32/22.85             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.32/22.85           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.32/22.85           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.32/22.85    (2)  op(e0, e1) = all_52_11
% 153.32/22.85    (3)   ~ (e2 = e0)
% 153.32/22.85    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.85    (5)  op(e1, e1) = e0
% 153.32/22.85    (6)   ~ (all_52_11 = e0)
% 153.32/22.85    (7)  op(e2, e2) = e2
% 153.32/22.85    (8)   ~ (e2 = e1)
% 153.32/22.85  
% 153.32/22.85  Begin of proof
% 153.32/22.85  | 
% 153.32/22.85  | BETA: splitting (1) gives:
% 153.32/22.85  | 
% 153.32/22.85  | Case 1:
% 153.32/22.85  | | 
% 153.32/22.85  | |   (9)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.32/22.85  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.32/22.85  | |        $i(all_57_4)
% 153.32/22.85  | | 
% 153.32/22.85  | | ALPHA: (9) implies:
% 153.32/22.85  | |   (10)  op(e1, e1) = e2
% 153.32/22.85  | | 
% 153.32/22.85  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #1006.
% 153.32/22.85  | | 
% 153.32/22.85  | Case 2:
% 153.32/22.85  | | 
% 153.32/22.85  | |   (11)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 153.32/22.85  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.32/22.85  | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.32/22.85  | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2,
% 153.32/22.85  | |             e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.32/22.85  | | 
% 153.32/22.85  | | REF_CLOSE: (2), (4), (6), (7), (8), (11) are inconsistent by sub-proof #954.
% 153.32/22.85  | | 
% 153.32/22.85  | End of split
% 153.32/22.85  | 
% 153.32/22.85  End of proof
% 153.32/22.85  
% 153.32/22.85  Sub-proof #529 shows that the following formulas are inconsistent:
% 153.32/22.85  ----------------------------------------------------------------
% 153.32/22.85    (1)  op(e0, e2) = all_52_7
% 153.32/22.85    (2)   ~ (all_52_3 = all_52_7)
% 153.32/22.85    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.85    (4)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.32/22.85             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.32/22.85           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.32/22.85           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.32/22.85             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.32/22.85           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.32/22.85           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.32/22.85    (5)  op(e0, e0) = e2
% 153.32/22.85    (6)  op(e0, e3) = all_52_3
% 153.32/22.85    (7)  op(e0, e0) = all_57_15
% 153.32/22.85    (8)  op(e0, e2) = e0
% 153.32/22.85  
% 153.32/22.85  Begin of proof
% 153.32/22.85  | 
% 153.32/22.85  | BETA: splitting (4) gives:
% 153.32/22.85  | 
% 153.32/22.85  | Case 1:
% 153.32/22.85  | | 
% 153.32/22.85  | |   (9)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.32/22.85  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.32/22.85  | |        $i(all_57_0)
% 153.32/22.85  | | 
% 153.32/22.85  | | ALPHA: (9) implies:
% 153.32/22.85  | |   (10)  op(e0, e3) = e0
% 153.32/22.85  | | 
% 153.32/22.85  | | REF_CLOSE: (1), (2), (3), (6), (8), (10) are inconsistent by sub-proof
% 153.32/22.85  | |            #1123.
% 153.32/22.85  | | 
% 153.32/22.85  | Case 2:
% 153.32/22.85  | | 
% 153.32/22.85  | |   (11)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 153.32/22.85  | |             = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 153.32/22.85  | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.32/22.85  | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 153.32/22.85  | |             e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.32/22.85  | | 
% 153.32/22.85  | | BETA: splitting (11) gives:
% 153.32/22.85  | | 
% 153.32/22.85  | | Case 1:
% 153.32/22.85  | | | 
% 153.32/22.85  | | |   (12)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.32/22.85  | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.32/22.85  | | |         op(e0, e3) = e0 & $i(all_57_1)
% 153.32/22.85  | | | 
% 153.32/22.85  | | | ALPHA: (12) implies:
% 153.32/22.85  | | |   (13)  op(e0, e3) = e0
% 153.32/22.85  | | | 
% 153.32/22.85  | | | REF_CLOSE: (1), (2), (3), (6), (8), (13) are inconsistent by sub-proof
% 153.32/22.85  | | |            #1123.
% 153.32/22.85  | | | 
% 153.32/22.85  | | Case 2:
% 153.32/22.85  | | | 
% 153.32/22.85  | | |   (14)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.32/22.85  | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.32/22.85  | | |         op(e0, e2) = e0 & $i(all_57_3)
% 153.32/22.85  | | | 
% 153.32/22.85  | | | ALPHA: (14) implies:
% 153.32/22.85  | | |   (15)   ~ (all_57_15 = e2)
% 153.32/22.85  | | | 
% 153.32/22.85  | | | REF_CLOSE: (3), (5), (7), (15) are inconsistent by sub-proof #901.
% 153.32/22.85  | | | 
% 153.32/22.85  | | End of split
% 153.32/22.85  | | 
% 153.32/22.85  | End of split
% 153.32/22.85  | 
% 153.32/22.85  End of proof
% 153.32/22.85  
% 153.32/22.85  Sub-proof #530 shows that the following formulas are inconsistent:
% 153.32/22.85  ----------------------------------------------------------------
% 153.32/22.85    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.85           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (2)  op(e1, e1) = e0
% 153.32/22.86    (3)   ~ (all_52_13 = e2)
% 153.32/22.86    (4)  op(e2, e0) = all_52_13
% 153.32/22.86    (5)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 =
% 153.32/22.86             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.32/22.86           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 153.32/22.86         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 153.32/22.86             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 153.32/22.86           all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (5) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (6)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12
% 153.32/22.86  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.32/22.86  | |        all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (6) implies:
% 153.32/22.86  | |   (7)  op(e2, e0) = e2
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #1156.
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (8)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14
% 153.32/22.86  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 153.32/22.86  | |        all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (8) implies:
% 153.32/22.86  | |   (9)   ~ (all_57_14 = e0)
% 153.32/22.86  | |   (10)  op(e1, e1) = all_57_14
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (1), (2), (9), (10) are inconsistent by sub-proof #1026.
% 153.32/22.86  | | 
% 153.32/22.86  | End of split
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #531 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)  op(e3, e3) = e0
% 153.32/22.86    (2)   ~ (e2 = e0)
% 153.32/22.86    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (4)  op(e2, e2) = e2
% 153.32/22.86    (5)  all_57_5 = e0
% 153.32/22.86    (6)   ~ (e2 = e1)
% 153.32/22.86    (7)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.32/22.86             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.32/22.86           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 153.32/22.86           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 153.32/22.86             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.32/22.86             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.32/22.86           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.32/22.86           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.32/22.86           $i(all_57_7) & $i(all_57_10))
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (7) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (8)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.32/22.86  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.32/22.86  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (8) implies:
% 153.32/22.86  | |   (9)  op(e3, e3) = e2
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #1073.
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (10)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.32/22.86  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.32/22.86  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.32/22.86  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.32/22.86  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.32/22.86  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #532.
% 153.32/22.86  | | 
% 153.32/22.86  | End of split
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #532 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (2)  op(e2, e2) = e2
% 153.32/22.86    (3)  all_57_5 = e0
% 153.32/22.86    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.32/22.86             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.32/22.86           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.32/22.86           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.32/22.86           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 153.32/22.86           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.32/22.86    (5)   ~ (e2 = e1)
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (4) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (6)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.32/22.86  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.32/22.86  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (6) implies:
% 153.32/22.86  | |   (7)   ~ (all_57_5 = e0)
% 153.32/22.86  | | 
% 153.32/22.86  | | REDUCE: (3), (7) imply:
% 153.32/22.86  | |   (8)  $false
% 153.32/22.86  | | 
% 153.32/22.86  | | CLOSE: (8) is inconsistent.
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.32/22.86  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.32/22.86  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (9) implies:
% 153.32/22.86  | |   (10)  op(e2, e2) = e1
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1158.
% 153.32/22.86  | | 
% 153.32/22.86  | End of split
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #533 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)  op(e3, e3) = e0
% 153.32/22.86    (2)  all_56_1 = e1
% 153.32/22.86    (3)   ~ (e3 = e1)
% 153.32/22.86    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.86         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.86    (6)  all_56_4 = e2
% 153.32/22.86    (7)  op(e3, e0) = all_52_12
% 153.32/22.86    (8)   ~ (e3 = e0)
% 153.32/22.86    (9)   ~ (all_52_12 = e3)
% 153.32/22.86    (10)   ~ (e3 = e2)
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (5) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 153.32/22.86  | |           e3)
% 153.32/22.86  | | 
% 153.32/22.86  | | BETA: splitting (11) gives:
% 153.32/22.86  | | 
% 153.32/22.86  | | Case 1:
% 153.32/22.86  | | | 
% 153.32/22.86  | | |   (12)  all_56_0 = e3 & op(e3, e3) = e3
% 153.32/22.86  | | | 
% 153.32/22.86  | | | ALPHA: (12) implies:
% 153.32/22.86  | | |   (13)  op(e3, e3) = e3
% 153.32/22.86  | | | 
% 153.32/22.86  | | | REF_CLOSE: (1), (4), (8), (13) are inconsistent by sub-proof #1141.
% 153.32/22.86  | | | 
% 153.32/22.86  | | Case 2:
% 153.32/22.86  | | | 
% 153.32/22.86  | | |   (14)  all_56_1 = e3 & op(e3, e2) = e3
% 153.32/22.86  | | | 
% 153.32/22.86  | | | ALPHA: (14) implies:
% 153.32/22.86  | | |   (15)  all_56_1 = e3
% 153.32/22.86  | | | 
% 153.32/22.86  | | | REF_CLOSE: (2), (3), (15) are inconsistent by sub-proof #1069.
% 153.32/22.86  | | | 
% 153.32/22.86  | | End of split
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (16)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 153.32/22.86  | |           e3)
% 153.32/22.86  | | 
% 153.32/22.86  | | BETA: splitting (16) gives:
% 153.32/22.86  | | 
% 153.32/22.86  | | Case 1:
% 153.32/22.86  | | | 
% 153.32/22.86  | | |   (17)  all_56_4 = e3 & op(e3, e1) = e3
% 153.32/22.86  | | | 
% 153.32/22.86  | | | REF_CLOSE: (6), (10), (17) are inconsistent by sub-proof #943.
% 153.32/22.86  | | | 
% 153.32/22.86  | | Case 2:
% 153.32/22.86  | | | 
% 153.32/22.86  | | |   (18)  all_56_9 = e3 & op(e3, e0) = e3
% 153.32/22.86  | | | 
% 153.32/22.86  | | | ALPHA: (18) implies:
% 153.32/22.86  | | |   (19)  op(e3, e0) = e3
% 153.32/22.86  | | | 
% 153.32/22.86  | | | REF_CLOSE: (4), (7), (9), (19) are inconsistent by sub-proof #1082.
% 153.32/22.86  | | | 
% 153.32/22.86  | | End of split
% 153.32/22.86  | | 
% 153.32/22.86  | End of split
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #534 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.32/22.86             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.32/22.86           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.32/22.86           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.32/22.86             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.32/22.86           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.32/22.86           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.32/22.86    (2)  op(e3, e3) = e0
% 153.32/22.86    (3)  op(e1, e1) = all_4_2
% 153.32/22.86    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (5)  op(e1, e1) = e1
% 153.32/22.86    (6)  op(e2, e2) = e2
% 153.32/22.86    (7)   ~ (e1 = e0)
% 153.32/22.86    (8)   ~ (e2 = e1)
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (1) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (9)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.32/22.86  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.32/22.86  | |        $i(all_57_4)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (9) implies:
% 153.32/22.86  | |   (10)  op(e1, e1) = e2
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (3), (4), (5), (8), (10) are inconsistent by sub-proof #1044.
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (11)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 153.32/22.86  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.32/22.86  | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.32/22.86  | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2,
% 153.32/22.86  | |             e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (2), (4), (6), (7), (8), (11) are inconsistent by sub-proof #537.
% 153.32/22.86  | | 
% 153.32/22.86  | End of split
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #535 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (2)   ~ (all_52_14 = e1)
% 153.32/22.86    (3)  op(e1, e0) = all_52_14
% 153.32/22.86    (4)   ~ (all_52_13 = e2)
% 153.32/22.86    (5)  op(e2, e0) = all_52_13
% 153.32/22.86    (6)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 =
% 153.32/22.86             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.32/22.86           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 153.32/22.86         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 153.32/22.86             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 153.32/22.86           all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (6) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (7)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12
% 153.32/22.86  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.32/22.86  | |        all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (7) implies:
% 153.32/22.86  | |   (8)  op(e2, e0) = e2
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1156.
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (9)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14
% 153.32/22.86  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 153.32/22.86  | |        all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (9) implies:
% 153.32/22.86  | |   (10)  op(e1, e0) = e1
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #961.
% 153.32/22.86  | | 
% 153.32/22.86  | End of split
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #536 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)  op(e3, e3) = e0
% 153.32/22.86    (2)  op(e1, e1) = all_4_2
% 153.32/22.86    (3)   ~ (e2 = e0)
% 153.32/22.86    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.32/22.86             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.32/22.86           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.32/22.86           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.32/22.86             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.32/22.86           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.32/22.86           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.32/22.86           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.32/22.86           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.32/22.86           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 153.32/22.86           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.32/22.86         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.32/22.86             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.32/22.86           $i(all_57_7))
% 153.32/22.86    (6)  op(e0, e3) = all_52_3
% 153.32/22.86    (7)   ~ (all_4_2 = e2)
% 153.32/22.86    (8)  op(e2, e2) = e2
% 153.32/22.86    (9)   ~ (e1 = e0)
% 153.32/22.86    (10)   ~ (all_52_3 = e0)
% 153.32/22.86    (11)   ~ (e2 = e1)
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (5) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (12)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 153.32/22.86  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.32/22.86  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.32/22.86  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.32/22.86  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.32/22.86  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.32/22.86  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.32/22.86  | |           $i(all_57_3))
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (1), (3), (4), (6), (10), (12) are inconsistent by sub-proof
% 153.32/22.86  | |            #538.
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (13)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.32/22.86  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.32/22.86  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.32/22.86  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.32/22.86  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.32/22.86  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.32/22.86  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.32/22.86  | |           $i(all_57_7))
% 153.32/22.86  | | 
% 153.32/22.86  | | BETA: splitting (13) gives:
% 153.32/22.86  | | 
% 153.32/22.86  | | Case 1:
% 153.32/22.86  | | | 
% 153.32/22.86  | | |   (14)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.32/22.86  | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.32/22.86  | | |         op(e0, e2) = e0 & $i(all_57_4)
% 153.32/22.86  | | | 
% 153.32/22.86  | | | ALPHA: (14) implies:
% 153.32/22.86  | | |   (15)  op(e1, e1) = e2
% 153.32/22.86  | | | 
% 153.32/22.86  | | | REF_CLOSE: (2), (4), (7), (15) are inconsistent by sub-proof #1169.
% 153.32/22.86  | | | 
% 153.32/22.86  | | Case 2:
% 153.32/22.86  | | | 
% 153.32/22.86  | | |   (16)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.32/22.86  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.32/22.86  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 153.32/22.86  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.32/22.86  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.32/22.86  | | | 
% 153.32/22.86  | | | REF_CLOSE: (1), (4), (8), (9), (11), (16) are inconsistent by sub-proof
% 153.32/22.86  | | |            #537.
% 153.32/22.86  | | | 
% 153.32/22.86  | | End of split
% 153.32/22.86  | | 
% 153.32/22.86  | End of split
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #537 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)  op(e3, e3) = e0
% 153.32/22.86    (2)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.32/22.86             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.32/22.86           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 153.32/22.86           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 153.32/22.86             e1) = e0 & $i(all_57_7))
% 153.32/22.86    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (4)  op(e2, e2) = e2
% 153.32/22.86    (5)   ~ (e1 = e0)
% 153.32/22.86    (6)   ~ (e2 = e1)
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (2) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (7)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.32/22.86  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.32/22.86  | |        $i(all_57_6)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (7) implies:
% 153.32/22.86  | |   (8)  op(e3, e3) = e1
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #957.
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (9)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.32/22.86  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.32/22.86  | |        $i(all_57_7)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (9) implies:
% 153.32/22.86  | |   (10)  op(e2, e2) = e1
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #1158.
% 153.32/22.86  | | 
% 153.32/22.86  | End of split
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #538 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)  op(e3, e3) = e0
% 153.32/22.86    (2)   ~ (e2 = e0)
% 153.32/22.86    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (4)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.32/22.86             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.32/22.86           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.32/22.86           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.32/22.86             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.32/22.86           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.32/22.86           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.32/22.86    (5)  op(e0, e3) = all_52_3
% 153.32/22.86    (6)   ~ (all_52_3 = e0)
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (4) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (7)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.32/22.86  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.32/22.86  | |        $i(all_57_0)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (7) implies:
% 153.32/22.86  | |   (8)  op(e0, e3) = e0
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #1142.
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (9)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 153.32/22.86  | |            = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0
% 153.32/22.86  | |          & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 153.32/22.86  | |            e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.32/22.86  | |          all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.32/22.86  | | 
% 153.32/22.86  | | BETA: splitting (9) gives:
% 153.32/22.86  | | 
% 153.32/22.86  | | Case 1:
% 153.32/22.86  | | | 
% 153.32/22.86  | | |   (10)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.32/22.86  | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.32/22.86  | | |         op(e0, e3) = e0 & $i(all_57_1)
% 153.32/22.86  | | | 
% 153.32/22.86  | | | ALPHA: (10) implies:
% 153.32/22.86  | | |   (11)  op(e0, e3) = e0
% 153.32/22.86  | | | 
% 153.32/22.86  | | | REF_CLOSE: (3), (5), (6), (11) are inconsistent by sub-proof #1142.
% 153.32/22.86  | | | 
% 153.32/22.86  | | Case 2:
% 153.32/22.86  | | | 
% 153.32/22.86  | | |   (12)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.32/22.86  | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.32/22.86  | | |         op(e0, e2) = e0 & $i(all_57_3)
% 153.32/22.86  | | | 
% 153.32/22.86  | | | ALPHA: (12) implies:
% 153.32/22.86  | | |   (13)  op(e3, e3) = e2
% 153.32/22.86  | | | 
% 153.32/22.86  | | | REF_CLOSE: (1), (2), (3), (13) are inconsistent by sub-proof #1073.
% 153.32/22.86  | | | 
% 153.32/22.86  | | End of split
% 153.32/22.86  | | 
% 153.32/22.86  | End of split
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #539 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)   ~ (all_52_1 = e0)
% 153.32/22.86    (2)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.32/22.86    (3)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.32/22.86    (4)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.32/22.86         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.32/22.86    (5)   ~ (all_10_2 = e1)
% 153.32/22.86    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (7)  all_54_10 = all_4_2
% 153.32/22.86    (8)  op(e1, e0) = all_52_14
% 153.32/22.86    (9)   ~ (all_10_2 = e3)
% 153.32/22.86    (10)  op(e2, e0) = all_52_13
% 153.32/22.86    (11)   ~ (all_52_14 = all_4_2)
% 153.32/22.86    (12)   ~ (all_4_2 = e2)
% 153.32/22.86    (13)  op(e2, e2) = e2
% 153.32/22.86    (14)  op(e2, e1) = all_52_9
% 153.32/22.86    (15)   ~ (all_4_2 = e3)
% 153.32/22.86    (16)  op(e1, e0) = e1
% 153.32/22.86    (17)   ~ (all_10_2 = e2)
% 153.32/22.86    (18)   ~ (all_52_9 = all_4_2)
% 153.32/22.86    (19)   ~ (all_52_13 = all_10_2)
% 153.32/22.86    (20)  all_54_15 = all_10_2
% 153.32/22.86    (21)  op(e2, e3) = all_52_1
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (2) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (22)  all_54_15 = e3
% 153.32/22.86  | | 
% 153.32/22.86  | | COMBINE_EQS: (20), (22) imply:
% 153.32/22.86  | |   (23)  all_10_2 = e3
% 153.32/22.86  | | 
% 153.32/22.86  | | REDUCE: (9), (23) imply:
% 153.32/22.86  | |   (24)  $false
% 153.32/22.86  | | 
% 153.32/22.86  | | CLOSE: (24) is inconsistent.
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (25)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.32/22.86  | | 
% 153.32/22.86  | | BETA: splitting (25) gives:
% 153.32/22.86  | | 
% 153.32/22.86  | | Case 1:
% 153.32/22.86  | | | 
% 153.32/22.86  | | |   (26)  all_54_15 = e2
% 153.32/22.86  | | | 
% 153.32/22.86  | | | COMBINE_EQS: (20), (26) imply:
% 153.32/22.86  | | |   (27)  all_10_2 = e2
% 153.32/22.86  | | | 
% 153.32/22.86  | | | REDUCE: (17), (27) imply:
% 153.32/22.86  | | |   (28)  $false
% 153.32/22.86  | | | 
% 153.32/22.86  | | | CLOSE: (28) is inconsistent.
% 153.32/22.86  | | | 
% 153.32/22.86  | | Case 2:
% 153.32/22.86  | | | 
% 153.32/22.86  | | |   (29)   ~ (all_54_15 = e2)
% 153.32/22.86  | | |   (30)  all_54_15 = e1 | all_54_15 = e0
% 153.32/22.86  | | | 
% 153.32/22.86  | | | BETA: splitting (30) gives:
% 153.32/22.86  | | | 
% 153.32/22.86  | | | Case 1:
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | |   (31)  all_54_15 = e1
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | | COMBINE_EQS: (20), (31) imply:
% 153.32/22.86  | | | |   (32)  all_10_2 = e1
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | | REDUCE: (5), (32) imply:
% 153.32/22.86  | | | |   (33)  $false
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | | CLOSE: (33) is inconsistent.
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | Case 2:
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | |   (34)  all_54_15 = e0
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | | COMBINE_EQS: (20), (34) imply:
% 153.32/22.86  | | | |   (35)  all_10_2 = e0
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | | REDUCE: (19), (35) imply:
% 153.32/22.86  | | | |   (36)   ~ (all_52_13 = e0)
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | | REDUCE: (17), (35) imply:
% 153.32/22.86  | | | |   (37)   ~ (e2 = e0)
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | | SIMP: (37) implies:
% 153.32/22.86  | | | |   (38)   ~ (e2 = e0)
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | | BETA: splitting (4) gives:
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | | Case 1:
% 153.32/22.86  | | | | | 
% 153.32/22.86  | | | | |   (39)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2,
% 153.32/22.86  | | | | |             e2) = e0)
% 153.32/22.86  | | | | | 
% 153.32/22.86  | | | | | REF_CLOSE: (1), (6), (13), (21), (38), (39) are inconsistent by
% 153.32/22.86  | | | | |            sub-proof #541.
% 153.32/22.86  | | | | | 
% 153.32/22.86  | | | | Case 2:
% 153.32/22.86  | | | | | 
% 153.32/22.86  | | | | |   (40)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2,
% 153.32/22.86  | | | | |             e0) = e0)
% 153.32/22.86  | | | | | 
% 153.32/22.86  | | | | | BETA: splitting (40) gives:
% 153.32/22.86  | | | | | 
% 153.32/22.86  | | | | | Case 1:
% 153.32/22.86  | | | | | | 
% 153.32/22.86  | | | | | |   (41)  all_56_5 = e0 & op(e2, e1) = e0
% 153.32/22.86  | | | | | | 
% 153.32/22.86  | | | | | | ALPHA: (41) implies:
% 153.32/22.86  | | | | | |   (42)  op(e2, e1) = e0
% 153.32/22.86  | | | | | | 
% 153.32/22.86  | | | | | | GROUND_INST: instantiating (6) with all_52_14, e1, e0, e1,
% 153.32/22.86  | | | | | |              simplifying with (8), (16) gives:
% 153.32/22.86  | | | | | |   (43)  all_52_14 = e1
% 153.32/22.86  | | | | | | 
% 153.32/22.86  | | | | | | GROUND_INST: instantiating (6) with all_52_9, e0, e1, e2,
% 153.32/22.86  | | | | | |              simplifying with (14), (42) gives:
% 153.32/22.86  | | | | | |   (44)  all_52_9 = e0
% 153.32/22.86  | | | | | | 
% 153.32/22.86  | | | | | | REDUCE: (18), (44) imply:
% 153.32/22.86  | | | | | |   (45)   ~ (all_4_2 = e0)
% 153.32/22.86  | | | | | | 
% 153.32/22.86  | | | | | | REF_CLOSE: (3), (7), (11), (12), (15), (43), (45) are inconsistent
% 153.32/22.86  | | | | | |            by sub-proof #697.
% 153.32/22.86  | | | | | | 
% 153.32/22.86  | | | | | Case 2:
% 153.32/22.86  | | | | | | 
% 153.32/22.86  | | | | | |   (46)  all_56_10 = e0 & op(e2, e0) = e0
% 153.32/22.86  | | | | | | 
% 153.32/22.86  | | | | | | REF_CLOSE: (6), (10), (36), (46) are inconsistent by sub-proof #540.
% 153.32/22.86  | | | | | | 
% 153.32/22.86  | | | | | End of split
% 153.32/22.86  | | | | | 
% 153.32/22.86  | | | | End of split
% 153.32/22.86  | | | | 
% 153.32/22.86  | | | End of split
% 153.32/22.86  | | | 
% 153.32/22.86  | | End of split
% 153.32/22.86  | | 
% 153.32/22.86  | End of split
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #540 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)  all_56_10 = e0 & op(e2, e0) = e0
% 153.32/22.86    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (3)  op(e2, e0) = all_52_13
% 153.32/22.86    (4)   ~ (all_52_13 = e0)
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | ALPHA: (1) implies:
% 153.32/22.86  |   (5)  op(e2, e0) = e0
% 153.32/22.86  | 
% 153.32/22.86  | GROUND_INST: instantiating (2) with all_52_13, e0, e0, e2, simplifying with
% 153.32/22.86  |              (3), (5) gives:
% 153.32/22.86  |   (6)  all_52_13 = e0
% 153.32/22.86  | 
% 153.32/22.86  | REDUCE: (4), (6) imply:
% 153.32/22.86  |   (7)  $false
% 153.32/22.86  | 
% 153.32/22.86  | CLOSE: (7) is inconsistent.
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #541 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)   ~ (all_52_1 = e0)
% 153.32/22.86    (2)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 153.32/22.86    (3)   ~ (e2 = e0)
% 153.32/22.86    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (5)  op(e2, e2) = e2
% 153.32/22.86    (6)  op(e2, e3) = all_52_1
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (2) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (7)  all_56_2 = e0 & op(e2, e3) = e0
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (1), (4), (6), (7) are inconsistent by sub-proof #840.
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (8)  all_56_3 = e0 & op(e2, e2) = e0
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (8) implies:
% 153.32/22.86  | |   (9)  op(e2, e2) = e0
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #1145.
% 153.32/22.86  | | 
% 153.32/22.86  | End of split
% 153.32/22.86  | 
% 153.32/22.86  End of proof
% 153.32/22.86  
% 153.32/22.86  Sub-proof #542 shows that the following formulas are inconsistent:
% 153.32/22.86  ----------------------------------------------------------------
% 153.32/22.86    (1)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 153.32/22.86             e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.32/22.86           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 =
% 153.32/22.86           e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 153.32/22.86           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 153.32/22.86           = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.32/22.86    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.86           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.86    (3)  op(e3, e3) = e0
% 153.32/22.86  
% 153.32/22.86  Begin of proof
% 153.32/22.86  | 
% 153.32/22.86  | BETA: splitting (1) gives:
% 153.32/22.86  | 
% 153.32/22.86  | Case 1:
% 153.32/22.86  | | 
% 153.32/22.86  | |   (4)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 153.32/22.86  | |          = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0
% 153.32/22.86  | |        & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)
% 153.32/22.86  | | 
% 153.32/22.86  | | ALPHA: (4) implies:
% 153.32/22.86  | |   (5)   ~ (all_57_10 = e0)
% 153.32/22.86  | |   (6)  op(e3, e3) = all_57_10
% 153.32/22.86  | | 
% 153.32/22.86  | | REF_CLOSE: (2), (3), (5), (6) are inconsistent by sub-proof #543.
% 153.32/22.86  | | 
% 153.32/22.86  | Case 2:
% 153.32/22.86  | | 
% 153.32/22.87  | |   (7)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 153.32/22.87  | |          = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 153.32/22.87  | |        & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)
% 153.32/22.87  | | 
% 153.32/22.87  | | ALPHA: (7) implies:
% 153.32/22.87  | |   (8)   ~ (all_57_10 = e0)
% 153.32/22.87  | |   (9)  op(e3, e3) = all_57_10
% 153.32/22.87  | | 
% 153.32/22.87  | | REF_CLOSE: (2), (3), (8), (9) are inconsistent by sub-proof #543.
% 153.32/22.87  | | 
% 153.32/22.87  | End of split
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #543 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (2)  op(e3, e3) = all_57_10
% 153.32/22.87    (3)  op(e3, e3) = e0
% 153.32/22.87    (4)   ~ (all_57_10 = e0)
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | GROUND_INST: instantiating (1) with e0, all_57_10, e3, e3, simplifying with
% 153.32/22.87  |              (2), (3) gives:
% 153.32/22.87  |   (5)  all_57_10 = e0
% 153.32/22.87  | 
% 153.32/22.87  | REDUCE: (4), (5) imply:
% 153.32/22.87  |   (6)  $false
% 153.32/22.87  | 
% 153.32/22.87  | CLOSE: (6) is inconsistent.
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #544 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)  op(e0, e0) = all_10_2
% 153.32/22.87    (2)   ~ (all_10_2 = e1)
% 153.32/22.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (4)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.32/22.87             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.32/22.87           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.32/22.87           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.32/22.87           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.32/22.87           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 153.32/22.87    (5)   ~ (all_52_9 = e2)
% 153.32/22.87    (6)  op(e2, e1) = all_52_9
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | BETA: splitting (4) gives:
% 153.32/22.87  | 
% 153.32/22.87  | Case 1:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (7)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.32/22.87  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.32/22.87  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 153.32/22.87  | | 
% 153.32/22.87  | | ALPHA: (7) implies:
% 153.32/22.87  | |   (8)  op(e0, e0) = e1
% 153.32/22.87  | | 
% 153.32/22.87  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1116.
% 153.32/22.87  | | 
% 153.32/22.87  | Case 2:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (9)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 153.32/22.87  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.32/22.87  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 153.32/22.87  | | 
% 153.32/22.87  | | ALPHA: (9) implies:
% 153.32/22.87  | |   (10)  op(e2, e1) = e2
% 153.32/22.87  | | 
% 153.32/22.87  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1157.
% 153.32/22.87  | | 
% 153.32/22.87  | End of split
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #545 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)  op(e3, e3) = e0
% 153.32/22.87    (2)  op(e0, e0) = all_10_2
% 153.32/22.87    (3)   ~ (e2 = e0)
% 153.32/22.87    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (5)  op(e2, e2) = e2
% 153.32/22.87    (6)   ~ (all_10_2 = e2)
% 153.32/22.87    (7)   ~ (e2 = e1)
% 153.32/22.87    (8)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.32/22.87             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.32/22.87           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 153.32/22.87           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 153.32/22.87             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.32/22.87             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.32/22.87           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.32/22.87           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.32/22.87           $i(all_57_7) & $i(all_57_10))
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | BETA: splitting (8) gives:
% 153.32/22.87  | 
% 153.32/22.87  | Case 1:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (9)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.32/22.87  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.32/22.87  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 153.32/22.87  | | 
% 153.32/22.87  | | ALPHA: (9) implies:
% 153.32/22.87  | |   (10)  op(e3, e3) = e2
% 153.32/22.87  | | 
% 153.32/22.87  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1073.
% 153.32/22.87  | | 
% 153.32/22.87  | Case 2:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (11)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.32/22.87  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.32/22.87  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.32/22.87  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.32/22.87  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.32/22.87  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.32/22.87  | | 
% 153.32/22.87  | | REF_CLOSE: (2), (4), (5), (6), (7), (11) are inconsistent by sub-proof
% 153.32/22.87  | |            #1084.
% 153.32/22.87  | | 
% 153.32/22.87  | End of split
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #546 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.32/22.87    (2)  op(e0, e0) = all_10_2
% 153.32/22.87    (3)   ~ (all_10_2 = e1)
% 153.32/22.87    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (5)   ~ (all_10_2 = e3)
% 153.32/22.87    (6)  op(e2, e2) = e2
% 153.32/22.87    (7)   ~ (e3 = e2)
% 153.32/22.87    (8)   ~ (all_10_2 = e2)
% 153.32/22.87    (9)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.32/22.87             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.32/22.87           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.32/22.87           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.32/22.87           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.32/22.87           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.32/22.87           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.32/22.87           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.32/22.87           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.32/22.87           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 153.32/22.87           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.32/22.87           $i(all_57_14))
% 153.32/22.87    (10)  all_54_15 = all_10_2
% 153.32/22.87    (11)  op(e2, e3) = all_52_1
% 153.32/22.87    (12)   ~ (all_52_1 = e2)
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | BETA: splitting (9) gives:
% 153.32/22.87  | 
% 153.32/22.87  | Case 1:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (13)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 153.32/22.87  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.32/22.87  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 153.32/22.87  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 153.32/22.87  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.32/22.87  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.32/22.87  | | 
% 153.32/22.87  | | REF_CLOSE: (4), (11), (12), (13) are inconsistent by sub-proof #1180.
% 153.32/22.87  | | 
% 153.32/22.87  | Case 2:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (14)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 153.32/22.87  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 153.32/22.87  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.32/22.87  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 153.32/22.87  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.32/22.87  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.32/22.87  | | 
% 153.32/22.87  | | BETA: splitting (14) gives:
% 153.32/22.87  | | 
% 153.32/22.87  | | Case 1:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (15)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.32/22.87  | | |         (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.32/22.87  | | |         op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.32/22.87  | | |         $i(all_57_14)
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (15) implies:
% 153.32/22.87  | | |   (16)  op(e2, e2) = e3
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (4), (6), (7), (16) are inconsistent by sub-proof #1179.
% 153.32/22.87  | | | 
% 153.32/22.87  | | Case 2:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (17)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.32/22.87  | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.32/22.87  | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.32/22.87  | | |         $i(all_57_14)
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (17) implies:
% 153.32/22.87  | | |   (18)  op(e0, e0) = e3
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10), (18) are inconsistent by
% 153.32/22.87  | | |            sub-proof #701.
% 153.32/22.87  | | | 
% 153.32/22.87  | | End of split
% 153.32/22.87  | | 
% 153.32/22.87  | End of split
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #547 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)   ~ (e3 = e1)
% 153.32/22.87    (2)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.32/22.87         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.32/22.87    (3)   ~ (e2 = e0)
% 153.32/22.87    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (5)  all_56_6 = e1
% 153.32/22.87    (6)  op(e1, e3) = e1
% 153.32/22.87    (7)   ~ (e3 = e0)
% 153.32/22.87    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.32/22.87         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.32/22.87    (9)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.32/22.87         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.32/22.87    (10)  op(e3, e3) = e1
% 153.32/22.87    (11)   ~ (e1 = e0)
% 153.32/22.87    (12)   ~ (e3 = e2)
% 153.32/22.87    (13)   ~ (e2 = e1)
% 153.32/22.87    (14)  op(e1, e3) = all_52_2
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | BETA: splitting (8) gives:
% 153.32/22.87  | 
% 153.32/22.87  | Case 1:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (15)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 153.32/22.87  | |           e0)
% 153.32/22.87  | | 
% 153.32/22.87  | | BETA: splitting (15) gives:
% 153.32/22.87  | | 
% 153.32/22.87  | | Case 1:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (16)  all_56_0 = e0 & op(e3, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (16) implies:
% 153.32/22.87  | | |   (17)  op(e3, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (4), (10), (11), (17) are inconsistent by sub-proof #957.
% 153.32/22.87  | | | 
% 153.32/22.87  | | Case 2:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (18)  all_56_2 = e0 & op(e2, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (18) implies:
% 153.32/22.87  | | |   (19)  all_56_2 = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | BETA: splitting (2) gives:
% 153.32/22.87  | | | 
% 153.32/22.87  | | | Case 1:
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | |   (20)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3)
% 153.32/22.87  | | | |           = e3)
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 153.32/22.87  | | | |            (13), (14), (20) are inconsistent by sub-proof #550.
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | Case 2:
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | |   (21)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3)
% 153.32/22.87  | | | |           = e3)
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | | BETA: splitting (21) gives:
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | | Case 1:
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | |   (22)  all_56_6 = e3 & op(e1, e3) = e3
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | | REF_CLOSE: (1), (5), (22) are inconsistent by sub-proof #785.
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | Case 2:
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | |   (23)  all_56_12 = e3 & op(e0, e3) = e3
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | | ALPHA: (23) implies:
% 153.32/22.87  | | | | |   (24)  all_56_12 = e3
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | | REF_CLOSE: (3), (4), (5), (9), (10), (12), (13), (19), (24) are
% 153.32/22.87  | | | | |            inconsistent by sub-proof #548.
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | End of split
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | End of split
% 153.32/22.87  | | | 
% 153.32/22.87  | | End of split
% 153.32/22.87  | | 
% 153.32/22.87  | Case 2:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (25)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 153.32/22.87  | |           e0)
% 153.32/22.87  | | 
% 153.32/22.87  | | BETA: splitting (25) gives:
% 153.32/22.87  | | 
% 153.32/22.87  | | Case 1:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (26)  all_56_6 = e0 & op(e1, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (26) implies:
% 153.32/22.87  | | |   (27)  op(e1, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (4), (6), (11), (14), (27) are inconsistent by sub-proof #1127.
% 153.32/22.87  | | | 
% 153.32/22.87  | | Case 2:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (28)  all_56_12 = e0 & op(e0, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (28) implies:
% 153.32/22.87  | | |   (29)  all_56_12 = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | BETA: splitting (2) gives:
% 153.32/22.87  | | | 
% 153.32/22.87  | | | Case 1:
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | |   (30)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3)
% 153.32/22.87  | | | |           = e3)
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 153.32/22.87  | | | |            (13), (14), (30) are inconsistent by sub-proof #550.
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | Case 2:
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | |   (31)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3)
% 153.32/22.87  | | | |           = e3)
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | | BETA: splitting (31) gives:
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | | Case 1:
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | |   (32)  all_56_6 = e3 & op(e1, e3) = e3
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | | REF_CLOSE: (1), (5), (32) are inconsistent by sub-proof #785.
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | Case 2:
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | |   (33)  all_56_12 = e3 & op(e0, e3) = e3
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | | ALPHA: (33) implies:
% 153.32/22.87  | | | | |   (34)  all_56_12 = e3
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | | REF_CLOSE: (7), (29), (34) are inconsistent by sub-proof #1052.
% 153.32/22.87  | | | | | 
% 153.32/22.87  | | | | End of split
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | End of split
% 153.32/22.87  | | | 
% 153.32/22.87  | | End of split
% 153.32/22.87  | | 
% 153.32/22.87  | End of split
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #548 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)   ~ (e2 = e0)
% 153.32/22.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (3)  all_56_6 = e1
% 153.32/22.87    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.32/22.87         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.32/22.87    (5)  op(e3, e3) = e1
% 153.32/22.87    (6)  all_56_2 = e0
% 153.32/22.87    (7)   ~ (e3 = e2)
% 153.32/22.87    (8)   ~ (e2 = e1)
% 153.32/22.87    (9)  all_56_12 = e3
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | BETA: splitting (4) gives:
% 153.32/22.87  | 
% 153.32/22.87  | Case 1:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 153.32/22.87  | |           e2)
% 153.32/22.87  | | 
% 153.32/22.87  | | REF_CLOSE: (1), (2), (5), (6), (8), (10) are inconsistent by sub-proof #549.
% 153.32/22.87  | | 
% 153.32/22.87  | Case 2:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (11)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 153.32/22.87  | |           e2)
% 153.32/22.87  | | 
% 153.32/22.87  | | BETA: splitting (11) gives:
% 153.32/22.87  | | 
% 153.32/22.87  | | Case 1:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (12)  all_56_6 = e2 & op(e1, e3) = e2
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (12) implies:
% 153.32/22.87  | | |   (13)  all_56_6 = e2
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #1172.
% 153.32/22.87  | | | 
% 153.32/22.87  | | Case 2:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (14)  all_56_12 = e2 & op(e0, e3) = e2
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (14) implies:
% 153.32/22.87  | | |   (15)  all_56_12 = e2
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (7), (9), (15) are inconsistent by sub-proof #869.
% 153.32/22.87  | | | 
% 153.32/22.87  | | End of split
% 153.32/22.87  | | 
% 153.32/22.87  | End of split
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #549 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 153.32/22.87    (2)   ~ (e2 = e0)
% 153.32/22.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (4)  op(e3, e3) = e1
% 153.32/22.87    (5)  all_56_2 = e0
% 153.32/22.87    (6)   ~ (e2 = e1)
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | BETA: splitting (1) gives:
% 153.32/22.87  | 
% 153.32/22.87  | Case 1:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 153.32/22.87  | | 
% 153.32/22.87  | | ALPHA: (7) implies:
% 153.32/22.87  | |   (8)  op(e3, e3) = e2
% 153.32/22.87  | | 
% 153.32/22.87  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #1074.
% 153.32/22.87  | | 
% 153.32/22.87  | Case 2:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (9)  all_56_2 = e2 & op(e2, e3) = e2
% 153.32/22.87  | | 
% 153.32/22.87  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #994.
% 153.32/22.87  | | 
% 153.32/22.87  | End of split
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #550 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)   ~ (e3 = e1)
% 153.32/22.87    (2)   ~ (e2 = e0)
% 153.32/22.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (4)  all_56_6 = e1
% 153.32/22.87    (5)  op(e1, e3) = e1
% 153.32/22.87    (6)   ~ (e3 = e0)
% 153.32/22.87    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.32/22.87         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.32/22.87    (8)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.32/22.87         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.32/22.87    (9)  op(e3, e3) = e1
% 153.32/22.87    (10)   ~ (e1 = e0)
% 153.32/22.87    (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 153.32/22.87    (12)   ~ (e3 = e2)
% 153.32/22.87    (13)   ~ (e2 = e1)
% 153.32/22.87    (14)  op(e1, e3) = all_52_2
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | BETA: splitting (11) gives:
% 153.32/22.87  | 
% 153.32/22.87  | Case 1:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (15)  all_56_0 = e3 & op(e3, e3) = e3
% 153.32/22.87  | | 
% 153.32/22.87  | | ALPHA: (15) implies:
% 153.32/22.87  | |   (16)  op(e3, e3) = e3
% 153.32/22.87  | | 
% 153.32/22.87  | | REF_CLOSE: (1), (3), (9), (16) are inconsistent by sub-proof #1178.
% 153.32/22.87  | | 
% 153.32/22.87  | Case 2:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (17)  all_56_2 = e3 & op(e2, e3) = e3
% 153.32/22.87  | | 
% 153.32/22.87  | | ALPHA: (17) implies:
% 153.32/22.87  | |   (18)  all_56_2 = e3
% 153.32/22.87  | | 
% 153.32/22.87  | | BETA: splitting (8) gives:
% 153.32/22.87  | | 
% 153.32/22.87  | | Case 1:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (19)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 153.32/22.87  | | |           e2)
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (3), (9), (12), (13), (18), (19) are inconsistent by sub-proof
% 153.32/22.87  | | |            #933.
% 153.32/22.87  | | | 
% 153.32/22.87  | | Case 2:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (20)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 153.32/22.87  | | |           e2)
% 153.32/22.87  | | | 
% 153.32/22.87  | | | BETA: splitting (20) gives:
% 153.32/22.87  | | | 
% 153.32/22.87  | | | Case 1:
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | |   (21)  all_56_6 = e2 & op(e1, e3) = e2
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | | ALPHA: (21) implies:
% 153.32/22.87  | | | |   (22)  all_56_6 = e2
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | | REF_CLOSE: (4), (13), (22) are inconsistent by sub-proof #1172.
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | Case 2:
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | |   (23)  all_56_12 = e2 & op(e0, e3) = e2
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | | ALPHA: (23) implies:
% 153.32/22.87  | | | |   (24)  all_56_12 = e2
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (10), (14), (18), (24) are
% 153.32/22.87  | | | |            inconsistent by sub-proof #551.
% 153.32/22.87  | | | | 
% 153.32/22.87  | | | End of split
% 153.32/22.87  | | | 
% 153.32/22.87  | | End of split
% 153.32/22.87  | | 
% 153.32/22.87  | End of split
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #551 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)   ~ (e2 = e0)
% 153.32/22.87    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (3)  op(e1, e3) = e1
% 153.32/22.87    (4)   ~ (e3 = e0)
% 153.32/22.87    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.32/22.87         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.32/22.87    (6)  op(e3, e3) = e1
% 153.32/22.87    (7)   ~ (e1 = e0)
% 153.32/22.87    (8)  all_56_12 = e2
% 153.32/22.87    (9)  all_56_2 = e3
% 153.32/22.87    (10)  op(e1, e3) = all_52_2
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | BETA: splitting (5) gives:
% 153.32/22.87  | 
% 153.32/22.87  | Case 1:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 153.32/22.87  | |           e0)
% 153.32/22.87  | | 
% 153.32/22.87  | | BETA: splitting (11) gives:
% 153.32/22.87  | | 
% 153.32/22.87  | | Case 1:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (12)  all_56_0 = e0 & op(e3, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (12) implies:
% 153.32/22.87  | | |   (13)  op(e3, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (2), (6), (7), (13) are inconsistent by sub-proof #957.
% 153.32/22.87  | | | 
% 153.32/22.87  | | Case 2:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (14)  all_56_2 = e0 & op(e2, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (14) implies:
% 153.32/22.87  | | |   (15)  all_56_2 = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (4), (9), (15) are inconsistent by sub-proof #1137.
% 153.32/22.87  | | | 
% 153.32/22.87  | | End of split
% 153.32/22.87  | | 
% 153.32/22.87  | Case 2:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 153.32/22.87  | |           e0)
% 153.32/22.87  | | 
% 153.32/22.87  | | BETA: splitting (16) gives:
% 153.32/22.87  | | 
% 153.32/22.87  | | Case 1:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (17)  all_56_6 = e0 & op(e1, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (17) implies:
% 153.32/22.87  | | |   (18)  op(e1, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (2), (3), (7), (10), (18) are inconsistent by sub-proof #1127.
% 153.32/22.87  | | | 
% 153.32/22.87  | | Case 2:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (19)  all_56_12 = e0 & op(e0, e3) = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (19) implies:
% 153.32/22.87  | | |   (20)  all_56_12 = e0
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (1), (8), (20) are inconsistent by sub-proof #1119.
% 153.32/22.87  | | | 
% 153.32/22.87  | | End of split
% 153.32/22.87  | | 
% 153.32/22.87  | End of split
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #552 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)   ~ (e3 = e1)
% 153.32/22.87    (2)  all_56_4 = e0
% 153.32/22.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.87         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.87    (5)   ~ (e3 = e0)
% 153.32/22.87    (6)  op(e3, e3) = e1
% 153.32/22.87    (7)  all_56_15 = e3 & op(e0, e0) = e3
% 153.32/22.87    (8)   ~ (e3 = e2)
% 153.32/22.87    (9)  all_56_9 = e2
% 153.32/22.87    (10)  all_56_15 = e2
% 153.32/22.87    (11)  all_56_1 = e3
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | ALPHA: (7) implies:
% 153.32/22.87  |   (12)  all_56_15 = e3
% 153.32/22.87  | 
% 153.32/22.87  | COMBINE_EQS: (10), (12) imply:
% 153.32/22.87  |   (13)  e3 = e2
% 153.32/22.87  | 
% 153.32/22.87  | COMBINE_EQS: (11), (13) imply:
% 153.32/22.87  |   (14)  all_56_1 = e2
% 153.32/22.87  | 
% 153.32/22.87  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (14) are inconsistent by
% 153.32/22.87  |            sub-proof #555.
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #553 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)   ~ (e3 = e1)
% 153.32/22.87    (2)  all_56_4 = e0
% 153.32/22.87    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.87         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.87    (5)   ~ (e3 = e0)
% 153.32/22.87    (6)  op(e3, e3) = e1
% 153.32/22.87    (7)   ~ (e3 = e2)
% 153.32/22.87    (8)  all_56_9 = e2
% 153.32/22.87    (9)  all_56_9 = e3 & op(e3, e0) = e3
% 153.32/22.87    (10)  all_56_1 = e3
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | ALPHA: (9) implies:
% 153.32/22.87  |   (11)  all_56_9 = e3
% 153.32/22.87  | 
% 153.32/22.87  | COMBINE_EQS: (8), (11) imply:
% 153.32/22.87  |   (12)  e3 = e2
% 153.32/22.87  | 
% 153.32/22.87  | SIMP: (12) implies:
% 153.32/22.87  |   (13)  e3 = e2
% 153.32/22.87  | 
% 153.32/22.87  | COMBINE_EQS: (10), (13) imply:
% 153.32/22.87  |   (14)  all_56_1 = e2
% 153.32/22.87  | 
% 153.32/22.87  | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (14) are inconsistent by
% 153.32/22.87  |            sub-proof #555.
% 153.32/22.87  | 
% 153.32/22.87  End of proof
% 153.32/22.87  
% 153.32/22.87  Sub-proof #554 shows that the following formulas are inconsistent:
% 153.32/22.87  ----------------------------------------------------------------
% 153.32/22.87    (1)   ~ (e3 = e1)
% 153.32/22.87    (2)   ~ (e2 = e0)
% 153.32/22.87    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.32/22.87         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.32/22.87    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.87           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.87    (5)  all_56_10 = e0
% 153.32/22.87    (6)   ~ (e1 = e0)
% 153.32/22.87    (7)   ~ (e3 = e2)
% 153.32/22.87    (8)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.32/22.87         (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.32/22.87    (9)   ~ (e2 = e1)
% 153.32/22.87    (10)  all_56_2 = e3
% 153.32/22.87    (11)  op(e2, e2) = e0
% 153.32/22.87  
% 153.32/22.87  Begin of proof
% 153.32/22.87  | 
% 153.32/22.87  | BETA: splitting (8) gives:
% 153.32/22.87  | 
% 153.32/22.87  | Case 1:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (12)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 153.32/22.87  | |           e1)
% 153.32/22.87  | | 
% 153.32/22.87  | | BETA: splitting (12) gives:
% 153.32/22.87  | | 
% 153.32/22.87  | | Case 1:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (13)  all_56_2 = e1 & op(e2, e3) = e1
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (1), (10), (13) are inconsistent by sub-proof #791.
% 153.32/22.87  | | | 
% 153.32/22.87  | | Case 2:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (14)  all_56_3 = e1 & op(e2, e2) = e1
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (14) implies:
% 153.32/22.87  | | |   (15)  op(e2, e2) = e1
% 153.32/22.87  | | | 
% 153.32/22.87  | | | REF_CLOSE: (4), (6), (11), (15) are inconsistent by sub-proof #853.
% 153.32/22.87  | | | 
% 153.32/22.87  | | End of split
% 153.32/22.87  | | 
% 153.32/22.87  | Case 2:
% 153.32/22.87  | | 
% 153.32/22.87  | |   (16)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 153.32/22.87  | |           e1)
% 153.32/22.87  | | 
% 153.32/22.87  | | BETA: splitting (16) gives:
% 153.32/22.87  | | 
% 153.32/22.87  | | Case 1:
% 153.32/22.87  | | | 
% 153.32/22.87  | | |   (17)  all_56_5 = e1 & op(e2, e1) = e1
% 153.32/22.87  | | | 
% 153.32/22.87  | | | ALPHA: (17) implies:
% 153.32/22.87  | | |   (18)  all_56_5 = e1
% 153.32/22.87  | | | 
% 153.32/22.88  | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (18) are inconsistent
% 153.32/22.88  | | |            by sub-proof #565.
% 153.32/22.88  | | | 
% 153.32/22.88  | | Case 2:
% 153.32/22.88  | | | 
% 153.32/22.88  | | |   (19)  all_56_10 = e1 & op(e2, e0) = e1
% 153.32/22.88  | | | 
% 153.32/22.88  | | | REF_CLOSE: (5), (6), (19) are inconsistent by sub-proof #1131.
% 153.32/22.88  | | | 
% 153.32/22.88  | | End of split
% 153.32/22.88  | | 
% 153.32/22.88  | End of split
% 153.32/22.88  | 
% 153.32/22.88  End of proof
% 153.32/22.88  
% 153.32/22.88  Sub-proof #555 shows that the following formulas are inconsistent:
% 153.32/22.88  ----------------------------------------------------------------
% 153.32/22.88    (1)   ~ (e3 = e1)
% 153.32/22.88    (2)  all_56_4 = e0
% 153.32/22.88    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.88    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.88         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.88    (5)   ~ (e3 = e0)
% 153.32/22.88    (6)  op(e3, e3) = e1
% 153.32/22.88    (7)  all_56_1 = e2
% 153.32/22.88    (8)   ~ (e3 = e2)
% 153.32/22.88    (9)  all_56_9 = e2
% 153.32/22.88  
% 153.32/22.88  Begin of proof
% 153.32/22.88  | 
% 153.32/22.88  | BETA: splitting (4) gives:
% 153.32/22.88  | 
% 153.32/22.88  | Case 1:
% 153.32/22.88  | | 
% 153.32/22.88  | |   (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 153.32/22.88  | |           e3)
% 153.32/22.88  | | 
% 153.32/22.88  | | BETA: splitting (10) gives:
% 153.32/22.88  | | 
% 153.32/22.88  | | Case 1:
% 153.32/22.88  | | | 
% 153.32/22.88  | | |   (11)  all_56_0 = e3 & op(e3, e3) = e3
% 153.32/22.88  | | | 
% 153.32/22.88  | | | ALPHA: (11) implies:
% 153.32/22.88  | | |   (12)  op(e3, e3) = e3
% 153.32/22.88  | | | 
% 153.32/22.88  | | | REF_CLOSE: (1), (3), (6), (12) are inconsistent by sub-proof #1178.
% 153.32/22.88  | | | 
% 153.32/22.88  | | Case 2:
% 153.32/22.88  | | | 
% 153.32/22.88  | | |   (13)  all_56_1 = e3 & op(e3, e2) = e3
% 153.32/22.88  | | | 
% 153.32/22.88  | | | ALPHA: (13) implies:
% 153.32/22.88  | | |   (14)  all_56_1 = e3
% 153.32/22.88  | | | 
% 153.32/22.88  | | | REF_CLOSE: (7), (8), (14) are inconsistent by sub-proof #950.
% 153.32/22.88  | | | 
% 153.32/22.88  | | End of split
% 153.32/22.88  | | 
% 153.32/22.88  | Case 2:
% 153.32/22.88  | | 
% 153.32/22.88  | |   (15)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 153.32/22.88  | |           e3)
% 153.32/22.88  | | 
% 153.32/22.88  | | BETA: splitting (15) gives:
% 153.32/22.88  | | 
% 153.32/22.88  | | Case 1:
% 153.32/22.88  | | | 
% 153.32/22.88  | | |   (16)  all_56_4 = e3 & op(e3, e1) = e3
% 153.32/22.88  | | | 
% 153.32/22.88  | | | REF_CLOSE: (2), (5), (16) are inconsistent by sub-proof #641.
% 153.32/22.88  | | | 
% 153.32/22.88  | | Case 2:
% 153.32/22.88  | | | 
% 153.32/22.88  | | |   (17)  all_56_9 = e3 & op(e3, e0) = e3
% 153.32/22.88  | | | 
% 153.32/22.88  | | | ALPHA: (17) implies:
% 153.32/22.88  | | |   (18)  all_56_9 = e3
% 153.32/22.88  | | | 
% 153.32/22.88  | | | REF_CLOSE: (8), (9), (18) are inconsistent by sub-proof #964.
% 153.32/22.88  | | | 
% 153.32/22.88  | | End of split
% 153.32/22.88  | | 
% 153.32/22.88  | End of split
% 153.32/22.88  | 
% 153.32/22.88  End of proof
% 153.32/22.88  
% 153.32/22.88  Sub-proof #556 shows that the following formulas are inconsistent:
% 153.32/22.88  ----------------------------------------------------------------
% 153.32/22.88    (1)  op(e0, e1) = all_52_11
% 153.32/22.88    (2)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 153.32/22.88         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.32/22.88    (3)  all_56_13 = e2
% 153.32/22.88    (4)   ~ (e3 = e1)
% 153.32/22.88    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.32/22.88         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.32/22.88    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.32/22.88         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.32/22.88    (7)  op(e3, e2) = all_52_4
% 153.32/22.88    (8)  op(e0, e2) = all_52_7
% 153.32/22.88    (9)   ~ (all_52_14 = e2)
% 153.32/22.88    (10)   ~ (all_52_3 = all_52_7)
% 153.32/22.88    (11)  op(e1, e1) = all_4_2
% 153.32/22.88    (12)   ~ (e2 = e0)
% 153.32/22.88    (13)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.32/22.88          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.32/22.88    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.88            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.88    (15)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.88          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.88    (16)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.32/22.88          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.32/22.88    (17)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 153.32/22.88          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 153.32/22.88    (18)  op(e0, e0) = e2
% 153.32/22.88    (19)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.88              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.32/22.88                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.32/22.88                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.32/22.88    (20)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.32/22.88          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.32/22.88    (21)  op(e1, e0) = all_52_14
% 153.32/22.88    (22)   ~ (all_52_13 = e2)
% 153.32/22.88    (23)   ~ (e3 = e0)
% 153.32/22.88    (24)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.32/22.88          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.32/22.88    (25)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.32/22.88          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.32/22.88    (26)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.32/22.88          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.88    (27)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 153.32/22.88            all_57_15 & $i(all_57_15))
% 153.32/22.88    (28)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.32/22.88          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.32/22.88    (29)  op(e3, e3) = e1
% 153.32/22.88    (30)  op(e2, e0) = all_52_13
% 153.32/22.88    (31)  op(e0, e3) = all_52_3
% 153.32/22.88    (32)  op(e1, e1) = e1
% 153.32/22.88    (33)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.32/22.88          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.32/22.88    (34)   ~ (all_52_7 = e0)
% 153.32/22.88    (35)   ~ (e1 = e0)
% 153.32/22.88    (36)   ~ (all_52_1 = e1)
% 153.32/22.88    (37)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.32/22.88          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.32/22.88    (38)   ~ (e3 = e2)
% 153.32/22.88    (39)  all_56_9 = e2
% 153.32/22.88    (40)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.32/22.88          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.32/22.88    (41)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.32/22.88          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.32/22.88    (42)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 153.32/22.88          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 153.32/22.88    (43)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.32/22.88          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.32/22.88    (44)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.32/22.88          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.32/22.88    (45)   ~ (e2 = e1)
% 153.32/22.88    (46)   ~ (all_52_4 = e0)
% 153.32/22.88    (47)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.32/22.88          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.32/22.88    (48)   ~ (all_52_11 = e2)
% 153.32/22.88    (49)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.32/22.88          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.32/22.88    (50)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.32/22.88          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 153.32/22.88            e1)
% 153.32/22.88    (51)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 153.32/22.88          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 153.32/22.88    (52)  op(e2, e2) = e0
% 153.32/22.88    (53)  op(e2, e3) = all_52_1
% 153.32/22.88  
% 153.32/22.88  Begin of proof
% 153.32/22.88  | 
% 153.32/22.88  | BETA: splitting (47) gives:
% 153.32/22.88  | 
% 153.32/22.88  | Case 1:
% 153.32/22.88  | | 
% 153.32/22.88  | |   (54)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 153.32/22.88  | |           e1)
% 153.32/22.88  | | 
% 153.32/22.88  | | BETA: splitting (54) gives:
% 153.32/22.88  | | 
% 153.32/22.88  | | Case 1:
% 153.32/22.88  | | | 
% 153.32/22.88  | | |   (55)  all_56_1 = e1 & op(e3, e2) = e1
% 153.32/22.88  | | | 
% 153.32/22.88  | | | ALPHA: (55) implies:
% 153.32/22.88  | | |   (56)  all_56_1 = e1
% 153.32/22.88  | | | 
% 153.32/22.88  | | | REF_CLOSE: (4), (7), (12), (14), (15), (23), (26), (29), (35), (38), (39),
% 153.32/22.88  | | |            (46), (56) are inconsistent by sub-proof #592.
% 153.32/22.88  | | | 
% 153.32/22.88  | | Case 2:
% 153.32/22.88  | | | 
% 153.32/22.88  | | |   (57)  all_56_3 = e1 & op(e2, e2) = e1
% 153.32/22.88  | | | 
% 153.32/22.88  | | | ALPHA: (57) implies:
% 153.32/22.88  | | |   (58)  op(e2, e2) = e1
% 153.32/22.88  | | | 
% 153.32/22.88  | | | REF_CLOSE: (14), (35), (52), (58) are inconsistent by sub-proof #853.
% 153.32/22.88  | | | 
% 153.32/22.88  | | End of split
% 153.32/22.88  | | 
% 153.32/22.88  | Case 2:
% 153.32/22.88  | | 
% 153.32/22.88  | |   (59)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 153.32/22.88  | |           e1)
% 153.32/22.88  | | 
% 153.32/22.88  | | BETA: splitting (59) gives:
% 153.32/22.88  | | 
% 153.32/22.88  | | Case 1:
% 153.32/22.88  | | | 
% 153.32/22.88  | | |   (60)  all_56_7 = e1 & op(e1, e2) = e1
% 153.32/22.88  | | | 
% 153.32/22.88  | | | ALPHA: (60) implies:
% 153.32/22.88  | | |   (61)  all_56_7 = e1
% 153.32/22.88  | | | 
% 153.32/22.88  | | | BETA: splitting (50) gives:
% 153.32/22.88  | | | 
% 153.32/22.88  | | | Case 1:
% 153.32/22.88  | | | | 
% 153.32/22.88  | | | |   (62)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0,
% 153.32/22.88  | | | |             e2) = e1)
% 153.32/22.88  | | | | 
% 153.32/22.88  | | | | BETA: splitting (62) gives:
% 153.32/22.88  | | | | 
% 153.32/22.88  | | | | Case 1:
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | |   (63)  all_56_12 = e1 & op(e0, e3) = e1
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | | ALPHA: (63) implies:
% 153.32/22.88  | | | | |   (64)  all_56_12 = e1
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | | BETA: splitting (26) gives:
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | | Case 1:
% 153.32/22.88  | | | | | | 
% 153.32/22.88  | | | | | |   (65)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3,
% 153.32/22.88  | | | | | |             e2) = e0)
% 153.32/22.88  | | | | | | 
% 153.32/22.88  | | | | | | REF_CLOSE: (7), (14), (29), (35), (46), (65) are inconsistent by
% 153.32/22.88  | | | | | |            sub-proof #937.
% 153.32/22.88  | | | | | | 
% 153.32/22.88  | | | | | Case 2:
% 153.32/22.88  | | | | | | 
% 153.32/22.88  | | | | | |   (66)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3,
% 153.32/22.88  | | | | | |             e0) = e0)
% 153.32/22.88  | | | | | | 
% 153.32/22.88  | | | | | | BETA: splitting (66) gives:
% 153.32/22.88  | | | | | | 
% 153.32/22.88  | | | | | | Case 1:
% 153.32/22.88  | | | | | | | 
% 153.32/22.88  | | | | | | |   (67)  all_56_4 = e0 & op(e3, e1) = e0
% 153.32/22.88  | | | | | | | 
% 153.32/22.88  | | | | | | | ALPHA: (67) implies:
% 153.32/22.88  | | | | | | |   (68)  all_56_4 = e0
% 153.32/22.88  | | | | | | | 
% 153.32/22.88  | | | | | | | BETA: splitting (19) gives:
% 153.32/22.88  | | | | | | | 
% 153.32/22.88  | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | 
% 153.32/22.88  | | | | | | | |   (69)  all_56_15 = e0 & op(e0, e0) = e0
% 153.32/22.88  | | | | | | | | 
% 153.32/22.88  | | | | | | | | ALPHA: (69) implies:
% 153.32/22.88  | | | | | | | |   (70)  op(e0, e0) = e0
% 153.32/22.88  | | | | | | | | 
% 153.32/22.88  | | | | | | | | REF_CLOSE: (12), (14), (18), (70) are inconsistent by sub-proof
% 153.32/22.88  | | | | | | | |            #1043.
% 153.32/22.88  | | | | | | | | 
% 153.32/22.88  | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | 
% 153.32/22.88  | | | | | | | |   (71)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 &
% 153.32/22.88  | | | | | | | |             op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.32/22.88  | | | | | | | |             e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) |
% 153.32/22.88  | | | | | | | |           (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 &
% 153.32/22.88  | | | | | | | |             op(e0, e1) = e0))
% 153.32/22.88  | | | | | | | | 
% 153.32/22.88  | | | | | | | | ALPHA: (71) implies:
% 153.32/22.88  | | | | | | | |   (72)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 &
% 153.32/22.88  | | | | | | | |           op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.32/22.88  | | | | | | | | 
% 153.32/22.88  | | | | | | | | BETA: splitting (17) gives:
% 153.32/22.88  | | | | | | | | 
% 153.32/22.88  | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | 
% 153.32/22.88  | | | | | | | | |   (73)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 &
% 153.32/22.88  | | | | | | | | |           op(e2, e1) = e2)
% 153.32/22.88  | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | BETA: splitting (73) gives:
% 153.32/22.88  | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | |   (74)  all_56_4 = e2 & op(e3, e1) = e2
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | ALPHA: (74) implies:
% 153.32/22.88  | | | | | | | | | |   (75)  all_56_4 = e2
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | REF_CLOSE: (7), (12), (14), (26), (29), (35), (39), (46),
% 153.32/22.88  | | | | | | | | | |            (75) are inconsistent by sub-proof #583.
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | |   (76)  all_56_5 = e2 & op(e2, e1) = e2
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | ALPHA: (76) implies:
% 153.32/22.88  | | | | | | | | | |   (77)  all_56_5 = e2
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | BETA: splitting (49) gives:
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | |   (78)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 153.32/22.88  | | | | | | | | | | |           & op(e2, e2) = e3)
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | BETA: splitting (78) gives:
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | |   (79)  all_56_1 = e3 & op(e3, e2) = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | ALPHA: (79) implies:
% 153.32/22.88  | | | | | | | | | | | |   (80)  all_56_1 = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | BETA: splitting (40) gives:
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | |   (81)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 153.32/22.88  | | | | | | | | | | | | |           & op(e2, e2) = e1)
% 153.32/22.88  | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | REF_CLOSE: (14), (35), (36), (52), (53), (81) are
% 153.32/22.88  | | | | | | | | | | | | |            inconsistent by sub-proof #603.
% 153.32/22.88  | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | |   (82)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 153.32/22.88  | | | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 153.32/22.88  | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | BETA: splitting (82) gives:
% 153.32/22.88  | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | |   (83)  all_56_5 = e1 & op(e2, e1) = e1
% 153.32/22.88  | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | ALPHA: (83) implies:
% 153.32/22.88  | | | | | | | | | | | | | |   (84)  all_56_5 = e1
% 153.32/22.88  | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (12), (13), (14), (15), (22),
% 153.32/22.88  | | | | | | | | | | | | | |            (23), (24), (26), (28), (29), (30), (35), (38),
% 153.32/22.88  | | | | | | | | | | | | | |            (39), (41), (45), (47), (64), (68), (80), (84) are
% 153.32/22.88  | | | | | | | | | | | | | |            inconsistent by sub-proof #571.
% 153.32/22.88  | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | |   (85)  all_56_10 = e1 & op(e2, e0) = e1
% 153.32/22.88  | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | ALPHA: (85) implies:
% 153.32/22.88  | | | | | | | | | | | | | |   (86)  all_56_10 = e1
% 153.32/22.88  | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | BETA: splitting (37) gives:
% 153.32/22.88  | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | |   (87)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 153.32/22.88  | | | | | | | | | | | | | | |           & op(e1, e2) = e2)
% 153.32/22.88  | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 153.32/22.88  | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | |   (88)  all_56_6 = e2 & op(e1, e3) = e2
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | ALPHA: (88) implies:
% 153.32/22.88  | | | | | | | | | | | | | | | |   (89)  all_56_6 = e2
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | |   (90)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | |           & op(e1, e2) = e3)
% 153.32/22.88  | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | BETA: splitting (90) gives:
% 153.32/22.88  | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | |   (91)  all_56_6 = e3 & op(e1, e3) = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (89), (91) are inconsistent by sub-proof
% 153.32/22.88  | | | | | | | | | | | | | | | | | |            #570.
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | |   (92)  all_56_7 = e3 & op(e1, e2) = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 153.32/22.88  | | | | | | | | | | | | | | | | | |   (93)  all_56_7 = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (93) imply:
% 153.32/22.88  | | | | | | | | | | | | | | | | | |   (94)  e3 = e1
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | SIMP: (94) implies:
% 153.32/22.88  | | | | | | | | | | | | | | | | | |   (95)  e3 = e1
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (95) imply:
% 153.32/22.88  | | | | | | | | | | | | | | | | | |   (96)  all_56_1 = e1
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (15), (23), (29), (38), (39), (68),
% 153.32/22.88  | | | | | | | | | | | | | | | | | |            (96) are inconsistent by sub-proof #593.
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | |   (97)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 153.32/22.88  | | | | | | | | | | | | | | | | |           e3 & op(e1, e0) = e3)
% 153.32/22.88  | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 153.32/22.88  | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | |   (98)  all_56_8 = e3 & op(e1, e1) = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 153.32/22.88  | | | | | | | | | | | | | | | | | |   (99)  all_56_8 = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | |   (100)  op(e1, e1) = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (12), (14), (16), (23), (24), (28),
% 153.32/22.88  | | | | | | | | | | | | | | | | | |            (29), (35), (37), (38), (44), (45), (64), (99),
% 153.32/22.88  | | | | | | | | | | | | | | | | | |            (100) are inconsistent by sub-proof #569.
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | |   (101)  all_56_11 = e3 & op(e1, e0) = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 153.32/22.88  | | | | | | | | | | | | | | | | | |   (102)  all_56_11 = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | BETA: splitting (6) gives:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | |   (103)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (14), (23), (24), (29), (35), (64),
% 153.32/22.88  | | | | | | | | | | | | | | | | | | |            (89), (103) are inconsistent by sub-proof #568.
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | |   (104)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 153.32/22.88  | | | | | | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | BETA: splitting (104) gives:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | |   (105)  all_56_6 = e3 & op(e1, e3) = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | ALPHA: (105) implies:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | |   (106)  all_56_6 = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (89), (106) imply:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | |   (107)  e3 = e2
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | SIMP: (107) implies:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | |   (108)  e3 = e2
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (102), (108) imply:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | |   (109)  all_56_11 = e2
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (12), (35), (39), (72), (86), (109) are
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #567.
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | |   (110)  all_56_12 = e3 & op(e0, e3) = e3
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (15), (23), (29), (38), (39), (64),
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | |            (68), (80), (110) are inconsistent by sub-proof
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | |            #573.
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | |   (111)  all_56_7 = e2 & op(e1, e2) = e2
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | ALPHA: (111) implies:
% 153.32/22.88  | | | | | | | | | | | | | | | |   (112)  all_56_7 = e2
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | COMBINE_EQS: (61), (112) imply:
% 153.32/22.88  | | | | | | | | | | | | | | | |   (113)  e2 = e1
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (113) imply:
% 153.32/22.88  | | | | | | | | | | | | | | | |   (114)  all_56_5 = e1
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | REF_CLOSE: (3), (4), (5), (6), (12), (13), (14), (15), (22),
% 153.32/22.88  | | | | | | | | | | | | | | | |            (23), (24), (26), (28), (29), (30), (35), (38),
% 153.32/22.88  | | | | | | | | | | | | | | | |            (39), (41), (45), (47), (64), (68), (80), (114)
% 153.32/22.88  | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #571.
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | |   (115)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 153.32/22.88  | | | | | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 153.32/22.88  | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | BETA: splitting (115) gives:
% 153.32/22.88  | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | |   (116)  all_56_8 = e2 & op(e1, e1) = e2
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | ALPHA: (116) implies:
% 153.32/22.88  | | | | | | | | | | | | | | | |   (117)  all_56_8 = e2
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 153.32/22.88  | | | | | | | | | | | | | | | |            (11), (12), (13), (14), (15), (17), (18), (19),
% 153.32/22.88  | | | | | | | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 153.32/22.88  | | | | | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 153.32/22.88  | | | | | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 153.32/22.88  | | | | | | | | | | | | | | | |            (45), (46), (47), (48), (49), (51), (52), (53),
% 153.32/22.88  | | | | | | | | | | | | | | | |            (61), (64), (68), (80), (117) are inconsistent by
% 153.32/22.88  | | | | | | | | | | | | | | | |            sub-proof #558.
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | |   (118)  all_56_11 = e2 & op(e1, e0) = e2
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 153.32/22.88  | | | | | | | | | | | | | | | |   (119)  all_56_11 = e2
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | | REF_CLOSE: (12), (35), (39), (72), (86), (119) are
% 153.32/22.88  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #567.
% 153.32/22.88  | | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | |   (120)  all_56_3 = e3 & op(e2, e2) = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | ALPHA: (120) implies:
% 153.32/22.88  | | | | | | | | | | | |   (121)  op(e2, e2) = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | REF_CLOSE: (14), (23), (52), (121) are inconsistent by
% 153.32/22.88  | | | | | | | | | | | |            sub-proof #719.
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | |   (122)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 153.32/22.88  | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | BETA: splitting (122) gives:
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | |   (123)  all_56_7 = e3 & op(e1, e2) = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | REF_CLOSE: (4), (61), (123) are inconsistent by sub-proof
% 153.32/22.88  | | | | | | | | | | | |            #564.
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | |   (124)  all_56_13 = e3 & op(e0, e2) = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | REF_CLOSE: (3), (38), (124) are inconsistent by sub-proof
% 153.32/22.88  | | | | | | | | | | | |            #563.
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | 
% 153.32/22.88  | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | 
% 153.32/22.88  | | | | | | | | |   (125)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 &
% 153.32/22.88  | | | | | | | | |            op(e0, e1) = e2)
% 153.32/22.88  | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | BETA: splitting (125) gives:
% 153.32/22.88  | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | |   (126)  all_56_8 = e2 & op(e1, e1) = e2
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | ALPHA: (126) implies:
% 153.32/22.88  | | | | | | | | | |   (127)  all_56_8 = e2
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | BETA: splitting (49) gives:
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | |   (128)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3
% 153.32/22.88  | | | | | | | | | | |            & op(e2, e2) = e3)
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | BETA: splitting (128) gives:
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | |   (129)  all_56_1 = e3 & op(e3, e2) = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | ALPHA: (129) implies:
% 153.32/22.88  | | | | | | | | | | | |   (130)  all_56_1 = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10),
% 153.32/22.88  | | | | | | | | | | | |            (11), (12), (13), (14), (15), (17), (18), (19),
% 153.32/22.88  | | | | | | | | | | | |            (20), (21), (22), (23), (24), (25), (26), (27),
% 153.32/22.88  | | | | | | | | | | | |            (28), (29), (30), (31), (32), (33), (34), (35),
% 153.32/22.88  | | | | | | | | | | | |            (36), (37), (38), (39), (40), (41), (42), (43),
% 153.32/22.88  | | | | | | | | | | | |            (45), (46), (47), (48), (49), (51), (52), (53),
% 153.32/22.88  | | | | | | | | | | | |            (61), (64), (68), (127), (130) are inconsistent by
% 153.32/22.88  | | | | | | | | | | | |            sub-proof #558.
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | |   (131)  all_56_3 = e3 & op(e2, e2) = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | ALPHA: (131) implies:
% 153.32/22.88  | | | | | | | | | | | |   (132)  op(e2, e2) = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | REF_CLOSE: (14), (23), (52), (132) are inconsistent by
% 153.32/22.88  | | | | | | | | | | | |            sub-proof #719.
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | |   (133)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 =
% 153.32/22.88  | | | | | | | | | | |            e3 & op(e0, e2) = e3)
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | BETA: splitting (133) gives:
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | Case 1:
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | |   (134)  all_56_7 = e3 & op(e1, e2) = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | REF_CLOSE: (4), (61), (134) are inconsistent by sub-proof
% 153.32/22.88  | | | | | | | | | | | |            #564.
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | |   (135)  all_56_13 = e3 & op(e0, e2) = e3
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | | REF_CLOSE: (3), (38), (135) are inconsistent by sub-proof
% 153.32/22.88  | | | | | | | | | | | |            #563.
% 153.32/22.88  | | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | Case 2:
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | |   (136)  all_56_14 = e2 & op(e0, e1) = e2
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | ALPHA: (136) implies:
% 153.32/22.88  | | | | | | | | | |   (137)  op(e0, e1) = e2
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | | REF_CLOSE: (1), (14), (48), (137) are inconsistent by
% 153.32/22.88  | | | | | | | | | |            sub-proof #1092.
% 153.32/22.88  | | | | | | | | | | 
% 153.32/22.88  | | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | | 
% 153.32/22.88  | | | | | | | | End of split
% 153.32/22.88  | | | | | | | | 
% 153.32/22.88  | | | | | | | End of split
% 153.32/22.88  | | | | | | | 
% 153.32/22.88  | | | | | | Case 2:
% 153.32/22.88  | | | | | | | 
% 153.32/22.88  | | | | | | |   (138)  all_56_9 = e0 & op(e3, e0) = e0
% 153.32/22.88  | | | | | | | 
% 153.32/22.88  | | | | | | | REF_CLOSE: (12), (39), (138) are inconsistent by sub-proof #746.
% 153.32/22.88  | | | | | | | 
% 153.32/22.88  | | | | | | End of split
% 153.32/22.88  | | | | | | 
% 153.32/22.88  | | | | | End of split
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | Case 2:
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | |   (139)  all_56_13 = e1 & op(e0, e2) = e1
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | | REF_CLOSE: (3), (4), (5), (7), (12), (14), (15), (23), (26), (29),
% 153.32/22.88  | | | | |            (35), (38), (39), (45), (46), (139) are inconsistent by
% 153.32/22.88  | | | | |            sub-proof #557.
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | End of split
% 153.32/22.88  | | | | 
% 153.32/22.88  | | | Case 2:
% 153.32/22.88  | | | | 
% 153.32/22.88  | | | |   (140)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0,
% 153.32/22.88  | | | |              e0) = e1)
% 153.32/22.88  | | | | 
% 153.32/22.88  | | | | BETA: splitting (140) gives:
% 153.32/22.88  | | | | 
% 153.32/22.88  | | | | Case 1:
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | |   (141)  all_56_14 = e1 & op(e0, e1) = e1
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | | ALPHA: (141) implies:
% 153.32/22.88  | | | | |   (142)  all_56_14 = e1
% 153.32/22.88  | | | | |   (143)  op(e0, e1) = e1
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 153.32/22.88  | | | | |            (13), (14), (15), (17), (18), (19), (20), (21), (23), (25),
% 153.32/22.88  | | | | |            (26), (27), (28), (29), (31), (32), (33), (34), (35), (36),
% 153.32/22.88  | | | | |            (37), (38), (39), (40), (43), (45), (46), (48), (49), (51),
% 153.32/22.88  | | | | |            (52), (53), (61), (142), (143) are inconsistent by
% 153.32/22.88  | | | | |            sub-proof #559.
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | Case 2:
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | |   (144)  all_56_15 = e1 & op(e0, e0) = e1
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | | ALPHA: (144) implies:
% 153.32/22.88  | | | | |   (145)  op(e0, e0) = e1
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | | REF_CLOSE: (14), (18), (45), (145) are inconsistent by sub-proof #978.
% 153.32/22.88  | | | | | 
% 153.32/22.88  | | | | End of split
% 153.32/22.88  | | | | 
% 153.32/22.88  | | | End of split
% 153.32/22.88  | | | 
% 153.32/22.88  | | Case 2:
% 153.32/22.88  | | | 
% 153.32/22.88  | | |   (146)  all_56_13 = e1 & op(e0, e2) = e1
% 153.32/22.88  | | | 
% 153.32/22.88  | | | REF_CLOSE: (3), (4), (5), (7), (12), (14), (15), (23), (26), (29), (35),
% 153.32/22.88  | | |            (38), (39), (45), (46), (146) are inconsistent by sub-proof
% 153.32/22.88  | | |            #557.
% 153.32/22.88  | | | 
% 153.32/22.88  | | End of split
% 153.32/22.88  | | 
% 153.32/22.88  | End of split
% 153.32/22.88  | 
% 153.32/22.88  End of proof
% 153.32/22.88  
% 153.32/22.88  Sub-proof #557 shows that the following formulas are inconsistent:
% 153.32/22.88  ----------------------------------------------------------------
% 153.32/22.88    (1)  all_56_13 = e1 & op(e0, e2) = e1
% 153.32/22.88    (2)  all_56_13 = e2
% 153.32/22.88    (3)   ~ (e3 = e1)
% 153.32/22.88    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.32/22.88         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.32/22.88    (5)  op(e3, e2) = all_52_4
% 153.32/22.88    (6)   ~ (e2 = e0)
% 153.32/22.88    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.88           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.88    (8)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.88         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.88    (9)   ~ (e3 = e0)
% 153.32/22.88    (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.32/22.88          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.88    (11)  op(e3, e3) = e1
% 153.32/22.88    (12)   ~ (e1 = e0)
% 153.32/22.88    (13)   ~ (e3 = e2)
% 153.32/22.88    (14)  all_56_9 = e2
% 153.32/22.88    (15)   ~ (e2 = e1)
% 153.32/22.88    (16)   ~ (all_52_4 = e0)
% 153.32/22.88  
% 153.32/22.88  Begin of proof
% 153.32/22.88  | 
% 153.32/22.88  | ALPHA: (1) implies:
% 153.32/22.88  |   (17)  all_56_13 = e1
% 153.32/22.88  | 
% 153.32/22.88  | COMBINE_EQS: (2), (17) imply:
% 153.32/22.88  |   (18)  e2 = e1
% 153.32/22.88  | 
% 153.32/22.88  | COMBINE_EQS: (14), (18) imply:
% 153.32/22.88  |   (19)  all_56_9 = e1
% 153.32/22.88  | 
% 153.32/22.88  | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13), (15),
% 153.32/22.88  |            (16), (19) are inconsistent by sub-proof #913.
% 153.32/22.88  | 
% 153.32/22.88  End of proof
% 153.32/22.88  
% 153.32/22.88  Sub-proof #558 shows that the following formulas are inconsistent:
% 153.32/22.88  ----------------------------------------------------------------
% 153.32/22.88    (1)  op(e0, e1) = all_52_11
% 153.32/22.89    (2)  all_56_8 = e2
% 153.32/22.89    (3)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 153.32/22.89         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.32/22.89    (4)  all_56_13 = e2
% 153.32/22.89    (5)   ~ (e3 = e1)
% 153.32/22.89    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.32/22.89         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.32/22.89    (7)  all_56_4 = e0
% 153.32/22.89    (8)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.32/22.89         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.32/22.89    (9)  op(e3, e2) = all_52_4
% 153.32/22.89    (10)  all_56_7 = e1
% 153.32/22.89    (11)  op(e0, e2) = all_52_7
% 153.32/22.89    (12)   ~ (all_52_14 = e2)
% 153.32/22.89    (13)   ~ (all_52_3 = all_52_7)
% 153.32/22.89    (14)  op(e1, e1) = all_4_2
% 153.32/22.89    (15)   ~ (e2 = e0)
% 153.32/22.89    (16)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.32/22.89          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.32/22.89    (17)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.89    (18)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.89          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.89    (19)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 153.32/22.89          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 153.32/22.89    (20)  op(e0, e0) = e2
% 153.32/22.89    (21)  all_56_12 = e1
% 153.32/22.89    (22)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.89              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.32/22.89                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.32/22.89                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.32/22.89    (23)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.32/22.89          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.32/22.89    (24)  op(e1, e0) = all_52_14
% 153.32/22.89    (25)   ~ (all_52_13 = e2)
% 153.32/22.89    (26)   ~ (e3 = e0)
% 153.32/22.89    (27)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.32/22.89          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.32/22.89    (28)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.32/22.89          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.32/22.89    (29)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.32/22.89          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.89    (30)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 153.32/22.89            all_57_15 & $i(all_57_15))
% 153.32/22.89    (31)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.32/22.89          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.32/22.89    (32)  op(e3, e3) = e1
% 153.32/22.89    (33)  op(e2, e0) = all_52_13
% 153.32/22.89    (34)  op(e0, e3) = all_52_3
% 153.32/22.89    (35)  op(e1, e1) = e1
% 153.32/22.89    (36)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.32/22.89          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.32/22.89    (37)   ~ (all_52_7 = e0)
% 153.32/22.89    (38)   ~ (e1 = e0)
% 153.32/22.89    (39)   ~ (all_52_1 = e1)
% 153.32/22.89    (40)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.32/22.89          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.32/22.89    (41)   ~ (e3 = e2)
% 153.32/22.89    (42)  all_56_9 = e2
% 153.32/22.89    (43)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.32/22.89          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.32/22.89    (44)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.32/22.89          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.32/22.89    (45)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) = e1) |
% 153.32/22.89          (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) = e1)
% 153.32/22.89    (46)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.32/22.89          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.32/22.89    (47)   ~ (e2 = e1)
% 153.32/22.89    (48)   ~ (all_52_4 = e0)
% 153.32/22.89    (49)  all_56_1 = e3
% 153.32/22.89    (50)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.32/22.89          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.32/22.89    (51)   ~ (all_52_11 = e2)
% 153.32/22.89    (52)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.32/22.89          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.32/22.89    (53)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 153.32/22.89          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 153.32/22.89    (54)  op(e2, e2) = e0
% 153.32/22.89    (55)  op(e2, e3) = all_52_1
% 153.32/22.89  
% 153.32/22.89  Begin of proof
% 153.32/22.89  | 
% 153.32/22.89  | BETA: splitting (45) gives:
% 153.32/22.89  | 
% 153.32/22.89  | Case 1:
% 153.32/22.89  | | 
% 153.32/22.89  | |   (56)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_5 = e1 & op(e2, e1) =
% 153.32/22.89  | |           e1)
% 153.32/22.89  | | 
% 153.32/22.89  | | BETA: splitting (56) gives:
% 153.32/22.89  | | 
% 153.32/22.89  | | Case 1:
% 153.32/22.89  | | | 
% 153.32/22.89  | | |   (57)  all_56_4 = e1 & op(e3, e1) = e1
% 153.32/22.89  | | | 
% 153.32/22.89  | | | ALPHA: (57) implies:
% 153.32/22.89  | | |   (58)  all_56_4 = e1
% 153.32/22.89  | | | 
% 153.32/22.89  | | | REF_CLOSE: (15), (17), (26), (29), (32), (38), (42), (49), (58) are
% 153.32/22.89  | | |            inconsistent by sub-proof #566.
% 153.32/22.89  | | | 
% 153.32/22.89  | | Case 2:
% 153.32/22.89  | | | 
% 153.32/22.89  | | |   (59)  all_56_5 = e1 & op(e2, e1) = e1
% 153.32/22.89  | | | 
% 153.32/22.89  | | | ALPHA: (59) implies:
% 153.32/22.89  | | |   (60)  all_56_5 = e1
% 153.32/22.89  | | | 
% 153.32/22.89  | | | REF_CLOSE: (4), (5), (6), (7), (8), (15), (16), (17), (18), (21), (25),
% 153.32/22.89  | | |            (26), (27), (29), (31), (32), (33), (38), (41), (42), (44),
% 153.32/22.89  | | |            (47), (49), (50), (60) are inconsistent by sub-proof #571.
% 153.32/22.89  | | | 
% 153.32/22.89  | | End of split
% 153.32/22.89  | | 
% 153.32/22.89  | Case 2:
% 153.32/22.89  | | 
% 153.32/22.89  | |   (61)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_14 = e1 & op(e0, e1) =
% 153.32/22.89  | |           e1)
% 153.32/22.89  | | 
% 153.32/22.89  | | BETA: splitting (61) gives:
% 153.32/22.89  | | 
% 153.32/22.89  | | Case 1:
% 153.32/22.89  | | | 
% 153.32/22.89  | | |   (62)  all_56_8 = e1 & op(e1, e1) = e1
% 153.32/22.89  | | | 
% 153.32/22.89  | | | ALPHA: (62) implies:
% 153.32/22.89  | | |   (63)  all_56_8 = e1
% 153.32/22.89  | | | 
% 153.32/22.89  | | | COMBINE_EQS: (2), (63) imply:
% 153.32/22.89  | | |   (64)  e2 = e1
% 153.32/22.89  | | | 
% 153.32/22.89  | | | REF_CLOSE: (6), (15), (17), (26), (29), (32), (38), (41), (42), (47),
% 153.32/22.89  | | |            (49), (64) are inconsistent by sub-proof #581.
% 153.32/22.89  | | | 
% 153.32/22.89  | | Case 2:
% 153.32/22.89  | | | 
% 153.32/22.89  | | |   (65)  all_56_14 = e1 & op(e0, e1) = e1
% 153.32/22.89  | | | 
% 153.32/22.89  | | | ALPHA: (65) implies:
% 153.32/22.89  | | |   (66)  all_56_14 = e1
% 153.32/22.89  | | |   (67)  op(e0, e1) = e1
% 153.32/22.89  | | | 
% 153.32/22.89  | | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (11), (12), (13), (14),
% 153.32/22.89  | | |            (15), (16), (17), (18), (19), (20), (22), (23), (24), (26),
% 153.32/22.89  | | |            (28), (29), (30), (31), (32), (34), (35), (36), (37), (38),
% 153.32/22.89  | | |            (39), (40), (41), (42), (43), (46), (47), (48), (51), (52),
% 153.32/22.89  | | |            (53), (54), (55), (66), (67) are inconsistent by sub-proof
% 153.32/22.89  | | |            #559.
% 153.32/22.89  | | | 
% 153.32/22.89  | | End of split
% 153.32/22.89  | | 
% 153.32/22.89  | End of split
% 153.32/22.89  | 
% 153.32/22.89  End of proof
% 153.32/22.89  
% 153.32/22.89  Sub-proof #559 shows that the following formulas are inconsistent:
% 153.32/22.89  ----------------------------------------------------------------
% 153.32/22.89    (1)  op(e0, e1) = all_52_11
% 153.32/22.89    (2)  op(e0, e1) = e1
% 153.32/22.89    (3)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 153.32/22.89         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.32/22.89    (4)  all_56_13 = e2
% 153.32/22.89    (5)   ~ (e3 = e1)
% 153.32/22.89    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.32/22.89         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.32/22.89    (7)  op(e3, e2) = all_52_4
% 153.32/22.89    (8)  all_56_7 = e1
% 153.32/22.89    (9)  op(e0, e2) = all_52_7
% 153.32/22.89    (10)   ~ (all_52_14 = e2)
% 153.32/22.89    (11)   ~ (all_52_3 = all_52_7)
% 153.32/22.89    (12)  op(e1, e1) = all_4_2
% 153.32/22.89    (13)   ~ (e2 = e0)
% 153.32/22.89    (14)  all_56_14 = e1
% 153.32/22.89    (15)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.32/22.89          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.32/22.89    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.89    (17)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.89          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.89    (18)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 153.32/22.89          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 153.32/22.89    (19)  op(e0, e0) = e2
% 153.32/22.89    (20)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.89              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.32/22.89                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.32/22.89                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.32/22.89    (21)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.32/22.89          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.32/22.89    (22)  op(e1, e0) = all_52_14
% 153.32/22.89    (23)   ~ (e3 = e0)
% 153.32/22.89    (24)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.32/22.89          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.32/22.89    (25)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.32/22.89          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.89    (26)  (all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) =
% 153.32/22.89            all_57_15 & $i(all_57_15))
% 153.32/22.89    (27)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.32/22.89          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.32/22.89    (28)  op(e3, e3) = e1
% 153.32/22.89    (29)  op(e0, e3) = all_52_3
% 153.32/22.89    (30)  op(e1, e1) = e1
% 153.32/22.89    (31)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.32/22.89          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.32/22.89    (32)   ~ (all_52_7 = e0)
% 153.32/22.89    (33)   ~ (e1 = e0)
% 153.32/22.89    (34)   ~ (all_52_1 = e1)
% 153.32/22.89    (35)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.32/22.89          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.32/22.89    (36)   ~ (e3 = e2)
% 153.32/22.89    (37)  all_56_9 = e2
% 153.32/22.89    (38)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.32/22.89          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.32/22.89    (39)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.32/22.89          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.32/22.89    (40)   ~ (e2 = e1)
% 153.32/22.89    (41)   ~ (all_52_4 = e0)
% 153.32/22.89    (42)   ~ (all_52_11 = e2)
% 153.32/22.89    (43)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.32/22.89          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.32/22.89    (44)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 153.32/22.89          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 153.32/22.89    (45)  op(e2, e2) = e0
% 153.32/22.89    (46)  op(e2, e3) = all_52_1
% 153.32/22.89  
% 153.32/22.89  Begin of proof
% 153.32/22.89  | 
% 153.32/22.89  | BETA: splitting (25) gives:
% 153.32/22.89  | 
% 153.32/22.89  | Case 1:
% 153.32/22.89  | | 
% 153.32/22.89  | |   (47)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 153.32/22.89  | |           e0)
% 153.32/22.89  | | 
% 153.32/22.89  | | REF_CLOSE: (7), (16), (28), (33), (41), (47) are inconsistent by sub-proof
% 153.32/22.89  | |            #937.
% 153.32/22.89  | | 
% 153.32/22.89  | Case 2:
% 153.32/22.89  | | 
% 153.32/22.89  | |   (48)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 153.32/22.89  | |           e0)
% 153.32/22.89  | | 
% 153.32/22.89  | | BETA: splitting (48) gives:
% 153.32/22.89  | | 
% 153.32/22.89  | | Case 1:
% 153.32/22.89  | | | 
% 153.32/22.89  | | |   (49)  all_56_4 = e0 & op(e3, e1) = e0
% 153.32/22.89  | | | 
% 153.32/22.89  | | | ALPHA: (49) implies:
% 153.32/22.89  | | |   (50)  all_56_4 = e0
% 153.32/22.89  | | | 
% 153.32/22.89  | | | BETA: splitting (20) gives:
% 153.32/22.89  | | | 
% 153.32/22.89  | | | Case 1:
% 153.32/22.89  | | | | 
% 153.32/22.89  | | | |   (51)  all_56_15 = e0 & op(e0, e0) = e0
% 153.32/22.89  | | | | 
% 153.32/22.89  | | | | ALPHA: (51) implies:
% 153.32/22.89  | | | |   (52)  op(e0, e0) = e0
% 153.32/22.89  | | | | 
% 153.32/22.89  | | | | REF_CLOSE: (13), (16), (19), (52) are inconsistent by sub-proof #1043.
% 153.32/22.89  | | | | 
% 153.32/22.89  | | | Case 2:
% 153.32/22.89  | | | | 
% 153.32/22.89  | | | |   (53)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 153.32/22.89  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 153.32/22.89  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 153.32/22.89  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 153.32/22.89  | | | | 
% 153.32/22.89  | | | | ALPHA: (53) implies:
% 153.32/22.89  | | | |   (54)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 153.32/22.89  | | | |             e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.32/22.89  | | | |   (55)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0)
% 153.32/22.89  | | | |           = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.32/22.89  | | | | 
% 153.32/22.89  | | | | BETA: splitting (54) gives:
% 153.32/22.89  | | | | 
% 153.32/22.89  | | | | Case 1:
% 153.32/22.89  | | | | | 
% 153.32/22.89  | | | | |   (56)  all_56_12 = e0 & op(e0, e3) = e0
% 153.32/22.89  | | | | | 
% 153.32/22.89  | | | | | ALPHA: (56) implies:
% 153.32/22.89  | | | | |   (57)  op(e0, e3) = e0
% 153.32/22.89  | | | | | 
% 153.32/22.89  | | | | | BETA: splitting (35) gives:
% 153.32/22.89  | | | | | 
% 153.32/22.89  | | | | | Case 1:
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | |   (58)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1,
% 153.32/22.89  | | | | | |             e2) = e2)
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | | BETA: splitting (58) gives:
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | | Case 1:
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | |   (59)  all_56_6 = e2 & op(e1, e3) = e2
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | ALPHA: (59) implies:
% 153.32/22.89  | | | | | | |   (60)  all_56_6 = e2
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | BETA: splitting (26) gives:
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | |   (61)  all_57_8 = e0 & op(e0, e1) = e0
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | | ALPHA: (61) implies:
% 153.32/22.89  | | | | | | | |   (62)  op(e0, e1) = e0
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | | REF_CLOSE: (2), (16), (33), (62) are inconsistent by sub-proof
% 153.32/22.89  | | | | | | | |            #899.
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | |   (63)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 153.32/22.89  | | | | | | | |         $i(all_57_15)
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | | ALPHA: (63) implies:
% 153.32/22.89  | | | | | | | |   (64)   ~ (all_57_15 = e1)
% 153.32/22.89  | | | | | | | |   (65)  op(e0, e0) = all_57_15
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | | BETA: splitting (18) gives:
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | | 
% 153.32/22.89  | | | | | | | | |   (66)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 &
% 153.32/22.89  | | | | | | | | |           op(e2, e1) = e2)
% 153.32/22.89  | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | BETA: splitting (66) gives:
% 153.32/22.89  | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | |   (67)  all_56_4 = e2 & op(e3, e1) = e2
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | ALPHA: (67) implies:
% 153.32/22.89  | | | | | | | | | |   (68)  all_56_4 = e2
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | REF_CLOSE: (7), (13), (16), (25), (28), (33), (37), (41),
% 153.32/22.89  | | | | | | | | | |            (68) are inconsistent by sub-proof #583.
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | |   (69)  all_56_5 = e2 & op(e2, e1) = e2
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | ALPHA: (69) implies:
% 153.32/22.89  | | | | | | | | | |   (70)  all_56_5 = e2
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | BETA: splitting (44) gives:
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | |   (71)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 153.32/22.89  | | | | | | | | | | |           & op(e1, e2) = e3)
% 153.32/22.89  | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | BETA: splitting (71) gives:
% 153.32/22.89  | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | |   (72)  all_56_6 = e3 & op(e1, e3) = e3
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | REF_CLOSE: (36), (60), (72) are inconsistent by sub-proof
% 153.32/22.89  | | | | | | | | | | | |            #570.
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | |   (73)  all_56_7 = e3 & op(e1, e2) = e3
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | ALPHA: (73) implies:
% 153.32/22.89  | | | | | | | | | | | |   (74)  all_56_7 = e3
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | REF_CLOSE: (5), (8), (74) are inconsistent by sub-proof
% 153.32/22.89  | | | | | | | | | | | |            #1106.
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | End of split
% 153.32/22.89  | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | |   (75)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 153.32/22.89  | | | | | | | | | | |           e3 & op(e1, e0) = e3)
% 153.32/22.89  | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | BETA: splitting (75) gives:
% 153.32/22.89  | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | |   (76)  all_56_8 = e3 & op(e1, e1) = e3
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | ALPHA: (76) implies:
% 153.32/22.89  | | | | | | | | | | | |   (77)  op(e1, e1) = e3
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | REF_CLOSE: (5), (16), (30), (77) are inconsistent by
% 153.32/22.89  | | | | | | | | | | | |            sub-proof #734.
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | |   (78)  all_56_11 = e3 & op(e1, e0) = e3
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | ALPHA: (78) implies:
% 153.32/22.89  | | | | | | | | | | | |   (79)  all_56_11 = e3
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | BETA: splitting (38) gives:
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | |   (80)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1
% 153.32/22.89  | | | | | | | | | | | | |           & op(e2, e2) = e1)
% 153.32/22.89  | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | REF_CLOSE: (16), (33), (34), (45), (46), (80) are
% 153.32/22.89  | | | | | | | | | | | | |            inconsistent by sub-proof #603.
% 153.32/22.89  | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | |   (81)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 =
% 153.32/22.89  | | | | | | | | | | | | |           e1 & op(e2, e0) = e1)
% 153.32/22.89  | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | BETA: splitting (81) gives:
% 153.32/22.89  | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | |   (82)  all_56_5 = e1 & op(e2, e1) = e1
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | ALPHA: (82) implies:
% 153.32/22.89  | | | | | | | | | | | | | |   (83)  all_56_5 = e1
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | COMBINE_EQS: (70), (83) imply:
% 153.32/22.89  | | | | | | | | | | | | | |   (84)  e2 = e1
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | SIMP: (84) implies:
% 153.32/22.89  | | | | | | | | | | | | | |   (85)  e2 = e1
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | COMBINE_EQS: (37), (85) imply:
% 153.32/22.89  | | | | | | | | | | | | | |   (86)  all_56_9 = e1
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (13), (16), (17), (23), (28), (36),
% 153.32/22.89  | | | | | | | | | | | | | |            (40), (50), (86) are inconsistent by sub-proof
% 153.32/22.89  | | | | | | | | | | | | | |            #914.
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | |   (87)  all_56_10 = e1 & op(e2, e0) = e1
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | ALPHA: (87) implies:
% 153.32/22.89  | | | | | | | | | | | | | |   (88)  all_56_10 = e1
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | |   (89)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 153.32/22.89  | | | | | | | | | | | | | | |           & op(e2, e1) = e3)
% 153.32/22.89  | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 153.32/22.89  | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | |   (90)  all_56_4 = e3 & op(e3, e1) = e3
% 153.32/22.89  | | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | | REF_CLOSE: (23), (50), (90) are inconsistent by sub-proof
% 153.32/22.89  | | | | | | | | | | | | | | | |            #641.
% 153.32/22.89  | | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | |   (91)  all_56_5 = e3 & op(e2, e1) = e3
% 153.32/22.89  | | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | | ALPHA: (91) implies:
% 153.32/22.89  | | | | | | | | | | | | | | | |   (92)  all_56_5 = e3
% 153.32/22.89  | | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (92) imply:
% 153.32/22.89  | | | | | | | | | | | | | | | |   (93)  e3 = e2
% 153.32/22.89  | | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | | COMBINE_EQS: (79), (93) imply:
% 153.32/22.89  | | | | | | | | | | | | | | | |   (94)  all_56_11 = e2
% 153.32/22.89  | | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | | REF_CLOSE: (13), (33), (37), (55), (88), (94) are
% 153.32/22.89  | | | | | | | | | | | | | | | |            inconsistent by sub-proof #567.
% 153.32/22.89  | | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | End of split
% 153.32/22.89  | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | |   (95)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 153.32/22.89  | | | | | | | | | | | | | | |           e3 & op(e0, e1) = e3)
% 153.32/22.89  | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | | REF_CLOSE: (5), (14), (16), (30), (95) are inconsistent by
% 153.32/22.89  | | | | | | | | | | | | | | |            sub-proof #638.
% 153.32/22.89  | | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | | End of split
% 153.32/22.89  | | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | | End of split
% 153.32/22.89  | | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | | End of split
% 153.32/22.89  | | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | | End of split
% 153.32/22.89  | | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | End of split
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | End of split
% 153.32/22.89  | | | | | | | | | 
% 153.32/22.89  | | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | | 
% 153.32/22.89  | | | | | | | | |   (96)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 &
% 153.32/22.89  | | | | | | | | |           op(e0, e1) = e2)
% 153.32/22.89  | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | BETA: splitting (96) gives:
% 153.32/22.89  | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | |   (97)  all_56_8 = e2 & op(e1, e1) = e2
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | ALPHA: (97) implies:
% 153.32/22.89  | | | | | | | | | |   (98)  op(e1, e1) = e2
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 153.32/22.89  | | | | | | | | | |            (15), (16), (17), (19), (21), (23), (24), (25),
% 153.32/22.89  | | | | | | | | | |            (27), (28), (29), (30), (31), (33), (34), (36),
% 153.32/22.89  | | | | | | | | | |            (37), (38), (39), (40), (43), (44), (45), (46),
% 153.32/22.89  | | | | | | | | | |            (50), (54), (55), (57), (64), (65), (98) are
% 153.32/22.89  | | | | | | | | | |            inconsistent by sub-proof #560.
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | |   (99)  all_56_14 = e2 & op(e0, e1) = e2
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | ALPHA: (99) implies:
% 153.32/22.89  | | | | | | | | | |   (100)  op(e0, e1) = e2
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | | REF_CLOSE: (1), (16), (42), (100) are inconsistent by
% 153.32/22.89  | | | | | | | | | |            sub-proof #1092.
% 153.32/22.89  | | | | | | | | | | 
% 153.32/22.89  | | | | | | | | | End of split
% 153.32/22.89  | | | | | | | | | 
% 153.32/22.89  | | | | | | | | End of split
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | End of split
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | Case 2:
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | |   (101)  all_56_7 = e2 & op(e1, e2) = e2
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | ALPHA: (101) implies:
% 153.32/22.89  | | | | | | |   (102)  all_56_7 = e2
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | COMBINE_EQS: (8), (102) imply:
% 153.32/22.89  | | | | | | |   (103)  e2 = e1
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | COMBINE_EQS: (37), (103) imply:
% 153.32/22.89  | | | | | | |   (104)  all_56_9 = e1
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | REF_CLOSE: (5), (6), (13), (16), (17), (23), (28), (36), (40),
% 153.32/22.89  | | | | | | |            (50), (104) are inconsistent by sub-proof #914.
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | End of split
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | Case 2:
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | |   (105)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 &
% 153.32/22.89  | | | | | |            op(e1, e0) = e2)
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | | BETA: splitting (105) gives:
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | | Case 1:
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | |   (106)  all_56_8 = e2 & op(e1, e1) = e2
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | ALPHA: (106) implies:
% 153.32/22.89  | | | | | | |   (107)  op(e1, e1) = e2
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | BETA: splitting (26) gives:
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | Case 1:
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | |   (108)  all_57_8 = e0 & op(e0, e1) = e0
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | | ALPHA: (108) implies:
% 153.32/22.89  | | | | | | | |   (109)  op(e0, e1) = e0
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | | REF_CLOSE: (2), (16), (33), (109) are inconsistent by sub-proof
% 153.32/22.89  | | | | | | | |            #899.
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | Case 2:
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | |   (110)   ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 153.32/22.89  | | | | | | | |          $i(all_57_15)
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | | ALPHA: (110) implies:
% 153.32/22.89  | | | | | | | |   (111)   ~ (all_57_15 = e1)
% 153.32/22.89  | | | | | | | |   (112)  op(e0, e0) = all_57_15
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 153.32/22.89  | | | | | | | |            (15), (16), (17), (19), (21), (23), (24), (25), (27),
% 153.32/22.89  | | | | | | | |            (28), (29), (30), (31), (33), (34), (36), (37), (38),
% 153.32/22.89  | | | | | | | |            (39), (40), (43), (44), (45), (46), (50), (54), (55),
% 153.32/22.89  | | | | | | | |            (57), (107), (111), (112) are inconsistent by
% 153.32/22.89  | | | | | | | |            sub-proof #560.
% 153.32/22.89  | | | | | | | | 
% 153.32/22.89  | | | | | | | End of split
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | Case 2:
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | |   (113)  all_56_11 = e2 & op(e1, e0) = e2
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | ALPHA: (113) implies:
% 153.32/22.89  | | | | | | |   (114)  op(e1, e0) = e2
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | | REF_CLOSE: (10), (16), (22), (114) are inconsistent by sub-proof
% 153.32/22.89  | | | | | | |            #974.
% 153.32/22.89  | | | | | | | 
% 153.32/22.89  | | | | | | End of split
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | End of split
% 153.32/22.89  | | | | | 
% 153.32/22.89  | | | | Case 2:
% 153.32/22.89  | | | | | 
% 153.32/22.89  | | | | |   (115)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0,
% 153.32/22.89  | | | | |              e1) = e0)
% 153.32/22.89  | | | | | 
% 153.32/22.89  | | | | | BETA: splitting (115) gives:
% 153.32/22.89  | | | | | 
% 153.32/22.89  | | | | | Case 1:
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | |   (116)  all_56_13 = e0 & op(e0, e2) = e0
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | | ALPHA: (116) implies:
% 153.32/22.89  | | | | | |   (117)  op(e0, e2) = e0
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | | REF_CLOSE: (9), (16), (32), (117) are inconsistent by sub-proof
% 153.32/22.89  | | | | | |            #1036.
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | Case 2:
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | |   (118)  all_56_14 = e0 & op(e0, e1) = e0
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | | ALPHA: (118) implies:
% 153.32/22.89  | | | | | |   (119)  op(e0, e1) = e0
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | | REF_CLOSE: (2), (16), (33), (119) are inconsistent by sub-proof
% 153.32/22.89  | | | | | |            #899.
% 153.32/22.89  | | | | | | 
% 153.32/22.89  | | | | | End of split
% 153.32/22.89  | | | | | 
% 153.32/22.89  | | | | End of split
% 153.32/22.89  | | | | 
% 153.32/22.89  | | | End of split
% 153.32/22.89  | | | 
% 153.32/22.89  | | Case 2:
% 153.32/22.89  | | | 
% 153.32/22.89  | | |   (120)  all_56_9 = e0 & op(e3, e0) = e0
% 153.32/22.89  | | | 
% 153.32/22.89  | | | REF_CLOSE: (13), (37), (120) are inconsistent by sub-proof #746.
% 153.32/22.89  | | | 
% 153.32/22.89  | | End of split
% 153.32/22.89  | | 
% 153.32/22.89  | End of split
% 153.32/22.89  | 
% 153.32/22.89  End of proof
% 153.32/22.89  
% 153.32/22.89  Sub-proof #560 shows that the following formulas are inconsistent:
% 153.32/22.89  ----------------------------------------------------------------
% 153.32/22.89    (1)  all_56_13 = e2
% 153.32/22.89    (2)   ~ (e3 = e1)
% 153.32/22.89    (3)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.32/22.89         (all_56_14 = e0 & op(e0, e1) = e0)
% 153.32/22.89    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.32/22.89         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.32/22.89    (5)  all_56_4 = e0
% 153.32/22.89    (6)  op(e1, e1) = e2
% 153.32/22.89    (7)  all_56_7 = e1
% 153.32/22.89    (8)  op(e0, e2) = all_52_7
% 153.32/22.89    (9)   ~ (all_52_3 = all_52_7)
% 153.32/22.89    (10)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 153.32/22.89          (all_56_11 = e0 & op(e1, e0) = e0)
% 153.32/22.89    (11)  op(e1, e1) = all_4_2
% 153.32/22.89    (12)   ~ (e2 = e0)
% 153.32/22.89    (13)  all_56_14 = e1
% 153.32/22.89    (14)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.32/22.89          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.32/22.89    (15)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.89            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.89    (16)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.89          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.89    (17)  op(e0, e3) = e0
% 153.32/22.89    (18)  op(e0, e0) = e2
% 153.32/22.89    (19)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.32/22.89          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.32/22.89    (20)   ~ (e3 = e0)
% 153.32/22.90    (21)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.32/22.90          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.32/22.90    (22)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.32/22.90          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.90    (23)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.32/22.90          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.32/22.90    (24)  op(e3, e3) = e1
% 153.32/22.90    (25)  op(e0, e3) = all_52_3
% 153.32/22.90    (26)   ~ (all_57_15 = e1)
% 153.32/22.90    (27)  op(e1, e1) = e1
% 153.32/22.90    (28)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.32/22.90          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.32/22.90    (29)   ~ (e1 = e0)
% 153.32/22.90    (30)   ~ (all_52_1 = e1)
% 153.32/22.90    (31)  op(e0, e0) = all_57_15
% 153.32/22.90    (32)   ~ (e3 = e2)
% 153.32/22.90    (33)  all_56_9 = e2
% 153.32/22.90    (34)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.32/22.90          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.32/22.90    (35)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.32/22.90          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.32/22.90    (36)   ~ (e2 = e1)
% 153.32/22.90    (37)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.32/22.90          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.32/22.90    (38)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 153.32/22.90          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 153.32/22.90    (39)  op(e2, e2) = e0
% 153.32/22.90    (40)  op(e2, e3) = all_52_1
% 153.32/22.90  
% 153.32/22.90  Begin of proof
% 153.32/22.90  | 
% 153.32/22.90  | BETA: splitting (10) gives:
% 153.32/22.90  | 
% 153.32/22.90  | Case 1:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (41)  all_56_9 = e0 & op(e3, e0) = e0
% 153.32/22.90  | | 
% 153.32/22.90  | | ALPHA: (41) implies:
% 153.32/22.90  | |   (42)  all_56_9 = e0
% 153.32/22.90  | | 
% 153.32/22.90  | | REF_CLOSE: (12), (33), (42) are inconsistent by sub-proof #776.
% 153.32/22.90  | | 
% 153.32/22.90  | Case 2:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (43)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.32/22.90  | |           e0)
% 153.32/22.90  | | 
% 153.32/22.90  | | BETA: splitting (43) gives:
% 153.32/22.90  | | 
% 153.32/22.90  | | Case 1:
% 153.32/22.90  | | | 
% 153.32/22.90  | | |   (44)  all_56_10 = e0 & op(e2, e0) = e0
% 153.32/22.90  | | | 
% 153.32/22.90  | | | ALPHA: (44) implies:
% 153.32/22.90  | | |   (45)  all_56_10 = e0
% 153.32/22.90  | | | 
% 153.32/22.90  | | | BETA: splitting (34) gives:
% 153.32/22.90  | | | 
% 153.32/22.90  | | | Case 1:
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | |   (46)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2)
% 153.32/22.90  | | | |           = e1)
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | | REF_CLOSE: (15), (29), (30), (39), (40), (46) are inconsistent by
% 153.32/22.90  | | | |            sub-proof #603.
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | Case 2:
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | |   (47)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0)
% 153.32/22.90  | | | |           = e1)
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | | BETA: splitting (47) gives:
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | | Case 1:
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | |   (48)  all_56_5 = e1 & op(e2, e1) = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | ALPHA: (48) implies:
% 153.32/22.90  | | | | |   (49)  all_56_5 = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | BETA: splitting (37) gives:
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | Case 1:
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | |   (50)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2,
% 153.32/22.90  | | | | | |             e2) = e3)
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | | BETA: splitting (50) gives:
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | | Case 1:
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | |   (51)  all_56_1 = e3 & op(e3, e2) = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | ALPHA: (51) implies:
% 153.32/22.90  | | | | | | |   (52)  all_56_1 = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | BETA: splitting (28) gives:
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | |   (53)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 &
% 153.32/22.90  | | | | | | | |           op(e2, e2) = e3)
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | | BETA: splitting (53) gives:
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | |   (54)  all_56_2 = e3 & op(e2, e3) = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | ALPHA: (54) implies:
% 153.32/22.90  | | | | | | | | |   (55)  all_56_2 = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | REF_CLOSE: (12), (14), (15), (32), (36), (39), (45), (49),
% 153.32/22.90  | | | | | | | | |            (55) are inconsistent by sub-proof #565.
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | |   (56)  all_56_3 = e3 & op(e2, e2) = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | ALPHA: (56) implies:
% 153.32/22.90  | | | | | | | | |   (57)  op(e2, e2) = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | REF_CLOSE: (15), (20), (39), (57) are inconsistent by
% 153.32/22.90  | | | | | | | | |            sub-proof #719.
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | |   (58)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 &
% 153.32/22.90  | | | | | | | |           op(e2, e0) = e3)
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | | BETA: splitting (58) gives:
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | |   (59)  all_56_5 = e3 & op(e2, e1) = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | ALPHA: (59) implies:
% 153.32/22.90  | | | | | | | | |   (60)  all_56_5 = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | COMBINE_EQS: (49), (60) imply:
% 153.32/22.90  | | | | | | | | |   (61)  e3 = e1
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | COMBINE_EQS: (52), (61) imply:
% 153.32/22.90  | | | | | | | | |   (62)  all_56_1 = e1
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | REF_CLOSE: (2), (5), (15), (16), (20), (24), (32), (33), (62)
% 153.32/22.90  | | | | | | | | |            are inconsistent by sub-proof #593.
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | |   (63)  all_56_10 = e3 & op(e2, e0) = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | REF_CLOSE: (20), (45), (63) are inconsistent by sub-proof
% 153.32/22.90  | | | | | | | | |            #813.
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | End of split
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | Case 2:
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | |   (64)  all_56_3 = e3 & op(e2, e2) = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | ALPHA: (64) implies:
% 153.32/22.90  | | | | | | |   (65)  op(e2, e2) = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | REF_CLOSE: (15), (20), (39), (65) are inconsistent by sub-proof
% 153.32/22.90  | | | | | | |            #719.
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | End of split
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | Case 2:
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | |   (66)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0,
% 153.32/22.90  | | | | | |             e2) = e3)
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | | BETA: splitting (66) gives:
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | | Case 1:
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | |   (67)  all_56_7 = e3 & op(e1, e2) = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | REF_CLOSE: (2), (7), (67) are inconsistent by sub-proof #564.
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | Case 2:
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | |   (68)  all_56_13 = e3 & op(e0, e2) = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | REF_CLOSE: (1), (32), (68) are inconsistent by sub-proof #563.
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | End of split
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | End of split
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | Case 2:
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | |   (69)  all_56_10 = e1 & op(e2, e0) = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | ALPHA: (69) implies:
% 153.32/22.90  | | | | |   (70)  all_56_10 = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | REF_CLOSE: (29), (45), (70) are inconsistent by sub-proof #963.
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | End of split
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | End of split
% 153.32/22.90  | | | 
% 153.32/22.90  | | Case 2:
% 153.32/22.90  | | | 
% 153.32/22.90  | | |   (71)  all_56_11 = e0 & op(e1, e0) = e0
% 153.32/22.90  | | | 
% 153.32/22.90  | | | ALPHA: (71) implies:
% 153.32/22.90  | | |   (72)  all_56_11 = e0
% 153.32/22.90  | | | 
% 153.32/22.90  | | | BETA: splitting (21) gives:
% 153.32/22.90  | | | 
% 153.32/22.90  | | | Case 1:
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | |   (73)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0)
% 153.32/22.90  | | | |           = e1)
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | | BETA: splitting (73) gives:
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | | Case 1:
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | |   (74)  all_56_9 = e1 & op(e3, e0) = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | ALPHA: (74) implies:
% 153.32/22.90  | | | | |   (75)  all_56_9 = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | REF_CLOSE: (2), (4), (5), (12), (15), (16), (20), (24), (32), (36),
% 153.32/22.90  | | | | |            (75) are inconsistent by sub-proof #914.
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | Case 2:
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | |   (76)  all_56_10 = e1 & op(e2, e0) = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | ALPHA: (76) implies:
% 153.32/22.90  | | | | |   (77)  all_56_10 = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | BETA: splitting (38) gives:
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | Case 1:
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | |   (78)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1,
% 153.32/22.90  | | | | | |             e2) = e3)
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | | BETA: splitting (78) gives:
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | | Case 1:
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | |   (79)  all_56_6 = e3 & op(e1, e3) = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | ALPHA: (79) implies:
% 153.32/22.90  | | | | | | |   (80)  all_56_6 = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | BETA: splitting (37) gives:
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | |   (81)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 &
% 153.32/22.90  | | | | | | | |           op(e2, e2) = e3)
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | | BETA: splitting (81) gives:
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | |   (82)  all_56_1 = e3 & op(e3, e2) = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | ALPHA: (82) implies:
% 153.32/22.90  | | | | | | | | |   (83)  all_56_1 = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | BETA: splitting (23) gives:
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | |   (84)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 &
% 153.32/22.90  | | | | | | | | | |           op(e2, e3) = e2)
% 153.32/22.90  | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | BETA: splitting (84) gives:
% 153.32/22.90  | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | |   (85)  all_56_0 = e2 & op(e3, e3) = e2
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | ALPHA: (85) implies:
% 153.32/22.90  | | | | | | | | | | |   (86)  op(e3, e3) = e2
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | REF_CLOSE: (2), (12), (15), (19), (20), (22), (29), (33),
% 153.32/22.90  | | | | | | | | | | |            (36), (83), (86) are inconsistent by sub-proof
% 153.32/22.90  | | | | | | | | | | |            #654.
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | |   (87)  all_56_2 = e2 & op(e2, e3) = e2
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | ALPHA: (87) implies:
% 153.32/22.90  | | | | | | | | | | |   (88)  all_56_2 = e2
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | BETA: splitting (35) gives:
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | |   (89)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 =
% 153.32/22.90  | | | | | | | | | | | |           e3 & op(e2, e0) = e3)
% 153.32/22.90  | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | BETA: splitting (89) gives:
% 153.32/22.90  | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | |   (90)  all_56_9 = e3 & op(e3, e0) = e3
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | REF_CLOSE: (32), (33), (90) are inconsistent by sub-proof
% 153.32/22.90  | | | | | | | | | | | | |            #594.
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | |   (91)  all_56_10 = e3 & op(e2, e0) = e3
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | REF_CLOSE: (2), (5), (15), (16), (20), (24), (32), (33),
% 153.32/22.90  | | | | | | | | | | | | |            (77), (83), (91) are inconsistent by sub-proof
% 153.32/22.90  | | | | | | | | | | | | |            #562.
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | |   (92)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 =
% 153.32/22.90  | | | | | | | | | | | |           e3 & op(e0, e0) = e3)
% 153.32/22.90  | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | BETA: splitting (92) gives:
% 153.32/22.90  | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | |   (93)  all_56_11 = e3 & op(e1, e0) = e3
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | REF_CLOSE: (20), (72), (93) are inconsistent by sub-proof
% 153.32/22.90  | | | | | | | | | | | | |            #561.
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | |   (94)  all_56_15 = e3 & op(e0, e0) = e3
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | ALPHA: (94) implies:
% 153.32/22.90  | | | | | | | | | | | | |   (95)  op(e0, e0) = e3
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | BETA: splitting (28) gives:
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | |   (96)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3
% 153.32/22.90  | | | | | | | | | | | | | |           & op(e2, e2) = e3)
% 153.32/22.90  | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | BETA: splitting (96) gives:
% 153.32/22.90  | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | |   (97)  all_56_2 = e3 & op(e2, e3) = e3
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 153.32/22.90  | | | | | | | | | | | | | | |   (98)  all_56_2 = e3
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | REF_CLOSE: (32), (88), (98) are inconsistent by sub-proof
% 153.32/22.90  | | | | | | | | | | | | | | |            #685.
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | |   (99)  all_56_3 = e3 & op(e2, e2) = e3
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 153.32/22.90  | | | | | | | | | | | | | | |   (100)  op(e2, e2) = e3
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | REF_CLOSE: (15), (20), (39), (100) are inconsistent by
% 153.32/22.90  | | | | | | | | | | | | | | |            sub-proof #719.
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | |   (101)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 =
% 153.32/22.90  | | | | | | | | | | | | | |            e3 & op(e2, e0) = e3)
% 153.32/22.90  | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 153.32/22.90  | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with e3, all_57_15, e0, e0,
% 153.32/22.90  | | | | | | | | | | | | | | |              simplifying with (31), (95) gives:
% 153.32/22.90  | | | | | | | | | | | | | | |   (102)  all_57_15 = e3
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with e2, all_57_15, e0, e0,
% 153.32/22.90  | | | | | | | | | | | | | | |              simplifying with (18), (31) gives:
% 153.32/22.90  | | | | | | | | | | | | | | |   (103)  all_57_15 = e2
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_4_2, e1, e1, e1,
% 153.32/22.90  | | | | | | | | | | | | | | |              simplifying with (11), (27) gives:
% 153.32/22.90  | | | | | | | | | | | | | | |   (104)  all_4_2 = e1
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | GROUND_INST: instantiating (15) with all_4_2, e2, e1, e1,
% 153.32/22.90  | | | | | | | | | | | | | | |              simplifying with (6), (11) gives:
% 153.32/22.90  | | | | | | | | | | | | | | |   (105)  all_4_2 = e2
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | COMBINE_EQS: (102), (103) imply:
% 153.32/22.90  | | | | | | | | | | | | | | |   (106)  e3 = e2
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | SIMP: (106) implies:
% 153.32/22.90  | | | | | | | | | | | | | | |   (107)  e3 = e2
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | COMBINE_EQS: (104), (105) imply:
% 153.32/22.90  | | | | | | | | | | | | | | |   (108)  e2 = e1
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | SIMP: (108) implies:
% 153.32/22.90  | | | | | | | | | | | | | | |   (109)  e2 = e1
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | COMBINE_EQS: (107), (109) imply:
% 153.32/22.90  | | | | | | | | | | | | | | |   (110)  e3 = e1
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | COMBINE_EQS: (83), (110) imply:
% 153.32/22.90  | | | | | | | | | | | | | | |   (111)  all_56_1 = e1
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (15), (16), (20), (24), (32), (33),
% 153.32/22.90  | | | | | | | | | | | | | | |            (111) are inconsistent by sub-proof #593.
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | |   (112)  all_56_10 = e3 & op(e2, e0) = e3
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (15), (16), (20), (24), (32), (33),
% 153.32/22.90  | | | | | | | | | | | | | | |            (77), (83), (112) are inconsistent by sub-proof
% 153.32/22.90  | | | | | | | | | | | | | | |            #562.
% 153.32/22.90  | | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | |   (113)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2
% 153.32/22.90  | | | | | | | | | |            & op(e0, e3) = e2)
% 153.32/22.90  | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | BETA: splitting (113) gives:
% 153.32/22.90  | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | |   (114)  all_56_6 = e2 & op(e1, e3) = e2
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | ALPHA: (114) implies:
% 153.32/22.90  | | | | | | | | | | |   (115)  all_56_6 = e2
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | REF_CLOSE: (32), (80), (115) are inconsistent by sub-proof
% 153.32/22.90  | | | | | | | | | | |            #1057.
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | |   (116)  all_56_12 = e2 & op(e0, e3) = e2
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | ALPHA: (116) implies:
% 153.32/22.90  | | | | | | | | | | |   (117)  all_56_12 = e2
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | | REF_CLOSE: (3), (8), (9), (12), (13), (15), (17), (25), (29),
% 153.32/22.90  | | | | | | | | | | |            (117) are inconsistent by sub-proof #1117.
% 153.32/22.90  | | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | |   (118)  all_56_3 = e3 & op(e2, e2) = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | ALPHA: (118) implies:
% 153.32/22.90  | | | | | | | | |   (119)  op(e2, e2) = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | REF_CLOSE: (15), (20), (39), (119) are inconsistent by
% 153.32/22.90  | | | | | | | | |            sub-proof #719.
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | |   (120)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 &
% 153.32/22.90  | | | | | | | |            op(e0, e2) = e3)
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | | BETA: splitting (120) gives:
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | | Case 1:
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | |   (121)  all_56_7 = e3 & op(e1, e2) = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | REF_CLOSE: (2), (7), (121) are inconsistent by sub-proof #564.
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | Case 2:
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | |   (122)  all_56_13 = e3 & op(e0, e2) = e3
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | | REF_CLOSE: (1), (32), (122) are inconsistent by sub-proof
% 153.32/22.90  | | | | | | | | |            #563.
% 153.32/22.90  | | | | | | | | | 
% 153.32/22.90  | | | | | | | | End of split
% 153.32/22.90  | | | | | | | | 
% 153.32/22.90  | | | | | | | End of split
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | Case 2:
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | |   (123)  all_56_7 = e3 & op(e1, e2) = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | REF_CLOSE: (2), (7), (123) are inconsistent by sub-proof #564.
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | End of split
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | Case 2:
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | |   (124)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 &
% 153.32/22.90  | | | | | |            op(e1, e0) = e3)
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | | BETA: splitting (124) gives:
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | | Case 1:
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | |   (125)  all_56_8 = e3 & op(e1, e1) = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | ALPHA: (125) implies:
% 153.32/22.90  | | | | | | |   (126)  op(e1, e1) = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | REF_CLOSE: (6), (15), (32), (126) are inconsistent by sub-proof
% 153.32/22.90  | | | | | | |            #834.
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | Case 2:
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | |   (127)  all_56_11 = e3 & op(e1, e0) = e3
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | | REF_CLOSE: (20), (72), (127) are inconsistent by sub-proof #561.
% 153.32/22.90  | | | | | | | 
% 153.32/22.90  | | | | | | End of split
% 153.32/22.90  | | | | | | 
% 153.32/22.90  | | | | | End of split
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | End of split
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | Case 2:
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | |   (128)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0,
% 153.32/22.90  | | | |              e0) = e1)
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | | BETA: splitting (128) gives:
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | | Case 1:
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | |   (129)  all_56_11 = e1 & op(e1, e0) = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | ALPHA: (129) implies:
% 153.32/22.90  | | | | |   (130)  all_56_11 = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | REF_CLOSE: (29), (72), (130) are inconsistent by sub-proof #745.
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | Case 2:
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | |   (131)  all_56_15 = e1 & op(e0, e0) = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | ALPHA: (131) implies:
% 153.32/22.90  | | | | |   (132)  op(e0, e0) = e1
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | | REF_CLOSE: (15), (26), (31), (132) are inconsistent by sub-proof #940.
% 153.32/22.90  | | | | | 
% 153.32/22.90  | | | | End of split
% 153.32/22.90  | | | | 
% 153.32/22.90  | | | End of split
% 153.32/22.90  | | | 
% 153.32/22.90  | | End of split
% 153.32/22.90  | | 
% 153.32/22.90  | End of split
% 153.32/22.90  | 
% 153.32/22.90  End of proof
% 153.32/22.90  
% 153.32/22.90  Sub-proof #561 shows that the following formulas are inconsistent:
% 153.32/22.90  ----------------------------------------------------------------
% 153.32/22.90    (1)  all_56_11 = e3 & op(e1, e0) = e3
% 153.32/22.90    (2)  all_56_11 = e0
% 153.32/22.90    (3)   ~ (e3 = e0)
% 153.32/22.90  
% 153.32/22.90  Begin of proof
% 153.32/22.90  | 
% 153.32/22.90  | ALPHA: (1) implies:
% 153.32/22.90  |   (4)  all_56_11 = e3
% 153.32/22.90  | 
% 153.32/22.90  | COMBINE_EQS: (2), (4) imply:
% 153.32/22.90  |   (5)  e3 = e0
% 153.32/22.90  | 
% 153.32/22.90  | REDUCE: (3), (5) imply:
% 153.32/22.90  |   (6)  $false
% 153.32/22.90  | 
% 153.32/22.90  | CLOSE: (6) is inconsistent.
% 153.32/22.90  | 
% 153.32/22.90  End of proof
% 153.32/22.90  
% 153.32/22.90  Sub-proof #562 shows that the following formulas are inconsistent:
% 153.32/22.90  ----------------------------------------------------------------
% 153.32/22.90    (1)   ~ (e3 = e1)
% 153.32/22.90    (2)  all_56_4 = e0
% 153.32/22.90    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.90    (4)  all_56_10 = e3 & op(e2, e0) = e3
% 153.32/22.90    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.90         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.90    (6)  all_56_10 = e1
% 153.32/22.90    (7)   ~ (e3 = e0)
% 153.32/22.90    (8)  op(e3, e3) = e1
% 153.32/22.90    (9)   ~ (e3 = e2)
% 153.32/22.90    (10)  all_56_9 = e2
% 153.32/22.90    (11)  all_56_1 = e3
% 153.32/22.90  
% 153.32/22.90  Begin of proof
% 153.32/22.90  | 
% 153.32/22.90  | ALPHA: (4) implies:
% 153.32/22.90  |   (12)  all_56_10 = e3
% 153.32/22.90  | 
% 153.32/22.90  | COMBINE_EQS: (6), (12) imply:
% 153.32/22.90  |   (13)  e3 = e1
% 153.32/22.90  | 
% 153.32/22.90  | COMBINE_EQS: (11), (13) imply:
% 153.32/22.90  |   (14)  all_56_1 = e1
% 153.32/22.90  | 
% 153.32/22.90  | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (14) are inconsistent by
% 153.32/22.90  |            sub-proof #593.
% 153.32/22.90  | 
% 153.32/22.90  End of proof
% 153.32/22.90  
% 153.32/22.90  Sub-proof #563 shows that the following formulas are inconsistent:
% 153.32/22.90  ----------------------------------------------------------------
% 153.32/22.90    (1)  all_56_13 = e3 & op(e0, e2) = e3
% 153.32/22.90    (2)  all_56_13 = e2
% 153.32/22.90    (3)   ~ (e3 = e2)
% 153.32/22.90  
% 153.32/22.90  Begin of proof
% 153.32/22.90  | 
% 153.32/22.90  | ALPHA: (1) implies:
% 153.32/22.90  |   (4)  all_56_13 = e3
% 153.32/22.90  | 
% 153.32/22.90  | COMBINE_EQS: (2), (4) imply:
% 153.32/22.90  |   (5)  e3 = e2
% 153.32/22.90  | 
% 153.32/22.90  | REDUCE: (3), (5) imply:
% 153.32/22.90  |   (6)  $false
% 153.32/22.90  | 
% 153.32/22.90  | CLOSE: (6) is inconsistent.
% 153.32/22.90  | 
% 153.32/22.90  End of proof
% 153.32/22.90  
% 153.32/22.90  Sub-proof #564 shows that the following formulas are inconsistent:
% 153.32/22.90  ----------------------------------------------------------------
% 153.32/22.90    (1)  all_56_7 = e3 & op(e1, e2) = e3
% 153.32/22.90    (2)  all_56_7 = e1
% 153.32/22.90    (3)   ~ (e3 = e1)
% 153.32/22.90  
% 153.32/22.90  Begin of proof
% 153.32/22.90  | 
% 153.32/22.90  | ALPHA: (1) implies:
% 153.32/22.90  |   (4)  all_56_7 = e3
% 153.32/22.90  | 
% 153.32/22.90  | COMBINE_EQS: (2), (4) imply:
% 153.32/22.90  |   (5)  e3 = e1
% 153.32/22.90  | 
% 153.32/22.90  | REDUCE: (3), (5) imply:
% 153.32/22.90  |   (6)  $false
% 153.32/22.90  | 
% 153.32/22.90  | CLOSE: (6) is inconsistent.
% 153.32/22.90  | 
% 153.32/22.90  End of proof
% 153.32/22.90  
% 153.32/22.90  Sub-proof #565 shows that the following formulas are inconsistent:
% 153.32/22.90  ----------------------------------------------------------------
% 153.32/22.90    (1)  all_56_5 = e1
% 153.32/22.90    (2)   ~ (e2 = e0)
% 153.32/22.90    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.32/22.90         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.32/22.90    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.90    (5)  all_56_10 = e0
% 153.32/22.90    (6)   ~ (e3 = e2)
% 153.32/22.90    (7)   ~ (e2 = e1)
% 153.32/22.90    (8)  all_56_2 = e3
% 153.32/22.90    (9)  op(e2, e2) = e0
% 153.32/22.90  
% 153.32/22.90  Begin of proof
% 153.32/22.90  | 
% 153.32/22.90  | BETA: splitting (3) gives:
% 153.32/22.90  | 
% 153.32/22.90  | Case 1:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (10)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 153.32/22.90  | |           e2)
% 153.32/22.90  | | 
% 153.32/22.90  | | REF_CLOSE: (2), (4), (6), (8), (9), (10) are inconsistent by sub-proof #577.
% 153.32/22.90  | | 
% 153.32/22.90  | Case 2:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (11)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 153.32/22.90  | |           e2)
% 153.32/22.90  | | 
% 153.32/22.90  | | BETA: splitting (11) gives:
% 153.32/22.90  | | 
% 153.32/22.90  | | Case 1:
% 153.32/22.90  | | | 
% 153.32/22.90  | | |   (12)  all_56_5 = e2 & op(e2, e1) = e2
% 153.32/22.90  | | | 
% 153.32/22.90  | | | REF_CLOSE: (1), (7), (12) are inconsistent by sub-proof #672.
% 153.32/22.90  | | | 
% 153.32/22.90  | | Case 2:
% 153.32/22.90  | | | 
% 153.32/22.90  | | |   (13)  all_56_10 = e2 & op(e2, e0) = e2
% 153.32/22.90  | | | 
% 153.32/22.90  | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #1132.
% 153.32/22.90  | | | 
% 153.32/22.90  | | End of split
% 153.32/22.90  | | 
% 153.32/22.90  | End of split
% 153.32/22.90  | 
% 153.32/22.90  End of proof
% 153.32/22.90  
% 153.32/22.90  Sub-proof #566 shows that the following formulas are inconsistent:
% 153.32/22.90  ----------------------------------------------------------------
% 153.32/22.90    (1)   ~ (e2 = e0)
% 153.32/22.90    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.90    (3)   ~ (e3 = e0)
% 153.32/22.90    (4)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.32/22.90         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.90    (5)  op(e3, e3) = e1
% 153.32/22.90    (6)  all_56_4 = e1
% 153.32/22.90    (7)   ~ (e1 = e0)
% 153.32/22.90    (8)  all_56_9 = e2
% 153.32/22.90    (9)  all_56_1 = e3
% 153.32/22.90  
% 153.32/22.90  Begin of proof
% 153.32/22.90  | 
% 153.32/22.90  | BETA: splitting (4) gives:
% 153.32/22.90  | 
% 153.32/22.90  | Case 1:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 153.32/22.90  | |           e0)
% 153.32/22.90  | | 
% 153.32/22.90  | | REF_CLOSE: (2), (3), (5), (7), (9), (10) are inconsistent by sub-proof #951.
% 153.32/22.90  | | 
% 153.32/22.90  | Case 2:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (11)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 153.32/22.90  | |           e0)
% 153.32/22.90  | | 
% 153.32/22.90  | | BETA: splitting (11) gives:
% 153.32/22.90  | | 
% 153.32/22.90  | | Case 1:
% 153.32/22.90  | | | 
% 153.32/22.90  | | |   (12)  all_56_4 = e0 & op(e3, e1) = e0
% 153.32/22.90  | | | 
% 153.32/22.90  | | | ALPHA: (12) implies:
% 153.32/22.90  | | |   (13)  all_56_4 = e0
% 153.32/22.90  | | | 
% 153.32/22.90  | | | REF_CLOSE: (6), (7), (13) are inconsistent by sub-proof #657.
% 153.32/22.90  | | | 
% 153.32/22.90  | | Case 2:
% 153.32/22.90  | | | 
% 153.32/22.90  | | |   (14)  all_56_9 = e0 & op(e3, e0) = e0
% 153.32/22.90  | | | 
% 153.32/22.90  | | | ALPHA: (14) implies:
% 153.32/22.90  | | |   (15)  all_56_9 = e0
% 153.32/22.90  | | | 
% 153.32/22.90  | | | REF_CLOSE: (1), (8), (15) are inconsistent by sub-proof #776.
% 153.32/22.90  | | | 
% 153.32/22.90  | | End of split
% 153.32/22.90  | | 
% 153.32/22.90  | End of split
% 153.32/22.90  | 
% 153.32/22.90  End of proof
% 153.32/22.90  
% 153.32/22.90  Sub-proof #567 shows that the following formulas are inconsistent:
% 153.32/22.90  ----------------------------------------------------------------
% 153.32/22.90    (1)  all_56_11 = e2
% 153.32/22.90    (2)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 153.32/22.90         (all_56_11 = e0 & op(e1, e0) = e0)
% 153.32/22.90    (3)   ~ (e2 = e0)
% 153.32/22.90    (4)  all_56_10 = e1
% 153.32/22.90    (5)   ~ (e1 = e0)
% 153.32/22.90    (6)  all_56_9 = e2
% 153.32/22.90  
% 153.32/22.90  Begin of proof
% 153.32/22.90  | 
% 153.32/22.90  | BETA: splitting (2) gives:
% 153.32/22.90  | 
% 153.32/22.90  | Case 1:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (7)  all_56_9 = e0 & op(e3, e0) = e0
% 153.32/22.90  | | 
% 153.32/22.90  | | REF_CLOSE: (3), (6), (7) are inconsistent by sub-proof #746.
% 153.32/22.90  | | 
% 153.32/22.90  | Case 2:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (8)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.32/22.90  | |          e0)
% 153.32/22.90  | | 
% 153.32/22.90  | | BETA: splitting (8) gives:
% 153.32/22.90  | | 
% 153.32/22.90  | | Case 1:
% 153.32/22.90  | | | 
% 153.32/22.90  | | |   (9)  all_56_10 = e0 & op(e2, e0) = e0
% 153.32/22.90  | | | 
% 153.32/22.90  | | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #884.
% 153.32/22.90  | | | 
% 153.32/22.90  | | Case 2:
% 153.32/22.90  | | | 
% 153.32/22.90  | | |   (10)  all_56_11 = e0 & op(e1, e0) = e0
% 153.32/22.90  | | | 
% 153.32/22.90  | | | REF_CLOSE: (1), (3), (10) are inconsistent by sub-proof #1149.
% 153.32/22.90  | | | 
% 153.32/22.90  | | End of split
% 153.32/22.90  | | 
% 153.32/22.90  | End of split
% 153.32/22.90  | 
% 153.32/22.90  End of proof
% 153.32/22.90  
% 153.32/22.90  Sub-proof #568 shows that the following formulas are inconsistent:
% 153.32/22.90  ----------------------------------------------------------------
% 153.32/22.90    (1)   ~ (e3 = e1)
% 153.32/22.90    (2)  all_56_6 = e2
% 153.32/22.90    (3)   ~ (e2 = e0)
% 153.32/22.90    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.90    (5)  all_56_12 = e1
% 153.32/22.90    (6)   ~ (e3 = e0)
% 153.32/22.90    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.32/22.90         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.32/22.90    (8)  op(e3, e3) = e1
% 153.32/22.90    (9)   ~ (e1 = e0)
% 153.32/22.90    (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 153.32/22.90  
% 153.32/22.90  Begin of proof
% 153.32/22.90  | 
% 153.32/22.90  | BETA: splitting (10) gives:
% 153.32/22.90  | 
% 153.32/22.90  | Case 1:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (11)  all_56_0 = e3 & op(e3, e3) = e3
% 153.32/22.90  | | 
% 153.32/22.90  | | ALPHA: (11) implies:
% 153.32/22.90  | |   (12)  op(e3, e3) = e3
% 153.32/22.90  | | 
% 153.32/22.90  | | REF_CLOSE: (1), (4), (8), (12) are inconsistent by sub-proof #1178.
% 153.32/22.90  | | 
% 153.32/22.90  | Case 2:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (13)  all_56_2 = e3 & op(e2, e3) = e3
% 153.32/22.90  | | 
% 153.32/22.90  | | ALPHA: (13) implies:
% 153.32/22.90  | |   (14)  all_56_2 = e3
% 153.32/22.90  | | 
% 153.32/22.90  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (14) are inconsistent by
% 153.32/22.90  | |            sub-proof #930.
% 153.32/22.90  | | 
% 153.32/22.90  | End of split
% 153.32/22.90  | 
% 153.32/22.90  End of proof
% 153.32/22.90  
% 153.32/22.90  Sub-proof #569 shows that the following formulas are inconsistent:
% 153.32/22.90  ----------------------------------------------------------------
% 153.32/22.90    (1)  all_56_8 = e3
% 153.32/22.90    (2)   ~ (e3 = e1)
% 153.32/22.90    (3)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.32/22.90         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.32/22.90    (4)   ~ (e2 = e0)
% 153.32/22.90    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.90           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.90    (6)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.32/22.90         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.32/22.90    (7)  all_56_12 = e1
% 153.32/22.90    (8)   ~ (e3 = e0)
% 153.32/22.90    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.32/22.90         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.32/22.90    (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.32/22.90          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.32/22.90    (11)  op(e3, e3) = e1
% 153.32/22.90    (12)   ~ (e1 = e0)
% 153.32/22.90    (13)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.32/22.90          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.32/22.90    (14)  op(e1, e1) = e3
% 153.32/22.90    (15)   ~ (e3 = e2)
% 153.32/22.90    (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.32/22.90          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.32/22.90    (17)   ~ (e2 = e1)
% 153.32/22.90  
% 153.32/22.90  Begin of proof
% 153.32/22.90  | 
% 153.32/22.90  | BETA: splitting (3) gives:
% 153.32/22.90  | 
% 153.32/22.90  | Case 1:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (18)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 153.32/22.90  | |           e3)
% 153.32/22.90  | | 
% 153.32/22.90  | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (12), (15), (17), (18)
% 153.32/22.90  | |            are inconsistent by sub-proof #927.
% 153.32/22.90  | | 
% 153.32/22.90  | Case 2:
% 153.32/22.90  | | 
% 153.32/22.90  | |   (19)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 153.32/22.90  | |           e3)
% 153.32/22.90  | | 
% 153.32/22.90  | | BETA: splitting (19) gives:
% 153.32/22.90  | | 
% 153.32/22.90  | | Case 1:
% 153.32/22.90  | | | 
% 153.32/22.90  | | |   (20)  all_56_6 = e3 & op(e1, e3) = e3
% 153.32/22.90  | | | 
% 153.32/22.90  | | | ALPHA: (20) implies:
% 153.32/22.90  | | |   (21)  all_56_6 = e3
% 153.32/22.90  | | | 
% 153.32/22.90  | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (12), (13), (14), (15), (16),
% 153.32/22.90  | | |            (17), (21) are inconsistent by sub-proof #607.
% 153.32/22.90  | | | 
% 153.32/22.90  | | Case 2:
% 153.32/22.90  | | | 
% 153.32/22.90  | | |   (22)  all_56_12 = e3 & op(e0, e3) = e3
% 153.32/22.90  | | | 
% 153.32/22.90  | | | REF_CLOSE: (2), (7), (22) are inconsistent by sub-proof #919.
% 153.32/22.90  | | | 
% 153.32/22.90  | | End of split
% 153.32/22.90  | | 
% 153.32/22.90  | End of split
% 153.32/22.90  | 
% 153.32/22.90  End of proof
% 153.32/22.90  
% 153.32/22.90  Sub-proof #570 shows that the following formulas are inconsistent:
% 153.32/22.90  ----------------------------------------------------------------
% 153.32/22.90    (1)  all_56_6 = e3 & op(e1, e3) = e3
% 153.32/22.90    (2)  all_56_6 = e2
% 153.32/22.90    (3)   ~ (e3 = e2)
% 153.32/22.90  
% 153.32/22.90  Begin of proof
% 153.32/22.90  | 
% 153.32/22.90  | ALPHA: (1) implies:
% 153.32/22.91  |   (4)  all_56_6 = e3
% 153.32/22.91  | 
% 153.32/22.91  | COMBINE_EQS: (2), (4) imply:
% 153.32/22.91  |   (5)  e3 = e2
% 153.32/22.91  | 
% 153.32/22.91  | REDUCE: (3), (5) imply:
% 153.32/22.91  |   (6)  $false
% 153.32/22.91  | 
% 153.32/22.91  | CLOSE: (6) is inconsistent.
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #571 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  all_56_13 = e2
% 153.32/22.91    (2)   ~ (e3 = e1)
% 153.32/22.91    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.32/22.91         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.32/22.91    (4)  all_56_4 = e0
% 153.32/22.91    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.32/22.91         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.32/22.91    (6)  all_56_5 = e1
% 153.32/22.91    (7)   ~ (e2 = e0)
% 153.32/22.91    (8)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.32/22.91         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.32/22.91    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.91    (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.91          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.91    (11)  all_56_12 = e1
% 153.32/22.91    (12)   ~ (all_52_13 = e2)
% 153.32/22.91    (13)   ~ (e3 = e0)
% 153.32/22.91    (14)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.32/22.91          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.32/22.91    (15)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.32/22.91          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.91    (16)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.32/22.91          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.32/22.91    (17)  op(e3, e3) = e1
% 153.32/22.91    (18)  op(e2, e0) = all_52_13
% 153.32/22.91    (19)   ~ (e1 = e0)
% 153.32/22.91    (20)   ~ (e3 = e2)
% 153.32/22.91    (21)  all_56_9 = e2
% 153.32/22.91    (22)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.32/22.91          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.32/22.91    (23)   ~ (e2 = e1)
% 153.32/22.91    (24)  all_56_1 = e3
% 153.32/22.91    (25)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.32/22.91          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | BETA: splitting (8) gives:
% 153.32/22.91  | 
% 153.32/22.91  | Case 1:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (26)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 153.32/22.91  | |           e2)
% 153.32/22.91  | | 
% 153.32/22.91  | | BETA: splitting (26) gives:
% 153.32/22.91  | | 
% 153.32/22.91  | | Case 1:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (27)  all_56_2 = e2 & op(e2, e3) = e2
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (27) implies:
% 153.32/22.91  | | |   (28)  all_56_2 = e2
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (2), (4), (5), (7), (9), (10), (11), (13), (14), (16), (17),
% 153.32/22.91  | | |            (19), (20), (21), (23), (24), (28) are inconsistent by
% 153.32/22.91  | | |            sub-proof #572.
% 153.32/22.91  | | | 
% 153.32/22.91  | | Case 2:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (29)  all_56_3 = e2 & op(e2, e2) = e2
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (29) implies:
% 153.32/22.91  | | |   (30)  op(e2, e2) = e2
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (1), (2), (7), (9), (13), (19), (22), (23), (24), (25), (30)
% 153.32/22.91  | | |            are inconsistent by sub-proof #1108.
% 153.32/22.91  | | | 
% 153.32/22.91  | | End of split
% 153.32/22.91  | | 
% 153.32/22.91  | Case 2:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (31)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 153.32/22.91  | |           e2)
% 153.32/22.91  | | 
% 153.32/22.91  | | BETA: splitting (31) gives:
% 153.32/22.91  | | 
% 153.32/22.91  | | Case 1:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (32)  all_56_5 = e2 & op(e2, e1) = e2
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (32) implies:
% 153.32/22.91  | | |   (33)  all_56_5 = e2
% 153.32/22.91  | | | 
% 153.32/22.91  | | | COMBINE_EQS: (6), (33) imply:
% 153.32/22.91  | | |   (34)  e2 = e1
% 153.32/22.91  | | | 
% 153.32/22.91  | | | COMBINE_EQS: (21), (34) imply:
% 153.32/22.91  | | |   (35)  all_56_9 = e1
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (3), (7), (9), (13), (15), (17), (19), (20), (23), (24), (35)
% 153.32/22.91  | | |            are inconsistent by sub-proof #945.
% 153.32/22.91  | | | 
% 153.32/22.91  | | Case 2:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (36)  all_56_10 = e2 & op(e2, e0) = e2
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (36) implies:
% 153.32/22.91  | | |   (37)  op(e2, e0) = e2
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (9), (12), (18), (37) are inconsistent by sub-proof #1156.
% 153.32/22.91  | | | 
% 153.32/22.91  | | End of split
% 153.32/22.91  | | 
% 153.32/22.91  | End of split
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #572 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)   ~ (e3 = e1)
% 153.32/22.91    (2)  all_56_4 = e0
% 153.32/22.91    (3)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.32/22.91         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.32/22.91    (4)   ~ (e2 = e0)
% 153.32/22.91    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.91    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.91         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.91    (7)  all_56_12 = e1
% 153.32/22.91    (8)   ~ (e3 = e0)
% 153.32/22.91    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.32/22.91         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.32/22.91    (10)  all_56_2 = e2
% 153.32/22.91    (11)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.32/22.91          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.32/22.91    (12)  op(e3, e3) = e1
% 153.32/22.91    (13)   ~ (e1 = e0)
% 153.32/22.91    (14)   ~ (e3 = e2)
% 153.32/22.91    (15)  all_56_9 = e2
% 153.32/22.91    (16)   ~ (e2 = e1)
% 153.32/22.91    (17)  all_56_1 = e3
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | BETA: splitting (9) gives:
% 153.32/22.91  | 
% 153.32/22.91  | Case 1:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (18)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 153.32/22.91  | |           e0)
% 153.32/22.91  | | 
% 153.32/22.91  | | REF_CLOSE: (4), (5), (10), (12), (13), (18) are inconsistent by sub-proof
% 153.32/22.91  | |            #574.
% 153.32/22.91  | | 
% 153.32/22.91  | Case 2:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (19)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 153.32/22.91  | |           e0)
% 153.32/22.91  | | 
% 153.32/22.91  | | BETA: splitting (19) gives:
% 153.32/22.91  | | 
% 153.32/22.91  | | Case 1:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (20)  all_56_6 = e0 & op(e1, e3) = e0
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (20) implies:
% 153.32/22.91  | | |   (21)  all_56_6 = e0
% 153.32/22.91  | | | 
% 153.32/22.91  | | | BETA: splitting (3) gives:
% 153.32/22.91  | | | 
% 153.32/22.91  | | | Case 1:
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | |   (22)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3)
% 153.32/22.91  | | | |           = e3)
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (11), (12), (13), (14), (16),
% 153.32/22.91  | | | |            (22) are inconsistent by sub-proof #927.
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | Case 2:
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | |   (23)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3)
% 153.32/22.91  | | | |           = e3)
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | | BETA: splitting (23) gives:
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | | Case 1:
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | |   (24)  all_56_6 = e3 & op(e1, e3) = e3
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | ALPHA: (24) implies:
% 153.32/22.91  | | | | |   (25)  all_56_6 = e3
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | REF_CLOSE: (8), (21), (25) are inconsistent by sub-proof #784.
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | Case 2:
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | |   (26)  all_56_12 = e3 & op(e0, e3) = e3
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (12), (14), (15), (17), (26)
% 153.32/22.91  | | | | |            are inconsistent by sub-proof #573.
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | End of split
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | End of split
% 153.32/22.91  | | | 
% 153.32/22.91  | | Case 2:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (27)  all_56_12 = e0 & op(e0, e3) = e0
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (27) implies:
% 153.32/22.91  | | |   (28)  all_56_12 = e0
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (7), (13), (28) are inconsistent by sub-proof #1051.
% 153.32/22.91  | | | 
% 153.32/22.91  | | End of split
% 153.32/22.91  | | 
% 153.32/22.91  | End of split
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #573 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)   ~ (e3 = e1)
% 153.32/22.91    (2)  all_56_4 = e0
% 153.32/22.91    (3)  all_56_12 = e3 & op(e0, e3) = e3
% 153.32/22.91    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.91    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.91         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.91    (6)  all_56_12 = e1
% 153.32/22.91    (7)   ~ (e3 = e0)
% 153.32/22.91    (8)  op(e3, e3) = e1
% 153.32/22.91    (9)   ~ (e3 = e2)
% 153.32/22.91    (10)  all_56_9 = e2
% 153.32/22.91    (11)  all_56_1 = e3
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | ALPHA: (3) implies:
% 153.32/22.91  |   (12)  all_56_12 = e3
% 153.32/22.91  | 
% 153.32/22.91  | COMBINE_EQS: (6), (12) imply:
% 153.32/22.91  |   (13)  e3 = e1
% 153.32/22.91  | 
% 153.32/22.91  | COMBINE_EQS: (11), (13) imply:
% 153.32/22.91  |   (14)  all_56_1 = e1
% 153.32/22.91  | 
% 153.32/22.91  | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (14) are inconsistent by
% 153.32/22.91  |            sub-proof #593.
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #574 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 153.32/22.91    (2)   ~ (e2 = e0)
% 153.32/22.91    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.91    (4)  all_56_2 = e2
% 153.32/22.91    (5)  op(e3, e3) = e1
% 153.32/22.91    (6)   ~ (e1 = e0)
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | BETA: splitting (1) gives:
% 153.32/22.91  | 
% 153.32/22.91  | Case 1:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 153.32/22.91  | | 
% 153.32/22.91  | | ALPHA: (7) implies:
% 153.32/22.91  | |   (8)  op(e3, e3) = e0
% 153.32/22.91  | | 
% 153.32/22.91  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #957.
% 153.32/22.91  | | 
% 153.32/22.91  | Case 2:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (9)  all_56_2 = e0 & op(e2, e3) = e0
% 153.32/22.91  | | 
% 153.32/22.91  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #726.
% 153.32/22.91  | | 
% 153.32/22.91  | End of split
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #575 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  all_56_12 = e3 & op(e0, e3) = e3
% 153.32/22.91    (2)  all_56_12 = e2
% 153.32/22.91    (3)   ~ (e3 = e2)
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | ALPHA: (1) implies:
% 153.32/22.91  |   (4)  all_56_12 = e3
% 153.32/22.91  | 
% 153.32/22.91  | COMBINE_EQS: (2), (4) imply:
% 153.32/22.91  |   (5)  e3 = e2
% 153.32/22.91  | 
% 153.32/22.91  | REDUCE: (3), (5) imply:
% 153.32/22.91  |   (6)  $false
% 153.32/22.91  | 
% 153.32/22.91  | CLOSE: (6) is inconsistent.
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #576 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  all_56_6 = e3 & op(e1, e3) = e3
% 153.32/22.91    (2)  all_56_6 = e0
% 153.32/22.91    (3)   ~ (e3 = e0)
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | ALPHA: (1) implies:
% 153.32/22.91  |   (4)  all_56_6 = e3
% 153.32/22.91  | 
% 153.32/22.91  | COMBINE_EQS: (2), (4) imply:
% 153.32/22.91  |   (5)  e3 = e0
% 153.32/22.91  | 
% 153.32/22.91  | REDUCE: (3), (5) imply:
% 153.32/22.91  |   (6)  $false
% 153.32/22.91  | 
% 153.32/22.91  | CLOSE: (6) is inconsistent.
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #577 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)   ~ (e2 = e0)
% 153.32/22.91    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.91    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 153.32/22.91    (4)   ~ (e3 = e2)
% 153.32/22.91    (5)  all_56_2 = e3
% 153.32/22.91    (6)  op(e2, e2) = e0
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | BETA: splitting (3) gives:
% 153.32/22.91  | 
% 153.32/22.91  | Case 1:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (7)  all_56_2 = e2 & op(e2, e3) = e2
% 153.32/22.91  | | 
% 153.32/22.91  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #934.
% 153.32/22.91  | | 
% 153.32/22.91  | Case 2:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (8)  all_56_3 = e2 & op(e2, e2) = e2
% 153.32/22.91  | | 
% 153.32/22.91  | | ALPHA: (8) implies:
% 153.32/22.91  | |   (9)  op(e2, e2) = e2
% 153.32/22.91  | | 
% 153.32/22.91  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #1145.
% 153.32/22.91  | | 
% 153.32/22.91  | End of split
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #578 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 153.32/22.91         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.32/22.91    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.32/22.91         (all_56_14 = e0 & op(e0, e1) = e0)
% 153.32/22.91    (3)  all_56_4 = e0
% 153.32/22.91    (4)  op(e1, e1) = e2
% 153.32/22.91    (5)  op(e0, e2) = all_52_7
% 153.32/22.91    (6)   ~ (e2 = e0)
% 153.32/22.91    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.91    (8)  all_56_5 = e2
% 153.32/22.91    (9)   ~ (e3 = e0)
% 153.32/22.91    (10)   ~ (all_52_7 = e0)
% 153.32/22.91    (11)   ~ (e3 = e2)
% 153.32/22.91    (12)  all_56_12 = e2
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | BETA: splitting (1) gives:
% 153.32/22.91  | 
% 153.32/22.91  | Case 1:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (13)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) =
% 153.32/22.91  | |           e3)
% 153.32/22.91  | | 
% 153.32/22.91  | | REF_CLOSE: (3), (8), (9), (11), (13) are inconsistent by sub-proof #640.
% 153.32/22.91  | | 
% 153.32/22.91  | Case 2:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (14)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 153.32/22.91  | |           e3)
% 153.32/22.91  | | 
% 153.32/22.91  | | BETA: splitting (14) gives:
% 153.32/22.91  | | 
% 153.32/22.91  | | Case 1:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (15)  all_56_8 = e3 & op(e1, e1) = e3
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (15) implies:
% 153.32/22.91  | | |   (16)  op(e1, e1) = e3
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (4), (7), (11), (16) are inconsistent by sub-proof #834.
% 153.32/22.91  | | | 
% 153.32/22.91  | | Case 2:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (17)  all_56_14 = e3 & op(e0, e1) = e3
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (17) implies:
% 153.32/22.91  | | |   (18)  all_56_14 = e3
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (2), (5), (6), (7), (9), (10), (12), (18) are inconsistent by
% 153.32/22.91  | | |            sub-proof #621.
% 153.32/22.91  | | | 
% 153.32/22.91  | | End of split
% 153.32/22.91  | | 
% 153.32/22.91  | End of split
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #579 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)   ~ (e3 = e1)
% 153.32/22.91    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.32/22.91         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.32/22.91    (3)  all_56_4 = e0
% 153.32/22.91    (4)   ~ (e2 = e0)
% 153.32/22.91    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.91    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.32/22.91         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.32/22.91    (7)  op(e0, e0) = e2
% 153.32/22.91    (8)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.91             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.32/22.91               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.32/22.91               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.32/22.91    (9)   ~ (e3 = e0)
% 153.32/22.91    (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.32/22.91          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.91    (11)  op(e3, e3) = e1
% 153.32/22.91    (12)  all_56_14 = e3
% 153.32/22.91    (13)   ~ (e1 = e0)
% 153.32/22.91    (14)   ~ (e3 = e2)
% 153.32/22.91    (15)  all_56_9 = e2
% 153.32/22.91    (16)  all_56_12 = e2
% 153.32/22.91    (17)   ~ (e2 = e1)
% 153.32/22.91    (18)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.32/22.91          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 153.32/22.91            e1)
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | BETA: splitting (6) gives:
% 153.32/22.91  | 
% 153.32/22.91  | Case 1:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (19)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 153.32/22.91  | |           e3)
% 153.32/22.91  | | 
% 153.32/22.91  | | BETA: splitting (19) gives:
% 153.32/22.91  | | 
% 153.32/22.91  | | Case 1:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (20)  all_56_0 = e3 & op(e3, e3) = e3
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (20) implies:
% 153.32/22.91  | | |   (21)  op(e3, e3) = e3
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (1), (5), (11), (21) are inconsistent by sub-proof #1178.
% 153.32/22.91  | | | 
% 153.32/22.91  | | Case 2:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (22)  all_56_1 = e3 & op(e3, e2) = e3
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (22) implies:
% 153.32/22.91  | | |   (23)  all_56_1 = e3
% 153.32/22.91  | | | 
% 153.32/22.91  | | | BETA: splitting (18) gives:
% 153.32/22.91  | | | 
% 153.32/22.91  | | | Case 1:
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | |   (24)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0,
% 153.32/22.91  | | | |             e2) = e1)
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | | BETA: splitting (24) gives:
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | | Case 1:
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | |   (25)  all_56_12 = e1 & op(e0, e3) = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | ALPHA: (25) implies:
% 153.32/22.91  | | | | |   (26)  all_56_12 = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | COMBINE_EQS: (16), (26) imply:
% 153.32/22.91  | | | | |   (27)  e2 = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | REF_CLOSE: (2), (4), (5), (9), (10), (11), (13), (14), (15), (17),
% 153.32/22.91  | | | | |            (23), (27) are inconsistent by sub-proof #581.
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | Case 2:
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | |   (28)  all_56_13 = e1 & op(e0, e2) = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | ALPHA: (28) implies:
% 153.32/22.91  | | | | |   (29)  all_56_13 = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | BETA: splitting (8) gives:
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | Case 1:
% 153.32/22.91  | | | | | | 
% 153.32/22.91  | | | | | |   (30)  all_56_15 = e0 & op(e0, e0) = e0
% 153.32/22.91  | | | | | | 
% 153.32/22.91  | | | | | | ALPHA: (30) implies:
% 153.32/22.91  | | | | | |   (31)  op(e0, e0) = e0
% 153.32/22.91  | | | | | | 
% 153.32/22.91  | | | | | | REF_CLOSE: (4), (5), (7), (31) are inconsistent by sub-proof #1043.
% 153.32/22.91  | | | | | | 
% 153.32/22.91  | | | | | Case 2:
% 153.32/22.91  | | | | | | 
% 153.32/22.91  | | | | | |   (32)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 &
% 153.32/22.91  | | | | | |             op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 153.32/22.91  | | | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.32/22.91  | | | | | |             op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 153.32/22.91  | | | | | | 
% 153.32/22.91  | | | | | | ALPHA: (32) implies:
% 153.32/22.91  | | | | | |   (33)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.32/22.91  | | | | | |           op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.32/22.91  | | | | | | 
% 153.32/22.91  | | | | | | REF_CLOSE: (4), (9), (12), (13), (16), (29), (33) are inconsistent
% 153.32/22.91  | | | | | |            by sub-proof #580.
% 153.32/22.91  | | | | | | 
% 153.32/22.91  | | | | | End of split
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | End of split
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | Case 2:
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | |   (34)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0,
% 153.32/22.91  | | | |             e0) = e1)
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | | BETA: splitting (34) gives:
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | | Case 1:
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | |   (35)  all_56_14 = e1 & op(e0, e1) = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | ALPHA: (35) implies:
% 153.32/22.91  | | | | |   (36)  all_56_14 = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | COMBINE_EQS: (12), (36) imply:
% 153.32/22.91  | | | | |   (37)  e3 = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | SIMP: (37) implies:
% 153.32/22.91  | | | | |   (38)  e3 = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | COMBINE_EQS: (23), (38) imply:
% 153.32/22.91  | | | | |   (39)  all_56_1 = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | REF_CLOSE: (1), (3), (5), (6), (9), (11), (14), (15), (39) are
% 153.32/22.91  | | | | |            inconsistent by sub-proof #593.
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | Case 2:
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | |   (40)  all_56_15 = e1 & op(e0, e0) = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | ALPHA: (40) implies:
% 153.32/22.91  | | | | |   (41)  op(e0, e0) = e1
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | | REF_CLOSE: (5), (7), (17), (41) are inconsistent by sub-proof #978.
% 153.32/22.91  | | | | | 
% 153.32/22.91  | | | | End of split
% 153.32/22.91  | | | | 
% 153.32/22.91  | | | End of split
% 153.32/22.91  | | | 
% 153.32/22.91  | | End of split
% 153.32/22.91  | | 
% 153.32/22.91  | Case 2:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (42)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 153.32/22.91  | |           e3)
% 153.32/22.91  | | 
% 153.32/22.91  | | BETA: splitting (42) gives:
% 153.32/22.91  | | 
% 153.32/22.91  | | Case 1:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (43)  all_56_4 = e3 & op(e3, e1) = e3
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (3), (9), (43) are inconsistent by sub-proof #641.
% 153.32/22.91  | | | 
% 153.32/22.91  | | Case 2:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (44)  all_56_9 = e3 & op(e3, e0) = e3
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (14), (15), (44) are inconsistent by sub-proof #594.
% 153.32/22.91  | | | 
% 153.32/22.91  | | End of split
% 153.32/22.91  | | 
% 153.32/22.91  | End of split
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #580 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.32/22.91         (all_56_14 = e0 & op(e0, e1) = e0)
% 153.32/22.91    (2)   ~ (e2 = e0)
% 153.32/22.91    (3)  all_56_13 = e1
% 153.32/22.91    (4)   ~ (e3 = e0)
% 153.32/22.91    (5)  all_56_14 = e3
% 153.32/22.91    (6)   ~ (e1 = e0)
% 153.32/22.91    (7)  all_56_12 = e2
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | BETA: splitting (1) gives:
% 153.32/22.91  | 
% 153.32/22.91  | Case 1:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (8)  all_56_12 = e0 & op(e0, e3) = e0
% 153.32/22.91  | | 
% 153.32/22.91  | | ALPHA: (8) implies:
% 153.32/22.91  | |   (9)  all_56_12 = e0
% 153.32/22.91  | | 
% 153.32/22.91  | | REF_CLOSE: (2), (7), (9) are inconsistent by sub-proof #1119.
% 153.32/22.91  | | 
% 153.32/22.91  | Case 2:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (10)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 153.32/22.91  | |           e0)
% 153.32/22.91  | | 
% 153.32/22.91  | | BETA: splitting (10) gives:
% 153.32/22.91  | | 
% 153.32/22.91  | | Case 1:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (11)  all_56_13 = e0 & op(e0, e2) = e0
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #1011.
% 153.32/22.91  | | | 
% 153.32/22.91  | | Case 2:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (12)  all_56_14 = e0 & op(e0, e1) = e0
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #622.
% 153.32/22.91  | | | 
% 153.32/22.91  | | End of split
% 153.32/22.91  | | 
% 153.32/22.91  | End of split
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #581 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.32/22.91         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.32/22.91    (2)   ~ (e2 = e0)
% 153.32/22.91    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.91    (4)  e2 = e1
% 153.32/22.91    (5)   ~ (e3 = e0)
% 153.32/22.91    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.32/22.91         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.91    (7)  op(e3, e3) = e1
% 153.32/22.91    (8)   ~ (e1 = e0)
% 153.32/22.91    (9)   ~ (e3 = e2)
% 153.32/22.91    (10)  all_56_9 = e2
% 153.32/22.91    (11)   ~ (e2 = e1)
% 153.32/22.91    (12)  all_56_1 = e3
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | SIMP: (4) implies:
% 153.32/22.91  |   (13)  e2 = e1
% 153.32/22.91  | 
% 153.32/22.91  | COMBINE_EQS: (10), (13) imply:
% 153.32/22.91  |   (14)  all_56_9 = e1
% 153.32/22.91  | 
% 153.32/22.91  | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (14) are
% 153.32/22.91  |            inconsistent by sub-proof #945.
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #582 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  all_56_4 = e0
% 153.32/22.91    (2)  all_56_5 = e2
% 153.32/22.91    (3)   ~ (e3 = e0)
% 153.32/22.91    (4)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3)
% 153.32/22.91    (5)   ~ (e3 = e2)
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | BETA: splitting (4) gives:
% 153.32/22.91  | 
% 153.32/22.91  | Case 1:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (6)  all_56_4 = e3 & op(e3, e1) = e3
% 153.32/22.91  | | 
% 153.32/22.91  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #915.
% 153.32/22.91  | | 
% 153.32/22.91  | Case 2:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (7)  all_56_5 = e3 & op(e2, e1) = e3
% 153.32/22.91  | | 
% 153.32/22.91  | | ALPHA: (7) implies:
% 153.32/22.91  | |   (8)  all_56_5 = e3
% 153.32/22.91  | | 
% 153.32/22.91  | | COMBINE_EQS: (2), (8) imply:
% 153.32/22.91  | |   (9)  e3 = e2
% 153.32/22.91  | | 
% 153.32/22.91  | | SIMP: (9) implies:
% 153.32/22.91  | |   (10)  e3 = e2
% 153.32/22.91  | | 
% 153.32/22.91  | | REDUCE: (5), (10) imply:
% 153.32/22.91  | |   (11)  $false
% 153.32/22.91  | | 
% 153.32/22.91  | | CLOSE: (11) is inconsistent.
% 153.32/22.91  | | 
% 153.32/22.91  | End of split
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #583 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  op(e3, e2) = all_52_4
% 153.32/22.91    (2)   ~ (e2 = e0)
% 153.32/22.91    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.91    (4)  all_56_4 = e2
% 153.32/22.91    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.32/22.91         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.91    (6)  op(e3, e3) = e1
% 153.32/22.91    (7)   ~ (e1 = e0)
% 153.32/22.91    (8)  all_56_9 = e2
% 153.32/22.91    (9)   ~ (all_52_4 = e0)
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | BETA: splitting (5) gives:
% 153.32/22.91  | 
% 153.32/22.91  | Case 1:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 153.32/22.91  | |           e0)
% 153.32/22.91  | | 
% 153.32/22.91  | | REF_CLOSE: (1), (3), (6), (7), (9), (10) are inconsistent by sub-proof #937.
% 153.32/22.91  | | 
% 153.32/22.91  | Case 2:
% 153.32/22.91  | | 
% 153.32/22.91  | |   (11)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 153.32/22.91  | |           e0)
% 153.32/22.91  | | 
% 153.32/22.91  | | BETA: splitting (11) gives:
% 153.32/22.91  | | 
% 153.32/22.91  | | Case 1:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (12)  all_56_4 = e0 & op(e3, e1) = e0
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (12) implies:
% 153.32/22.91  | | |   (13)  all_56_4 = e0
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (2), (4), (13) are inconsistent by sub-proof #936.
% 153.32/22.91  | | | 
% 153.32/22.91  | | Case 2:
% 153.32/22.91  | | | 
% 153.32/22.91  | | |   (14)  all_56_9 = e0 & op(e3, e0) = e0
% 153.32/22.91  | | | 
% 153.32/22.91  | | | ALPHA: (14) implies:
% 153.32/22.91  | | |   (15)  all_56_9 = e0
% 153.32/22.91  | | | 
% 153.32/22.91  | | | REF_CLOSE: (2), (8), (15) are inconsistent by sub-proof #776.
% 153.32/22.91  | | | 
% 153.32/22.91  | | End of split
% 153.32/22.91  | | 
% 153.32/22.91  | End of split
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #584 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  all_56_10 = e1 & op(e2, e0) = e1
% 153.32/22.91    (2)  all_56_10 = e3
% 153.32/22.91    (3)   ~ (e3 = e1)
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | ALPHA: (1) implies:
% 153.32/22.91  |   (4)  all_56_10 = e1
% 153.32/22.91  | 
% 153.32/22.91  | COMBINE_EQS: (2), (4) imply:
% 153.32/22.91  |   (5)  e3 = e1
% 153.32/22.91  | 
% 153.32/22.91  | REDUCE: (3), (5) imply:
% 153.32/22.91  |   (6)  $false
% 153.32/22.91  | 
% 153.32/22.91  | CLOSE: (6) is inconsistent.
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #585 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  all_56_13 = e3 & op(e0, e2) = e3
% 153.32/22.91    (2)  all_56_13 = e1
% 153.32/22.91    (3)   ~ (e3 = e1)
% 153.32/22.91  
% 153.32/22.91  Begin of proof
% 153.32/22.91  | 
% 153.32/22.91  | ALPHA: (1) implies:
% 153.32/22.91  |   (4)  all_56_13 = e3
% 153.32/22.91  | 
% 153.32/22.91  | COMBINE_EQS: (2), (4) imply:
% 153.32/22.91  |   (5)  e3 = e1
% 153.32/22.91  | 
% 153.32/22.91  | REDUCE: (3), (5) imply:
% 153.32/22.91  |   (6)  $false
% 153.32/22.91  | 
% 153.32/22.91  | CLOSE: (6) is inconsistent.
% 153.32/22.91  | 
% 153.32/22.91  End of proof
% 153.32/22.91  
% 153.32/22.91  Sub-proof #586 shows that the following formulas are inconsistent:
% 153.32/22.91  ----------------------------------------------------------------
% 153.32/22.91    (1)  all_54_6 = all_52_9
% 153.32/22.91    (2)   ~ (e3 = e1)
% 153.32/22.91    (3)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.32/22.91         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.32/22.91    (4)  all_56_5 = e1
% 153.32/22.91    (5)   ~ (e2 = e0)
% 153.32/22.91    (6)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.32/22.91         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.32/22.91    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.91           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.91    (8)   ~ (all_52_9 = e3)
% 153.32/22.92    (9)   ~ (all_52_1 = all_52_9)
% 153.32/22.92    (10)   ~ (all_52_13 = e2)
% 153.32/22.92    (11)  all_56_10 = e1
% 153.32/22.92    (12)   ~ (e3 = e0)
% 153.32/22.92    (13)  op(e2, e0) = all_52_13
% 153.32/22.92    (14)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.32/22.92          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.32/22.92    (15)   ~ (e1 = e0)
% 153.32/22.92    (16)   ~ (all_52_9 = e1)
% 153.32/22.92    (17)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 153.32/22.92    (18)   ~ (e3 = e2)
% 153.32/22.92    (19)   ~ (all_52_9 = e0)
% 153.32/22.92    (20)   ~ (e2 = e1)
% 153.32/22.92    (21)  op(e2, e3) = all_52_1
% 153.32/22.92  
% 153.32/22.92  Begin of proof
% 153.32/22.92  | 
% 153.32/22.92  | BETA: splitting (6) gives:
% 153.32/22.92  | 
% 153.32/22.92  | Case 1:
% 153.32/22.92  | | 
% 153.32/22.92  | |   (22)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 153.32/22.92  | |           e2)
% 153.32/22.92  | | 
% 153.32/22.92  | | BETA: splitting (22) gives:
% 153.32/22.92  | | 
% 153.32/22.92  | | Case 1:
% 153.32/22.92  | | | 
% 153.32/22.92  | | |   (23)  all_56_2 = e2 & op(e2, e3) = e2
% 153.32/22.92  | | | 
% 153.32/22.92  | | | ALPHA: (23) implies:
% 153.32/22.92  | | |   (24)  op(e2, e3) = e2
% 153.32/22.92  | | | 
% 153.32/22.92  | | | REF_CLOSE: (1), (7), (8), (9), (16), (17), (19), (21), (24) are
% 153.32/22.92  | | |            inconsistent by sub-proof #599.
% 153.32/22.92  | | | 
% 153.32/22.92  | | Case 2:
% 153.32/22.92  | | | 
% 153.32/22.92  | | |   (25)  all_56_3 = e2 & op(e2, e2) = e2
% 153.32/22.92  | | | 
% 153.32/22.92  | | | ALPHA: (25) implies:
% 153.32/22.92  | | |   (26)  op(e2, e2) = e2
% 153.32/22.92  | | | 
% 153.32/22.92  | | | REF_CLOSE: (2), (3), (4), (5), (7), (11), (12), (14), (15), (18), (26) are
% 153.32/22.92  | | |            inconsistent by sub-proof #681.
% 153.32/22.92  | | | 
% 153.32/22.92  | | End of split
% 153.32/22.92  | | 
% 153.32/22.92  | Case 2:
% 153.32/22.92  | | 
% 153.32/22.92  | |   (27)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 153.32/22.92  | |           e2)
% 153.32/22.92  | | 
% 153.32/22.92  | | BETA: splitting (27) gives:
% 153.32/22.92  | | 
% 153.32/22.92  | | Case 1:
% 153.32/22.92  | | | 
% 153.32/22.92  | | |   (28)  all_56_5 = e2 & op(e2, e1) = e2
% 153.32/22.92  | | | 
% 153.32/22.92  | | | REF_CLOSE: (4), (20), (28) are inconsistent by sub-proof #680.
% 153.32/22.92  | | | 
% 153.32/22.92  | | Case 2:
% 153.32/22.92  | | | 
% 153.32/22.92  | | |   (29)  all_56_10 = e2 & op(e2, e0) = e2
% 153.32/22.92  | | | 
% 153.32/22.92  | | | ALPHA: (29) implies:
% 153.32/22.92  | | |   (30)  op(e2, e0) = e2
% 153.32/22.92  | | | 
% 153.32/22.92  | | | REF_CLOSE: (7), (10), (13), (30) are inconsistent by sub-proof #1156.
% 153.32/22.92  | | | 
% 153.32/22.92  | | End of split
% 153.32/22.92  | | 
% 153.32/22.92  | End of split
% 153.32/22.92  | 
% 153.32/22.92  End of proof
% 153.32/22.92  
% 153.32/22.92  Sub-proof #587 shows that the following formulas are inconsistent:
% 153.32/22.92  ----------------------------------------------------------------
% 153.32/22.92    (1)  all_54_6 = all_52_9
% 153.32/22.92    (2)  all_57_6 = e3
% 153.32/22.92    (3)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.32/22.92         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.32/22.92    (4)   ~ (all_52_6 = e1)
% 153.32/22.92    (5)   ~ (e3 = e1)
% 153.32/22.92    (6)  op(e3, e2) = all_52_4
% 153.32/22.92    (7)  all_54_14 = all_52_11
% 153.32/22.92    (8)   ~ (e2 = e0)
% 153.32/22.92    (9)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.32/22.92         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.32/22.92    (10)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.32/22.92            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.32/22.92    (11)   ~ (all_52_3 = all_52_11)
% 153.32/22.92    (12)   ~ (all_52_9 = e3)
% 153.32/22.92    (13)   ~ (all_52_14 = e1)
% 153.32/22.92    (14)  op(e0, e0) = e2
% 153.32/22.92    (15)   ~ (all_52_11 = e3)
% 153.32/22.92    (16)   ~ (all_52_1 = all_52_9)
% 153.32/22.92    (17)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.32/22.92              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.32/22.92                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.32/22.92                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.32/22.92    (18)  op(e1, e0) = all_52_14
% 153.32/22.92    (19)   ~ (all_52_13 = e2)
% 153.32/22.92    (20)   ~ (all_52_4 = e3)
% 153.32/22.92    (21)  all_56_10 = e1
% 153.32/22.92    (22)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.32/22.92    (23)  op(e3, e0) = all_52_12
% 153.32/22.92    (24)   ~ (e3 = e0)
% 153.32/22.92    (25)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.32/22.92          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.32/22.92    (26)  op(e3, e3) = e1
% 153.32/22.92    (27)  op(e1, e2) = all_52_6
% 153.32/22.92    (28)   ~ (all_52_12 = e3)
% 153.32/22.92    (29)  op(e2, e0) = all_52_13
% 153.32/22.92    (30)  op(e0, e3) = all_52_3
% 153.32/22.92    (31)  all_57_14 = e1
% 153.32/22.92    (32)  op(e1, e1) = e1
% 153.32/22.92    (33)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.32/22.92          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.32/22.92    (34)  op(e2, e1) = all_52_9
% 153.32/22.92    (35)   ~ (e1 = e0)
% 153.32/22.92    (36)   ~ (all_52_9 = e1)
% 153.32/22.92    (37)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 153.32/22.92    (38)   ~ (e3 = e2)
% 153.32/22.92    (39)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.32/22.92          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.32/22.92    (40)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.32/22.92          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.32/22.92    (41)   ~ (all_52_9 = e0)
% 153.32/22.92    (42)  all_56_15 = e2
% 153.32/22.92    (43)   ~ (e2 = e1)
% 153.32/22.92    (44)   ~ (all_52_11 = e1)
% 153.32/22.92    (45)  op(e1, e3) = all_52_2
% 153.32/22.92    (46)   ~ (all_52_11 = e2)
% 153.32/22.92    (47)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.32/22.92              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.32/22.92            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.32/22.92            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.32/22.92            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.32/22.92            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.32/22.92            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.32/22.92            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.32/22.92            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.32/22.92            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.32/22.92            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.32/22.92            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.32/22.92            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.32/22.92            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.32/22.92            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.32/22.92            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.32/22.92            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.32/22.92            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.32/22.92            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.32/22.92            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.32/22.92            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.32/22.92            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.32/22.92            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.32/22.92            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.32/22.92            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.32/22.92            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.32/22.92            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.32/22.92            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.32/22.92            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.32/22.92            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.32/22.92            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.32/22.92            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.32/22.92            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.32/22.92            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.32/22.92            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.32/22.92            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.32/22.92            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.32/22.92            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.32/22.92            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.32/22.92            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.32/22.92            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.32/22.92            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.32/22.92            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.32/22.92            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.32/22.92            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.32/22.92            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.32/22.92            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.32/22.92            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.32/22.92              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.32/22.92            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.32/22.92            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.32/22.92              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.32/22.92            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.32/22.92            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.32/22.92                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.32/22.92                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.32/22.92                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.32/22.92                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.32/22.92                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.32/22.92                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.32/22.92                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.32/22.92              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.32/22.92                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.32/22.92                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.32/22.92                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.32/22.92                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.32/22.92                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.32/22.92                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.32/22.92                $i(all_57_7))))
% 153.32/22.92    (48)  op(e2, e2) = e0
% 153.32/22.92    (49)  op(e2, e3) = all_52_1
% 153.32/22.92  
% 153.32/22.92  Begin of proof
% 153.32/22.92  | 
% 153.32/22.92  | BETA: splitting (22) gives:
% 153.32/22.92  | 
% 153.32/22.92  | Case 1:
% 153.32/22.92  | | 
% 153.32/22.92  | |   (50)  all_54_14 = e3
% 153.32/22.92  | | 
% 153.32/22.92  | | REF_CLOSE: (7), (15), (50) are inconsistent by sub-proof #903.
% 153.32/22.92  | | 
% 153.32/22.92  | Case 2:
% 153.32/22.92  | | 
% 153.32/22.92  | |   (51)   ~ (all_54_14 = e3)
% 153.32/22.92  | |   (52)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.32/22.92  | | 
% 153.32/22.92  | | BETA: splitting (52) gives:
% 153.32/22.92  | | 
% 153.32/22.92  | | Case 1:
% 153.32/22.92  | | | 
% 153.32/22.92  | | |   (53)  all_54_14 = e2
% 153.32/22.92  | | | 
% 153.32/22.92  | | | REF_CLOSE: (7), (46), (53) are inconsistent by sub-proof #902.
% 153.32/22.92  | | | 
% 153.32/22.92  | | Case 2:
% 153.32/22.92  | | | 
% 153.32/22.92  | | |   (54)   ~ (all_54_14 = e2)
% 153.32/22.92  | | |   (55)  all_54_14 = e1 | all_54_14 = e0
% 153.32/22.92  | | | 
% 153.32/22.92  | | | BETA: splitting (40) gives:
% 153.32/22.92  | | | 
% 153.32/22.92  | | | Case 1:
% 153.32/22.92  | | | | 
% 153.32/22.92  | | | |   (56)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0)
% 153.32/22.92  | | | |           = e3)
% 153.32/22.92  | | | | 
% 153.32/22.92  | | | | BETA: splitting (56) gives:
% 153.32/22.92  | | | | 
% 153.32/22.92  | | | | Case 1:
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | |   (57)  all_56_9 = e3 & op(e3, e0) = e3
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | | ALPHA: (57) implies:
% 153.32/22.92  | | | | |   (58)  op(e3, e0) = e3
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | | REF_CLOSE: (10), (23), (28), (58) are inconsistent by sub-proof #1082.
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | Case 2:
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | |   (59)  all_56_10 = e3 & op(e2, e0) = e3
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | | ALPHA: (59) implies:
% 153.32/22.92  | | | | |   (60)  all_56_10 = e3
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | | REF_CLOSE: (5), (21), (60) are inconsistent by sub-proof #677.
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | End of split
% 153.32/22.92  | | | | 
% 153.32/22.92  | | | Case 2:
% 153.32/22.92  | | | | 
% 153.32/22.92  | | | |   (61)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0,
% 153.32/22.92  | | | |             e0) = e3)
% 153.32/22.92  | | | | 
% 153.32/22.92  | | | | BETA: splitting (61) gives:
% 153.32/22.92  | | | | 
% 153.32/22.92  | | | | Case 1:
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | |   (62)  all_56_11 = e3 & op(e1, e0) = e3
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | | ALPHA: (62) implies:
% 153.32/22.92  | | | | |   (63)  all_56_11 = e3
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | | BETA: splitting (47) gives:
% 153.32/22.92  | | | | | 
% 153.32/22.92  | | | | | Case 1:
% 153.32/22.92  | | | | | | 
% 153.32/22.92  | | | | | |   (64)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.32/22.92  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.32/22.92  | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.32/22.92  | | | | | |           $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 & all_57_15
% 153.32/22.92  | | | | | |           = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2,
% 153.32/22.92  | | | | | |             e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.32/22.92  | | | | | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.32/22.92  | | | | | |         | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.32/22.92  | | | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 153.32/22.92  | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0)
% 153.32/22.92  | | | | | |           & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.32/22.92  | | | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.32/22.92  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 153.32/22.92  | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_14)) | (all_57_3 =
% 153.32/22.92  | | | | | |           e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.32/22.92  | | | | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1,
% 153.32/22.92  | | | | | |             e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.32/22.92  | | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.32/22.92  | | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.32/22.92  | | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.32/22.92  | | | | | |           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 153.32/22.92  | | | | | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.32/22.92  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3
% 153.32/22.92  | | | | | |           & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3)
% 153.32/22.92  | | | | | |           & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.32/22.92  | | | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.32/22.92  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.32/22.92  | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 =
% 153.32/22.92  | | | | | |           e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.32/22.92  | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 153.32/22.92  | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.32/22.92  | | | | | |           $i(all_57_10))
% 153.32/22.92  | | | | | | 
% 153.32/22.92  | | | | | | BETA: splitting (64) gives:
% 153.32/22.92  | | | | | | 
% 153.32/22.92  | | | | | | Case 1:
% 153.32/22.92  | | | | | | | 
% 153.32/22.92  | | | | | | |   (65)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.32/22.92  | | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.32/22.92  | | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.32/22.92  | | | | | | |           $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 &
% 153.32/22.92  | | | | | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 153.32/22.92  | | | | | | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.32/22.92  | | | | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.32/22.92  | | | | | | |           $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3 &  ~
% 153.32/22.92  | | | | | | |           (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.32/22.92  | | | | | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1,
% 153.32/22.92  | | | | | | |             e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.32/22.92  | | | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.32/22.92  | | | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 153.32/22.92  | | | | | | |           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.32/22.92  | | | | | | |           $i(all_57_2) & $i(all_57_14))
% 153.32/22.92  | | | | | | | 
% 153.32/22.92  | | | | | | | BETA: splitting (65) gives:
% 153.32/22.92  | | | | | | | 
% 153.32/22.92  | | | | | | | Case 1:
% 153.32/22.92  | | | | | | | | 
% 153.32/22.92  | | | | | | | |   (66)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.32/22.92  | | | | | | | |           ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.32/22.92  | | | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.32/22.92  | | | | | | | |           $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 &
% 153.32/22.92  | | | | | | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 153.32/22.92  | | | | | | | |             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.32/22.92  | | | | | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2)
% 153.32/22.92  | | | | | | | |           & $i(all_57_12))
% 153.32/22.92  | | | | | | | | 
% 153.32/22.92  | | | | | | | | BETA: splitting (66) gives:
% 153.32/22.92  | | | | | | | | 
% 153.32/22.92  | | | | | | | | Case 1:
% 153.32/22.92  | | | | | | | | | 
% 153.32/22.92  | | | | | | | | |   (67)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.32/22.92  | | | | | | | | |         ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.32/22.92  | | | | | | | | |         all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.32/22.92  | | | | | | | | |         $i(all_57_1) & $i(all_57_12)
% 153.32/22.92  | | | | | | | | | 
% 153.32/22.92  | | | | | | | | | ALPHA: (67) implies:
% 153.32/22.92  | | | | | | | | |   (68)  op(e2, e3) = e2
% 153.32/22.92  | | | | | | | | | 
% 153.32/22.92  | | | | | | | | | REF_CLOSE: (1), (10), (12), (16), (36), (37), (41), (49), (68)
% 153.32/22.92  | | | | | | | | |            are inconsistent by sub-proof #599.
% 153.32/22.92  | | | | | | | | | 
% 153.32/22.92  | | | | | | | | Case 2:
% 153.32/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | |   (69)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) & 
% 153.47/22.92  | | | | | | | | |         ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.47/22.92  | | | | | | | | |         all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.47/22.92  | | | | | | | | |         $i(all_57_2) & $i(all_57_12)
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | ALPHA: (69) implies:
% 153.47/22.92  | | | | | | | | |   (70)  op(e2, e3) = e2
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | REF_CLOSE: (1), (10), (12), (16), (36), (37), (41), (49), (70)
% 153.47/22.92  | | | | | | | | |            are inconsistent by sub-proof #599.
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | End of split
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | Case 2:
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | |   (71)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 153.47/22.92  | | | | | | | |           ~ (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.47/22.92  | | | | | | | |             e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.47/22.92  | | | | | | | |           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 153.47/22.92  | | | | | | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 153.47/22.92  | | | | | | | |             e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.92  | | | | | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2)
% 153.47/22.92  | | | | | | | |           & $i(all_57_14))
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | | BETA: splitting (71) gives:
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | | Case 1:
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | |   (72)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 153.47/22.92  | | | | | | | | |         ~ (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.47/22.92  | | | | | | | | |           e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.47/22.92  | | | | | | | | |         & $i(all_57_0) & $i(all_57_14)
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | ALPHA: (72) implies:
% 153.47/22.92  | | | | | | | | |   (73)  op(e2, e2) = e3
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | REF_CLOSE: (10), (24), (48), (73) are inconsistent by
% 153.47/22.92  | | | | | | | | |            sub-proof #719.
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | Case 2:
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | |   (74)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) & 
% 153.47/22.92  | | | | | | | | |         ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 153.47/22.92  | | | | | | | | |         all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.47/22.92  | | | | | | | | |         $i(all_57_2) & $i(all_57_14)
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | ALPHA: (74) implies:
% 153.47/22.92  | | | | | | | | |   (75)   ~ (all_57_14 = e3)
% 153.47/22.92  | | | | | | | | |   (76)  op(e1, e3) = e1
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | REDUCE: (31), (75) imply:
% 153.47/22.92  | | | | | | | | |   (77)   ~ (e3 = e1)
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | BETA: splitting (55) gives:
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | Case 1:
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | |   (78)  all_54_14 = e1
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | | REF_CLOSE: (7), (44), (78) are inconsistent by sub-proof
% 153.47/22.92  | | | | | | | | | |            #753.
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | Case 2:
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | |   (79)  all_54_14 = e0
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | | COMBINE_EQS: (7), (79) imply:
% 153.47/22.92  | | | | | | | | | |   (80)  all_52_11 = e0
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | | SIMP: (80) implies:
% 153.47/22.92  | | | | | | | | | |   (81)  all_52_11 = e0
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | | REDUCE: (11), (81) imply:
% 153.47/22.92  | | | | | | | | | |   (82)   ~ (all_52_3 = e0)
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | | REDUCE: (15), (81) imply:
% 153.47/22.92  | | | | | | | | | |   (83)   ~ (e3 = e0)
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | | REDUCE: (46), (81) imply:
% 153.47/22.92  | | | | | | | | | |   (84)   ~ (e2 = e0)
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | | REDUCE: (44), (81) imply:
% 153.47/22.92  | | | | | | | | | |   (85)   ~ (e1 = e0)
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | | REF_CLOSE: (5), (8), (9), (10), (12), (24), (25), (26), (30),
% 153.47/22.92  | | | | | | | | | |            (33), (34), (35), (38), (39), (43), (45), (48),
% 153.47/22.92  | | | | | | | | | |            (76), (82) are inconsistent by sub-proof #598.
% 153.47/22.92  | | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | End of split
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | End of split
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | End of split
% 153.47/22.92  | | | | | | | 
% 153.47/22.92  | | | | | | Case 2:
% 153.47/22.92  | | | | | | | 
% 153.47/22.92  | | | | | | |   (86)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.92  | | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 153.47/22.92  | | | | | | |           e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.92  | | | | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 &
% 153.47/22.92  | | | | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 153.47/22.92  | | | | | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.47/22.92  | | | | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.47/22.92  | | | | | | |           $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.47/22.92  | | | | | | |           (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2
% 153.47/22.92  | | | | | | |           & op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.47/22.92  | | | | | | |           all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 =
% 153.47/22.92  | | | | | | |           e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.47/22.92  | | | | | | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.92  | | | | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.47/22.92  | | | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.47/22.92  | | | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.47/22.92  | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2,
% 153.47/22.92  | | | | | | |             e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.47/22.92  | | | | | | | 
% 153.47/22.92  | | | | | | | BETA: splitting (86) gives:
% 153.47/22.92  | | | | | | | 
% 153.47/22.92  | | | | | | | Case 1:
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | |   (87)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) & 
% 153.47/22.92  | | | | | | | |           ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 153.47/22.92  | | | | | | | |             e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.92  | | | | | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 &
% 153.47/22.92  | | | | | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 153.47/22.92  | | | | | | | |             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.47/22.92  | | | | | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5)
% 153.47/22.92  | | | | | | | |           & $i(all_57_10))
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | | REF_CLOSE: (6), (10), (20), (87) are inconsistent by sub-proof
% 153.47/22.92  | | | | | | | |            #863.
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | Case 2:
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | |   (88)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.47/22.92  | | | | | | | |           ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.47/22.92  | | | | | | | |           all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.92  | | | | | | | |           $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 153.47/22.92  | | | | | | | |           all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.47/22.92  | | | | | | | |             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.92  | | | | | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5)
% 153.47/22.92  | | | | | | | |           & $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 & 
% 153.47/22.92  | | | | | | | |           ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.47/22.92  | | | | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2,
% 153.47/22.92  | | | | | | | |             e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | | BETA: splitting (88) gives:
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | | Case 1:
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | |   (89)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.47/22.92  | | | | | | | | |         ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.47/22.92  | | | | | | | | |         all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.92  | | | | | | | | |         $i(all_57_3) & $i(all_57_14)
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | ALPHA: (89) implies:
% 153.47/22.92  | | | | | | | | |   (90)  op(e3, e3) = e2
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | REF_CLOSE: (10), (26), (43), (90) are inconsistent by
% 153.47/22.92  | | | | | | | | |            sub-proof #1074.
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | Case 2:
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | |   (91)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &
% 153.47/22.92  | | | | | | | | |            ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.47/22.92  | | | | | | | | |           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2
% 153.47/22.92  | | | | | | | | |           & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 153.47/22.92  | | | | | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.47/22.92  | | | | | | | | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.47/22.92  | | | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.47/22.92  | | | | | | | | |           $i(all_57_7) & $i(all_57_10))
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | | REF_CLOSE: (4), (10), (27), (35), (48), (91) are inconsistent
% 153.47/22.92  | | | | | | | | |            by sub-proof #720.
% 153.47/22.92  | | | | | | | | | 
% 153.47/22.92  | | | | | | | | End of split
% 153.47/22.92  | | | | | | | | 
% 153.47/22.92  | | | | | | | End of split
% 153.47/22.92  | | | | | | | 
% 153.47/22.92  | | | | | | End of split
% 153.47/22.92  | | | | | | 
% 153.47/22.92  | | | | | Case 2:
% 153.47/22.92  | | | | | | 
% 153.47/22.92  | | | | | |   (92)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.47/22.92  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 153.47/22.92  | | | | | |           e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.47/22.92  | | | | | |           $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 & all_57_10
% 153.47/22.92  | | | | | |           = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3,
% 153.47/22.92  | | | | | |             e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.47/22.92  | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.47/22.92  | | | | | |           $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~
% 153.47/22.92  | | | | | |           (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 153.47/22.92  | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 &
% 153.47/22.92  | | | | | |           op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.47/22.92  | | | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.47/22.92  | | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 153.47/22.92  | | | | | |           e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.47/22.92  | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.47/22.92  | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1)
% 153.47/22.92  | | | | | |           & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 153.47/22.92  | | | | | |           e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.47/22.92  | | | | | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~
% 153.47/22.92  | | | | | |           (all_57_9 = e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 153.47/22.92  | | | | | |           op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 & op(e2,
% 153.47/22.92  | | | | | |             e0) = e2 & $i(all_57_9) & $i(all_57_12)) | (all_57_10 =
% 153.47/22.92  | | | | | |           e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 153.47/22.92  | | | | | |             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1,
% 153.47/22.92  | | | | | |             e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.47/22.92  | | | | | |           $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.47/22.92  | | | | | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.47/22.92  | | | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0)
% 153.47/22.92  | | | | | |           = all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12
% 153.47/22.92  | | | | | |           = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.47/22.92  | | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.47/22.92  | | | | | |           all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.47/22.92  | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.47/22.92  | | | | | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 153.47/22.92  | | | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.47/22.92  | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.92  | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.47/22.92  | | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.47/22.92  | | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.47/22.92  | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.47/22.92  | | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.47/22.92  | | | | | |               e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.47/22.92  | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.47/22.92  | | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.47/22.92  | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.47/22.92  | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.47/22.92  | | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.47/22.92  | | | | | |               e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.47/22.92  | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.47/22.92  | | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 153.47/22.92  | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.47/22.92  | | | | | |               $i(all_57_7))))
% 153.47/22.92  | | | | | | 
% 153.47/22.92  | | | | | | BETA: splitting (92) gives:
% 153.47/22.92  | | | | | | 
% 153.47/22.92  | | | | | | Case 1:
% 153.47/22.92  | | | | | | | 
% 153.47/22.92  | | | | | | |   (93)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.47/22.92  | | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 153.47/22.92  | | | | | | |           e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.47/22.92  | | | | | | |           $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 &
% 153.47/22.92  | | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 153.47/22.92  | | | | | | |             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 153.47/22.92  | | | | | | |             e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.47/22.92  | | | | | | |           $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~
% 153.47/22.92  | | | | | | |           (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 153.47/22.92  | | | | | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 &
% 153.47/22.93  | | | | | | |           op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.47/22.93  | | | | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.47/22.93  | | | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 153.47/22.93  | | | | | | |           e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.47/22.93  | | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.47/22.93  | | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 =
% 153.47/22.93  | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.47/22.93  | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10)
% 153.47/22.93  | | | | | | |           & $i(all_57_13))
% 153.47/22.93  | | | | | | | 
% 153.47/22.93  | | | | | | | BETA: splitting (93) gives:
% 153.47/22.93  | | | | | | | 
% 153.47/22.93  | | | | | | | Case 1:
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | |   (94)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) & 
% 153.47/22.93  | | | | | | | |           ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 153.47/22.93  | | | | | | | |             e1) = e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.47/22.93  | | | | | | | |           $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 &
% 153.47/22.93  | | | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 153.47/22.93  | | | | | | | |             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.47/22.93  | | | | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.47/22.93  | | | | | | | |           $i(all_57_6) & $i(all_57_12))
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | | BETA: splitting (94) gives:
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | | Case 1:
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | |   (95)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) & 
% 153.47/22.93  | | | | | | | | |         ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 153.47/22.93  | | | | | | | | |           e1) = e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.47/22.93  | | | | | | | | |         $i(all_57_8) & $i(all_57_10)
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | ALPHA: (95) implies:
% 153.47/22.93  | | | | | | | | |   (96)  op(e0, e0) = e1
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | REF_CLOSE: (3), (8), (10), (17), (21), (24), (35), (38), (43),
% 153.47/22.93  | | | | | | | | |            (63), (96) are inconsistent by sub-proof #588.
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | Case 2:
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | |   (97)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.47/22.93  | | | | | | | | |         ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.47/22.93  | | | | | | | | |         all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.47/22.93  | | | | | | | | |         $i(all_57_6) & $i(all_57_12)
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | ALPHA: (97) implies:
% 153.47/22.93  | | | | | | | | |   (98)   ~ (all_57_6 = e3)
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | REDUCE: (2), (98) imply:
% 153.47/22.93  | | | | | | | | |   (99)  $false
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | CLOSE: (99) is inconsistent.
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | End of split
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | Case 2:
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | |   (100)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) & 
% 153.47/22.93  | | | | | | | |            ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 153.47/22.93  | | | | | | | |              e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1
% 153.47/22.93  | | | | | | | |            & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 153.47/22.93  | | | | | | | |            all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 153.47/22.93  | | | | | | | |              = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.47/22.93  | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.47/22.93  | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.47/22.93  | | | | | | | |            all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 153.47/22.93  | | | | | | | |              = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.47/22.93  | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.47/22.93  | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | | BETA: splitting (100) gives:
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | | Case 1:
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | |   (101)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &
% 153.47/22.93  | | | | | | | | |           ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2,
% 153.47/22.93  | | | | | | | | |            e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1
% 153.47/22.93  | | | | | | | | |          & $i(all_57_8) & $i(all_57_12)
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | ALPHA: (101) implies:
% 153.47/22.93  | | | | | | | | |   (102)  op(e0, e0) = e1
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | REF_CLOSE: (3), (8), (10), (17), (21), (24), (35), (38), (43),
% 153.47/22.93  | | | | | | | | |            (63), (102) are inconsistent by sub-proof #588.
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | Case 2:
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | |   (103)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.47/22.93  | | | | | | | | |            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 153.47/22.93  | | | | | | | | |            op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 153.47/22.93  | | | | | | | | |            all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 153.47/22.93  | | | | | | | | |          (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.47/22.93  | | | | | | | | |            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 153.47/22.93  | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.47/22.93  | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | REF_CLOSE: (10), (23), (28), (103) are inconsistent by
% 153.47/22.93  | | | | | | | | |            sub-proof #1081.
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | End of split
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | End of split
% 153.47/22.93  | | | | | | | 
% 153.47/22.93  | | | | | | Case 2:
% 153.47/22.93  | | | | | | | 
% 153.47/22.93  | | | | | | |   (104)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) & 
% 153.47/22.93  | | | | | | |            ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.47/22.93  | | | | | | |            all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.47/22.93  | | | | | | |            $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 &
% 153.47/22.93  | | | | | | |            all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 153.47/22.93  | | | | | | |              e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.47/22.93  | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 153.47/22.93  | | | | | | |            & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 & 
% 153.47/22.93  | | | | | | |            ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.47/22.93  | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1,
% 153.47/22.93  | | | | | | |              e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 153.47/22.93  | | | | | | |          (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 153.47/22.93  | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.47/22.93  | | | | | | |            all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.47/22.93  | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.47/22.93  | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12
% 153.47/22.93  | | | | | | |                = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.47/22.93  | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 153.47/22.93  | | | | | | |                  e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.47/22.93  | | | | | | |                all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 153.47/22.93  | | | | | | |                  = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.47/22.93  | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 153.47/22.93  | | | | | | |                all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15
% 153.47/22.93  | | | | | | |                  = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.47/22.93  | | | | | | |                op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.47/22.93  | | | | | | |                all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.47/22.93  | | | | | | |                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.93  | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.47/22.93  | | | | | | |                all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 153.47/22.93  | | | | | | |                  = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.47/22.93  | | | | | | |                op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.47/22.93  | | | | | | |                all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15
% 153.47/22.93  | | | | | | |                  = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.47/22.93  | | | | | | |                op(e0, e1) = e0 & $i(all_57_7))))
% 153.47/22.93  | | | | | | | 
% 153.47/22.93  | | | | | | | BETA: splitting (104) gives:
% 153.47/22.93  | | | | | | | 
% 153.47/22.93  | | | | | | | Case 1:
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | |   (105)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &
% 153.47/22.93  | | | | | | | |             ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.47/22.93  | | | | | | | |            all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.47/22.93  | | | | | | | |            $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 &
% 153.47/22.93  | | | | | | | |            all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 153.47/22.93  | | | | | | | |              e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.47/22.93  | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.47/22.93  | | | | | | | |            $i(all_57_9) & $i(all_57_14))
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | | REF_CLOSE: (10), (26), (35), (105) are inconsistent by sub-proof
% 153.47/22.93  | | | | | | | |            #956.
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | Case 2:
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | |   (106)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0)
% 153.47/22.93  | | | | | | | |            &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 153.47/22.93  | | | | | | | |            op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.47/22.93  | | | | | | | |            all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 153.47/22.93  | | | | | | | |          (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2)
% 153.47/22.93  | | | | | | | |            &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 153.47/22.93  | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.47/22.93  | | | | | | | |            e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.47/22.93  | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.47/22.93  | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.47/22.93  | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.47/22.93  | | | | | | | |                  e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.47/22.93  | | | | | | | |              (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.47/22.93  | | | | | | | |                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.47/22.93  | | | | | | | |                all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.47/22.93  | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &
% 153.47/22.93  | | | | | | | |                 ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 153.47/22.93  | | | | | | | |                  e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) =
% 153.47/22.93  | | | | | | | |                e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 153.47/22.93  | | | | | | | |                e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 153.47/22.93  | | | | | | | |                op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0,
% 153.47/22.93  | | | | | | | |                  e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.47/22.93  | | | | | | | |                all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.47/22.93  | | | | | | | |                (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.47/22.93  | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.47/22.93  | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 153.47/22.93  | | | | | | | |                  e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.47/22.93  | | | | | | | |                op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.47/22.93  | | | | | | | |                $i(all_57_7))))
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | | BETA: splitting (106) gives:
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | | Case 1:
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | |   (107)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0)
% 153.47/22.93  | | | | | | | | |          &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 153.47/22.93  | | | | | | | | |          op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.47/22.93  | | | | | | | | |          all_57_13 & $i(all_57_12) & $i(all_57_13)
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | ALPHA: (107) implies:
% 153.47/22.93  | | | | | | | | |   (108)  op(e2, e0) = e2
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | REF_CLOSE: (10), (19), (29), (108) are inconsistent by
% 153.47/22.93  | | | | | | | | |            sub-proof #1156.
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | Case 2:
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | |   (109)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.47/22.93  | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.47/22.93  | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 153.47/22.93  | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.47/22.93  | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.47/22.93  | | | | | | | | |                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.47/22.93  | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.47/22.93  | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.93  | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 153.47/22.93  | | | | | | | | |                &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.47/22.93  | | | | | | | | |                op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.47/22.93  | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 153.47/22.93  | | | | | | | | |                e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.47/22.93  | | | | | | | | |                (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 153.47/22.93  | | | | | | | | |                = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.93  | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.47/22.93  | | | | | | | | |                  e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.47/22.93  | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.47/22.93  | | | | | | | | |                $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 153.47/22.93  | | | | | | | | |                &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 153.47/22.93  | | | | | | | | |                op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.47/22.93  | | | | | | | | |                op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.47/22.93  | | | | | | | | |                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.47/22.93  | | | | | | | | |                (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 153.47/22.93  | | | | | | | | |                = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | BETA: splitting (109) gives:
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | Case 1:
% 153.47/22.93  | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | |   (110)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.47/22.93  | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.47/22.93  | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 153.47/22.93  | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 153.47/22.93  | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | ALPHA: (110) implies:
% 153.47/22.93  | | | | | | | | | |   (111)  op(e1, e0) = e1
% 153.47/22.93  | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | REF_CLOSE: (10), (13), (18), (111) are inconsistent by
% 153.47/22.93  | | | | | | | | | |            sub-proof #961.
% 153.47/22.93  | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | Case 2:
% 153.47/22.93  | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | |   (112)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.47/22.93  | | | | | | | | | |              = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.47/22.93  | | | | | | | | | |              (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.47/22.93  | | | | | | | | | |              op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.93  | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 153.47/22.93  | | | | | | | | | |              &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.47/22.93  | | | | | | | | | |              op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.47/22.93  | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 153.47/22.93  | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.47/22.93  | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 153.47/22.93  | | | | | | | | | |              = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.93  | | | | | | | | | |            (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.47/22.93  | | | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.47/22.93  | | | | | | | | | |              all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.47/22.93  | | | | | | | | | |              $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 153.47/22.93  | | | | | | | | | |              &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 153.47/22.93  | | | | | | | | | |              op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.47/22.93  | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.47/22.93  | | | | | | | | | |              e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.47/22.93  | | | | | | | | | |              (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 153.47/22.93  | | | | | | | | | |              = all_57_7 & op(e0, e1) = e0 & $i(all_57_7)))
% 153.47/22.93  | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | ALPHA: (112) implies:
% 153.47/22.93  | | | | | | | | | |   (113)  op(e0, e0) = all_57_15
% 153.47/22.93  | | | | | | | | | |   (114)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.47/22.93  | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.47/22.93  | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.93  | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &
% 153.47/22.93  | | | | | | | | | |             ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1,
% 153.47/22.93  | | | | | | | | | |              e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 153.47/22.93  | | | | | | | | | |            e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 153.47/22.93  | | | | | | | | | |            e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.47/22.93  | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 153.47/22.93  | | | | | | | | | |              e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.47/22.93  | | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.93  | | | | | | | | | |            (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.47/22.93  | | | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.47/22.93  | | | | | | | | | |          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 153.47/22.93  | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.47/22.93  | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.47/22.93  | | | | | | | | | |            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &
% 153.47/22.93  | | | | | | | | | |             ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 153.47/22.93  | | | | | | | | | |              e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) =
% 153.47/22.93  | | | | | | | | | |            e0 & $i(all_57_7))
% 153.47/22.93  | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | BETA: splitting (114) gives:
% 153.47/22.93  | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | Case 1:
% 153.47/22.93  | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | |   (115)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.47/22.93  | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.47/22.93  | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.93  | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 153.47/22.93  | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.47/22.93  | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.47/22.93  | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 153.47/22.93  | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.47/22.93  | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 153.47/22.93  | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.47/22.93  | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | REF_CLOSE: (5), (10), (14), (24), (32), (48), (113), (115)
% 153.47/22.93  | | | | | | | | | | |            are inconsistent by sub-proof #717.
% 153.47/22.93  | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | Case 2:
% 153.47/22.93  | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | |   (116)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.47/22.93  | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.47/22.93  | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.47/22.93  | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 153.47/22.93  | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 153.47/22.93  | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.47/22.93  | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.47/22.93  | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.47/22.93  | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 153.47/22.93  | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.47/22.93  | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | BETA: splitting (116) gives:
% 153.47/22.93  | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | Case 1:
% 153.47/22.93  | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | |   (117)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.47/22.93  | | | | | | | | | | | |            e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.47/22.93  | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.47/22.93  | | | | | | | | | | | |          $i(all_57_4)
% 153.47/22.93  | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | ALPHA: (117) implies:
% 153.47/22.93  | | | | | | | | | | | |   (118)   ~ (all_57_15 = e2)
% 153.47/22.93  | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | REF_CLOSE: (10), (14), (113), (118) are inconsistent by
% 153.47/22.93  | | | | | | | | | | | |            sub-proof #901.
% 153.47/22.93  | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | Case 2:
% 153.47/22.93  | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | |   (119)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 153.47/22.93  | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.47/22.93  | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.47/22.93  | | | | | | | | | | | |            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 153.47/22.93  | | | | | | | | | | | |            &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.47/22.93  | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 153.47/22.93  | | | | | | | | | | | |              e1) = e0 & $i(all_57_7))
% 153.47/22.93  | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | BETA: splitting (119) gives:
% 153.47/22.93  | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | Case 1:
% 153.47/22.93  | | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | |   (120)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 153.47/22.93  | | | | | | | | | | | | |            e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.47/22.93  | | | | | | | | | | | | |          op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.47/22.93  | | | | | | | | | | | | |          $i(all_57_6)
% 153.47/22.93  | | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | | ALPHA: (120) implies:
% 153.47/22.93  | | | | | | | | | | | | |   (121)   ~ (all_57_6 = e3)
% 153.47/22.93  | | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | | REDUCE: (2), (121) imply:
% 153.47/22.93  | | | | | | | | | | | | |   (122)  $false
% 153.47/22.93  | | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | | CLOSE: (122) is inconsistent.
% 153.47/22.93  | | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | Case 2:
% 153.47/22.93  | | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | |   (123)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 153.47/22.93  | | | | | | | | | | | | |            e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.47/22.93  | | | | | | | | | | | | |          op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.47/22.93  | | | | | | | | | | | | |          $i(all_57_7)
% 153.47/22.93  | | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | | ALPHA: (123) implies:
% 153.47/22.93  | | | | | | | | | | | | |   (124)  op(e2, e2) = e1
% 153.47/22.93  | | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | | REF_CLOSE: (10), (35), (48), (124) are inconsistent by
% 153.47/22.93  | | | | | | | | | | | | |            sub-proof #853.
% 153.47/22.93  | | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | | End of split
% 153.47/22.93  | | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | | End of split
% 153.47/22.93  | | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | | End of split
% 153.47/22.93  | | | | | | | | | | 
% 153.47/22.93  | | | | | | | | | End of split
% 153.47/22.93  | | | | | | | | | 
% 153.47/22.93  | | | | | | | | End of split
% 153.47/22.93  | | | | | | | | 
% 153.47/22.93  | | | | | | | End of split
% 153.47/22.93  | | | | | | | 
% 153.47/22.93  | | | | | | End of split
% 153.47/22.93  | | | | | | 
% 153.47/22.93  | | | | | End of split
% 153.47/22.93  | | | | | 
% 153.47/22.93  | | | | Case 2:
% 153.47/22.93  | | | | | 
% 153.47/22.93  | | | | |   (125)  all_56_15 = e3 & op(e0, e0) = e3
% 153.47/22.93  | | | | | 
% 153.47/22.93  | | | | | ALPHA: (125) implies:
% 153.47/22.93  | | | | |   (126)  all_56_15 = e3
% 153.47/22.93  | | | | | 
% 153.47/22.93  | | | | | COMBINE_EQS: (42), (126) imply:
% 153.47/22.93  | | | | |   (127)  e3 = e2
% 153.47/22.93  | | | | | 
% 153.47/22.93  | | | | | REDUCE: (38), (127) imply:
% 153.47/22.93  | | | | |   (128)  $false
% 153.47/22.93  | | | | | 
% 153.47/22.93  | | | | | CLOSE: (128) is inconsistent.
% 153.47/22.93  | | | | | 
% 153.47/22.93  | | | | End of split
% 153.47/22.93  | | | | 
% 153.47/22.93  | | | End of split
% 153.47/22.93  | | | 
% 153.47/22.93  | | End of split
% 153.47/22.93  | | 
% 153.47/22.93  | End of split
% 153.47/22.93  | 
% 153.47/22.93  End of proof
% 153.47/22.93  
% 153.47/22.93  Sub-proof #588 shows that the following formulas are inconsistent:
% 153.47/22.93  ----------------------------------------------------------------
% 153.47/22.93    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.47/22.93         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.47/22.93    (2)  all_56_11 = e3
% 153.47/22.93    (3)   ~ (e2 = e0)
% 153.47/22.93    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.93    (5)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.47/22.93             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.47/22.93               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.47/22.93               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.47/22.93    (6)  op(e0, e0) = e1
% 153.47/22.93    (7)  all_56_10 = e1
% 153.47/22.93    (8)   ~ (e3 = e0)
% 153.47/22.93    (9)   ~ (e1 = e0)
% 153.47/22.93    (10)   ~ (e3 = e2)
% 153.47/22.93    (11)   ~ (e2 = e1)
% 153.47/22.93  
% 153.47/22.93  Begin of proof
% 153.47/22.93  | 
% 153.47/22.93  | BETA: splitting (5) gives:
% 153.47/22.93  | 
% 153.47/22.93  | Case 1:
% 153.47/22.93  | | 
% 153.47/22.93  | |   (12)  all_56_15 = e0 & op(e0, e0) = e0
% 153.47/22.93  | | 
% 153.47/22.93  | | ALPHA: (12) implies:
% 153.47/22.93  | |   (13)  op(e0, e0) = e0
% 153.47/22.93  | | 
% 153.47/22.93  | | REF_CLOSE: (4), (6), (9), (13) are inconsistent by sub-proof #1040.
% 153.47/22.93  | | 
% 153.47/22.93  | Case 2:
% 153.47/22.93  | | 
% 153.47/22.93  | |   (14)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.47/22.93  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 153.47/22.93  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.47/22.93  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 153.47/22.93  | | 
% 153.47/22.93  | | ALPHA: (14) implies:
% 153.47/22.93  | |   (15)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.47/22.93  | |           e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.47/22.93  | | 
% 153.47/22.93  | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (15) are
% 153.47/22.93  | |            inconsistent by sub-proof #589.
% 153.47/22.93  | | 
% 153.47/22.93  | End of split
% 153.47/22.93  | 
% 153.47/22.93  End of proof
% 153.47/22.93  
% 153.47/22.93  Sub-proof #589 shows that the following formulas are inconsistent:
% 153.47/22.93  ----------------------------------------------------------------
% 153.47/22.93    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.47/22.93         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.47/22.93    (2)  all_56_11 = e3
% 153.47/22.93    (3)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 153.47/22.93         (all_56_11 = e0 & op(e1, e0) = e0)
% 153.47/22.93    (4)   ~ (e2 = e0)
% 153.47/22.93    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.93    (6)  op(e0, e0) = e1
% 153.47/22.93    (7)  all_56_10 = e1
% 153.47/22.93    (8)   ~ (e3 = e0)
% 153.47/22.93    (9)   ~ (e1 = e0)
% 153.47/22.93    (10)   ~ (e3 = e2)
% 153.47/22.93    (11)   ~ (e2 = e1)
% 153.47/22.93  
% 153.47/22.93  Begin of proof
% 153.47/22.93  | 
% 153.47/22.93  | BETA: splitting (3) gives:
% 153.47/22.93  | 
% 153.47/22.93  | Case 1:
% 153.47/22.93  | | 
% 153.47/22.93  | |   (12)  all_56_9 = e0 & op(e3, e0) = e0
% 153.47/22.93  | | 
% 153.47/22.93  | | ALPHA: (12) implies:
% 153.47/22.93  | |   (13)  all_56_9 = e0
% 153.47/22.93  | | 
% 153.47/22.93  | | BETA: splitting (1) gives:
% 153.47/22.93  | | 
% 153.47/22.93  | | Case 1:
% 153.47/22.93  | | | 
% 153.47/22.93  | | |   (14)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 153.47/22.93  | | |           e2)
% 153.47/22.93  | | | 
% 153.47/22.93  | | | BETA: splitting (14) gives:
% 153.47/22.93  | | | 
% 153.47/22.93  | | | Case 1:
% 153.47/22.93  | | | | 
% 153.47/22.93  | | | |   (15)  all_56_9 = e2 & op(e3, e0) = e2
% 153.47/22.93  | | | | 
% 153.47/22.93  | | | | REF_CLOSE: (4), (13), (15) are inconsistent by sub-proof #906.
% 153.47/22.93  | | | | 
% 153.47/22.93  | | | Case 2:
% 153.47/22.93  | | | | 
% 153.47/22.93  | | | |   (16)  all_56_10 = e2 & op(e2, e0) = e2
% 153.47/22.93  | | | | 
% 153.47/22.93  | | | | REF_CLOSE: (7), (11), (16) are inconsistent by sub-proof #679.
% 153.47/22.93  | | | | 
% 153.47/22.93  | | | End of split
% 153.47/22.93  | | | 
% 153.47/22.93  | | Case 2:
% 153.47/22.93  | | | 
% 153.47/22.93  | | |   (17)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0)
% 153.47/22.93  | | |           = e2)
% 153.47/22.93  | | | 
% 153.47/22.93  | | | REF_CLOSE: (2), (5), (6), (10), (11), (17) are inconsistent by sub-proof
% 153.47/22.93  | | |            #590.
% 153.47/22.93  | | | 
% 153.47/22.93  | | End of split
% 153.47/22.93  | | 
% 153.47/22.93  | Case 2:
% 153.47/22.93  | | 
% 153.47/22.93  | |   (18)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.47/22.93  | |           e0)
% 153.47/22.93  | | 
% 153.47/22.93  | | BETA: splitting (18) gives:
% 153.47/22.93  | | 
% 153.47/22.93  | | Case 1:
% 153.47/22.93  | | | 
% 153.47/22.93  | | |   (19)  all_56_10 = e0 & op(e2, e0) = e0
% 153.47/22.93  | | | 
% 153.47/22.93  | | | REF_CLOSE: (7), (9), (19) are inconsistent by sub-proof #884.
% 153.47/22.93  | | | 
% 153.47/22.93  | | Case 2:
% 153.47/22.93  | | | 
% 153.47/22.93  | | |   (20)  all_56_11 = e0 & op(e1, e0) = e0
% 153.47/22.93  | | | 
% 153.47/22.93  | | | ALPHA: (20) implies:
% 153.47/22.93  | | |   (21)  all_56_11 = e0
% 153.47/22.93  | | | 
% 153.47/22.93  | | | REF_CLOSE: (2), (8), (21) are inconsistent by sub-proof #772.
% 153.47/22.93  | | | 
% 153.47/22.93  | | End of split
% 153.47/22.93  | | 
% 153.47/22.93  | End of split
% 153.47/22.93  | 
% 153.47/22.93  End of proof
% 153.47/22.93  
% 153.47/22.93  Sub-proof #590 shows that the following formulas are inconsistent:
% 153.47/22.93  ----------------------------------------------------------------
% 153.47/22.93    (1)  all_56_11 = e3
% 153.47/22.93    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.93    (3)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.47/22.93    (4)  op(e0, e0) = e1
% 153.47/22.93    (5)   ~ (e3 = e2)
% 153.47/22.93    (6)   ~ (e2 = e1)
% 153.47/22.93  
% 153.47/22.93  Begin of proof
% 153.47/22.93  | 
% 153.47/22.93  | BETA: splitting (3) gives:
% 153.47/22.93  | 
% 153.47/22.93  | Case 1:
% 153.47/22.93  | | 
% 153.47/22.93  | |   (7)  all_56_11 = e2 & op(e1, e0) = e2
% 153.47/22.93  | | 
% 153.47/22.93  | | ALPHA: (7) implies:
% 153.47/22.93  | |   (8)  all_56_11 = e2
% 153.47/22.93  | | 
% 153.47/22.93  | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #591.
% 153.47/22.93  | | 
% 153.47/22.93  | Case 2:
% 153.47/22.93  | | 
% 153.47/22.93  | |   (9)  all_56_15 = e2 & op(e0, e0) = e2
% 153.47/22.93  | | 
% 153.47/22.93  | | ALPHA: (9) implies:
% 153.47/22.93  | |   (10)  op(e0, e0) = e2
% 153.47/22.93  | | 
% 153.47/22.93  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #978.
% 153.47/22.93  | | 
% 153.47/22.93  | End of split
% 153.47/22.93  | 
% 153.47/22.93  End of proof
% 153.47/22.93  
% 153.47/22.93  Sub-proof #591 shows that the following formulas are inconsistent:
% 153.47/22.93  ----------------------------------------------------------------
% 153.47/22.93    (1)  all_56_11 = e3
% 153.47/22.93    (2)  all_56_11 = e2
% 153.47/22.93    (3)   ~ (e3 = e2)
% 153.47/22.93  
% 153.47/22.93  Begin of proof
% 153.47/22.93  | 
% 153.47/22.93  | COMBINE_EQS: (1), (2) imply:
% 153.47/22.93  |   (4)  e3 = e2
% 153.47/22.93  | 
% 153.47/22.93  | SIMP: (4) implies:
% 153.47/22.93  |   (5)  e3 = e2
% 153.47/22.93  | 
% 153.47/22.93  | REDUCE: (3), (5) imply:
% 153.47/22.93  |   (6)  $false
% 153.47/22.93  | 
% 153.47/22.93  | CLOSE: (6) is inconsistent.
% 153.47/22.93  | 
% 153.47/22.93  End of proof
% 153.47/22.93  
% 153.47/22.93  Sub-proof #592 shows that the following formulas are inconsistent:
% 153.47/22.93  ----------------------------------------------------------------
% 153.47/22.93    (1)  all_56_1 = e1
% 153.47/22.93    (2)   ~ (e3 = e1)
% 153.47/22.93    (3)  op(e3, e2) = all_52_4
% 153.47/22.93    (4)   ~ (e2 = e0)
% 153.47/22.93    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.93    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.47/22.93         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.47/22.93    (7)   ~ (e3 = e0)
% 153.47/22.93    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.47/22.93         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.47/22.93    (9)  op(e3, e3) = e1
% 153.47/22.93    (10)   ~ (e1 = e0)
% 153.47/22.93    (11)   ~ (e3 = e2)
% 153.47/22.93    (12)  all_56_9 = e2
% 153.47/22.93    (13)   ~ (all_52_4 = e0)
% 153.47/22.93  
% 153.47/22.93  Begin of proof
% 153.47/22.93  | 
% 153.47/22.93  | BETA: splitting (8) gives:
% 153.47/22.93  | 
% 153.47/22.93  | Case 1:
% 153.47/22.93  | | 
% 153.47/22.93  | |   (14)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 153.47/22.93  | |           e0)
% 153.47/22.93  | | 
% 153.47/22.93  | | REF_CLOSE: (3), (5), (9), (10), (13), (14) are inconsistent by sub-proof
% 153.47/22.93  | |            #937.
% 153.47/22.93  | | 
% 153.47/22.93  | Case 2:
% 153.47/22.93  | | 
% 153.47/22.93  | |   (15)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 153.47/22.93  | |           e0)
% 153.47/22.93  | | 
% 153.47/22.93  | | BETA: splitting (15) gives:
% 153.47/22.93  | | 
% 153.47/22.93  | | Case 1:
% 153.47/22.93  | | | 
% 153.47/22.93  | | |   (16)  all_56_4 = e0 & op(e3, e1) = e0
% 153.47/22.93  | | | 
% 153.47/22.93  | | | ALPHA: (16) implies:
% 153.47/22.93  | | |   (17)  all_56_4 = e0
% 153.47/22.93  | | | 
% 153.47/22.93  | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (11), (12), (17) are inconsistent
% 153.47/22.93  | | |            by sub-proof #593.
% 153.47/22.93  | | | 
% 153.47/22.93  | | Case 2:
% 153.47/22.93  | | | 
% 153.47/22.93  | | |   (18)  all_56_9 = e0 & op(e3, e0) = e0
% 153.47/22.93  | | | 
% 153.47/22.93  | | | REF_CLOSE: (4), (12), (18) are inconsistent by sub-proof #746.
% 153.47/22.93  | | | 
% 153.47/22.93  | | End of split
% 153.47/22.93  | | 
% 153.47/22.93  | End of split
% 153.47/22.93  | 
% 153.47/22.93  End of proof
% 153.47/22.93  
% 153.47/22.93  Sub-proof #593 shows that the following formulas are inconsistent:
% 153.47/22.93  ----------------------------------------------------------------
% 153.47/22.93    (1)  all_56_1 = e1
% 153.47/22.93    (2)   ~ (e3 = e1)
% 153.47/22.93    (3)  all_56_4 = e0
% 153.47/22.93    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.93           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.93    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.47/22.93         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.47/22.93    (6)   ~ (e3 = e0)
% 153.47/22.93    (7)  op(e3, e3) = e1
% 153.47/22.93    (8)   ~ (e3 = e2)
% 153.47/22.93    (9)  all_56_9 = e2
% 153.47/22.93  
% 153.47/22.93  Begin of proof
% 153.47/22.93  | 
% 153.47/22.93  | BETA: splitting (5) gives:
% 153.47/22.93  | 
% 153.47/22.93  | Case 1:
% 153.47/22.93  | | 
% 153.47/22.93  | |   (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 153.47/22.93  | |           e3)
% 153.47/22.93  | | 
% 153.47/22.93  | | BETA: splitting (10) gives:
% 153.47/22.93  | | 
% 153.47/22.93  | | Case 1:
% 153.47/22.93  | | | 
% 153.47/22.93  | | |   (11)  all_56_0 = e3 & op(e3, e3) = e3
% 153.47/22.93  | | | 
% 153.47/22.93  | | | ALPHA: (11) implies:
% 153.47/22.93  | | |   (12)  op(e3, e3) = e3
% 153.47/22.93  | | | 
% 153.47/22.93  | | | REF_CLOSE: (2), (4), (7), (12) are inconsistent by sub-proof #1178.
% 153.47/22.93  | | | 
% 153.47/22.93  | | Case 2:
% 153.47/22.93  | | | 
% 153.47/22.93  | | |   (13)  all_56_1 = e3 & op(e3, e2) = e3
% 153.47/22.93  | | | 
% 153.47/22.93  | | | ALPHA: (13) implies:
% 153.47/22.93  | | |   (14)  all_56_1 = e3
% 153.47/22.93  | | | 
% 153.47/22.93  | | | COMBINE_EQS: (1), (14) imply:
% 153.47/22.93  | | |   (15)  e3 = e1
% 153.47/22.93  | | | 
% 153.47/22.93  | | | REDUCE: (2), (15) imply:
% 153.47/22.93  | | |   (16)  $false
% 153.47/22.93  | | | 
% 153.47/22.93  | | | CLOSE: (16) is inconsistent.
% 153.47/22.93  | | | 
% 153.47/22.93  | | End of split
% 153.47/22.93  | | 
% 153.47/22.93  | Case 2:
% 153.47/22.93  | | 
% 153.47/22.93  | |   (17)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 153.47/22.93  | |           e3)
% 153.47/22.93  | | 
% 153.47/22.93  | | BETA: splitting (17) gives:
% 153.47/22.93  | | 
% 153.47/22.93  | | Case 1:
% 153.47/22.93  | | | 
% 153.47/22.93  | | |   (18)  all_56_4 = e3 & op(e3, e1) = e3
% 153.47/22.93  | | | 
% 153.47/22.93  | | | REF_CLOSE: (3), (6), (18) are inconsistent by sub-proof #641.
% 153.47/22.93  | | | 
% 153.47/22.93  | | Case 2:
% 153.47/22.93  | | | 
% 153.47/22.93  | | |   (19)  all_56_9 = e3 & op(e3, e0) = e3
% 153.47/22.93  | | | 
% 153.47/22.93  | | | REF_CLOSE: (8), (9), (19) are inconsistent by sub-proof #594.
% 153.47/22.94  | | | 
% 153.47/22.94  | | End of split
% 153.47/22.94  | | 
% 153.47/22.94  | End of split
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #594 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)  all_56_9 = e3 & op(e3, e0) = e3
% 153.47/22.94    (2)  all_56_9 = e2
% 153.47/22.94    (3)   ~ (e3 = e2)
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | ALPHA: (1) implies:
% 153.47/22.94  |   (4)  all_56_9 = e3
% 153.47/22.94  | 
% 153.47/22.94  | COMBINE_EQS: (2), (4) imply:
% 153.47/22.94  |   (5)  e3 = e2
% 153.47/22.94  | 
% 153.47/22.94  | REDUCE: (3), (5) imply:
% 153.47/22.94  |   (6)  $false
% 153.47/22.94  | 
% 153.47/22.94  | CLOSE: (6) is inconsistent.
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #595 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)  all_56_1 = e2
% 153.47/22.94    (2)  all_56_1 = e1
% 153.47/22.94    (3)   ~ (e2 = e1)
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | COMBINE_EQS: (1), (2) imply:
% 153.47/22.94  |   (4)  e2 = e1
% 153.47/22.94  | 
% 153.47/22.94  | SIMP: (4) implies:
% 153.47/22.94  |   (5)  e2 = e1
% 153.47/22.94  | 
% 153.47/22.94  | REDUCE: (3), (5) imply:
% 153.47/22.94  |   (6)  $false
% 153.47/22.94  | 
% 153.47/22.94  | CLOSE: (6) is inconsistent.
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #596 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 153.47/22.94    (2)  op(e3, e2) = all_52_4
% 153.47/22.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (4)   ~ (all_52_4 = e3)
% 153.47/22.94    (5)   ~ (e3 = e0)
% 153.47/22.94    (6)  op(e2, e2) = e0
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | BETA: splitting (1) gives:
% 153.47/22.94  | 
% 153.47/22.94  | Case 1:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (7)  all_56_1 = e3 & op(e3, e2) = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | ALPHA: (7) implies:
% 153.47/22.94  | |   (8)  op(e3, e2) = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1166.
% 153.47/22.94  | | 
% 153.47/22.94  | Case 2:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (9)  all_56_3 = e3 & op(e2, e2) = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | ALPHA: (9) implies:
% 153.47/22.94  | |   (10)  op(e2, e2) = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #719.
% 153.47/22.94  | | 
% 153.47/22.94  | End of split
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #597 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)  op(e2, e2) = e1
% 153.47/22.94    (2)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.47/22.94         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.47/22.94    (3)   ~ (e2 = e0)
% 153.47/22.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (5)  all_56_5 = e2
% 153.47/22.94    (6)  all_56_10 = e1
% 153.47/22.94    (7)   ~ (e3 = e0)
% 153.47/22.94    (8)   ~ (e1 = e0)
% 153.47/22.94    (9)  all_56_2 = e3
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | BETA: splitting (2) gives:
% 153.47/22.94  | 
% 153.47/22.94  | Case 1:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (10)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 153.47/22.94  | |           e0)
% 153.47/22.94  | | 
% 153.47/22.94  | | BETA: splitting (10) gives:
% 153.47/22.94  | | 
% 153.47/22.94  | | Case 1:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (11)  all_56_2 = e0 & op(e2, e3) = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | REF_CLOSE: (7), (9), (11) are inconsistent by sub-proof #932.
% 153.47/22.94  | | | 
% 153.47/22.94  | | Case 2:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (12)  all_56_3 = e0 & op(e2, e2) = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | ALPHA: (12) implies:
% 153.47/22.94  | | |   (13)  op(e2, e2) = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | REF_CLOSE: (1), (4), (8), (13) are inconsistent by sub-proof #853.
% 153.47/22.94  | | | 
% 153.47/22.94  | | End of split
% 153.47/22.94  | | 
% 153.47/22.94  | Case 2:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (14)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.47/22.94  | |           e0)
% 153.47/22.94  | | 
% 153.47/22.94  | | BETA: splitting (14) gives:
% 153.47/22.94  | | 
% 153.47/22.94  | | Case 1:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (15)  all_56_5 = e0 & op(e2, e1) = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | ALPHA: (15) implies:
% 153.47/22.94  | | |   (16)  all_56_5 = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | COMBINE_EQS: (5), (16) imply:
% 153.47/22.94  | | |   (17)  e2 = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | REDUCE: (3), (17) imply:
% 153.47/22.94  | | |   (18)  $false
% 153.47/22.94  | | | 
% 153.47/22.94  | | | CLOSE: (18) is inconsistent.
% 153.47/22.94  | | | 
% 153.47/22.94  | | Case 2:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (19)  all_56_10 = e0 & op(e2, e0) = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | REF_CLOSE: (6), (8), (19) are inconsistent by sub-proof #884.
% 153.47/22.94  | | | 
% 153.47/22.94  | | End of split
% 153.47/22.94  | | 
% 153.47/22.94  | End of split
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #598 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)   ~ (e3 = e1)
% 153.47/22.94    (2)   ~ (e2 = e0)
% 153.47/22.94    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.47/22.94         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.47/22.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (5)   ~ (all_52_9 = e3)
% 153.47/22.94    (6)  op(e1, e3) = e1
% 153.47/22.94    (7)   ~ (e3 = e0)
% 153.47/22.94    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.47/22.94         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.47/22.94    (9)  op(e3, e3) = e1
% 153.47/22.94    (10)  op(e0, e3) = all_52_3
% 153.47/22.94    (11)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.47/22.94          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.47/22.94    (12)  op(e2, e1) = all_52_9
% 153.47/22.94    (13)   ~ (e1 = e0)
% 153.47/22.94    (14)   ~ (e3 = e2)
% 153.47/22.94    (15)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.47/22.94          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.47/22.94    (16)   ~ (all_52_3 = e0)
% 153.47/22.94    (17)   ~ (e2 = e1)
% 153.47/22.94    (18)  op(e1, e3) = all_52_2
% 153.47/22.94    (19)  op(e2, e2) = e0
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | BETA: splitting (8) gives:
% 153.47/22.94  | 
% 153.47/22.94  | Case 1:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 153.47/22.94  | |           e0)
% 153.47/22.94  | | 
% 153.47/22.94  | | BETA: splitting (20) gives:
% 153.47/22.94  | | 
% 153.47/22.94  | | Case 1:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (21)  all_56_0 = e0 & op(e3, e3) = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | ALPHA: (21) implies:
% 153.47/22.94  | | |   (22)  op(e3, e3) = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | REF_CLOSE: (4), (9), (13), (22) are inconsistent by sub-proof #957.
% 153.47/22.94  | | | 
% 153.47/22.94  | | Case 2:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (23)  all_56_2 = e0 & op(e2, e3) = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | ALPHA: (23) implies:
% 153.47/22.94  | | |   (24)  all_56_2 = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (11), (12), (13), (14), (15),
% 153.47/22.94  | | |            (17), (19), (24) are inconsistent by sub-proof #646.
% 153.47/22.94  | | | 
% 153.47/22.94  | | End of split
% 153.47/22.94  | | 
% 153.47/22.94  | Case 2:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (25)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 153.47/22.94  | |           e0)
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (4), (6), (10), (13), (16), (18), (25) are inconsistent by
% 153.47/22.94  | |            sub-proof #669.
% 153.47/22.94  | | 
% 153.47/22.94  | End of split
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #599 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)  all_54_6 = all_52_9
% 153.47/22.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (3)  op(e2, e3) = e2
% 153.47/22.94    (4)   ~ (all_52_9 = e3)
% 153.47/22.94    (5)   ~ (all_52_1 = all_52_9)
% 153.47/22.94    (6)   ~ (all_52_9 = e1)
% 153.47/22.94    (7)  all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 153.47/22.94    (8)   ~ (all_52_9 = e0)
% 153.47/22.94    (9)  op(e2, e3) = all_52_1
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | BETA: splitting (7) gives:
% 153.47/22.94  | 
% 153.47/22.94  | Case 1:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (10)  all_54_6 = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | COMBINE_EQS: (1), (10) imply:
% 153.47/22.94  | |   (11)  all_52_9 = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | REDUCE: (4), (11) imply:
% 153.47/22.94  | |   (12)  $false
% 153.47/22.94  | | 
% 153.47/22.94  | | CLOSE: (12) is inconsistent.
% 153.47/22.94  | | 
% 153.47/22.94  | Case 2:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (13)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (9), (13) are inconsistent by
% 153.47/22.94  | |            sub-proof #648.
% 153.47/22.94  | | 
% 153.47/22.94  | End of split
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #600 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (2)  op(e3, e1) = all_22_1
% 153.47/22.94    (3)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) =
% 153.47/22.94           all_57_10 & $i(all_57_10))
% 153.47/22.94    (4)   ~ (e3 = e0)
% 153.47/22.94    (5)  op(e3, e3) = e1
% 153.47/22.94    (6)  ( ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0 & op(e3, e1) = all_34_1
% 153.47/22.94           & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e3, e1) =
% 153.47/22.94           all_34_1 & $i(all_34_1))
% 153.47/22.94    (7)  op(e3, e1) = e0
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | BETA: splitting (3) gives:
% 153.47/22.94  | 
% 153.47/22.94  | Case 1:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (8)  all_57_6 = e3 & op(e3, e1) = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | ALPHA: (8) implies:
% 153.47/22.94  | |   (9)  op(e3, e1) = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | BETA: splitting (6) gives:
% 153.47/22.94  | | 
% 153.47/22.94  | | Case 1:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (10)   ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0 & op(e3, e1) =
% 153.47/22.94  | | |         all_34_1 & $i(all_34_0) & $i(all_34_1)
% 153.47/22.94  | | | 
% 153.47/22.94  | | | ALPHA: (10) implies:
% 153.47/22.94  | | |   (11)  op(e3, e1) = all_34_1
% 153.47/22.94  | | | 
% 153.47/22.94  | | | REF_CLOSE: (1), (2), (4), (7), (9), (11) are inconsistent by sub-proof
% 153.47/22.94  | | |            #601.
% 153.47/22.94  | | | 
% 153.47/22.94  | | Case 2:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (12)   ~ (all_34_1 = e2) & op(e3, e1) = all_34_1 & $i(all_34_1)
% 153.47/22.94  | | | 
% 153.47/22.94  | | | ALPHA: (12) implies:
% 153.47/22.94  | | |   (13)  op(e3, e1) = all_34_1
% 153.47/22.94  | | | 
% 153.47/22.94  | | | REF_CLOSE: (1), (2), (4), (7), (9), (13) are inconsistent by sub-proof
% 153.47/22.94  | | |            #601.
% 153.47/22.94  | | | 
% 153.47/22.94  | | End of split
% 153.47/22.94  | | 
% 153.47/22.94  | Case 2:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (14)   ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10)
% 153.47/22.94  | | 
% 153.47/22.94  | | ALPHA: (14) implies:
% 153.47/22.94  | |   (15)   ~ (all_57_10 = e1)
% 153.47/22.94  | |   (16)  op(e3, e3) = all_57_10
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (1), (5), (15), (16) are inconsistent by sub-proof #893.
% 153.47/22.94  | | 
% 153.47/22.94  | End of split
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #601 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)  op(e3, e1) = all_34_1
% 153.47/22.94    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (3)  op(e3, e1) = e3
% 153.47/22.94    (4)  op(e3, e1) = all_22_1
% 153.47/22.94    (5)   ~ (e3 = e0)
% 153.47/22.94    (6)  op(e3, e1) = e0
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | GROUND_INST: instantiating (2) with e0, all_34_1, e1, e3, simplifying with
% 153.47/22.94  |              (1), (6) gives:
% 153.47/22.94  |   (7)  all_34_1 = e0
% 153.47/22.94  | 
% 153.47/22.94  | GROUND_INST: instantiating (2) with all_22_1, all_34_1, e1, e3, simplifying
% 153.47/22.94  |              with (1), (4) gives:
% 153.47/22.94  |   (8)  all_34_1 = all_22_1
% 153.47/22.94  | 
% 153.47/22.94  | GROUND_INST: instantiating (2) with e3, all_34_1, e1, e3, simplifying with
% 153.47/22.94  |              (1), (3) gives:
% 153.47/22.94  |   (9)  all_34_1 = e3
% 153.47/22.94  | 
% 153.47/22.94  | COMBINE_EQS: (7), (8) imply:
% 153.47/22.94  |   (10)  all_22_1 = e0
% 153.47/22.94  | 
% 153.47/22.94  | COMBINE_EQS: (8), (9) imply:
% 153.47/22.94  |   (11)  all_22_1 = e3
% 153.47/22.94  | 
% 153.47/22.94  | COMBINE_EQS: (10), (11) imply:
% 153.47/22.94  |   (12)  e3 = e0
% 153.47/22.94  | 
% 153.47/22.94  | REDUCE: (5), (12) imply:
% 153.47/22.94  |   (13)  $false
% 153.47/22.94  | 
% 153.47/22.94  | CLOSE: (13) is inconsistent.
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #602 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)   ~ (e3 = e1)
% 153.47/22.94    (2)   ~ (e2 = e0)
% 153.47/22.94    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (4)  op(e3, e3) = e1
% 153.47/22.94    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.47/22.94             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.47/22.94           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.47/22.94               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.47/22.94             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.47/22.94         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.47/22.94             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.94           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.47/22.94               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.47/22.94             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 153.47/22.94    (6)  op(e2, e2) = e0
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | BETA: splitting (5) gives:
% 153.47/22.94  | 
% 153.47/22.94  | Case 1:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2)
% 153.47/22.94  | |          | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.47/22.94  | |        ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 153.47/22.94  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 153.47/22.94  | |              e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 153.47/22.94  | |            $i(all_57_15)))
% 153.47/22.94  | | 
% 153.47/22.94  | | ALPHA: (7) implies:
% 153.47/22.94  | |   (8)  op(e3, e3) = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1178.
% 153.47/22.94  | | 
% 153.47/22.94  | Case 2:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3)
% 153.47/22.94  | |          | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.94  | |        ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.47/22.94  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.47/22.94  | |              e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.47/22.94  | |            $i(all_57_15)))
% 153.47/22.94  | | 
% 153.47/22.94  | | ALPHA: (9) implies:
% 153.47/22.94  | |   (10)  op(e2, e2) = e2
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #1145.
% 153.47/22.94  | | 
% 153.47/22.94  | End of split
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #603 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (2)   ~ (e1 = e0)
% 153.47/22.94    (3)   ~ (all_52_1 = e1)
% 153.47/22.94    (4)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 153.47/22.94    (5)  op(e2, e2) = e0
% 153.47/22.94    (6)  op(e2, e3) = all_52_1
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | BETA: splitting (4) gives:
% 153.47/22.94  | 
% 153.47/22.94  | Case 1:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (7)  all_56_2 = e1 & op(e2, e3) = e1
% 153.47/22.94  | | 
% 153.47/22.94  | | ALPHA: (7) implies:
% 153.47/22.94  | |   (8)  op(e2, e3) = e1
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #1177.
% 153.47/22.94  | | 
% 153.47/22.94  | Case 2:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (9)  all_56_3 = e1 & op(e2, e2) = e1
% 153.47/22.94  | | 
% 153.47/22.94  | | ALPHA: (9) implies:
% 153.47/22.94  | |   (10)  op(e2, e2) = e1
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #853.
% 153.47/22.94  | | 
% 153.47/22.94  | End of split
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #604 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)   ~ (all_44_2 = e2) | ( ~ (all_44_0 = e0) & op(all_44_1, e3) = all_44_0 &
% 153.47/22.94           op(e3, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 153.47/22.94             e1) & op(e3, e2) = all_44_1 & $i(all_44_1))
% 153.47/22.94    (2)  op(e3, e2) = all_52_4
% 153.47/22.94    (3)   ~ (all_52_4 = e2)
% 153.47/22.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (5)  all_54_1 = all_52_4
% 153.47/22.94    (6)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 153.47/22.94    (7)  op(e1, e3) = e0
% 153.47/22.94    (8)  all_44_2 = e2
% 153.47/22.94    (9)   ~ (all_52_4 = e0)
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | BETA: splitting (6) gives:
% 153.47/22.94  | 
% 153.47/22.94  | Case 1:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (10)  all_54_1 = e2
% 153.47/22.94  | | 
% 153.47/22.94  | | COMBINE_EQS: (5), (10) imply:
% 153.47/22.94  | |   (11)  all_52_4 = e2
% 153.47/22.94  | | 
% 153.47/22.94  | | REDUCE: (3), (11) imply:
% 153.47/22.94  | |   (12)  $false
% 153.47/22.94  | | 
% 153.47/22.94  | | CLOSE: (12) is inconsistent.
% 153.47/22.94  | | 
% 153.47/22.94  | Case 2:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (13)  all_54_1 = e1 | all_54_1 = e0
% 153.47/22.94  | | 
% 153.47/22.94  | | BETA: splitting (13) gives:
% 153.47/22.94  | | 
% 153.47/22.94  | | Case 1:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (14)  all_54_1 = e1
% 153.47/22.94  | | | 
% 153.47/22.94  | | | COMBINE_EQS: (5), (14) imply:
% 153.47/22.94  | | |   (15)  all_52_4 = e1
% 153.47/22.94  | | | 
% 153.47/22.94  | | | REDUCE: (2), (15) imply:
% 153.47/22.94  | | |   (16)  op(e3, e2) = e1
% 153.47/22.94  | | | 
% 153.47/22.94  | | | BETA: splitting (1) gives:
% 153.47/22.94  | | | 
% 153.47/22.94  | | | Case 1:
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | |   (17)   ~ (all_44_2 = e2)
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | | REDUCE: (8), (17) imply:
% 153.47/22.94  | | | |   (18)  $false
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | | CLOSE: (18) is inconsistent.
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | Case 2:
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | |   (19)  ( ~ (all_44_0 = e0) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 153.47/22.94  | | | |           all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1)
% 153.47/22.94  | | | |           & op(e3, e2) = all_44_1 & $i(all_44_1))
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | | REF_CLOSE: (4), (7), (16), (19) are inconsistent by sub-proof #642.
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | End of split
% 153.47/22.94  | | | 
% 153.47/22.94  | | Case 2:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (20)  all_54_1 = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | COMBINE_EQS: (5), (20) imply:
% 153.47/22.94  | | |   (21)  all_52_4 = e0
% 153.47/22.94  | | | 
% 153.47/22.94  | | | REDUCE: (9), (21) imply:
% 153.47/22.94  | | |   (22)  $false
% 153.47/22.94  | | | 
% 153.47/22.94  | | | CLOSE: (22) is inconsistent.
% 153.47/22.94  | | | 
% 153.47/22.94  | | End of split
% 153.47/22.94  | | 
% 153.47/22.94  | End of split
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #605 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)  op(e0, e1) = all_52_11
% 153.47/22.94    (2)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 153.47/22.94         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.47/22.94    (3)   ~ (e3 = e1)
% 153.47/22.94    (4)   ~ (e2 = e0)
% 153.47/22.94    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (6)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.47/22.94         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.47/22.94    (7)   ~ (all_52_11 = e3)
% 153.47/22.94    (8)   ~ (e3 = e0)
% 153.47/22.94    (9)  op(e2, e1) = e2
% 153.47/22.94    (10)   ~ (e1 = e0)
% 153.47/22.94    (11)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.47/22.94          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.47/22.94    (12)   ~ (e3 = e2)
% 153.47/22.94    (13)   ~ (all_52_8 = e3)
% 153.47/22.94    (14)  op(e3, e1) = all_52_8
% 153.47/22.94    (15)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.47/22.94          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.47/22.94    (16)   ~ (e2 = e1)
% 153.47/22.94    (17)  all_56_6 = e3
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | BETA: splitting (2) gives:
% 153.47/22.94  | 
% 153.47/22.94  | Case 1:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (18)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) =
% 153.47/22.94  | |           e3)
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (5), (9), (12), (13), (14), (18) are inconsistent by sub-proof
% 153.47/22.94  | |            #623.
% 153.47/22.94  | | 
% 153.47/22.94  | Case 2:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (19)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 153.47/22.94  | |           e3)
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (15), (16),
% 153.47/22.94  | |            (17), (19) are inconsistent by sub-proof #606.
% 153.47/22.94  | | 
% 153.47/22.94  | End of split
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #606 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)  op(e0, e1) = all_52_11
% 153.47/22.94    (2)   ~ (e3 = e1)
% 153.47/22.94    (3)   ~ (e2 = e0)
% 153.47/22.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (5)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.47/22.94         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.47/22.94    (6)   ~ (all_52_11 = e3)
% 153.47/22.94    (7)   ~ (e3 = e0)
% 153.47/22.94    (8)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.47/22.94    (9)   ~ (e1 = e0)
% 153.47/22.94    (10)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.47/22.94          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.47/22.94    (11)   ~ (e3 = e2)
% 153.47/22.94    (12)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.47/22.94          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.47/22.94    (13)   ~ (e2 = e1)
% 153.47/22.94    (14)  all_56_6 = e3
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | BETA: splitting (8) gives:
% 153.47/22.94  | 
% 153.47/22.94  | Case 1:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (15)  all_56_8 = e3 & op(e1, e1) = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | ALPHA: (15) implies:
% 153.47/22.94  | |   (16)  all_56_8 = e3
% 153.47/22.94  | |   (17)  op(e1, e1) = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (10), (11), (12), (13), (14), (16),
% 153.47/22.94  | |            (17) are inconsistent by sub-proof #607.
% 153.47/22.94  | | 
% 153.47/22.94  | Case 2:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (18)  all_56_14 = e3 & op(e0, e1) = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | ALPHA: (18) implies:
% 153.47/22.94  | |   (19)  op(e0, e1) = e3
% 153.47/22.94  | | 
% 153.47/22.94  | | REF_CLOSE: (1), (4), (6), (19) are inconsistent by sub-proof #1147.
% 153.47/22.94  | | 
% 153.47/22.94  | End of split
% 153.47/22.94  | 
% 153.47/22.94  End of proof
% 153.47/22.94  
% 153.47/22.94  Sub-proof #607 shows that the following formulas are inconsistent:
% 153.47/22.94  ----------------------------------------------------------------
% 153.47/22.94    (1)  all_56_8 = e3
% 153.47/22.94    (2)   ~ (e3 = e1)
% 153.47/22.94    (3)   ~ (e2 = e0)
% 153.47/22.94    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.94           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.94    (5)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.47/22.94         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.47/22.94    (6)   ~ (e3 = e0)
% 153.47/22.94    (7)   ~ (e1 = e0)
% 153.47/22.94    (8)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.47/22.94         (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.47/22.94    (9)  op(e1, e1) = e3
% 153.47/22.94    (10)   ~ (e3 = e2)
% 153.47/22.94    (11)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.47/22.94          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.47/22.94    (12)   ~ (e2 = e1)
% 153.47/22.94    (13)  all_56_6 = e3
% 153.47/22.94  
% 153.47/22.94  Begin of proof
% 153.47/22.94  | 
% 153.47/22.94  | BETA: splitting (8) gives:
% 153.47/22.94  | 
% 153.47/22.94  | Case 1:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (14)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 153.47/22.94  | |           e2)
% 153.47/22.94  | | 
% 153.47/22.94  | | BETA: splitting (14) gives:
% 153.47/22.94  | | 
% 153.47/22.94  | | Case 1:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (15)  all_56_6 = e2 & op(e1, e3) = e2
% 153.47/22.94  | | | 
% 153.47/22.94  | | | REF_CLOSE: (10), (13), (15) are inconsistent by sub-proof #779.
% 153.47/22.94  | | | 
% 153.47/22.94  | | Case 2:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (16)  all_56_7 = e2 & op(e1, e2) = e2
% 153.47/22.94  | | | 
% 153.47/22.94  | | | ALPHA: (16) implies:
% 153.47/22.94  | | |   (17)  all_56_7 = e2
% 153.47/22.94  | | | 
% 153.47/22.94  | | | BETA: splitting (5) gives:
% 153.47/22.94  | | | 
% 153.47/22.94  | | | Case 1:
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | |   (18)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2)
% 153.47/22.94  | | | |           = e1)
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | | BETA: splitting (18) gives:
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | | Case 1:
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | |   (19)  all_56_6 = e1 & op(e1, e3) = e1
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | | REF_CLOSE: (2), (13), (19) are inconsistent by sub-proof #792.
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | Case 2:
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | |   (20)  all_56_7 = e1 & op(e1, e2) = e1
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | | REF_CLOSE: (12), (17), (20) are inconsistent by sub-proof #612.
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | End of split
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | Case 2:
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | |   (21)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0)
% 153.47/22.94  | | | |           = e1)
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | | BETA: splitting (21) gives:
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | | Case 1:
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | |   (22)  all_56_8 = e1 & op(e1, e1) = e1
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | | ALPHA: (22) implies:
% 153.47/22.94  | | | | |   (23)  op(e1, e1) = e1
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | | REF_CLOSE: (2), (4), (9), (23) are inconsistent by sub-proof #734.
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | Case 2:
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | |   (24)  all_56_11 = e1 & op(e1, e0) = e1
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | | ALPHA: (24) implies:
% 153.47/22.94  | | | | |   (25)  all_56_11 = e1
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | | BETA: splitting (11) gives:
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | | Case 1:
% 153.47/22.94  | | | | | | 
% 153.47/22.94  | | | | | |   (26)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1,
% 153.47/22.94  | | | | | |             e2) = e0)
% 153.47/22.94  | | | | | | 
% 153.47/22.94  | | | | | | BETA: splitting (26) gives:
% 153.47/22.94  | | | | | | 
% 153.47/22.94  | | | | | | Case 1:
% 153.47/22.94  | | | | | | | 
% 153.47/22.94  | | | | | | |   (27)  all_56_6 = e0 & op(e1, e3) = e0
% 153.47/22.94  | | | | | | | 
% 153.47/22.94  | | | | | | | ALPHA: (27) implies:
% 153.47/22.94  | | | | | | |   (28)  all_56_6 = e0
% 153.47/22.94  | | | | | | | 
% 153.47/22.94  | | | | | | | REF_CLOSE: (6), (13), (28) are inconsistent by sub-proof #784.
% 153.47/22.94  | | | | | | | 
% 153.47/22.94  | | | | | | Case 2:
% 153.47/22.94  | | | | | | | 
% 153.47/22.94  | | | | | | |   (29)  all_56_7 = e0 & op(e1, e2) = e0
% 153.47/22.94  | | | | | | | 
% 153.47/22.94  | | | | | | | REF_CLOSE: (3), (17), (29) are inconsistent by sub-proof #611.
% 153.47/22.94  | | | | | | | 
% 153.47/22.94  | | | | | | End of split
% 153.47/22.94  | | | | | | 
% 153.47/22.94  | | | | | Case 2:
% 153.47/22.94  | | | | | | 
% 153.47/22.94  | | | | | |   (30)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1,
% 153.47/22.94  | | | | | |             e0) = e0)
% 153.47/22.94  | | | | | | 
% 153.47/22.94  | | | | | | REF_CLOSE: (4), (6), (7), (9), (25), (30) are inconsistent by
% 153.47/22.94  | | | | | |            sub-proof #610.
% 153.47/22.94  | | | | | | 
% 153.47/22.94  | | | | | End of split
% 153.47/22.94  | | | | | 
% 153.47/22.94  | | | | End of split
% 153.47/22.94  | | | | 
% 153.47/22.94  | | | End of split
% 153.47/22.94  | | | 
% 153.47/22.94  | | End of split
% 153.47/22.94  | | 
% 153.47/22.94  | Case 2:
% 153.47/22.94  | | 
% 153.47/22.94  | |   (31)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 153.47/22.94  | |           e2)
% 153.47/22.94  | | 
% 153.47/22.94  | | BETA: splitting (31) gives:
% 153.47/22.94  | | 
% 153.47/22.94  | | Case 1:
% 153.47/22.94  | | | 
% 153.47/22.94  | | |   (32)  all_56_8 = e2 & op(e1, e1) = e2
% 153.47/22.95  | | | 
% 153.47/22.95  | | | ALPHA: (32) implies:
% 153.47/22.95  | | |   (33)  op(e1, e1) = e2
% 153.47/22.95  | | | 
% 153.47/22.95  | | | REF_CLOSE: (4), (9), (10), (33) are inconsistent by sub-proof #834.
% 153.47/22.95  | | | 
% 153.47/22.95  | | Case 2:
% 153.47/22.95  | | | 
% 153.47/22.95  | | |   (34)  all_56_11 = e2 & op(e1, e0) = e2
% 153.47/22.95  | | | 
% 153.47/22.95  | | | ALPHA: (34) implies:
% 153.47/22.95  | | |   (35)  all_56_11 = e2
% 153.47/22.95  | | | 
% 153.47/22.95  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (11), (12), (13), (35) are
% 153.47/22.95  | | |            inconsistent by sub-proof #608.
% 153.47/22.95  | | | 
% 153.47/22.95  | | End of split
% 153.47/22.95  | | 
% 153.47/22.95  | End of split
% 153.47/22.95  | 
% 153.47/22.95  End of proof
% 153.47/22.95  
% 153.47/22.95  Sub-proof #608 shows that the following formulas are inconsistent:
% 153.47/22.95  ----------------------------------------------------------------
% 153.47/22.95    (1)  all_56_8 = e3
% 153.47/22.95    (2)   ~ (e3 = e1)
% 153.47/22.95    (3)  all_56_11 = e2
% 153.47/22.95    (4)   ~ (e2 = e0)
% 153.47/22.95    (5)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.47/22.95         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.47/22.95    (6)   ~ (e3 = e0)
% 153.47/22.95    (7)   ~ (e1 = e0)
% 153.47/22.95    (8)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.47/22.95         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.47/22.95    (9)   ~ (e2 = e1)
% 153.47/22.95    (10)  all_56_6 = e3
% 153.47/22.95  
% 153.47/22.95  Begin of proof
% 153.47/22.95  | 
% 153.47/22.95  | BETA: splitting (8) gives:
% 153.47/22.95  | 
% 153.47/22.95  | Case 1:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (11)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) =
% 153.47/22.95  | |           e0)
% 153.47/22.95  | | 
% 153.47/22.95  | | BETA: splitting (11) gives:
% 153.47/22.95  | | 
% 153.47/22.95  | | Case 1:
% 153.47/22.95  | | | 
% 153.47/22.95  | | |   (12)  all_56_6 = e0 & op(e1, e3) = e0
% 153.47/22.95  | | | 
% 153.47/22.95  | | | REF_CLOSE: (6), (10), (12) are inconsistent by sub-proof #778.
% 153.47/22.95  | | | 
% 153.47/22.95  | | Case 2:
% 153.47/22.95  | | | 
% 153.47/22.95  | | |   (13)  all_56_7 = e0 & op(e1, e2) = e0
% 153.47/22.95  | | | 
% 153.47/22.95  | | | ALPHA: (13) implies:
% 153.47/22.95  | | |   (14)  all_56_7 = e0
% 153.47/22.95  | | | 
% 153.47/22.95  | | | REF_CLOSE: (1), (2), (3), (5), (7), (9), (10), (14) are inconsistent by
% 153.47/22.95  | | |            sub-proof #609.
% 153.47/22.95  | | | 
% 153.47/22.95  | | End of split
% 153.47/22.95  | | 
% 153.47/22.95  | Case 2:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (15)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.47/22.95  | |           e0)
% 153.47/22.95  | | 
% 153.47/22.95  | | BETA: splitting (15) gives:
% 153.47/22.95  | | 
% 153.47/22.95  | | Case 1:
% 153.47/22.95  | | | 
% 153.47/22.95  | | |   (16)  all_56_8 = e0 & op(e1, e1) = e0
% 153.47/22.95  | | | 
% 153.47/22.95  | | | REF_CLOSE: (1), (6), (16) are inconsistent by sub-proof #1150.
% 153.47/22.95  | | | 
% 153.47/22.95  | | Case 2:
% 153.47/22.95  | | | 
% 153.47/22.95  | | |   (17)  all_56_11 = e0 & op(e1, e0) = e0
% 153.47/22.95  | | | 
% 153.47/22.95  | | | REF_CLOSE: (3), (4), (17) are inconsistent by sub-proof #1149.
% 153.47/22.95  | | | 
% 153.47/22.95  | | End of split
% 153.47/22.95  | | 
% 153.47/22.95  | End of split
% 153.47/22.95  | 
% 153.47/22.95  End of proof
% 153.47/22.95  
% 153.47/22.95  Sub-proof #609 shows that the following formulas are inconsistent:
% 153.47/22.95  ----------------------------------------------------------------
% 153.47/22.95    (1)  all_56_8 = e3
% 153.47/22.95    (2)   ~ (e3 = e1)
% 153.47/22.95    (3)  all_56_11 = e2
% 153.47/22.95    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.47/22.95         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.47/22.95    (5)   ~ (e1 = e0)
% 153.47/22.95    (6)  all_56_7 = e0
% 153.47/22.95    (7)   ~ (e2 = e1)
% 153.47/22.95    (8)  all_56_6 = e3
% 153.47/22.95  
% 153.47/22.95  Begin of proof
% 153.47/22.95  | 
% 153.47/22.95  | BETA: splitting (4) gives:
% 153.47/22.95  | 
% 153.47/22.95  | Case 1:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (9)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1)
% 153.47/22.95  | | 
% 153.47/22.95  | | BETA: splitting (9) gives:
% 153.47/22.95  | | 
% 153.47/22.95  | | Case 1:
% 153.47/22.95  | | | 
% 153.47/22.95  | | |   (10)  all_56_6 = e1 & op(e1, e3) = e1
% 153.47/22.95  | | | 
% 153.47/22.95  | | | REF_CLOSE: (2), (8), (10) are inconsistent by sub-proof #792.
% 153.47/22.95  | | | 
% 153.47/22.95  | | Case 2:
% 153.47/22.95  | | | 
% 153.47/22.95  | | |   (11)  all_56_7 = e1 & op(e1, e2) = e1
% 153.47/22.95  | | | 
% 153.47/22.95  | | | ALPHA: (11) implies:
% 153.47/22.95  | | |   (12)  all_56_7 = e1
% 153.47/22.95  | | | 
% 153.47/22.95  | | | REF_CLOSE: (5), (6), (12) are inconsistent by sub-proof #987.
% 153.47/22.95  | | | 
% 153.47/22.95  | | End of split
% 153.47/22.95  | | 
% 153.47/22.95  | Case 2:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (13)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 153.47/22.95  | |           e1)
% 153.47/22.95  | | 
% 153.47/22.95  | | REF_CLOSE: (1), (2), (3), (7), (13) are inconsistent by sub-proof #644.
% 153.47/22.95  | | 
% 153.47/22.95  | End of split
% 153.47/22.95  | 
% 153.47/22.95  End of proof
% 153.47/22.95  
% 153.47/22.95  Sub-proof #610 shows that the following formulas are inconsistent:
% 153.47/22.95  ----------------------------------------------------------------
% 153.47/22.95    (1)  all_56_11 = e1
% 153.47/22.95    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.95    (3)   ~ (e3 = e0)
% 153.47/22.95    (4)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.47/22.95    (5)   ~ (e1 = e0)
% 153.47/22.95    (6)  op(e1, e1) = e3
% 153.47/22.95  
% 153.47/22.95  Begin of proof
% 153.47/22.95  | 
% 153.47/22.95  | BETA: splitting (4) gives:
% 153.47/22.95  | 
% 153.47/22.95  | Case 1:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (7)  all_56_8 = e0 & op(e1, e1) = e0
% 153.47/22.95  | | 
% 153.47/22.95  | | ALPHA: (7) implies:
% 153.47/22.95  | |   (8)  op(e1, e1) = e0
% 153.47/22.95  | | 
% 153.47/22.95  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #896.
% 153.47/22.95  | | 
% 153.47/22.95  | Case 2:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (9)  all_56_11 = e0 & op(e1, e0) = e0
% 153.47/22.95  | | 
% 153.47/22.95  | | ALPHA: (9) implies:
% 153.47/22.95  | |   (10)  all_56_11 = e0
% 153.47/22.95  | | 
% 153.47/22.95  | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #745.
% 153.47/22.95  | | 
% 153.47/22.95  | End of split
% 153.47/22.95  | 
% 153.47/22.95  End of proof
% 153.47/22.95  
% 153.47/22.95  Sub-proof #611 shows that the following formulas are inconsistent:
% 153.47/22.95  ----------------------------------------------------------------
% 153.47/22.95    (1)  all_56_7 = e0 & op(e1, e2) = e0
% 153.47/22.95    (2)  all_56_7 = e2
% 153.47/22.95    (3)   ~ (e2 = e0)
% 153.47/22.95  
% 153.47/22.95  Begin of proof
% 153.47/22.95  | 
% 153.47/22.95  | ALPHA: (1) implies:
% 153.47/22.95  |   (4)  all_56_7 = e0
% 153.47/22.95  | 
% 153.47/22.95  | COMBINE_EQS: (2), (4) imply:
% 153.47/22.95  |   (5)  e2 = e0
% 153.47/22.95  | 
% 153.47/22.95  | REDUCE: (3), (5) imply:
% 153.47/22.95  |   (6)  $false
% 153.47/22.95  | 
% 153.47/22.95  | CLOSE: (6) is inconsistent.
% 153.47/22.95  | 
% 153.47/22.95  End of proof
% 153.47/22.95  
% 153.47/22.95  Sub-proof #612 shows that the following formulas are inconsistent:
% 153.47/22.95  ----------------------------------------------------------------
% 153.47/22.95    (1)  all_56_7 = e1 & op(e1, e2) = e1
% 153.47/22.95    (2)  all_56_7 = e2
% 153.47/22.95    (3)   ~ (e2 = e1)
% 153.47/22.95  
% 153.47/22.95  Begin of proof
% 153.47/22.95  | 
% 153.47/22.95  | ALPHA: (1) implies:
% 153.47/22.95  |   (4)  all_56_7 = e1
% 153.47/22.95  | 
% 153.47/22.95  | COMBINE_EQS: (2), (4) imply:
% 153.47/22.95  |   (5)  e2 = e1
% 153.47/22.95  | 
% 153.47/22.95  | REDUCE: (3), (5) imply:
% 153.47/22.95  |   (6)  $false
% 153.47/22.95  | 
% 153.47/22.95  | CLOSE: (6) is inconsistent.
% 153.47/22.95  | 
% 153.47/22.95  End of proof
% 153.47/22.95  
% 153.47/22.95  Sub-proof #613 shows that the following formulas are inconsistent:
% 153.47/22.95  ----------------------------------------------------------------
% 153.47/22.95    (1)   ~ (e2 = e0)
% 153.47/22.95    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.95    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 153.47/22.95    (4)  op(e2, e2) = e0
% 153.47/22.95    (5)  op(e2, e3) = all_52_1
% 153.47/22.95    (6)   ~ (all_52_1 = e2)
% 153.47/22.95  
% 153.47/22.95  Begin of proof
% 153.47/22.95  | 
% 153.47/22.95  | BETA: splitting (3) gives:
% 153.47/22.95  | 
% 153.47/22.95  | Case 1:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (7)  all_56_2 = e2 & op(e2, e3) = e2
% 153.47/22.95  | | 
% 153.47/22.95  | | ALPHA: (7) implies:
% 153.47/22.95  | |   (8)  op(e2, e3) = e2
% 153.47/22.95  | | 
% 153.47/22.95  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #1181.
% 153.47/22.95  | | 
% 153.47/22.95  | Case 2:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (9)  all_56_3 = e2 & op(e2, e2) = e2
% 153.47/22.95  | | 
% 153.47/22.95  | | ALPHA: (9) implies:
% 153.47/22.95  | |   (10)  op(e2, e2) = e2
% 153.47/22.95  | | 
% 153.47/22.95  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #1145.
% 153.47/22.95  | | 
% 153.47/22.95  | End of split
% 153.47/22.95  | 
% 153.47/22.95  End of proof
% 153.47/22.95  
% 153.47/22.95  Sub-proof #614 shows that the following formulas are inconsistent:
% 153.47/22.95  ----------------------------------------------------------------
% 153.47/22.95    (1)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.47/22.95             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.95           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.47/22.95               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.47/22.95             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.47/22.95         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.47/22.95             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.95           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 153.47/22.95               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 153.47/22.95             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 153.47/22.95    (2)   ~ (e2 = e0)
% 153.47/22.95    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.95    (4)  op(e1, e1) = e0
% 153.47/22.95    (5)  op(e0, e0) = e2
% 153.47/22.95    (6)   ~ (e1 = e0)
% 153.47/22.95  
% 153.47/22.95  Begin of proof
% 153.47/22.95  | 
% 153.47/22.95  | BETA: splitting (1) gives:
% 153.47/22.95  | 
% 153.47/22.95  | Case 1:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3)
% 153.47/22.95  | |          | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.95  | |        ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 153.47/22.95  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 153.47/22.95  | |              e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 153.47/22.95  | |            $i(all_57_15)))
% 153.47/22.95  | | 
% 153.47/22.95  | | ALPHA: (7) implies:
% 153.47/22.95  | |   (8)  op(e1, e1) = e1
% 153.47/22.95  | | 
% 153.47/22.95  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #1038.
% 153.47/22.95  | | 
% 153.47/22.95  | Case 2:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3)
% 153.47/22.95  | |          | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.95  | |        ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.47/22.95  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.47/22.95  | |              e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.47/22.95  | |            $i(all_57_14)))
% 153.47/22.95  | | 
% 153.47/22.95  | | ALPHA: (9) implies:
% 153.47/22.95  | |   (10)  op(e0, e0) = e0
% 153.47/22.95  | | 
% 153.47/22.95  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #1043.
% 153.47/22.95  | | 
% 153.47/22.95  | End of split
% 153.47/22.95  | 
% 153.47/22.95  End of proof
% 153.47/22.95  
% 153.47/22.95  Sub-proof #615 shows that the following formulas are inconsistent:
% 153.47/22.95  ----------------------------------------------------------------
% 153.47/22.95    (1)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.47/22.95    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.95    (3)   ~ (all_52_14 = e1)
% 153.47/22.95    (4)  op(e0, e0) = e2
% 153.47/22.95    (5)  op(e1, e0) = all_52_14
% 153.47/22.95    (6)   ~ (e2 = e1)
% 153.47/22.95  
% 153.47/22.95  Begin of proof
% 153.47/22.95  | 
% 153.47/22.95  | BETA: splitting (1) gives:
% 153.47/22.95  | 
% 153.47/22.95  | Case 1:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (7)  all_56_11 = e1 & op(e1, e0) = e1
% 153.47/22.95  | | 
% 153.47/22.95  | | ALPHA: (7) implies:
% 153.47/22.95  | |   (8)  op(e1, e0) = e1
% 153.47/22.95  | | 
% 153.47/22.95  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #961.
% 153.47/22.95  | | 
% 153.47/22.95  | Case 2:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (9)  all_56_15 = e1 & op(e0, e0) = e1
% 153.47/22.95  | | 
% 153.47/22.95  | | ALPHA: (9) implies:
% 153.47/22.95  | |   (10)  op(e0, e0) = e1
% 153.47/22.95  | | 
% 153.47/22.95  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #978.
% 153.47/22.95  | | 
% 153.47/22.95  | End of split
% 153.47/22.95  | 
% 153.47/22.95  End of proof
% 153.47/22.95  
% 153.47/22.95  Sub-proof #616 shows that the following formulas are inconsistent:
% 153.47/22.95  ----------------------------------------------------------------
% 153.47/22.95    (1)  all_56_9 = e1 & op(e3, e0) = e1
% 153.47/22.95    (2)  all_56_9 = e0
% 153.47/22.95    (3)   ~ (e1 = e0)
% 153.47/22.95  
% 153.47/22.95  Begin of proof
% 153.47/22.95  | 
% 153.47/22.95  | ALPHA: (1) implies:
% 153.47/22.95  |   (4)  all_56_9 = e1
% 153.47/22.95  | 
% 153.47/22.95  | COMBINE_EQS: (2), (4) imply:
% 153.47/22.95  |   (5)  e1 = e0
% 153.47/22.95  | 
% 153.47/22.95  | REDUCE: (3), (5) imply:
% 153.47/22.95  |   (6)  $false
% 153.47/22.95  | 
% 153.47/22.95  | CLOSE: (6) is inconsistent.
% 153.47/22.95  | 
% 153.47/22.95  End of proof
% 153.47/22.95  
% 153.47/22.95  Sub-proof #617 shows that the following formulas are inconsistent:
% 153.47/22.95  ----------------------------------------------------------------
% 153.47/22.95    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.95           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.95    (2)  op(e1, e2) = e2
% 153.47/22.95    (3)   ~ (e1 = e0)
% 153.47/22.95    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.47/22.95             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.47/22.95           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.47/22.95           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.47/22.95           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 153.47/22.95           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.47/22.95    (5)   ~ (e2 = e1)
% 153.47/22.95    (6)  op(e2, e2) = e0
% 153.47/22.95  
% 153.47/22.95  Begin of proof
% 153.47/22.95  | 
% 153.47/22.95  | BETA: splitting (4) gives:
% 153.47/22.95  | 
% 153.47/22.95  | Case 1:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.47/22.95  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.47/22.95  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 153.47/22.95  | | 
% 153.47/22.95  | | ALPHA: (7) implies:
% 153.47/22.95  | |   (8)  op(e1, e2) = e1
% 153.47/22.95  | | 
% 153.47/22.95  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #711.
% 153.47/22.95  | | 
% 153.47/22.95  | Case 2:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.47/22.95  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.47/22.95  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 153.47/22.95  | | 
% 153.47/22.95  | | ALPHA: (9) implies:
% 153.47/22.95  | |   (10)  op(e2, e2) = e1
% 153.47/22.95  | | 
% 153.47/22.95  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #853.
% 153.47/22.95  | | 
% 153.47/22.95  | End of split
% 153.47/22.95  | 
% 153.47/22.95  End of proof
% 153.47/22.95  
% 153.47/22.95  Sub-proof #618 shows that the following formulas are inconsistent:
% 153.47/22.95  ----------------------------------------------------------------
% 153.47/22.95    (1)  op(e0, e1) = all_52_11
% 153.47/22.95    (2)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 153.47/22.95         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.47/22.95    (3)   ~ (e3 = e1)
% 153.47/22.95    (4)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.47/22.95         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.47/22.95    (5)   ~ (all_52_2 = all_52_6)
% 153.47/22.95    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.47/22.95         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.47/22.95    (7)  op(e3, e2) = all_52_4
% 153.47/22.95    (8)  op(e1, e1) = e2
% 153.47/22.95    (9)  op(e0, e2) = all_52_7
% 153.47/22.95    (10)  op(e1, e1) = all_4_2
% 153.47/22.95    (11)   ~ (e2 = e0)
% 153.47/22.95    (12)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.47/22.95          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.47/22.95    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.95            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.95    (14)  all_56_6 = e0
% 153.47/22.95    (15)  op(e1, e3) = e0
% 153.47/22.95    (16)  op(e1, e1) = e0
% 153.47/22.95    (17)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 153.47/22.95            all_57_14 & $i(all_57_14))
% 153.47/22.95    (18)  op(e0, e0) = e2
% 153.47/22.95    (19)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.47/22.95              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.47/22.95                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.47/22.95                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.47/22.95    (20)   ~ (all_52_13 = e2)
% 153.47/22.95    (21)   ~ (all_52_4 = e3)
% 153.47/22.95    (22)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 153.47/22.95            all_57_12 & $i(all_57_12))
% 153.47/22.95    (23)  op(e3, e0) = all_52_12
% 153.47/22.95    (24)   ~ (e3 = e0)
% 153.47/22.95    (25)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 153.47/22.95            all_57_15 & $i(all_57_15))
% 153.47/22.95    (26)   ~ (all_52_11 = e0)
% 153.47/22.95    (27)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.47/22.95          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.47/22.95    (28)  op(e1, e2) = all_52_6
% 153.47/22.95    (29)   ~ (all_52_12 = e3)
% 153.47/22.95    (30)  op(e2, e0) = all_52_13
% 153.47/22.95    (31)   ~ (all_52_7 = e0)
% 153.47/22.95    (32)   ~ (e1 = e0)
% 153.47/22.95    (33)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.47/22.95              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.47/22.95            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.47/22.95                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.47/22.95              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.47/22.95          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.47/22.95              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.95            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.47/22.95                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.47/22.95              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.47/22.95          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.47/22.95              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.95            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.47/22.95                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.47/22.95              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.47/22.95          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.47/22.95              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.95            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.47/22.95                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.47/22.95                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.47/22.95                $i(all_57_14))))
% 153.47/22.95    (34)   ~ (e3 = e2)
% 153.47/22.95    (35)   ~ (all_52_8 = e3)
% 153.47/22.95    (36)  op(e3, e1) = all_52_8
% 153.47/22.95    (37)  op(e3, e3) = e3
% 153.47/22.95    (38)   ~ (e2 = e1)
% 153.47/22.95    (39)  op(e1, e3) = all_52_2
% 153.47/22.95    (40)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.47/22.95              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.47/22.95            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.47/22.95            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.47/22.95            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.47/22.95            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.47/22.95            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.47/22.95            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.47/22.95            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.47/22.95            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.47/22.95            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.47/22.95            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.47/22.95            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.47/22.95            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.95            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.47/22.95            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.47/22.95            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.47/22.95            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.47/22.95            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.47/22.95            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.47/22.95            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.47/22.95            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.95            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.47/22.95            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.47/22.95            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.47/22.95            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.47/22.95            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.47/22.95            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.47/22.95            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.47/22.95            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.47/22.95            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.47/22.95            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.47/22.95            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.47/22.95            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.47/22.95            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.47/22.95            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.47/22.95            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.47/22.95            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.47/22.95            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.47/22.95            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.47/22.95            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.47/22.95            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.47/22.95            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.47/22.95            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.47/22.95            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.47/22.95            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.47/22.95            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.47/22.95            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.47/22.95              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.47/22.95            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.47/22.95            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.47/22.95              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.47/22.95            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.47/22.95            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.47/22.95                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.47/22.95                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.95                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.47/22.95                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.47/22.95                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.47/22.95                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.47/22.95                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.95              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.47/22.95                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.47/22.95                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.47/22.95                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.47/22.95                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.47/22.95                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.47/22.95                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.47/22.95                $i(all_57_7))))
% 153.47/22.95    (41)  op(e2, e2) = e0
% 153.47/22.95    (42)  op(e2, e3) = all_52_1
% 153.47/22.95  
% 153.47/22.95  Begin of proof
% 153.47/22.95  | 
% 153.47/22.95  | BETA: splitting (27) gives:
% 153.47/22.95  | 
% 153.47/22.95  | Case 1:
% 153.47/22.95  | | 
% 153.47/22.95  | |   (43)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 153.47/22.95  | |           e2)
% 153.47/22.95  | | 
% 153.47/22.95  | | BETA: splitting (43) gives:
% 153.47/22.95  | | 
% 153.47/22.95  | | Case 1:
% 153.47/22.95  | | | 
% 153.47/22.95  | | |   (44)  all_56_0 = e2 & op(e3, e3) = e2
% 153.47/22.95  | | | 
% 153.47/22.95  | | | ALPHA: (44) implies:
% 153.47/22.95  | | |   (45)  op(e3, e3) = e2
% 153.47/22.95  | | | 
% 153.47/22.95  | | | REF_CLOSE: (8), (10), (11), (13), (18), (33), (34), (38), (41), (45) are
% 153.47/22.95  | | |            inconsistent by sub-proof #629.
% 153.47/22.95  | | | 
% 153.47/22.95  | | Case 2:
% 153.47/22.95  | | | 
% 153.47/22.95  | | |   (46)  all_56_2 = e2 & op(e2, e3) = e2
% 153.47/22.95  | | | 
% 153.47/22.95  | | | ALPHA: (46) implies:
% 153.47/22.95  | | |   (47)  op(e2, e3) = e2
% 153.47/22.95  | | | 
% 153.47/22.95  | | | BETA: splitting (40) gives:
% 153.47/22.95  | | | 
% 153.47/22.95  | | | Case 1:
% 153.47/22.95  | | | | 
% 153.47/22.95  | | | |   (48)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.47/22.95  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.47/22.95  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.47/22.95  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.47/22.95  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.47/22.95  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.47/22.95  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.47/22.95  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.47/22.95  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.47/22.95  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.47/22.95  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.47/22.95  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.95  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.47/22.95  | | | |           $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.47/22.95  | | | |           (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 153.47/22.95  | | | |           & op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.95  | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 =
% 153.47/22.95  | | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.47/22.95  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.47/22.95  | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 153.47/22.95  | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 153.47/22.95  | | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.47/22.95  | | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.47/22.95  | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.47/22.95  | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.95  | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.47/22.95  | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.47/22.95  | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 153.47/22.95  | | | |           & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.47/22.95  | | | |           $i(all_57_7) & $i(all_57_10))
% 153.47/22.95  | | | | 
% 153.47/22.95  | | | | BETA: splitting (48) gives:
% 153.47/22.95  | | | | 
% 153.47/22.95  | | | | Case 1:
% 153.47/22.95  | | | | | 
% 153.47/22.95  | | | | |   (49)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.47/22.95  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 153.47/22.95  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.47/22.95  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.47/22.95  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.47/22.95  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 153.47/22.95  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.47/22.95  | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.47/22.95  | | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.47/22.95  | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.47/22.95  | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.47/22.95  | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.47/22.95  | | | | |           & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.47/22.95  | | | | |           $i(all_57_14))
% 153.47/22.95  | | | | | 
% 153.47/22.95  | | | | | REF_CLOSE: (13), (15), (17), (25), (32), (39), (49) are inconsistent
% 153.47/22.95  | | | | |            by sub-proof #630.
% 153.47/22.95  | | | | | 
% 153.47/22.96  | | | | Case 2:
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | |   (50)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.96  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.47/22.96  | | | | |           & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.47/22.96  | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.47/22.96  | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.47/22.96  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.47/22.96  | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1
% 153.47/22.96  | | | | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2)
% 153.47/22.96  | | | | |           & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1
% 153.47/22.96  | | | | |           & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.47/22.96  | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.47/22.96  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.47/22.96  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.47/22.96  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.47/22.96  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.47/22.96  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.47/22.96  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | | BETA: splitting (50) gives:
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | | Case 1:
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | |   (51)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.96  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 153.47/22.96  | | | | | |           e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.96  | | | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15
% 153.47/22.96  | | | | | |           = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3,
% 153.47/22.96  | | | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.47/22.96  | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | | REF_CLOSE: (7), (13), (21), (51) are inconsistent by sub-proof #863.
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | Case 2:
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | |   (52)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.47/22.96  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3
% 153.47/22.96  | | | | | |           & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3)
% 153.47/22.96  | | | | | |           & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.47/22.96  | | | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.47/22.96  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.47/22.96  | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 =
% 153.47/22.96  | | | | | |           e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.47/22.96  | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 153.47/22.96  | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.47/22.96  | | | | | |           $i(all_57_10))
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | | BETA: splitting (52) gives:
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | | Case 1:
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | |   (53)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.47/22.96  | | | | | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3
% 153.47/22.96  | | | | | | |         & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3)
% 153.47/22.96  | | | | | | |         & $i(all_57_14)
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | | ALPHA: (53) implies:
% 153.47/22.96  | | | | | | |   (54)  op(e3, e3) = e2
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | | REF_CLOSE: (8), (10), (11), (13), (18), (33), (34), (38), (41),
% 153.47/22.96  | | | | | | |            (54) are inconsistent by sub-proof #629.
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | Case 2:
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | |   (55)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.47/22.96  | | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.47/22.96  | | | | | | |           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.47/22.96  | | | | | | |           $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 153.47/22.96  | | | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.47/22.96  | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.47/22.96  | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.47/22.96  | | | | | | |           $i(all_57_10))
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | | BETA: splitting (55) gives:
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | |   (56)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.47/22.96  | | | | | | | |         (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.47/22.96  | | | | | | | |         all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.47/22.96  | | | | | | | |         $i(all_57_5) & $i(all_57_14)
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | | ALPHA: (56) implies:
% 153.47/22.96  | | | | | | | |   (57)  op(e1, e2) = e1
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | | BETA: splitting (19) gives:
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | |   (58)  all_56_15 = e0 & op(e0, e0) = e0
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | ALPHA: (58) implies:
% 153.47/22.96  | | | | | | | | |   (59)  op(e0, e0) = e0
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | REF_CLOSE: (11), (13), (18), (59) are inconsistent by
% 153.47/22.96  | | | | | | | | |            sub-proof #1043.
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | |   (60)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 &
% 153.47/22.96  | | | | | | | | |             op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.47/22.96  | | | | | | | | |             e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) |
% 153.47/22.96  | | | | | | | | |           (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0
% 153.47/22.96  | | | | | | | | |             & op(e0, e1) = e0))
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | ALPHA: (60) implies:
% 153.47/22.96  | | | | | | | | |   (61)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.47/22.96  | | | | | | | | |           op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 153.47/22.96  | | | | | | | | |           e0)
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | BETA: splitting (4) gives:
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | |   (62)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 &
% 153.47/22.96  | | | | | | | | | |           op(e2, e3) = e1)
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | REF_CLOSE: (3), (13), (37), (38), (42), (47), (62) are
% 153.47/22.96  | | | | | | | | | |            inconsistent by sub-proof #841.
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | |   (63)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1
% 153.47/22.96  | | | | | | | | | |           & op(e0, e3) = e1)
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | BETA: splitting (63) gives:
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | |   (64)  all_56_6 = e1 & op(e1, e3) = e1
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | ALPHA: (64) implies:
% 153.47/22.96  | | | | | | | | | | |   (65)  op(e1, e3) = e1
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | REF_CLOSE: (5), (13), (28), (39), (57), (65) are inconsistent
% 153.47/22.96  | | | | | | | | | | |            by sub-proof #911.
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | |   (66)  all_56_12 = e1 & op(e0, e3) = e1
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | ALPHA: (66) implies:
% 153.47/22.96  | | | | | | | | | | |   (67)  all_56_12 = e1
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | REF_CLOSE: (1), (9), (13), (26), (31), (32), (61), (67) are
% 153.47/22.96  | | | | | | | | | | |            inconsistent by sub-proof #798.
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | End of split
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | End of split
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | End of split
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | |   (68)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.47/22.96  | | | | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 153.47/22.96  | | | | | | | |         e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.47/22.96  | | | | | | | |         $i(all_57_7) & $i(all_57_10)
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | | ALPHA: (68) implies:
% 153.47/22.96  | | | | | | | |   (69)  op(e2, e2) = e1
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | | REF_CLOSE: (13), (32), (41), (69) are inconsistent by sub-proof
% 153.47/22.96  | | | | | | | |            #853.
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | End of split
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | End of split
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | End of split
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | End of split
% 153.47/22.96  | | | | 
% 153.47/22.96  | | | Case 2:
% 153.47/22.96  | | | | 
% 153.47/22.96  | | | |   (70)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.47/22.96  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.47/22.96  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.47/22.96  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.47/22.96  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.47/22.96  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.47/22.96  | | | |           e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.47/22.96  | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.47/22.96  | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.47/22.96  | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.47/22.96  | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.47/22.96  | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.47/22.96  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.47/22.96  | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.47/22.96  | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.47/22.96  | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.47/22.96  | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0 &
% 153.47/22.96  | | | |           all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 = e0) &
% 153.47/22.96  | | | |           op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.47/22.96  | | | |           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 153.47/22.96  | | | |         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 153.47/22.96  | | | |           (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.47/22.96  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.47/22.96  | | | |           $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.47/22.96  | | | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.47/22.96  | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.47/22.96  | | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.47/22.96  | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.47/22.96  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.47/22.96  | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.47/22.96  | | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.47/22.96  | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3)
% 153.47/22.96  | | | |               & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.47/22.96  | | | |               e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.47/22.96  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.47/22.96  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.47/22.96  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.47/22.96  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.47/22.96  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.96  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.96  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.47/22.96  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.47/22.96  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.47/22.96  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.47/22.96  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.47/22.96  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.47/22.96  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.47/22.96  | | | | 
% 153.47/22.96  | | | | REF_CLOSE: (1), (3), (13), (16), (17), (18), (20), (22), (23), (24),
% 153.47/22.96  | | | |            (26), (29), (30), (32), (35), (36), (37), (38), (41), (70)
% 153.47/22.96  | | | |            are inconsistent by sub-proof #625.
% 153.47/22.96  | | | | 
% 153.47/22.96  | | | End of split
% 153.47/22.96  | | | 
% 153.47/22.96  | | End of split
% 153.47/22.96  | | 
% 153.47/22.96  | Case 2:
% 153.47/22.96  | | 
% 153.47/22.96  | |   (71)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 153.47/22.96  | |           e2)
% 153.47/22.96  | | 
% 153.47/22.96  | | BETA: splitting (71) gives:
% 153.47/22.96  | | 
% 153.47/22.96  | | Case 1:
% 153.47/22.96  | | | 
% 153.47/22.96  | | |   (72)  all_56_6 = e2 & op(e1, e3) = e2
% 153.47/22.96  | | | 
% 153.47/22.96  | | | ALPHA: (72) implies:
% 153.47/22.96  | | |   (73)  all_56_6 = e2
% 153.47/22.96  | | | 
% 153.47/22.96  | | | REF_CLOSE: (11), (14), (73) are inconsistent by sub-proof #724.
% 153.47/22.96  | | | 
% 153.47/22.96  | | Case 2:
% 153.47/22.96  | | | 
% 153.47/22.96  | | |   (74)  all_56_12 = e2 & op(e0, e3) = e2
% 153.47/22.96  | | | 
% 153.47/22.96  | | | ALPHA: (74) implies:
% 153.47/22.96  | | |   (75)  all_56_12 = e2
% 153.47/22.96  | | | 
% 153.47/22.96  | | | BETA: splitting (40) gives:
% 153.47/22.96  | | | 
% 153.47/22.96  | | | Case 1:
% 153.47/22.96  | | | | 
% 153.47/22.96  | | | |   (76)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.47/22.96  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.47/22.96  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.47/22.96  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.47/22.96  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.47/22.96  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.47/22.96  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.47/22.96  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.47/22.96  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.47/22.96  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.47/22.96  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.47/22.96  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.96  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.47/22.96  | | | |           $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.47/22.96  | | | |           (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 153.47/22.96  | | | |           & op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.96  | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 =
% 153.47/22.96  | | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.47/22.96  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.47/22.96  | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 153.47/22.96  | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 153.47/22.96  | | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.47/22.96  | | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.47/22.96  | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.47/22.96  | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.96  | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.47/22.96  | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.47/22.96  | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 153.47/22.96  | | | |           & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.47/22.96  | | | |           $i(all_57_7) & $i(all_57_10))
% 153.47/22.96  | | | | 
% 153.47/22.96  | | | | BETA: splitting (76) gives:
% 153.47/22.96  | | | | 
% 153.47/22.96  | | | | Case 1:
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | |   (77)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.47/22.96  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 153.47/22.96  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.47/22.96  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.47/22.96  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.47/22.96  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 153.47/22.96  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.47/22.96  | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.47/22.96  | | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.47/22.96  | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.47/22.96  | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.47/22.96  | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.47/22.96  | | | | |           & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.47/22.96  | | | | |           $i(all_57_14))
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | | REF_CLOSE: (13), (15), (17), (25), (32), (39), (77) are inconsistent
% 153.47/22.96  | | | | |            by sub-proof #630.
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | Case 2:
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | |   (78)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.96  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.47/22.96  | | | | |           & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.47/22.96  | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.47/22.96  | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.47/22.96  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.47/22.96  | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1
% 153.47/22.96  | | | | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2)
% 153.47/22.96  | | | | |           & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1
% 153.47/22.96  | | | | |           & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.47/22.96  | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.47/22.96  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.47/22.96  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.47/22.96  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.47/22.96  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.47/22.96  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.47/22.96  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | | BETA: splitting (78) gives:
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | | Case 1:
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | |   (79)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.96  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 153.47/22.96  | | | | | |           e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.96  | | | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15
% 153.47/22.96  | | | | | |           = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3,
% 153.47/22.96  | | | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.47/22.96  | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | | REF_CLOSE: (7), (13), (21), (79) are inconsistent by sub-proof #863.
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | Case 2:
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | |   (80)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.47/22.96  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3
% 153.47/22.96  | | | | | |           & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3)
% 153.47/22.96  | | | | | |           & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.47/22.96  | | | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.47/22.96  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.47/22.96  | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 =
% 153.47/22.96  | | | | | |           e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.47/22.96  | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 153.47/22.96  | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.47/22.96  | | | | | |           $i(all_57_10))
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | | BETA: splitting (80) gives:
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | | Case 1:
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | |   (81)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.47/22.96  | | | | | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3
% 153.47/22.96  | | | | | | |         & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3)
% 153.47/22.96  | | | | | | |         & $i(all_57_14)
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | | ALPHA: (81) implies:
% 153.47/22.96  | | | | | | |   (82)  op(e3, e3) = e2
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | | REF_CLOSE: (3), (4), (6), (13), (14), (24), (32), (34), (38),
% 153.47/22.96  | | | | | | |            (75), (82) are inconsistent by sub-proof #782.
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | Case 2:
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | |   (83)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.47/22.96  | | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.47/22.96  | | | | | | |           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.47/22.96  | | | | | | |           $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 153.47/22.96  | | | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.47/22.96  | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.47/22.96  | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.47/22.96  | | | | | | |           $i(all_57_10))
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | | BETA: splitting (83) gives:
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | |   (84)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.47/22.96  | | | | | | | |         (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.47/22.96  | | | | | | | |         all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.47/22.96  | | | | | | | |         $i(all_57_5) & $i(all_57_14)
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | | ALPHA: (84) implies:
% 153.47/22.96  | | | | | | | |   (85)  op(e1, e2) = e1
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | | BETA: splitting (19) gives:
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | |   (86)  all_56_15 = e0 & op(e0, e0) = e0
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | ALPHA: (86) implies:
% 153.47/22.96  | | | | | | | | |   (87)  op(e0, e0) = e0
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | REF_CLOSE: (11), (13), (18), (87) are inconsistent by
% 153.47/22.96  | | | | | | | | |            sub-proof #1043.
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | |   (88)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 &
% 153.47/22.96  | | | | | | | | |             op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.47/22.96  | | | | | | | | |             e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) |
% 153.47/22.96  | | | | | | | | |           (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0
% 153.47/22.96  | | | | | | | | |             & op(e0, e1) = e0))
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | ALPHA: (88) implies:
% 153.47/22.96  | | | | | | | | |   (89)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.47/22.96  | | | | | | | | |           op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 153.47/22.96  | | | | | | | | |           e0)
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | BETA: splitting (4) gives:
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | |   (90)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 &
% 153.47/22.96  | | | | | | | | | |           op(e2, e3) = e1)
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | BETA: splitting (90) gives:
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | |   (91)  all_56_0 = e1 & op(e3, e3) = e1
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | ALPHA: (91) implies:
% 153.47/22.96  | | | | | | | | | | |   (92)  op(e3, e3) = e1
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | REF_CLOSE: (3), (13), (37), (92) are inconsistent by
% 153.47/22.96  | | | | | | | | | | |            sub-proof #1178.
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | |   (93)  all_56_2 = e1 & op(e2, e3) = e1
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | ALPHA: (93) implies:
% 153.47/22.96  | | | | | | | | | | |   (94)  op(e2, e3) = e1
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | BETA: splitting (12) gives:
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | |   (95)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2
% 153.47/22.96  | | | | | | | | | | | |           & op(e2, e2) = e2)
% 153.47/22.96  | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | REF_CLOSE: (11), (13), (38), (41), (42), (94), (95) are
% 153.47/22.96  | | | | | | | | | | | |            inconsistent by sub-proof #624.
% 153.47/22.96  | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | |   (96)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 =
% 153.47/22.96  | | | | | | | | | | | |           e2 & op(e2, e0) = e2)
% 153.47/22.96  | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | BETA: splitting (96) gives:
% 153.47/22.96  | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | |   (97)  all_56_5 = e2 & op(e2, e1) = e2
% 153.47/22.96  | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | ALPHA: (97) implies:
% 153.47/22.96  | | | | | | | | | | | | |   (98)  op(e2, e1) = e2
% 153.47/22.96  | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | BETA: splitting (2) gives:
% 153.47/22.96  | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | |   (99)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 153.47/22.96  | | | | | | | | | | | | | |           & op(e2, e1) = e3)
% 153.47/22.96  | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | | REF_CLOSE: (13), (34), (35), (36), (98), (99) are
% 153.47/22.96  | | | | | | | | | | | | | |            inconsistent by sub-proof #623.
% 153.47/22.96  | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | |   (100)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 153.47/22.96  | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 153.47/22.96  | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | | BETA: splitting (100) gives:
% 153.47/22.96  | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | | |   (101)  all_56_8 = e3 & op(e1, e1) = e3
% 153.47/22.96  | | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 153.47/22.96  | | | | | | | | | | | | | | |   (102)  op(e1, e1) = e3
% 153.47/22.96  | | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | | | REF_CLOSE: (13), (16), (24), (102) are inconsistent by
% 153.47/22.96  | | | | | | | | | | | | | | |            sub-proof #896.
% 153.47/22.96  | | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | | |   (103)  all_56_14 = e3 & op(e0, e1) = e3
% 153.47/22.96  | | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 153.47/22.96  | | | | | | | | | | | | | | |   (104)  all_56_14 = e3
% 153.47/22.96  | | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (13), (24), (31), (75), (89), (104) are
% 153.47/22.96  | | | | | | | | | | | | | | |            inconsistent by sub-proof #621.
% 153.47/22.96  | | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | | End of split
% 153.47/22.96  | | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | End of split
% 153.47/22.96  | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | |   (105)  all_56_10 = e2 & op(e2, e0) = e2
% 153.47/22.96  | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | ALPHA: (105) implies:
% 153.47/22.96  | | | | | | | | | | | | |   (106)  op(e2, e0) = e2
% 153.47/22.96  | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | | REF_CLOSE: (13), (20), (30), (106) are inconsistent by
% 153.47/22.96  | | | | | | | | | | | | |            sub-proof #1156.
% 153.47/22.96  | | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | | End of split
% 153.47/22.96  | | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | End of split
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | End of split
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | |   (107)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1
% 153.47/22.96  | | | | | | | | | |            & op(e0, e3) = e1)
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | BETA: splitting (107) gives:
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | Case 1:
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | |   (108)  all_56_6 = e1 & op(e1, e3) = e1
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | ALPHA: (108) implies:
% 153.47/22.96  | | | | | | | | | | |   (109)  op(e1, e3) = e1
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | REF_CLOSE: (5), (13), (28), (39), (85), (109) are
% 153.47/22.96  | | | | | | | | | | |            inconsistent by sub-proof #911.
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | |   (110)  all_56_12 = e1 & op(e0, e3) = e1
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | | REF_CLOSE: (38), (75), (110) are inconsistent by sub-proof
% 153.47/22.96  | | | | | | | | | | |            #789.
% 153.47/22.96  | | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | | End of split
% 153.47/22.96  | | | | | | | | | | 
% 153.47/22.96  | | | | | | | | | End of split
% 153.47/22.96  | | | | | | | | | 
% 153.47/22.96  | | | | | | | | End of split
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | Case 2:
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | |   (111)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 153.47/22.96  | | | | | | | |          ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 153.47/22.96  | | | | | | | |            e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.47/22.96  | | | | | | | |          $i(all_57_7) & $i(all_57_10)
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | | ALPHA: (111) implies:
% 153.47/22.96  | | | | | | | |   (112)  op(e2, e2) = e1
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | | REF_CLOSE: (13), (32), (41), (112) are inconsistent by sub-proof
% 153.47/22.96  | | | | | | | |            #853.
% 153.47/22.96  | | | | | | | | 
% 153.47/22.96  | | | | | | | End of split
% 153.47/22.96  | | | | | | | 
% 153.47/22.96  | | | | | | End of split
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | End of split
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | End of split
% 153.47/22.96  | | | | 
% 153.47/22.96  | | | Case 2:
% 153.47/22.96  | | | | 
% 153.47/22.96  | | | |   (113)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.47/22.96  | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.47/22.96  | | | |            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.47/22.96  | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.47/22.96  | | | |            (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.47/22.96  | | | |            op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.47/22.96  | | | |            e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.47/22.96  | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.47/22.96  | | | |            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.47/22.96  | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.47/22.96  | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.47/22.96  | | | |            (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.47/22.96  | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.47/22.96  | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.47/22.96  | | | |            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.47/22.96  | | | |            all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.47/22.96  | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 153.47/22.96  | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 = e0) &
% 153.47/22.96  | | | |            op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.47/22.96  | | | |            all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 153.47/22.96  | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 153.47/22.96  | | | |            (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.47/22.96  | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.47/22.96  | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.47/22.96  | | | |            (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.47/22.96  | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.47/22.96  | | | |            all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 153.47/22.96  | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0)
% 153.47/22.96  | | | |            & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.47/22.96  | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14))
% 153.47/22.96  | | | |          | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.47/22.96  | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3)
% 153.47/22.96  | | | |                & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.47/22.96  | | | |                e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.47/22.96  | | | |                (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.47/22.96  | | | |                all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.47/22.96  | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.47/22.96  | | | |                (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.47/22.96  | | | |                op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.96  | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.96  | | | |                (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.47/22.96  | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.47/22.96  | | | |                all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.47/22.96  | | | |                & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.47/22.96  | | | |                e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.47/22.96  | | | |                (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.47/22.96  | | | |                op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.47/22.96  | | | | 
% 153.47/22.96  | | | | BETA: splitting (113) gives:
% 153.47/22.96  | | | | 
% 153.47/22.96  | | | | Case 1:
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | |   (114)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.47/22.96  | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.47/22.96  | | | | |            & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.47/22.96  | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.47/22.96  | | | | |            (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.47/22.96  | | | | |            op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 153.47/22.96  | | | | |            = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.47/22.96  | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.47/22.96  | | | | |            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.47/22.96  | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12))
% 153.47/22.96  | | | | |          | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.47/22.96  | | | | |            (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.47/22.96  | | | | |            & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10)
% 153.47/22.96  | | | | |            & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.47/22.96  | | | | |            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.47/22.96  | | | | |            all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 153.47/22.96  | | | | |            = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | | BETA: splitting (114) gives:
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | | Case 1:
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | |   (115)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.47/22.96  | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 153.47/22.96  | | | | | |            e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.47/22.96  | | | | | |            $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 &
% 153.47/22.96  | | | | | |            all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1)
% 153.47/22.96  | | | | | |            & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.47/22.96  | | | | | |            all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.47/22.96  | | | | | |            $i(all_57_12))
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | | REF_CLOSE: (3), (13), (35), (36), (37), (115) are inconsistent by
% 153.47/22.96  | | | | | |            sub-proof #860.
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | Case 2:
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | |   (116)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.47/22.96  | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.47/22.96  | | | | | |            e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.47/22.96  | | | | | |            $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 153.47/22.96  | | | | | |            all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 153.47/22.96  | | | | | |              e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2,
% 153.47/22.96  | | | | | |              e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.47/22.96  | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.47/22.96  | | | | | |            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.47/22.96  | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1,
% 153.47/22.96  | | | | | |              e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | | REF_CLOSE: (13), (18), (23), (29), (38), (116) are inconsistent by
% 153.47/22.96  | | | | | |            sub-proof #976.
% 153.47/22.96  | | | | | | 
% 153.47/22.96  | | | | | End of split
% 153.47/22.96  | | | | | 
% 153.47/22.96  | | | | Case 2:
% 153.47/22.96  | | | | | 
% 153.47/22.97  | | | | |   (117)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.47/22.97  | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9
% 153.47/22.97  | | | | |            & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.47/22.97  | | | | |            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.47/22.97  | | | | |            (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.47/22.97  | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.47/22.97  | | | | |            = e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 153.47/22.97  | | | | |            all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1)
% 153.47/22.97  | | | | |            & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) =
% 153.47/22.97  | | | | |            e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.47/22.97  | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 153.47/22.97  | | | | |            (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.47/22.97  | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 153.47/22.97  | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.47/22.97  | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 =
% 153.47/22.97  | | | | |                e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2,
% 153.47/22.97  | | | | |                  e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.97  | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.47/22.97  | | | | |                (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.47/22.97  | | | | |                all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.47/22.97  | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.47/22.97  | | | | |                (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.47/22.97  | | | | |                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.47/22.97  | | | | |                $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.47/22.97  | | | | |                (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.47/22.97  | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.47/22.97  | | | | |                $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.47/22.97  | | | | |                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.47/22.97  | | | | |                & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.47/22.97  | | | | |                $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.47/22.97  | | | | |                (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.47/22.97  | | | | |                & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.47/22.97  | | | | |                $i(all_57_7))))
% 153.47/22.97  | | | | | 
% 153.47/22.97  | | | | | BETA: splitting (117) gives:
% 153.47/22.97  | | | | | 
% 153.47/22.97  | | | | | Case 1:
% 153.47/22.97  | | | | | | 
% 153.47/22.97  | | | | | |   (118)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.47/22.97  | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.47/22.97  | | | | | |            all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.47/22.97  | | | | | |            $i(all_57_9) & $i(all_57_12)) | (all_57_10 = e0 &
% 153.47/22.97  | | | | | |            all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 = e0)
% 153.47/22.97  | | | | | |            & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 153.47/22.97  | | | | | |            all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.47/22.97  | | | | | |            $i(all_57_14))
% 153.47/22.97  | | | | | | 
% 153.47/22.97  | | | | | | BETA: splitting (118) gives:
% 153.47/22.97  | | | | | | 
% 153.47/22.97  | | | | | | Case 1:
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | |   (119)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.47/22.97  | | | | | | |          (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.47/22.97  | | | | | | |          all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.47/22.97  | | | | | | |          $i(all_57_9) & $i(all_57_12)
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | | ALPHA: (119) implies:
% 153.47/22.97  | | | | | | |   (120)  op(e3, e3) = e0
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | | REF_CLOSE: (3), (4), (6), (13), (14), (15), (24), (32), (34),
% 153.47/22.97  | | | | | | |            (38), (39), (75), (120) are inconsistent by sub-proof
% 153.47/22.97  | | | | | | |            #619.
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | Case 2:
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | |   (121)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 153.47/22.97  | | | | | | |          (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.47/22.97  | | | | | | |          all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.47/22.97  | | | | | | |          $i(all_57_9) & $i(all_57_14)
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | | ALPHA: (121) implies:
% 153.47/22.97  | | | | | | |   (122)  op(e3, e3) = e0
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | | REF_CLOSE: (3), (4), (6), (13), (14), (15), (24), (32), (34),
% 153.47/22.97  | | | | | | |            (38), (39), (75), (122) are inconsistent by sub-proof
% 153.47/22.97  | | | | | | |            #619.
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | End of split
% 153.47/22.97  | | | | | | 
% 153.47/22.97  | | | | | Case 2:
% 153.47/22.97  | | | | | | 
% 153.47/22.97  | | | | | |   (123)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.47/22.97  | | | | | |            (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.47/22.97  | | | | | |            e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.47/22.97  | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.47/22.97  | | | | | |            all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 =
% 153.47/22.97  | | | | | |              e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1,
% 153.47/22.97  | | | | | |              e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.47/22.97  | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15)
% 153.47/22.97  | | | | | |            & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &
% 153.47/22.97  | | | | | |                 ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.47/22.97  | | | | | |                  e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.47/22.97  | | | | | |              (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.47/22.97  | | | | | |                ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.47/22.97  | | | | | |                  e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.47/22.97  | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.47/22.97  | | | | | |                ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.47/22.97  | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.97  | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) & 
% 153.47/22.97  | | | | | |                ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.47/22.97  | | | | | |                  e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.47/22.97  | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.47/22.97  | | | | | |                ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.47/22.97  | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.47/22.97  | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 153.47/22.97  | | | | | |                ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.47/22.97  | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.47/22.97  | | | | | | 
% 153.47/22.97  | | | | | | BETA: splitting (123) gives:
% 153.47/22.97  | | | | | | 
% 153.47/22.97  | | | | | | Case 1:
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | |   (124)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) & 
% 153.47/22.97  | | | | | | |          ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0)
% 153.47/22.97  | | | | | | |          = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.47/22.97  | | | | | | |          $i(all_57_12) & $i(all_57_13)
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | | ALPHA: (124) implies:
% 153.47/22.97  | | | | | | |   (125)  op(e2, e0) = e2
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | | REF_CLOSE: (13), (20), (30), (125) are inconsistent by sub-proof
% 153.47/22.97  | | | | | | |            #1156.
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | Case 2:
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | |   (126)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 153.47/22.97  | | | | | | |            ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.47/22.97  | | | | | | |            all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.47/22.97  | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.47/22.97  | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12
% 153.47/22.97  | | | | | | |                = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.47/22.97  | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 153.47/22.97  | | | | | | |                  e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.47/22.97  | | | | | | |                all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 153.47/22.97  | | | | | | |                  = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.47/22.97  | | | | | | |                op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 153.47/22.97  | | | | | | |                all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15
% 153.47/22.97  | | | | | | |                  = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.47/22.97  | | | | | | |                op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.47/22.97  | | | | | | |                all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.47/22.97  | | | | | | |                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.97  | | | | | | |                op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.47/22.97  | | | | | | |                all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 153.47/22.97  | | | | | | |                  = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.47/22.97  | | | | | | |                op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.47/22.97  | | | | | | |                all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15
% 153.47/22.97  | | | | | | |                  = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.47/22.97  | | | | | | |                op(e0, e1) = e0 & $i(all_57_7))))
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | | BETA: splitting (126) gives:
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | | Case 1:
% 153.47/22.97  | | | | | | | | 
% 153.47/22.97  | | | | | | | |   (127)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &
% 153.47/22.97  | | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.47/22.97  | | | | | | | |          all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.47/22.97  | | | | | | | |          $i(all_57_11) & $i(all_57_14)
% 153.47/22.97  | | | | | | | | 
% 153.47/22.97  | | | | | | | | ALPHA: (127) implies:
% 153.47/22.97  | | | | | | | |   (128)   ~ (all_57_14 = e0)
% 153.47/22.97  | | | | | | | |   (129)  op(e1, e1) = all_57_14
% 153.47/22.97  | | | | | | | | 
% 153.47/22.97  | | | | | | | | REF_CLOSE: (13), (16), (128), (129) are inconsistent by
% 153.47/22.97  | | | | | | | |            sub-proof #1026.
% 153.47/22.97  | | | | | | | | 
% 153.47/22.97  | | | | | | | Case 2:
% 153.47/22.97  | | | | | | | | 
% 153.47/22.97  | | | | | | | |   (130)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 =
% 153.47/22.97  | | | | | | | |              e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.47/22.97  | | | | | | | |              (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.47/22.97  | | | | | | | |                e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.47/22.97  | | | | | | | |            (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1)
% 153.47/22.97  | | | | | | | |              &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.47/22.97  | | | | | | | |              op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.47/22.97  | | | | | | | |            (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3)
% 153.47/22.97  | | | | | | | |              &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 153.47/22.97  | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.47/22.97  | | | | | | | |            | (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.47/22.97  | | | | | | | |                e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.47/22.97  | | | | | | | |              & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4))
% 153.47/22.97  | | | | | | | |            | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 153.47/22.97  | | | | | | | |                e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.47/22.97  | | | | | | | |              op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.47/22.97  | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 & 
% 153.47/22.97  | | | | | | | |              ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 153.47/22.97  | | | | | | | |                e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) =
% 153.47/22.97  | | | | | | | |              e0 & $i(all_57_7)))
% 153.47/22.97  | | | | | | | | 
% 153.47/22.97  | | | | | | | | ALPHA: (130) implies:
% 153.47/22.97  | | | | | | | |   (131)  op(e0, e0) = all_57_15
% 153.47/22.97  | | | | | | | |   (132)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 153.47/22.97  | | | | | | | |            ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.47/22.97  | | | | | | | |              e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.47/22.97  | | | | | | | |          (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.47/22.97  | | | | | | | |            ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.47/22.97  | | | | | | | |              e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.47/22.97  | | | | | | | |          (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.47/22.97  | | | | | | | |            ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.47/22.97  | | | | | | | |            all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.97  | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) & 
% 153.47/22.97  | | | | | | | |            ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.47/22.97  | | | | | | | |              e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.47/22.97  | | | | | | | |          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.47/22.97  | | | | | | | |            ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.47/22.97  | | | | | | | |            all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.47/22.97  | | | | | | | |          (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 153.47/22.97  | | | | | | | |            ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.47/22.97  | | | | | | | |            all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.47/22.97  | | | | | | | | 
% 153.47/22.97  | | | | | | | | REF_CLOSE: (1), (13), (17), (18), (22), (26), (32), (41), (131),
% 153.47/22.97  | | | | | | | |            (132) are inconsistent by sub-proof #626.
% 153.47/22.97  | | | | | | | | 
% 153.47/22.97  | | | | | | | End of split
% 153.47/22.97  | | | | | | | 
% 153.47/22.97  | | | | | | End of split
% 153.47/22.97  | | | | | | 
% 153.47/22.97  | | | | | End of split
% 153.47/22.97  | | | | | 
% 153.47/22.97  | | | | End of split
% 153.47/22.97  | | | | 
% 153.47/22.97  | | | End of split
% 153.47/22.97  | | | 
% 153.47/22.97  | | End of split
% 153.47/22.97  | | 
% 153.47/22.97  | End of split
% 153.47/22.97  | 
% 153.47/22.97  End of proof
% 153.47/22.97  
% 153.47/22.97  Sub-proof #619 shows that the following formulas are inconsistent:
% 153.47/22.97  ----------------------------------------------------------------
% 153.47/22.97    (1)  op(e3, e3) = e0
% 153.47/22.97    (2)   ~ (e3 = e1)
% 153.47/22.97    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.47/22.97         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.47/22.97    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.47/22.97         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.47/22.97    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.97    (6)  all_56_6 = e0
% 153.47/22.97    (7)  op(e1, e3) = e0
% 153.47/22.97    (8)   ~ (e3 = e0)
% 153.47/22.97    (9)   ~ (e1 = e0)
% 153.47/22.97    (10)   ~ (e3 = e2)
% 153.47/22.97    (11)  all_56_12 = e2
% 153.47/22.97    (12)   ~ (e2 = e1)
% 153.47/22.97    (13)  op(e1, e3) = all_52_2
% 153.47/22.97  
% 153.47/22.97  Begin of proof
% 153.47/22.97  | 
% 153.47/22.97  | BETA: splitting (3) gives:
% 153.47/22.97  | 
% 153.47/22.97  | Case 1:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (14)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 153.47/22.97  | |           e1)
% 153.47/22.97  | | 
% 153.47/22.97  | | BETA: splitting (14) gives:
% 153.47/22.97  | | 
% 153.47/22.97  | | Case 1:
% 153.47/22.97  | | | 
% 153.47/22.97  | | |   (15)  all_56_0 = e1 & op(e3, e3) = e1
% 153.47/22.97  | | | 
% 153.47/22.97  | | | ALPHA: (15) implies:
% 153.47/22.97  | | |   (16)  op(e3, e3) = e1
% 153.47/22.97  | | | 
% 153.47/22.97  | | | REF_CLOSE: (1), (5), (9), (16) are inconsistent by sub-proof #957.
% 153.47/22.97  | | | 
% 153.47/22.97  | | Case 2:
% 153.47/22.97  | | | 
% 153.47/22.97  | | |   (17)  all_56_2 = e1 & op(e2, e3) = e1
% 153.47/22.97  | | | 
% 153.47/22.97  | | | ALPHA: (17) implies:
% 153.47/22.97  | | |   (18)  all_56_2 = e1
% 153.47/22.97  | | | 
% 153.47/22.97  | | | BETA: splitting (4) gives:
% 153.47/22.97  | | | 
% 153.47/22.97  | | | Case 1:
% 153.47/22.97  | | | | 
% 153.47/22.97  | | | |   (19)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3)
% 153.47/22.97  | | | |           = e3)
% 153.47/22.97  | | | | 
% 153.47/22.97  | | | | REF_CLOSE: (1), (2), (5), (8), (18), (19) are inconsistent by sub-proof
% 153.47/22.97  | | | |            #620.
% 153.47/22.97  | | | | 
% 153.47/22.97  | | | Case 2:
% 153.47/22.97  | | | | 
% 153.47/22.97  | | | |   (20)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3)
% 153.47/22.97  | | | |           = e3)
% 153.47/22.97  | | | | 
% 153.47/22.97  | | | | REF_CLOSE: (6), (8), (10), (11), (20) are inconsistent by sub-proof
% 153.47/22.97  | | | |            #783.
% 153.47/22.97  | | | | 
% 153.47/22.97  | | | End of split
% 153.47/22.97  | | | 
% 153.47/22.97  | | End of split
% 153.47/22.97  | | 
% 153.47/22.97  | Case 2:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (21)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 153.47/22.97  | |           e1)
% 153.47/22.97  | | 
% 153.47/22.97  | | BETA: splitting (21) gives:
% 153.47/22.97  | | 
% 153.47/22.97  | | Case 1:
% 153.47/22.97  | | | 
% 153.47/22.97  | | |   (22)  all_56_6 = e1 & op(e1, e3) = e1
% 153.47/22.97  | | | 
% 153.47/22.97  | | | ALPHA: (22) implies:
% 153.47/22.97  | | |   (23)  op(e1, e3) = e1
% 153.47/22.97  | | | 
% 153.47/22.97  | | | REF_CLOSE: (5), (7), (9), (13), (23) are inconsistent by sub-proof #1127.
% 153.47/22.97  | | | 
% 153.47/22.97  | | Case 2:
% 153.47/22.97  | | | 
% 153.47/22.97  | | |   (24)  all_56_12 = e1 & op(e0, e3) = e1
% 153.47/22.97  | | | 
% 153.47/22.97  | | | ALPHA: (24) implies:
% 153.47/22.97  | | |   (25)  all_56_12 = e1
% 153.47/22.97  | | | 
% 153.47/22.97  | | | REF_CLOSE: (11), (12), (25) are inconsistent by sub-proof #1122.
% 153.47/22.97  | | | 
% 153.47/22.97  | | End of split
% 153.47/22.97  | | 
% 153.47/22.97  | End of split
% 153.47/22.97  | 
% 153.47/22.97  End of proof
% 153.47/22.97  
% 153.47/22.97  Sub-proof #620 shows that the following formulas are inconsistent:
% 153.47/22.97  ----------------------------------------------------------------
% 153.47/22.97    (1)  op(e3, e3) = e0
% 153.47/22.97    (2)   ~ (e3 = e1)
% 153.47/22.97    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.97    (4)   ~ (e3 = e0)
% 153.47/22.97    (5)  all_56_2 = e1
% 153.47/22.97    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 153.47/22.97  
% 153.47/22.97  Begin of proof
% 153.47/22.97  | 
% 153.47/22.97  | BETA: splitting (6) gives:
% 153.47/22.97  | 
% 153.47/22.97  | Case 1:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (7)  all_56_0 = e3 & op(e3, e3) = e3
% 153.47/22.97  | | 
% 153.47/22.97  | | ALPHA: (7) implies:
% 153.47/22.97  | |   (8)  op(e3, e3) = e3
% 153.47/22.97  | | 
% 153.47/22.97  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1141.
% 153.47/22.97  | | 
% 153.47/22.97  | Case 2:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (9)  all_56_2 = e3 & op(e2, e3) = e3
% 153.47/22.97  | | 
% 153.47/22.97  | | ALPHA: (9) implies:
% 153.47/22.97  | |   (10)  all_56_2 = e3
% 153.47/22.97  | | 
% 153.47/22.97  | | REF_CLOSE: (2), (5), (10) are inconsistent by sub-proof #1053.
% 153.47/22.97  | | 
% 153.47/22.97  | End of split
% 153.47/22.97  | 
% 153.47/22.97  End of proof
% 153.47/22.97  
% 153.47/22.97  Sub-proof #621 shows that the following formulas are inconsistent:
% 153.47/22.97  ----------------------------------------------------------------
% 153.47/22.97    (1)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.47/22.97         (all_56_14 = e0 & op(e0, e1) = e0)
% 153.47/22.97    (2)  op(e0, e2) = all_52_7
% 153.47/22.97    (3)   ~ (e2 = e0)
% 153.47/22.97    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.97    (5)   ~ (e3 = e0)
% 153.47/22.97    (6)  all_56_14 = e3
% 153.47/22.97    (7)   ~ (all_52_7 = e0)
% 153.47/22.97    (8)  all_56_12 = e2
% 153.47/22.97  
% 153.47/22.97  Begin of proof
% 153.47/22.97  | 
% 153.47/22.97  | BETA: splitting (1) gives:
% 153.47/22.97  | 
% 153.47/22.97  | Case 1:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (9)  all_56_12 = e0 & op(e0, e3) = e0
% 153.47/22.97  | | 
% 153.47/22.97  | | ALPHA: (9) implies:
% 153.47/22.97  | |   (10)  all_56_12 = e0
% 153.47/22.97  | | 
% 153.47/22.97  | | REF_CLOSE: (3), (8), (10) are inconsistent by sub-proof #1119.
% 153.47/22.97  | | 
% 153.47/22.97  | Case 2:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (11)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 153.47/22.97  | |           e0)
% 153.47/22.97  | | 
% 153.47/22.97  | | BETA: splitting (11) gives:
% 153.47/22.97  | | 
% 153.47/22.97  | | Case 1:
% 153.47/22.97  | | | 
% 153.47/22.97  | | |   (12)  all_56_13 = e0 & op(e0, e2) = e0
% 153.47/22.97  | | | 
% 153.47/22.97  | | | ALPHA: (12) implies:
% 153.47/22.97  | | |   (13)  op(e0, e2) = e0
% 153.47/22.97  | | | 
% 153.47/22.97  | | | REF_CLOSE: (2), (4), (7), (13) are inconsistent by sub-proof #1036.
% 153.47/22.97  | | | 
% 153.47/22.97  | | Case 2:
% 153.47/22.97  | | | 
% 153.47/22.97  | | |   (14)  all_56_14 = e0 & op(e0, e1) = e0
% 153.47/22.97  | | | 
% 153.47/22.97  | | | REF_CLOSE: (5), (6), (14) are inconsistent by sub-proof #622.
% 153.47/22.97  | | | 
% 153.47/22.97  | | End of split
% 153.47/22.97  | | 
% 153.47/22.97  | End of split
% 153.47/22.97  | 
% 153.47/22.97  End of proof
% 153.47/22.97  
% 153.47/22.97  Sub-proof #622 shows that the following formulas are inconsistent:
% 153.47/22.97  ----------------------------------------------------------------
% 153.47/22.97    (1)  all_56_14 = e0 & op(e0, e1) = e0
% 153.47/22.97    (2)  all_56_14 = e3
% 153.47/22.97    (3)   ~ (e3 = e0)
% 153.47/22.97  
% 153.47/22.97  Begin of proof
% 153.47/22.97  | 
% 153.47/22.97  | ALPHA: (1) implies:
% 153.47/22.97  |   (4)  all_56_14 = e0
% 153.47/22.97  | 
% 153.47/22.97  | COMBINE_EQS: (2), (4) imply:
% 153.47/22.97  |   (5)  e3 = e0
% 153.47/22.97  | 
% 153.47/22.97  | SIMP: (5) implies:
% 153.47/22.97  |   (6)  e3 = e0
% 153.47/22.97  | 
% 153.47/22.97  | REDUCE: (3), (6) imply:
% 153.47/22.97  |   (7)  $false
% 153.47/22.97  | 
% 153.47/22.97  | CLOSE: (7) is inconsistent.
% 153.47/22.97  | 
% 153.47/22.97  End of proof
% 153.47/22.97  
% 153.47/22.97  Sub-proof #623 shows that the following formulas are inconsistent:
% 153.47/22.97  ----------------------------------------------------------------
% 153.47/22.97    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.97    (2)  op(e2, e1) = e2
% 153.47/22.97    (3)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3)
% 153.47/22.97    (4)   ~ (e3 = e2)
% 153.47/22.97    (5)   ~ (all_52_8 = e3)
% 153.47/22.97    (6)  op(e3, e1) = all_52_8
% 153.47/22.97  
% 153.47/22.97  Begin of proof
% 153.47/22.97  | 
% 153.47/22.97  | BETA: splitting (3) gives:
% 153.47/22.97  | 
% 153.47/22.97  | Case 1:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (7)  all_56_4 = e3 & op(e3, e1) = e3
% 153.47/22.97  | | 
% 153.47/22.97  | | ALPHA: (7) implies:
% 153.47/22.97  | |   (8)  op(e3, e1) = e3
% 153.47/22.97  | | 
% 153.47/22.97  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #1164.
% 153.47/22.97  | | 
% 153.47/22.97  | Case 2:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (9)  all_56_5 = e3 & op(e2, e1) = e3
% 153.47/22.97  | | 
% 153.47/22.97  | | ALPHA: (9) implies:
% 153.47/22.97  | |   (10)  op(e2, e1) = e3
% 153.47/22.97  | | 
% 153.47/22.97  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #1135.
% 153.47/22.97  | | 
% 153.47/22.97  | End of split
% 153.47/22.97  | 
% 153.47/22.97  End of proof
% 153.47/22.97  
% 153.47/22.97  Sub-proof #624 shows that the following formulas are inconsistent:
% 153.47/22.97  ----------------------------------------------------------------
% 153.47/22.97    (1)   ~ (e2 = e0)
% 153.47/22.97    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.97    (3)  op(e2, e3) = e1
% 153.47/22.97    (4)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 153.47/22.97    (5)   ~ (e2 = e1)
% 153.47/22.97    (6)  op(e2, e2) = e0
% 153.47/22.97    (7)  op(e2, e3) = all_52_1
% 153.47/22.97  
% 153.47/22.97  Begin of proof
% 153.47/22.97  | 
% 153.47/22.97  | BETA: splitting (4) gives:
% 153.47/22.97  | 
% 153.47/22.97  | Case 1:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (8)  all_56_2 = e2 & op(e2, e3) = e2
% 153.47/22.97  | | 
% 153.47/22.97  | | ALPHA: (8) implies:
% 153.47/22.97  | |   (9)  op(e2, e3) = e2
% 153.47/22.97  | | 
% 153.47/22.97  | | REF_CLOSE: (2), (3), (5), (7), (9) are inconsistent by sub-proof #842.
% 153.47/22.97  | | 
% 153.47/22.97  | Case 2:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (10)  all_56_3 = e2 & op(e2, e2) = e2
% 153.47/22.97  | | 
% 153.47/22.97  | | ALPHA: (10) implies:
% 153.47/22.97  | |   (11)  op(e2, e2) = e2
% 153.47/22.97  | | 
% 153.47/22.97  | | REF_CLOSE: (1), (2), (6), (11) are inconsistent by sub-proof #1145.
% 153.47/22.97  | | 
% 153.47/22.97  | End of split
% 153.47/22.97  | 
% 153.47/22.97  End of proof
% 153.47/22.97  
% 153.47/22.97  Sub-proof #625 shows that the following formulas are inconsistent:
% 153.47/22.97  ----------------------------------------------------------------
% 153.47/22.97    (1)  op(e0, e1) = all_52_11
% 153.47/22.97    (2)   ~ (e3 = e1)
% 153.47/22.97    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.97           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.97    (4)  op(e1, e1) = e0
% 153.47/22.97    (5)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 153.47/22.97           all_57_14 & $i(all_57_14))
% 153.47/22.97    (6)  op(e0, e0) = e2
% 153.47/22.97    (7)   ~ (all_52_13 = e2)
% 153.47/22.97    (8)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 153.47/22.97           all_57_12 & $i(all_57_12))
% 153.47/22.97    (9)  op(e3, e0) = all_52_12
% 153.47/22.97    (10)   ~ (e3 = e0)
% 153.47/22.97    (11)   ~ (all_52_11 = e0)
% 153.47/22.97    (12)   ~ (all_52_12 = e3)
% 153.47/22.97    (13)  op(e2, e0) = all_52_13
% 153.47/22.97    (14)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.47/22.97              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.47/22.97            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.47/22.97            = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.47/22.97            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.47/22.97            op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.47/22.97            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2)
% 153.47/22.97            = all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0) =
% 153.47/22.97            e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &
% 153.47/22.97             ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 153.47/22.97            op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.47/22.97            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.47/22.97            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 153.47/22.97            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.47/22.97            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~
% 153.47/22.97            (all_57_9 = e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.47/22.97            all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.47/22.97            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.47/22.97            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.47/22.97            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.47/22.97            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.47/22.97              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.47/22.97            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.47/22.97            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.47/22.97              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.47/22.97            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.47/22.97            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.47/22.97                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.47/22.97                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.97                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.47/22.97                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.47/22.97                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.47/22.97                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.47/22.97                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.97              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.47/22.97                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.47/22.97                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.47/22.97                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.47/22.97                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.47/22.97                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.47/22.97                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.47/22.97                $i(all_57_7))))
% 153.47/22.97    (15)   ~ (e1 = e0)
% 153.47/22.97    (16)   ~ (all_52_8 = e3)
% 153.47/22.97    (17)  op(e3, e1) = all_52_8
% 153.47/22.97    (18)  op(e3, e3) = e3
% 153.47/22.97    (19)   ~ (e2 = e1)
% 153.47/22.97    (20)  op(e2, e2) = e0
% 153.47/22.97  
% 153.47/22.97  Begin of proof
% 153.47/22.97  | 
% 153.47/22.97  | BETA: splitting (14) gives:
% 153.47/22.97  | 
% 153.47/22.97  | Case 1:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (21)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 153.47/22.97  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.47/22.97  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 153.47/22.97  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 153.47/22.97  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.47/22.97  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 153.47/22.97  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 153.47/22.97  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.47/22.97  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.47/22.97  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.47/22.97  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.47/22.97  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.47/22.97  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 153.47/22.97  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 153.47/22.97  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.47/22.97  | |           $i(all_57_13))
% 153.47/22.97  | | 
% 153.47/22.97  | | BETA: splitting (21) gives:
% 153.47/22.97  | | 
% 153.47/22.97  | | Case 1:
% 153.47/22.97  | | | 
% 153.47/22.97  | | |   (22)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.47/22.97  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.47/22.97  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.47/22.97  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 153.47/22.97  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.47/22.97  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.47/22.97  | | |           $i(all_57_6) & $i(all_57_12))
% 153.47/22.97  | | | 
% 153.47/22.97  | | | REF_CLOSE: (2), (3), (16), (17), (18), (22) are inconsistent by sub-proof
% 153.47/22.97  | | |            #860.
% 153.47/22.97  | | | 
% 153.47/22.97  | | Case 2:
% 153.47/22.97  | | | 
% 153.47/22.97  | | |   (23)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.47/22.97  | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.47/22.97  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.47/22.97  | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10
% 153.47/22.97  | | |             = e0) &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 153.47/22.97  | | |             e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.47/22.97  | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 153.47/22.97  | | |           &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.47/22.97  | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.47/22.97  | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.47/22.97  | | | 
% 153.47/22.97  | | | REF_CLOSE: (3), (6), (9), (12), (19), (23) are inconsistent by sub-proof
% 153.47/22.97  | | |            #976.
% 153.47/22.97  | | | 
% 153.47/22.97  | | End of split
% 153.47/22.97  | | 
% 153.47/22.97  | Case 2:
% 153.47/22.97  | | 
% 153.47/22.97  | |   (24)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.47/22.97  | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.47/22.97  | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.47/22.97  | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 153.47/22.97  | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.47/22.97  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 153.47/22.97  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.47/22.97  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 153.47/22.97  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.47/22.97  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 153.47/22.97  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.47/22.97  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.47/22.97  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.47/22.97  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.47/22.97  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.47/22.97  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 153.47/22.97  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.47/22.97  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.47/22.97  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 153.47/22.97  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.47/22.97  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.47/22.97  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 153.47/22.97  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.47/22.97  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 153.47/22.97  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.47/22.97  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.47/22.97  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.47/22.97  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.47/22.97  | |               $i(all_57_7))))
% 153.47/22.97  | | 
% 153.47/22.97  | | BETA: splitting (24) gives:
% 153.47/22.97  | | 
% 153.47/22.97  | | Case 1:
% 153.47/22.97  | | | 
% 153.47/22.97  | | |   (25)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.47/22.97  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.47/22.97  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.47/22.97  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.47/22.97  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.47/22.97  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.47/22.97  | | |           $i(all_57_9) & $i(all_57_14))
% 153.47/22.97  | | | 
% 153.47/22.97  | | | REF_CLOSE: (3), (10), (18), (25) are inconsistent by sub-proof #975.
% 153.47/22.97  | | | 
% 153.47/22.97  | | Case 2:
% 153.47/22.97  | | | 
% 153.47/22.98  | | |   (26)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.47/22.98  | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.47/22.98  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.47/22.98  | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 153.47/22.98  | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.47/22.98  | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.47/22.98  | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.47/22.98  | | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 153.47/22.98  | | |                 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.47/22.98  | | |               op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.47/22.98  | | |             (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.47/22.98  | | |               (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.47/22.98  | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.47/22.98  | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3)
% 153.47/22.98  | | |               = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.47/22.98  | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.47/22.98  | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.47/22.98  | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4))
% 153.47/22.98  | | |             | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.47/22.98  | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.47/22.98  | | |               op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 153.47/22.98  | | |               = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2)
% 153.47/22.98  | | |               = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.47/22.98  | | |               $i(all_57_7))))
% 153.47/22.98  | | | 
% 153.47/22.98  | | | BETA: splitting (26) gives:
% 153.47/22.98  | | | 
% 153.47/22.98  | | | Case 1:
% 153.47/22.98  | | | | 
% 153.47/22.98  | | | |   (27)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.47/22.98  | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.47/22.98  | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.47/22.98  | | | |         $i(all_57_13)
% 153.47/22.98  | | | | 
% 153.47/22.98  | | | | ALPHA: (27) implies:
% 153.47/22.98  | | | |   (28)  op(e2, e0) = e2
% 153.47/22.98  | | | | 
% 153.47/22.98  | | | | REF_CLOSE: (3), (7), (13), (28) are inconsistent by sub-proof #1156.
% 153.47/22.98  | | | | 
% 153.47/22.98  | | | Case 2:
% 153.47/22.98  | | | | 
% 153.47/22.98  | | | |   (29)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.47/22.98  | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.47/22.98  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.47/22.98  | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.47/22.98  | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.47/22.98  | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 153.47/22.98  | | | |               & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.47/22.98  | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 153.47/22.98  | | | |               & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 153.47/22.98  | | | |               e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.47/22.98  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.47/22.98  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.98  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.98  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.47/22.98  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.47/22.98  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.47/22.98  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.47/22.98  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.47/22.98  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.47/22.98  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.47/22.98  | | | | 
% 153.47/22.98  | | | | BETA: splitting (29) gives:
% 153.47/22.98  | | | | 
% 153.47/22.98  | | | | Case 1:
% 153.47/22.98  | | | | | 
% 153.47/22.98  | | | | |   (30)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.47/22.98  | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.47/22.98  | | | | |         op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.47/22.98  | | | | |         $i(all_57_14)
% 153.47/22.98  | | | | | 
% 153.47/22.98  | | | | | ALPHA: (30) implies:
% 153.47/22.98  | | | | |   (31)   ~ (all_57_14 = e0)
% 153.47/22.98  | | | | |   (32)  op(e1, e1) = all_57_14
% 153.47/22.98  | | | | | 
% 153.47/22.98  | | | | | REF_CLOSE: (3), (4), (31), (32) are inconsistent by sub-proof #1026.
% 153.47/22.98  | | | | | 
% 153.47/22.98  | | | | Case 2:
% 153.47/22.98  | | | | | 
% 153.47/22.98  | | | | |   (33)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.47/22.98  | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3)
% 153.47/22.98  | | | | |             & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.47/22.98  | | | | |             e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.47/22.98  | | | | |             (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.47/22.98  | | | | |             all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.47/22.98  | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.47/22.98  | | | | |             (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.47/22.98  | | | | |             op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.98  | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.98  | | | | |             (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.47/22.98  | | | | |             & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.47/22.98  | | | | |             all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.47/22.98  | | | | |             & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.47/22.98  | | | | |             e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.47/22.98  | | | | |             (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.47/22.98  | | | | |             op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7)))
% 153.47/22.98  | | | | | 
% 153.47/22.98  | | | | | ALPHA: (33) implies:
% 153.47/22.98  | | | | |   (34)  op(e0, e0) = all_57_15
% 153.47/22.98  | | | | |   (35)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.47/22.98  | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.47/22.98  | | | | |           op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 153.47/22.98  | | | | |           = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3)
% 153.47/22.98  | | | | |           = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.47/22.98  | | | | |           $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.47/22.98  | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.47/22.98  | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.98  | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.98  | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.98  | | | | |           op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 153.47/22.98  | | | | |           = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 153.47/22.98  | | | | |           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.47/22.98  | | | | |           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.47/22.98  | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.47/22.98  | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.47/22.98  | | | | | 
% 153.47/22.98  | | | | | REF_CLOSE: (1), (3), (5), (6), (8), (11), (15), (20), (34), (35) are
% 153.47/22.98  | | | | |            inconsistent by sub-proof #626.
% 153.47/22.98  | | | | | 
% 153.47/22.98  | | | | End of split
% 153.47/22.98  | | | | 
% 153.47/22.98  | | | End of split
% 153.47/22.98  | | | 
% 153.47/22.98  | | End of split
% 153.47/22.98  | | 
% 153.47/22.98  | End of split
% 153.47/22.98  | 
% 153.47/22.98  End of proof
% 153.47/22.98  
% 153.47/22.98  Sub-proof #626 shows that the following formulas are inconsistent:
% 153.47/22.98  ----------------------------------------------------------------
% 153.47/22.98    (1)  op(e0, e1) = all_52_11
% 153.47/22.98    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.98    (3)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 153.47/22.98           all_57_14 & $i(all_57_14))
% 153.47/22.98    (4)  op(e0, e0) = e2
% 153.47/22.98    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.47/22.98             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.98           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.47/22.98           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.47/22.98             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.47/22.98           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.47/22.98           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.47/22.98           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.47/22.98           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.47/22.98           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 153.47/22.98           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.47/22.98         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.47/22.98             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.47/22.98           $i(all_57_7))
% 153.47/22.98    (6)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 153.47/22.98           all_57_12 & $i(all_57_12))
% 153.47/22.98    (7)   ~ (all_52_11 = e0)
% 153.47/22.98    (8)   ~ (e1 = e0)
% 153.47/22.98    (9)  op(e0, e0) = all_57_15
% 153.47/22.98    (10)  op(e2, e2) = e0
% 153.47/22.98  
% 153.47/22.98  Begin of proof
% 153.47/22.98  | 
% 153.47/22.98  | BETA: splitting (5) gives:
% 153.47/22.98  | 
% 153.47/22.98  | Case 1:
% 153.47/22.98  | | 
% 153.47/22.98  | |   (11)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 153.47/22.98  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.47/22.98  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.47/22.98  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.47/22.98  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.47/22.98  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.47/22.98  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.47/22.98  | |           $i(all_57_3))
% 153.47/22.98  | | 
% 153.47/22.98  | | REF_CLOSE: (2), (3), (4), (6), (9), (11) are inconsistent by sub-proof #627.
% 153.47/22.98  | | 
% 153.47/22.98  | Case 2:
% 153.47/22.98  | | 
% 153.47/22.98  | |   (12)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.47/22.98  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.47/22.98  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.47/22.98  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.47/22.98  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.47/22.98  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.47/22.98  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.47/22.98  | |           $i(all_57_7))
% 153.47/22.98  | | 
% 153.47/22.98  | | BETA: splitting (12) gives:
% 153.47/22.98  | | 
% 153.47/22.98  | | Case 1:
% 153.47/22.98  | | | 
% 153.47/22.98  | | |   (13)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.47/22.98  | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.98  | | |         op(e0, e2) = e0 & $i(all_57_4)
% 153.47/22.98  | | | 
% 153.47/22.98  | | | ALPHA: (13) implies:
% 153.47/22.98  | | |   (14)   ~ (all_57_15 = e2)
% 153.47/22.98  | | | 
% 153.47/22.98  | | | REF_CLOSE: (2), (4), (9), (14) are inconsistent by sub-proof #901.
% 153.47/22.98  | | | 
% 153.47/22.98  | | Case 2:
% 153.47/22.98  | | | 
% 153.47/22.98  | | |   (15)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.47/22.98  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.47/22.98  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 153.47/22.98  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.47/22.98  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.47/22.98  | | | 
% 153.47/22.98  | | | REF_CLOSE: (1), (2), (7), (8), (10), (15) are inconsistent by sub-proof
% 153.47/22.98  | | |            #804.
% 153.47/22.98  | | | 
% 153.47/22.98  | | End of split
% 153.47/22.98  | | 
% 153.47/22.98  | End of split
% 153.47/22.98  | 
% 153.47/22.98  End of proof
% 153.47/22.98  
% 153.47/22.98  Sub-proof #627 shows that the following formulas are inconsistent:
% 153.47/22.98  ----------------------------------------------------------------
% 153.47/22.98    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.98    (2)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.47/22.98             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.98           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.47/22.98           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.47/22.98             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.47/22.98           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.47/22.98           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.47/22.98    (3)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 153.47/22.98           all_57_14 & $i(all_57_14))
% 153.47/22.98    (4)  op(e0, e0) = e2
% 153.47/22.98    (5)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 153.47/22.98           all_57_12 & $i(all_57_12))
% 153.47/22.98    (6)  op(e0, e0) = all_57_15
% 153.47/22.98  
% 153.47/22.98  Begin of proof
% 153.47/22.98  | 
% 153.47/22.98  | BETA: splitting (2) gives:
% 153.47/22.98  | 
% 153.47/22.98  | Case 1:
% 153.47/22.98  | | 
% 153.47/22.98  | |   (7)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.47/22.98  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.98  | |        $i(all_57_0)
% 153.47/22.98  | | 
% 153.47/22.98  | | ALPHA: (7) implies:
% 153.47/22.98  | |   (8)  all_57_12 = e3
% 153.47/22.98  | |   (9)   ~ (all_57_0 = e2)
% 153.47/22.98  | | 
% 153.47/22.98  | | REF_CLOSE: (5), (8), (9) are inconsistent by sub-proof #832.
% 153.47/22.98  | | 
% 153.47/22.98  | Case 2:
% 153.47/22.98  | | 
% 153.47/22.98  | |   (10)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 153.47/22.98  | |             = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 153.47/22.98  | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.47/22.98  | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 153.47/22.98  | |             e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.47/22.98  | | 
% 153.47/22.98  | | REF_CLOSE: (1), (3), (4), (6), (10) are inconsistent by sub-proof #628.
% 153.47/22.98  | | 
% 153.47/22.98  | End of split
% 153.47/22.98  | 
% 153.47/22.98  End of proof
% 153.47/22.98  
% 153.47/22.98  Sub-proof #628 shows that the following formulas are inconsistent:
% 153.47/22.98  ----------------------------------------------------------------
% 153.47/22.98    (1)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.47/22.98             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.47/22.98           $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.47/22.98           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 153.47/22.98             e2) = e0 & $i(all_57_3))
% 153.47/22.98    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.98    (3)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 153.47/22.98           all_57_14 & $i(all_57_14))
% 153.47/22.98    (4)  op(e0, e0) = e2
% 153.47/22.98    (5)  op(e0, e0) = all_57_15
% 153.47/22.98  
% 153.47/22.98  Begin of proof
% 153.47/22.98  | 
% 153.47/22.98  | BETA: splitting (1) gives:
% 153.47/22.98  | 
% 153.47/22.98  | Case 1:
% 153.47/22.98  | | 
% 153.47/22.98  | |   (6)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.47/22.98  | |          e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.47/22.98  | |        $i(all_57_1)
% 153.47/22.98  | | 
% 153.47/22.98  | | ALPHA: (6) implies:
% 153.47/22.98  | |   (7)   ~ (all_57_1 = e1)
% 153.47/22.98  | |   (8)  op(e1, e1) = e3
% 153.47/22.98  | | 
% 153.47/22.98  | | REF_CLOSE: (2), (3), (7), (8) are inconsistent by sub-proof #815.
% 153.47/22.98  | | 
% 153.47/22.98  | Case 2:
% 153.47/22.98  | | 
% 153.47/22.98  | |   (9)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 153.47/22.98  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.47/22.98  | |        $i(all_57_3)
% 153.47/22.98  | | 
% 153.47/22.98  | | ALPHA: (9) implies:
% 153.47/22.98  | |   (10)   ~ (all_57_15 = e2)
% 153.47/22.98  | | 
% 153.47/22.98  | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #901.
% 153.47/22.98  | | 
% 153.47/22.98  | End of split
% 153.47/22.98  | 
% 153.47/22.98  End of proof
% 153.47/22.98  
% 153.47/22.98  Sub-proof #629 shows that the following formulas are inconsistent:
% 153.47/22.98  ----------------------------------------------------------------
% 153.47/22.98    (1)  op(e1, e1) = e2
% 153.47/22.98    (2)  op(e1, e1) = all_4_2
% 153.47/22.98    (3)   ~ (e2 = e0)
% 153.47/22.98    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.98    (5)  op(e3, e3) = e2
% 153.47/22.98    (6)  op(e0, e0) = e2
% 153.47/22.98    (7)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.47/22.98             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.47/22.98           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.47/22.98               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.47/22.98             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.47/22.98         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.47/22.98             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.98           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.47/22.98               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.47/22.98             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.47/22.98         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.47/22.98             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.98           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.47/22.98               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.47/22.98             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.47/22.98         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.47/22.98             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.98           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 153.47/22.98               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 153.47/22.98             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 153.47/22.98    (8)   ~ (e3 = e2)
% 153.47/22.98    (9)   ~ (e2 = e1)
% 153.47/22.98    (10)  op(e2, e2) = e0
% 153.47/22.98  
% 153.47/22.98  Begin of proof
% 153.47/22.98  | 
% 153.47/22.98  | BETA: splitting (7) gives:
% 153.47/22.98  | 
% 153.47/22.98  | Case 1:
% 153.47/22.98  | | 
% 153.47/22.98  | |   (11)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.47/22.98  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.47/22.98  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.47/22.98  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.47/22.98  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.47/22.98  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 153.47/22.98  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 153.47/22.98  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.98  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.47/22.98  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.47/22.98  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.47/22.98  | |               $i(all_57_15))))
% 153.47/22.98  | | 
% 153.47/22.98  | | REF_CLOSE: (3), (4), (5), (8), (10), (11) are inconsistent by sub-proof
% 153.47/22.98  | |            #662.
% 153.47/22.98  | | 
% 153.47/22.98  | Case 2:
% 153.47/22.98  | | 
% 153.47/22.98  | |   (12)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.47/22.98  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.47/22.98  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.47/22.98  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.47/22.98  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.47/22.98  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 153.47/22.98  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 153.47/22.98  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.47/22.98  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 153.47/22.98  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 153.47/22.98  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 153.47/22.98  | |               all_57_14 & $i(all_57_14))))
% 153.47/22.98  | | 
% 153.47/22.98  | | BETA: splitting (12) gives:
% 153.47/22.98  | | 
% 153.47/22.98  | | Case 1:
% 153.47/22.98  | | | 
% 153.47/22.98  | | |   (13)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.47/22.98  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.47/22.98  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.47/22.98  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.47/22.98  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.47/22.98  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.47/22.98  | | | 
% 153.47/22.98  | | | ALPHA: (13) implies:
% 153.47/22.98  | | |   (14)  op(e1, e1) = e1
% 153.47/22.98  | | | 
% 153.47/22.98  | | | REF_CLOSE: (1), (2), (4), (9), (14) are inconsistent by sub-proof #1044.
% 153.47/22.98  | | | 
% 153.47/22.98  | | Case 2:
% 153.47/22.98  | | | 
% 153.47/22.98  | | |   (15)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 153.47/22.98  | | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.47/22.98  | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 153.47/22.98  | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.47/22.98  | | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 153.47/22.98  | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 153.47/22.98  | | | 
% 153.47/22.98  | | | ALPHA: (15) implies:
% 153.47/22.98  | | |   (16)  op(e0, e0) = e0
% 153.47/22.98  | | | 
% 153.47/22.98  | | | REF_CLOSE: (3), (4), (6), (16) are inconsistent by sub-proof #1043.
% 153.47/22.98  | | | 
% 153.47/22.98  | | End of split
% 153.47/22.98  | | 
% 153.47/22.98  | End of split
% 153.47/22.98  | 
% 153.47/22.98  End of proof
% 153.47/22.98  
% 153.47/22.98  Sub-proof #630 shows that the following formulas are inconsistent:
% 153.47/22.98  ----------------------------------------------------------------
% 153.47/22.98    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.98    (2)  op(e1, e3) = e0
% 153.47/22.98    (3)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 153.47/22.98           all_57_14 & $i(all_57_14))
% 153.47/22.98    (4)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 153.47/22.98           all_57_15 & $i(all_57_15))
% 153.47/22.98    (5)   ~ (e1 = e0)
% 153.47/22.98    (6)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.47/22.98             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.47/22.98           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.47/22.98           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.47/22.98           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.47/22.98           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.47/22.98           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.47/22.98           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.47/22.98           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.47/22.98           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 153.47/22.98           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.47/22.98           $i(all_57_14))
% 153.47/22.98    (7)  op(e1, e3) = all_52_2
% 153.47/22.98  
% 153.47/22.98  Begin of proof
% 153.47/22.98  | 
% 153.47/22.98  | BETA: splitting (6) gives:
% 153.47/22.98  | 
% 153.47/22.98  | Case 1:
% 153.47/22.98  | | 
% 153.47/22.98  | |   (8)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 153.47/22.98  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.47/22.98  | |          all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 153.47/22.98  | |        (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 153.47/22.98  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.47/22.98  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.47/22.98  | | 
% 153.47/22.98  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #814.
% 153.47/22.98  | | 
% 153.47/22.98  | Case 2:
% 153.47/22.98  | | 
% 153.47/22.98  | |   (9)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 153.47/22.98  | |            = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1
% 153.47/22.98  | |          & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.47/22.98  | |        (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 153.47/22.98  | |            = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.47/22.98  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.47/22.98  | | 
% 153.47/22.98  | | BETA: splitting (9) gives:
% 153.47/22.98  | | 
% 153.47/22.98  | | Case 1:
% 153.47/22.98  | | | 
% 153.47/22.98  | | |   (10)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.47/22.98  | | |         (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.47/22.98  | | |         op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.47/22.98  | | |         $i(all_57_14)
% 153.47/22.98  | | | 
% 153.47/22.98  | | | ALPHA: (10) implies:
% 153.47/22.98  | | |   (11)  op(e1, e3) = e1
% 153.47/22.98  | | | 
% 153.47/22.98  | | | REF_CLOSE: (1), (2), (5), (7), (11) are inconsistent by sub-proof #1127.
% 153.47/22.98  | | | 
% 153.47/22.98  | | Case 2:
% 153.47/22.98  | | | 
% 153.47/22.98  | | |   (12)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.47/22.98  | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.98  | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.47/22.98  | | |         $i(all_57_14)
% 153.47/22.98  | | | 
% 153.47/22.98  | | | ALPHA: (12) implies:
% 153.47/22.98  | | |   (13)   ~ (all_57_2 = e0)
% 153.47/22.98  | | |   (14)  op(e0, e0) = e3
% 153.47/22.98  | | | 
% 153.47/22.98  | | | REF_CLOSE: (1), (4), (13), (14) are inconsistent by sub-proof #833.
% 153.47/22.98  | | | 
% 153.47/22.98  | | End of split
% 153.47/22.98  | | 
% 153.47/22.98  | End of split
% 153.47/22.98  | 
% 153.47/22.98  End of proof
% 153.47/22.98  
% 153.47/22.98  Sub-proof #631 shows that the following formulas are inconsistent:
% 153.47/22.98  ----------------------------------------------------------------
% 153.47/22.98    (1)  all_54_10 = e1 | all_54_10 = e0
% 153.47/22.98    (2)  op(e3, e2) = all_52_4
% 153.47/22.98    (3)  op(e1, e1) = all_4_2
% 153.47/22.98    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.98           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.98    (5)   ~ (all_52_2 = all_4_2)
% 153.47/22.98    (6)  all_54_10 = all_4_2
% 153.47/22.98    (7)  op(e0, e0) = e2
% 153.47/22.98    (8)  op(e1, e0) = all_52_14
% 153.47/22.98    (9)   ~ (all_52_13 = e2)
% 153.47/22.98    (10)   ~ (all_52_4 = e3)
% 153.47/22.98    (11)  op(e3, e0) = all_52_12
% 153.47/22.98    (12)   ~ (e3 = e0)
% 153.47/22.98    (13)   ~ (all_4_2 = e0)
% 153.47/22.98    (14)  op(e1, e2) = all_52_6
% 153.47/22.98    (15)   ~ (all_52_12 = e3)
% 153.47/22.98    (16)  op(e2, e0) = all_52_13
% 153.47/22.98    (17)   ~ (all_52_14 = all_4_2)
% 153.47/22.98    (18)   ~ (all_4_2 = e2)
% 153.47/22.98    (19)   ~ (all_4_2 = e3)
% 153.47/22.98    (20)   ~ (e3 = e2)
% 153.47/22.98    (21)   ~ (all_52_8 = e3)
% 153.47/22.98    (22)  op(e3, e1) = all_52_8
% 153.47/22.98    (23)  op(e3, e3) = e3
% 153.47/22.98    (24)  op(e1, e3) = all_52_2
% 153.47/22.99    (25)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.47/22.99              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.47/22.99            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.47/22.99            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.47/22.99            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.47/22.99            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.47/22.99            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.47/22.99            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.47/22.99            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.47/22.99            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.47/22.99            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.47/22.99            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.47/22.99            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.47/22.99            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.47/22.99            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.47/22.99            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.47/22.99            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.47/22.99            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.47/22.99            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.47/22.99            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.47/22.99            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.47/22.99            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.47/22.99            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.47/22.99            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.47/22.99            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.47/22.99            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.47/22.99            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.47/22.99            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.47/22.99            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.47/22.99            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.47/22.99            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.47/22.99            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.47/22.99            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.47/22.99            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.47/22.99            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.47/22.99            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.47/22.99            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.47/22.99            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.47/22.99            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.47/22.99            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.47/22.99            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.47/22.99            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.47/22.99            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.47/22.99            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.47/22.99            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.47/22.99            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.47/22.99            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.47/22.99            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.47/22.99              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.47/22.99            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.47/22.99            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.47/22.99              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.47/22.99            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.47/22.99            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.47/22.99                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.47/22.99                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.47/22.99                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.47/22.99                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.47/22.99                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.47/22.99                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.47/22.99                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.47/22.99              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.47/22.99                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.47/22.99                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.47/22.99                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.47/22.99                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.47/22.99                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.47/22.99                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.47/22.99                $i(all_57_7))))
% 153.47/22.99    (26)   ~ (all_52_6 = all_4_2)
% 153.47/22.99    (27)  op(e2, e2) = e0
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (1) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (28)  all_54_10 = e1
% 153.47/22.99  | | 
% 153.47/22.99  | | COMBINE_EQS: (6), (28) imply:
% 153.47/22.99  | |   (29)  all_4_2 = e1
% 153.47/22.99  | | 
% 153.47/22.99  | | SIMP: (29) implies:
% 153.47/22.99  | |   (30)  all_4_2 = e1
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (5), (30) imply:
% 153.47/22.99  | |   (31)   ~ (all_52_2 = e1)
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (26), (30) imply:
% 153.47/22.99  | |   (32)   ~ (all_52_6 = e1)
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (17), (30) imply:
% 153.47/22.99  | |   (33)   ~ (all_52_14 = e1)
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (19), (30) imply:
% 153.47/22.99  | |   (34)   ~ (e3 = e1)
% 153.47/22.99  | | 
% 153.47/22.99  | | SIMP: (34) implies:
% 153.47/22.99  | |   (35)   ~ (e3 = e1)
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (18), (30) imply:
% 153.47/22.99  | |   (36)   ~ (e2 = e1)
% 153.47/22.99  | | 
% 153.47/22.99  | | SIMP: (36) implies:
% 153.47/22.99  | |   (37)   ~ (e2 = e1)
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (13), (30) imply:
% 153.47/22.99  | |   (38)   ~ (e1 = e0)
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (3), (30) imply:
% 153.47/22.99  | |   (39)  op(e1, e1) = e1
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (2), (3), (4), (7), (8), (9), (10), (11), (12), (14), (15), (16),
% 153.47/22.99  | |            (20), (21), (22), (23), (24), (25), (27), (31), (32), (33), (35),
% 153.47/22.99  | |            (37), (38), (39) are inconsistent by sub-proof #716.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (40)  all_54_10 = e0
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (6), (13), (40) are inconsistent by sub-proof #1033.
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #632 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)   ~ (e3 = e1)
% 153.47/22.99    (2)  op(e0, e0) = all_10_2
% 153.47/22.99    (3)  op(e0, e2) = all_52_7
% 153.47/22.99    (4)   ~ (e2 = e0)
% 153.47/22.99    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.99    (6)  op(e0, e0) = e3
% 153.47/22.99    (7)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.47/22.99             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.47/22.99               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.47/22.99               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.47/22.99    (8)   ~ (e3 = e0)
% 153.47/22.99    (9)   ~ (all_52_7 = e0)
% 153.47/22.99    (10)   ~ (e1 = e0)
% 153.47/22.99    (11)   ~ (e3 = e2)
% 153.47/22.99    (12)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.47/22.99          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 153.47/22.99            e2)
% 153.47/22.99    (13)   ~ (all_10_2 = e2)
% 153.47/22.99    (14)   ~ (e2 = e1)
% 153.47/22.99    (15)  all_56_12 = e3
% 153.47/22.99    (16)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.47/22.99          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 153.47/22.99            e1)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (7) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (17)  all_56_15 = e0 & op(e0, e0) = e0
% 153.47/22.99  | | 
% 153.47/22.99  | | ALPHA: (17) implies:
% 153.47/22.99  | |   (18)  op(e0, e0) = e0
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (5), (6), (8), (18) are inconsistent by sub-proof #1143.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (19)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.47/22.99  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 153.47/22.99  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.47/22.99  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 153.47/22.99  | | 
% 153.47/22.99  | | ALPHA: (19) implies:
% 153.47/22.99  | |   (20)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 153.47/22.99  | |           e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.47/22.99  | | 
% 153.47/22.99  | | BETA: splitting (20) gives:
% 153.47/22.99  | | 
% 153.47/22.99  | | Case 1:
% 153.47/22.99  | | | 
% 153.47/22.99  | | |   (21)  all_56_12 = e0 & op(e0, e3) = e0
% 153.47/22.99  | | | 
% 153.47/22.99  | | | REF_CLOSE: (8), (15), (21) are inconsistent by sub-proof #635.
% 153.47/22.99  | | | 
% 153.47/22.99  | | Case 2:
% 153.47/22.99  | | | 
% 153.47/22.99  | | |   (22)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1)
% 153.47/22.99  | | |           = e0)
% 153.47/22.99  | | | 
% 153.47/22.99  | | | BETA: splitting (22) gives:
% 153.47/22.99  | | | 
% 153.47/22.99  | | | Case 1:
% 153.47/22.99  | | | | 
% 153.47/22.99  | | | |   (23)  all_56_13 = e0 & op(e0, e2) = e0
% 153.47/22.99  | | | | 
% 153.47/22.99  | | | | ALPHA: (23) implies:
% 153.47/22.99  | | | |   (24)  op(e0, e2) = e0
% 153.47/22.99  | | | | 
% 153.47/22.99  | | | | REF_CLOSE: (3), (5), (9), (24) are inconsistent by sub-proof #1036.
% 153.47/22.99  | | | | 
% 153.47/22.99  | | | Case 2:
% 153.47/22.99  | | | | 
% 153.47/22.99  | | | |   (25)  all_56_14 = e0 & op(e0, e1) = e0
% 153.47/22.99  | | | | 
% 153.47/22.99  | | | | ALPHA: (25) implies:
% 153.47/22.99  | | | |   (26)  op(e0, e1) = e0
% 153.47/22.99  | | | | 
% 153.47/22.99  | | | | BETA: splitting (16) gives:
% 153.47/22.99  | | | | 
% 153.47/22.99  | | | | Case 1:
% 153.47/22.99  | | | | | 
% 153.47/22.99  | | | | |   (27)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0,
% 153.47/22.99  | | | | |             e2) = e1)
% 153.47/22.99  | | | | | 
% 153.47/22.99  | | | | | BETA: splitting (27) gives:
% 153.47/22.99  | | | | | 
% 153.47/22.99  | | | | | Case 1:
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | |   (28)  all_56_12 = e1 & op(e0, e3) = e1
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | | REF_CLOSE: (1), (15), (28) are inconsistent by sub-proof #992.
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | Case 2:
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | |   (29)  all_56_13 = e1 & op(e0, e2) = e1
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | | ALPHA: (29) implies:
% 153.47/22.99  | | | | | |   (30)  all_56_13 = e1
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | | BETA: splitting (12) gives:
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | | Case 1:
% 153.47/22.99  | | | | | | | 
% 153.47/22.99  | | | | | | |   (31)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 &
% 153.47/22.99  | | | | | | |           op(e0, e2) = e2)
% 153.47/22.99  | | | | | | | 
% 153.47/22.99  | | | | | | | BETA: splitting (31) gives:
% 153.47/22.99  | | | | | | | 
% 153.47/22.99  | | | | | | | Case 1:
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | |   (32)  all_56_12 = e2 & op(e0, e3) = e2
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | | ALPHA: (32) implies:
% 153.47/22.99  | | | | | | | |   (33)  all_56_12 = e2
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | | REF_CLOSE: (11), (15), (33) are inconsistent by sub-proof #869.
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | Case 2:
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | |   (34)  all_56_13 = e2 & op(e0, e2) = e2
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | | REF_CLOSE: (14), (30), (34) are inconsistent by sub-proof #739.
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | End of split
% 153.47/22.99  | | | | | | | 
% 153.47/22.99  | | | | | | Case 2:
% 153.47/22.99  | | | | | | | 
% 153.47/22.99  | | | | | | |   (35)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 &
% 153.47/22.99  | | | | | | |           op(e0, e0) = e2)
% 153.47/22.99  | | | | | | | 
% 153.47/22.99  | | | | | | | BETA: splitting (35) gives:
% 153.47/22.99  | | | | | | | 
% 153.47/22.99  | | | | | | | Case 1:
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | |   (36)  all_56_14 = e2 & op(e0, e1) = e2
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | | ALPHA: (36) implies:
% 153.47/22.99  | | | | | | | |   (37)  op(e0, e1) = e2
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | | REF_CLOSE: (4), (5), (8), (10), (15), (20), (30), (37) are
% 153.47/22.99  | | | | | | | |            inconsistent by sub-proof #633.
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | Case 2:
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | |   (38)  all_56_15 = e2 & op(e0, e0) = e2
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | | ALPHA: (38) implies:
% 153.47/22.99  | | | | | | | |   (39)  op(e0, e0) = e2
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | | REF_CLOSE: (2), (5), (13), (39) are inconsistent by sub-proof
% 153.47/22.99  | | | | | | | |            #1097.
% 153.47/22.99  | | | | | | | | 
% 153.47/22.99  | | | | | | | End of split
% 153.47/22.99  | | | | | | | 
% 153.47/22.99  | | | | | | End of split
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | End of split
% 153.47/22.99  | | | | | 
% 153.47/22.99  | | | | Case 2:
% 153.47/22.99  | | | | | 
% 153.47/22.99  | | | | |   (40)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0,
% 153.47/22.99  | | | | |             e0) = e1)
% 153.47/22.99  | | | | | 
% 153.47/22.99  | | | | | BETA: splitting (40) gives:
% 153.47/22.99  | | | | | 
% 153.47/22.99  | | | | | Case 1:
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | |   (41)  all_56_14 = e1 & op(e0, e1) = e1
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | | ALPHA: (41) implies:
% 153.47/22.99  | | | | | |   (42)  op(e0, e1) = e1
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | | REF_CLOSE: (5), (10), (26), (42) are inconsistent by sub-proof #899.
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | Case 2:
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | |   (43)  all_56_15 = e1 & op(e0, e0) = e1
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | | ALPHA: (43) implies:
% 153.47/22.99  | | | | | |   (44)  op(e0, e0) = e1
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | | REF_CLOSE: (1), (5), (6), (44) are inconsistent by sub-proof #1022.
% 153.47/22.99  | | | | | | 
% 153.47/22.99  | | | | | End of split
% 153.47/22.99  | | | | | 
% 153.47/22.99  | | | | End of split
% 153.47/22.99  | | | | 
% 153.47/22.99  | | | End of split
% 153.47/22.99  | | | 
% 153.47/22.99  | | End of split
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #633 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.47/22.99         (all_56_14 = e0 & op(e0, e1) = e0)
% 153.47/22.99    (2)   ~ (e2 = e0)
% 153.47/22.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.99    (4)  all_56_13 = e1
% 153.47/22.99    (5)   ~ (e3 = e0)
% 153.47/22.99    (6)  op(e0, e1) = e2
% 153.47/22.99    (7)   ~ (e1 = e0)
% 153.47/22.99    (8)  all_56_12 = e3
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (1) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (9)  all_56_12 = e0 & op(e0, e3) = e0
% 153.47/22.99  | | 
% 153.47/22.99  | | ALPHA: (9) implies:
% 153.47/22.99  | |   (10)  all_56_12 = e0
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (5), (8), (10) are inconsistent by sub-proof #1052.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (11)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 153.47/22.99  | |           e0)
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (2), (3), (4), (6), (7), (11) are inconsistent by sub-proof #634.
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #634 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)   ~ (e2 = e0)
% 153.47/22.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.99    (3)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.47/22.99    (4)  all_56_13 = e1
% 153.47/22.99    (5)  op(e0, e1) = e2
% 153.47/22.99    (6)   ~ (e1 = e0)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (3) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (7)  all_56_13 = e0 & op(e0, e2) = e0
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #1011.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (8)  all_56_14 = e0 & op(e0, e1) = e0
% 153.47/22.99  | | 
% 153.47/22.99  | | ALPHA: (8) implies:
% 153.47/22.99  | |   (9)  op(e0, e1) = e0
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #1008.
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #635 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  all_56_12 = e0 & op(e0, e3) = e0
% 153.47/22.99    (2)  all_56_12 = e3
% 153.47/22.99    (3)   ~ (e3 = e0)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | ALPHA: (1) implies:
% 153.47/22.99  |   (4)  all_56_12 = e0
% 153.47/22.99  | 
% 153.47/22.99  | COMBINE_EQS: (2), (4) imply:
% 153.47/22.99  |   (5)  e3 = e0
% 153.47/22.99  | 
% 153.47/22.99  | REDUCE: (3), (5) imply:
% 153.47/22.99  |   (6)  $false
% 153.47/22.99  | 
% 153.47/22.99  | CLOSE: (6) is inconsistent.
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #636 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)   ~ (all_52_1 = e0)
% 153.47/22.99    (2)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 153.47/22.99    (3)   ~ (all_52_1 = e1)
% 153.47/22.99    (4)  all_54_4 = all_52_1
% 153.47/22.99    (5)   ~ (all_52_1 = e2)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (2) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (6)  all_54_4 = e2
% 153.47/22.99  | | 
% 153.47/22.99  | | COMBINE_EQS: (4), (6) imply:
% 153.47/22.99  | |   (7)  all_52_1 = e2
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (5), (7) imply:
% 153.47/22.99  | |   (8)  $false
% 153.47/22.99  | | 
% 153.47/22.99  | | CLOSE: (8) is inconsistent.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (9)  all_54_4 = e1 | all_54_4 = e0
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #795.
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #637 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 153.47/22.99         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.47/22.99    (2)   ~ (e3 = e1)
% 153.47/22.99    (3)  all_56_4 = e0
% 153.47/22.99    (4)  all_56_14 = e1
% 153.47/22.99    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.99    (6)  all_56_5 = e2
% 153.47/22.99    (7)   ~ (e3 = e0)
% 153.47/22.99    (8)  op(e1, e1) = e1
% 153.47/22.99    (9)   ~ (e3 = e2)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (1) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (10)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) =
% 153.47/22.99  | |           e3)
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (3), (6), (7), (9), (10) are inconsistent by sub-proof #640.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (11)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) =
% 153.47/22.99  | |           e3)
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (2), (4), (5), (8), (11) are inconsistent by sub-proof #638.
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #638 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)   ~ (e3 = e1)
% 153.47/22.99    (2)  all_56_14 = e1
% 153.47/22.99    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.99    (4)  op(e1, e1) = e1
% 153.47/22.99    (5)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (5) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (6)  all_56_8 = e3 & op(e1, e1) = e3
% 153.47/22.99  | | 
% 153.47/22.99  | | ALPHA: (6) implies:
% 153.47/22.99  | |   (7)  op(e1, e1) = e3
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #734.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (8)  all_56_14 = e3 & op(e0, e1) = e3
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (1), (2), (8) are inconsistent by sub-proof #639.
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #639 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  all_56_14 = e3 & op(e0, e1) = e3
% 153.47/22.99    (2)  all_56_14 = e1
% 153.47/22.99    (3)   ~ (e3 = e1)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | ALPHA: (1) implies:
% 153.47/22.99  |   (4)  all_56_14 = e3
% 153.47/22.99  | 
% 153.47/22.99  | COMBINE_EQS: (2), (4) imply:
% 153.47/22.99  |   (5)  e3 = e1
% 153.47/22.99  | 
% 153.47/22.99  | REDUCE: (3), (5) imply:
% 153.47/22.99  |   (6)  $false
% 153.47/22.99  | 
% 153.47/22.99  | CLOSE: (6) is inconsistent.
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #640 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  all_56_4 = e0
% 153.47/22.99    (2)  all_56_5 = e2
% 153.47/22.99    (3)   ~ (e3 = e0)
% 153.47/22.99    (4)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3)
% 153.47/22.99    (5)   ~ (e3 = e2)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (4) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (6)  all_56_4 = e3 & op(e3, e1) = e3
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #641.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (7)  all_56_5 = e3 & op(e2, e1) = e3
% 153.47/22.99  | | 
% 153.47/22.99  | | ALPHA: (7) implies:
% 153.47/22.99  | |   (8)  all_56_5 = e3
% 153.47/22.99  | | 
% 153.47/22.99  | | COMBINE_EQS: (2), (8) imply:
% 153.47/22.99  | |   (9)  e3 = e2
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (5), (9) imply:
% 153.47/22.99  | |   (10)  $false
% 153.47/22.99  | | 
% 153.47/22.99  | | CLOSE: (10) is inconsistent.
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #641 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  all_56_4 = e3 & op(e3, e1) = e3
% 153.47/22.99    (2)  all_56_4 = e0
% 153.47/22.99    (3)   ~ (e3 = e0)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | ALPHA: (1) implies:
% 153.47/22.99  |   (4)  all_56_4 = e3
% 153.47/22.99  | 
% 153.47/22.99  | COMBINE_EQS: (2), (4) imply:
% 153.47/22.99  |   (5)  e3 = e0
% 153.47/22.99  | 
% 153.47/22.99  | REDUCE: (3), (5) imply:
% 153.47/22.99  |   (6)  $false
% 153.47/22.99  | 
% 153.47/22.99  | CLOSE: (6) is inconsistent.
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #642 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  ( ~ (all_44_0 = e0) & op(all_44_1, e3) = all_44_0 & op(e3, e2) = all_44_1
% 153.47/22.99           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e3, e2) =
% 153.47/22.99           all_44_1 & $i(all_44_1))
% 153.47/22.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.99    (3)  op(e1, e3) = e0
% 153.47/22.99    (4)  op(e3, e2) = e1
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (1) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (5)   ~ (all_44_0 = e0) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 153.47/22.99  | |        all_44_1 & $i(all_44_0) & $i(all_44_1)
% 153.47/22.99  | | 
% 153.47/22.99  | | ALPHA: (5) implies:
% 153.47/22.99  | |   (6)   ~ (all_44_0 = e0)
% 153.47/22.99  | |   (7)  op(e3, e2) = all_44_1
% 153.47/22.99  | |   (8)  op(all_44_1, e3) = all_44_0
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (2), (3), (4), (6), (7), (8) are inconsistent by sub-proof #1017.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (9)   ~ (all_44_1 = e1) & op(e3, e2) = all_44_1 & $i(all_44_1)
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #1016.
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #643 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  all_56_8 = e3
% 153.47/22.99    (2)   ~ (e3 = e1)
% 153.47/22.99    (3)  all_56_11 = e2
% 153.47/22.99    (4)   ~ (e2 = e0)
% 153.47/22.99    (5)  all_56_7 = e3
% 153.47/22.99    (6)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1) |
% 153.47/22.99         (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.47/22.99    (7)   ~ (e3 = e0)
% 153.47/22.99    (8)   ~ (e1 = e0)
% 153.47/22.99    (9)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.47/22.99         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.47/22.99    (10)   ~ (e2 = e1)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (6) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (11)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) =
% 153.47/22.99  | |           e1)
% 153.47/22.99  | | 
% 153.47/22.99  | | BETA: splitting (11) gives:
% 153.47/22.99  | | 
% 153.47/22.99  | | Case 1:
% 153.47/22.99  | | | 
% 153.47/22.99  | | |   (12)  all_56_6 = e1 & op(e1, e3) = e1
% 153.47/22.99  | | | 
% 153.47/22.99  | | | ALPHA: (12) implies:
% 153.47/22.99  | | |   (13)  all_56_6 = e1
% 153.47/22.99  | | | 
% 153.47/22.99  | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (13) are inconsistent by
% 153.47/22.99  | | |            sub-proof #1148.
% 153.47/22.99  | | | 
% 153.47/22.99  | | Case 2:
% 153.47/22.99  | | | 
% 153.47/22.99  | | |   (14)  all_56_7 = e1 & op(e1, e2) = e1
% 153.47/22.99  | | | 
% 153.47/22.99  | | | REF_CLOSE: (2), (5), (14) are inconsistent by sub-proof #1126.
% 153.47/22.99  | | | 
% 153.47/22.99  | | End of split
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (15)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) =
% 153.47/22.99  | |           e1)
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (1), (2), (3), (10), (15) are inconsistent by sub-proof #644.
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #644 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  all_56_8 = e3
% 153.47/22.99    (2)   ~ (e3 = e1)
% 153.47/22.99    (3)  all_56_11 = e2
% 153.47/22.99    (4)  (all_56_8 = e1 & op(e1, e1) = e1) | (all_56_11 = e1 & op(e1, e0) = e1)
% 153.47/22.99    (5)   ~ (e2 = e1)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (4) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (6)  all_56_8 = e1 & op(e1, e1) = e1
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #645.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (7)  all_56_11 = e1 & op(e1, e0) = e1
% 153.47/22.99  | | 
% 153.47/22.99  | | ALPHA: (7) implies:
% 153.47/22.99  | |   (8)  all_56_11 = e1
% 153.47/22.99  | | 
% 153.47/22.99  | | COMBINE_EQS: (3), (8) imply:
% 153.47/22.99  | |   (9)  e2 = e1
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (5), (9) imply:
% 153.47/22.99  | |   (10)  $false
% 153.47/22.99  | | 
% 153.47/22.99  | | CLOSE: (10) is inconsistent.
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #645 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  all_56_8 = e1 & op(e1, e1) = e1
% 153.47/22.99    (2)  all_56_8 = e3
% 153.47/22.99    (3)   ~ (e3 = e1)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | ALPHA: (1) implies:
% 153.47/22.99  |   (4)  all_56_8 = e1
% 153.47/22.99  | 
% 153.47/22.99  | COMBINE_EQS: (2), (4) imply:
% 153.47/22.99  |   (5)  e3 = e1
% 153.47/22.99  | 
% 153.47/22.99  | REDUCE: (3), (5) imply:
% 153.47/22.99  |   (6)  $false
% 153.47/22.99  | 
% 153.47/22.99  | CLOSE: (6) is inconsistent.
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #646 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)   ~ (e3 = e1)
% 153.47/22.99    (2)   ~ (e2 = e0)
% 153.47/22.99    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.47/22.99         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.47/22.99    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.99    (5)   ~ (all_52_9 = e3)
% 153.47/22.99    (6)   ~ (e3 = e0)
% 153.47/22.99    (7)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.47/22.99         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.47/22.99    (8)  op(e2, e1) = all_52_9
% 153.47/22.99    (9)   ~ (e1 = e0)
% 153.47/22.99    (10)  all_56_2 = e0
% 153.47/22.99    (11)   ~ (e3 = e2)
% 153.47/22.99    (12)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.47/22.99          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.47/22.99    (13)   ~ (e2 = e1)
% 153.47/22.99    (14)  op(e2, e2) = e0
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (7) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (15)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 153.47/22.99  | |           e3)
% 153.47/22.99  | | 
% 153.47/22.99  | | BETA: splitting (15) gives:
% 153.47/22.99  | | 
% 153.47/22.99  | | Case 1:
% 153.47/22.99  | | | 
% 153.47/22.99  | | |   (16)  all_56_2 = e3 & op(e2, e3) = e3
% 153.47/22.99  | | | 
% 153.47/22.99  | | | ALPHA: (16) implies:
% 153.47/22.99  | | |   (17)  all_56_2 = e3
% 153.47/22.99  | | | 
% 153.47/22.99  | | | REF_CLOSE: (6), (10), (17) are inconsistent by sub-proof #1137.
% 153.47/22.99  | | | 
% 153.47/22.99  | | Case 2:
% 153.47/22.99  | | | 
% 153.47/22.99  | | |   (18)  all_56_3 = e3 & op(e2, e2) = e3
% 153.47/22.99  | | | 
% 153.47/22.99  | | | ALPHA: (18) implies:
% 153.47/22.99  | | |   (19)  op(e2, e2) = e3
% 153.47/22.99  | | | 
% 153.47/22.99  | | | REF_CLOSE: (4), (6), (14), (19) are inconsistent by sub-proof #719.
% 153.47/22.99  | | | 
% 153.47/22.99  | | End of split
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (20)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 153.47/22.99  | |           e3)
% 153.47/22.99  | | 
% 153.47/22.99  | | BETA: splitting (20) gives:
% 153.47/22.99  | | 
% 153.47/22.99  | | Case 1:
% 153.47/22.99  | | | 
% 153.47/22.99  | | |   (21)  all_56_5 = e3 & op(e2, e1) = e3
% 153.47/22.99  | | | 
% 153.47/22.99  | | | REF_CLOSE: (4), (5), (8), (21) are inconsistent by sub-proof #647.
% 153.47/22.99  | | | 
% 153.47/22.99  | | Case 2:
% 153.47/22.99  | | | 
% 153.47/22.99  | | |   (22)  all_56_10 = e3 & op(e2, e0) = e3
% 153.47/22.99  | | | 
% 153.47/22.99  | | | ALPHA: (22) implies:
% 153.47/22.99  | | |   (23)  all_56_10 = e3
% 153.47/22.99  | | |   (24)  op(e2, e0) = e3
% 153.47/22.99  | | | 
% 153.47/22.99  | | | REF_CLOSE: (1), (2), (3), (4), (9), (10), (11), (12), (13), (14), (23),
% 153.47/22.99  | | |            (24) are inconsistent by sub-proof #670.
% 153.47/22.99  | | | 
% 153.47/22.99  | | End of split
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #647 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  all_56_5 = e3 & op(e2, e1) = e3
% 153.47/22.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.99    (3)  op(e2, e1) = all_52_9
% 153.47/22.99    (4)   ~ (all_52_9 = e3)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | ALPHA: (1) implies:
% 153.47/22.99  |   (5)  op(e2, e1) = e3
% 153.47/22.99  | 
% 153.47/22.99  | GROUND_INST: instantiating (2) with all_52_9, e3, e1, e2, simplifying with
% 153.47/22.99  |              (3), (5) gives:
% 153.47/22.99  |   (6)  all_52_9 = e3
% 153.47/22.99  | 
% 153.47/22.99  | REDUCE: (4), (6) imply:
% 153.47/22.99  |   (7)  $false
% 153.47/22.99  | 
% 153.47/22.99  | CLOSE: (7) is inconsistent.
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #648 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  all_54_6 = all_52_9
% 153.47/22.99    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/22.99           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/22.99    (3)  op(e2, e3) = e2
% 153.47/22.99    (4)   ~ (all_52_1 = all_52_9)
% 153.47/22.99    (5)   ~ (all_52_9 = e1)
% 153.47/22.99    (6)   ~ (all_52_9 = e0)
% 153.47/22.99    (7)  all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 153.47/22.99    (8)  op(e2, e3) = all_52_1
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (7) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (9)  all_54_6 = e2
% 153.47/22.99  | | 
% 153.47/22.99  | | COMBINE_EQS: (1), (9) imply:
% 153.47/22.99  | |   (10)  all_52_9 = e2
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (4), (10) imply:
% 153.47/22.99  | |   (11)   ~ (all_52_1 = e2)
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (2), (3), (8), (11) are inconsistent by sub-proof #1181.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (12)  all_54_6 = e1 | all_54_6 = e0
% 153.47/22.99  | | 
% 153.47/22.99  | | REF_CLOSE: (1), (5), (6), (12) are inconsistent by sub-proof #649.
% 153.47/22.99  | | 
% 153.47/22.99  | End of split
% 153.47/22.99  | 
% 153.47/22.99  End of proof
% 153.47/22.99  
% 153.47/22.99  Sub-proof #649 shows that the following formulas are inconsistent:
% 153.47/22.99  ----------------------------------------------------------------
% 153.47/22.99    (1)  all_54_6 = e1 | all_54_6 = e0
% 153.47/22.99    (2)  all_54_6 = all_52_9
% 153.47/22.99    (3)   ~ (all_52_9 = e1)
% 153.47/22.99    (4)   ~ (all_52_9 = e0)
% 153.47/22.99  
% 153.47/22.99  Begin of proof
% 153.47/22.99  | 
% 153.47/22.99  | BETA: splitting (1) gives:
% 153.47/22.99  | 
% 153.47/22.99  | Case 1:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (5)  all_54_6 = e1
% 153.47/22.99  | | 
% 153.47/22.99  | | COMBINE_EQS: (2), (5) imply:
% 153.47/22.99  | |   (6)  all_52_9 = e1
% 153.47/22.99  | | 
% 153.47/22.99  | | REDUCE: (3), (6) imply:
% 153.47/22.99  | |   (7)  $false
% 153.47/22.99  | | 
% 153.47/22.99  | | CLOSE: (7) is inconsistent.
% 153.47/22.99  | | 
% 153.47/22.99  | Case 2:
% 153.47/22.99  | | 
% 153.47/22.99  | |   (8)  all_54_6 = e0
% 153.47/23.00  | | 
% 153.47/23.00  | | COMBINE_EQS: (2), (8) imply:
% 153.47/23.00  | |   (9)  all_52_9 = e0
% 153.47/23.00  | | 
% 153.47/23.00  | | REDUCE: (4), (9) imply:
% 153.47/23.00  | |   (10)  $false
% 153.47/23.00  | | 
% 153.47/23.00  | | CLOSE: (10) is inconsistent.
% 153.47/23.00  | | 
% 153.47/23.00  | End of split
% 153.47/23.00  | 
% 153.47/23.00  End of proof
% 153.47/23.00  
% 153.47/23.00  Sub-proof #650 shows that the following formulas are inconsistent:
% 153.47/23.00  ----------------------------------------------------------------
% 153.47/23.00    (1)  all_54_6 = all_52_9
% 153.47/23.00    (2)  all_54_6 = e3
% 153.47/23.00    (3)   ~ (all_52_9 = e3)
% 153.47/23.00  
% 153.47/23.00  Begin of proof
% 153.47/23.00  | 
% 153.47/23.00  | COMBINE_EQS: (1), (2) imply:
% 153.47/23.00  |   (4)  all_52_9 = e3
% 153.47/23.00  | 
% 153.47/23.00  | SIMP: (4) implies:
% 153.47/23.00  |   (5)  all_52_9 = e3
% 153.47/23.00  | 
% 153.47/23.00  | REDUCE: (3), (5) imply:
% 153.47/23.00  |   (6)  $false
% 153.47/23.00  | 
% 153.47/23.00  | CLOSE: (6) is inconsistent.
% 153.47/23.00  | 
% 153.47/23.00  End of proof
% 153.47/23.00  
% 153.47/23.00  Sub-proof #651 shows that the following formulas are inconsistent:
% 153.47/23.00  ----------------------------------------------------------------
% 153.47/23.00    (1)   ~ (e3 = e1)
% 153.47/23.00    (2)  all_56_4 = e0
% 153.47/23.00    (3)   ~ (e2 = e0)
% 153.47/23.00    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/23.00    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.47/23.00         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.47/23.00    (6)  op(e3, e3) = e2
% 153.47/23.00    (7)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.47/23.00         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.47/23.00    (8)   ~ (e3 = e0)
% 153.47/23.00    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.47/23.00         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.47/23.00    (10)   ~ (e1 = e0)
% 153.47/23.00    (11)   ~ (e3 = e2)
% 153.47/23.00    (12)  all_56_9 = e2
% 153.47/23.00    (13)   ~ (e2 = e1)
% 153.47/23.00  
% 153.47/23.00  Begin of proof
% 153.47/23.00  | 
% 153.47/23.00  | BETA: splitting (5) gives:
% 153.47/23.00  | 
% 153.47/23.00  | Case 1:
% 153.47/23.00  | | 
% 153.47/23.00  | |   (14)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 153.47/23.00  | |           e3)
% 153.47/23.00  | | 
% 153.47/23.00  | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14)
% 153.47/23.00  | |            are inconsistent by sub-proof #653.
% 153.47/23.00  | | 
% 153.47/23.00  | Case 2:
% 153.47/23.00  | | 
% 153.47/23.00  | |   (15)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 153.47/23.00  | |           e3)
% 153.47/23.00  | | 
% 153.47/23.00  | | REF_CLOSE: (2), (8), (11), (12), (15) are inconsistent by sub-proof #652.
% 153.47/23.00  | | 
% 153.47/23.00  | End of split
% 153.47/23.00  | 
% 153.47/23.00  End of proof
% 153.47/23.00  
% 153.47/23.00  Sub-proof #652 shows that the following formulas are inconsistent:
% 153.47/23.00  ----------------------------------------------------------------
% 153.47/23.00    (1)  all_56_4 = e0
% 153.47/23.00    (2)   ~ (e3 = e0)
% 153.47/23.00    (3)   ~ (e3 = e2)
% 153.47/23.00    (4)  all_56_9 = e2
% 153.47/23.00    (5)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.47/23.00  
% 153.47/23.00  Begin of proof
% 153.47/23.00  | 
% 153.47/23.00  | BETA: splitting (5) gives:
% 153.47/23.00  | 
% 153.47/23.00  | Case 1:
% 153.47/23.00  | | 
% 153.47/23.00  | |   (6)  all_56_4 = e3 & op(e3, e1) = e3
% 153.47/23.00  | | 
% 153.47/23.00  | | REF_CLOSE: (1), (2), (6) are inconsistent by sub-proof #915.
% 153.47/23.00  | | 
% 153.47/23.00  | Case 2:
% 153.47/23.00  | | 
% 153.47/23.00  | |   (7)  all_56_9 = e3 & op(e3, e0) = e3
% 153.47/23.00  | | 
% 153.47/23.00  | | ALPHA: (7) implies:
% 153.47/23.00  | |   (8)  all_56_9 = e3
% 153.47/23.00  | | 
% 153.47/23.00  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #964.
% 153.47/23.00  | | 
% 153.47/23.00  | End of split
% 153.47/23.00  | 
% 153.47/23.00  End of proof
% 153.47/23.00  
% 153.47/23.00  Sub-proof #653 shows that the following formulas are inconsistent:
% 153.47/23.00  ----------------------------------------------------------------
% 153.47/23.00    (1)   ~ (e3 = e1)
% 153.47/23.00    (2)   ~ (e2 = e0)
% 153.47/23.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/23.00    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3)
% 153.47/23.00    (5)  op(e3, e3) = e2
% 153.47/23.00    (6)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.47/23.00         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.47/23.00    (7)   ~ (e3 = e0)
% 153.47/23.00    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.47/23.00         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.47/23.00    (9)   ~ (e1 = e0)
% 153.47/23.00    (10)   ~ (e3 = e2)
% 153.47/23.00    (11)  all_56_9 = e2
% 153.47/23.00    (12)   ~ (e2 = e1)
% 153.47/23.00  
% 153.47/23.00  Begin of proof
% 153.47/23.00  | 
% 153.47/23.00  | BETA: splitting (4) gives:
% 153.47/23.00  | 
% 153.47/23.00  | Case 1:
% 153.47/23.00  | | 
% 153.47/23.00  | |   (13)  all_56_0 = e3 & op(e3, e3) = e3
% 153.47/23.00  | | 
% 153.47/23.00  | | ALPHA: (13) implies:
% 153.47/23.00  | |   (14)  op(e3, e3) = e3
% 153.47/23.00  | | 
% 153.47/23.00  | | REF_CLOSE: (3), (5), (10), (14) are inconsistent by sub-proof #1085.
% 153.47/23.00  | | 
% 153.47/23.00  | Case 2:
% 153.47/23.00  | | 
% 153.47/23.00  | |   (15)  all_56_1 = e3 & op(e3, e2) = e3
% 153.47/23.00  | | 
% 153.47/23.00  | | ALPHA: (15) implies:
% 153.47/23.00  | |   (16)  all_56_1 = e3
% 153.47/23.00  | | 
% 153.47/23.00  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (16) are
% 153.47/23.00  | |            inconsistent by sub-proof #654.
% 153.47/23.00  | | 
% 153.47/23.00  | End of split
% 153.47/23.00  | 
% 153.47/23.00  End of proof
% 153.47/23.00  
% 153.47/23.00  Sub-proof #654 shows that the following formulas are inconsistent:
% 153.47/23.00  ----------------------------------------------------------------
% 153.47/23.00    (1)   ~ (e3 = e1)
% 153.47/23.00    (2)   ~ (e2 = e0)
% 153.47/23.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.47/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.47/23.00    (4)  op(e3, e3) = e2
% 153.68/23.00    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.68/23.00         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.68/23.00    (6)   ~ (e3 = e0)
% 153.68/23.00    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.68/23.00         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.68/23.00    (8)   ~ (e1 = e0)
% 153.68/23.00    (9)  all_56_9 = e2
% 153.68/23.00    (10)   ~ (e2 = e1)
% 153.68/23.00    (11)  all_56_1 = e3
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | BETA: splitting (7) gives:
% 153.68/23.00  | 
% 153.68/23.00  | Case 1:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 153.68/23.00  | |           e0)
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (2), (3), (4), (6), (11), (12) are inconsistent by sub-proof
% 153.68/23.00  | |            #659.
% 153.68/23.00  | | 
% 153.68/23.00  | Case 2:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (13)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 153.68/23.00  | |           e0)
% 153.68/23.00  | | 
% 153.68/23.00  | | BETA: splitting (13) gives:
% 153.68/23.00  | | 
% 153.68/23.00  | | Case 1:
% 153.68/23.00  | | | 
% 153.68/23.00  | | |   (14)  all_56_4 = e0 & op(e3, e1) = e0
% 153.68/23.00  | | | 
% 153.68/23.00  | | | ALPHA: (14) implies:
% 153.68/23.00  | | |   (15)  all_56_4 = e0
% 153.68/23.00  | | | 
% 153.68/23.00  | | | BETA: splitting (5) gives:
% 153.68/23.00  | | | 
% 153.68/23.00  | | | Case 1:
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | |   (16)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2)
% 153.68/23.00  | | | |           = e1)
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | | REF_CLOSE: (1), (3), (4), (10), (11), (16) are inconsistent by sub-proof
% 153.68/23.00  | | | |            #658.
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | Case 2:
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | |   (17)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0)
% 153.68/23.00  | | | |           = e1)
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | | REF_CLOSE: (8), (9), (10), (15), (17) are inconsistent by sub-proof
% 153.68/23.00  | | | |            #655.
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | End of split
% 153.68/23.00  | | | 
% 153.68/23.00  | | Case 2:
% 153.68/23.00  | | | 
% 153.68/23.00  | | |   (18)  all_56_9 = e0 & op(e3, e0) = e0
% 153.68/23.00  | | | 
% 153.68/23.00  | | | REF_CLOSE: (2), (9), (18) are inconsistent by sub-proof #746.
% 153.68/23.00  | | | 
% 153.68/23.00  | | End of split
% 153.68/23.00  | | 
% 153.68/23.00  | End of split
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #655 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.68/23.00    (2)  all_56_4 = e0
% 153.68/23.00    (3)   ~ (e1 = e0)
% 153.68/23.00    (4)  all_56_9 = e2
% 153.68/23.00    (5)   ~ (e2 = e1)
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | BETA: splitting (1) gives:
% 153.68/23.00  | 
% 153.68/23.00  | Case 1:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (6)  all_56_4 = e1 & op(e3, e1) = e1
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (6) implies:
% 153.68/23.00  | |   (7)  all_56_4 = e1
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #657.
% 153.68/23.00  | | 
% 153.68/23.00  | Case 2:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (8)  all_56_9 = e1 & op(e3, e0) = e1
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #656.
% 153.68/23.00  | | 
% 153.68/23.00  | End of split
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #656 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)  all_56_9 = e1 & op(e3, e0) = e1
% 153.68/23.00    (2)  all_56_9 = e2
% 153.68/23.00    (3)   ~ (e2 = e1)
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | ALPHA: (1) implies:
% 153.68/23.00  |   (4)  all_56_9 = e1
% 153.68/23.00  | 
% 153.68/23.00  | COMBINE_EQS: (2), (4) imply:
% 153.68/23.00  |   (5)  e2 = e1
% 153.68/23.00  | 
% 153.68/23.00  | REDUCE: (3), (5) imply:
% 153.68/23.00  |   (6)  $false
% 153.68/23.00  | 
% 153.68/23.00  | CLOSE: (6) is inconsistent.
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #657 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)  all_56_4 = e1
% 153.68/23.00    (2)  all_56_4 = e0
% 153.68/23.00    (3)   ~ (e1 = e0)
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | COMBINE_EQS: (1), (2) imply:
% 153.68/23.00  |   (4)  e1 = e0
% 153.68/23.00  | 
% 153.68/23.00  | SIMP: (4) implies:
% 153.68/23.00  |   (5)  e1 = e0
% 153.68/23.00  | 
% 153.68/23.00  | REDUCE: (3), (5) imply:
% 153.68/23.00  |   (6)  $false
% 153.68/23.00  | 
% 153.68/23.00  | CLOSE: (6) is inconsistent.
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #658 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)   ~ (e3 = e1)
% 153.68/23.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.00    (3)  op(e3, e3) = e2
% 153.68/23.00    (4)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1)
% 153.68/23.00    (5)   ~ (e2 = e1)
% 153.68/23.00    (6)  all_56_1 = e3
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | BETA: splitting (4) gives:
% 153.68/23.00  | 
% 153.68/23.00  | Case 1:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (7) implies:
% 153.68/23.00  | |   (8)  op(e3, e3) = e1
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1074.
% 153.68/23.00  | | 
% 153.68/23.00  | Case 2:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (9)  all_56_1 = e1 & op(e3, e2) = e1
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #1112.
% 153.68/23.00  | | 
% 153.68/23.00  | End of split
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #659 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)   ~ (e2 = e0)
% 153.68/23.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.00    (3)  op(e3, e3) = e2
% 153.68/23.00    (4)   ~ (e3 = e0)
% 153.68/23.00    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 153.68/23.00    (6)  all_56_1 = e3
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | BETA: splitting (5) gives:
% 153.68/23.00  | 
% 153.68/23.00  | Case 1:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (7) implies:
% 153.68/23.00  | |   (8)  op(e3, e3) = e0
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1073.
% 153.68/23.00  | | 
% 153.68/23.00  | Case 2:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (9)  all_56_1 = e0 & op(e3, e2) = e0
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #1114.
% 153.68/23.00  | | 
% 153.68/23.00  | End of split
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #660 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)  op(e3, e2) = all_52_4
% 153.68/23.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.00    (3)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3)
% 153.68/23.00    (4)  op(e3, e3) = e2
% 153.68/23.00    (5)   ~ (all_52_4 = e3)
% 153.68/23.00    (6)   ~ (e3 = e2)
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | BETA: splitting (3) gives:
% 153.68/23.00  | 
% 153.68/23.00  | Case 1:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (7)  all_56_0 = e3 & op(e3, e3) = e3
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (7) implies:
% 153.68/23.00  | |   (8)  op(e3, e3) = e3
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1085.
% 153.68/23.00  | | 
% 153.68/23.00  | Case 2:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (9)  all_56_1 = e3 & op(e3, e2) = e3
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (9) implies:
% 153.68/23.00  | |   (10)  op(e3, e2) = e3
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1166.
% 153.68/23.00  | | 
% 153.68/23.00  | End of split
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #661 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)  all_54_11 = all_52_14
% 153.68/23.00    (2)  all_54_11 = e3
% 153.68/23.00    (3)   ~ (all_52_14 = e3)
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | COMBINE_EQS: (1), (2) imply:
% 153.68/23.00  |   (4)  all_52_14 = e3
% 153.68/23.00  | 
% 153.68/23.00  | SIMP: (4) implies:
% 153.68/23.00  |   (5)  all_52_14 = e3
% 153.68/23.00  | 
% 153.68/23.00  | REDUCE: (3), (5) imply:
% 153.68/23.00  |   (6)  $false
% 153.68/23.00  | 
% 153.68/23.00  | CLOSE: (6) is inconsistent.
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #662 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)   ~ (e2 = e0)
% 153.68/23.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.00    (3)  op(e3, e3) = e2
% 153.68/23.00    (4)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.68/23.00             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.00           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.68/23.00               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.68/23.00             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.00         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.68/23.00             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.00           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.68/23.00               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.68/23.00             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 153.68/23.00    (5)   ~ (e3 = e2)
% 153.68/23.00    (6)  op(e2, e2) = e0
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | BETA: splitting (4) gives:
% 153.68/23.00  | 
% 153.68/23.00  | Case 1:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2)
% 153.68/23.00  | |          | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.00  | |        ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 153.68/23.00  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 153.68/23.00  | |              e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 153.68/23.00  | |            $i(all_57_15)))
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (7) implies:
% 153.68/23.00  | |   (8)  op(e3, e3) = e3
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1085.
% 153.68/23.00  | | 
% 153.68/23.00  | Case 2:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3)
% 153.68/23.00  | |          | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.00  | |        ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.68/23.00  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.68/23.00  | |              e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.68/23.00  | |            $i(all_57_15)))
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (9) implies:
% 153.68/23.00  | |   (10)  op(e2, e2) = e2
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #1145.
% 153.68/23.00  | | 
% 153.68/23.00  | End of split
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #663 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.00    (2)  op(e3, e1) = e3
% 153.68/23.00    (3)  op(e3, e1) = e0
% 153.68/23.00    (4)   ~ (e3 = e0)
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | GROUND_INST: instantiating (1) with e0, e3, e1, e3, simplifying with (2), (3)
% 153.68/23.00  |              gives:
% 153.68/23.00  |   (5)  e3 = e0
% 153.68/23.00  | 
% 153.68/23.00  | REDUCE: (4), (5) imply:
% 153.68/23.00  |   (6)  $false
% 153.68/23.00  | 
% 153.68/23.00  | CLOSE: (6) is inconsistent.
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #664 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)   ~ (e2 = e0)
% 153.68/23.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.00    (3)   ~ (e1 = e0)
% 153.68/23.00    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.68/23.00             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.68/23.00           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.68/23.00           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.68/23.00           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 153.68/23.00           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.68/23.00    (5)  op(e0, e0) = e0
% 153.68/23.00    (6)  op(e2, e2) = e0
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | BETA: splitting (4) gives:
% 153.68/23.00  | 
% 153.68/23.00  | Case 1:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.68/23.00  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.68/23.00  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (7) implies:
% 153.68/23.00  | |   (8)  op(e0, e0) = e2
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1043.
% 153.68/23.00  | | 
% 153.68/23.00  | Case 2:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.68/23.00  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.68/23.00  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (9) implies:
% 153.68/23.00  | |   (10)  op(e2, e2) = e1
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #853.
% 153.68/23.00  | | 
% 153.68/23.00  | End of split
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #665 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)   ~ (all_52_6 = e1)
% 153.68/23.00    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.00    (3)  op(e1, e3) = e0
% 153.68/23.00    (4)  op(e1, e2) = all_52_6
% 153.68/23.00    (5)   ~ (e1 = e0)
% 153.68/23.00    (6)  op(e1, e3) = all_52_2
% 153.68/23.00    (7)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_7 = e1 & op(e1, e2) = e1)
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | BETA: splitting (7) gives:
% 153.68/23.00  | 
% 153.68/23.00  | Case 1:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (8)  all_56_6 = e1 & op(e1, e3) = e1
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (8) implies:
% 153.68/23.00  | |   (9)  op(e1, e3) = e1
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (2), (3), (5), (6), (9) are inconsistent by sub-proof #1127.
% 153.68/23.00  | | 
% 153.68/23.00  | Case 2:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (10)  all_56_7 = e1 & op(e1, e2) = e1
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (10) implies:
% 153.68/23.00  | |   (11)  op(e1, e2) = e1
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (1), (2), (4), (11) are inconsistent by sub-proof #1042.
% 153.68/23.00  | | 
% 153.68/23.00  | End of split
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #666 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)  op(e3, e2) = all_52_4
% 153.68/23.00    (2)   ~ (e2 = e0)
% 153.68/23.00    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.00    (4)  op(e3, e3) = e2
% 153.68/23.00    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 153.68/23.00    (6)   ~ (all_52_4 = e0)
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | BETA: splitting (5) gives:
% 153.68/23.00  | 
% 153.68/23.00  | Case 1:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 153.68/23.00  | | 
% 153.68/23.00  | | ALPHA: (7) implies:
% 153.68/23.00  | |   (8)  op(e3, e3) = e0
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1073.
% 153.68/23.00  | | 
% 153.68/23.00  | Case 2:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (9)  all_56_1 = e0 & op(e3, e2) = e0
% 153.68/23.00  | | 
% 153.68/23.00  | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #1013.
% 153.68/23.00  | | 
% 153.68/23.00  | End of split
% 153.68/23.00  | 
% 153.68/23.00  End of proof
% 153.68/23.00  
% 153.68/23.00  Sub-proof #667 shows that the following formulas are inconsistent:
% 153.68/23.00  ----------------------------------------------------------------
% 153.68/23.00    (1)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.68/23.00    (2)   ~ (e3 = e1)
% 153.68/23.00    (3)  all_56_10 = e3
% 153.68/23.00    (4)   ~ (all_14_2 = e0)
% 153.68/23.00    (5)  op(e3, e3) = all_14_2
% 153.68/23.00    (6)   ~ (all_10_2 = e1)
% 153.68/23.00    (7)   ~ (e2 = e0)
% 153.68/23.00    (8)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.68/23.00         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.68/23.00    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.00           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.00    (10)  op(e2, e0) = e3
% 153.68/23.00    (11)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.68/23.00          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.68/23.00    (12)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.68/23.00    (13)  op(e2, e0) = all_52_13
% 153.68/23.00    (14)  op(e0, e3) = all_52_3
% 153.68/23.00    (15)  all_54_0 = all_14_2
% 153.68/23.00    (16)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.68/23.00              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.00            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.68/23.00                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.68/23.00              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.00          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.68/23.00              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.00            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.68/23.00                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.68/23.00              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.00          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.68/23.00              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.00            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.68/23.00                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.68/23.00              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.00          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.68/23.00              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.00            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.68/23.00                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.68/23.00                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.68/23.00                $i(all_57_14))))
% 153.68/23.00    (17)   ~ (all_14_2 = e2)
% 153.68/23.00    (18)  op(e1, e1) = e3
% 153.68/23.00    (19)   ~ (e3 = e2)
% 153.68/23.00    (20)   ~ (all_14_2 = e1)
% 153.68/23.00    (21)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.68/23.00          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.68/23.00    (22)   ~ (all_10_2 = e2)
% 153.68/23.00    (23)   ~ (all_52_3 = all_10_2)
% 153.68/23.00    (24)   ~ (e2 = e1)
% 153.68/23.00    (25)   ~ (all_52_13 = all_10_2)
% 153.68/23.00    (26)  all_54_15 = all_10_2
% 153.68/23.00    (27)  op(e1, e3) = all_52_2
% 153.68/23.00    (28)  op(e2, e2) = e0
% 153.68/23.00  
% 153.68/23.00  Begin of proof
% 153.68/23.00  | 
% 153.68/23.00  | GROUND_INST: instantiating (9) with all_52_13, e3, e0, e2, simplifying with
% 153.68/23.00  |              (10), (13) gives:
% 153.68/23.00  |   (29)  all_52_13 = e3
% 153.68/23.00  | 
% 153.68/23.00  | REDUCE: (25), (29) imply:
% 153.68/23.00  |   (30)   ~ (all_10_2 = e3)
% 153.68/23.00  | 
% 153.68/23.00  | SIMP: (30) implies:
% 153.68/23.00  |   (31)   ~ (all_10_2 = e3)
% 153.68/23.00  | 
% 153.68/23.00  | BETA: splitting (16) gives:
% 153.68/23.00  | 
% 153.68/23.00  | Case 1:
% 153.68/23.00  | | 
% 153.68/23.00  | |   (32)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.68/23.00  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.68/23.00  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.68/23.00  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.68/23.00  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.68/23.00  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 153.68/23.00  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 153.68/23.00  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.00  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.68/23.00  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.68/23.00  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.68/23.00  | |               $i(all_57_15))))
% 153.68/23.00  | | 
% 153.68/23.00  | | BETA: splitting (32) gives:
% 153.68/23.00  | | 
% 153.68/23.00  | | Case 1:
% 153.68/23.00  | | | 
% 153.68/23.00  | | |   (33)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.68/23.00  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.68/23.00  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.68/23.00  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.68/23.00  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.68/23.00  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.68/23.00  | | | 
% 153.68/23.00  | | | ALPHA: (33) implies:
% 153.68/23.00  | | |   (34)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 153.68/23.00  | | |             e1) = all_57_14 & $i(all_57_14))
% 153.68/23.00  | | | 
% 153.68/23.00  | | | BETA: splitting (1) gives:
% 153.68/23.00  | | | 
% 153.68/23.00  | | | Case 1:
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | |   (35)  all_54_15 = e3
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | | COMBINE_EQS: (26), (35) imply:
% 153.68/23.00  | | | |   (36)  all_10_2 = e3
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | | REDUCE: (31), (36) imply:
% 153.68/23.00  | | | |   (37)  $false
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | | CLOSE: (37) is inconsistent.
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | Case 2:
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | |   (38)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | | BETA: splitting (38) gives:
% 153.68/23.00  | | | | 
% 153.68/23.00  | | | | Case 1:
% 153.68/23.00  | | | | | 
% 153.68/23.00  | | | | |   (39)  all_54_15 = e2
% 153.68/23.00  | | | | | 
% 153.68/23.00  | | | | | COMBINE_EQS: (26), (39) imply:
% 153.68/23.00  | | | | |   (40)  all_10_2 = e2
% 153.68/23.00  | | | | | 
% 153.68/23.00  | | | | | REDUCE: (22), (40) imply:
% 153.68/23.00  | | | | |   (41)  $false
% 153.68/23.00  | | | | | 
% 153.68/23.00  | | | | | CLOSE: (41) is inconsistent.
% 153.68/23.00  | | | | | 
% 153.68/23.00  | | | | Case 2:
% 153.68/23.00  | | | | | 
% 153.68/23.00  | | | | |   (42)   ~ (all_54_15 = e2)
% 153.68/23.00  | | | | |   (43)  all_54_15 = e1 | all_54_15 = e0
% 153.68/23.00  | | | | | 
% 153.68/23.00  | | | | | BETA: splitting (34) gives:
% 153.68/23.00  | | | | | 
% 153.68/23.00  | | | | | Case 1:
% 153.68/23.00  | | | | | | 
% 153.68/23.00  | | | | | |   (44)  all_57_1 = e1 & op(e1, e3) = e1
% 153.68/23.00  | | | | | | 
% 153.68/23.00  | | | | | | ALPHA: (44) implies:
% 153.68/23.00  | | | | | |   (45)  op(e1, e3) = e1
% 153.68/23.00  | | | | | | 
% 153.68/23.01  | | | | | | BETA: splitting (43) gives:
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | | Case 1:
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | |   (46)  all_54_15 = e1
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | | REF_CLOSE: (6), (26), (46) are inconsistent by sub-proof #1047.
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | Case 2:
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | |   (47)  all_54_15 = e0
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | | COMBINE_EQS: (26), (47) imply:
% 153.68/23.01  | | | | | | |   (48)  all_10_2 = e0
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | | SIMP: (48) implies:
% 153.68/23.01  | | | | | | |   (49)  all_10_2 = e0
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | | REDUCE: (23), (49) imply:
% 153.68/23.01  | | | | | | |   (50)   ~ (all_52_3 = e0)
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | | REDUCE: (22), (49) imply:
% 153.68/23.01  | | | | | | |   (51)   ~ (e2 = e0)
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | | REDUCE: (6), (49) imply:
% 153.68/23.01  | | | | | | |   (52)   ~ (e1 = e0)
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | | SIMP: (52) implies:
% 153.68/23.01  | | | | | | |   (53)   ~ (e1 = e0)
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12),
% 153.68/23.01  | | | | | | |            (14), (15), (17), (19), (20), (21), (24), (27), (28),
% 153.68/23.01  | | | | | | |            (45), (50), (53) are inconsistent by sub-proof #668.
% 153.68/23.01  | | | | | | | 
% 153.68/23.01  | | | | | | End of split
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | Case 2:
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | |   (54)   ~ (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14)
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | | ALPHA: (54) implies:
% 153.68/23.01  | | | | | |   (55)   ~ (all_57_14 = e3)
% 153.68/23.01  | | | | | |   (56)  op(e1, e1) = all_57_14
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | | REF_CLOSE: (9), (18), (55), (56) are inconsistent by sub-proof #816.
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | End of split
% 153.68/23.01  | | | | | 
% 153.68/23.01  | | | | End of split
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | End of split
% 153.68/23.01  | | | 
% 153.68/23.01  | | Case 2:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (57)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 153.68/23.01  | | |             e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.68/23.01  | | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 153.68/23.01  | | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.68/23.01  | | |         ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0,
% 153.68/23.01  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (57) implies:
% 153.68/23.01  | | |   (58)  op(e2, e2) = e2
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (7), (9), (28), (58) are inconsistent by sub-proof #1145.
% 153.68/23.01  | | | 
% 153.68/23.01  | | End of split
% 153.68/23.01  | | 
% 153.68/23.01  | Case 2:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (59)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.68/23.01  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.68/23.01  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.68/23.01  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.01  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.68/23.01  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 153.68/23.01  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 153.68/23.01  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.01  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 153.68/23.01  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 153.68/23.01  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 153.68/23.01  | |               all_57_14 & $i(all_57_14))))
% 153.68/23.01  | | 
% 153.68/23.01  | | BETA: splitting (59) gives:
% 153.68/23.01  | | 
% 153.68/23.01  | | Case 1:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (60)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.68/23.01  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.68/23.01  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.68/23.01  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.01  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.68/23.01  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (60) implies:
% 153.68/23.01  | | |   (61)  op(e1, e1) = e1
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (2), (9), (18), (61) are inconsistent by sub-proof #734.
% 153.68/23.01  | | | 
% 153.68/23.01  | | Case 2:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (62)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 153.68/23.01  | | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.68/23.01  | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 153.68/23.01  | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.01  | | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 153.68/23.01  | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (62) implies:
% 153.68/23.01  | | |   (63)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.68/23.01  | | |             e2) = all_57_12 & $i(all_57_12))
% 153.68/23.01  | | | 
% 153.68/23.01  | | | BETA: splitting (63) gives:
% 153.68/23.01  | | | 
% 153.68/23.01  | | | Case 1:
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | |   (64)  all_57_11 = e2 & op(e2, e0) = e2
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | ALPHA: (64) implies:
% 153.68/23.01  | | | |   (65)  op(e2, e0) = e2
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | REF_CLOSE: (9), (10), (19), (65) are inconsistent by sub-proof #854.
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | Case 2:
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | |   (66)   ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12)
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | ALPHA: (66) implies:
% 153.68/23.01  | | | |   (67)   ~ (all_57_12 = e0)
% 153.68/23.01  | | | |   (68)  op(e2, e2) = all_57_12
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | REF_CLOSE: (9), (28), (67), (68) are inconsistent by sub-proof #856.
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | End of split
% 153.68/23.01  | | | 
% 153.68/23.01  | | End of split
% 153.68/23.01  | | 
% 153.68/23.01  | End of split
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #668 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)   ~ (e3 = e1)
% 153.68/23.01    (2)  all_56_10 = e3
% 153.68/23.01    (3)   ~ (all_14_2 = e0)
% 153.68/23.01    (4)  op(e3, e3) = all_14_2
% 153.68/23.01    (5)   ~ (e2 = e0)
% 153.68/23.01    (6)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.68/23.01         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.68/23.01    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.01    (8)  op(e2, e0) = e3
% 153.68/23.01    (9)  op(e1, e3) = e1
% 153.68/23.01    (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.68/23.01          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.68/23.01    (11)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.68/23.01    (12)  op(e0, e3) = all_52_3
% 153.68/23.01    (13)  all_54_0 = all_14_2
% 153.68/23.01    (14)   ~ (e1 = e0)
% 153.68/23.01    (15)   ~ (all_14_2 = e2)
% 153.68/23.01    (16)   ~ (e3 = e2)
% 153.68/23.01    (17)   ~ (all_14_2 = e1)
% 153.68/23.01    (18)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.68/23.01          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.68/23.01    (19)   ~ (all_52_3 = e0)
% 153.68/23.01    (20)   ~ (e2 = e1)
% 153.68/23.01    (21)  op(e1, e3) = all_52_2
% 153.68/23.01    (22)  op(e2, e2) = e0
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | BETA: splitting (10) gives:
% 153.68/23.01  | 
% 153.68/23.01  | Case 1:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (23)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 153.68/23.01  | |           e0)
% 153.68/23.01  | | 
% 153.68/23.01  | | BETA: splitting (23) gives:
% 153.68/23.01  | | 
% 153.68/23.01  | | Case 1:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (24)  all_56_0 = e0 & op(e3, e3) = e0
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (24) implies:
% 153.68/23.01  | | |   (25)  op(e3, e3) = e0
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (3), (4), (7), (11), (13), (15), (17), (25) are inconsistent by
% 153.68/23.01  | | |            sub-proof #1139.
% 153.68/23.01  | | | 
% 153.68/23.01  | | Case 2:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (26)  all_56_2 = e0 & op(e2, e3) = e0
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (26) implies:
% 153.68/23.01  | | |   (27)  all_56_2 = e0
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (14), (16), (18), (20), (22),
% 153.68/23.01  | | |            (27) are inconsistent by sub-proof #670.
% 153.68/23.01  | | | 
% 153.68/23.01  | | End of split
% 153.68/23.01  | | 
% 153.68/23.01  | Case 2:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (28)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 153.68/23.01  | |           e0)
% 153.68/23.01  | | 
% 153.68/23.01  | | REF_CLOSE: (7), (9), (12), (14), (19), (21), (28) are inconsistent by
% 153.68/23.01  | |            sub-proof #669.
% 153.68/23.01  | | 
% 153.68/23.01  | End of split
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #669 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.01    (2)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.68/23.01    (3)  op(e1, e3) = e1
% 153.68/23.01    (4)  op(e0, e3) = all_52_3
% 153.68/23.01    (5)   ~ (e1 = e0)
% 153.68/23.01    (6)   ~ (all_52_3 = e0)
% 153.68/23.01    (7)  op(e1, e3) = all_52_2
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | BETA: splitting (2) gives:
% 153.68/23.01  | 
% 153.68/23.01  | Case 1:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (8)  all_56_6 = e0 & op(e1, e3) = e0
% 153.68/23.01  | | 
% 153.68/23.01  | | ALPHA: (8) implies:
% 153.68/23.01  | |   (9)  op(e1, e3) = e0
% 153.68/23.01  | | 
% 153.68/23.01  | | REF_CLOSE: (1), (3), (5), (7), (9) are inconsistent by sub-proof #1127.
% 153.68/23.01  | | 
% 153.68/23.01  | Case 2:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (10)  all_56_12 = e0 & op(e0, e3) = e0
% 153.68/23.01  | | 
% 153.68/23.01  | | ALPHA: (10) implies:
% 153.68/23.01  | |   (11)  op(e0, e3) = e0
% 153.68/23.01  | | 
% 153.68/23.01  | | REF_CLOSE: (1), (4), (6), (11) are inconsistent by sub-proof #1142.
% 153.68/23.01  | | 
% 153.68/23.01  | End of split
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #670 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)   ~ (e3 = e1)
% 153.68/23.01    (2)  all_56_10 = e3
% 153.68/23.01    (3)   ~ (e2 = e0)
% 153.68/23.01    (4)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.68/23.01         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.68/23.01    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.01    (6)  op(e2, e0) = e3
% 153.68/23.01    (7)   ~ (e1 = e0)
% 153.68/23.01    (8)  all_56_2 = e0
% 153.68/23.01    (9)   ~ (e3 = e2)
% 153.68/23.01    (10)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.68/23.01          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.68/23.01    (11)   ~ (e2 = e1)
% 153.68/23.01    (12)  op(e2, e2) = e0
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | BETA: splitting (10) gives:
% 153.68/23.01  | 
% 153.68/23.01  | Case 1:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (13)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 153.68/23.01  | |           e1)
% 153.68/23.01  | | 
% 153.68/23.01  | | BETA: splitting (13) gives:
% 153.68/23.01  | | 
% 153.68/23.01  | | Case 1:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (14)  all_56_2 = e1 & op(e2, e3) = e1
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (14) implies:
% 153.68/23.01  | | |   (15)  all_56_2 = e1
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (7), (8), (15) are inconsistent by sub-proof #1060.
% 153.68/23.01  | | | 
% 153.68/23.01  | | Case 2:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (16)  all_56_3 = e1 & op(e2, e2) = e1
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (16) implies:
% 153.68/23.01  | | |   (17)  op(e2, e2) = e1
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (5), (7), (12), (17) are inconsistent by sub-proof #853.
% 153.68/23.01  | | | 
% 153.68/23.01  | | End of split
% 153.68/23.01  | | 
% 153.68/23.01  | Case 2:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (18)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) =
% 153.68/23.01  | |           e1)
% 153.68/23.01  | | 
% 153.68/23.01  | | BETA: splitting (18) gives:
% 153.68/23.01  | | 
% 153.68/23.01  | | Case 1:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (19)  all_56_5 = e1 & op(e2, e1) = e1
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (19) implies:
% 153.68/23.01  | | |   (20)  all_56_5 = e1
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (11), (12), (20) are inconsistent
% 153.68/23.01  | | |            by sub-proof #671.
% 153.68/23.01  | | | 
% 153.68/23.01  | | Case 2:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (21)  all_56_10 = e1 & op(e2, e0) = e1
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (21) implies:
% 153.68/23.01  | | |   (22)  all_56_10 = e1
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (1), (2), (22) are inconsistent by sub-proof #677.
% 153.68/23.01  | | | 
% 153.68/23.01  | | End of split
% 153.68/23.01  | | 
% 153.68/23.01  | End of split
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #671 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)  all_56_5 = e1
% 153.68/23.01    (2)   ~ (e2 = e0)
% 153.68/23.01    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.68/23.01         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.68/23.01    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.01    (5)  op(e2, e0) = e3
% 153.68/23.01    (6)  all_56_2 = e0
% 153.68/23.01    (7)   ~ (e3 = e2)
% 153.68/23.01    (8)   ~ (e2 = e1)
% 153.68/23.01    (9)  op(e2, e2) = e0
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | BETA: splitting (3) gives:
% 153.68/23.01  | 
% 153.68/23.01  | Case 1:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (10)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 153.68/23.01  | |           e2)
% 153.68/23.01  | | 
% 153.68/23.01  | | REF_CLOSE: (2), (4), (6), (9), (10) are inconsistent by sub-proof #673.
% 153.68/23.01  | | 
% 153.68/23.01  | Case 2:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (11)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 153.68/23.01  | |           e2)
% 153.68/23.01  | | 
% 153.68/23.01  | | BETA: splitting (11) gives:
% 153.68/23.01  | | 
% 153.68/23.01  | | Case 1:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (12)  all_56_5 = e2 & op(e2, e1) = e2
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (1), (8), (12) are inconsistent by sub-proof #672.
% 153.68/23.01  | | | 
% 153.68/23.01  | | Case 2:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (13)  all_56_10 = e2 & op(e2, e0) = e2
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (13) implies:
% 153.68/23.01  | | |   (14)  op(e2, e0) = e2
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (4), (5), (7), (14) are inconsistent by sub-proof #854.
% 153.68/23.01  | | | 
% 153.68/23.01  | | End of split
% 153.68/23.01  | | 
% 153.68/23.01  | End of split
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #672 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)  all_56_5 = e2 & op(e2, e1) = e2
% 153.68/23.01    (2)  all_56_5 = e1
% 153.68/23.01    (3)   ~ (e2 = e1)
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | ALPHA: (1) implies:
% 153.68/23.01  |   (4)  all_56_5 = e2
% 153.68/23.01  | 
% 153.68/23.01  | COMBINE_EQS: (2), (4) imply:
% 153.68/23.01  |   (5)  e2 = e1
% 153.68/23.01  | 
% 153.68/23.01  | SIMP: (5) implies:
% 153.68/23.01  |   (6)  e2 = e1
% 153.68/23.01  | 
% 153.68/23.01  | REDUCE: (3), (6) imply:
% 153.68/23.01  |   (7)  $false
% 153.68/23.01  | 
% 153.68/23.01  | CLOSE: (7) is inconsistent.
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #673 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)   ~ (e2 = e0)
% 153.68/23.01    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.01    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 153.68/23.01    (4)  all_56_2 = e0
% 153.68/23.01    (5)  op(e2, e2) = e0
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | BETA: splitting (3) gives:
% 153.68/23.01  | 
% 153.68/23.01  | Case 1:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (6)  all_56_2 = e2 & op(e2, e3) = e2
% 153.68/23.01  | | 
% 153.68/23.01  | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #994.
% 153.68/23.01  | | 
% 153.68/23.01  | Case 2:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (7)  all_56_3 = e2 & op(e2, e2) = e2
% 153.68/23.01  | | 
% 153.68/23.01  | | ALPHA: (7) implies:
% 153.68/23.01  | |   (8)  op(e2, e2) = e2
% 153.68/23.01  | | 
% 153.68/23.01  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1145.
% 153.68/23.01  | | 
% 153.68/23.01  | End of split
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #674 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)   ~ (e3 = e1)
% 153.68/23.01    (2)  all_56_10 = e3
% 153.68/23.01    (3)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.68/23.01         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.68/23.01    (4)   ~ (e2 = e0)
% 153.68/23.01    (5)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.68/23.01         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.68/23.01    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.01    (7)  op(e2, e0) = e3
% 153.68/23.01    (8)   ~ (e3 = e0)
% 153.68/23.01    (9)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3)
% 153.68/23.01    (10)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.68/23.01          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.68/23.01    (11)   ~ (e1 = e0)
% 153.68/23.01    (12)   ~ (e3 = e2)
% 153.68/23.01    (13)   ~ (all_52_8 = e3)
% 153.68/23.01    (14)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 153.68/23.01          (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2, e0) = e1)
% 153.68/23.01    (15)  op(e3, e1) = all_52_8
% 153.68/23.01    (16)   ~ (e2 = e1)
% 153.68/23.01    (17)  op(e2, e2) = e0
% 153.68/23.01    (18)  op(e2, e3) = all_52_1
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | BETA: splitting (9) gives:
% 153.68/23.01  | 
% 153.68/23.01  | Case 1:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (19)  all_56_4 = e3 & op(e3, e1) = e3
% 153.68/23.01  | | 
% 153.68/23.01  | | ALPHA: (19) implies:
% 153.68/23.01  | |   (20)  op(e3, e1) = e3
% 153.68/23.01  | | 
% 153.68/23.01  | | REF_CLOSE: (6), (13), (15), (20) are inconsistent by sub-proof #1164.
% 153.68/23.01  | | 
% 153.68/23.01  | Case 2:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (21)  all_56_5 = e3 & op(e2, e1) = e3
% 153.68/23.01  | | 
% 153.68/23.01  | | ALPHA: (21) implies:
% 153.68/23.01  | |   (22)  all_56_5 = e3
% 153.68/23.01  | | 
% 153.68/23.01  | | BETA: splitting (5) gives:
% 153.68/23.01  | | 
% 153.68/23.01  | | Case 1:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (23)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 153.68/23.01  | | |           e2)
% 153.68/23.01  | | | 
% 153.68/23.01  | | | BETA: splitting (23) gives:
% 153.68/23.01  | | | 
% 153.68/23.01  | | | Case 1:
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | |   (24)  all_56_2 = e2 & op(e2, e3) = e2
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | ALPHA: (24) implies:
% 153.68/23.01  | | | |   (25)  op(e2, e3) = e2
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | BETA: splitting (14) gives:
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | Case 1:
% 153.68/23.01  | | | | | 
% 153.68/23.01  | | | | |   (26)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2,
% 153.68/23.01  | | | | |             e2) = e1)
% 153.68/23.01  | | | | | 
% 153.68/23.01  | | | | | REF_CLOSE: (6), (11), (16), (17), (18), (25), (26) are inconsistent by
% 153.68/23.01  | | | | |            sub-proof #686.
% 153.68/23.01  | | | | | 
% 153.68/23.01  | | | | Case 2:
% 153.68/23.01  | | | | | 
% 153.68/23.01  | | | | |   (27)  (all_56_5 = e1 & op(e2, e1) = e1) | (all_56_10 = e1 & op(e2,
% 153.68/23.01  | | | | |             e0) = e1)
% 153.68/23.01  | | | | | 
% 153.68/23.01  | | | | | BETA: splitting (27) gives:
% 153.68/23.01  | | | | | 
% 153.68/23.01  | | | | | Case 1:
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | |   (28)  all_56_5 = e1 & op(e2, e1) = e1
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | | ALPHA: (28) implies:
% 153.68/23.01  | | | | | |   (29)  all_56_5 = e1
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | | COMBINE_EQS: (22), (29) imply:
% 153.68/23.01  | | | | | |   (30)  e3 = e1
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12),
% 153.68/23.01  | | | | | |            (16), (17), (22), (30) are inconsistent by sub-proof
% 153.68/23.01  | | | | | |            #675.
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | Case 2:
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | |   (31)  all_56_10 = e1 & op(e2, e0) = e1
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | | ALPHA: (31) implies:
% 153.68/23.01  | | | | | |   (32)  all_56_10 = e1
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | | COMBINE_EQS: (2), (32) imply:
% 153.68/23.01  | | | | | |   (33)  e3 = e1
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (10), (11), (12),
% 153.68/23.01  | | | | | |            (16), (17), (22), (33) are inconsistent by sub-proof
% 153.68/23.01  | | | | | |            #675.
% 153.68/23.01  | | | | | | 
% 153.68/23.01  | | | | | End of split
% 153.68/23.01  | | | | | 
% 153.68/23.01  | | | | End of split
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | Case 2:
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | |   (34)  all_56_3 = e2 & op(e2, e2) = e2
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | ALPHA: (34) implies:
% 153.68/23.01  | | | |   (35)  op(e2, e2) = e2
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | REF_CLOSE: (4), (6), (17), (35) are inconsistent by sub-proof #1145.
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | End of split
% 153.68/23.01  | | | 
% 153.68/23.01  | | Case 2:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (36)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 153.68/23.01  | | |           e2)
% 153.68/23.01  | | | 
% 153.68/23.01  | | | BETA: splitting (36) gives:
% 153.68/23.01  | | | 
% 153.68/23.01  | | | Case 1:
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | |   (37)  all_56_5 = e2 & op(e2, e1) = e2
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | ALPHA: (37) implies:
% 153.68/23.01  | | | |   (38)  all_56_5 = e2
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | COMBINE_EQS: (22), (38) imply:
% 153.68/23.01  | | | |   (39)  e3 = e2
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | REDUCE: (12), (39) imply:
% 153.68/23.01  | | | |   (40)  $false
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | CLOSE: (40) is inconsistent.
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | Case 2:
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | |   (41)  all_56_10 = e2 & op(e2, e0) = e2
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | ALPHA: (41) implies:
% 153.68/23.01  | | | |   (42)  op(e2, e0) = e2
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | | REF_CLOSE: (6), (7), (12), (42) are inconsistent by sub-proof #854.
% 153.68/23.01  | | | | 
% 153.68/23.01  | | | End of split
% 153.68/23.01  | | | 
% 153.68/23.01  | | End of split
% 153.68/23.01  | | 
% 153.68/23.01  | End of split
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #675 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)   ~ (e3 = e1)
% 153.68/23.01    (2)  e3 = e1
% 153.68/23.01    (3)  all_56_10 = e3
% 153.68/23.01    (4)  all_56_5 = e3
% 153.68/23.01    (5)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.68/23.01         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.68/23.01    (6)   ~ (e2 = e0)
% 153.68/23.01    (7)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.68/23.01         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.68/23.01    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.01    (9)   ~ (e3 = e0)
% 153.68/23.01    (10)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.68/23.01          (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.68/23.01    (11)   ~ (e1 = e0)
% 153.68/23.01    (12)   ~ (e3 = e2)
% 153.68/23.01    (13)   ~ (e2 = e1)
% 153.68/23.01    (14)  op(e2, e2) = e0
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | COMBINE_EQS: (2), (3) imply:
% 153.68/23.01  |   (15)  all_56_10 = e1
% 153.68/23.01  | 
% 153.68/23.01  | COMBINE_EQS: (2), (4) imply:
% 153.68/23.01  |   (16)  all_56_5 = e1
% 153.68/23.01  | 
% 153.68/23.01  | REF_CLOSE: (1), (5), (6), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 153.68/23.01  |            (16) are inconsistent by sub-proof #676.
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #676 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)   ~ (e3 = e1)
% 153.68/23.01    (2)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.68/23.01         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.68/23.01    (3)  all_56_5 = e1
% 153.68/23.01    (4)   ~ (e2 = e0)
% 153.68/23.01    (5)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.68/23.01         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.68/23.01    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.01    (7)  all_56_10 = e1
% 153.68/23.01    (8)   ~ (e3 = e0)
% 153.68/23.01    (9)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.68/23.01         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.68/23.01    (10)   ~ (e1 = e0)
% 153.68/23.01    (11)   ~ (e3 = e2)
% 153.68/23.01    (12)   ~ (e2 = e1)
% 153.68/23.01    (13)  op(e2, e2) = e0
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | BETA: splitting (9) gives:
% 153.68/23.01  | 
% 153.68/23.01  | Case 1:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (14)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 153.68/23.01  | |           e3)
% 153.68/23.01  | | 
% 153.68/23.01  | | BETA: splitting (14) gives:
% 153.68/23.01  | | 
% 153.68/23.01  | | Case 1:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (15)  all_56_2 = e3 & op(e2, e3) = e3
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (15) implies:
% 153.68/23.01  | | |   (16)  all_56_2 = e3
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 153.68/23.01  | | |            (16) are inconsistent by sub-proof #678.
% 153.68/23.01  | | | 
% 153.68/23.01  | | Case 2:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (17)  all_56_3 = e3 & op(e2, e2) = e3
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (17) implies:
% 153.68/23.01  | | |   (18)  op(e2, e2) = e3
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (6), (8), (13), (18) are inconsistent by sub-proof #719.
% 153.68/23.01  | | | 
% 153.68/23.01  | | End of split
% 153.68/23.01  | | 
% 153.68/23.01  | Case 2:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (19)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 153.68/23.01  | |           e3)
% 153.68/23.01  | | 
% 153.68/23.01  | | BETA: splitting (19) gives:
% 153.68/23.01  | | 
% 153.68/23.01  | | Case 1:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (20)  all_56_5 = e3 & op(e2, e1) = e3
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (1), (3), (20) are inconsistent by sub-proof #684.
% 153.68/23.01  | | | 
% 153.68/23.01  | | Case 2:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (21)  all_56_10 = e3 & op(e2, e0) = e3
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (21) implies:
% 153.68/23.01  | | |   (22)  all_56_10 = e3
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (1), (7), (22) are inconsistent by sub-proof #677.
% 153.68/23.01  | | | 
% 153.68/23.01  | | End of split
% 153.68/23.01  | | 
% 153.68/23.01  | End of split
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #677 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)  all_56_10 = e3
% 153.68/23.01    (2)  all_56_10 = e1
% 153.68/23.01    (3)   ~ (e3 = e1)
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | COMBINE_EQS: (1), (2) imply:
% 153.68/23.01  |   (4)  e3 = e1
% 153.68/23.01  | 
% 153.68/23.01  | SIMP: (4) implies:
% 153.68/23.01  |   (5)  e3 = e1
% 153.68/23.01  | 
% 153.68/23.01  | REDUCE: (3), (5) imply:
% 153.68/23.01  |   (6)  $false
% 153.68/23.01  | 
% 153.68/23.01  | CLOSE: (6) is inconsistent.
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #678 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)   ~ (e3 = e1)
% 153.68/23.01    (2)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.68/23.01         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.68/23.01    (3)  all_56_5 = e1
% 153.68/23.01    (4)   ~ (e2 = e0)
% 153.68/23.01    (5)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.68/23.01         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.68/23.01    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.01           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.01    (7)  all_56_10 = e1
% 153.68/23.01    (8)   ~ (e3 = e0)
% 153.68/23.01    (9)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.68/23.01         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.68/23.01    (10)   ~ (e1 = e0)
% 153.68/23.01    (11)   ~ (e3 = e2)
% 153.68/23.01    (12)   ~ (e2 = e1)
% 153.68/23.01    (13)  all_56_2 = e3
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | BETA: splitting (5) gives:
% 153.68/23.01  | 
% 153.68/23.01  | Case 1:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (14)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 153.68/23.01  | |           e2)
% 153.68/23.01  | | 
% 153.68/23.01  | | BETA: splitting (14) gives:
% 153.68/23.01  | | 
% 153.68/23.01  | | Case 1:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (15)  all_56_2 = e2 & op(e2, e3) = e2
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (15) implies:
% 153.68/23.01  | | |   (16)  all_56_2 = e2
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (11), (13), (16) are inconsistent by sub-proof #685.
% 153.68/23.01  | | | 
% 153.68/23.01  | | Case 2:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (17)  all_56_3 = e2 & op(e2, e2) = e2
% 153.68/23.01  | | | 
% 153.68/23.01  | | | ALPHA: (17) implies:
% 153.68/23.01  | | |   (18)  op(e2, e2) = e2
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (18) are
% 153.68/23.01  | | |            inconsistent by sub-proof #681.
% 153.68/23.01  | | | 
% 153.68/23.01  | | End of split
% 153.68/23.01  | | 
% 153.68/23.01  | Case 2:
% 153.68/23.01  | | 
% 153.68/23.01  | |   (19)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 153.68/23.01  | |           e2)
% 153.68/23.01  | | 
% 153.68/23.01  | | BETA: splitting (19) gives:
% 153.68/23.01  | | 
% 153.68/23.01  | | Case 1:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (20)  all_56_5 = e2 & op(e2, e1) = e2
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (3), (12), (20) are inconsistent by sub-proof #680.
% 153.68/23.01  | | | 
% 153.68/23.01  | | Case 2:
% 153.68/23.01  | | | 
% 153.68/23.01  | | |   (21)  all_56_10 = e2 & op(e2, e0) = e2
% 153.68/23.01  | | | 
% 153.68/23.01  | | | REF_CLOSE: (7), (12), (21) are inconsistent by sub-proof #679.
% 153.68/23.01  | | | 
% 153.68/23.01  | | End of split
% 153.68/23.01  | | 
% 153.68/23.01  | End of split
% 153.68/23.01  | 
% 153.68/23.01  End of proof
% 153.68/23.01  
% 153.68/23.01  Sub-proof #679 shows that the following formulas are inconsistent:
% 153.68/23.01  ----------------------------------------------------------------
% 153.68/23.01    (1)  all_56_10 = e2 & op(e2, e0) = e2
% 153.68/23.01    (2)  all_56_10 = e1
% 153.68/23.01    (3)   ~ (e2 = e1)
% 153.68/23.01  
% 153.68/23.01  Begin of proof
% 153.68/23.01  | 
% 153.68/23.01  | ALPHA: (1) implies:
% 153.68/23.01  |   (4)  all_56_10 = e2
% 153.68/23.01  | 
% 153.68/23.01  | COMBINE_EQS: (2), (4) imply:
% 153.68/23.02  |   (5)  e2 = e1
% 153.68/23.02  | 
% 153.68/23.02  | SIMP: (5) implies:
% 153.68/23.02  |   (6)  e2 = e1
% 153.68/23.02  | 
% 153.68/23.02  | REDUCE: (3), (6) imply:
% 153.68/23.02  |   (7)  $false
% 153.68/23.02  | 
% 153.68/23.02  | CLOSE: (7) is inconsistent.
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #680 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)  all_56_5 = e2 & op(e2, e1) = e2
% 153.68/23.02    (2)  all_56_5 = e1
% 153.68/23.02    (3)   ~ (e2 = e1)
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | ALPHA: (1) implies:
% 153.68/23.02  |   (4)  all_56_5 = e2
% 153.68/23.02  | 
% 153.68/23.02  | COMBINE_EQS: (2), (4) imply:
% 153.68/23.02  |   (5)  e2 = e1
% 153.68/23.02  | 
% 153.68/23.02  | REDUCE: (3), (5) imply:
% 153.68/23.02  |   (6)  $false
% 153.68/23.02  | 
% 153.68/23.02  | CLOSE: (6) is inconsistent.
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #681 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)   ~ (e3 = e1)
% 153.68/23.02    (2)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.68/23.02         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.68/23.02    (3)  all_56_5 = e1
% 153.68/23.02    (4)   ~ (e2 = e0)
% 153.68/23.02    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.02    (6)  all_56_10 = e1
% 153.68/23.02    (7)   ~ (e3 = e0)
% 153.68/23.02    (8)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 153.68/23.02         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 153.68/23.02    (9)  op(e2, e2) = e2
% 153.68/23.02    (10)   ~ (e1 = e0)
% 153.68/23.02    (11)   ~ (e3 = e2)
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | BETA: splitting (2) gives:
% 153.68/23.02  | 
% 153.68/23.02  | Case 1:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (12)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 153.68/23.02  | |           e0)
% 153.68/23.02  | | 
% 153.68/23.02  | | BETA: splitting (12) gives:
% 153.68/23.02  | | 
% 153.68/23.02  | | Case 1:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (13)  all_56_2 = e0 & op(e2, e3) = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (13) implies:
% 153.68/23.02  | | |   (14)  all_56_2 = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | BETA: splitting (8) gives:
% 153.68/23.02  | | | 
% 153.68/23.02  | | | Case 1:
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | |   (15)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2)
% 153.68/23.02  | | | |           = e3)
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | BETA: splitting (15) gives:
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | Case 1:
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | |   (16)  all_56_2 = e3 & op(e2, e3) = e3
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | ALPHA: (16) implies:
% 153.68/23.02  | | | | |   (17)  all_56_2 = e3
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | COMBINE_EQS: (14), (17) imply:
% 153.68/23.02  | | | | |   (18)  e3 = e0
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | REDUCE: (7), (18) imply:
% 153.68/23.02  | | | | |   (19)  $false
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | CLOSE: (19) is inconsistent.
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | Case 2:
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | |   (20)  all_56_3 = e3 & op(e2, e2) = e3
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | ALPHA: (20) implies:
% 153.68/23.02  | | | | |   (21)  op(e2, e2) = e3
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | REF_CLOSE: (5), (9), (11), (21) are inconsistent by sub-proof #1179.
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | End of split
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | Case 2:
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | |   (22)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0)
% 153.68/23.02  | | | |           = e3)
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | BETA: splitting (22) gives:
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | Case 1:
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | |   (23)  all_56_5 = e3 & op(e2, e1) = e3
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | REF_CLOSE: (1), (3), (23) are inconsistent by sub-proof #684.
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | Case 2:
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | |   (24)  all_56_10 = e3 & op(e2, e0) = e3
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | REF_CLOSE: (1), (6), (24) are inconsistent by sub-proof #683.
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | End of split
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | End of split
% 153.68/23.02  | | | 
% 153.68/23.02  | | Case 2:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (25)  all_56_3 = e0 & op(e2, e2) = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (25) implies:
% 153.68/23.02  | | |   (26)  op(e2, e2) = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REF_CLOSE: (4), (5), (9), (26) are inconsistent by sub-proof #1145.
% 153.68/23.02  | | | 
% 153.68/23.02  | | End of split
% 153.68/23.02  | | 
% 153.68/23.02  | Case 2:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (27)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.68/23.02  | |           e0)
% 153.68/23.02  | | 
% 153.68/23.02  | | BETA: splitting (27) gives:
% 153.68/23.02  | | 
% 153.68/23.02  | | Case 1:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (28)  all_56_5 = e0 & op(e2, e1) = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (28) implies:
% 153.68/23.02  | | |   (29)  all_56_5 = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REF_CLOSE: (3), (10), (29) are inconsistent by sub-proof #682.
% 153.68/23.02  | | | 
% 153.68/23.02  | | Case 2:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (30)  all_56_10 = e0 & op(e2, e0) = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (30) implies:
% 153.68/23.02  | | |   (31)  all_56_10 = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REF_CLOSE: (6), (10), (31) are inconsistent by sub-proof #963.
% 153.68/23.02  | | | 
% 153.68/23.02  | | End of split
% 153.68/23.02  | | 
% 153.68/23.02  | End of split
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #682 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)  all_56_5 = e1
% 153.68/23.02    (2)  all_56_5 = e0
% 153.68/23.02    (3)   ~ (e1 = e0)
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | COMBINE_EQS: (1), (2) imply:
% 153.68/23.02  |   (4)  e1 = e0
% 153.68/23.02  | 
% 153.68/23.02  | SIMP: (4) implies:
% 153.68/23.02  |   (5)  e1 = e0
% 153.68/23.02  | 
% 153.68/23.02  | REDUCE: (3), (5) imply:
% 153.68/23.02  |   (6)  $false
% 153.68/23.02  | 
% 153.68/23.02  | CLOSE: (6) is inconsistent.
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #683 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)  all_56_10 = e3 & op(e2, e0) = e3
% 153.68/23.02    (2)  all_56_10 = e1
% 153.68/23.02    (3)   ~ (e3 = e1)
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | ALPHA: (1) implies:
% 153.68/23.02  |   (4)  all_56_10 = e3
% 153.68/23.02  | 
% 153.68/23.02  | COMBINE_EQS: (2), (4) imply:
% 153.68/23.02  |   (5)  e3 = e1
% 153.68/23.02  | 
% 153.68/23.02  | REDUCE: (3), (5) imply:
% 153.68/23.02  |   (6)  $false
% 153.68/23.02  | 
% 153.68/23.02  | CLOSE: (6) is inconsistent.
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #684 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)  all_56_5 = e3 & op(e2, e1) = e3
% 153.68/23.02    (2)  all_56_5 = e1
% 153.68/23.02    (3)   ~ (e3 = e1)
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | ALPHA: (1) implies:
% 153.68/23.02  |   (4)  all_56_5 = e3
% 153.68/23.02  | 
% 153.68/23.02  | COMBINE_EQS: (2), (4) imply:
% 153.68/23.02  |   (5)  e3 = e1
% 153.68/23.02  | 
% 153.68/23.02  | REDUCE: (3), (5) imply:
% 153.68/23.02  |   (6)  $false
% 153.68/23.02  | 
% 153.68/23.02  | CLOSE: (6) is inconsistent.
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #685 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)  all_56_2 = e3
% 153.68/23.02    (2)  all_56_2 = e2
% 153.68/23.02    (3)   ~ (e3 = e2)
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | COMBINE_EQS: (1), (2) imply:
% 153.68/23.02  |   (4)  e3 = e2
% 153.68/23.02  | 
% 153.68/23.02  | SIMP: (4) implies:
% 153.68/23.02  |   (5)  e3 = e2
% 153.68/23.02  | 
% 153.68/23.02  | REDUCE: (3), (5) imply:
% 153.68/23.02  |   (6)  $false
% 153.68/23.02  | 
% 153.68/23.02  | CLOSE: (6) is inconsistent.
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #686 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.02    (2)  op(e2, e3) = e2
% 153.68/23.02    (3)   ~ (e1 = e0)
% 153.68/23.02    (4)  (all_56_2 = e1 & op(e2, e3) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 153.68/23.02    (5)   ~ (e2 = e1)
% 153.68/23.02    (6)  op(e2, e2) = e0
% 153.68/23.02    (7)  op(e2, e3) = all_52_1
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | BETA: splitting (4) gives:
% 153.68/23.02  | 
% 153.68/23.02  | Case 1:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (8)  all_56_2 = e1 & op(e2, e3) = e1
% 153.68/23.02  | | 
% 153.68/23.02  | | ALPHA: (8) implies:
% 153.68/23.02  | |   (9)  op(e2, e3) = e1
% 153.68/23.02  | | 
% 153.68/23.02  | | REF_CLOSE: (1), (2), (5), (7), (9) are inconsistent by sub-proof #842.
% 153.68/23.02  | | 
% 153.68/23.02  | Case 2:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (10)  all_56_3 = e1 & op(e2, e2) = e1
% 153.68/23.02  | | 
% 153.68/23.02  | | ALPHA: (10) implies:
% 153.68/23.02  | |   (11)  op(e2, e2) = e1
% 153.68/23.02  | | 
% 153.68/23.02  | | REF_CLOSE: (1), (3), (6), (11) are inconsistent by sub-proof #853.
% 153.68/23.02  | | 
% 153.68/23.02  | End of split
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #687 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)  op(e3, e3) = e0
% 153.68/23.02    (2)   ~ (e3 = e1)
% 153.68/23.02    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.68/23.02         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.68/23.02    (4)   ~ (e2 = e0)
% 153.68/23.02    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.02    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.68/23.02         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.68/23.02    (7)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.68/23.02         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.68/23.02    (8)   ~ (e3 = e0)
% 153.68/23.02    (9)   ~ (e1 = e0)
% 153.68/23.02    (10)  all_56_9 = e0
% 153.68/23.02    (11)   ~ (e3 = e2)
% 153.68/23.02    (12)   ~ (all_52_8 = e3)
% 153.68/23.02    (13)  op(e3, e1) = all_52_8
% 153.68/23.02    (14)   ~ (e2 = e1)
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | BETA: splitting (6) gives:
% 153.68/23.02  | 
% 153.68/23.02  | Case 1:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (15)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 153.68/23.02  | |           e3)
% 153.68/23.02  | | 
% 153.68/23.02  | | BETA: splitting (15) gives:
% 153.68/23.02  | | 
% 153.68/23.02  | | Case 1:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (16)  all_56_0 = e3 & op(e3, e3) = e3
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (16) implies:
% 153.68/23.02  | | |   (17)  op(e3, e3) = e3
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REF_CLOSE: (1), (5), (8), (17) are inconsistent by sub-proof #1141.
% 153.68/23.02  | | | 
% 153.68/23.02  | | Case 2:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (18)  all_56_1 = e3 & op(e3, e2) = e3
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (18) implies:
% 153.68/23.02  | | |   (19)  all_56_1 = e3
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (14), (19) are
% 153.68/23.02  | | |            inconsistent by sub-proof #905.
% 153.68/23.02  | | | 
% 153.68/23.02  | | End of split
% 153.68/23.02  | | 
% 153.68/23.02  | Case 2:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (20)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 153.68/23.02  | |           e3)
% 153.68/23.02  | | 
% 153.68/23.02  | | BETA: splitting (20) gives:
% 153.68/23.02  | | 
% 153.68/23.02  | | Case 1:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (21)  all_56_4 = e3 & op(e3, e1) = e3
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (21) implies:
% 153.68/23.02  | | |   (22)  op(e3, e1) = e3
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REF_CLOSE: (5), (12), (13), (22) are inconsistent by sub-proof #1164.
% 153.68/23.02  | | | 
% 153.68/23.02  | | Case 2:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (23)  all_56_9 = e3 & op(e3, e0) = e3
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (23) implies:
% 153.68/23.02  | | |   (24)  all_56_9 = e3
% 153.68/23.02  | | | 
% 153.68/23.02  | | | COMBINE_EQS: (10), (24) imply:
% 153.68/23.02  | | |   (25)  e3 = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REDUCE: (8), (25) imply:
% 153.68/23.02  | | |   (26)  $false
% 153.68/23.02  | | | 
% 153.68/23.02  | | | CLOSE: (26) is inconsistent.
% 153.68/23.02  | | | 
% 153.68/23.02  | | End of split
% 153.68/23.02  | | 
% 153.68/23.02  | End of split
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #688 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)  ( ~ (all_16_0 = e3) & op(all_16_1, e2) = all_16_0 & op(e2, e0) = all_16_1
% 153.68/23.02           & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e1) & op(e2, e0) =
% 153.68/23.02           all_16_1 & $i(all_16_1))
% 153.68/23.02    (2)  all_56_10 = e1 & op(e2, e0) = e1
% 153.68/23.02    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.02    (4)  ( ~ (all_18_0 = e1) & op(all_18_1, e2) = all_18_0 & op(e2, e0) = all_18_1
% 153.68/23.02           & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e3) & op(e2, e0) =
% 153.68/23.02           all_18_1 & $i(all_18_1))
% 153.68/23.02    (5)  op(e1, e2) = e3
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | ALPHA: (2) implies:
% 153.68/23.02  |   (6)  op(e2, e0) = e1
% 153.68/23.02  | 
% 153.68/23.02  | BETA: splitting (1) gives:
% 153.68/23.02  | 
% 153.68/23.02  | Case 1:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (7)   ~ (all_16_0 = e3) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 153.68/23.02  | |        all_16_1 & $i(all_16_0) & $i(all_16_1)
% 153.68/23.02  | | 
% 153.68/23.02  | | ALPHA: (7) implies:
% 153.68/23.02  | |   (8)   ~ (all_16_0 = e3)
% 153.68/23.02  | |   (9)  op(e2, e0) = all_16_1
% 153.68/23.02  | |   (10)  op(all_16_1, e2) = all_16_0
% 153.68/23.02  | | 
% 153.68/23.02  | | BETA: splitting (4) gives:
% 153.68/23.02  | | 
% 153.68/23.02  | | Case 1:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (11)   ~ (all_18_0 = e1) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 153.68/23.02  | | |         all_18_1 & $i(all_18_0) & $i(all_18_1)
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (11) implies:
% 153.68/23.02  | | |   (12)  op(e2, e0) = all_18_1
% 153.68/23.02  | | |   (13)  op(all_18_1, e2) = all_18_0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | GROUND_INST: instantiating (3) with all_16_1, all_18_1, e0, e2,
% 153.68/23.02  | | |              simplifying with (9), (12) gives:
% 153.68/23.02  | | |   (14)  all_18_1 = all_16_1
% 153.68/23.02  | | | 
% 153.68/23.02  | | | GROUND_INST: instantiating (3) with e1, all_18_1, e0, e2, simplifying with
% 153.68/23.02  | | |              (6), (12) gives:
% 153.68/23.02  | | |   (15)  all_18_1 = e1
% 153.68/23.02  | | | 
% 153.68/23.02  | | | GROUND_INST: instantiating (3) with all_16_0, all_18_0, e2, all_16_1,
% 153.68/23.02  | | |              simplifying with (10) gives:
% 153.68/23.02  | | |   (16)  all_18_0 = all_16_0 |  ~ (op(all_16_1, e2) = all_18_0)
% 153.68/23.02  | | | 
% 153.68/23.02  | | | GROUND_INST: instantiating (3) with e3, all_18_0, e2, e1, simplifying with
% 153.68/23.02  | | |              (5) gives:
% 153.68/23.02  | | |   (17)  all_18_0 = e3 |  ~ (op(e1, e2) = all_18_0)
% 153.68/23.02  | | | 
% 153.68/23.02  | | | COMBINE_EQS: (14), (15) imply:
% 153.68/23.02  | | |   (18)  all_16_1 = e1
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REDUCE: (13), (15) imply:
% 153.68/23.02  | | |   (19)  op(e1, e2) = all_18_0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | BETA: splitting (16) gives:
% 153.68/23.02  | | | 
% 153.68/23.02  | | | Case 1:
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | |   (20)   ~ (op(all_16_1, e2) = all_18_0)
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | REDUCE: (18), (20) imply:
% 153.68/23.02  | | | |   (21)   ~ (op(e1, e2) = all_18_0)
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | PRED_UNIFY: (19), (21) imply:
% 153.68/23.02  | | | |   (22)  $false
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | CLOSE: (22) is inconsistent.
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | Case 2:
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | |   (23)  all_18_0 = all_16_0
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | BETA: splitting (17) gives:
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | Case 1:
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | |   (24)   ~ (op(e1, e2) = all_18_0)
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | PRED_UNIFY: (19), (24) imply:
% 153.68/23.02  | | | | |   (25)  $false
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | CLOSE: (25) is inconsistent.
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | Case 2:
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | |   (26)  all_18_0 = e3
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | COMBINE_EQS: (23), (26) imply:
% 153.68/23.02  | | | | |   (27)  all_16_0 = e3
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | SIMP: (27) implies:
% 153.68/23.02  | | | | |   (28)  all_16_0 = e3
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | REDUCE: (8), (28) imply:
% 153.68/23.02  | | | | |   (29)  $false
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | | CLOSE: (29) is inconsistent.
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | End of split
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | End of split
% 153.68/23.02  | | | 
% 153.68/23.02  | | Case 2:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (30)   ~ (all_18_1 = e3) & op(e2, e0) = all_18_1 & $i(all_18_1)
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (30) implies:
% 153.68/23.02  | | |   (31)  op(e2, e0) = all_18_1
% 153.68/23.02  | | | 
% 153.68/23.02  | | | GROUND_INST: instantiating (3) with all_16_1, all_18_1, e0, e2,
% 153.68/23.02  | | |              simplifying with (9), (31) gives:
% 153.68/23.02  | | |   (32)  all_18_1 = all_16_1
% 153.68/23.02  | | | 
% 153.68/23.02  | | | GROUND_INST: instantiating (3) with e1, all_18_1, e0, e2, simplifying with
% 153.68/23.02  | | |              (6), (31) gives:
% 153.68/23.02  | | |   (33)  all_18_1 = e1
% 153.68/23.02  | | | 
% 153.68/23.02  | | | GROUND_INST: instantiating (3) with e3, all_16_0, e2, e1, simplifying with
% 153.68/23.02  | | |              (5) gives:
% 153.68/23.02  | | |   (34)  all_16_0 = e3 |  ~ (op(e1, e2) = all_16_0)
% 153.68/23.02  | | | 
% 153.68/23.02  | | | COMBINE_EQS: (32), (33) imply:
% 153.68/23.02  | | |   (35)  all_16_1 = e1
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REDUCE: (10), (35) imply:
% 153.68/23.02  | | |   (36)  op(e1, e2) = all_16_0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | BETA: splitting (34) gives:
% 153.68/23.02  | | | 
% 153.68/23.02  | | | Case 1:
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | |   (37)   ~ (op(e1, e2) = all_16_0)
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | PRED_UNIFY: (36), (37) imply:
% 153.68/23.02  | | | |   (38)  $false
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | CLOSE: (38) is inconsistent.
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | Case 2:
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | |   (39)  all_16_0 = e3
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | REDUCE: (8), (39) imply:
% 153.68/23.02  | | | |   (40)  $false
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | CLOSE: (40) is inconsistent.
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | End of split
% 153.68/23.02  | | | 
% 153.68/23.02  | | End of split
% 153.68/23.02  | | 
% 153.68/23.02  | Case 2:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (41)   ~ (all_16_1 = e1) & op(e2, e0) = all_16_1 & $i(all_16_1)
% 153.68/23.02  | | 
% 153.68/23.02  | | ALPHA: (41) implies:
% 153.68/23.02  | |   (42)   ~ (all_16_1 = e1)
% 153.68/23.02  | |   (43)  op(e2, e0) = all_16_1
% 153.68/23.02  | | 
% 153.68/23.02  | | BETA: splitting (4) gives:
% 153.68/23.02  | | 
% 153.68/23.02  | | Case 1:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (44)   ~ (all_18_0 = e1) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 153.68/23.02  | | |         all_18_1 & $i(all_18_0) & $i(all_18_1)
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (44) implies:
% 153.68/23.02  | | |   (45)  op(e2, e0) = all_18_1
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REF_CLOSE: (3), (6), (42), (43), (45) are inconsistent by sub-proof #689.
% 153.68/23.02  | | | 
% 153.68/23.02  | | Case 2:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (46)   ~ (all_18_1 = e3) & op(e2, e0) = all_18_1 & $i(all_18_1)
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (46) implies:
% 153.68/23.02  | | |   (47)  op(e2, e0) = all_18_1
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REF_CLOSE: (3), (6), (42), (43), (47) are inconsistent by sub-proof #689.
% 153.68/23.02  | | | 
% 153.68/23.02  | | End of split
% 153.68/23.02  | | 
% 153.68/23.02  | End of split
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #689 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)  op(e2, e0) = e1
% 153.68/23.02    (2)  op(e2, e0) = all_16_1
% 153.68/23.02    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.02    (4)   ~ (all_16_1 = e1)
% 153.68/23.02    (5)  op(e2, e0) = all_18_1
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | GROUND_INST: instantiating (3) with all_16_1, all_18_1, e0, e2, simplifying
% 153.68/23.02  |              with (2), (5) gives:
% 153.68/23.02  |   (6)  all_18_1 = all_16_1
% 153.68/23.02  | 
% 153.68/23.02  | GROUND_INST: instantiating (3) with e1, all_18_1, e0, e2, simplifying with
% 153.68/23.02  |              (1), (5) gives:
% 153.68/23.02  |   (7)  all_18_1 = e1
% 153.68/23.02  | 
% 153.68/23.02  | COMBINE_EQS: (6), (7) imply:
% 153.68/23.02  |   (8)  all_16_1 = e1
% 153.68/23.02  | 
% 153.68/23.02  | REDUCE: (4), (8) imply:
% 153.68/23.02  |   (9)  $false
% 153.68/23.02  | 
% 153.68/23.02  | CLOSE: (9) is inconsistent.
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #690 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.02    (2)   ~ (all_52_1 = e3)
% 153.68/23.02    (3)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 153.68/23.02    (4)   ~ (e3 = e0)
% 153.68/23.02    (5)  op(e2, e2) = e0
% 153.68/23.02    (6)  op(e2, e3) = all_52_1
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | BETA: splitting (3) gives:
% 153.68/23.02  | 
% 153.68/23.02  | Case 1:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (7)  all_56_2 = e3 & op(e2, e3) = e3
% 153.68/23.02  | | 
% 153.68/23.02  | | REF_CLOSE: (1), (2), (6), (7) are inconsistent by sub-proof #917.
% 153.68/23.02  | | 
% 153.68/23.02  | Case 2:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (8)  all_56_3 = e3 & op(e2, e2) = e3
% 153.68/23.02  | | 
% 153.68/23.02  | | ALPHA: (8) implies:
% 153.68/23.02  | |   (9)  op(e2, e2) = e3
% 153.68/23.02  | | 
% 153.68/23.02  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #719.
% 153.68/23.02  | | 
% 153.68/23.02  | End of split
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #691 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)   ~ (all_52_1 = e0)
% 153.68/23.02    (2)   ~ (e3 = e1)
% 153.68/23.02    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.68/23.02         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.68/23.02    (4)   ~ (all_14_2 = e0)
% 153.68/23.02    (5)  op(e3, e3) = all_14_2
% 153.68/23.02    (6)   ~ (e2 = e0)
% 153.68/23.02    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.02    (8)   ~ (e3 = e0)
% 153.68/23.02    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.68/23.02         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.68/23.02    (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.68/23.02          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.68/23.02    (11)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.68/23.02    (12)  all_54_0 = all_14_2
% 153.68/23.02    (13)   ~ (e1 = e0)
% 153.68/23.02    (14)   ~ (all_14_2 = e2)
% 153.68/23.02    (15)   ~ (e3 = e2)
% 153.68/23.02    (16)   ~ (all_14_2 = e1)
% 153.68/23.02    (17)  op(e3, e3) = e3
% 153.68/23.02    (18)   ~ (e2 = e1)
% 153.68/23.02    (19)  all_56_6 = e3
% 153.68/23.02    (20)  op(e2, e3) = all_52_1
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | BETA: splitting (9) gives:
% 153.68/23.02  | 
% 153.68/23.02  | Case 1:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (21)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 153.68/23.02  | |           e0)
% 153.68/23.02  | | 
% 153.68/23.02  | | REF_CLOSE: (1), (4), (5), (7), (11), (12), (14), (16), (20), (21) are
% 153.68/23.02  | |            inconsistent by sub-proof #692.
% 153.68/23.02  | | 
% 153.68/23.02  | Case 2:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (22)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 153.68/23.02  | |           e0)
% 153.68/23.02  | | 
% 153.68/23.02  | | BETA: splitting (22) gives:
% 153.68/23.02  | | 
% 153.68/23.02  | | Case 1:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (23)  all_56_6 = e0 & op(e1, e3) = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (23) implies:
% 153.68/23.02  | | |   (24)  all_56_6 = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REF_CLOSE: (8), (19), (24) are inconsistent by sub-proof #784.
% 153.68/23.02  | | | 
% 153.68/23.02  | | Case 2:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (25)  all_56_12 = e0 & op(e0, e3) = e0
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REF_CLOSE: (2), (3), (6), (7), (10), (13), (15), (17), (18), (19), (20),
% 153.68/23.02  | | |            (25) are inconsistent by sub-proof #777.
% 153.68/23.02  | | | 
% 153.68/23.02  | | End of split
% 153.68/23.02  | | 
% 153.68/23.02  | End of split
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #692 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 153.68/23.02    (2)   ~ (all_52_1 = e0)
% 153.68/23.02    (3)   ~ (all_14_2 = e0)
% 153.68/23.02    (4)  op(e3, e3) = all_14_2
% 153.68/23.02    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.02    (6)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.68/23.02    (7)  all_54_0 = all_14_2
% 153.68/23.02    (8)   ~ (all_14_2 = e2)
% 153.68/23.02    (9)   ~ (all_14_2 = e1)
% 153.68/23.02    (10)  op(e2, e3) = all_52_1
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | BETA: splitting (1) gives:
% 153.68/23.02  | 
% 153.68/23.02  | Case 1:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (11)  all_56_0 = e0 & op(e3, e3) = e0
% 153.68/23.02  | | 
% 153.68/23.02  | | ALPHA: (11) implies:
% 153.68/23.02  | |   (12)  op(e3, e3) = e0
% 153.68/23.02  | | 
% 153.68/23.02  | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (12) are inconsistent by
% 153.68/23.02  | |            sub-proof #1139.
% 153.68/23.02  | | 
% 153.68/23.02  | Case 2:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (13)  all_56_2 = e0 & op(e2, e3) = e0
% 153.68/23.02  | | 
% 153.68/23.02  | | REF_CLOSE: (2), (5), (10), (13) are inconsistent by sub-proof #840.
% 153.68/23.02  | | 
% 153.68/23.02  | End of split
% 153.68/23.02  | 
% 153.68/23.02  End of proof
% 153.68/23.02  
% 153.68/23.02  Sub-proof #693 shows that the following formulas are inconsistent:
% 153.68/23.02  ----------------------------------------------------------------
% 153.68/23.02    (1)  op(e0, e1) = all_52_11
% 153.68/23.02    (2)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.68/23.02    (3)   ~ (e3 = e1)
% 153.68/23.02    (4)   ~ (all_52_11 = all_10_2)
% 153.68/23.02    (5)  op(e0, e2) = all_52_7
% 153.68/23.02    (6)   ~ (all_10_2 = e1)
% 153.68/23.02    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.02           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.02    (8)   ~ (all_10_2 = e3)
% 153.68/23.02    (9)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.68/23.02             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.02           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.68/23.02           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.68/23.02             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.68/23.02           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.02           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.68/23.02           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.68/23.02           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.68/23.02           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 153.68/23.02           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.68/23.02         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.68/23.02             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.02           $i(all_57_7))
% 153.68/23.02    (10)   ~ (e3 = e0)
% 153.68/23.02    (11)  op(e0, e3) = all_52_3
% 153.68/23.02    (12)   ~ (all_52_7 = e0)
% 153.68/23.02    (13)   ~ (e1 = e0)
% 153.68/23.02    (14)   ~ (e3 = e2)
% 153.68/23.02    (15)   ~ (all_10_2 = e2)
% 153.68/23.02    (16)   ~ (all_52_3 = all_10_2)
% 153.68/23.02    (17)  op(e3, e3) = e3
% 153.68/23.02    (18)  all_54_15 = all_10_2
% 153.68/23.02    (19)  op(e2, e2) = e0
% 153.68/23.02  
% 153.68/23.02  Begin of proof
% 153.68/23.02  | 
% 153.68/23.02  | BETA: splitting (9) gives:
% 153.68/23.02  | 
% 153.68/23.02  | Case 1:
% 153.68/23.02  | | 
% 153.68/23.02  | |   (20)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 153.68/23.02  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.68/23.02  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.68/23.02  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.68/23.02  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.68/23.02  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.68/23.02  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.68/23.02  | |           $i(all_57_3))
% 153.68/23.02  | | 
% 153.68/23.02  | | BETA: splitting (20) gives:
% 153.68/23.02  | | 
% 153.68/23.02  | | Case 1:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (21)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.68/23.02  | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.68/23.02  | | |         op(e0, e3) = e0 & $i(all_57_0)
% 153.68/23.02  | | | 
% 153.68/23.02  | | | ALPHA: (21) implies:
% 153.68/23.02  | | |   (22)  op(e2, e2) = e3
% 153.68/23.02  | | | 
% 153.68/23.02  | | | REF_CLOSE: (7), (10), (19), (22) are inconsistent by sub-proof #719.
% 153.68/23.02  | | | 
% 153.68/23.02  | | Case 2:
% 153.68/23.02  | | | 
% 153.68/23.02  | | |   (23)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.68/23.02  | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.68/23.02  | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 153.68/23.02  | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.68/23.02  | | |           & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.68/23.02  | | | 
% 153.68/23.02  | | | BETA: splitting (23) gives:
% 153.68/23.02  | | | 
% 153.68/23.02  | | | Case 1:
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | |   (24)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.68/23.02  | | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.68/23.02  | | | |         op(e0, e3) = e0 & $i(all_57_1)
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | ALPHA: (24) implies:
% 153.68/23.02  | | | |   (25)  op(e1, e1) = e3
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | BETA: splitting (2) gives:
% 153.68/23.02  | | | | 
% 153.68/23.02  | | | | Case 1:
% 153.68/23.02  | | | | | 
% 153.68/23.02  | | | | |   (26)  all_54_15 = e3
% 153.68/23.03  | | | | | 
% 153.68/23.03  | | | | | COMBINE_EQS: (18), (26) imply:
% 153.68/23.03  | | | | |   (27)  all_10_2 = e3
% 153.68/23.03  | | | | | 
% 153.68/23.03  | | | | | REDUCE: (8), (27) imply:
% 153.68/23.03  | | | | |   (28)  $false
% 153.68/23.03  | | | | | 
% 153.68/23.03  | | | | | CLOSE: (28) is inconsistent.
% 153.68/23.03  | | | | | 
% 153.68/23.03  | | | | Case 2:
% 153.68/23.03  | | | | | 
% 153.68/23.03  | | | | |   (29)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.68/23.03  | | | | | 
% 153.68/23.03  | | | | | BETA: splitting (29) gives:
% 153.68/23.03  | | | | | 
% 153.68/23.03  | | | | | Case 1:
% 153.68/23.03  | | | | | | 
% 153.68/23.03  | | | | | |   (30)  all_54_15 = e2
% 153.68/23.03  | | | | | | 
% 153.68/23.03  | | | | | | COMBINE_EQS: (18), (30) imply:
% 153.68/23.03  | | | | | |   (31)  all_10_2 = e2
% 153.68/23.03  | | | | | | 
% 153.68/23.03  | | | | | | REDUCE: (15), (31) imply:
% 153.68/23.03  | | | | | |   (32)  $false
% 153.68/23.03  | | | | | | 
% 153.68/23.03  | | | | | | CLOSE: (32) is inconsistent.
% 153.68/23.03  | | | | | | 
% 153.68/23.03  | | | | | Case 2:
% 153.68/23.03  | | | | | | 
% 153.68/23.03  | | | | | |   (33)  all_54_15 = e1 | all_54_15 = e0
% 153.68/23.03  | | | | | | 
% 153.68/23.03  | | | | | | REF_CLOSE: (1), (4), (6), (7), (9), (11), (14), (16), (17), (18),
% 153.68/23.03  | | | | | |            (25), (33) are inconsistent by sub-proof #694.
% 153.68/23.03  | | | | | | 
% 153.68/23.03  | | | | | End of split
% 153.68/23.03  | | | | | 
% 153.68/23.03  | | | | End of split
% 153.68/23.03  | | | | 
% 153.68/23.03  | | | Case 2:
% 153.68/23.03  | | | | 
% 153.68/23.03  | | | |   (34)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.68/23.03  | | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.68/23.03  | | | |         op(e0, e2) = e0 & $i(all_57_3)
% 153.68/23.03  | | | | 
% 153.68/23.03  | | | | ALPHA: (34) implies:
% 153.68/23.03  | | | |   (35)  op(e3, e3) = e2
% 153.68/23.03  | | | | 
% 153.68/23.03  | | | | REF_CLOSE: (7), (14), (17), (35) are inconsistent by sub-proof #1085.
% 153.68/23.03  | | | | 
% 153.68/23.03  | | | End of split
% 153.68/23.03  | | | 
% 153.68/23.03  | | End of split
% 153.68/23.03  | | 
% 153.68/23.03  | Case 2:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (36)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.68/23.03  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.68/23.03  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.03  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.68/23.03  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.68/23.03  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.68/23.03  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.03  | |           $i(all_57_7))
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (3), (5), (7), (12), (13), (17), (19), (36) are inconsistent by
% 153.68/23.03  | |            sub-proof #823.
% 153.68/23.03  | | 
% 153.68/23.03  | End of split
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #694 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)  op(e0, e1) = all_52_11
% 153.68/23.03    (2)   ~ (all_52_11 = all_10_2)
% 153.68/23.03    (3)   ~ (all_10_2 = e1)
% 153.68/23.03    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.03    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.68/23.03             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.03           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.68/23.03           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.68/23.03             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.68/23.03           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.03           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.68/23.03           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.68/23.03           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.68/23.03           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 153.68/23.03           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.68/23.03         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.68/23.03             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.03           $i(all_57_7))
% 153.68/23.03    (6)  op(e0, e3) = all_52_3
% 153.68/23.03    (7)  op(e1, e1) = e3
% 153.68/23.03    (8)   ~ (e3 = e2)
% 153.68/23.03    (9)  all_54_15 = e1 | all_54_15 = e0
% 153.68/23.03    (10)   ~ (all_52_3 = all_10_2)
% 153.68/23.03    (11)  op(e3, e3) = e3
% 153.68/23.03    (12)  all_54_15 = all_10_2
% 153.68/23.03  
% 153.68/23.03  Begin of proof
% 153.68/23.03  | 
% 153.68/23.03  | BETA: splitting (9) gives:
% 153.68/23.03  | 
% 153.68/23.03  | Case 1:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (13)  all_54_15 = e1
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (3), (12), (13) are inconsistent by sub-proof #1047.
% 153.68/23.03  | | 
% 153.68/23.03  | Case 2:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (14)  all_54_15 = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | COMBINE_EQS: (12), (14) imply:
% 153.68/23.03  | |   (15)  all_10_2 = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | SIMP: (15) implies:
% 153.68/23.03  | |   (16)  all_10_2 = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | REDUCE: (10), (16) imply:
% 153.68/23.03  | |   (17)   ~ (all_52_3 = e0)
% 153.68/23.03  | | 
% 153.68/23.03  | | REDUCE: (2), (16) imply:
% 153.68/23.03  | |   (18)   ~ (all_52_11 = e0)
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (11), (17), (18) are inconsistent
% 153.68/23.03  | |            by sub-proof #695.
% 153.68/23.03  | | 
% 153.68/23.03  | End of split
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #695 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)  op(e0, e1) = all_52_11
% 153.68/23.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.03    (3)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.68/23.03             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.03           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.68/23.03           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.68/23.03             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.68/23.03           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.03           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.68/23.03           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.68/23.03           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.68/23.03           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 153.68/23.03           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.68/23.03         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.68/23.03             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.03           $i(all_57_7))
% 153.68/23.03    (4)   ~ (all_52_11 = e0)
% 153.68/23.03    (5)  op(e0, e3) = all_52_3
% 153.68/23.03    (6)  op(e1, e1) = e3
% 153.68/23.03    (7)   ~ (e3 = e2)
% 153.68/23.03    (8)   ~ (all_52_3 = e0)
% 153.68/23.03    (9)  op(e3, e3) = e3
% 153.68/23.03  
% 153.68/23.03  Begin of proof
% 153.68/23.03  | 
% 153.68/23.03  | BETA: splitting (3) gives:
% 153.68/23.03  | 
% 153.68/23.03  | Case 1:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (10)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 153.68/23.03  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.68/23.03  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.68/23.03  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.68/23.03  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.68/23.03  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.68/23.03  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.68/23.03  | |           $i(all_57_3))
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (2), (5), (7), (8), (9), (10) are inconsistent by sub-proof #852.
% 153.68/23.03  | | 
% 153.68/23.03  | Case 2:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (11)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.68/23.03  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.68/23.03  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.03  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.68/23.03  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.68/23.03  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.68/23.03  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.03  | |           $i(all_57_7))
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (1), (2), (4), (6), (7), (11) are inconsistent by sub-proof #696.
% 153.68/23.03  | | 
% 153.68/23.03  | End of split
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #696 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.68/23.03             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.68/23.03           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.68/23.03           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.68/23.03             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.68/23.03           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.68/23.03           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.68/23.03    (2)  op(e0, e1) = all_52_11
% 153.68/23.03    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.03    (4)   ~ (all_52_11 = e0)
% 153.68/23.03    (5)  op(e1, e1) = e3
% 153.68/23.03    (6)   ~ (e3 = e2)
% 153.68/23.03  
% 153.68/23.03  Begin of proof
% 153.68/23.03  | 
% 153.68/23.03  | BETA: splitting (1) gives:
% 153.68/23.03  | 
% 153.68/23.03  | Case 1:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (7)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.68/23.03  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.68/23.03  | |        $i(all_57_4)
% 153.68/23.03  | | 
% 153.68/23.03  | | ALPHA: (7) implies:
% 153.68/23.03  | |   (8)  op(e1, e1) = e2
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #834.
% 153.68/23.03  | | 
% 153.68/23.03  | Case 2:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (9)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 153.68/23.03  | |            = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 153.68/23.03  | |          & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 153.68/23.03  | |            e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.68/23.03  | |          all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #851.
% 153.68/23.03  | | 
% 153.68/23.03  | End of split
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #697 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.68/23.03    (2)  all_54_10 = all_4_2
% 153.68/23.03    (3)  all_52_14 = e1
% 153.68/23.03    (4)   ~ (all_52_14 = all_4_2)
% 153.68/23.03    (5)   ~ (all_4_2 = e2)
% 153.68/23.03    (6)   ~ (all_4_2 = e0)
% 153.68/23.03    (7)   ~ (all_4_2 = e3)
% 153.68/23.03  
% 153.68/23.03  Begin of proof
% 153.68/23.03  | 
% 153.68/23.03  | SIMP: (6) implies:
% 153.68/23.03  |   (8)   ~ (all_4_2 = e0)
% 153.68/23.03  | 
% 153.68/23.03  | REDUCE: (3), (4) imply:
% 153.68/23.03  |   (9)   ~ (all_4_2 = e1)
% 153.68/23.03  | 
% 153.68/23.03  | SIMP: (9) implies:
% 153.68/23.03  |   (10)   ~ (all_4_2 = e1)
% 153.68/23.03  | 
% 153.68/23.03  | BETA: splitting (1) gives:
% 153.68/23.03  | 
% 153.68/23.03  | Case 1:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (11)  all_54_10 = e3
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (2), (7), (11) are inconsistent by sub-proof #1173.
% 153.68/23.03  | | 
% 153.68/23.03  | Case 2:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (12)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | BETA: splitting (12) gives:
% 153.68/23.03  | | 
% 153.68/23.03  | | Case 1:
% 153.68/23.03  | | | 
% 153.68/23.03  | | |   (13)  all_54_10 = e2
% 153.68/23.03  | | | 
% 153.68/23.03  | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #1168.
% 153.68/23.03  | | | 
% 153.68/23.03  | | Case 2:
% 153.68/23.03  | | | 
% 153.68/23.03  | | |   (14)  all_54_10 = e1 | all_54_10 = e0
% 153.68/23.03  | | | 
% 153.68/23.03  | | | BETA: splitting (14) gives:
% 153.68/23.03  | | | 
% 153.68/23.03  | | | Case 1:
% 153.68/23.03  | | | | 
% 153.68/23.03  | | | |   (15)  all_54_10 = e1
% 153.68/23.03  | | | | 
% 153.68/23.03  | | | | REF_CLOSE: (2), (10), (15) are inconsistent by sub-proof #1167.
% 153.68/23.03  | | | | 
% 153.68/23.03  | | | Case 2:
% 153.68/23.03  | | | | 
% 153.68/23.03  | | | |   (16)  all_54_10 = e0
% 153.68/23.03  | | | | 
% 153.68/23.03  | | | | REF_CLOSE: (2), (8), (16) are inconsistent by sub-proof #1033.
% 153.68/23.03  | | | | 
% 153.68/23.03  | | | End of split
% 153.68/23.03  | | | 
% 153.68/23.03  | | End of split
% 153.68/23.03  | | 
% 153.68/23.03  | End of split
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #698 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)   ~ (all_14_2 = e0)
% 153.68/23.03    (2)  op(e3, e3) = all_14_2
% 153.68/23.03    (3)  op(e3, e2) = all_52_4
% 153.68/23.03    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.03    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 153.68/23.03    (6)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.68/23.03    (7)  all_54_0 = all_14_2
% 153.68/23.03    (8)   ~ (all_14_2 = e2)
% 153.68/23.03    (9)   ~ (all_14_2 = e1)
% 153.68/23.03    (10)   ~ (all_52_4 = e0)
% 153.68/23.03  
% 153.68/23.03  Begin of proof
% 153.68/23.03  | 
% 153.68/23.03  | BETA: splitting (5) gives:
% 153.68/23.03  | 
% 153.68/23.03  | Case 1:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (11)  all_56_0 = e0 & op(e3, e3) = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | ALPHA: (11) implies:
% 153.68/23.03  | |   (12)  op(e3, e3) = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (12) are inconsistent by
% 153.68/23.03  | |            sub-proof #1139.
% 153.68/23.03  | | 
% 153.68/23.03  | Case 2:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (13)  all_56_1 = e0 & op(e3, e2) = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (3), (4), (10), (13) are inconsistent by sub-proof #1013.
% 153.68/23.03  | | 
% 153.68/23.03  | End of split
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #699 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.68/23.03             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.68/23.03           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 153.68/23.03           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.68/23.03           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.68/23.03           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 153.68/23.03           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3)
% 153.68/23.03           = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.68/23.03           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.68/23.03           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.68/23.03           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.68/23.03           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 153.68/23.03            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 153.68/23.03             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.68/23.03    (2)  op(e0, e0) = all_10_2
% 153.68/23.03    (3)  op(e3, e2) = all_52_4
% 153.68/23.03    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.03    (5)   ~ (all_52_4 = e3)
% 153.68/23.03    (6)   ~ (e1 = e0)
% 153.68/23.03    (7)   ~ (e3 = e2)
% 153.68/23.03    (8)   ~ (all_10_2 = e2)
% 153.68/23.03    (9)  op(e3, e3) = e3
% 153.68/23.03    (10)  op(e2, e2) = e0
% 153.68/23.03  
% 153.68/23.03  Begin of proof
% 153.68/23.03  | 
% 153.68/23.03  | BETA: splitting (1) gives:
% 153.68/23.03  | 
% 153.68/23.03  | Case 1:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (11)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 153.68/23.03  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.68/23.03  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 153.68/23.03  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 153.68/23.03  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.68/23.03  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (3), (4), (5), (11) are inconsistent by sub-proof #863.
% 153.68/23.03  | | 
% 153.68/23.03  | Case 2:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (12)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 153.68/23.03  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 153.68/23.03  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.68/23.03  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.68/23.03  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.68/23.03  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.68/23.03  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.68/23.03  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.68/23.03  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.68/23.03  | | 
% 153.68/23.03  | | BETA: splitting (12) gives:
% 153.68/23.03  | | 
% 153.68/23.03  | | Case 1:
% 153.68/23.03  | | | 
% 153.68/23.03  | | |   (13)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.68/23.03  | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.68/23.03  | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.68/23.03  | | |         $i(all_57_14)
% 153.68/23.03  | | | 
% 153.68/23.03  | | | ALPHA: (13) implies:
% 153.68/23.03  | | |   (14)  op(e3, e3) = e2
% 153.68/23.03  | | | 
% 153.68/23.03  | | | REF_CLOSE: (4), (7), (9), (14) are inconsistent by sub-proof #1085.
% 153.68/23.03  | | | 
% 153.68/23.03  | | Case 2:
% 153.68/23.03  | | | 
% 153.68/23.03  | | |   (15)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.68/23.03  | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.68/23.03  | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.68/23.03  | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7
% 153.68/23.03  | | |             = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 153.68/23.03  | | |             e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.68/23.03  | | |           $i(all_57_7) & $i(all_57_10))
% 153.68/23.03  | | | 
% 153.68/23.03  | | | REF_CLOSE: (2), (4), (6), (8), (10), (15) are inconsistent by sub-proof
% 153.68/23.03  | | |            #700.
% 153.68/23.03  | | | 
% 153.68/23.03  | | End of split
% 153.68/23.03  | | 
% 153.68/23.03  | End of split
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #700 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)  op(e0, e0) = all_10_2
% 153.68/23.03    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.03    (3)   ~ (e1 = e0)
% 153.68/23.03    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.68/23.03             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.68/23.03           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.68/23.03           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.68/23.03           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 153.68/23.03           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.68/23.03    (5)   ~ (all_10_2 = e2)
% 153.68/23.03    (6)  op(e2, e2) = e0
% 153.68/23.03  
% 153.68/23.03  Begin of proof
% 153.68/23.03  | 
% 153.68/23.03  | BETA: splitting (4) gives:
% 153.68/23.03  | 
% 153.68/23.03  | Case 1:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.68/23.03  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.68/23.03  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 153.68/23.03  | | 
% 153.68/23.03  | | ALPHA: (7) implies:
% 153.68/23.03  | |   (8)  op(e0, e0) = e2
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1097.
% 153.68/23.03  | | 
% 153.68/23.03  | Case 2:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.68/23.03  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.68/23.03  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 153.68/23.03  | | 
% 153.68/23.03  | | ALPHA: (9) implies:
% 153.68/23.03  | |   (10)  op(e2, e2) = e1
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #853.
% 153.68/23.03  | | 
% 153.68/23.03  | End of split
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #701 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)  all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.68/23.03    (2)  op(e0, e0) = all_10_2
% 153.68/23.03    (3)   ~ (all_10_2 = e1)
% 153.68/23.03    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.03    (5)  op(e0, e0) = e3
% 153.68/23.03    (6)   ~ (all_10_2 = e3)
% 153.68/23.03    (7)   ~ (all_10_2 = e2)
% 153.68/23.03    (8)  all_54_15 = all_10_2
% 153.68/23.03  
% 153.68/23.03  Begin of proof
% 153.68/23.03  | 
% 153.68/23.03  | BETA: splitting (1) gives:
% 153.68/23.03  | 
% 153.68/23.03  | Case 1:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (9)  all_54_15 = e3
% 153.68/23.03  | | 
% 153.68/23.03  | | COMBINE_EQS: (8), (9) imply:
% 153.68/23.03  | |   (10)  all_10_2 = e3
% 153.68/23.03  | | 
% 153.68/23.03  | | REDUCE: (6), (10) imply:
% 153.68/23.03  | |   (11)  $false
% 153.68/23.03  | | 
% 153.68/23.03  | | CLOSE: (11) is inconsistent.
% 153.68/23.03  | | 
% 153.68/23.03  | Case 2:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (12)   ~ (all_54_15 = e3)
% 153.68/23.03  | |   (13)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (13) are inconsistent by
% 153.68/23.03  | |            sub-proof #702.
% 153.68/23.03  | | 
% 153.68/23.03  | End of split
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #702 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)  op(e0, e0) = all_10_2
% 153.68/23.03    (2)   ~ (all_10_2 = e1)
% 153.68/23.03    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.03    (4)  op(e0, e0) = e3
% 153.68/23.03    (5)   ~ (all_10_2 = e3)
% 153.68/23.03    (6)  all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 153.68/23.03    (7)   ~ (all_10_2 = e2)
% 153.68/23.03    (8)  all_54_15 = all_10_2
% 153.68/23.03  
% 153.68/23.03  Begin of proof
% 153.68/23.03  | 
% 153.68/23.03  | BETA: splitting (6) gives:
% 153.68/23.03  | 
% 153.68/23.03  | Case 1:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (9)  all_54_15 = e2
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (7), (8), (9) are inconsistent by sub-proof #1048.
% 153.68/23.03  | | 
% 153.68/23.03  | Case 2:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (10)  all_54_15 = e1 | all_54_15 = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (10) are inconsistent by sub-proof
% 153.68/23.03  | |            #703.
% 153.68/23.03  | | 
% 153.68/23.03  | End of split
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #703 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)  op(e0, e0) = all_10_2
% 153.68/23.03    (2)   ~ (all_10_2 = e1)
% 153.68/23.03    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.03    (4)  op(e0, e0) = e3
% 153.68/23.03    (5)   ~ (all_10_2 = e3)
% 153.68/23.03    (6)  all_54_15 = e1 | all_54_15 = e0
% 153.68/23.03    (7)  all_54_15 = all_10_2
% 153.68/23.03  
% 153.68/23.03  Begin of proof
% 153.68/23.03  | 
% 153.68/23.03  | BETA: splitting (6) gives:
% 153.68/23.03  | 
% 153.68/23.03  | Case 1:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (8)  all_54_15 = e1
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (2), (7), (8) are inconsistent by sub-proof #1047.
% 153.68/23.03  | | 
% 153.68/23.03  | Case 2:
% 153.68/23.03  | | 
% 153.68/23.03  | |   (9)  all_54_15 = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | COMBINE_EQS: (7), (9) imply:
% 153.68/23.03  | |   (10)  all_10_2 = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | SIMP: (10) implies:
% 153.68/23.03  | |   (11)  all_10_2 = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | REDUCE: (5), (11) imply:
% 153.68/23.03  | |   (12)   ~ (e3 = e0)
% 153.68/23.03  | | 
% 153.68/23.03  | | SIMP: (12) implies:
% 153.68/23.03  | |   (13)   ~ (e3 = e0)
% 153.68/23.03  | | 
% 153.68/23.03  | | REDUCE: (1), (11) imply:
% 153.68/23.03  | |   (14)  op(e0, e0) = e0
% 153.68/23.03  | | 
% 153.68/23.03  | | REF_CLOSE: (3), (4), (13), (14) are inconsistent by sub-proof #1143.
% 153.68/23.03  | | 
% 153.68/23.03  | End of split
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #704 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.03    (2)  op(e2, e1) = all_52_9
% 153.68/23.03    (3)  op(e2, e1) = e1
% 153.68/23.03    (4)   ~ (all_52_9 = e1)
% 153.68/23.03  
% 153.68/23.03  Begin of proof
% 153.68/23.03  | 
% 153.68/23.03  | GROUND_INST: instantiating (1) with all_52_9, e1, e1, e2, simplifying with
% 153.68/23.03  |              (2), (3) gives:
% 153.68/23.03  |   (5)  all_52_9 = e1
% 153.68/23.03  | 
% 153.68/23.03  | REDUCE: (4), (5) imply:
% 153.68/23.03  |   (6)  $false
% 153.68/23.03  | 
% 153.68/23.03  | CLOSE: (6) is inconsistent.
% 153.68/23.03  | 
% 153.68/23.03  End of proof
% 153.68/23.03  
% 153.68/23.03  Sub-proof #705 shows that the following formulas are inconsistent:
% 153.68/23.03  ----------------------------------------------------------------
% 153.68/23.03    (1)   ~ (e3 = e1)
% 153.68/23.03    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.68/23.03         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.68/23.03    (3)  op(e2, e2) = e1
% 153.68/23.03    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.68/23.03         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.68/23.03    (5)   ~ (all_52_14 = e2)
% 153.68/23.03    (6)  op(e1, e1) = all_4_2
% 153.68/23.03    (7)   ~ (e2 = e0)
% 153.68/23.03    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.03           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.03    (9)  op(e3, e3) = e2
% 153.68/23.03    (10)  op(e0, e0) = e2
% 153.68/23.03    (11)  op(e1, e0) = all_52_14
% 153.68/23.03    (12)   ~ (all_52_13 = e2)
% 153.68/23.03    (13)   ~ (e3 = e0)
% 153.68/23.03    (14)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.68/23.03          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.68/23.03    (15)  op(e2, e0) = all_52_13
% 153.68/23.03    (16)   ~ (e1 = e0)
% 153.68/23.03    (17)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.68/23.03          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.68/23.03    (18)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.68/23.03              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.03            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.68/23.03                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.68/23.03              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.03          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.68/23.03              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.03            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.68/23.03                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.68/23.03              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.03          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.68/23.03              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.03            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.68/23.03                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.68/23.03              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.03          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.68/23.03              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.03            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.68/23.03                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.68/23.03                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.68/23.03                $i(all_57_14))))
% 153.68/23.03    (19)   ~ (e3 = e2)
% 153.68/23.03    (20)   ~ (e2 = e1)
% 153.68/23.04    (21)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.68/23.04              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.68/23.04            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.68/23.04            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.68/23.04            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.68/23.04            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.68/23.04            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.68/23.04            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.68/23.04            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.68/23.04            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.68/23.04            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.68/23.04            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.68/23.04            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.68/23.04            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.68/23.04            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.68/23.04            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.68/23.04            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.68/23.04            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.68/23.04            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.04            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.68/23.04            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.68/23.04            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.68/23.04            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.68/23.04            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.68/23.04            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.04            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.68/23.04            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.68/23.04            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.04            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.04            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.68/23.04            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.68/23.04            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.68/23.04            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.68/23.04            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.68/23.04            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.04            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.68/23.04            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.04            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.68/23.04            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.68/23.04            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.04            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.68/23.04            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.68/23.04            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.04            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.68/23.04            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.68/23.04            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.04            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.68/23.04            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.68/23.04              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.68/23.04            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.68/23.04            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.68/23.04              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.68/23.04            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.68/23.04            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.68/23.04                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.68/23.04                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.04                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.68/23.04                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.68/23.04                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.68/23.04                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.68/23.04                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.68/23.04              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.68/23.04                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.68/23.04                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.04                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.68/23.04                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.68/23.04                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.68/23.04                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.04                $i(all_57_7))))
% 153.68/23.04    (22)  op(e2, e3) = all_52_1
% 153.68/23.04    (23)   ~ (all_52_1 = e2)
% 153.68/23.04  
% 153.68/23.04  Begin of proof
% 153.68/23.04  | 
% 153.68/23.04  | BETA: splitting (17) gives:
% 153.68/23.04  | 
% 153.68/23.04  | Case 1:
% 153.68/23.04  | | 
% 153.68/23.04  | |   (24)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 153.68/23.04  | |           e2)
% 153.68/23.04  | | 
% 153.68/23.04  | | BETA: splitting (24) gives:
% 153.68/23.04  | | 
% 153.68/23.04  | | Case 1:
% 153.68/23.04  | | | 
% 153.68/23.04  | | |   (25)  all_56_6 = e2 & op(e1, e3) = e2
% 153.68/23.04  | | | 
% 153.68/23.04  | | | ALPHA: (25) implies:
% 153.68/23.04  | | |   (26)  all_56_6 = e2
% 153.68/23.04  | | | 
% 153.68/23.04  | | | REF_CLOSE: (1), (2), (4), (7), (8), (9), (13), (14), (16), (19), (20),
% 153.68/23.04  | | |            (26) are inconsistent by sub-proof #1050.
% 153.68/23.04  | | | 
% 153.68/23.04  | | Case 2:
% 153.68/23.04  | | | 
% 153.68/23.04  | | |   (27)  all_56_7 = e2 & op(e1, e2) = e2
% 153.68/23.04  | | | 
% 153.68/23.04  | | | ALPHA: (27) implies:
% 153.68/23.04  | | |   (28)  op(e1, e2) = e2
% 153.68/23.04  | | | 
% 153.68/23.04  | | | REF_CLOSE: (1), (3), (6), (7), (8), (9), (10), (12), (15), (16), (18),
% 153.68/23.04  | | |            (19), (20), (21), (22), (23), (28) are inconsistent by
% 153.68/23.04  | | |            sub-proof #708.
% 153.68/23.04  | | | 
% 153.68/23.04  | | End of split
% 153.68/23.04  | | 
% 153.68/23.04  | Case 2:
% 153.68/23.04  | | 
% 153.68/23.04  | |   (29)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 153.68/23.04  | |           e2)
% 153.68/23.04  | | 
% 153.68/23.04  | | BETA: splitting (29) gives:
% 153.68/23.04  | | 
% 153.68/23.04  | | Case 1:
% 153.68/23.04  | | | 
% 153.68/23.04  | | |   (30)  all_56_8 = e2 & op(e1, e1) = e2
% 153.68/23.04  | | | 
% 153.68/23.04  | | | ALPHA: (30) implies:
% 153.68/23.04  | | |   (31)  op(e1, e1) = e2
% 153.68/23.04  | | | 
% 153.68/23.04  | | | REF_CLOSE: (3), (6), (7), (8), (9), (10), (18), (19), (20), (31) are
% 153.68/23.04  | | |            inconsistent by sub-proof #706.
% 153.68/23.04  | | | 
% 153.68/23.04  | | Case 2:
% 153.68/23.04  | | | 
% 153.68/23.04  | | |   (32)  all_56_11 = e2 & op(e1, e0) = e2
% 153.68/23.04  | | | 
% 153.68/23.04  | | | ALPHA: (32) implies:
% 153.68/23.04  | | |   (33)  op(e1, e0) = e2
% 153.68/23.04  | | | 
% 153.68/23.04  | | | REF_CLOSE: (5), (8), (11), (33) are inconsistent by sub-proof #974.
% 153.68/23.04  | | | 
% 153.68/23.04  | | End of split
% 153.68/23.04  | | 
% 153.68/23.04  | End of split
% 153.68/23.04  | 
% 153.68/23.04  End of proof
% 153.68/23.04  
% 153.68/23.04  Sub-proof #706 shows that the following formulas are inconsistent:
% 153.68/23.04  ----------------------------------------------------------------
% 153.68/23.04    (1)  op(e2, e2) = e1
% 153.68/23.04    (2)  op(e1, e1) = e2
% 153.68/23.04    (3)  op(e1, e1) = all_4_2
% 153.68/23.04    (4)   ~ (e2 = e0)
% 153.68/23.04    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.04    (6)  op(e3, e3) = e2
% 153.68/23.04    (7)  op(e0, e0) = e2
% 153.68/23.04    (8)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.68/23.04             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.04           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.68/23.04               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.68/23.04             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.04         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.68/23.04             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.68/23.04               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.68/23.04             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.04         (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.68/23.04             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.68/23.04               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.68/23.04             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.04         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.68/23.04             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 153.68/23.04               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 153.68/23.04             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 153.68/23.04    (9)   ~ (e3 = e2)
% 153.68/23.04    (10)   ~ (e2 = e1)
% 153.68/23.04  
% 153.68/23.04  Begin of proof
% 153.68/23.04  | 
% 153.68/23.04  | BETA: splitting (8) gives:
% 153.68/23.04  | 
% 153.68/23.04  | Case 1:
% 153.68/23.04  | | 
% 153.68/23.04  | |   (11)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.68/23.04  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.68/23.04  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.68/23.04  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.68/23.04  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.68/23.04  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 153.68/23.04  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 153.68/23.04  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.68/23.04  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.68/23.04  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.68/23.04  | |               $i(all_57_15))))
% 153.68/23.04  | | 
% 153.68/23.04  | | REF_CLOSE: (1), (5), (6), (9), (10), (11) are inconsistent by sub-proof
% 153.68/23.04  | |            #761.
% 153.68/23.04  | | 
% 153.68/23.04  | Case 2:
% 153.68/23.04  | | 
% 153.68/23.04  | |   (12)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.68/23.04  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.68/23.04  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.68/23.04  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.04  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.68/23.04  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 153.68/23.04  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 153.68/23.04  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 153.68/23.04  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 153.68/23.04  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 153.68/23.04  | |               all_57_14 & $i(all_57_14))))
% 153.68/23.04  | | 
% 153.68/23.04  | | REF_CLOSE: (2), (3), (4), (5), (7), (10), (12) are inconsistent by sub-proof
% 153.68/23.04  | |            #707.
% 153.68/23.04  | | 
% 153.68/23.04  | End of split
% 153.68/23.04  | 
% 153.68/23.04  End of proof
% 153.68/23.04  
% 153.68/23.04  Sub-proof #707 shows that the following formulas are inconsistent:
% 153.68/23.04  ----------------------------------------------------------------
% 153.68/23.04    (1)  op(e1, e1) = e2
% 153.68/23.04    (2)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.68/23.04             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.68/23.04               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.68/23.04             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.04         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.68/23.04             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 153.68/23.04               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 153.68/23.04             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 153.68/23.04    (3)  op(e1, e1) = all_4_2
% 153.68/23.04    (4)   ~ (e2 = e0)
% 153.68/23.04    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.04    (6)  op(e0, e0) = e2
% 153.68/23.04    (7)   ~ (e2 = e1)
% 153.68/23.04  
% 153.68/23.04  Begin of proof
% 153.68/23.04  | 
% 153.68/23.04  | BETA: splitting (2) gives:
% 153.68/23.04  | 
% 153.68/23.04  | Case 1:
% 153.68/23.04  | | 
% 153.68/23.04  | |   (8)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3)
% 153.68/23.04  | |          | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04  | |        ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 153.68/23.04  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 153.68/23.04  | |              e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 153.68/23.04  | |            $i(all_57_15)))
% 153.68/23.04  | | 
% 153.68/23.04  | | ALPHA: (8) implies:
% 153.68/23.04  | |   (9)  op(e1, e1) = e1
% 153.68/23.04  | | 
% 153.68/23.04  | | REF_CLOSE: (1), (3), (5), (7), (9) are inconsistent by sub-proof #1044.
% 153.68/23.04  | | 
% 153.68/23.04  | Case 2:
% 153.68/23.04  | | 
% 153.68/23.04  | |   (10)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 153.68/23.04  | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.68/23.04  | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 153.68/23.04  | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.04  | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 153.68/23.04  | |               e1) = all_57_14 & $i(all_57_14)))
% 153.68/23.04  | | 
% 153.68/23.04  | | ALPHA: (10) implies:
% 153.68/23.04  | |   (11)  op(e0, e0) = e0
% 153.68/23.04  | | 
% 153.68/23.04  | | REF_CLOSE: (4), (5), (6), (11) are inconsistent by sub-proof #1043.
% 153.68/23.04  | | 
% 153.68/23.04  | End of split
% 153.68/23.04  | 
% 153.68/23.04  End of proof
% 153.68/23.04  
% 153.68/23.04  Sub-proof #708 shows that the following formulas are inconsistent:
% 153.68/23.04  ----------------------------------------------------------------
% 153.68/23.04    (1)   ~ (e3 = e1)
% 153.68/23.04    (2)  op(e2, e2) = e1
% 153.68/23.04    (3)  op(e1, e1) = all_4_2
% 153.68/23.04    (4)   ~ (e2 = e0)
% 153.68/23.04    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.04           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.04    (6)  op(e3, e3) = e2
% 153.68/23.04    (7)  op(e0, e0) = e2
% 153.68/23.04    (8)   ~ (all_52_13 = e2)
% 153.68/23.04    (9)  op(e2, e0) = all_52_13
% 153.68/23.04    (10)  op(e1, e2) = e2
% 153.68/23.04    (11)   ~ (e1 = e0)
% 153.68/23.04    (12)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.68/23.04              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.04            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.68/23.04                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.68/23.04              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.04          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.68/23.04              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.68/23.04                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.68/23.04              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.04          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.68/23.04              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.68/23.04                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.68/23.04              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.68/23.04          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.68/23.04              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.68/23.04                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.68/23.04                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.68/23.04                $i(all_57_14))))
% 153.68/23.04    (13)   ~ (e3 = e2)
% 153.68/23.04    (14)   ~ (e2 = e1)
% 153.68/23.04    (15)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.68/23.04              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.68/23.04            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.68/23.04            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.68/23.04            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.68/23.04            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.68/23.04            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.68/23.04            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.68/23.04            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.68/23.04            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.68/23.04            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.68/23.04            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.68/23.04            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.68/23.04            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.68/23.04            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.68/23.04            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.68/23.04            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.68/23.04            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.68/23.04            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.04            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.68/23.04            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.68/23.04            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.68/23.04            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.68/23.04            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.68/23.04            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.04            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.68/23.04            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.68/23.04            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.04            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.04            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.68/23.04            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.68/23.04            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.68/23.04            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.68/23.04            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.68/23.04            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.04            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.68/23.04            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.04            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.68/23.04            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.68/23.04            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.04            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.68/23.04            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.68/23.04            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.04            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.68/23.04            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.68/23.04            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.04            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.68/23.04            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.68/23.04              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.68/23.04            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.68/23.04            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.68/23.04              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.68/23.04            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.68/23.04            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.68/23.04                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.68/23.04                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.04                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.68/23.04                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.68/23.04                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.68/23.04                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.68/23.04                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.68/23.04              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.68/23.04                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.68/23.04                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.04                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.68/23.04                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.68/23.04                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.68/23.04                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.04                $i(all_57_7))))
% 153.68/23.04    (16)  op(e2, e3) = all_52_1
% 153.68/23.04    (17)   ~ (all_52_1 = e2)
% 153.68/23.04  
% 153.68/23.04  Begin of proof
% 153.68/23.04  | 
% 153.68/23.04  | BETA: splitting (12) gives:
% 153.68/23.04  | 
% 153.68/23.04  | Case 1:
% 153.68/23.04  | | 
% 153.68/23.04  | |   (18)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.68/23.04  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.68/23.04  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.68/23.04  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.68/23.04  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.68/23.04  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 153.68/23.04  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 153.68/23.04  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.68/23.04  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.68/23.04  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.68/23.04  | |               $i(all_57_15))))
% 153.68/23.04  | | 
% 153.68/23.04  | | REF_CLOSE: (2), (5), (6), (13), (14), (18) are inconsistent by sub-proof
% 153.68/23.04  | |            #761.
% 153.68/23.04  | | 
% 153.68/23.04  | Case 2:
% 153.68/23.04  | | 
% 153.68/23.04  | |   (19)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.68/23.04  | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.68/23.04  | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.68/23.04  | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.04  | |           ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.68/23.04  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 153.68/23.04  | |           op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 153.68/23.04  | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.68/23.04  | |           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 153.68/23.04  | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 153.68/23.04  | |               op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 153.68/23.04  | |               all_57_14 & $i(all_57_14))))
% 153.68/23.04  | | 
% 153.68/23.04  | | BETA: splitting (19) gives:
% 153.68/23.04  | | 
% 153.68/23.04  | | Case 1:
% 153.68/23.04  | | | 
% 153.68/23.04  | | |   (20)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.68/23.04  | | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.68/23.04  | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.68/23.04  | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.04  | | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 153.68/23.04  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.68/23.04  | | | 
% 153.68/23.04  | | | ALPHA: (20) implies:
% 153.68/23.04  | | |   (21)  op(e1, e1) = e1
% 153.68/23.04  | | |   (22)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 153.68/23.04  | | |             e2) = all_57_12 & $i(all_57_12))
% 153.68/23.04  | | | 
% 153.68/23.04  | | | BETA: splitting (15) gives:
% 153.68/23.04  | | | 
% 153.68/23.04  | | | Case 1:
% 153.68/23.04  | | | | 
% 153.68/23.04  | | | |   (23)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.68/23.04  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.68/23.04  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.68/23.04  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.68/23.04  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.68/23.04  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.68/23.04  | | | |           e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.68/23.04  | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.68/23.04  | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.68/23.04  | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.68/23.04  | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.68/23.04  | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.68/23.04  | | | |           op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.68/23.04  | | | |           $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.68/23.04  | | | |           (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 153.68/23.04  | | | |           & op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.68/23.04  | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 =
% 153.68/23.04  | | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.68/23.04  | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.68/23.04  | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 153.68/23.04  | | | |           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 153.68/23.04  | | | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.68/23.04  | | | |           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.68/23.04  | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.68/23.04  | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.68/23.04  | | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.68/23.04  | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.68/23.04  | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10
% 153.68/23.04  | | | |           & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.68/23.04  | | | |           $i(all_57_7) & $i(all_57_10))
% 153.68/23.04  | | | | 
% 153.68/23.04  | | | | BETA: splitting (23) gives:
% 153.68/23.04  | | | | 
% 153.68/23.04  | | | | Case 1:
% 153.68/23.04  | | | | | 
% 153.68/23.04  | | | | |   (24)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.68/23.04  | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12
% 153.68/23.04  | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.68/23.04  | | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.68/23.04  | | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.68/23.04  | | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0)
% 153.68/23.04  | | | | |           = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.68/23.04  | | | | |           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) &
% 153.68/23.04  | | | | |           op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.68/23.04  | | | | |           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.68/23.04  | | | | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.68/23.04  | | | | |           (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.68/23.04  | | | | |           & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.68/23.04  | | | | |           $i(all_57_14))
% 153.68/23.04  | | | | | 
% 153.68/23.04  | | | | | BETA: splitting (24) gives:
% 153.68/23.04  | | | | | 
% 153.68/23.04  | | | | | Case 1:
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | |   (25)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.68/23.04  | | | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.68/23.04  | | | | | |           all_57_12 & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.68/23.04  | | | | | |           $i(all_57_1) & $i(all_57_12)) | (all_57_0 = e2 & all_57_15
% 153.68/23.04  | | | | | |           = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2,
% 153.68/23.04  | | | | | |             e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.68/23.04  | | | | | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | | REF_CLOSE: (5), (16), (17), (25) are inconsistent by sub-proof
% 153.68/23.04  | | | | | |            #1180.
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | Case 2:
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | |   (26)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.68/23.04  | | | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 153.68/23.04  | | | | | |           & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0)
% 153.68/23.04  | | | | | |           & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.68/23.04  | | | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.68/23.04  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 153.68/23.04  | | | | | |             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | | REF_CLOSE: (1), (2), (5), (7), (13), (26) are inconsistent by
% 153.68/23.04  | | | | | |            sub-proof #730.
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | End of split
% 153.68/23.04  | | | | | 
% 153.68/23.04  | | | | Case 2:
% 153.68/23.04  | | | | | 
% 153.68/23.04  | | | | |   (27)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.04  | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3
% 153.68/23.04  | | | | |           & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.68/23.04  | | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.68/23.04  | | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.68/23.04  | | | | |           all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0,
% 153.68/23.04  | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1
% 153.68/23.04  | | | | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2)
% 153.68/23.04  | | | | |           & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1
% 153.68/23.04  | | | | |           & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.68/23.04  | | | | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.68/23.04  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.68/23.04  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.68/23.04  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.68/23.04  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.68/23.04  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.68/23.04  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.68/23.04  | | | | | 
% 153.68/23.04  | | | | | BETA: splitting (27) gives:
% 153.68/23.04  | | | | | 
% 153.68/23.04  | | | | | Case 1:
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | |   (28)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.04  | | | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) =
% 153.68/23.04  | | | | | |           e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.68/23.04  | | | | | |           $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15
% 153.68/23.04  | | | | | |           = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3,
% 153.68/23.04  | | | | | |             e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.68/23.04  | | | | | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | | REF_CLOSE: (3), (5), (6), (14), (21), (28) are inconsistent by
% 153.68/23.04  | | | | | |            sub-proof #712.
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | Case 2:
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | |   (29)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.68/23.04  | | | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3
% 153.68/23.04  | | | | | |           & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3)
% 153.68/23.04  | | | | | |           & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.68/23.04  | | | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.68/23.04  | | | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.68/23.04  | | | | | |             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 =
% 153.68/23.04  | | | | | |           e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.68/23.04  | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 153.68/23.04  | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.68/23.04  | | | | | |           $i(all_57_10))
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | | BETA: splitting (29) gives:
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | | Case 1:
% 153.68/23.04  | | | | | | | 
% 153.68/23.04  | | | | | | |   (30)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.68/23.04  | | | | | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3
% 153.68/23.04  | | | | | | |         & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3)
% 153.68/23.04  | | | | | | |         & $i(all_57_14)
% 153.68/23.04  | | | | | | | 
% 153.68/23.04  | | | | | | | ALPHA: (30) implies:
% 153.68/23.04  | | | | | | |   (31)  op(e1, e2) = e1
% 153.68/23.04  | | | | | | | 
% 153.68/23.04  | | | | | | | REF_CLOSE: (5), (10), (14), (31) are inconsistent by sub-proof
% 153.68/23.04  | | | | | | |            #711.
% 153.68/23.04  | | | | | | | 
% 153.68/23.04  | | | | | | Case 2:
% 153.68/23.04  | | | | | | | 
% 153.68/23.04  | | | | | | |   (32)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.68/23.04  | | | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.68/23.04  | | | | | | |           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.68/23.04  | | | | | | |           $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 153.68/23.04  | | | | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.68/23.04  | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.04  | | | | | | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.68/23.04  | | | | | | |           $i(all_57_10))
% 153.68/23.04  | | | | | | | 
% 153.68/23.04  | | | | | | | BETA: splitting (32) gives:
% 153.68/23.04  | | | | | | | 
% 153.68/23.04  | | | | | | | Case 1:
% 153.68/23.04  | | | | | | | | 
% 153.68/23.04  | | | | | | | |   (33)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.68/23.04  | | | | | | | |         (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 153.68/23.04  | | | | | | | |         all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.68/23.04  | | | | | | | |         $i(all_57_5) & $i(all_57_14)
% 153.68/23.04  | | | | | | | | 
% 153.68/23.04  | | | | | | | | ALPHA: (33) implies:
% 153.68/23.04  | | | | | | | |   (34)  op(e1, e2) = e1
% 153.68/23.04  | | | | | | | | 
% 153.68/23.04  | | | | | | | | REF_CLOSE: (5), (10), (14), (34) are inconsistent by sub-proof
% 153.68/23.04  | | | | | | | |            #711.
% 153.68/23.04  | | | | | | | | 
% 153.68/23.04  | | | | | | | Case 2:
% 153.68/23.04  | | | | | | | | 
% 153.68/23.04  | | | | | | | |   (35)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.68/23.04  | | | | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 153.68/23.04  | | | | | | | |         e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.68/23.04  | | | | | | | |         $i(all_57_7) & $i(all_57_10)
% 153.68/23.04  | | | | | | | | 
% 153.68/23.04  | | | | | | | | ALPHA: (35) implies:
% 153.68/23.04  | | | | | | | |   (36)   ~ (all_57_7 = e2)
% 153.68/23.04  | | | | | | | | 
% 153.68/23.04  | | | | | | | | REF_CLOSE: (2), (5), (22), (36) are inconsistent by sub-proof
% 153.68/23.04  | | | | | | | |            #713.
% 153.68/23.04  | | | | | | | | 
% 153.68/23.04  | | | | | | | End of split
% 153.68/23.04  | | | | | | | 
% 153.68/23.04  | | | | | | End of split
% 153.68/23.04  | | | | | | 
% 153.68/23.04  | | | | | End of split
% 153.68/23.04  | | | | | 
% 153.68/23.04  | | | | End of split
% 153.68/23.04  | | | | 
% 153.68/23.04  | | | Case 2:
% 153.68/23.04  | | | | 
% 153.68/23.05  | | | |   (37)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.68/23.05  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.05  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.05  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.68/23.05  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.68/23.05  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.68/23.05  | | | |           e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.68/23.05  | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.68/23.05  | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.68/23.05  | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.68/23.05  | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.68/23.05  | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.05  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.68/23.05  | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.68/23.05  | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.68/23.05  | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.68/23.05  | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0 &
% 153.68/23.05  | | | |           all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 = e0) &
% 153.68/23.05  | | | |           op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 153.68/23.05  | | | |           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 153.68/23.05  | | | |         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~
% 153.68/23.05  | | | |           (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.05  | | | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.68/23.05  | | | |           $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.68/23.05  | | | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.68/23.05  | | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.68/23.05  | | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.68/23.05  | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.68/23.05  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.68/23.05  | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.68/23.05  | | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.68/23.05  | | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3)
% 153.68/23.05  | | | |               & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.68/23.05  | | | |               e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.68/23.05  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.68/23.05  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.68/23.05  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.68/23.05  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.68/23.05  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.68/23.05  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.05  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.68/23.05  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.68/23.05  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.68/23.05  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.68/23.05  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.68/23.05  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.68/23.05  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.68/23.05  | | | | 
% 153.68/23.05  | | | | BETA: splitting (37) gives:
% 153.68/23.05  | | | | 
% 153.68/23.05  | | | | Case 1:
% 153.68/23.05  | | | | | 
% 153.68/23.05  | | | | |   (38)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.68/23.05  | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.68/23.05  | | | | |           & op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.05  | | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.68/23.05  | | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.68/23.05  | | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1)
% 153.68/23.05  | | | | |           = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.68/23.05  | | | | |           all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) &
% 153.68/23.05  | | | | |           op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.68/23.05  | | | | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.68/23.05  | | | | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.68/23.05  | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3
% 153.68/23.05  | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.68/23.05  | | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.68/23.05  | | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.68/23.05  | | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.68/23.05  | | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.68/23.05  | | | | | 
% 153.68/23.05  | | | | | BETA: splitting (38) gives:
% 153.68/23.05  | | | | | 
% 153.68/23.05  | | | | | Case 1:
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | |   (39)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.68/23.05  | | | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) =
% 153.68/23.05  | | | | | |           e3 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.68/23.05  | | | | | |           $i(all_57_8) & $i(all_57_10)) | (all_57_7 = e2 & all_57_10
% 153.68/23.05  | | | | | |           = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3,
% 153.68/23.05  | | | | | |             e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.68/23.05  | | | | | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.68/23.05  | | | | | |           $i(all_57_12))
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | | REF_CLOSE: (5), (6), (7), (14), (39) are inconsistent by sub-proof
% 153.68/23.05  | | | | | |            #710.
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | Case 2:
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | |   (40)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.68/23.05  | | | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.68/23.05  | | | | | |           e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.68/23.05  | | | | | |           $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12
% 153.68/23.05  | | | | | |           = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3,
% 153.68/23.05  | | | | | |             e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.68/23.05  | | | | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 153.68/23.05  | | | | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.68/23.05  | | | | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 153.68/23.05  | | | | | |           e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.68/23.05  | | | | | |           $i(all_57_10) & $i(all_57_13))
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | | BETA: splitting (40) gives:
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | | Case 1:
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | |   (41)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.68/23.05  | | | | | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.68/23.05  | | | | | | |         e2 & op(e0, e1) = all_57_8 & op(e0, e0) = e1 &
% 153.68/23.05  | | | | | | |         $i(all_57_8) & $i(all_57_12)
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | | ALPHA: (41) implies:
% 153.68/23.05  | | | | | | |   (42)  op(e0, e0) = e1
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | | REF_CLOSE: (5), (7), (14), (42) are inconsistent by sub-proof
% 153.68/23.05  | | | | | | |            #978.
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | Case 2:
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | |   (43)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.68/23.05  | | | | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) =
% 153.68/23.05  | | | | | | |           e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.68/23.05  | | | | | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.68/23.05  | | | | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 =
% 153.68/23.05  | | | | | | |             e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.05  | | | | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10)
% 153.68/23.05  | | | | | | |           & $i(all_57_13))
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | | REF_CLOSE: (2), (5), (11), (21), (43) are inconsistent by
% 153.68/23.05  | | | | | | |            sub-proof #765.
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | End of split
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | End of split
% 153.68/23.05  | | | | | 
% 153.68/23.05  | | | | Case 2:
% 153.68/23.05  | | | | | 
% 153.68/23.05  | | | | |   (44)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.68/23.05  | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.05  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.68/23.05  | | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.68/23.05  | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.68/23.05  | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0)
% 153.68/23.05  | | | | |           = e1 & $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 &
% 153.68/23.05  | | | | |           all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 153.68/23.05  | | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.68/23.05  | | | | |           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) |
% 153.68/23.05  | | | | |         (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.68/23.05  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.68/23.05  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.68/23.05  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.68/23.05  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.68/23.05  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 153.68/23.05  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.68/23.05  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.68/23.05  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.68/23.05  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.68/23.05  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 153.68/23.05  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.68/23.05  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.68/23.05  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.68/23.05  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.68/23.05  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.05  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.68/23.05  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.68/23.05  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.68/23.05  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.68/23.05  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.05  | | | | |               $i(all_57_7))))
% 153.68/23.05  | | | | | 
% 153.68/23.05  | | | | | BETA: splitting (44) gives:
% 153.68/23.05  | | | | | 
% 153.68/23.05  | | | | | Case 1:
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | |   (45)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.68/23.05  | | | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9
% 153.68/23.05  | | | | | |           & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 153.68/23.05  | | | | | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.68/23.05  | | | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.68/23.05  | | | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1,
% 153.68/23.05  | | | | | |             e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | | REF_CLOSE: (4), (5), (6), (45) are inconsistent by sub-proof #1037.
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | Case 2:
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | |   (46)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.68/23.05  | | | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.68/23.05  | | | | | |           e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.68/23.05  | | | | | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.68/23.05  | | | | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0)
% 153.68/23.05  | | | | | |           & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.68/23.05  | | | | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.68/23.05  | | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.68/23.05  | | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.68/23.05  | | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2)
% 153.68/23.05  | | | | | |               = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 =
% 153.68/23.05  | | | | | |               e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.68/23.05  | | | | | |               (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1)
% 153.68/23.05  | | | | | |               = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 153.68/23.05  | | | | | |               e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.68/23.05  | | | | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.05  | | | | | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5
% 153.68/23.05  | | | | | |               = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.05  | | | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1)
% 153.68/23.05  | | | | | |               = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 153.68/23.05  | | | | | |               e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.68/23.05  | | | | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.68/23.05  | | | | | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 153.68/23.05  | | | | | |               = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.68/23.05  | | | | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.68/23.05  | | | | | |               all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | | BETA: splitting (46) gives:
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | | Case 1:
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | |   (47)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.68/23.05  | | | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) =
% 153.68/23.05  | | | | | | |         e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.68/23.05  | | | | | | |         $i(all_57_12) & $i(all_57_13)
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | | ALPHA: (47) implies:
% 153.68/23.05  | | | | | | |   (48)  op(e2, e0) = e2
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | | REF_CLOSE: (5), (8), (9), (48) are inconsistent by sub-proof
% 153.68/23.05  | | | | | | |            #1156.
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | Case 2:
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | |   (49)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 153.68/23.05  | | | | | | |           ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.68/23.05  | | | | | | |           all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.68/23.05  | | | | | | |           $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 153.68/23.05  | | | | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 153.68/23.05  | | | | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.68/23.05  | | | | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.05  | | | | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.68/23.05  | | | | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.68/23.05  | | | | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.68/23.05  | | | | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.68/23.05  | | | | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.68/23.05  | | | | | | |               e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.68/23.05  | | | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.68/23.05  | | | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.68/23.05  | | | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.68/23.05  | | | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.05  | | | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.68/23.05  | | | | | | |               e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.68/23.05  | | | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.68/23.05  | | | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 153.68/23.05  | | | | | | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.05  | | | | | | |               $i(all_57_7))))
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | | BETA: splitting (49) gives:
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | | Case 1:
% 153.68/23.05  | | | | | | | | 
% 153.68/23.05  | | | | | | | |   (50)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) & 
% 153.68/23.05  | | | | | | | |         ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) =
% 153.68/23.05  | | | | | | | |         all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.68/23.05  | | | | | | | |         $i(all_57_11) & $i(all_57_14)
% 153.68/23.05  | | | | | | | | 
% 153.68/23.05  | | | | | | | | ALPHA: (50) implies:
% 153.68/23.05  | | | | | | | |   (51)  op(e2, e2) = e0
% 153.68/23.05  | | | | | | | | 
% 153.68/23.05  | | | | | | | | REF_CLOSE: (2), (5), (11), (51) are inconsistent by sub-proof
% 153.68/23.05  | | | | | | | |            #853.
% 153.68/23.05  | | | | | | | | 
% 153.68/23.05  | | | | | | | Case 2:
% 153.68/23.05  | | | | | | | | 
% 153.68/23.05  | | | | | | | |   (52)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0
% 153.68/23.05  | | | | | | | |             & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.68/23.05  | | | | | | | |             (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.68/23.05  | | | | | | | |               e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.68/23.05  | | | | | | | |           (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 153.68/23.05  | | | | | | | |              ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.68/23.05  | | | | | | | |               e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.68/23.05  | | | | | | | |           (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &
% 153.68/23.05  | | | | | | | |              ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.05  | | | | | | | |             all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.68/23.05  | | | | | | | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &
% 153.68/23.05  | | | | | | | |              ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.68/23.05  | | | | | | | |               e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.68/23.05  | | | | | | | |           (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &
% 153.68/23.05  | | | | | | | |              ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.68/23.05  | | | | | | | |             all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.68/23.05  | | | | | | | |           (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 153.68/23.05  | | | | | | | |              ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.68/23.05  | | | | | | | |             all_57_7 & op(e0, e1) = e0 & $i(all_57_7)))
% 153.68/23.05  | | | | | | | | 
% 153.68/23.05  | | | | | | | | ALPHA: (52) implies:
% 153.68/23.05  | | | | | | | |   (53)  op(e0, e0) = all_57_15
% 153.68/23.05  | | | | | | | |   (54)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) & 
% 153.68/23.05  | | | | | | | |           ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.68/23.05  | | | | | | | |             e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.68/23.05  | | | | | | | |         (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.68/23.05  | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.68/23.05  | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.68/23.05  | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.68/23.05  | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.05  | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5
% 153.68/23.05  | | | | | | | |           = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.05  | | | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1)
% 153.68/23.05  | | | | | | | |           = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 153.68/23.05  | | | | | | | |           e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.68/23.05  | | | | | | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.68/23.05  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 153.68/23.05  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.68/23.05  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.68/23.05  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.68/23.05  | | | | | | | | 
% 153.68/23.05  | | | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (14), (21), (22), (53),
% 153.68/23.05  | | | | | | | |            (54) are inconsistent by sub-proof #709.
% 153.68/23.05  | | | | | | | | 
% 153.68/23.05  | | | | | | | End of split
% 153.68/23.05  | | | | | | | 
% 153.68/23.05  | | | | | | End of split
% 153.68/23.05  | | | | | | 
% 153.68/23.05  | | | | | End of split
% 153.68/23.05  | | | | | 
% 153.68/23.05  | | | | End of split
% 153.68/23.05  | | | | 
% 153.68/23.05  | | | End of split
% 153.68/23.05  | | | 
% 153.68/23.05  | | Case 2:
% 153.68/23.05  | | | 
% 153.68/23.05  | | |   (55)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 153.68/23.05  | | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.68/23.05  | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 153.68/23.05  | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.68/23.05  | | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 153.68/23.05  | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 153.68/23.05  | | | 
% 153.68/23.05  | | | ALPHA: (55) implies:
% 153.68/23.05  | | |   (56)  op(e0, e0) = e0
% 153.68/23.05  | | | 
% 153.68/23.05  | | | REF_CLOSE: (4), (5), (7), (56) are inconsistent by sub-proof #1043.
% 153.68/23.05  | | | 
% 153.68/23.05  | | End of split
% 153.68/23.05  | | 
% 153.68/23.05  | End of split
% 153.68/23.05  | 
% 153.68/23.05  End of proof
% 153.68/23.05  
% 153.68/23.05  Sub-proof #709 shows that the following formulas are inconsistent:
% 153.68/23.05  ----------------------------------------------------------------
% 153.68/23.05    (1)   ~ (e3 = e1)
% 153.68/23.05    (2)  op(e2, e2) = e1
% 153.68/23.05    (3)  op(e1, e1) = all_4_2
% 153.68/23.05    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.05    (5)  op(e3, e3) = e2
% 153.68/23.05    (6)  op(e0, e0) = e2
% 153.68/23.05    (7)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.68/23.05             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.05           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.68/23.05           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.68/23.05             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.68/23.05           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.05           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.68/23.05           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.68/23.05           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.68/23.05           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 153.68/23.05           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.68/23.05         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.68/23.05             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.05           $i(all_57_7))
% 153.68/23.05    (8)  op(e1, e1) = e1
% 153.68/23.05    (9)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.68/23.05           all_57_12 & $i(all_57_12))
% 153.68/23.05    (10)  op(e0, e0) = all_57_15
% 153.68/23.05    (11)   ~ (e2 = e1)
% 153.68/23.05  
% 153.68/23.05  Begin of proof
% 153.68/23.05  | 
% 153.68/23.05  | BETA: splitting (7) gives:
% 153.68/23.05  | 
% 153.68/23.05  | Case 1:
% 153.68/23.05  | | 
% 153.68/23.05  | |   (12)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 153.68/23.05  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.68/23.05  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.68/23.05  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.68/23.05  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.68/23.05  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.68/23.05  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.68/23.05  | |           $i(all_57_3))
% 153.68/23.05  | | 
% 153.68/23.05  | | BETA: splitting (12) gives:
% 153.68/23.05  | | 
% 153.68/23.05  | | Case 1:
% 153.68/23.05  | | | 
% 153.68/23.05  | | |   (13)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.68/23.05  | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.68/23.05  | | |         op(e0, e3) = e0 & $i(all_57_0)
% 153.68/23.05  | | | 
% 153.68/23.05  | | | ALPHA: (13) implies:
% 153.68/23.05  | | |   (14)  op(e2, e2) = e3
% 153.68/23.05  | | | 
% 153.68/23.05  | | | REF_CLOSE: (1), (2), (4), (14) are inconsistent by sub-proof #1136.
% 153.68/23.05  | | | 
% 153.68/23.05  | | Case 2:
% 153.68/23.05  | | | 
% 153.68/23.05  | | |   (15)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.68/23.05  | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.68/23.05  | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 153.68/23.05  | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.68/23.05  | | |           & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.68/23.05  | | | 
% 153.68/23.05  | | | REF_CLOSE: (1), (4), (6), (8), (10), (15) are inconsistent by sub-proof
% 153.68/23.05  | | |            #718.
% 153.68/23.05  | | | 
% 153.68/23.05  | | End of split
% 153.68/23.05  | | 
% 153.68/23.05  | Case 2:
% 153.68/23.05  | | 
% 153.68/23.05  | |   (16)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.68/23.05  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.68/23.05  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.05  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.68/23.05  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.68/23.05  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.68/23.05  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.05  | |           $i(all_57_7))
% 153.68/23.05  | | 
% 153.68/23.05  | | BETA: splitting (16) gives:
% 153.68/23.05  | | 
% 153.68/23.05  | | Case 1:
% 153.68/23.05  | | | 
% 153.68/23.05  | | |   (17)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.05  | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.68/23.05  | | |         op(e0, e2) = e0 & $i(all_57_4)
% 153.68/23.05  | | | 
% 153.68/23.05  | | | ALPHA: (17) implies:
% 153.68/23.05  | | |   (18)  op(e1, e1) = e2
% 153.68/23.05  | | | 
% 153.68/23.05  | | | REF_CLOSE: (3), (4), (8), (11), (18) are inconsistent by sub-proof #1044.
% 153.68/23.05  | | | 
% 153.68/23.05  | | Case 2:
% 153.68/23.05  | | | 
% 153.68/23.05  | | |   (19)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.68/23.05  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.68/23.05  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 153.68/23.05  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.68/23.05  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.68/23.05  | | | 
% 153.68/23.05  | | | BETA: splitting (19) gives:
% 153.68/23.05  | | | 
% 153.68/23.05  | | | Case 1:
% 153.68/23.05  | | | | 
% 153.68/23.05  | | | |   (20)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.68/23.05  | | | |         (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.68/23.05  | | | |         op(e0, e1) = e0 & $i(all_57_6)
% 153.68/23.05  | | | | 
% 153.68/23.05  | | | | ALPHA: (20) implies:
% 153.68/23.05  | | | |   (21)  op(e3, e3) = e1
% 153.68/23.05  | | | | 
% 153.68/23.05  | | | | REF_CLOSE: (4), (5), (11), (21) are inconsistent by sub-proof #1074.
% 153.68/23.05  | | | | 
% 153.68/23.05  | | | Case 2:
% 153.68/23.05  | | | | 
% 153.68/23.05  | | | |   (22)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.68/23.05  | | | |         (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.68/23.05  | | | |         op(e0, e1) = e0 & $i(all_57_7)
% 153.68/23.05  | | | | 
% 153.68/23.05  | | | | ALPHA: (22) implies:
% 153.68/23.05  | | | |   (23)   ~ (all_57_7 = e2)
% 153.68/23.05  | | | | 
% 153.68/23.05  | | | | REF_CLOSE: (2), (4), (9), (23) are inconsistent by sub-proof #713.
% 153.68/23.05  | | | | 
% 153.68/23.05  | | | End of split
% 153.68/23.05  | | | 
% 153.68/23.05  | | End of split
% 153.68/23.05  | | 
% 153.68/23.05  | End of split
% 153.68/23.05  | 
% 153.68/23.05  End of proof
% 153.68/23.05  
% 153.68/23.05  Sub-proof #710 shows that the following formulas are inconsistent:
% 153.68/23.05  ----------------------------------------------------------------
% 153.68/23.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.05    (2)  op(e3, e3) = e2
% 153.68/23.05    (3)  op(e0, e0) = e2
% 153.68/23.05    (4)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.68/23.05             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.68/23.05           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.68/23.05           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.68/23.05           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.68/23.05           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 153.68/23.05    (5)   ~ (e2 = e1)
% 153.68/23.05  
% 153.68/23.05  Begin of proof
% 153.68/23.05  | 
% 153.68/23.05  | BETA: splitting (4) gives:
% 153.68/23.05  | 
% 153.68/23.05  | Case 1:
% 153.68/23.05  | | 
% 153.68/23.05  | |   (6)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.68/23.05  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.68/23.05  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 153.68/23.05  | | 
% 153.68/23.05  | | ALPHA: (6) implies:
% 153.68/23.05  | |   (7)  op(e0, e0) = e1
% 153.68/23.05  | | 
% 153.68/23.05  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #978.
% 153.68/23.05  | | 
% 153.68/23.05  | Case 2:
% 153.68/23.05  | | 
% 153.68/23.05  | |   (8)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 153.68/23.05  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.68/23.05  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 153.68/23.05  | | 
% 153.68/23.05  | | ALPHA: (8) implies:
% 153.68/23.05  | |   (9)  op(e3, e3) = e1
% 153.68/23.05  | | 
% 153.68/23.05  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #1074.
% 153.68/23.05  | | 
% 153.68/23.05  | End of split
% 153.68/23.05  | 
% 153.68/23.05  End of proof
% 153.68/23.05  
% 153.68/23.05  Sub-proof #711 shows that the following formulas are inconsistent:
% 153.68/23.05  ----------------------------------------------------------------
% 153.68/23.05    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.05    (2)  op(e1, e2) = e2
% 153.68/23.05    (3)  op(e1, e2) = e1
% 153.68/23.05    (4)   ~ (e2 = e1)
% 153.68/23.05  
% 153.68/23.05  Begin of proof
% 153.68/23.05  | 
% 153.68/23.05  | GROUND_INST: instantiating (1) with e2, e1, e2, e1, simplifying with (2), (3)
% 153.68/23.05  |              gives:
% 153.68/23.05  |   (5)  e2 = e1
% 153.68/23.05  | 
% 153.68/23.05  | REDUCE: (4), (5) imply:
% 153.68/23.05  |   (6)  $false
% 153.68/23.05  | 
% 153.68/23.05  | CLOSE: (6) is inconsistent.
% 153.68/23.05  | 
% 153.68/23.05  End of proof
% 153.68/23.05  
% 153.68/23.05  Sub-proof #712 shows that the following formulas are inconsistent:
% 153.68/23.05  ----------------------------------------------------------------
% 153.68/23.05    (1)  op(e1, e1) = all_4_2
% 153.68/23.05    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.05    (3)  op(e3, e3) = e2
% 153.68/23.05    (4)  op(e1, e1) = e1
% 153.68/23.05    (5)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.68/23.05             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.68/23.05           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 153.68/23.05           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.68/23.05           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.68/23.05           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.68/23.05    (6)   ~ (e2 = e1)
% 153.68/23.05  
% 153.68/23.05  Begin of proof
% 153.68/23.05  | 
% 153.68/23.05  | BETA: splitting (5) gives:
% 153.68/23.05  | 
% 153.68/23.05  | Case 1:
% 153.68/23.05  | | 
% 153.68/23.05  | |   (7)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.68/23.05  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.68/23.05  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 153.68/23.05  | | 
% 153.68/23.05  | | ALPHA: (7) implies:
% 153.68/23.05  | |   (8)  op(e1, e1) = e2
% 153.68/23.05  | | 
% 153.68/23.05  | | REF_CLOSE: (1), (2), (4), (6), (8) are inconsistent by sub-proof #1044.
% 153.68/23.05  | | 
% 153.68/23.05  | Case 2:
% 153.68/23.05  | | 
% 153.68/23.05  | |   (9)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 153.68/23.05  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.68/23.05  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 153.68/23.05  | | 
% 153.68/23.05  | | ALPHA: (9) implies:
% 153.68/23.05  | |   (10)   ~ (all_57_10 = e2)
% 153.68/23.05  | |   (11)  op(e3, e3) = all_57_10
% 153.68/23.05  | | 
% 153.68/23.05  | | REF_CLOSE: (2), (3), (10), (11) are inconsistent by sub-proof #1031.
% 153.68/23.05  | | 
% 153.68/23.05  | End of split
% 153.68/23.05  | 
% 153.68/23.05  End of proof
% 153.68/23.05  
% 153.68/23.05  Sub-proof #713 shows that the following formulas are inconsistent:
% 153.68/23.05  ----------------------------------------------------------------
% 153.68/23.05    (1)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 153.68/23.05           all_57_12 & $i(all_57_12))
% 153.68/23.05    (2)   ~ (all_57_7 = e2)
% 153.68/23.05    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.05    (4)  op(e2, e2) = e1
% 153.68/23.05  
% 153.68/23.05  Begin of proof
% 153.68/23.05  | 
% 153.68/23.05  | BETA: splitting (1) gives:
% 153.68/23.05  | 
% 153.68/23.05  | Case 1:
% 153.68/23.05  | | 
% 153.68/23.05  | |   (5)  all_57_7 = e2 & op(e2, e1) = e2
% 153.68/23.05  | | 
% 153.68/23.05  | | ALPHA: (5) implies:
% 153.68/23.05  | |   (6)  all_57_7 = e2
% 153.68/23.05  | | 
% 153.68/23.05  | | REDUCE: (2), (6) imply:
% 153.68/23.05  | |   (7)  $false
% 153.68/23.05  | | 
% 153.68/23.05  | | CLOSE: (7) is inconsistent.
% 153.68/23.05  | | 
% 153.68/23.05  | Case 2:
% 153.68/23.05  | | 
% 153.68/23.05  | |   (8)   ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12)
% 153.68/23.05  | | 
% 153.68/23.05  | | ALPHA: (8) implies:
% 153.68/23.05  | |   (9)   ~ (all_57_12 = e1)
% 153.68/23.05  | |   (10)  op(e2, e2) = all_57_12
% 153.68/23.05  | | 
% 153.68/23.05  | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #1014.
% 153.68/23.05  | | 
% 153.68/23.05  | End of split
% 153.68/23.05  | 
% 153.68/23.05  End of proof
% 153.68/23.05  
% 153.68/23.05  Sub-proof #714 shows that the following formulas are inconsistent:
% 153.68/23.05  ----------------------------------------------------------------
% 153.68/23.05    (1)  all_54_10 = e1 | all_54_10 = e0
% 153.68/23.05    (2)  op(e2, e2) = e1
% 153.68/23.05    (3)  op(e3, e2) = all_52_4
% 153.68/23.05    (4)  op(e0, e2) = all_52_7
% 153.68/23.05    (5)   ~ (all_52_14 = e2)
% 153.68/23.05    (6)  op(e1, e1) = all_4_2
% 153.68/23.05    (7)   ~ (e2 = e0)
% 153.68/23.05    (8)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.68/23.05         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 153.68/23.05    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.05           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.05    (10)   ~ (all_52_2 = all_4_2)
% 153.68/23.05    (11)  ( ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 153.68/23.05            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e2,
% 153.68/23.05              e1) = all_20_1 & $i(all_20_1))
% 153.68/23.05    (12)  all_54_10 = all_4_2
% 153.68/23.06    (13)  op(e0, e0) = e2
% 153.68/23.06    (14)  op(e1, e0) = all_52_14
% 153.68/23.06    (15)   ~ (all_52_13 = e2)
% 153.68/23.06    (16)   ~ (all_52_4 = e3)
% 153.68/23.06    (17)  op(e2, e1) = all_38_1
% 153.68/23.06    (18)  op(e3, e0) = all_52_12
% 153.68/23.06    (19)   ~ (e3 = e0)
% 153.68/23.06    (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.68/23.06          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.68/23.06    (21)  all_56_2 = e2
% 153.68/23.06    (22)   ~ (all_4_2 = e0)
% 153.68/23.06    (23)  op(e1, e2) = all_52_6
% 153.68/23.06    (24)   ~ (all_52_12 = e3)
% 153.68/23.06    (25)  op(e2, e0) = all_52_13
% 153.68/23.06    (26)   ~ (all_52_9 = e2)
% 153.68/23.06    (27)   ~ (all_52_14 = all_4_2)
% 153.68/23.06    (28)  op(e0, e3) = all_52_3
% 153.68/23.06    (29)   ~ (all_4_2 = e2)
% 153.68/23.06    (30)  op(e2, e1) = all_52_9
% 153.68/23.06    (31)   ~ (all_52_7 = e0)
% 153.68/23.06    (32)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.68/23.06          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.68/23.06    (33)   ~ (all_4_2 = e3)
% 153.68/23.06    (34)   ~ (e3 = e2)
% 153.68/23.06    (35)   ~ (all_52_8 = e3)
% 153.68/23.06    (36)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.68/23.06          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.68/23.06    (37)  op(e2, e1) = e3
% 153.68/23.06    (38)   ~ (all_52_3 = e0)
% 153.68/23.06    (39)  op(e3, e1) = all_52_8
% 153.68/23.06    (40)  op(e3, e3) = e3
% 153.68/23.06    (41)  op(e1, e3) = all_52_2
% 153.68/23.06    (42)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.68/23.06              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.68/23.06            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.68/23.06            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.68/23.06            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.68/23.06            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.68/23.06            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.68/23.06            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.68/23.06            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.68/23.06            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.68/23.06            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.68/23.06            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.68/23.06            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.68/23.06            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.68/23.06            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.68/23.06            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.68/23.06            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.68/23.06            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.68/23.06            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.06            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.68/23.06            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.68/23.06            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.68/23.06            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.68/23.06            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.68/23.06            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.06            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.68/23.06            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.68/23.06            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.06            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.06            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.68/23.06            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.68/23.06            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.68/23.06            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.68/23.06            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.68/23.06            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.06            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.68/23.06            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.06            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.68/23.06            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.68/23.06            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.06            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.68/23.06            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.68/23.06            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.06            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.68/23.06            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.68/23.06            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.06            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.68/23.06            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.68/23.06              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.68/23.06            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.68/23.06            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.68/23.06              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.68/23.06            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.68/23.06            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.68/23.06                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.68/23.06                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.06                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.68/23.06                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.68/23.06                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.68/23.06                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.68/23.06                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.68/23.06              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.68/23.06                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.68/23.06                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.06                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.68/23.06                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.68/23.06                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.68/23.06                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.06                $i(all_57_7))))
% 153.68/23.06    (43)   ~ (all_52_6 = all_4_2)
% 153.68/23.06  
% 153.68/23.06  Begin of proof
% 153.68/23.06  | 
% 153.68/23.06  | BETA: splitting (1) gives:
% 153.68/23.06  | 
% 153.68/23.06  | Case 1:
% 153.68/23.06  | | 
% 153.68/23.06  | |   (44)  all_54_10 = e1
% 153.68/23.06  | | 
% 153.68/23.06  | | COMBINE_EQS: (12), (44) imply:
% 153.68/23.06  | |   (45)  all_4_2 = e1
% 153.68/23.06  | | 
% 153.68/23.06  | | REDUCE: (10), (45) imply:
% 153.68/23.06  | |   (46)   ~ (all_52_2 = e1)
% 153.68/23.06  | | 
% 153.68/23.06  | | REDUCE: (43), (45) imply:
% 153.68/23.06  | |   (47)   ~ (all_52_6 = e1)
% 153.68/23.06  | | 
% 153.68/23.06  | | REDUCE: (27), (45) imply:
% 153.68/23.06  | |   (48)   ~ (all_52_14 = e1)
% 153.68/23.06  | | 
% 153.68/23.06  | | REDUCE: (33), (45) imply:
% 153.68/23.06  | |   (49)   ~ (e3 = e1)
% 153.68/23.06  | | 
% 153.68/23.06  | | SIMP: (49) implies:
% 153.68/23.06  | |   (50)   ~ (e3 = e1)
% 153.68/23.06  | | 
% 153.68/23.06  | | REDUCE: (29), (45) imply:
% 153.68/23.06  | |   (51)   ~ (e2 = e1)
% 153.68/23.06  | | 
% 153.68/23.06  | | SIMP: (51) implies:
% 153.68/23.06  | |   (52)   ~ (e2 = e1)
% 153.68/23.06  | | 
% 153.68/23.06  | | REDUCE: (22), (45) imply:
% 153.68/23.06  | |   (53)   ~ (e1 = e0)
% 153.68/23.06  | | 
% 153.68/23.06  | | REDUCE: (6), (45) imply:
% 153.68/23.06  | |   (54)  op(e1, e1) = e1
% 153.68/23.06  | | 
% 153.68/23.06  | | BETA: splitting (32) gives:
% 153.68/23.06  | | 
% 153.68/23.06  | | Case 1:
% 153.68/23.06  | | | 
% 153.68/23.06  | | |   (55)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) =
% 153.68/23.06  | | |           e2)
% 153.68/23.06  | | | 
% 153.68/23.06  | | | BETA: splitting (55) gives:
% 153.68/23.06  | | | 
% 153.68/23.06  | | | Case 1:
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | |   (56)  all_56_6 = e2 & op(e1, e3) = e2
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | | ALPHA: (56) implies:
% 153.68/23.06  | | | |   (57)  all_56_6 = e2
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | | BETA: splitting (20) gives:
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | | Case 1:
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | |   (58)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2,
% 153.68/23.06  | | | | |             e3) = e0)
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | | REF_CLOSE: (7), (9), (19), (21), (40), (58) are inconsistent by
% 153.68/23.06  | | | | |            sub-proof #725.
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | Case 2:
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | |   (59)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0,
% 153.68/23.06  | | | | |             e3) = e0)
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | | BETA: splitting (59) gives:
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | | Case 1:
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | |   (60)  all_56_6 = e0 & op(e1, e3) = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | ALPHA: (60) implies:
% 153.68/23.06  | | | | | |   (61)  all_56_6 = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | REF_CLOSE: (7), (57), (61) are inconsistent by sub-proof #724.
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | Case 2:
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | |   (62)  all_56_12 = e0 & op(e0, e3) = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | ALPHA: (62) implies:
% 153.68/23.06  | | | | | |   (63)  op(e0, e3) = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | REF_CLOSE: (9), (28), (38), (63) are inconsistent by sub-proof
% 153.68/23.06  | | | | | |            #1142.
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | End of split
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | End of split
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | Case 2:
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | |   (64)  all_56_7 = e2 & op(e1, e2) = e2
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | | ALPHA: (64) implies:
% 153.68/23.06  | | | |   (65)  all_56_7 = e2
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | | BETA: splitting (36) gives:
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | | Case 1:
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | |   (66)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2,
% 153.68/23.06  | | | | |             e2) = e0)
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | | BETA: splitting (66) gives:
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | | Case 1:
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | |   (67)  all_56_1 = e0 & op(e3, e2) = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | REF_CLOSE: (9), (11), (17), (37), (67) are inconsistent by sub-proof
% 153.68/23.06  | | | | | |            #857.
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | Case 2:
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | |   (68)  all_56_3 = e0 & op(e2, e2) = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | ALPHA: (68) implies:
% 153.68/23.06  | | | | | |   (69)  op(e2, e2) = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | REF_CLOSE: (3), (6), (9), (13), (14), (15), (16), (18), (19), (23),
% 153.68/23.06  | | | | | |            (24), (25), (34), (35), (39), (40), (41), (42), (46),
% 153.68/23.06  | | | | | |            (47), (48), (50), (52), (53), (54), (69) are inconsistent
% 153.68/23.06  | | | | | |            by sub-proof #716.
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | End of split
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | Case 2:
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | |   (70)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0,
% 153.68/23.06  | | | | |             e2) = e0)
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | | BETA: splitting (70) gives:
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | | Case 1:
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | |   (71)  all_56_7 = e0 & op(e1, e2) = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | ALPHA: (71) implies:
% 153.68/23.06  | | | | | |   (72)  all_56_7 = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | COMBINE_EQS: (65), (72) imply:
% 153.68/23.06  | | | | | |   (73)  e2 = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | COMBINE_EQS: (21), (73) imply:
% 153.68/23.06  | | | | | |   (74)  all_56_2 = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | REF_CLOSE: (2), (7), (8), (9), (15), (25), (26), (30), (52), (74)
% 153.68/23.06  | | | | | |            are inconsistent by sub-proof #1154.
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | Case 2:
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | |   (75)  all_56_13 = e0 & op(e0, e2) = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | ALPHA: (75) implies:
% 153.68/23.06  | | | | | |   (76)  op(e0, e2) = e0
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | | REF_CLOSE: (4), (9), (31), (76) are inconsistent by sub-proof #1036.
% 153.68/23.06  | | | | | | 
% 153.68/23.06  | | | | | End of split
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | End of split
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | End of split
% 153.68/23.06  | | | 
% 153.68/23.06  | | Case 2:
% 153.68/23.06  | | | 
% 153.68/23.06  | | |   (77)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) =
% 153.68/23.06  | | |           e2)
% 153.68/23.06  | | | 
% 153.68/23.06  | | | REF_CLOSE: (5), (6), (9), (14), (52), (54), (77) are inconsistent by
% 153.68/23.06  | | |            sub-proof #715.
% 153.68/23.06  | | | 
% 153.68/23.06  | | End of split
% 153.68/23.06  | | 
% 153.68/23.06  | Case 2:
% 153.68/23.06  | | 
% 153.68/23.06  | |   (78)  all_54_10 = e0
% 153.68/23.06  | | 
% 153.68/23.06  | | COMBINE_EQS: (12), (78) imply:
% 153.68/23.06  | |   (79)  all_4_2 = e0
% 153.68/23.06  | | 
% 153.68/23.06  | | REDUCE: (22), (79) imply:
% 153.68/23.06  | |   (80)  $false
% 153.68/23.06  | | 
% 153.68/23.06  | | CLOSE: (80) is inconsistent.
% 153.68/23.06  | | 
% 153.68/23.06  | End of split
% 153.68/23.06  | 
% 153.68/23.06  End of proof
% 153.68/23.06  
% 153.68/23.06  Sub-proof #715 shows that the following formulas are inconsistent:
% 153.68/23.06  ----------------------------------------------------------------
% 153.68/23.06    (1)   ~ (all_52_14 = e2)
% 153.68/23.06    (2)  op(e1, e1) = all_4_2
% 153.68/23.06    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.06    (4)  op(e1, e0) = all_52_14
% 153.68/23.06    (5)  op(e1, e1) = e1
% 153.68/23.06    (6)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.68/23.06    (7)   ~ (e2 = e1)
% 153.68/23.06  
% 153.68/23.06  Begin of proof
% 153.68/23.06  | 
% 153.68/23.06  | BETA: splitting (6) gives:
% 153.68/23.06  | 
% 153.68/23.06  | Case 1:
% 153.68/23.06  | | 
% 153.68/23.06  | |   (8)  all_56_8 = e2 & op(e1, e1) = e2
% 153.68/23.06  | | 
% 153.68/23.06  | | ALPHA: (8) implies:
% 153.68/23.06  | |   (9)  op(e1, e1) = e2
% 153.68/23.06  | | 
% 153.68/23.06  | | REF_CLOSE: (2), (3), (5), (7), (9) are inconsistent by sub-proof #1044.
% 153.68/23.06  | | 
% 153.68/23.06  | Case 2:
% 153.68/23.06  | | 
% 153.68/23.06  | |   (10)  all_56_11 = e2 & op(e1, e0) = e2
% 153.68/23.06  | | 
% 153.68/23.06  | | ALPHA: (10) implies:
% 153.68/23.06  | |   (11)  op(e1, e0) = e2
% 153.68/23.06  | | 
% 153.68/23.06  | | REF_CLOSE: (1), (3), (4), (11) are inconsistent by sub-proof #974.
% 153.68/23.06  | | 
% 153.68/23.06  | End of split
% 153.68/23.06  | 
% 153.68/23.06  End of proof
% 153.68/23.06  
% 153.68/23.06  Sub-proof #716 shows that the following formulas are inconsistent:
% 153.68/23.06  ----------------------------------------------------------------
% 153.68/23.06    (1)   ~ (all_52_6 = e1)
% 153.68/23.06    (2)   ~ (e3 = e1)
% 153.68/23.06    (3)  op(e3, e2) = all_52_4
% 153.68/23.06    (4)  op(e1, e1) = all_4_2
% 153.68/23.06    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.06           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.06    (6)   ~ (all_52_14 = e1)
% 153.68/23.06    (7)  op(e0, e0) = e2
% 153.68/23.06    (8)  op(e1, e0) = all_52_14
% 153.68/23.06    (9)   ~ (all_52_13 = e2)
% 153.68/23.06    (10)   ~ (all_52_4 = e3)
% 153.68/23.06    (11)  op(e3, e0) = all_52_12
% 153.68/23.06    (12)   ~ (e3 = e0)
% 153.68/23.06    (13)  op(e1, e2) = all_52_6
% 153.68/23.06    (14)   ~ (all_52_12 = e3)
% 153.68/23.06    (15)  op(e2, e0) = all_52_13
% 153.68/23.06    (16)  op(e1, e1) = e1
% 153.68/23.06    (17)   ~ (e1 = e0)
% 153.68/23.06    (18)   ~ (e3 = e2)
% 153.68/23.06    (19)   ~ (all_52_8 = e3)
% 153.68/23.06    (20)  op(e3, e1) = all_52_8
% 153.68/23.06    (21)   ~ (all_52_2 = e1)
% 153.68/23.06    (22)  op(e3, e3) = e3
% 153.68/23.06    (23)   ~ (e2 = e1)
% 153.68/23.06    (24)  op(e1, e3) = all_52_2
% 153.68/23.06    (25)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.68/23.06              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.68/23.06            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.68/23.06            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.68/23.06            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.68/23.06            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.68/23.06            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.68/23.06            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.68/23.06            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.68/23.06            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.68/23.06            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.68/23.06            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.68/23.06            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.68/23.06            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.68/23.06            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.68/23.06            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.68/23.06            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.68/23.06            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.68/23.06            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.06            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.68/23.06            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.68/23.06            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.68/23.06            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.68/23.06            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.68/23.06            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.06            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.68/23.06            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.68/23.06            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.06            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.06            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.68/23.06            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.68/23.06            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.68/23.06            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.68/23.06            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.68/23.06            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.06            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.68/23.06            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.06            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.68/23.06            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.68/23.06            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.06            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.68/23.06            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.68/23.06            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.06            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.68/23.06            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.68/23.06            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.06            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.68/23.06            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.68/23.06              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.68/23.06            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.68/23.06            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.68/23.06              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.68/23.06            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.68/23.06            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.68/23.06                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.68/23.06                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.06                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.68/23.06                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.68/23.06                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.68/23.06                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.68/23.06                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.68/23.06              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.68/23.06                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.68/23.06                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.06                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.68/23.06                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.68/23.06                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.68/23.06                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.06                $i(all_57_7))))
% 153.68/23.06    (26)  op(e2, e2) = e0
% 153.68/23.06  
% 153.68/23.06  Begin of proof
% 153.68/23.06  | 
% 153.68/23.06  | BETA: splitting (25) gives:
% 153.68/23.06  | 
% 153.68/23.06  | Case 1:
% 153.68/23.06  | | 
% 153.68/23.06  | |   (27)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 153.68/23.06  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.68/23.06  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 153.68/23.06  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 153.68/23.06  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.68/23.06  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 153.68/23.06  | |         (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 153.68/23.06  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 153.68/23.06  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.68/23.06  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 153.68/23.06  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.68/23.06  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) |
% 153.68/23.06  | |         (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 153.68/23.06  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.68/23.06  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 153.68/23.06  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 153.68/23.06  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.68/23.06  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 153.68/23.06  | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 153.68/23.06  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 153.68/23.06  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.68/23.06  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.68/23.06  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.68/23.06  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.68/23.06  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.68/23.06  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.68/23.06  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.68/23.06  | | 
% 153.68/23.06  | | BETA: splitting (27) gives:
% 153.68/23.06  | | 
% 153.68/23.06  | | Case 1:
% 153.68/23.06  | | | 
% 153.68/23.06  | | |   (28)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.68/23.06  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.68/23.06  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.68/23.06  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 153.68/23.06  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.68/23.06  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.68/23.06  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 153.68/23.06  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.68/23.06  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.68/23.06  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 153.68/23.06  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.68/23.06  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 153.68/23.06  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.68/23.06  | | | 
% 153.68/23.06  | | | REF_CLOSE: (2), (5), (7), (16), (18), (21), (24), (28) are inconsistent by
% 153.68/23.06  | | |            sub-proof #722.
% 153.68/23.06  | | | 
% 153.68/23.06  | | Case 2:
% 153.68/23.06  | | | 
% 153.68/23.06  | | |   (29)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.06  | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.68/23.06  | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.68/23.06  | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5
% 153.68/23.06  | | |             = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 153.68/23.06  | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.68/23.06  | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 153.68/23.06  | | |           &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 153.68/23.06  | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.68/23.06  | | |           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 =
% 153.68/23.06  | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 153.68/23.06  | | |           & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 153.68/23.06  | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.68/23.06  | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.68/23.06  | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.68/23.06  | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.68/23.06  | | | 
% 153.68/23.06  | | | BETA: splitting (29) gives:
% 153.68/23.06  | | | 
% 153.68/23.06  | | | Case 1:
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | |   (30)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.06  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.68/23.06  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.68/23.06  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.68/23.06  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 153.68/23.06  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.68/23.06  | | | |           $i(all_57_5) & $i(all_57_10))
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | | REF_CLOSE: (3), (4), (5), (10), (16), (23), (30) are inconsistent by
% 153.68/23.06  | | | |            sub-proof #721.
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | Case 2:
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | |   (31)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.68/23.06  | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.68/23.06  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.68/23.06  | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.68/23.06  | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.68/23.06  | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 153.68/23.06  | | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 153.68/23.06  | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.68/23.06  | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.68/23.06  | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | | BETA: splitting (31) gives:
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | | Case 1:
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | |   (32)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.68/23.06  | | | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.68/23.06  | | | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.68/23.06  | | | | |         $i(all_57_14)
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | | ALPHA: (32) implies:
% 153.68/23.06  | | | | |   (33)  op(e3, e3) = e2
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | | REF_CLOSE: (5), (18), (22), (33) are inconsistent by sub-proof #1085.
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | Case 2:
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | |   (34)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.68/23.06  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.68/23.06  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.68/23.06  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.68/23.06  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.68/23.06  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.68/23.06  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | | REF_CLOSE: (1), (5), (13), (17), (26), (34) are inconsistent by
% 153.68/23.06  | | | | |            sub-proof #720.
% 153.68/23.06  | | | | | 
% 153.68/23.06  | | | | End of split
% 153.68/23.06  | | | | 
% 153.68/23.06  | | | End of split
% 153.68/23.06  | | | 
% 153.68/23.06  | | End of split
% 153.68/23.06  | | 
% 153.68/23.06  | Case 2:
% 153.68/23.06  | | 
% 153.68/23.06  | |   (35)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 153.68/23.06  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.68/23.06  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 153.68/23.06  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 153.68/23.06  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.68/23.06  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 153.68/23.06  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 153.68/23.06  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.68/23.06  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.68/23.06  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.68/23.06  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.06  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.68/23.06  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 153.68/23.06  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 153.68/23.06  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.68/23.06  | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 153.68/23.06  | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.68/23.06  | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 153.68/23.06  | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.68/23.06  | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.68/23.06  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 153.68/23.06  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.68/23.06  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 153.68/23.06  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.68/23.06  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 153.68/23.06  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.68/23.06  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.68/23.06  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.68/23.06  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.68/23.06  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.68/23.06  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 153.68/23.06  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.68/23.06  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.68/23.06  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 153.68/23.06  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.06  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.68/23.06  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 153.68/23.06  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.68/23.06  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 153.68/23.06  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.68/23.06  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.68/23.06  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.68/23.06  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.06  | |               $i(all_57_7))))
% 153.68/23.06  | | 
% 153.68/23.06  | | BETA: splitting (35) gives:
% 153.68/23.06  | | 
% 153.68/23.06  | | Case 1:
% 153.68/23.06  | | | 
% 153.68/23.06  | | |   (36)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.68/23.06  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.06  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.06  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 153.68/23.06  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.68/23.06  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.68/23.06  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 153.68/23.06  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 153.68/23.06  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 153.68/23.06  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 153.68/23.06  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 153.68/23.06  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.68/23.06  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 153.68/23.06  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.68/23.06  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.68/23.06  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.68/23.06  | | |           $i(all_57_13))
% 153.68/23.06  | | | 
% 153.68/23.06  | | | BETA: splitting (36) gives:
% 153.68/23.06  | | | 
% 153.68/23.06  | | | Case 1:
% 153.68/23.06  | | | | 
% 153.68/23.07  | | | |   (37)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.68/23.07  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.68/23.07  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.07  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.68/23.07  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.68/23.07  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.68/23.07  | | | |           e2 & $i(all_57_6) & $i(all_57_12))
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | | REF_CLOSE: (2), (5), (19), (20), (22), (37) are inconsistent by
% 153.68/23.07  | | | |            sub-proof #860.
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | Case 2:
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | |   (38)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.68/23.07  | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.68/23.07  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.68/23.07  | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 153.68/23.07  | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 153.68/23.07  | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 153.68/23.07  | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.68/23.07  | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 153.68/23.07  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 153.68/23.07  | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | | REF_CLOSE: (5), (7), (11), (14), (23), (38) are inconsistent by
% 153.68/23.07  | | | |            sub-proof #976.
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | End of split
% 153.68/23.07  | | | 
% 153.68/23.07  | | Case 2:
% 153.68/23.07  | | | 
% 153.68/23.07  | | |   (39)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.68/23.07  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.07  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.68/23.07  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.68/23.07  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.68/23.07  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.68/23.07  | | |           $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0
% 153.68/23.07  | | |           &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.68/23.07  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.68/23.07  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.68/23.07  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.68/23.07  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.68/23.07  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.68/23.07  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.68/23.07  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.68/23.07  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.07  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.68/23.07  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.68/23.07  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 153.68/23.07  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.68/23.07  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.68/23.07  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.68/23.07  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 153.68/23.07  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.68/23.07  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.07  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.68/23.07  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.68/23.07  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.68/23.07  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.68/23.07  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 153.68/23.07  | | | 
% 153.68/23.07  | | | BETA: splitting (39) gives:
% 153.68/23.07  | | | 
% 153.68/23.07  | | | Case 1:
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | |   (40)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.68/23.07  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.68/23.07  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.68/23.07  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.68/23.07  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.68/23.07  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.68/23.07  | | | |           e1 & $i(all_57_9) & $i(all_57_14))
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | | REF_CLOSE: (5), (12), (22), (40) are inconsistent by sub-proof #975.
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | Case 2:
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | |   (41)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.68/23.07  | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.68/23.07  | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.68/23.07  | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 153.68/23.07  | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.68/23.07  | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.68/23.07  | | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 153.68/23.07  | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 153.68/23.07  | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.68/23.07  | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.07  | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.68/23.07  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.68/23.07  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.68/23.07  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.68/23.07  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.68/23.07  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.68/23.07  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.07  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.68/23.07  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.68/23.07  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.68/23.07  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.68/23.07  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.68/23.07  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.68/23.07  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | | BETA: splitting (41) gives:
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | | Case 1:
% 153.68/23.07  | | | | | 
% 153.68/23.07  | | | | |   (42)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.68/23.07  | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.68/23.07  | | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.68/23.07  | | | | |         $i(all_57_13)
% 153.68/23.07  | | | | | 
% 153.68/23.07  | | | | | ALPHA: (42) implies:
% 153.68/23.07  | | | | |   (43)  op(e2, e0) = e2
% 153.68/23.07  | | | | | 
% 153.68/23.07  | | | | | REF_CLOSE: (5), (9), (15), (43) are inconsistent by sub-proof #1156.
% 153.68/23.07  | | | | | 
% 153.68/23.07  | | | | Case 2:
% 153.68/23.07  | | | | | 
% 153.68/23.07  | | | | |   (44)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.68/23.07  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.68/23.07  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.68/23.07  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.68/23.07  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.68/23.07  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 153.68/23.07  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.68/23.07  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.68/23.07  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.68/23.07  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.68/23.07  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 153.68/23.07  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.68/23.07  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.68/23.07  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.68/23.07  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.68/23.07  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.07  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.68/23.07  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.68/23.07  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.68/23.07  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.68/23.07  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.07  | | | | |               $i(all_57_7))))
% 153.68/23.07  | | | | | 
% 153.68/23.07  | | | | | BETA: splitting (44) gives:
% 153.68/23.07  | | | | | 
% 153.68/23.07  | | | | | Case 1:
% 153.68/23.07  | | | | | | 
% 153.68/23.07  | | | | | |   (45)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.68/23.07  | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.68/23.07  | | | | | |         & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.68/23.07  | | | | | |         $i(all_57_14)
% 153.68/23.07  | | | | | | 
% 153.68/23.07  | | | | | | ALPHA: (45) implies:
% 153.68/23.07  | | | | | |   (46)  op(e1, e0) = e1
% 153.68/23.07  | | | | | | 
% 153.68/23.07  | | | | | | REF_CLOSE: (5), (6), (8), (46) are inconsistent by sub-proof #961.
% 153.68/23.07  | | | | | | 
% 153.68/23.07  | | | | | Case 2:
% 153.68/23.07  | | | | | | 
% 153.68/23.07  | | | | | |   (47)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.68/23.07  | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.68/23.07  | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 153.68/23.07  | | | | | |               e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 153.68/23.07  | | | | | |             = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1,
% 153.68/23.07  | | | | | |               e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.68/23.07  | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.68/23.07  | | | | | |             (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.68/23.07  | | | | | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.68/23.07  | | | | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.68/23.07  | | | | | |             (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.68/23.07  | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.68/23.07  | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.68/23.07  | | | | | |             (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.68/23.07  | | | | | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.68/23.07  | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.68/23.07  | | | | | |             (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.68/23.07  | | | | | |             & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.07  | | | | | |             $i(all_57_7)))
% 153.68/23.07  | | | | | | 
% 153.68/23.07  | | | | | | ALPHA: (47) implies:
% 153.68/23.07  | | | | | |   (48)  op(e0, e0) = all_57_15
% 153.68/23.07  | | | | | |   (49)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.68/23.07  | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 153.68/23.07  | | | | | |           & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.68/23.07  | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 153.68/23.07  | | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 153.68/23.07  | | | | | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.68/23.07  | | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.68/23.07  | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.68/23.07  | | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.07  | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.68/23.07  | | | | | |           & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.68/23.07  | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.68/23.07  | | | | | |           & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.68/23.07  | | | | | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.68/23.07  | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.68/23.07  | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.68/23.07  | | | | | | 
% 153.68/23.07  | | | | | | BETA: splitting (49) gives:
% 153.68/23.07  | | | | | | 
% 153.68/23.07  | | | | | | Case 1:
% 153.68/23.07  | | | | | | | 
% 153.68/23.07  | | | | | | |   (50)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.68/23.07  | | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 153.68/23.07  | | | | | | |           e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.68/23.07  | | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.68/23.07  | | | | | | |             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.68/23.07  | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.68/23.07  | | | | | | |           = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 153.68/23.07  | | | | | | |             e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.68/23.07  | | | | | | |           $i(all_57_3))
% 153.68/23.07  | | | | | | | 
% 153.68/23.07  | | | | | | | REF_CLOSE: (2), (5), (7), (12), (16), (26), (48), (50) are
% 153.68/23.07  | | | | | | |            inconsistent by sub-proof #717.
% 153.68/23.07  | | | | | | | 
% 153.68/23.07  | | | | | | Case 2:
% 153.68/23.07  | | | | | | | 
% 153.68/23.07  | | | | | | |   (51)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.07  | | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.68/23.07  | | | | | | |           e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.68/23.07  | | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.68/23.07  | | | | | | |             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.68/23.07  | | | | | | |             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 153.68/23.07  | | | | | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 153.68/23.07  | | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.68/23.07  | | | | | | |           $i(all_57_7))
% 153.68/23.07  | | | | | | | 
% 153.68/23.07  | | | | | | | BETA: splitting (51) gives:
% 153.68/23.07  | | | | | | | 
% 153.68/23.07  | | | | | | | Case 1:
% 153.68/23.07  | | | | | | | | 
% 153.68/23.07  | | | | | | | |   (52)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.68/23.07  | | | | | | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.68/23.07  | | | | | | | |         e2 & op(e0, e2) = e0 & $i(all_57_4)
% 153.68/23.07  | | | | | | | | 
% 153.68/23.07  | | | | | | | | ALPHA: (52) implies:
% 153.68/23.07  | | | | | | | |   (53)  op(e1, e1) = e2
% 153.68/23.07  | | | | | | | | 
% 153.68/23.07  | | | | | | | | REF_CLOSE: (4), (5), (16), (23), (53) are inconsistent by
% 153.68/23.07  | | | | | | | |            sub-proof #1044.
% 153.68/23.07  | | | | | | | | 
% 153.68/23.07  | | | | | | | Case 2:
% 153.68/23.07  | | | | | | | | 
% 153.68/23.07  | | | | | | | |   (54)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.68/23.07  | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.68/23.07  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 153.68/23.07  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.68/23.07  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.68/23.07  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.68/23.07  | | | | | | | | 
% 153.68/23.07  | | | | | | | | REF_CLOSE: (2), (5), (17), (22), (26), (54) are inconsistent by
% 153.68/23.07  | | | | | | | |            sub-proof #824.
% 153.68/23.07  | | | | | | | | 
% 153.68/23.07  | | | | | | | End of split
% 153.68/23.07  | | | | | | | 
% 153.68/23.07  | | | | | | End of split
% 153.68/23.07  | | | | | | 
% 153.68/23.07  | | | | | End of split
% 153.68/23.07  | | | | | 
% 153.68/23.07  | | | | End of split
% 153.68/23.07  | | | | 
% 153.68/23.07  | | | End of split
% 153.68/23.07  | | | 
% 153.68/23.07  | | End of split
% 153.68/23.07  | | 
% 153.68/23.07  | End of split
% 153.68/23.07  | 
% 153.68/23.07  End of proof
% 153.68/23.07  
% 153.68/23.07  Sub-proof #717 shows that the following formulas are inconsistent:
% 153.68/23.07  ----------------------------------------------------------------
% 153.68/23.07    (1)   ~ (e3 = e1)
% 153.68/23.07    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.07    (3)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.68/23.07             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.07           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.68/23.07           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.68/23.07             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.68/23.07           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.68/23.07           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.68/23.07    (4)  op(e0, e0) = e2
% 153.68/23.07    (5)   ~ (e3 = e0)
% 153.68/23.07    (6)  op(e1, e1) = e1
% 153.68/23.07    (7)  op(e0, e0) = all_57_15
% 153.68/23.07    (8)  op(e2, e2) = e0
% 153.68/23.07  
% 153.68/23.07  Begin of proof
% 153.68/23.07  | 
% 153.68/23.07  | BETA: splitting (3) gives:
% 153.68/23.07  | 
% 153.68/23.07  | Case 1:
% 153.68/23.07  | | 
% 153.68/23.07  | |   (9)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.68/23.07  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.68/23.07  | |        $i(all_57_0)
% 153.68/23.07  | | 
% 153.68/23.07  | | ALPHA: (9) implies:
% 153.68/23.07  | |   (10)  op(e2, e2) = e3
% 153.68/23.07  | | 
% 153.68/23.07  | | REF_CLOSE: (2), (5), (8), (10) are inconsistent by sub-proof #719.
% 153.68/23.07  | | 
% 153.68/23.07  | Case 2:
% 153.68/23.07  | | 
% 153.68/23.07  | |   (11)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 153.68/23.07  | |             = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 153.68/23.07  | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.68/23.07  | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 153.68/23.07  | |             e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.68/23.07  | | 
% 153.68/23.07  | | REF_CLOSE: (1), (2), (4), (6), (7), (11) are inconsistent by sub-proof #718.
% 153.68/23.07  | | 
% 153.68/23.07  | End of split
% 153.68/23.07  | 
% 153.68/23.07  End of proof
% 153.68/23.07  
% 153.68/23.07  Sub-proof #718 shows that the following formulas are inconsistent:
% 153.68/23.07  ----------------------------------------------------------------
% 153.68/23.07    (1)   ~ (e3 = e1)
% 153.68/23.07    (2)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.68/23.07             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.68/23.07           $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.68/23.07           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 153.68/23.07             e2) = e0 & $i(all_57_3))
% 153.68/23.07    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.07    (4)  op(e0, e0) = e2
% 153.68/23.07    (5)  op(e1, e1) = e1
% 153.68/23.07    (6)  op(e0, e0) = all_57_15
% 153.68/23.07  
% 153.68/23.07  Begin of proof
% 153.68/23.07  | 
% 153.68/23.07  | BETA: splitting (2) gives:
% 153.68/23.07  | 
% 153.68/23.07  | Case 1:
% 153.68/23.07  | | 
% 153.68/23.07  | |   (7)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.68/23.07  | |          e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.68/23.07  | |        $i(all_57_1)
% 153.68/23.07  | | 
% 153.68/23.07  | | ALPHA: (7) implies:
% 153.68/23.07  | |   (8)  op(e1, e1) = e3
% 153.68/23.07  | | 
% 153.68/23.07  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #734.
% 153.68/23.07  | | 
% 153.68/23.07  | Case 2:
% 153.68/23.07  | | 
% 153.68/23.07  | |   (9)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 153.68/23.07  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.68/23.07  | |        $i(all_57_3)
% 153.68/23.07  | | 
% 153.68/23.07  | | ALPHA: (9) implies:
% 153.68/23.07  | |   (10)   ~ (all_57_15 = e2)
% 153.68/23.07  | | 
% 153.68/23.07  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #901.
% 153.68/23.07  | | 
% 153.68/23.07  | End of split
% 153.68/23.07  | 
% 153.68/23.07  End of proof
% 153.68/23.07  
% 153.68/23.07  Sub-proof #719 shows that the following formulas are inconsistent:
% 153.68/23.07  ----------------------------------------------------------------
% 153.68/23.07    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.07    (2)  op(e2, e2) = e3
% 153.68/23.07    (3)  op(e2, e2) = e0
% 153.68/23.07    (4)   ~ (e3 = e0)
% 153.68/23.07  
% 153.68/23.07  Begin of proof
% 153.68/23.07  | 
% 153.68/23.07  | GROUND_INST: instantiating (1) with e0, e3, e2, e2, simplifying with (2), (3)
% 153.68/23.07  |              gives:
% 153.68/23.07  |   (5)  e3 = e0
% 153.68/23.07  | 
% 153.68/23.07  | REDUCE: (4), (5) imply:
% 153.68/23.07  |   (6)  $false
% 153.68/23.07  | 
% 153.68/23.07  | CLOSE: (6) is inconsistent.
% 153.68/23.07  | 
% 153.68/23.07  End of proof
% 153.68/23.07  
% 153.68/23.07  Sub-proof #720 shows that the following formulas are inconsistent:
% 153.68/23.07  ----------------------------------------------------------------
% 153.68/23.07    (1)   ~ (all_52_6 = e1)
% 153.68/23.07    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.07    (3)  op(e1, e2) = all_52_6
% 153.68/23.07    (4)   ~ (e1 = e0)
% 153.68/23.07    (5)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.68/23.07             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.68/23.07           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.68/23.07           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.68/23.07           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 153.68/23.07           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.68/23.07    (6)  op(e2, e2) = e0
% 153.68/23.07  
% 153.68/23.07  Begin of proof
% 153.68/23.07  | 
% 153.68/23.07  | BETA: splitting (5) gives:
% 153.68/23.07  | 
% 153.68/23.07  | Case 1:
% 153.68/23.07  | | 
% 153.68/23.07  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 153.68/23.07  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.68/23.07  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 153.68/23.07  | | 
% 153.68/23.07  | | ALPHA: (7) implies:
% 153.68/23.07  | |   (8)  op(e1, e2) = e1
% 153.68/23.07  | | 
% 153.68/23.07  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1042.
% 153.68/23.07  | | 
% 153.68/23.07  | Case 2:
% 153.68/23.07  | | 
% 153.68/23.07  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 153.68/23.07  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.68/23.07  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 153.68/23.07  | | 
% 153.68/23.07  | | ALPHA: (9) implies:
% 153.68/23.07  | |   (10)  op(e2, e2) = e1
% 153.68/23.07  | | 
% 153.68/23.07  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #853.
% 153.68/23.07  | | 
% 153.68/23.07  | End of split
% 153.68/23.07  | 
% 153.68/23.07  End of proof
% 153.68/23.07  
% 153.68/23.07  Sub-proof #721 shows that the following formulas are inconsistent:
% 153.68/23.07  ----------------------------------------------------------------
% 153.68/23.07    (1)  op(e3, e2) = all_52_4
% 153.68/23.07    (2)  op(e1, e1) = all_4_2
% 153.68/23.07    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.07    (4)   ~ (all_52_4 = e3)
% 153.68/23.07    (5)  op(e1, e1) = e1
% 153.68/23.07    (6)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.68/23.07             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.68/23.07           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 153.68/23.07           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.68/23.07           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.68/23.07           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.68/23.07    (7)   ~ (e2 = e1)
% 153.68/23.07  
% 153.68/23.07  Begin of proof
% 153.68/23.07  | 
% 153.68/23.07  | BETA: splitting (6) gives:
% 153.68/23.07  | 
% 153.68/23.07  | Case 1:
% 153.68/23.07  | | 
% 153.68/23.07  | |   (8)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.68/23.07  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.68/23.07  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 153.68/23.07  | | 
% 153.68/23.07  | | ALPHA: (8) implies:
% 153.68/23.07  | |   (9)  op(e1, e1) = e2
% 153.68/23.07  | | 
% 153.68/23.07  | | REF_CLOSE: (2), (3), (5), (7), (9) are inconsistent by sub-proof #1044.
% 153.68/23.07  | | 
% 153.68/23.07  | Case 2:
% 153.68/23.07  | | 
% 153.68/23.07  | |   (10)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 153.68/23.07  | |           = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.68/23.07  | |         all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 153.68/23.07  | | 
% 153.68/23.07  | | ALPHA: (10) implies:
% 153.68/23.07  | |   (11)  op(e3, e2) = e3
% 153.68/23.07  | | 
% 153.68/23.07  | | REF_CLOSE: (1), (3), (4), (11) are inconsistent by sub-proof #1166.
% 153.68/23.07  | | 
% 153.68/23.07  | End of split
% 153.68/23.07  | 
% 153.68/23.07  End of proof
% 153.68/23.07  
% 153.68/23.07  Sub-proof #722 shows that the following formulas are inconsistent:
% 153.68/23.07  ----------------------------------------------------------------
% 153.68/23.07    (1)   ~ (e3 = e1)
% 153.68/23.07    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.68/23.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.68/23.07    (3)  op(e0, e0) = e2
% 153.68/23.07    (4)  op(e1, e1) = e1
% 153.68/23.07    (5)   ~ (e3 = e2)
% 153.68/23.07    (6)   ~ (all_52_2 = e1)
% 153.68/23.07    (7)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.68/23.07             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.68/23.07           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.68/23.07           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.68/23.07           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.68/23.07           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.68/23.07           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.68/23.07           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 153.68/23.07           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.68/23.07           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 153.68/23.07           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.68/23.07           $i(all_57_14))
% 153.68/23.07    (8)  op(e1, e3) = all_52_2
% 153.68/23.07  
% 153.68/23.07  Begin of proof
% 153.68/23.07  | 
% 153.68/23.07  | BETA: splitting (7) gives:
% 153.68/23.07  | 
% 153.68/23.07  | Case 1:
% 153.68/23.07  | | 
% 153.68/23.07  | |   (9)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 153.68/23.07  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.68/23.07  | |          all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 153.68/23.07  | |        (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 153.68/23.07  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.68/23.07  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.68/23.07  | | 
% 153.68/23.07  | | BETA: splitting (9) gives:
% 153.68/23.07  | | 
% 153.68/23.07  | | Case 1:
% 153.68/23.07  | | | 
% 153.68/23.07  | | |   (10)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.68/23.07  | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.68/23.07  | | |         op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.68/23.07  | | |         $i(all_57_12)
% 153.68/23.07  | | | 
% 153.68/23.07  | | | ALPHA: (10) implies:
% 153.68/23.07  | | |   (11)  op(e1, e1) = e3
% 153.68/23.07  | | | 
% 153.68/23.07  | | | REF_CLOSE: (1), (2), (4), (11) are inconsistent by sub-proof #734.
% 153.68/23.07  | | | 
% 153.68/23.07  | | Case 2:
% 153.68/23.07  | | | 
% 153.68/23.07  | | |   (12)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.68/23.07  | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.68/23.07  | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.68/23.07  | | |         $i(all_57_12)
% 153.68/23.07  | | | 
% 153.68/23.07  | | | ALPHA: (12) implies:
% 153.68/23.07  | | |   (13)  op(e0, e0) = e3
% 153.68/23.07  | | | 
% 153.68/23.07  | | | REF_CLOSE: (2), (3), (5), (13) are inconsistent by sub-proof #1087.
% 153.68/23.07  | | | 
% 153.68/23.07  | | End of split
% 153.68/23.07  | | 
% 153.68/23.07  | Case 2:
% 153.68/23.07  | | 
% 153.83/23.07  | |   (14)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 153.83/23.07  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 153.83/23.07  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.83/23.07  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 153.83/23.07  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.83/23.07  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.83/23.07  | | 
% 153.83/23.07  | | REF_CLOSE: (2), (3), (5), (6), (8), (14) are inconsistent by sub-proof #723.
% 153.83/23.07  | | 
% 153.83/23.07  | End of split
% 153.83/23.07  | 
% 153.83/23.07  End of proof
% 153.83/23.07  
% 153.83/23.07  Sub-proof #723 shows that the following formulas are inconsistent:
% 153.83/23.07  ----------------------------------------------------------------
% 153.83/23.07    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.07    (2)  op(e0, e0) = e2
% 153.83/23.07    (3)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.83/23.07             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.83/23.07           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 153.83/23.07           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 153.83/23.07             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 153.83/23.07             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.83/23.07    (4)   ~ (e3 = e2)
% 153.83/23.07    (5)   ~ (all_52_2 = e1)
% 153.83/23.07    (6)  op(e1, e3) = all_52_2
% 153.83/23.07  
% 153.83/23.07  Begin of proof
% 153.83/23.07  | 
% 153.83/23.07  | BETA: splitting (3) gives:
% 153.83/23.07  | 
% 153.83/23.07  | Case 1:
% 153.83/23.07  | | 
% 153.83/23.07  | |   (7)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.83/23.07  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.83/23.07  | |        op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 153.83/23.07  | | 
% 153.83/23.07  | | ALPHA: (7) implies:
% 153.83/23.07  | |   (8)  op(e1, e3) = e1
% 153.83/23.07  | | 
% 153.83/23.07  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #1046.
% 153.83/23.07  | | 
% 153.83/23.07  | Case 2:
% 153.83/23.07  | | 
% 153.83/23.07  | |   (9)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 153.83/23.07  | |          e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.83/23.07  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 153.83/23.07  | | 
% 153.83/23.07  | | ALPHA: (9) implies:
% 153.83/23.07  | |   (10)  op(e0, e0) = e3
% 153.83/23.07  | | 
% 153.83/23.07  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #1087.
% 153.83/23.07  | | 
% 153.83/23.07  | End of split
% 153.83/23.07  | 
% 153.83/23.07  End of proof
% 153.83/23.07  
% 153.83/23.07  Sub-proof #724 shows that the following formulas are inconsistent:
% 153.83/23.07  ----------------------------------------------------------------
% 153.83/23.07    (1)  all_56_6 = e2
% 153.83/23.07    (2)  all_56_6 = e0
% 153.83/23.07    (3)   ~ (e2 = e0)
% 153.83/23.07  
% 153.83/23.07  Begin of proof
% 153.83/23.07  | 
% 153.83/23.07  | COMBINE_EQS: (1), (2) imply:
% 153.83/23.07  |   (4)  e2 = e0
% 153.83/23.07  | 
% 153.83/23.07  | SIMP: (4) implies:
% 153.83/23.07  |   (5)  e2 = e0
% 153.83/23.07  | 
% 153.83/23.07  | REDUCE: (3), (5) imply:
% 153.83/23.07  |   (6)  $false
% 153.83/23.07  | 
% 153.83/23.07  | CLOSE: (6) is inconsistent.
% 153.83/23.07  | 
% 153.83/23.07  End of proof
% 153.83/23.07  
% 153.83/23.07  Sub-proof #725 shows that the following formulas are inconsistent:
% 153.83/23.07  ----------------------------------------------------------------
% 153.83/23.07    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 153.83/23.07    (2)   ~ (e2 = e0)
% 153.83/23.07    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.07           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.07    (4)   ~ (e3 = e0)
% 153.83/23.07    (5)  all_56_2 = e2
% 153.83/23.07    (6)  op(e3, e3) = e3
% 153.83/23.07  
% 153.83/23.07  Begin of proof
% 153.83/23.07  | 
% 153.83/23.07  | BETA: splitting (1) gives:
% 153.83/23.07  | 
% 153.83/23.07  | Case 1:
% 153.83/23.07  | | 
% 153.83/23.07  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 153.83/23.07  | | 
% 153.83/23.07  | | ALPHA: (7) implies:
% 153.83/23.07  | |   (8)  op(e3, e3) = e0
% 153.83/23.07  | | 
% 153.83/23.07  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #1141.
% 153.83/23.07  | | 
% 153.83/23.07  | Case 2:
% 153.83/23.07  | | 
% 153.83/23.07  | |   (9)  all_56_2 = e0 & op(e2, e3) = e0
% 153.83/23.07  | | 
% 153.83/23.07  | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #726.
% 153.83/23.07  | | 
% 153.83/23.07  | End of split
% 153.83/23.07  | 
% 153.83/23.07  End of proof
% 153.83/23.07  
% 153.83/23.07  Sub-proof #726 shows that the following formulas are inconsistent:
% 153.83/23.07  ----------------------------------------------------------------
% 153.83/23.07    (1)  all_56_2 = e0 & op(e2, e3) = e0
% 153.83/23.07    (2)  all_56_2 = e2
% 153.83/23.07    (3)   ~ (e2 = e0)
% 153.83/23.07  
% 153.83/23.07  Begin of proof
% 153.83/23.07  | 
% 153.83/23.07  | ALPHA: (1) implies:
% 153.83/23.07  |   (4)  all_56_2 = e0
% 153.83/23.07  | 
% 153.83/23.07  | COMBINE_EQS: (2), (4) imply:
% 153.83/23.07  |   (5)  e2 = e0
% 153.83/23.07  | 
% 153.83/23.07  | REDUCE: (3), (5) imply:
% 153.83/23.07  |   (6)  $false
% 153.83/23.07  | 
% 153.83/23.07  | CLOSE: (6) is inconsistent.
% 153.83/23.07  | 
% 153.83/23.07  End of proof
% 153.83/23.07  
% 153.83/23.07  Sub-proof #727 shows that the following formulas are inconsistent:
% 153.83/23.07  ----------------------------------------------------------------
% 153.83/23.07    (1)   ~ (all_14_2 = e0)
% 153.83/23.08    (2)  op(e3, e3) = all_14_2
% 153.83/23.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (4)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.83/23.08             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.83/23.08           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.83/23.08           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.83/23.08           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.83/23.08           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 153.83/23.08    (5)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.83/23.08    (6)  all_54_0 = all_14_2
% 153.83/23.08    (7)   ~ (all_14_2 = e2)
% 153.83/23.08    (8)   ~ (all_52_8 = e3)
% 153.83/23.08    (9)   ~ (all_14_2 = e1)
% 153.83/23.08    (10)  op(e3, e1) = all_52_8
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (4) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (11)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 153.83/23.08  | |           = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.83/23.08  | |         all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (11) implies:
% 153.83/23.08  | |   (12)  op(e3, e1) = e3
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (3), (8), (10), (12) are inconsistent by sub-proof #1164.
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (13)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 153.83/23.08  | |           = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.83/23.08  | |         all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (13) implies:
% 153.83/23.08  | |   (14)  op(e3, e3) = e1
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (14) are inconsistent by
% 153.83/23.08  | |            sub-proof #728.
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #728 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)   ~ (all_14_2 = e0)
% 153.83/23.08    (2)  op(e3, e3) = all_14_2
% 153.83/23.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (4)  op(e3, e3) = e1
% 153.83/23.08    (5)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.83/23.08    (6)  all_54_0 = all_14_2
% 153.83/23.08    (7)   ~ (all_14_2 = e2)
% 153.83/23.08    (8)   ~ (all_14_2 = e1)
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (5) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (9)  all_54_0 = e3
% 153.83/23.08  | | 
% 153.83/23.08  | | COMBINE_EQS: (6), (9) imply:
% 153.83/23.08  | |   (10)  all_14_2 = e3
% 153.83/23.08  | | 
% 153.83/23.08  | | REDUCE: (8), (10) imply:
% 153.83/23.08  | |   (11)   ~ (e3 = e1)
% 153.83/23.08  | | 
% 153.83/23.08  | | REDUCE: (2), (10) imply:
% 153.83/23.08  | |   (12)  op(e3, e3) = e3
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (3), (4), (11), (12) are inconsistent by sub-proof #1178.
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (13)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (1), (6), (7), (8), (13) are inconsistent by sub-proof #1140.
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #729 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)   ~ (all_52_6 = e1)
% 153.83/23.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (3)  op(e1, e2) = all_52_6
% 153.83/23.08    (4)   ~ (e3 = e2)
% 153.83/23.08    (5)   ~ (all_52_8 = e3)
% 153.83/23.08    (6)  op(e3, e1) = all_52_8
% 153.83/23.08    (7)  op(e3, e3) = e3
% 153.83/23.08    (8)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.83/23.08             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.83/23.08           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 153.83/23.08           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 153.83/23.08             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 153.83/23.08             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.83/23.08           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.83/23.08           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.83/23.08           $i(all_57_7) & $i(all_57_10))
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (8) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (9)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 153.83/23.08  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 153.83/23.08  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (9) implies:
% 153.83/23.08  | |   (10)  op(e3, e3) = e2
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (2), (4), (7), (10) are inconsistent by sub-proof #1085.
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (11)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.83/23.08  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.83/23.08  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.83/23.08  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.83/23.08  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.83/23.08  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.83/23.08  | | 
% 153.83/23.08  | | BETA: splitting (11) gives:
% 153.83/23.08  | | 
% 153.83/23.08  | | Case 1:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (12)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.83/23.08  | | |         (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.83/23.08  | | |         op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.83/23.08  | | |         $i(all_57_14)
% 153.83/23.08  | | | 
% 153.83/23.08  | | | ALPHA: (12) implies:
% 153.83/23.08  | | |   (13)  op(e1, e2) = e1
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (1), (2), (3), (13) are inconsistent by sub-proof #1042.
% 153.83/23.08  | | | 
% 153.83/23.08  | | Case 2:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (14)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.83/23.08  | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.83/23.08  | | |         op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.83/23.08  | | |         $i(all_57_10)
% 153.83/23.08  | | | 
% 153.83/23.08  | | | ALPHA: (14) implies:
% 153.83/23.08  | | |   (15)  op(e3, e1) = e3
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (2), (5), (6), (15) are inconsistent by sub-proof #1164.
% 153.83/23.08  | | | 
% 153.83/23.08  | | End of split
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #730 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)   ~ (e3 = e1)
% 153.83/23.08    (2)  op(e2, e2) = e1
% 153.83/23.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (4)  op(e0, e0) = e2
% 153.83/23.08    (5)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.83/23.08             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.83/23.08           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 153.83/23.08           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 153.83/23.08             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 153.83/23.08             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.83/23.08    (6)   ~ (e3 = e2)
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (5) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (7)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 153.83/23.08  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.83/23.08  | |        op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (7) implies:
% 153.83/23.08  | |   (8)  op(e2, e2) = e3
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1136.
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (9)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 153.83/23.08  | |          e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.83/23.08  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (9) implies:
% 153.83/23.08  | |   (10)  op(e0, e0) = e3
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #1087.
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #731 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  op(e0, e1) = all_52_11
% 153.83/23.08    (2)  op(e0, e1) = e1
% 153.83/23.08    (3)  all_54_14 = all_52_11
% 153.83/23.08    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (5)   ~ (all_52_11 = e3)
% 153.83/23.08    (6)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.83/23.08    (7)   ~ (all_52_11 = e1)
% 153.83/23.08    (8)   ~ (all_52_11 = e2)
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (6) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (9)  all_54_14 = e3
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #903.
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (10)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.83/23.08  | | 
% 153.83/23.08  | | BETA: splitting (10) gives:
% 153.83/23.08  | | 
% 153.83/23.08  | | Case 1:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (11)  all_54_14 = e2
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (3), (8), (11) are inconsistent by sub-proof #902.
% 153.83/23.08  | | | 
% 153.83/23.08  | | Case 2:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (12)  all_54_14 = e1 | all_54_14 = e0
% 153.83/23.08  | | | 
% 153.83/23.08  | | | BETA: splitting (12) gives:
% 153.83/23.08  | | | 
% 153.83/23.08  | | | Case 1:
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | |   (13)  all_54_14 = e1
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | | REF_CLOSE: (3), (7), (13) are inconsistent by sub-proof #753.
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | Case 2:
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | |   (14)  all_54_14 = e0
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | | COMBINE_EQS: (3), (14) imply:
% 153.83/23.08  | | | |   (15)  all_52_11 = e0
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | | SIMP: (15) implies:
% 153.83/23.08  | | | |   (16)  all_52_11 = e0
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | | REDUCE: (7), (16) imply:
% 153.83/23.08  | | | |   (17)   ~ (e1 = e0)
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | | SIMP: (17) implies:
% 153.83/23.08  | | | |   (18)   ~ (e1 = e0)
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | | REDUCE: (1), (16) imply:
% 153.83/23.08  | | | |   (19)  op(e0, e1) = e0
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | | REF_CLOSE: (2), (4), (18), (19) are inconsistent by sub-proof #899.
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | End of split
% 153.83/23.08  | | | 
% 153.83/23.08  | | End of split
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #732 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.83/23.08    (2)   ~ (e3 = e1)
% 153.83/23.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (4)  op(e0, e0) = e3
% 153.83/23.08    (5)   ~ (all_52_14 = e1)
% 153.83/23.08    (6)  op(e1, e0) = all_52_14
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (1) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (7)  all_56_11 = e1 & op(e1, e0) = e1
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (7) implies:
% 153.83/23.08  | |   (8)  op(e1, e0) = e1
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #961.
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (9)  all_56_15 = e1 & op(e0, e0) = e1
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (9) implies:
% 153.83/23.08  | |   (10)  op(e0, e0) = e1
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #1022.
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #733 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  op(e0, e1) = all_52_11
% 153.83/23.08    (2)   ~ (e3 = e1)
% 153.83/23.08    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (4)   ~ (all_52_11 = e3)
% 153.83/23.08    (5)  op(e1, e1) = e1
% 153.83/23.08    (6)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (6) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (7)  all_56_8 = e3 & op(e1, e1) = e3
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (7) implies:
% 153.83/23.08  | |   (8)  op(e1, e1) = e3
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #734.
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (9)  all_56_14 = e3 & op(e0, e1) = e3
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (9) implies:
% 153.83/23.08  | |   (10)  op(e0, e1) = e3
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1147.
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #734 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (2)  op(e1, e1) = e3
% 153.83/23.08    (3)  op(e1, e1) = e1
% 153.83/23.08    (4)   ~ (e3 = e1)
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | GROUND_INST: instantiating (1) with e3, e1, e1, e1, simplifying with (2), (3)
% 153.83/23.08  |              gives:
% 153.83/23.08  |   (5)  e3 = e1
% 153.83/23.08  | 
% 153.83/23.08  | REDUCE: (4), (5) imply:
% 153.83/23.08  |   (6)  $false
% 153.83/23.08  | 
% 153.83/23.08  | CLOSE: (6) is inconsistent.
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #735 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)   ~ (e2 = e0)
% 153.83/23.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (3)  op(e3, e3) = e2
% 153.83/23.08    (4)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 153.83/23.08    (5)  ( ~ (all_36_0 = e1) & op(all_36_1, e3) = all_36_0 & op(e3, e2) = all_36_1
% 153.83/23.08           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e3, e2) =
% 153.83/23.08           all_36_1 & $i(all_36_1))
% 153.83/23.08    (6)  op(e0, e3) = e1
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (4) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (7) implies:
% 153.83/23.08  | |   (8)  op(e3, e3) = e0
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1073.
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (9)  all_56_1 = e0 & op(e3, e2) = e0
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (9) implies:
% 153.83/23.08  | |   (10)  op(e3, e2) = e0
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #767.
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #736 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  op(e2, e2) = e1
% 153.83/23.08    (2)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.83/23.08         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.83/23.08    (3)   ~ (e2 = e0)
% 153.83/23.08    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (5)  all_56_13 = e1
% 153.83/23.08    (6)   ~ (e3 = e0)
% 153.83/23.08    (7)  all_56_3 = e1
% 153.83/23.08    (8)   ~ (e1 = e0)
% 153.83/23.08    (9)   ~ (e3 = e2)
% 153.83/23.08    (10)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.83/23.08          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.83/23.08    (11)   ~ (e2 = e1)
% 153.83/23.08    (12)  all_56_1 = e3
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (10) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (13)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 153.83/23.08  | |           e0)
% 153.83/23.08  | | 
% 153.83/23.08  | | BETA: splitting (13) gives:
% 153.83/23.08  | | 
% 153.83/23.08  | | Case 1:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (14)  all_56_1 = e0 & op(e3, e2) = e0
% 153.83/23.08  | | | 
% 153.83/23.08  | | | ALPHA: (14) implies:
% 153.83/23.08  | | |   (15)  all_56_1 = e0
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (6), (12), (15) are inconsistent by sub-proof #1065.
% 153.83/23.08  | | | 
% 153.83/23.08  | | Case 2:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (16)  all_56_3 = e0 & op(e2, e2) = e0
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (7), (8), (16) are inconsistent by sub-proof #741.
% 153.83/23.08  | | | 
% 153.83/23.08  | | End of split
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (17)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 153.83/23.08  | |           e0)
% 153.83/23.08  | | 
% 153.83/23.08  | | BETA: splitting (17) gives:
% 153.83/23.08  | | 
% 153.83/23.08  | | Case 1:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (18)  all_56_7 = e0 & op(e1, e2) = e0
% 153.83/23.08  | | | 
% 153.83/23.08  | | | ALPHA: (18) implies:
% 153.83/23.08  | | |   (19)  all_56_7 = e0
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (1), (2), (3), (4), (5), (9), (11), (12), (19) are inconsistent
% 153.83/23.08  | | |            by sub-proof #738.
% 153.83/23.08  | | | 
% 153.83/23.08  | | Case 2:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (20)  all_56_13 = e0 & op(e0, e2) = e0
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (5), (8), (20) are inconsistent by sub-proof #737.
% 153.83/23.08  | | | 
% 153.83/23.08  | | End of split
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #737 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  all_56_13 = e0 & op(e0, e2) = e0
% 153.83/23.08    (2)  all_56_13 = e1
% 153.83/23.08    (3)   ~ (e1 = e0)
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | ALPHA: (1) implies:
% 153.83/23.08  |   (4)  all_56_13 = e0
% 153.83/23.08  | 
% 153.83/23.08  | COMBINE_EQS: (2), (4) imply:
% 153.83/23.08  |   (5)  e1 = e0
% 153.83/23.08  | 
% 153.83/23.08  | REDUCE: (3), (5) imply:
% 153.83/23.08  |   (6)  $false
% 153.83/23.08  | 
% 153.83/23.08  | CLOSE: (6) is inconsistent.
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #738 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  op(e2, e2) = e1
% 153.83/23.08    (2)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.83/23.08         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.83/23.08    (3)   ~ (e2 = e0)
% 153.83/23.08    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (5)  all_56_13 = e1
% 153.83/23.08    (6)   ~ (e3 = e2)
% 153.83/23.08    (7)  all_56_7 = e0
% 153.83/23.08    (8)   ~ (e2 = e1)
% 153.83/23.08    (9)  all_56_1 = e3
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (2) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (10)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 153.83/23.08  | |           e2)
% 153.83/23.08  | | 
% 153.83/23.08  | | BETA: splitting (10) gives:
% 153.83/23.08  | | 
% 153.83/23.08  | | Case 1:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (11)  all_56_1 = e2 & op(e3, e2) = e2
% 153.83/23.08  | | | 
% 153.83/23.08  | | | ALPHA: (11) implies:
% 153.83/23.08  | | |   (12)  all_56_1 = e2
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (6), (9), (12) are inconsistent by sub-proof #950.
% 153.83/23.08  | | | 
% 153.83/23.08  | | Case 2:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (13)  all_56_3 = e2 & op(e2, e2) = e2
% 153.83/23.08  | | | 
% 153.83/23.08  | | | ALPHA: (13) implies:
% 153.83/23.08  | | |   (14)  op(e2, e2) = e2
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (1), (4), (8), (14) are inconsistent by sub-proof #1158.
% 153.83/23.08  | | | 
% 153.83/23.08  | | End of split
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (15)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 153.83/23.08  | |           e2)
% 153.83/23.08  | | 
% 153.83/23.08  | | BETA: splitting (15) gives:
% 153.83/23.08  | | 
% 153.83/23.08  | | Case 1:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (16)  all_56_7 = e2 & op(e1, e2) = e2
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (3), (7), (16) are inconsistent by sub-proof #740.
% 153.83/23.08  | | | 
% 153.83/23.08  | | Case 2:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (17)  all_56_13 = e2 & op(e0, e2) = e2
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (5), (8), (17) are inconsistent by sub-proof #739.
% 153.83/23.08  | | | 
% 153.83/23.08  | | End of split
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #739 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  all_56_13 = e2 & op(e0, e2) = e2
% 153.83/23.08    (2)  all_56_13 = e1
% 153.83/23.08    (3)   ~ (e2 = e1)
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | ALPHA: (1) implies:
% 153.83/23.08  |   (4)  all_56_13 = e2
% 153.83/23.08  | 
% 153.83/23.08  | COMBINE_EQS: (2), (4) imply:
% 153.83/23.08  |   (5)  e2 = e1
% 153.83/23.08  | 
% 153.83/23.08  | REDUCE: (3), (5) imply:
% 153.83/23.08  |   (6)  $false
% 153.83/23.08  | 
% 153.83/23.08  | CLOSE: (6) is inconsistent.
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #740 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  all_56_7 = e2 & op(e1, e2) = e2
% 153.83/23.08    (2)  all_56_7 = e0
% 153.83/23.08    (3)   ~ (e2 = e0)
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | ALPHA: (1) implies:
% 153.83/23.08  |   (4)  all_56_7 = e2
% 153.83/23.08  | 
% 153.83/23.08  | COMBINE_EQS: (2), (4) imply:
% 153.83/23.08  |   (5)  e2 = e0
% 153.83/23.08  | 
% 153.83/23.08  | REDUCE: (3), (5) imply:
% 153.83/23.08  |   (6)  $false
% 153.83/23.08  | 
% 153.83/23.08  | CLOSE: (6) is inconsistent.
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #741 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  all_56_3 = e0 & op(e2, e2) = e0
% 153.83/23.08    (2)  all_56_3 = e1
% 153.83/23.08    (3)   ~ (e1 = e0)
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | ALPHA: (1) implies:
% 153.83/23.08  |   (4)  all_56_3 = e0
% 153.83/23.08  | 
% 153.83/23.08  | COMBINE_EQS: (2), (4) imply:
% 153.83/23.08  |   (5)  e1 = e0
% 153.83/23.08  | 
% 153.83/23.08  | REDUCE: (3), (5) imply:
% 153.83/23.08  |   (6)  $false
% 153.83/23.08  | 
% 153.83/23.08  | CLOSE: (6) is inconsistent.
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #742 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.83/23.08    (2)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.83/23.08         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.83/23.08    (3)   ~ (e3 = e1)
% 153.83/23.08    (4)  all_56_10 = e3
% 153.83/23.08    (5)  op(e0, e0) = all_10_2
% 153.83/23.08    (6)   ~ (e2 = e0)
% 153.83/23.08    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (8)  op(e0, e0) = e3
% 153.83/23.08    (9)  op(e2, e0) = e3
% 153.83/23.08    (10)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.83/23.08              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.83/23.08                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.83/23.08                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.83/23.08    (11)   ~ (e3 = e0)
% 153.83/23.08    (12)   ~ (e1 = e0)
% 153.83/23.08    (13)   ~ (e3 = e2)
% 153.83/23.08    (14)   ~ (all_10_2 = e2)
% 153.83/23.08    (15)   ~ (e2 = e1)
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (1) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (16)  all_56_11 = e1 & op(e1, e0) = e1
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (16) implies:
% 153.83/23.08  | |   (17)  all_56_11 = e1
% 153.83/23.08  | |   (18)  op(e1, e0) = e1
% 153.83/23.08  | | 
% 153.83/23.08  | | BETA: splitting (10) gives:
% 153.83/23.08  | | 
% 153.83/23.08  | | Case 1:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (19)  all_56_15 = e0 & op(e0, e0) = e0
% 153.83/23.08  | | | 
% 153.83/23.08  | | | ALPHA: (19) implies:
% 153.83/23.08  | | |   (20)  op(e0, e0) = e0
% 153.83/23.08  | | | 
% 153.83/23.08  | | | REF_CLOSE: (7), (8), (11), (20) are inconsistent by sub-proof #1143.
% 153.83/23.08  | | | 
% 153.83/23.08  | | Case 2:
% 153.83/23.08  | | | 
% 153.83/23.08  | | |   (21)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0)
% 153.83/23.08  | | |             = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0
% 153.83/23.08  | | |             & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.83/23.08  | | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 153.83/23.08  | | | 
% 153.83/23.08  | | | ALPHA: (21) implies:
% 153.83/23.08  | | |   (22)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.83/23.08  | | |           e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.83/23.08  | | | 
% 153.83/23.08  | | | BETA: splitting (2) gives:
% 153.83/23.08  | | | 
% 153.83/23.08  | | | Case 1:
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | |   (23)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0)
% 153.83/23.08  | | | |           = e2)
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | | BETA: splitting (23) gives:
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | | Case 1:
% 153.83/23.08  | | | | | 
% 153.83/23.08  | | | | |   (24)  all_56_9 = e2 & op(e3, e0) = e2
% 153.83/23.08  | | | | | 
% 153.83/23.08  | | | | | ALPHA: (24) implies:
% 153.83/23.08  | | | | |   (25)  all_56_9 = e2
% 153.83/23.08  | | | | | 
% 153.83/23.08  | | | | | REF_CLOSE: (4), (6), (11), (12), (17), (22), (25) are inconsistent by
% 153.83/23.08  | | | | |            sub-proof #744.
% 153.83/23.08  | | | | | 
% 153.83/23.08  | | | | Case 2:
% 153.83/23.08  | | | | | 
% 153.83/23.08  | | | | |   (26)  all_56_10 = e2 & op(e2, e0) = e2
% 153.83/23.08  | | | | | 
% 153.83/23.08  | | | | | ALPHA: (26) implies:
% 153.83/23.08  | | | | |   (27)  op(e2, e0) = e2
% 153.83/23.08  | | | | | 
% 153.83/23.08  | | | | | REF_CLOSE: (7), (9), (13), (27) are inconsistent by sub-proof #854.
% 153.83/23.08  | | | | | 
% 153.83/23.08  | | | | End of split
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | Case 2:
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | |   (28)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0,
% 153.83/23.08  | | | |             e0) = e2)
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | | REF_CLOSE: (5), (7), (14), (15), (18), (28) are inconsistent by
% 153.83/23.08  | | | |            sub-proof #743.
% 153.83/23.08  | | | | 
% 153.83/23.08  | | | End of split
% 153.83/23.08  | | | 
% 153.83/23.08  | | End of split
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (29)  all_56_15 = e1 & op(e0, e0) = e1
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (29) implies:
% 153.83/23.08  | |   (30)  op(e0, e0) = e1
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (3), (7), (8), (30) are inconsistent by sub-proof #1022.
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #743 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  op(e0, e0) = all_10_2
% 153.83/23.08    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.08           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.08    (3)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.83/23.08    (4)  op(e1, e0) = e1
% 153.83/23.08    (5)   ~ (all_10_2 = e2)
% 153.83/23.08    (6)   ~ (e2 = e1)
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (3) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (7)  all_56_11 = e2 & op(e1, e0) = e2
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (7) implies:
% 153.83/23.08  | |   (8)  op(e1, e0) = e2
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1125.
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (9)  all_56_15 = e2 & op(e0, e0) = e2
% 153.83/23.08  | | 
% 153.83/23.08  | | ALPHA: (9) implies:
% 153.83/23.08  | |   (10)  op(e0, e0) = e2
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1097.
% 153.83/23.08  | | 
% 153.83/23.08  | End of split
% 153.83/23.08  | 
% 153.83/23.08  End of proof
% 153.83/23.08  
% 153.83/23.08  Sub-proof #744 shows that the following formulas are inconsistent:
% 153.83/23.08  ----------------------------------------------------------------
% 153.83/23.08    (1)  all_56_10 = e3
% 153.83/23.08    (2)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 153.83/23.08         (all_56_11 = e0 & op(e1, e0) = e0)
% 153.83/23.08    (3)  all_56_11 = e1
% 153.83/23.08    (4)   ~ (e2 = e0)
% 153.83/23.08    (5)   ~ (e3 = e0)
% 153.83/23.08    (6)   ~ (e1 = e0)
% 153.83/23.08    (7)  all_56_9 = e2
% 153.83/23.08  
% 153.83/23.08  Begin of proof
% 153.83/23.08  | 
% 153.83/23.08  | BETA: splitting (2) gives:
% 153.83/23.08  | 
% 153.83/23.08  | Case 1:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (8)  all_56_9 = e0 & op(e3, e0) = e0
% 153.83/23.08  | | 
% 153.83/23.08  | | REF_CLOSE: (4), (7), (8) are inconsistent by sub-proof #746.
% 153.83/23.08  | | 
% 153.83/23.08  | Case 2:
% 153.83/23.08  | | 
% 153.83/23.08  | |   (9)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.83/23.08  | |          e0)
% 153.83/23.08  | | 
% 153.83/23.08  | | BETA: splitting (9) gives:
% 153.83/23.08  | | 
% 153.83/23.08  | | Case 1:
% 153.83/23.08  | | | 
% 153.83/23.09  | | |   (10)  all_56_10 = e0 & op(e2, e0) = e0
% 153.83/23.09  | | | 
% 153.83/23.09  | | | ALPHA: (10) implies:
% 153.83/23.09  | | |   (11)  all_56_10 = e0
% 153.83/23.09  | | | 
% 153.83/23.09  | | | REF_CLOSE: (1), (5), (11) are inconsistent by sub-proof #1134.
% 153.83/23.09  | | | 
% 153.83/23.09  | | Case 2:
% 153.83/23.09  | | | 
% 153.83/23.09  | | |   (12)  all_56_11 = e0 & op(e1, e0) = e0
% 153.83/23.09  | | | 
% 153.83/23.09  | | | ALPHA: (12) implies:
% 153.83/23.09  | | |   (13)  all_56_11 = e0
% 153.83/23.09  | | | 
% 153.83/23.09  | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #745.
% 153.83/23.09  | | | 
% 153.83/23.09  | | End of split
% 153.83/23.09  | | 
% 153.83/23.09  | End of split
% 153.83/23.09  | 
% 153.83/23.09  End of proof
% 153.83/23.09  
% 153.83/23.09  Sub-proof #745 shows that the following formulas are inconsistent:
% 153.83/23.09  ----------------------------------------------------------------
% 153.83/23.09    (1)  all_56_11 = e1
% 153.83/23.09    (2)  all_56_11 = e0
% 153.83/23.09    (3)   ~ (e1 = e0)
% 153.83/23.09  
% 153.83/23.09  Begin of proof
% 153.83/23.09  | 
% 153.83/23.09  | COMBINE_EQS: (1), (2) imply:
% 153.83/23.09  |   (4)  e1 = e0
% 153.83/23.09  | 
% 153.83/23.09  | SIMP: (4) implies:
% 153.83/23.09  |   (5)  e1 = e0
% 153.83/23.09  | 
% 153.83/23.09  | REDUCE: (3), (5) imply:
% 153.83/23.09  |   (6)  $false
% 153.83/23.09  | 
% 153.83/23.09  | CLOSE: (6) is inconsistent.
% 153.83/23.09  | 
% 153.83/23.09  End of proof
% 153.83/23.09  
% 153.83/23.09  Sub-proof #746 shows that the following formulas are inconsistent:
% 153.83/23.09  ----------------------------------------------------------------
% 153.83/23.09    (1)  all_56_9 = e0 & op(e3, e0) = e0
% 153.83/23.09    (2)  all_56_9 = e2
% 153.83/23.09    (3)   ~ (e2 = e0)
% 153.83/23.09  
% 153.83/23.09  Begin of proof
% 153.83/23.09  | 
% 153.83/23.09  | ALPHA: (1) implies:
% 153.83/23.09  |   (4)  all_56_9 = e0
% 153.83/23.09  | 
% 153.83/23.09  | COMBINE_EQS: (2), (4) imply:
% 153.83/23.09  |   (5)  e2 = e0
% 153.83/23.09  | 
% 153.83/23.09  | REDUCE: (3), (5) imply:
% 153.83/23.09  |   (6)  $false
% 153.83/23.09  | 
% 153.83/23.09  | CLOSE: (6) is inconsistent.
% 153.83/23.09  | 
% 153.83/23.09  End of proof
% 153.83/23.09  
% 153.83/23.09  Sub-proof #747 shows that the following formulas are inconsistent:
% 153.83/23.09  ----------------------------------------------------------------
% 153.83/23.09    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.83/23.09         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.83/23.09    (2)  all_56_10 = e3
% 153.83/23.09    (3)  all_56_9 = e1
% 153.83/23.09    (4)  op(e0, e0) = all_10_2
% 153.83/23.09    (5)   ~ (e2 = e0)
% 153.83/23.09    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.09    (7)  op(e0, e0) = e3
% 153.83/23.09    (8)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.83/23.09             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.83/23.09               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.83/23.09               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.83/23.09    (9)   ~ (all_52_13 = e2)
% 153.83/23.09    (10)   ~ (e3 = e0)
% 153.83/23.09    (11)  op(e2, e0) = all_52_13
% 153.83/23.09    (12)   ~ (e1 = e0)
% 153.83/23.09    (13)   ~ (all_10_2 = e2)
% 153.83/23.09    (14)   ~ (e2 = e1)
% 153.83/23.09  
% 153.83/23.09  Begin of proof
% 153.83/23.09  | 
% 153.83/23.09  | BETA: splitting (8) gives:
% 153.83/23.09  | 
% 153.83/23.09  | Case 1:
% 153.83/23.09  | | 
% 153.83/23.09  | |   (15)  all_56_15 = e0 & op(e0, e0) = e0
% 153.83/23.09  | | 
% 153.83/23.09  | | ALPHA: (15) implies:
% 153.83/23.09  | |   (16)  op(e0, e0) = e0
% 153.83/23.09  | | 
% 153.83/23.09  | | REF_CLOSE: (6), (7), (10), (16) are inconsistent by sub-proof #1143.
% 153.83/23.09  | | 
% 153.83/23.09  | Case 2:
% 153.83/23.09  | | 
% 153.83/23.09  | |   (17)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.83/23.09  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 153.83/23.09  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.83/23.09  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 153.83/23.09  | | 
% 153.83/23.09  | | ALPHA: (17) implies:
% 153.83/23.09  | |   (18)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.83/23.09  | |           e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.83/23.09  | | 
% 153.83/23.09  | | BETA: splitting (1) gives:
% 153.83/23.09  | | 
% 153.83/23.09  | | Case 1:
% 153.83/23.09  | | | 
% 153.83/23.09  | | |   (19)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 153.83/23.09  | | |           e2)
% 153.83/23.09  | | | 
% 153.83/23.09  | | | BETA: splitting (19) gives:
% 153.83/23.09  | | | 
% 153.83/23.09  | | | Case 1:
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | |   (20)  all_56_9 = e2 & op(e3, e0) = e2
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | | ALPHA: (20) implies:
% 153.83/23.09  | | | |   (21)  all_56_9 = e2
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | | REF_CLOSE: (3), (14), (21) are inconsistent by sub-proof #948.
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | Case 2:
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | |   (22)  all_56_10 = e2 & op(e2, e0) = e2
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | | ALPHA: (22) implies:
% 153.83/23.09  | | | |   (23)  op(e2, e0) = e2
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | | REF_CLOSE: (6), (9), (11), (23) are inconsistent by sub-proof #1156.
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | End of split
% 153.83/23.09  | | | 
% 153.83/23.09  | | Case 2:
% 153.83/23.09  | | | 
% 153.83/23.09  | | |   (24)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0)
% 153.83/23.09  | | |           = e2)
% 153.83/23.09  | | | 
% 153.83/23.09  | | | BETA: splitting (24) gives:
% 153.83/23.09  | | | 
% 153.83/23.09  | | | Case 1:
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | |   (25)  all_56_11 = e2 & op(e1, e0) = e2
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | | ALPHA: (25) implies:
% 153.83/23.09  | | | |   (26)  all_56_11 = e2
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | | REF_CLOSE: (2), (3), (5), (10), (12), (18), (26) are inconsistent by
% 153.83/23.09  | | | |            sub-proof #748.
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | Case 2:
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | |   (27)  all_56_15 = e2 & op(e0, e0) = e2
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | | ALPHA: (27) implies:
% 153.83/23.09  | | | |   (28)  op(e0, e0) = e2
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | | REF_CLOSE: (4), (6), (13), (28) are inconsistent by sub-proof #1097.
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | End of split
% 153.83/23.09  | | | 
% 153.83/23.09  | | End of split
% 153.83/23.09  | | 
% 153.83/23.09  | End of split
% 153.83/23.09  | 
% 153.83/23.09  End of proof
% 153.83/23.09  
% 153.83/23.09  Sub-proof #748 shows that the following formulas are inconsistent:
% 153.83/23.09  ----------------------------------------------------------------
% 153.83/23.09    (1)  all_56_10 = e3
% 153.83/23.09    (2)  all_56_9 = e1
% 153.83/23.09    (3)  all_56_11 = e2
% 153.83/23.09    (4)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) = e0) |
% 153.83/23.09         (all_56_11 = e0 & op(e1, e0) = e0)
% 153.83/23.09    (5)   ~ (e2 = e0)
% 153.83/23.09    (6)   ~ (e3 = e0)
% 153.83/23.09    (7)   ~ (e1 = e0)
% 153.83/23.09  
% 153.83/23.09  Begin of proof
% 153.83/23.09  | 
% 153.83/23.09  | BETA: splitting (4) gives:
% 153.83/23.09  | 
% 153.83/23.09  | Case 1:
% 153.83/23.09  | | 
% 153.83/23.09  | |   (8)  all_56_9 = e0 & op(e3, e0) = e0
% 153.83/23.09  | | 
% 153.83/23.09  | | REF_CLOSE: (2), (7), (8) are inconsistent by sub-proof #1063.
% 153.83/23.09  | | 
% 153.83/23.09  | Case 2:
% 153.83/23.09  | | 
% 153.83/23.09  | |   (9)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.83/23.09  | |          e0)
% 153.83/23.09  | | 
% 153.83/23.09  | | BETA: splitting (9) gives:
% 153.83/23.09  | | 
% 153.83/23.09  | | Case 1:
% 153.83/23.09  | | | 
% 153.83/23.09  | | |   (10)  all_56_10 = e0 & op(e2, e0) = e0
% 153.83/23.09  | | | 
% 153.83/23.09  | | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #749.
% 153.83/23.09  | | | 
% 153.83/23.09  | | Case 2:
% 153.83/23.09  | | | 
% 153.83/23.09  | | |   (11)  all_56_11 = e0 & op(e1, e0) = e0
% 153.83/23.09  | | | 
% 153.83/23.09  | | | REF_CLOSE: (3), (5), (11) are inconsistent by sub-proof #1149.
% 153.83/23.09  | | | 
% 153.83/23.09  | | End of split
% 153.83/23.09  | | 
% 153.83/23.09  | End of split
% 153.83/23.09  | 
% 153.83/23.09  End of proof
% 153.83/23.09  
% 153.83/23.09  Sub-proof #749 shows that the following formulas are inconsistent:
% 153.83/23.09  ----------------------------------------------------------------
% 153.83/23.09    (1)  all_56_10 = e0 & op(e2, e0) = e0
% 153.83/23.09    (2)  all_56_10 = e3
% 153.83/23.09    (3)   ~ (e3 = e0)
% 153.83/23.09  
% 153.83/23.09  Begin of proof
% 153.83/23.09  | 
% 153.83/23.09  | ALPHA: (1) implies:
% 153.83/23.09  |   (4)  all_56_10 = e0
% 153.83/23.09  | 
% 153.83/23.09  | COMBINE_EQS: (2), (4) imply:
% 153.83/23.09  |   (5)  e3 = e0
% 153.83/23.09  | 
% 153.83/23.09  | REDUCE: (3), (5) imply:
% 153.83/23.09  |   (6)  $false
% 153.83/23.09  | 
% 153.83/23.09  | CLOSE: (6) is inconsistent.
% 153.83/23.09  | 
% 153.83/23.09  End of proof
% 153.83/23.09  
% 153.83/23.09  Sub-proof #750 shows that the following formulas are inconsistent:
% 153.83/23.09  ----------------------------------------------------------------
% 153.83/23.09    (1)   ~ (all_52_7 = all_52_11)
% 153.83/23.09    (2)   ~ (all_52_6 = e1)
% 153.83/23.09    (3)   ~ (e3 = e1)
% 153.83/23.09    (4)  all_57_7 = e2
% 153.83/23.09    (5)  op(e0, e2) = all_52_7
% 153.83/23.09    (6)  all_54_14 = all_52_11
% 153.83/23.09    (7)  op(e1, e1) = all_4_2
% 153.83/23.09    (8)   ~ (e2 = e0)
% 153.83/23.09    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.83/23.09           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.83/23.09    (10)  op(e0, e0) = e3
% 153.83/23.09    (11)  op(e3, e3) = e2
% 153.83/23.09    (12)   ~ (all_52_14 = e1)
% 153.83/23.09    (13)  all_56_12 = e1
% 153.83/23.09    (14)   ~ (all_52_11 = e3)
% 153.83/23.09    (15)  op(e1, e0) = all_52_14
% 153.83/23.09    (16)   ~ (all_52_13 = e2)
% 153.83/23.09    (17)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.83/23.09    (18)  op(e3, e0) = all_52_12
% 153.83/23.09    (19)   ~ (e3 = e0)
% 153.83/23.09    (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.83/23.09          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.83/23.09    (21)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.83/23.09          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.83/23.09    (22)  op(e1, e2) = all_52_6
% 153.83/23.09    (23)   ~ (all_52_12 = e3)
% 153.83/23.09    (24)  op(e2, e0) = all_52_13
% 153.83/23.09    (25)  op(e1, e1) = e1
% 153.83/23.09    (26)   ~ (e1 = e0)
% 153.83/23.09    (27)   ~ (e3 = e2)
% 153.83/23.09    (28)   ~ (all_52_2 = e1)
% 153.83/23.09    (29)   ~ (e2 = e1)
% 153.83/23.09    (30)  all_56_2 = e3
% 153.83/23.09    (31)   ~ (all_52_11 = e1)
% 153.83/23.09    (32)  op(e1, e3) = all_52_2
% 153.83/23.09    (33)   ~ (all_52_11 = e2)
% 153.83/23.09    (34)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.83/23.09              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.83/23.09            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.83/23.09            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.83/23.09            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.83/23.09            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.83/23.09            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.83/23.09            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.83/23.09            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.83/23.09            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.83/23.09            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.83/23.09            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.83/23.09            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.83/23.09            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.83/23.09            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.83/23.09            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.83/23.09            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.83/23.09            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.83/23.09            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.83/23.09            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.83/23.09            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.83/23.09            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.83/23.09            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.83/23.09            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.83/23.09            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.83/23.09            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.83/23.09            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.83/23.09            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.83/23.09            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.83/23.09            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.83/23.09            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.83/23.09            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.83/23.09            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.83/23.09            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.83/23.09            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.83/23.09            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.83/23.09            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.83/23.09            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.83/23.09            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.83/23.09            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.83/23.09            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.83/23.09            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.83/23.09            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.83/23.09            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.83/23.09            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.83/23.09            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.83/23.09            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.83/23.09            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.83/23.09              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.83/23.09            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.83/23.09            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.83/23.09              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.83/23.09            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.83/23.09            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.83/23.09                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.83/23.09                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.83/23.09                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.83/23.09                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.83/23.09                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.83/23.09                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.83/23.09                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.83/23.09              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.83/23.09                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.83/23.09                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.83/23.09                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.83/23.09                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.83/23.09                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.83/23.09                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.83/23.09                $i(all_57_7))))
% 153.83/23.09    (35)  op(e2, e3) = all_52_1
% 153.83/23.09    (36)   ~ (all_52_1 = e2)
% 153.83/23.09  
% 153.83/23.09  Begin of proof
% 153.83/23.09  | 
% 153.83/23.09  | BETA: splitting (34) gives:
% 153.83/23.09  | 
% 153.83/23.09  | Case 1:
% 153.83/23.09  | | 
% 153.83/23.09  | |   (37)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 153.83/23.09  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.83/23.09  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 153.83/23.09  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 153.83/23.09  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.83/23.09  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 153.83/23.09  | |         (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 153.83/23.09  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 153.83/23.09  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.83/23.09  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 153.83/23.09  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.83/23.09  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) |
% 153.83/23.09  | |         (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 153.83/23.09  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.83/23.09  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 153.83/23.09  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 153.83/23.09  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.83/23.09  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 153.83/23.09  | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 153.83/23.09  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 153.83/23.09  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.83/23.09  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.83/23.09  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.83/23.09  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.83/23.09  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.83/23.09  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.83/23.09  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.83/23.09  | | 
% 153.83/23.09  | | BETA: splitting (37) gives:
% 153.83/23.09  | | 
% 153.83/23.09  | | Case 1:
% 153.83/23.09  | | | 
% 153.83/23.09  | | |   (38)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.83/23.09  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.83/23.09  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.83/23.09  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 153.83/23.09  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.83/23.09  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.83/23.09  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 153.83/23.09  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.83/23.09  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.83/23.09  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 153.83/23.09  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.83/23.09  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 153.83/23.09  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.83/23.09  | | | 
% 153.83/23.09  | | | BETA: splitting (38) gives:
% 153.83/23.09  | | | 
% 153.83/23.09  | | | Case 1:
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | |   (39)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.83/23.09  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.83/23.09  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.83/23.09  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.83/23.09  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.83/23.09  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.83/23.09  | | | |           e3 & $i(all_57_2) & $i(all_57_12))
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | | REF_CLOSE: (9), (35), (36), (39) are inconsistent by sub-proof #1180.
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | Case 2:
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | |   (40)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.83/23.09  | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.83/23.09  | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.83/23.09  | | | |           $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.83/23.09  | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.83/23.09  | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.83/23.09  | | | |           e3 & $i(all_57_2) & $i(all_57_14))
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | | REF_CLOSE: (9), (28), (32), (40) are inconsistent by sub-proof #1025.
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | End of split
% 153.83/23.09  | | | 
% 153.83/23.09  | | Case 2:
% 153.83/23.09  | | | 
% 153.83/23.09  | | |   (41)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.83/23.09  | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.83/23.09  | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.83/23.09  | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5
% 153.83/23.09  | | |             = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 153.83/23.09  | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.83/23.09  | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 153.83/23.09  | | |           &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 153.83/23.09  | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.83/23.09  | | |           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 =
% 153.83/23.09  | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 153.83/23.09  | | |           & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 153.83/23.09  | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.83/23.09  | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.83/23.09  | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.83/23.09  | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.83/23.09  | | | 
% 153.83/23.09  | | | BETA: splitting (41) gives:
% 153.83/23.09  | | | 
% 153.83/23.09  | | | Case 1:
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | |   (42)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.83/23.09  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.83/23.09  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.83/23.09  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.83/23.09  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 153.83/23.09  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.83/23.09  | | | |           $i(all_57_5) & $i(all_57_10))
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | | REF_CLOSE: (7), (9), (10), (25), (27), (29), (42) are inconsistent by
% 153.83/23.09  | | | |            sub-proof #1024.
% 153.83/23.09  | | | | 
% 153.83/23.09  | | | Case 2:
% 153.83/23.09  | | | | 
% 153.87/23.09  | | | |   (43)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.87/23.09  | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.87/23.09  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.87/23.09  | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 153.87/23.09  | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.87/23.09  | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 153.87/23.09  | | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 153.87/23.09  | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 153.87/23.09  | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.87/23.09  | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.87/23.09  | | | | 
% 153.87/23.09  | | | | BETA: splitting (43) gives:
% 153.87/23.09  | | | | 
% 153.87/23.09  | | | | Case 1:
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | |   (44)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.87/23.09  | | | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.87/23.09  | | | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.87/23.09  | | | | |         $i(all_57_14)
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | | ALPHA: (44) implies:
% 153.87/23.09  | | | | |   (45)  op(e1, e2) = e1
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | | REF_CLOSE: (2), (9), (22), (45) are inconsistent by sub-proof #1042.
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | Case 2:
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | |   (46)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.87/23.09  | | | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.87/23.09  | | | | |           & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.87/23.09  | | | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~
% 153.87/23.09  | | | | |           (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.87/23.09  | | | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.87/23.09  | | | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | | BETA: splitting (46) gives:
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | | Case 1:
% 153.87/23.09  | | | | | | 
% 153.87/23.09  | | | | | |   (47)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.87/23.09  | | | | | |         (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.87/23.09  | | | | | |         & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.87/23.09  | | | | | |         $i(all_57_14)
% 153.87/23.09  | | | | | | 
% 153.87/23.09  | | | | | | ALPHA: (47) implies:
% 153.87/23.09  | | | | | |   (48)  op(e0, e0) = e2
% 153.87/23.09  | | | | | | 
% 153.87/23.09  | | | | | | REF_CLOSE: (9), (10), (27), (48) are inconsistent by sub-proof
% 153.87/23.09  | | | | | |            #1087.
% 153.87/23.09  | | | | | | 
% 153.87/23.09  | | | | | Case 2:
% 153.87/23.09  | | | | | | 
% 153.87/23.09  | | | | | |   (49)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.87/23.09  | | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3
% 153.87/23.09  | | | | | |         & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.87/23.09  | | | | | |         $i(all_57_10)
% 153.87/23.09  | | | | | | 
% 153.87/23.09  | | | | | | ALPHA: (49) implies:
% 153.87/23.09  | | | | | |   (50)   ~ (all_57_7 = e2)
% 153.87/23.09  | | | | | | 
% 153.87/23.09  | | | | | | REDUCE: (4), (50) imply:
% 153.87/23.09  | | | | | |   (51)  $false
% 153.87/23.09  | | | | | | 
% 153.87/23.09  | | | | | | CLOSE: (51) is inconsistent.
% 153.87/23.09  | | | | | | 
% 153.87/23.09  | | | | | End of split
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | End of split
% 153.87/23.09  | | | | 
% 153.87/23.09  | | | End of split
% 153.87/23.09  | | | 
% 153.87/23.09  | | End of split
% 153.87/23.09  | | 
% 153.87/23.09  | Case 2:
% 153.87/23.09  | | 
% 153.87/23.09  | |   (52)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 153.87/23.09  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.87/23.09  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 153.87/23.09  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 153.87/23.09  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.87/23.09  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 153.87/23.09  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 153.87/23.09  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.87/23.09  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.87/23.09  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.87/23.09  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.87/23.09  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.87/23.09  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 153.87/23.09  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 153.87/23.09  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.87/23.09  | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 153.87/23.09  | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.87/23.09  | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 153.87/23.09  | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.87/23.09  | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.87/23.09  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 153.87/23.09  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.87/23.09  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 153.87/23.09  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.87/23.09  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 153.87/23.09  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.87/23.09  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.87/23.09  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.87/23.09  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.87/23.09  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.87/23.09  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 153.87/23.09  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.87/23.09  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.87/23.09  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 153.87/23.09  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.87/23.09  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.87/23.09  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 153.87/23.09  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.87/23.09  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 153.87/23.09  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.87/23.09  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.87/23.09  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.87/23.09  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.87/23.09  | |               $i(all_57_7))))
% 153.87/23.09  | | 
% 153.87/23.09  | | BETA: splitting (52) gives:
% 153.87/23.09  | | 
% 153.87/23.09  | | Case 1:
% 153.87/23.09  | | | 
% 153.87/23.09  | | |   (53)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.87/23.09  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.87/23.09  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.87/23.09  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 153.87/23.09  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.87/23.09  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.87/23.09  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 153.87/23.09  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 153.87/23.09  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 153.87/23.09  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 153.87/23.09  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 153.87/23.09  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.87/23.09  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 153.87/23.09  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.87/23.09  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.87/23.09  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.87/23.09  | | |           $i(all_57_13))
% 153.87/23.09  | | | 
% 153.87/23.09  | | | BETA: splitting (53) gives:
% 153.87/23.09  | | | 
% 153.87/23.09  | | | Case 1:
% 153.87/23.09  | | | | 
% 153.87/23.09  | | | |   (54)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.87/23.09  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.87/23.09  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.87/23.09  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.87/23.09  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.87/23.09  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.87/23.09  | | | |           e2 & $i(all_57_6) & $i(all_57_12))
% 153.87/23.09  | | | | 
% 153.87/23.09  | | | | BETA: splitting (54) gives:
% 153.87/23.09  | | | | 
% 153.87/23.09  | | | | Case 1:
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | |   (55)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.87/23.09  | | | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.87/23.09  | | | | |         op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.87/23.09  | | | | |         $i(all_57_10)
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | | ALPHA: (55) implies:
% 153.87/23.09  | | | | |   (56)  op(e0, e0) = e1
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | | REF_CLOSE: (3), (9), (10), (56) are inconsistent by sub-proof #1022.
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | Case 2:
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | |   (57)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.87/23.09  | | | | |         (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.87/23.09  | | | | |         op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.87/23.09  | | | | |         $i(all_57_12)
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | | ALPHA: (57) implies:
% 153.87/23.09  | | | | |   (58)  op(e3, e3) = e1
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | | REF_CLOSE: (8), (9), (13), (19), (20), (21), (26), (29), (30), (35),
% 153.87/23.09  | | | | |            (36), (58) are inconsistent by sub-proof #754.
% 153.87/23.09  | | | | | 
% 153.87/23.09  | | | | End of split
% 153.87/23.09  | | | | 
% 153.87/23.09  | | | Case 2:
% 153.87/23.09  | | | | 
% 153.87/23.09  | | | |   (59)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.87/23.09  | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.87/23.09  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.87/23.09  | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 153.87/23.09  | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 153.87/23.09  | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 153.87/23.09  | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.87/23.09  | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 153.87/23.09  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 153.87/23.09  | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.87/23.09  | | | | 
% 153.87/23.09  | | | | REF_CLOSE: (3), (9), (10), (18), (23), (59) are inconsistent by
% 153.87/23.09  | | | |            sub-proof #1020.
% 153.87/23.09  | | | | 
% 153.87/23.09  | | | End of split
% 153.87/23.09  | | | 
% 153.87/23.09  | | Case 2:
% 153.87/23.09  | | | 
% 153.87/23.10  | | |   (60)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.87/23.10  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.87/23.10  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.87/23.10  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.87/23.10  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.87/23.10  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.87/23.10  | | |           $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0
% 153.87/23.10  | | |           &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.87/23.10  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.87/23.10  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.87/23.10  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.87/23.10  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.87/23.10  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.87/23.10  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.87/23.10  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.87/23.10  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.87/23.10  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.87/23.10  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.87/23.10  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 153.87/23.10  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.87/23.10  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.87/23.10  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.87/23.10  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 153.87/23.10  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.87/23.10  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.87/23.10  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.87/23.10  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.87/23.10  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.87/23.10  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.87/23.10  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 153.87/23.10  | | | 
% 153.87/23.10  | | | BETA: splitting (60) gives:
% 153.87/23.10  | | | 
% 153.87/23.10  | | | Case 1:
% 153.87/23.10  | | | | 
% 153.87/23.10  | | | |   (61)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.87/23.10  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.87/23.10  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.87/23.10  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.87/23.10  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.87/23.10  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.87/23.10  | | | |           e1 & $i(all_57_9) & $i(all_57_14))
% 153.87/23.10  | | | | 
% 153.87/23.10  | | | | REF_CLOSE: (8), (9), (11), (61) are inconsistent by sub-proof #1037.
% 153.87/23.10  | | | | 
% 153.87/23.10  | | | Case 2:
% 153.87/23.10  | | | | 
% 153.87/23.10  | | | |   (62)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.87/23.10  | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.87/23.10  | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.87/23.10  | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 153.87/23.10  | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.87/23.10  | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.87/23.10  | | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 153.87/23.10  | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 153.87/23.10  | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.87/23.10  | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.87/23.10  | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.87/23.10  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.87/23.10  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.87/23.10  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.87/23.10  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.87/23.10  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.87/23.10  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.87/23.10  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.87/23.10  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.87/23.10  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.87/23.10  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.87/23.10  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.87/23.10  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.87/23.10  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.87/23.10  | | | | 
% 153.87/23.10  | | | | BETA: splitting (62) gives:
% 153.87/23.10  | | | | 
% 153.87/23.10  | | | | Case 1:
% 153.87/23.10  | | | | | 
% 153.87/23.10  | | | | |   (63)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.87/23.10  | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.87/23.10  | | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.87/23.10  | | | | |         $i(all_57_13)
% 153.87/23.10  | | | | | 
% 153.87/23.10  | | | | | ALPHA: (63) implies:
% 153.87/23.10  | | | | |   (64)  op(e2, e0) = e2
% 153.87/23.10  | | | | | 
% 153.87/23.10  | | | | | REF_CLOSE: (9), (16), (24), (64) are inconsistent by sub-proof #1156.
% 153.87/23.10  | | | | | 
% 153.87/23.10  | | | | Case 2:
% 153.87/23.10  | | | | | 
% 153.87/23.10  | | | | |   (65)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.87/23.10  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.87/23.10  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.87/23.10  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.87/23.10  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.87/23.10  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 153.87/23.10  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.87/23.10  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.87/23.10  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.87/23.10  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.87/23.10  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 153.87/23.10  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.87/23.10  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.87/23.10  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.87/23.10  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.87/23.10  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.87/23.10  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.87/23.10  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.87/23.10  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.87/23.10  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.87/23.10  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.87/23.10  | | | | |               $i(all_57_7))))
% 153.87/23.10  | | | | | 
% 153.87/23.10  | | | | | BETA: splitting (65) gives:
% 153.87/23.10  | | | | | 
% 153.87/23.10  | | | | | Case 1:
% 153.87/23.10  | | | | | | 
% 153.87/23.10  | | | | | |   (66)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.87/23.10  | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.87/23.10  | | | | | |         & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.87/23.10  | | | | | |         $i(all_57_14)
% 153.87/23.10  | | | | | | 
% 153.87/23.10  | | | | | | ALPHA: (66) implies:
% 153.87/23.10  | | | | | |   (67)  op(e1, e0) = e1
% 153.87/23.10  | | | | | | 
% 153.87/23.10  | | | | | | REF_CLOSE: (9), (12), (15), (67) are inconsistent by sub-proof #961.
% 153.87/23.10  | | | | | | 
% 153.87/23.10  | | | | | Case 2:
% 153.87/23.10  | | | | | | 
% 153.87/23.10  | | | | | |   (68)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.87/23.10  | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.87/23.10  | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 153.87/23.10  | | | | | |               e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 153.87/23.10  | | | | | |             = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1,
% 153.87/23.10  | | | | | |               e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.87/23.10  | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.87/23.10  | | | | | |             (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.87/23.10  | | | | | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.87/23.10  | | | | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.87/23.10  | | | | | |             (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.87/23.10  | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.87/23.10  | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.87/23.10  | | | | | |             (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.87/23.10  | | | | | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.87/23.10  | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.87/23.10  | | | | | |             (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.87/23.10  | | | | | |             & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.87/23.10  | | | | | |             $i(all_57_7)))
% 153.87/23.10  | | | | | | 
% 153.87/23.10  | | | | | | ALPHA: (68) implies:
% 153.87/23.10  | | | | | |   (69)  op(e0, e0) = all_57_15
% 153.87/23.10  | | | | | |   (70)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.87/23.10  | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 153.87/23.10  | | | | | |           & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.87/23.10  | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 153.87/23.10  | | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 153.87/23.10  | | | | | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.87/23.10  | | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.87/23.10  | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.87/23.10  | | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.87/23.10  | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 153.87/23.10  | | | | | |           & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.87/23.10  | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 153.87/23.10  | | | | | |           & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.87/23.10  | | | | | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.87/23.10  | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 153.87/23.10  | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.87/23.10  | | | | | | 
% 153.87/23.10  | | | | | | BETA: splitting (70) gives:
% 153.87/23.10  | | | | | | 
% 153.87/23.10  | | | | | | Case 1:
% 153.87/23.10  | | | | | | | 
% 153.87/23.10  | | | | | | |   (71)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.87/23.10  | | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 153.87/23.10  | | | | | | |           e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 153.87/23.10  | | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.87/23.10  | | | | | | |             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.87/23.10  | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.87/23.10  | | | | | | |           = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 153.87/23.10  | | | | | | |             e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.87/23.10  | | | | | | |           $i(all_57_3))
% 153.87/23.10  | | | | | | | 
% 153.87/23.10  | | | | | | | BETA: splitting (71) gives:
% 153.87/23.10  | | | | | | | 
% 153.87/23.10  | | | | | | | Case 1:
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | |   (72)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.87/23.10  | | | | | | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 153.87/23.10  | | | | | | | |         e3 & op(e0, e3) = e0 & $i(all_57_0)
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | | ALPHA: (72) implies:
% 153.87/23.10  | | | | | | | |   (73)   ~ (all_57_15 = e3)
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | | REF_CLOSE: (9), (10), (69), (73) are inconsistent by sub-proof
% 153.87/23.10  | | | | | | | |            #1019.
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | Case 2:
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | |   (74)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.87/23.10  | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.87/23.10  | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.87/23.10  | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.87/23.10  | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.87/23.10  | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | | BETA: splitting (74) gives:
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | | Case 1:
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | |   (75)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.87/23.10  | | | | | | | | |         ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.87/23.10  | | | | | | | | |           e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | | ALPHA: (75) implies:
% 153.87/23.10  | | | | | | | | |   (76)   ~ (all_57_15 = e3)
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | | REF_CLOSE: (9), (10), (69), (76) are inconsistent by sub-proof
% 153.87/23.10  | | | | | | | | |            #1019.
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | Case 2:
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | |   (77)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 153.87/23.10  | | | | | | | | |         ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.87/23.10  | | | | | | | | |         all_57_3 & op(e0, e2) = e0 & $i(all_57_3)
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | | ALPHA: (77) implies:
% 153.87/23.10  | | | | | | | | |   (78)  op(e0, e2) = e0
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | | REF_CLOSE: (1), (5), (6), (9), (14), (17), (31), (33), (78)
% 153.87/23.10  | | | | | | | | |            are inconsistent by sub-proof #751.
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | End of split
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | End of split
% 153.87/23.10  | | | | | | | 
% 153.87/23.10  | | | | | | Case 2:
% 153.87/23.10  | | | | | | | 
% 153.87/23.10  | | | | | | |   (79)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.87/23.10  | | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.87/23.10  | | | | | | |           e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.87/23.10  | | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.87/23.10  | | | | | | |             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.87/23.10  | | | | | | |             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 153.87/23.10  | | | | | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 153.87/23.10  | | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.87/23.10  | | | | | | |           $i(all_57_7))
% 153.87/23.10  | | | | | | | 
% 153.87/23.10  | | | | | | | BETA: splitting (79) gives:
% 153.87/23.10  | | | | | | | 
% 153.87/23.10  | | | | | | | Case 1:
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | |   (80)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.87/23.10  | | | | | | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.87/23.10  | | | | | | | |         e2 & op(e0, e2) = e0 & $i(all_57_4)
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | | ALPHA: (80) implies:
% 153.87/23.10  | | | | | | | |   (81)  op(e1, e1) = e2
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | | REF_CLOSE: (7), (9), (25), (29), (81) are inconsistent by
% 153.87/23.10  | | | | | | | |            sub-proof #1044.
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | Case 2:
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | |   (82)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.87/23.10  | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.87/23.10  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 153.87/23.10  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.87/23.10  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.87/23.10  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | | BETA: splitting (82) gives:
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | | Case 1:
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | |   (83)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.87/23.10  | | | | | | | | |         ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.87/23.10  | | | | | | | | |         all_57_6 & op(e0, e1) = e0 & $i(all_57_6)
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | | ALPHA: (83) implies:
% 153.87/23.10  | | | | | | | | |   (84)  op(e3, e3) = e1
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | | REF_CLOSE: (8), (9), (13), (19), (20), (21), (26), (29), (30),
% 153.87/23.10  | | | | | | | | |            (35), (36), (84) are inconsistent by sub-proof
% 153.87/23.10  | | | | | | | | |            #754.
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | Case 2:
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | |   (85)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 153.87/23.10  | | | | | | | | |         ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.87/23.10  | | | | | | | | |         all_57_7 & op(e0, e1) = e0 & $i(all_57_7)
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | | ALPHA: (85) implies:
% 153.87/23.10  | | | | | | | | |   (86)   ~ (all_57_7 = e2)
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | | REDUCE: (4), (86) imply:
% 153.87/23.10  | | | | | | | | |   (87)  $false
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | | CLOSE: (87) is inconsistent.
% 153.87/23.10  | | | | | | | | | 
% 153.87/23.10  | | | | | | | | End of split
% 153.87/23.10  | | | | | | | | 
% 153.87/23.10  | | | | | | | End of split
% 153.87/23.10  | | | | | | | 
% 153.87/23.10  | | | | | | End of split
% 153.87/23.10  | | | | | | 
% 153.87/23.10  | | | | | End of split
% 153.87/23.10  | | | | | 
% 153.87/23.10  | | | | End of split
% 153.87/23.10  | | | | 
% 153.87/23.10  | | | End of split
% 153.87/23.10  | | | 
% 153.87/23.10  | | End of split
% 153.87/23.10  | | 
% 153.87/23.10  | End of split
% 153.87/23.10  | 
% 153.87/23.10  End of proof
% 153.87/23.10  
% 153.87/23.10  Sub-proof #751 shows that the following formulas are inconsistent:
% 153.87/23.10  ----------------------------------------------------------------
% 153.87/23.10    (1)   ~ (all_52_7 = all_52_11)
% 153.87/23.10    (2)  op(e0, e2) = all_52_7
% 153.87/23.10    (3)  all_54_14 = all_52_11
% 153.87/23.10    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.87/23.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.87/23.10    (5)   ~ (all_52_11 = e3)
% 153.87/23.10    (6)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.87/23.10    (7)   ~ (all_52_11 = e1)
% 153.87/23.10    (8)   ~ (all_52_11 = e2)
% 153.87/23.10    (9)  op(e0, e2) = e0
% 153.87/23.10  
% 153.87/23.10  Begin of proof
% 153.87/23.10  | 
% 153.87/23.10  | BETA: splitting (6) gives:
% 153.87/23.10  | 
% 153.87/23.10  | Case 1:
% 153.87/23.10  | | 
% 153.87/23.10  | |   (10)  all_54_14 = e3
% 153.87/23.10  | | 
% 153.87/23.10  | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #903.
% 153.87/23.10  | | 
% 153.87/23.10  | Case 2:
% 153.87/23.10  | | 
% 153.87/23.10  | |   (11)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 153.87/23.10  | | 
% 153.87/23.10  | | BETA: splitting (11) gives:
% 153.87/23.10  | | 
% 153.87/23.10  | | Case 1:
% 153.87/23.10  | | | 
% 153.87/23.10  | | |   (12)  all_54_14 = e2
% 153.87/23.10  | | | 
% 153.87/23.10  | | | REF_CLOSE: (3), (8), (12) are inconsistent by sub-proof #902.
% 153.87/23.10  | | | 
% 153.87/23.10  | | Case 2:
% 153.87/23.10  | | | 
% 153.87/23.10  | | |   (13)  all_54_14 = e1 | all_54_14 = e0
% 153.87/23.10  | | | 
% 153.87/23.10  | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (13) are inconsistent by
% 153.87/23.10  | | |            sub-proof #752.
% 153.87/23.10  | | | 
% 153.87/23.10  | | End of split
% 153.87/23.10  | | 
% 153.87/23.10  | End of split
% 153.87/23.10  | 
% 153.87/23.10  End of proof
% 153.87/23.10  
% 153.87/23.10  Sub-proof #752 shows that the following formulas are inconsistent:
% 153.87/23.10  ----------------------------------------------------------------
% 153.87/23.10    (1)   ~ (all_52_7 = all_52_11)
% 153.87/23.10    (2)  op(e0, e2) = all_52_7
% 153.87/23.10    (3)  all_54_14 = all_52_11
% 153.87/23.10    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.87/23.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.87/23.10    (5)  all_54_14 = e1 | all_54_14 = e0
% 153.87/23.10    (6)   ~ (all_52_11 = e1)
% 153.87/23.10    (7)  op(e0, e2) = e0
% 153.87/23.10  
% 153.87/23.10  Begin of proof
% 153.87/23.10  | 
% 153.87/23.10  | BETA: splitting (5) gives:
% 153.87/23.10  | 
% 153.87/23.10  | Case 1:
% 153.87/23.10  | | 
% 153.87/23.10  | |   (8)  all_54_14 = e1
% 153.87/23.10  | | 
% 153.87/23.10  | | REF_CLOSE: (3), (6), (8) are inconsistent by sub-proof #753.
% 153.87/23.10  | | 
% 153.87/23.10  | Case 2:
% 153.87/23.10  | | 
% 153.87/23.10  | |   (9)  all_54_14 = e0
% 153.87/23.10  | | 
% 153.87/23.10  | | COMBINE_EQS: (3), (9) imply:
% 153.87/23.10  | |   (10)  all_52_11 = e0
% 153.87/23.10  | | 
% 153.87/23.10  | | SIMP: (10) implies:
% 153.87/23.10  | |   (11)  all_52_11 = e0
% 153.87/23.10  | | 
% 153.87/23.10  | | REDUCE: (1), (11) imply:
% 153.87/23.10  | |   (12)   ~ (all_52_7 = e0)
% 153.87/23.10  | | 
% 153.87/23.10  | | REF_CLOSE: (2), (4), (7), (12) are inconsistent by sub-proof #1036.
% 153.87/23.10  | | 
% 153.87/23.10  | End of split
% 153.87/23.10  | 
% 153.87/23.10  End of proof
% 153.87/23.10  
% 153.87/23.10  Sub-proof #753 shows that the following formulas are inconsistent:
% 153.87/23.10  ----------------------------------------------------------------
% 153.87/23.10    (1)  all_54_14 = all_52_11
% 153.87/23.10    (2)  all_54_14 = e1
% 153.87/23.10    (3)   ~ (all_52_11 = e1)
% 153.87/23.10  
% 153.87/23.10  Begin of proof
% 153.87/23.10  | 
% 153.87/23.10  | COMBINE_EQS: (1), (2) imply:
% 153.87/23.10  |   (4)  all_52_11 = e1
% 153.87/23.10  | 
% 153.87/23.10  | SIMP: (4) implies:
% 153.87/23.10  |   (5)  all_52_11 = e1
% 153.87/23.10  | 
% 153.87/23.10  | REDUCE: (3), (5) imply:
% 153.87/23.10  |   (6)  $false
% 153.87/23.10  | 
% 153.87/23.10  | CLOSE: (6) is inconsistent.
% 153.87/23.10  | 
% 153.87/23.10  End of proof
% 153.87/23.10  
% 153.87/23.10  Sub-proof #754 shows that the following formulas are inconsistent:
% 153.87/23.10  ----------------------------------------------------------------
% 153.87/23.10    (1)   ~ (e2 = e0)
% 153.87/23.10    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.87/23.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.87/23.10    (3)  all_56_12 = e1
% 153.87/23.10    (4)   ~ (e3 = e0)
% 153.87/23.10    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.87/23.10         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.87/23.10    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.87/23.10         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.87/23.10    (7)  op(e3, e3) = e1
% 153.87/23.10    (8)   ~ (e1 = e0)
% 153.87/23.10    (9)   ~ (e2 = e1)
% 153.87/23.10    (10)  all_56_2 = e3
% 153.87/23.10    (11)  op(e2, e3) = all_52_1
% 153.87/23.10    (12)   ~ (all_52_1 = e2)
% 153.87/23.10  
% 153.87/23.10  Begin of proof
% 153.87/23.10  | 
% 153.87/23.10  | BETA: splitting (6) gives:
% 153.87/23.10  | 
% 153.87/23.10  | Case 1:
% 153.87/23.10  | | 
% 153.87/23.10  | |   (13)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 153.87/23.10  | |           e2)
% 153.87/23.10  | | 
% 153.87/23.10  | | REF_CLOSE: (2), (7), (9), (11), (12), (13) are inconsistent by sub-proof
% 153.87/23.10  | |            #938.
% 153.87/23.10  | | 
% 153.87/23.10  | Case 2:
% 153.87/23.10  | | 
% 153.87/23.10  | |   (14)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 153.87/23.10  | |           e2)
% 153.87/23.10  | | 
% 153.87/23.10  | | BETA: splitting (14) gives:
% 153.87/23.10  | | 
% 153.87/23.10  | | Case 1:
% 153.87/23.10  | | | 
% 153.87/23.10  | | |   (15)  all_56_6 = e2 & op(e1, e3) = e2
% 153.87/23.10  | | | 
% 153.87/23.10  | | | ALPHA: (15) implies:
% 153.87/23.10  | | |   (16)  all_56_6 = e2
% 153.87/23.10  | | | 
% 153.87/23.10  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (16) are inconsistent
% 153.87/23.10  | | |            by sub-proof #930.
% 153.87/23.10  | | | 
% 153.87/23.10  | | Case 2:
% 153.87/23.10  | | | 
% 153.87/23.10  | | |   (17)  all_56_12 = e2 & op(e0, e3) = e2
% 153.87/23.10  | | | 
% 153.87/23.10  | | | ALPHA: (17) implies:
% 153.87/23.10  | | |   (18)  all_56_12 = e2
% 153.87/23.10  | | | 
% 153.87/23.10  | | | REF_CLOSE: (3), (9), (18) are inconsistent by sub-proof #1122.
% 153.87/23.10  | | | 
% 153.87/23.10  | | End of split
% 153.87/23.10  | | 
% 153.87/23.10  | End of split
% 153.87/23.10  | 
% 153.87/23.10  End of proof
% 153.87/23.10  
% 153.87/23.10  Sub-proof #755 shows that the following formulas are inconsistent:
% 153.87/23.10  ----------------------------------------------------------------
% 153.87/23.10    (1)  op(e0, e1) = all_52_11
% 153.87/23.10    (2)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 =
% 153.87/23.10             e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.87/23.10           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0,
% 153.87/23.10             e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 & 
% 153.87/23.10               ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.87/23.10               op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 153.87/23.10               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.87/23.10               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.87/23.10               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 153.87/23.10                 e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.87/23.10               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.87/23.10               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1,
% 153.87/23.10                 e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.87/23.10               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 153.87/23.10                 e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.87/23.10               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.87/23.10               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 153.87/23.10                 e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.87/23.10               $i(all_57_7))))
% 153.87/23.10    (3)  op(e0, e2) = all_52_7
% 153.87/23.10    (4)   ~ (e2 = e0)
% 153.87/23.10    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.87/23.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.87/23.10    (6)  op(e1, e1) = e0
% 153.87/23.10    (7)   ~ (all_52_11 = e0)
% 153.87/23.10    (8)  op(e0, e3) = all_52_3
% 153.87/23.10    (9)   ~ (all_52_7 = e0)
% 153.87/23.10    (10)   ~ (all_52_3 = e0)
% 153.87/23.10  
% 153.87/23.10  Begin of proof
% 153.87/23.10  | 
% 153.87/23.10  | BETA: splitting (2) gives:
% 153.87/23.10  | 
% 153.87/23.10  | Case 1:
% 153.87/23.10  | | 
% 153.87/23.10  | |   (11)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.87/23.10  | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1,
% 153.87/23.10  | |           e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 153.87/23.10  | | 
% 153.87/23.10  | | ALPHA: (11) implies:
% 153.87/23.10  | |   (12)   ~ (all_57_14 = e0)
% 153.87/23.10  | |   (13)  op(e1, e1) = all_57_14
% 153.87/23.10  | | 
% 153.87/23.10  | | REF_CLOSE: (5), (6), (12), (13) are inconsistent by sub-proof #1026.
% 153.87/23.10  | | 
% 153.87/23.10  | Case 2:
% 153.87/23.10  | | 
% 153.87/23.10  | |   (14)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12
% 153.87/23.10  | |             = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.87/23.10  | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.87/23.10  | |           (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.87/23.10  | |             (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.87/23.10  | |             op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 153.87/23.10  | |             e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.87/23.10  | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.87/23.10  | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.87/23.10  | |             (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.87/23.10  | |             op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 =
% 153.87/23.10  | |             e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.87/23.10  | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.87/23.10  | |           (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.87/23.10  | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.87/23.10  | |             op(e0, e1) = e0 & $i(all_57_7)))
% 153.87/23.10  | | 
% 153.87/23.10  | | ALPHA: (14) implies:
% 153.87/23.10  | |   (15)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 153.87/23.10  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.87/23.10  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.87/23.10  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.87/23.10  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.87/23.10  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.87/23.10  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.87/23.10  | |           $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.87/23.10  | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.87/23.10  | |           e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 153.87/23.10  | |           = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.87/23.10  | |           & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.87/23.10  | |         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15
% 153.87/23.10  | |             = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) =
% 153.87/23.10  | |           e0 & $i(all_57_7))
% 153.87/23.10  | | 
% 153.87/23.10  | | BETA: splitting (15) gives:
% 153.87/23.10  | | 
% 153.87/23.10  | | Case 1:
% 153.87/23.10  | | | 
% 153.87/23.10  | | |   (16)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.87/23.10  | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.87/23.10  | | |           op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 153.87/23.10  | | |           e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.87/23.10  | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.87/23.10  | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.87/23.10  | | |           (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.87/23.10  | | |           op(e0, e2) = e0 & $i(all_57_3))
% 153.87/23.10  | | | 
% 153.87/23.10  | | | REF_CLOSE: (3), (5), (8), (9), (10), (16) are inconsistent by sub-proof
% 153.87/23.10  | | |            #1035.
% 153.87/23.10  | | | 
% 153.87/23.10  | | Case 2:
% 153.87/23.10  | | | 
% 153.87/23.10  | | |   (17)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.87/23.10  | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.87/23.10  | | |           op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 =
% 153.87/23.10  | | |           e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 153.87/23.10  | | |           & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.87/23.10  | | |         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.87/23.10  | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.87/23.10  | | |           op(e0, e1) = e0 & $i(all_57_7))
% 153.87/23.10  | | | 
% 153.87/23.10  | | | REF_CLOSE: (1), (4), (5), (6), (7), (17) are inconsistent by sub-proof
% 153.87/23.10  | | |            #756.
% 153.87/23.10  | | | 
% 153.87/23.10  | | End of split
% 153.87/23.10  | | 
% 153.87/23.10  | End of split
% 153.87/23.10  | 
% 153.87/23.10  End of proof
% 153.87/23.10  
% 153.87/23.10  Sub-proof #756 shows that the following formulas are inconsistent:
% 153.87/23.10  ----------------------------------------------------------------
% 153.87/23.10    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.87/23.10             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.87/23.10           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.87/23.10           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.87/23.10             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.87/23.10           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.87/23.10           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.87/23.10    (2)  op(e0, e1) = all_52_11
% 153.87/23.10    (3)   ~ (e2 = e0)
% 153.87/23.10    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.87/23.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.87/23.10    (5)  op(e1, e1) = e0
% 153.87/23.10    (6)   ~ (all_52_11 = e0)
% 153.87/23.10  
% 153.87/23.10  Begin of proof
% 153.87/23.10  | 
% 153.87/23.10  | BETA: splitting (1) gives:
% 153.87/23.10  | 
% 153.87/23.10  | Case 1:
% 153.87/23.10  | | 
% 153.87/23.10  | |   (7)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.87/23.10  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.87/23.10  | |        $i(all_57_4)
% 153.87/23.10  | | 
% 153.87/23.10  | | ALPHA: (7) implies:
% 153.87/23.10  | |   (8)  op(e1, e1) = e2
% 153.87/23.10  | | 
% 153.87/23.10  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1006.
% 153.87/23.10  | | 
% 153.87/23.10  | Case 2:
% 153.87/23.10  | | 
% 153.87/23.10  | |   (9)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 153.87/23.10  | |            = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 153.87/23.10  | |          & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 153.87/23.10  | |            e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.87/23.10  | |          all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.87/23.10  | | 
% 153.87/23.10  | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #851.
% 153.87/23.10  | | 
% 153.87/23.10  | End of split
% 153.87/23.10  | 
% 153.87/23.10  End of proof
% 153.87/23.10  
% 153.87/23.10  Sub-proof #757 shows that the following formulas are inconsistent:
% 153.87/23.10  ----------------------------------------------------------------
% 153.87/23.10    (1)  op(e0, e1) = all_52_11
% 153.87/23.10    (2)   ~ (e3 = e1)
% 153.87/23.10    (3)   ~ (all_52_2 = all_52_14)
% 153.87/23.10    (4)   ~ (all_52_11 = all_10_2)
% 153.87/23.10    (5)  op(e2, e2) = e1
% 153.87/23.10    (6)  op(e0, e0) = all_10_2
% 153.87/23.10    (7)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.87/23.10    (8)  op(e1, e1) = all_4_2
% 153.87/23.10    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.87/23.10           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.87/23.10    (10)  all_54_10 = all_4_2
% 153.87/23.10    (11)  op(e1, e0) = all_52_14
% 153.87/23.10    (12)  op(e3, e3) = e1
% 153.87/23.10    (13)   ~ (all_52_14 = all_4_2)
% 153.87/23.10    (14)   ~ (all_4_2 = e2)
% 153.87/23.11    (15)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.87/23.11              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.87/23.11            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.87/23.11                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.87/23.11              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.87/23.11          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.87/23.11              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.87/23.11            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.87/23.11                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.87/23.11              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.87/23.11          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.87/23.11              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.87/23.11            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.87/23.11                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.87/23.11              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.87/23.11          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.87/23.11              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.87/23.11            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.87/23.11                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.87/23.11                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.87/23.11                $i(all_57_14))))
% 153.87/23.11    (16)   ~ (all_4_2 = e3)
% 153.87/23.11    (17)  op(e1, e0) = e1
% 153.87/23.11    (18)   ~ (e2 = e1)
% 153.87/23.11    (19)  op(e1, e3) = all_52_2
% 153.87/23.11    (20)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.87/23.11              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.87/23.11            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.87/23.11            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.87/23.11            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.87/23.11            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.87/23.11            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.87/23.11            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.87/23.11            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.87/23.11            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.87/23.11            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.87/23.11            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.87/23.11            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.87/23.11            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.87/23.11            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.87/23.11            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.87/23.11            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.87/23.11            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.87/23.11            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.87/23.11            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.87/23.11            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.87/23.11            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.87/23.11            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.87/23.11            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.87/23.11            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.87/23.11            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.87/23.11            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.87/23.11            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.87/23.11            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.87/23.11            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.87/23.11            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.87/23.11            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.87/23.11            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.87/23.11            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.87/23.11            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.87/23.11            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.87/23.11            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.87/23.11            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.87/23.11            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.87/23.11            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.87/23.11            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.87/23.11            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.87/23.11            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.87/23.11            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.87/23.11            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.87/23.11            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.87/23.11            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.87/23.11            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.87/23.11              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.87/23.11            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.87/23.11            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.87/23.11              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.87/23.11            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.87/23.11            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.87/23.11                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.87/23.11                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.87/23.11                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.87/23.11                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.87/23.11                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.87/23.11                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.87/23.11                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.87/23.11              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.87/23.11                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.87/23.11                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.87/23.11                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.87/23.11                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.87/23.11                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.87/23.11                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.87/23.11                $i(all_57_7))))
% 153.87/23.11  
% 153.87/23.11  Begin of proof
% 153.87/23.11  | 
% 153.87/23.11  | GROUND_INST: instantiating (9) with all_52_14, e1, e0, e1, simplifying with
% 153.87/23.11  |              (11), (17) gives:
% 153.87/23.11  |   (21)  all_52_14 = e1
% 153.87/23.11  | 
% 153.87/23.11  | REDUCE: (3), (21) imply:
% 153.87/23.11  |   (22)   ~ (all_52_2 = e1)
% 153.87/23.11  | 
% 153.87/23.11  | REDUCE: (13), (21) imply:
% 153.87/23.11  |   (23)   ~ (all_4_2 = e1)
% 153.87/23.11  | 
% 153.87/23.11  | SIMP: (23) implies:
% 153.87/23.11  |   (24)   ~ (all_4_2 = e1)
% 153.87/23.11  | 
% 153.87/23.11  | BETA: splitting (7) gives:
% 153.87/23.11  | 
% 153.87/23.11  | Case 1:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (25)  all_54_10 = e3
% 153.87/23.11  | | 
% 153.87/23.11  | | REF_CLOSE: (10), (16), (25) are inconsistent by sub-proof #1173.
% 153.87/23.11  | | 
% 153.87/23.11  | Case 2:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (26)   ~ (all_54_10 = e3)
% 153.87/23.11  | |   (27)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 153.87/23.11  | | 
% 153.87/23.11  | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (12), (14), (15), (16),
% 153.87/23.11  | |            (18), (19), (20), (22), (24), (27) are inconsistent by sub-proof
% 153.87/23.11  | |            #887.
% 153.87/23.11  | | 
% 153.87/23.11  | End of split
% 153.87/23.11  | 
% 153.87/23.11  End of proof
% 153.87/23.11  
% 153.87/23.11  Sub-proof #758 shows that the following formulas are inconsistent:
% 153.87/23.11  ----------------------------------------------------------------
% 153.87/23.11    (1)   ~ (all_52_12 = e1)
% 153.87/23.11    (2)  all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 153.87/23.11    (3)  all_54_3 = all_52_12
% 153.87/23.11    (4)   ~ (all_52_12 = e2)
% 153.87/23.11    (5)   ~ (all_52_12 = e0)
% 153.87/23.11  
% 153.87/23.11  Begin of proof
% 153.87/23.11  | 
% 153.87/23.11  | BETA: splitting (2) gives:
% 153.87/23.11  | 
% 153.87/23.11  | Case 1:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (6)  all_54_3 = e2
% 153.87/23.11  | | 
% 153.87/23.11  | | REF_CLOSE: (3), (4), (6) are inconsistent by sub-proof #760.
% 153.87/23.11  | | 
% 153.87/23.11  | Case 2:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (7)  all_54_3 = e1 | all_54_3 = e0
% 153.87/23.11  | | 
% 153.87/23.11  | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #759.
% 153.87/23.11  | | 
% 153.87/23.11  | End of split
% 153.87/23.11  | 
% 153.87/23.11  End of proof
% 153.87/23.11  
% 153.87/23.11  Sub-proof #759 shows that the following formulas are inconsistent:
% 153.87/23.11  ----------------------------------------------------------------
% 153.87/23.11    (1)  all_54_3 = e1 | all_54_3 = e0
% 153.87/23.11    (2)  all_54_3 = all_52_12
% 153.87/23.11    (3)   ~ (all_52_12 = e1)
% 153.87/23.11    (4)   ~ (all_52_12 = e0)
% 153.87/23.11  
% 153.87/23.11  Begin of proof
% 153.87/23.11  | 
% 153.87/23.11  | BETA: splitting (1) gives:
% 153.87/23.11  | 
% 153.87/23.11  | Case 1:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (5)  all_54_3 = e1
% 153.87/23.11  | | 
% 153.87/23.11  | | COMBINE_EQS: (2), (5) imply:
% 153.87/23.11  | |   (6)  all_52_12 = e1
% 153.87/23.11  | | 
% 153.87/23.11  | | SIMP: (6) implies:
% 153.87/23.11  | |   (7)  all_52_12 = e1
% 153.87/23.11  | | 
% 153.87/23.11  | | REDUCE: (3), (7) imply:
% 153.87/23.11  | |   (8)  $false
% 153.87/23.11  | | 
% 153.87/23.11  | | CLOSE: (8) is inconsistent.
% 153.87/23.11  | | 
% 153.87/23.11  | Case 2:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (9)  all_54_3 = e0
% 153.87/23.11  | | 
% 153.87/23.11  | | COMBINE_EQS: (2), (9) imply:
% 153.87/23.11  | |   (10)  all_52_12 = e0
% 153.87/23.11  | | 
% 153.87/23.11  | | SIMP: (10) implies:
% 153.87/23.11  | |   (11)  all_52_12 = e0
% 153.87/23.11  | | 
% 153.87/23.11  | | REDUCE: (4), (11) imply:
% 153.87/23.11  | |   (12)  $false
% 153.87/23.11  | | 
% 153.87/23.11  | | CLOSE: (12) is inconsistent.
% 153.87/23.11  | | 
% 153.87/23.11  | End of split
% 153.87/23.11  | 
% 153.87/23.11  End of proof
% 153.87/23.11  
% 153.87/23.11  Sub-proof #760 shows that the following formulas are inconsistent:
% 153.87/23.11  ----------------------------------------------------------------
% 153.87/23.11    (1)  all_54_3 = all_52_12
% 153.87/23.11    (2)  all_54_3 = e2
% 153.87/23.11    (3)   ~ (all_52_12 = e2)
% 153.87/23.11  
% 153.87/23.11  Begin of proof
% 153.87/23.11  | 
% 153.87/23.11  | COMBINE_EQS: (1), (2) imply:
% 153.87/23.11  |   (4)  all_52_12 = e2
% 153.87/23.11  | 
% 153.87/23.11  | SIMP: (4) implies:
% 153.87/23.11  |   (5)  all_52_12 = e2
% 153.87/23.11  | 
% 153.87/23.11  | REDUCE: (3), (5) imply:
% 153.87/23.11  |   (6)  $false
% 153.87/23.11  | 
% 153.87/23.11  | CLOSE: (6) is inconsistent.
% 153.87/23.11  | 
% 153.87/23.11  End of proof
% 153.87/23.11  
% 153.87/23.11  Sub-proof #761 shows that the following formulas are inconsistent:
% 153.87/23.11  ----------------------------------------------------------------
% 153.87/23.11    (1)  op(e2, e2) = e1
% 153.87/23.11    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.87/23.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.87/23.11    (3)  op(e3, e3) = e2
% 153.87/23.11    (4)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.87/23.11             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.87/23.11           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.87/23.11               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.87/23.11             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.87/23.11         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.87/23.11             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.87/23.11           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.87/23.11               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.87/23.11             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 153.87/23.11    (5)   ~ (e3 = e2)
% 153.87/23.11    (6)   ~ (e2 = e1)
% 153.87/23.11  
% 153.87/23.11  Begin of proof
% 153.87/23.11  | 
% 153.87/23.11  | BETA: splitting (4) gives:
% 153.87/23.11  | 
% 153.87/23.11  | Case 1:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2)
% 153.87/23.11  | |          | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.87/23.11  | |        ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 153.87/23.11  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 153.87/23.11  | |              e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 153.87/23.11  | |            $i(all_57_15)))
% 153.87/23.11  | | 
% 153.87/23.11  | | ALPHA: (7) implies:
% 153.87/23.11  | |   (8)  op(e3, e3) = e3
% 153.87/23.11  | | 
% 153.87/23.11  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1085.
% 153.87/23.11  | | 
% 153.87/23.11  | Case 2:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3)
% 153.87/23.11  | |          | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.87/23.11  | |        ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.87/23.11  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.87/23.11  | |              e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.87/23.11  | |            $i(all_57_15)))
% 153.87/23.11  | | 
% 153.87/23.11  | | ALPHA: (9) implies:
% 153.87/23.11  | |   (10)  op(e2, e2) = e2
% 153.87/23.11  | | 
% 153.87/23.11  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #1158.
% 153.87/23.11  | | 
% 153.87/23.11  | End of split
% 153.87/23.11  | 
% 153.87/23.11  End of proof
% 153.87/23.11  
% 153.87/23.11  Sub-proof #762 shows that the following formulas are inconsistent:
% 153.87/23.11  ----------------------------------------------------------------
% 153.87/23.11    (1)  op(e0, e1) = all_52_11
% 153.87/23.11    (2)  op(e2, e2) = e1
% 153.87/23.11    (3)  op(e0, e2) = all_52_7
% 153.87/23.11    (4)  op(e1, e1) = all_4_2
% 153.87/23.11    (5)   ~ (e2 = e0)
% 153.87/23.11    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.87/23.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.87/23.11    (7)  op(e3, e3) = e2
% 153.87/23.11    (8)   ~ (all_52_14 = e1)
% 153.87/23.11    (9)  op(e1, e0) = all_52_14
% 153.87/23.11    (10)   ~ (all_52_11 = e0)
% 153.87/23.11    (11)  op(e0, e3) = all_52_3
% 153.87/23.11    (12)  op(e1, e1) = e1
% 153.87/23.11    (13)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.87/23.11              e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.87/23.11            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.87/23.11            = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.87/23.11            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.87/23.11            op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.87/23.11            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2)
% 153.87/23.11            = all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0) =
% 153.87/23.11            e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &
% 153.87/23.11             ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 &
% 153.87/23.11            op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.87/23.11            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.87/23.11            (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 153.87/23.11            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.87/23.11            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~
% 153.87/23.11            (all_57_9 = e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.87/23.11            all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.87/23.11            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.87/23.11            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.87/23.11            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.87/23.11            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.87/23.11              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.87/23.11            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.87/23.11            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.87/23.11              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.87/23.11            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.87/23.11            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.87/23.11                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.87/23.11                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.87/23.11                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.87/23.11                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.87/23.11                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.87/23.11                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.87/23.11                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.87/23.11              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.87/23.11                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.87/23.11                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.87/23.11                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.87/23.11                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.87/23.11                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.87/23.11                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.87/23.11                $i(all_57_7))))
% 153.87/23.11    (14)   ~ (all_52_7 = e0)
% 153.87/23.11    (15)   ~ (e1 = e0)
% 153.87/23.11    (16)   ~ (all_52_3 = e0)
% 153.87/23.11    (17)   ~ (e2 = e1)
% 153.87/23.11    (18)  op(e0, e0) = e0
% 153.87/23.11  
% 153.87/23.11  Begin of proof
% 153.87/23.11  | 
% 153.87/23.11  | BETA: splitting (13) gives:
% 153.87/23.11  | 
% 153.87/23.11  | Case 1:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (19)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 153.87/23.11  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.87/23.11  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 153.87/23.11  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 153.87/23.11  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.87/23.11  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 153.87/23.11  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 153.87/23.11  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.87/23.11  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.87/23.11  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.87/23.11  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.87/23.11  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.87/23.11  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 153.87/23.11  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 153.87/23.11  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.87/23.11  | |           $i(all_57_13))
% 153.87/23.11  | | 
% 153.87/23.11  | | BETA: splitting (19) gives:
% 153.87/23.11  | | 
% 153.87/23.11  | | Case 1:
% 153.87/23.11  | | | 
% 153.87/23.11  | | |   (20)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.87/23.11  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.87/23.11  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.87/23.11  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 153.87/23.11  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.87/23.11  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.87/23.11  | | |           $i(all_57_6) & $i(all_57_12))
% 153.87/23.11  | | | 
% 153.87/23.11  | | | REF_CLOSE: (6), (7), (15), (17), (18), (20) are inconsistent by sub-proof
% 153.87/23.11  | | |            #766.
% 153.87/23.11  | | | 
% 153.87/23.11  | | Case 2:
% 153.87/23.11  | | | 
% 153.87/23.11  | | |   (21)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.87/23.11  | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.87/23.11  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.87/23.11  | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10
% 153.87/23.11  | | |             = e0) &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 153.87/23.11  | | |             e0) = e3 & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.87/23.11  | | |           $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 153.87/23.11  | | |           &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.87/23.11  | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.87/23.11  | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.87/23.11  | | | 
% 153.87/23.11  | | | BETA: splitting (21) gives:
% 153.87/23.11  | | | 
% 153.87/23.11  | | | Case 1:
% 153.87/23.11  | | | | 
% 153.87/23.11  | | | |   (22)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.87/23.11  | | | |         (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.87/23.11  | | | |         op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.87/23.11  | | | |         $i(all_57_12)
% 153.87/23.11  | | | | 
% 153.87/23.11  | | | | ALPHA: (22) implies:
% 153.87/23.11  | | | |   (23)  op(e0, e0) = e1
% 153.87/23.11  | | | | 
% 153.87/23.11  | | | | REF_CLOSE: (6), (15), (18), (23) are inconsistent by sub-proof #1040.
% 153.87/23.11  | | | | 
% 153.87/23.11  | | | Case 2:
% 153.87/23.11  | | | | 
% 153.87/23.11  | | | |   (24)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.87/23.11  | | | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.87/23.11  | | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.87/23.11  | | | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~
% 153.87/23.11  | | | |           (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3) =
% 153.87/23.11  | | | |           all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.87/23.11  | | | |           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.87/23.11  | | | | 
% 153.87/23.11  | | | | REF_CLOSE: (2), (6), (12), (15), (24) are inconsistent by sub-proof
% 153.87/23.11  | | | |            #765.
% 153.87/23.11  | | | | 
% 153.87/23.11  | | | End of split
% 153.87/23.11  | | | 
% 153.87/23.11  | | End of split
% 153.87/23.11  | | 
% 153.87/23.11  | Case 2:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (25)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.87/23.11  | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.87/23.11  | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.87/23.11  | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 153.87/23.11  | |             e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.87/23.11  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 153.87/23.11  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.87/23.11  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 153.87/23.11  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.87/23.11  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 153.87/23.11  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.87/23.11  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.87/23.11  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.87/23.11  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.87/23.11  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.87/23.11  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 153.87/23.11  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.87/23.11  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.87/23.11  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 153.87/23.11  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.87/23.11  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.87/23.11  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 153.87/23.11  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.87/23.11  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 153.87/23.11  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.87/23.11  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.87/23.11  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.87/23.11  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.87/23.11  | |               $i(all_57_7))))
% 153.87/23.11  | | 
% 153.87/23.11  | | BETA: splitting (25) gives:
% 153.87/23.11  | | 
% 153.87/23.11  | | Case 1:
% 153.87/23.11  | | | 
% 153.87/23.11  | | |   (26)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.87/23.11  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.87/23.11  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.87/23.11  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.87/23.11  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.87/23.11  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.87/23.11  | | |           $i(all_57_9) & $i(all_57_14))
% 153.87/23.11  | | | 
% 153.87/23.11  | | | REF_CLOSE: (5), (6), (7), (26) are inconsistent by sub-proof #1037.
% 153.87/23.11  | | | 
% 153.87/23.11  | | Case 2:
% 153.87/23.11  | | | 
% 153.87/23.11  | | |   (27)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.87/23.11  | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.87/23.11  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.87/23.11  | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 153.87/23.11  | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.87/23.11  | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.87/23.11  | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.87/23.11  | | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 153.87/23.11  | | |                 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.87/23.11  | | |               op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 153.87/23.11  | | |             (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.87/23.11  | | |               (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.87/23.11  | | |               op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.87/23.11  | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3)
% 153.87/23.11  | | |               = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.87/23.11  | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 153.87/23.11  | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.87/23.11  | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4))
% 153.87/23.11  | | |             | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.87/23.11  | | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.87/23.11  | | |               op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 153.87/23.11  | | |               = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2)
% 153.87/23.11  | | |               = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.87/23.11  | | |               $i(all_57_7))))
% 153.87/23.11  | | | 
% 153.87/23.11  | | | REF_CLOSE: (1), (3), (4), (6), (8), (9), (10), (11), (12), (14), (15),
% 153.87/23.11  | | |            (16), (17), (27) are inconsistent by sub-proof #763.
% 153.87/23.11  | | | 
% 153.87/23.11  | | End of split
% 153.87/23.11  | | 
% 153.87/23.11  | End of split
% 153.87/23.11  | 
% 153.87/23.11  End of proof
% 153.87/23.11  
% 153.87/23.11  Sub-proof #763 shows that the following formulas are inconsistent:
% 153.87/23.11  ----------------------------------------------------------------
% 153.87/23.11    (1)  op(e0, e1) = all_52_11
% 153.87/23.11    (2)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 =
% 153.87/23.11             e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.87/23.11           op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 =
% 153.87/23.11           e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.87/23.11           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 153.87/23.11           op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.87/23.11           all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 153.87/23.11               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.87/23.11               op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 153.87/23.11               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.87/23.11               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.87/23.11               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 153.87/23.11                 e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.87/23.11               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.87/23.11               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1,
% 153.87/23.11                 e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.87/23.11               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 153.87/23.11                 e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.87/23.11               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.87/23.11               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 153.87/23.11                 e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.87/23.11               $i(all_57_7))))
% 153.87/23.11    (3)  op(e0, e2) = all_52_7
% 153.87/23.11    (4)  op(e1, e1) = all_4_2
% 153.87/23.11    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.87/23.11           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.87/23.11    (6)   ~ (all_52_14 = e1)
% 153.87/23.11    (7)  op(e1, e0) = all_52_14
% 153.87/23.11    (8)   ~ (all_52_11 = e0)
% 153.87/23.11    (9)  op(e0, e3) = all_52_3
% 153.87/23.11    (10)  op(e1, e1) = e1
% 153.87/23.11    (11)   ~ (all_52_7 = e0)
% 153.87/23.11    (12)   ~ (e1 = e0)
% 153.87/23.11    (13)   ~ (all_52_3 = e0)
% 153.87/23.11    (14)   ~ (e2 = e1)
% 153.87/23.11  
% 153.87/23.11  Begin of proof
% 153.87/23.11  | 
% 153.87/23.11  | BETA: splitting (2) gives:
% 153.87/23.11  | 
% 153.87/23.11  | Case 1:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (15)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 153.87/23.11  | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & op(e1,
% 153.87/23.11  | |           e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) & $i(all_57_13)
% 153.87/23.11  | | 
% 153.87/23.11  | | ALPHA: (15) implies:
% 153.87/23.11  | |   (16)  op(e1, e1) = e0
% 153.87/23.11  | | 
% 153.87/23.11  | | REF_CLOSE: (5), (10), (12), (16) are inconsistent by sub-proof #1038.
% 153.87/23.11  | | 
% 153.87/23.11  | Case 2:
% 153.87/23.11  | | 
% 153.87/23.11  | |   (17)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.87/23.11  | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.87/23.11  | |           op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.87/23.11  | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.87/23.11  | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.87/23.11  | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.87/23.11  | |               op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 153.87/23.11  | |               e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.87/23.11  | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.87/23.11  | |             (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.87/23.11  | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.87/23.11  | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 153.87/23.11  | |               e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.87/23.11  | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.87/23.11  | |             (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.87/23.11  | |               (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.87/23.11  | |               op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 153.87/23.11  | |               e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 153.87/23.11  | |               e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.87/23.11  | | 
% 153.87/23.11  | | BETA: splitting (17) gives:
% 153.87/23.11  | | 
% 153.87/23.11  | | Case 1:
% 153.87/23.11  | | | 
% 153.87/23.11  | | |   (18)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.87/23.11  | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.87/23.11  | | |         op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.87/23.11  | | |         $i(all_57_14)
% 153.87/23.11  | | | 
% 153.87/23.11  | | | ALPHA: (18) implies:
% 153.87/23.11  | | |   (19)  op(e1, e0) = e1
% 153.87/23.11  | | | 
% 153.87/23.11  | | | REF_CLOSE: (5), (6), (7), (19) are inconsistent by sub-proof #961.
% 153.87/23.11  | | | 
% 153.87/23.11  | | Case 2:
% 153.87/23.11  | | | 
% 153.87/23.11  | | |   (20)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.87/23.11  | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.87/23.11  | | |             op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.87/23.11  | | |             $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1
% 153.87/23.11  | | |               = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 153.87/23.11  | | |               e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.87/23.11  | | |             & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.87/23.11  | | |             op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.87/23.11  | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 153.87/23.11  | | |               = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1,
% 153.87/23.11  | | |               e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0
% 153.87/23.11  | | |             & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 153.87/23.11  | | |             op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.87/23.11  | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 153.87/23.11  | | |               = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.87/23.11  | | |             all_57_7 & op(e0, e1) = e0 & $i(all_57_7)))
% 153.87/23.11  | | | 
% 153.87/23.11  | | | ALPHA: (20) implies:
% 153.87/23.11  | | |   (21)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.87/23.11  | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.87/23.12  | | |           op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 153.87/23.12  | | |           e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.87/23.12  | | |           all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.87/23.12  | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.87/23.12  | | |           (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.87/23.12  | | |           op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 153.87/23.12  | | |           e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.87/23.12  | | |           all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.87/23.12  | | |         (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.87/23.12  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.87/23.12  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 153.87/23.12  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.87/23.12  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.87/23.12  | | | 
% 153.87/23.12  | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (11), (13), (14), (21) are
% 153.87/23.12  | | |            inconsistent by sub-proof #764.
% 153.87/23.12  | | | 
% 153.87/23.12  | | End of split
% 153.87/23.12  | | 
% 153.87/23.12  | End of split
% 153.87/23.12  | 
% 153.87/23.12  End of proof
% 153.87/23.12  
% 153.87/23.12  Sub-proof #764 shows that the following formulas are inconsistent:
% 153.87/23.12  ----------------------------------------------------------------
% 153.87/23.12    (1)  op(e0, e1) = all_52_11
% 153.87/23.12    (2)  op(e0, e2) = all_52_7
% 153.87/23.12    (3)  op(e1, e1) = all_4_2
% 153.87/23.12    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.87/23.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.87/23.12    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.87/23.12             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.87/23.12           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.87/23.12           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.87/23.12             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.87/23.12           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.87/23.12           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.87/23.12           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.87/23.12           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.87/23.12           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 153.87/23.12           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.87/23.12         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.87/23.12             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.87/23.12           $i(all_57_7))
% 153.87/23.12    (6)   ~ (all_52_11 = e0)
% 153.87/23.12    (7)  op(e0, e3) = all_52_3
% 153.87/23.12    (8)  op(e1, e1) = e1
% 153.87/23.12    (9)   ~ (all_52_7 = e0)
% 153.87/23.12    (10)   ~ (all_52_3 = e0)
% 153.87/23.12    (11)   ~ (e2 = e1)
% 153.87/23.12  
% 153.87/23.12  Begin of proof
% 153.87/23.12  | 
% 153.87/23.12  | BETA: splitting (5) gives:
% 153.87/23.12  | 
% 153.87/23.12  | Case 1:
% 153.87/23.12  | | 
% 153.92/23.12  | |   (12)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 153.92/23.12  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.92/23.12  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.92/23.12  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.92/23.12  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.92/23.12  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.92/23.12  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.92/23.12  | |           $i(all_57_3))
% 153.92/23.12  | | 
% 153.92/23.12  | | REF_CLOSE: (2), (4), (7), (9), (10), (12) are inconsistent by sub-proof
% 153.92/23.12  | |            #1035.
% 153.92/23.12  | | 
% 153.92/23.12  | Case 2:
% 153.92/23.12  | | 
% 153.92/23.12  | |   (13)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.92/23.12  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.92/23.12  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.92/23.12  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.92/23.12  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.92/23.12  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.92/23.12  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.92/23.12  | |           $i(all_57_7))
% 153.92/23.12  | | 
% 153.92/23.12  | | BETA: splitting (13) gives:
% 153.92/23.12  | | 
% 153.92/23.12  | | Case 1:
% 153.92/23.12  | | | 
% 153.92/23.12  | | |   (14)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.92/23.12  | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.92/23.12  | | |         op(e0, e2) = e0 & $i(all_57_4)
% 153.92/23.12  | | | 
% 153.92/23.12  | | | ALPHA: (14) implies:
% 153.92/23.12  | | |   (15)  op(e1, e1) = e2
% 153.92/23.12  | | | 
% 153.92/23.12  | | | REF_CLOSE: (3), (4), (8), (11), (15) are inconsistent by sub-proof #1044.
% 153.92/23.12  | | | 
% 153.92/23.12  | | Case 2:
% 153.92/23.12  | | | 
% 153.92/23.12  | | |   (16)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.92/23.12  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.92/23.12  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 153.92/23.12  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 153.92/23.12  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.92/23.12  | | | 
% 153.92/23.12  | | | REF_CLOSE: (1), (4), (6), (16) are inconsistent by sub-proof #851.
% 153.92/23.12  | | | 
% 153.92/23.12  | | End of split
% 153.92/23.12  | | 
% 153.92/23.12  | End of split
% 153.92/23.12  | 
% 153.92/23.12  End of proof
% 153.92/23.12  
% 153.92/23.12  Sub-proof #765 shows that the following formulas are inconsistent:
% 153.92/23.12  ----------------------------------------------------------------
% 153.92/23.12    (1)  op(e2, e2) = e1
% 153.92/23.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.92/23.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.92/23.12    (3)  op(e1, e1) = e1
% 153.92/23.12    (4)   ~ (e1 = e0)
% 153.92/23.12    (5)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 153.92/23.12             e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.92/23.12           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 =
% 153.92/23.12           e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 153.92/23.12           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 153.92/23.12           = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.92/23.12  
% 153.92/23.12  Begin of proof
% 153.92/23.12  | 
% 153.92/23.12  | BETA: splitting (5) gives:
% 153.92/23.12  | 
% 153.92/23.12  | Case 1:
% 153.92/23.12  | | 
% 153.92/23.12  | |   (6)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 153.92/23.12  | |          = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0
% 153.92/23.12  | |        & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)
% 153.92/23.12  | | 
% 153.92/23.12  | | ALPHA: (6) implies:
% 153.92/23.12  | |   (7)  op(e2, e2) = e0
% 153.92/23.12  | | 
% 153.92/23.12  | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #853.
% 153.92/23.12  | | 
% 153.92/23.12  | Case 2:
% 153.92/23.12  | | 
% 153.92/23.12  | |   (8)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 153.92/23.12  | |          = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 153.92/23.12  | |        & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)
% 153.92/23.12  | | 
% 153.92/23.12  | | ALPHA: (8) implies:
% 153.92/23.12  | |   (9)  op(e1, e1) = e0
% 153.92/23.12  | | 
% 153.92/23.12  | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1038.
% 153.92/23.12  | | 
% 153.92/23.12  | End of split
% 153.92/23.12  | 
% 153.92/23.12  End of proof
% 153.92/23.12  
% 153.92/23.12  Sub-proof #766 shows that the following formulas are inconsistent:
% 153.92/23.12  ----------------------------------------------------------------
% 153.92/23.12    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.92/23.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.92/23.12    (2)  op(e3, e3) = e2
% 153.92/23.12    (3)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.92/23.12             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.92/23.12           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 153.92/23.12           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.92/23.12           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 153.92/23.12           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 153.92/23.12    (4)   ~ (e1 = e0)
% 153.92/23.12    (5)   ~ (e2 = e1)
% 153.92/23.12    (6)  op(e0, e0) = e0
% 153.92/23.12  
% 153.92/23.12  Begin of proof
% 153.92/23.12  | 
% 153.92/23.12  | BETA: splitting (3) gives:
% 153.92/23.12  | 
% 153.92/23.12  | Case 1:
% 153.92/23.12  | | 
% 153.92/23.12  | |   (7)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 153.92/23.12  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.92/23.12  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 153.92/23.12  | | 
% 153.92/23.12  | | ALPHA: (7) implies:
% 153.92/23.12  | |   (8)  op(e0, e0) = e1
% 153.92/23.12  | | 
% 153.92/23.12  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #1040.
% 153.92/23.12  | | 
% 153.92/23.12  | Case 2:
% 153.92/23.12  | | 
% 153.92/23.12  | |   (9)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 153.92/23.12  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.92/23.12  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 153.92/23.12  | | 
% 153.92/23.12  | | ALPHA: (9) implies:
% 153.92/23.12  | |   (10)  op(e3, e3) = e1
% 153.92/23.12  | | 
% 153.92/23.12  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1074.
% 153.92/23.12  | | 
% 153.92/23.12  | End of split
% 153.92/23.12  | 
% 153.92/23.12  End of proof
% 153.92/23.12  
% 153.92/23.12  Sub-proof #767 shows that the following formulas are inconsistent:
% 153.92/23.12  ----------------------------------------------------------------
% 153.92/23.12    (1)  ( ~ (all_36_0 = e1) & op(all_36_1, e3) = all_36_0 & op(e3, e2) = all_36_1
% 153.92/23.12           & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e0) & op(e3, e2) =
% 153.92/23.12           all_36_1 & $i(all_36_1))
% 153.92/23.12    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.92/23.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.92/23.12    (3)  op(e3, e2) = e0
% 153.92/23.12    (4)  op(e0, e3) = e1
% 153.92/23.12  
% 153.92/23.12  Begin of proof
% 153.92/23.12  | 
% 153.92/23.12  | BETA: splitting (1) gives:
% 153.92/23.12  | 
% 153.92/23.12  | Case 1:
% 153.92/23.12  | | 
% 153.92/23.12  | |   (5)   ~ (all_36_0 = e1) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 153.92/23.12  | |        all_36_1 & $i(all_36_0) & $i(all_36_1)
% 153.92/23.12  | | 
% 153.92/23.12  | | ALPHA: (5) implies:
% 153.92/23.12  | |   (6)   ~ (all_36_0 = e1)
% 153.92/23.12  | |   (7)  op(e3, e2) = all_36_1
% 153.92/23.12  | |   (8)  op(all_36_1, e3) = all_36_0
% 153.92/23.12  | | 
% 153.92/23.12  | | GROUND_INST: instantiating (2) with e0, all_36_1, e2, e3, simplifying with
% 153.92/23.12  | |              (3), (7) gives:
% 153.92/23.12  | |   (9)  all_36_1 = e0
% 153.92/23.12  | | 
% 153.92/23.12  | | GROUND_INST: instantiating (2) with e1, all_36_0, e3, e0, simplifying with
% 153.92/23.12  | |              (4) gives:
% 153.92/23.12  | |   (10)  all_36_0 = e1 |  ~ (op(e0, e3) = all_36_0)
% 153.92/23.12  | | 
% 153.92/23.12  | | REDUCE: (8), (9) imply:
% 153.92/23.12  | |   (11)  op(e0, e3) = all_36_0
% 153.92/23.12  | | 
% 153.92/23.12  | | BETA: splitting (10) gives:
% 153.92/23.12  | | 
% 153.92/23.12  | | Case 1:
% 153.92/23.12  | | | 
% 153.92/23.12  | | |   (12)   ~ (op(e0, e3) = all_36_0)
% 153.92/23.12  | | | 
% 153.92/23.12  | | | PRED_UNIFY: (11), (12) imply:
% 153.92/23.12  | | |   (13)  $false
% 153.92/23.12  | | | 
% 153.92/23.12  | | | CLOSE: (13) is inconsistent.
% 153.92/23.12  | | | 
% 153.92/23.12  | | Case 2:
% 153.92/23.12  | | | 
% 153.92/23.12  | | |   (14)  all_36_0 = e1
% 153.92/23.12  | | | 
% 153.92/23.12  | | | REDUCE: (6), (14) imply:
% 153.92/23.12  | | |   (15)  $false
% 153.92/23.12  | | | 
% 153.92/23.12  | | | CLOSE: (15) is inconsistent.
% 153.92/23.12  | | | 
% 153.92/23.12  | | End of split
% 153.92/23.12  | | 
% 153.92/23.12  | Case 2:
% 153.92/23.12  | | 
% 153.92/23.12  | |   (16)   ~ (all_36_1 = e0) & op(e3, e2) = all_36_1 & $i(all_36_1)
% 153.92/23.12  | | 
% 153.92/23.12  | | ALPHA: (16) implies:
% 153.92/23.12  | |   (17)   ~ (all_36_1 = e0)
% 153.92/23.12  | |   (18)  op(e3, e2) = all_36_1
% 153.92/23.12  | | 
% 153.92/23.12  | | GROUND_INST: instantiating (2) with e0, all_36_1, e2, e3, simplifying with
% 153.92/23.12  | |              (3), (18) gives:
% 153.92/23.12  | |   (19)  all_36_1 = e0
% 153.92/23.12  | | 
% 153.92/23.12  | | REDUCE: (17), (19) imply:
% 153.92/23.12  | |   (20)  $false
% 153.92/23.12  | | 
% 153.92/23.12  | | CLOSE: (20) is inconsistent.
% 153.92/23.12  | | 
% 153.92/23.12  | End of split
% 153.92/23.12  | 
% 153.92/23.12  End of proof
% 153.92/23.12  
% 153.92/23.12  Sub-proof #768 shows that the following formulas are inconsistent:
% 153.92/23.12  ----------------------------------------------------------------
% 153.92/23.12    (1)  all_54_1 = all_52_4
% 153.92/23.12    (2)  all_54_1 = e2
% 153.92/23.12    (3)   ~ (all_52_4 = e2)
% 153.92/23.12  
% 153.92/23.12  Begin of proof
% 153.92/23.12  | 
% 153.92/23.12  | COMBINE_EQS: (1), (2) imply:
% 153.92/23.12  |   (4)  all_52_4 = e2
% 153.92/23.12  | 
% 153.92/23.12  | SIMP: (4) implies:
% 153.92/23.12  |   (5)  all_52_4 = e2
% 153.92/23.12  | 
% 153.92/23.12  | REDUCE: (3), (5) imply:
% 153.92/23.12  |   (6)  $false
% 153.92/23.12  | 
% 153.92/23.12  | CLOSE: (6) is inconsistent.
% 153.92/23.12  | 
% 153.92/23.12  End of proof
% 153.92/23.12  
% 153.92/23.12  Sub-proof #769 shows that the following formulas are inconsistent:
% 153.92/23.12  ----------------------------------------------------------------
% 153.92/23.12    (1)  op(e0, e0) = all_10_2
% 153.92/23.12    (2)  op(e1, e1) = all_4_2
% 153.92/23.12    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.92/23.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.92/23.12    (4)  op(e1, e1) = e1
% 153.92/23.12    (5)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.92/23.12             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.92/23.12           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 153.92/23.12           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.92/23.12           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 153.92/23.12           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 153.92/23.12    (6)   ~ (all_10_2 = e2)
% 153.92/23.12    (7)   ~ (e2 = e1)
% 153.92/23.12  
% 153.92/23.12  Begin of proof
% 153.92/23.12  | 
% 153.92/23.12  | BETA: splitting (5) gives:
% 153.92/23.12  | 
% 153.92/23.12  | Case 1:
% 153.92/23.12  | | 
% 153.92/23.12  | |   (8)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 153.92/23.12  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.92/23.12  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 153.92/23.12  | | 
% 153.92/23.12  | | ALPHA: (8) implies:
% 153.92/23.12  | |   (9)  op(e1, e1) = e2
% 153.92/23.12  | | 
% 153.92/23.12  | | REF_CLOSE: (2), (3), (4), (7), (9) are inconsistent by sub-proof #1044.
% 153.92/23.12  | | 
% 153.92/23.12  | Case 2:
% 153.92/23.12  | | 
% 153.92/23.12  | |   (10)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 153.92/23.12  | |           = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.92/23.12  | |         all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 153.92/23.12  | | 
% 153.92/23.12  | | ALPHA: (10) implies:
% 153.92/23.12  | |   (11)  op(e0, e0) = e2
% 153.92/23.12  | | 
% 153.92/23.12  | | REF_CLOSE: (1), (3), (6), (11) are inconsistent by sub-proof #1097.
% 153.92/23.12  | | 
% 153.92/23.12  | End of split
% 153.92/23.12  | 
% 153.92/23.12  End of proof
% 153.92/23.12  
% 153.92/23.12  Sub-proof #770 shows that the following formulas are inconsistent:
% 153.92/23.12  ----------------------------------------------------------------
% 153.92/23.12    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.92/23.12         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.92/23.12    (2)   ~ (e3 = e1)
% 153.92/23.12    (3)  op(e0, e0) = all_10_2
% 153.92/23.12    (4)  op(e1, e1) = all_4_2
% 153.92/23.12    (5)   ~ (e2 = e0)
% 153.92/23.12    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.92/23.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.92/23.12    (7)  op(e0, e0) = e3
% 153.92/23.12    (8)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.92/23.12             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.92/23.12               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.92/23.12               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.92/23.12    (9)   ~ (e3 = e0)
% 153.92/23.12    (10)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.92/23.12          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.92/23.12    (11)  op(e2, e0) = all_52_13
% 153.92/23.12    (12)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 153.92/23.12    (13)   ~ (e1 = e0)
% 153.92/23.12    (14)   ~ (all_4_2 = e3)
% 153.92/23.12    (15)   ~ (e3 = e2)
% 153.92/23.12    (16)   ~ (all_10_2 = e2)
% 153.92/23.12    (17)   ~ (e2 = e1)
% 153.92/23.12  
% 153.92/23.12  Begin of proof
% 153.92/23.12  | 
% 153.92/23.12  | BETA: splitting (12) gives:
% 153.92/23.12  | 
% 153.92/23.12  | Case 1:
% 153.92/23.12  | | 
% 153.92/23.12  | |   (18)  all_56_8 = e3 & op(e1, e1) = e3
% 153.92/23.12  | | 
% 153.92/23.12  | | ALPHA: (18) implies:
% 153.92/23.12  | |   (19)  op(e1, e1) = e3
% 153.92/23.12  | | 
% 153.92/23.12  | | REF_CLOSE: (4), (6), (14), (19) are inconsistent by sub-proof #1078.
% 153.92/23.12  | | 
% 153.92/23.12  | Case 2:
% 153.92/23.12  | | 
% 153.92/23.12  | |   (20)  all_56_11 = e3 & op(e1, e0) = e3
% 153.92/23.12  | | 
% 153.92/23.12  | | ALPHA: (20) implies:
% 153.92/23.12  | |   (21)  all_56_11 = e3
% 153.92/23.12  | | 
% 153.92/23.12  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (15),
% 153.92/23.12  | |            (16), (17), (21) are inconsistent by sub-proof #771.
% 153.92/23.12  | | 
% 153.92/23.12  | End of split
% 153.92/23.12  | 
% 153.92/23.12  End of proof
% 153.92/23.12  
% 153.92/23.12  Sub-proof #771 shows that the following formulas are inconsistent:
% 153.93/23.12  ----------------------------------------------------------------
% 153.93/23.12    (1)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2, e0) = e2) |
% 153.93/23.12         (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.93/23.12    (2)   ~ (e3 = e1)
% 153.93/23.12    (3)  all_56_11 = e3
% 153.93/23.12    (4)  op(e0, e0) = all_10_2
% 153.93/23.12    (5)   ~ (e2 = e0)
% 153.93/23.12    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.12    (7)  op(e0, e0) = e3
% 153.93/23.12    (8)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.93/23.12             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.93/23.12               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.93/23.12               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.93/23.12    (9)   ~ (e3 = e0)
% 153.93/23.12    (10)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.93/23.12          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.93/23.12    (11)  op(e2, e0) = all_52_13
% 153.93/23.12    (12)   ~ (e1 = e0)
% 153.93/23.12    (13)   ~ (e3 = e2)
% 153.93/23.12    (14)   ~ (all_10_2 = e2)
% 153.93/23.12    (15)   ~ (e2 = e1)
% 153.93/23.12  
% 153.93/23.12  Begin of proof
% 153.93/23.12  | 
% 153.93/23.12  | BETA: splitting (8) gives:
% 153.93/23.12  | 
% 153.93/23.12  | Case 1:
% 153.93/23.12  | | 
% 153.93/23.12  | |   (16)  all_56_15 = e0 & op(e0, e0) = e0
% 153.93/23.12  | | 
% 153.93/23.12  | | ALPHA: (16) implies:
% 153.93/23.12  | |   (17)  op(e0, e0) = e0
% 153.93/23.12  | | 
% 153.93/23.12  | | REF_CLOSE: (6), (7), (9), (17) are inconsistent by sub-proof #1143.
% 153.93/23.12  | | 
% 153.93/23.12  | Case 2:
% 153.93/23.12  | | 
% 153.93/23.12  | |   (18)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.93/23.12  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 153.93/23.12  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.93/23.12  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 153.93/23.12  | | 
% 153.93/23.12  | | ALPHA: (18) implies:
% 153.93/23.12  | |   (19)  (all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.93/23.12  | |           e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.93/23.12  | | 
% 153.93/23.12  | | BETA: splitting (19) gives:
% 153.93/23.12  | | 
% 153.93/23.12  | | Case 1:
% 153.93/23.12  | | | 
% 153.93/23.12  | | |   (20)  all_56_9 = e0 & op(e3, e0) = e0
% 153.93/23.12  | | | 
% 153.93/23.12  | | | ALPHA: (20) implies:
% 153.93/23.12  | | |   (21)  all_56_9 = e0
% 153.93/23.12  | | | 
% 153.93/23.12  | | | BETA: splitting (10) gives:
% 153.93/23.12  | | | 
% 153.93/23.12  | | | Case 1:
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | |   (22)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0)
% 153.93/23.12  | | | |           = e1)
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | | BETA: splitting (22) gives:
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | | Case 1:
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | |   (23)  all_56_9 = e1 & op(e3, e0) = e1
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | | ALPHA: (23) implies:
% 153.93/23.12  | | | | |   (24)  all_56_9 = e1
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | | REF_CLOSE: (12), (21), (24) are inconsistent by sub-proof #946.
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | Case 2:
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | |   (25)  all_56_10 = e1 & op(e2, e0) = e1
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | | ALPHA: (25) implies:
% 153.93/23.12  | | | | |   (26)  op(e2, e0) = e1
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | | BETA: splitting (1) gives:
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | | Case 1:
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | |   (27)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 & op(e2,
% 153.93/23.12  | | | | | |             e0) = e2)
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | | BETA: splitting (27) gives:
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | | Case 1:
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | |   (28)  all_56_9 = e2 & op(e3, e0) = e2
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | | ALPHA: (28) implies:
% 153.93/23.12  | | | | | | |   (29)  all_56_9 = e2
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | | REF_CLOSE: (5), (21), (29) are inconsistent by sub-proof #776.
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | Case 2:
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | |   (30)  all_56_10 = e2 & op(e2, e0) = e2
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | | ALPHA: (30) implies:
% 153.93/23.12  | | | | | | |   (31)  op(e2, e0) = e2
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | | REF_CLOSE: (6), (11), (15), (26), (31) are inconsistent by
% 153.93/23.12  | | | | | | |            sub-proof #904.
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | End of split
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | Case 2:
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | |   (32)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 &
% 153.93/23.12  | | | | | |           op(e0, e0) = e2)
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | | REF_CLOSE: (3), (4), (6), (13), (14), (32) are inconsistent by
% 153.93/23.12  | | | | | |            sub-proof #774.
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | End of split
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | End of split
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | Case 2:
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | |   (33)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0,
% 153.93/23.12  | | | |             e0) = e1)
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | | REF_CLOSE: (2), (3), (6), (7), (33) are inconsistent by sub-proof #773.
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | End of split
% 153.93/23.12  | | | 
% 153.93/23.12  | | Case 2:
% 153.93/23.12  | | | 
% 153.93/23.12  | | |   (34)  (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.93/23.12  | | |           = e0)
% 153.93/23.12  | | | 
% 153.93/23.12  | | | BETA: splitting (34) gives:
% 153.93/23.12  | | | 
% 153.93/23.12  | | | Case 1:
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | |   (35)  all_56_10 = e0 & op(e2, e0) = e0
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | | ALPHA: (35) implies:
% 153.93/23.12  | | | |   (36)  all_56_10 = e0
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | | BETA: splitting (10) gives:
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | | Case 1:
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | |   (37)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2,
% 153.93/23.12  | | | | |             e0) = e1)
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | | BETA: splitting (37) gives:
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | | Case 1:
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | |   (38)  all_56_9 = e1 & op(e3, e0) = e1
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | | ALPHA: (38) implies:
% 153.93/23.12  | | | | | |   (39)  all_56_9 = e1
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | | BETA: splitting (1) gives:
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | | Case 1:
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | |   (40)  (all_56_9 = e2 & op(e3, e0) = e2) | (all_56_10 = e2 &
% 153.93/23.12  | | | | | | |           op(e2, e0) = e2)
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | | BETA: splitting (40) gives:
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | | Case 1:
% 153.93/23.12  | | | | | | | | 
% 153.93/23.12  | | | | | | | |   (41)  all_56_9 = e2 & op(e3, e0) = e2
% 153.93/23.12  | | | | | | | | 
% 153.93/23.12  | | | | | | | | ALPHA: (41) implies:
% 153.93/23.12  | | | | | | | |   (42)  all_56_9 = e2
% 153.93/23.12  | | | | | | | | 
% 153.93/23.12  | | | | | | | | REF_CLOSE: (15), (39), (42) are inconsistent by sub-proof #948.
% 153.93/23.12  | | | | | | | | 
% 153.93/23.12  | | | | | | | Case 2:
% 153.93/23.12  | | | | | | | | 
% 153.93/23.12  | | | | | | | |   (43)  all_56_10 = e2 & op(e2, e0) = e2
% 153.93/23.12  | | | | | | | | 
% 153.93/23.12  | | | | | | | | REF_CLOSE: (5), (36), (43) are inconsistent by sub-proof #1132.
% 153.93/23.12  | | | | | | | | 
% 153.93/23.12  | | | | | | | End of split
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | Case 2:
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | |   (44)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 &
% 153.93/23.12  | | | | | | |           op(e0, e0) = e2)
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | | REF_CLOSE: (3), (4), (6), (13), (14), (44) are inconsistent by
% 153.93/23.12  | | | | | | |            sub-proof #774.
% 153.93/23.12  | | | | | | | 
% 153.93/23.12  | | | | | | End of split
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | Case 2:
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | |   (45)  all_56_10 = e1 & op(e2, e0) = e1
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | | ALPHA: (45) implies:
% 153.93/23.12  | | | | | |   (46)  all_56_10 = e1
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | | REF_CLOSE: (12), (36), (46) are inconsistent by sub-proof #963.
% 153.93/23.12  | | | | | | 
% 153.93/23.12  | | | | | End of split
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | Case 2:
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | |   (47)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0,
% 153.93/23.12  | | | | |             e0) = e1)
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | | REF_CLOSE: (2), (3), (6), (7), (47) are inconsistent by sub-proof
% 153.93/23.12  | | | | |            #773.
% 153.93/23.12  | | | | | 
% 153.93/23.12  | | | | End of split
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | Case 2:
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | |   (48)  all_56_11 = e0 & op(e1, e0) = e0
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | | ALPHA: (48) implies:
% 153.93/23.12  | | | |   (49)  all_56_11 = e0
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | | REF_CLOSE: (3), (9), (49) are inconsistent by sub-proof #772.
% 153.93/23.12  | | | | 
% 153.93/23.12  | | | End of split
% 153.93/23.12  | | | 
% 153.93/23.12  | | End of split
% 153.93/23.12  | | 
% 153.93/23.12  | End of split
% 153.93/23.12  | 
% 153.93/23.12  End of proof
% 153.93/23.12  
% 153.93/23.12  Sub-proof #772 shows that the following formulas are inconsistent:
% 153.93/23.12  ----------------------------------------------------------------
% 153.93/23.12    (1)  all_56_11 = e3
% 153.93/23.12    (2)  all_56_11 = e0
% 153.93/23.12    (3)   ~ (e3 = e0)
% 153.93/23.12  
% 153.93/23.12  Begin of proof
% 153.93/23.12  | 
% 153.93/23.12  | COMBINE_EQS: (1), (2) imply:
% 153.93/23.12  |   (4)  e3 = e0
% 153.93/23.12  | 
% 153.93/23.12  | SIMP: (4) implies:
% 153.93/23.12  |   (5)  e3 = e0
% 153.93/23.12  | 
% 153.93/23.12  | REDUCE: (3), (5) imply:
% 153.93/23.12  |   (6)  $false
% 153.93/23.12  | 
% 153.93/23.12  | CLOSE: (6) is inconsistent.
% 153.93/23.12  | 
% 153.93/23.12  End of proof
% 153.93/23.12  
% 153.93/23.12  Sub-proof #773 shows that the following formulas are inconsistent:
% 153.93/23.12  ----------------------------------------------------------------
% 153.93/23.12    (1)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.93/23.12    (2)   ~ (e3 = e1)
% 153.93/23.12    (3)  all_56_11 = e3
% 153.93/23.12    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.12    (5)  op(e0, e0) = e3
% 153.93/23.12  
% 153.93/23.12  Begin of proof
% 153.93/23.12  | 
% 153.93/23.12  | BETA: splitting (1) gives:
% 153.93/23.12  | 
% 153.93/23.12  | Case 1:
% 153.93/23.12  | | 
% 153.93/23.12  | |   (6)  all_56_11 = e1 & op(e1, e0) = e1
% 153.93/23.12  | | 
% 153.93/23.12  | | ALPHA: (6) implies:
% 153.93/23.12  | |   (7)  all_56_11 = e1
% 153.93/23.12  | | 
% 153.93/23.12  | | COMBINE_EQS: (3), (7) imply:
% 153.93/23.12  | |   (8)  e3 = e1
% 153.93/23.12  | | 
% 153.93/23.12  | | REDUCE: (2), (8) imply:
% 153.93/23.12  | |   (9)  $false
% 153.93/23.12  | | 
% 153.93/23.12  | | CLOSE: (9) is inconsistent.
% 153.93/23.12  | | 
% 153.93/23.12  | Case 2:
% 153.93/23.12  | | 
% 153.93/23.12  | |   (10)  all_56_15 = e1 & op(e0, e0) = e1
% 153.93/23.12  | | 
% 153.93/23.12  | | ALPHA: (10) implies:
% 153.93/23.12  | |   (11)  op(e0, e0) = e1
% 153.93/23.12  | | 
% 153.93/23.12  | | REF_CLOSE: (2), (4), (5), (11) are inconsistent by sub-proof #1022.
% 153.93/23.12  | | 
% 153.93/23.12  | End of split
% 153.93/23.12  | 
% 153.93/23.12  End of proof
% 153.93/23.12  
% 153.93/23.12  Sub-proof #774 shows that the following formulas are inconsistent:
% 153.93/23.12  ----------------------------------------------------------------
% 153.93/23.12    (1)  all_56_11 = e3
% 153.93/23.12    (2)  op(e0, e0) = all_10_2
% 153.93/23.12    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.12    (4)  (all_56_11 = e2 & op(e1, e0) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 153.93/23.12    (5)   ~ (e3 = e2)
% 153.93/23.12    (6)   ~ (all_10_2 = e2)
% 153.93/23.12  
% 153.93/23.12  Begin of proof
% 153.93/23.12  | 
% 153.93/23.12  | BETA: splitting (4) gives:
% 153.93/23.12  | 
% 153.93/23.12  | Case 1:
% 153.93/23.12  | | 
% 153.93/23.12  | |   (7)  all_56_11 = e2 & op(e1, e0) = e2
% 153.93/23.12  | | 
% 153.93/23.12  | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #775.
% 153.93/23.12  | | 
% 153.93/23.12  | Case 2:
% 153.93/23.12  | | 
% 153.93/23.12  | |   (8)  all_56_15 = e2 & op(e0, e0) = e2
% 153.93/23.12  | | 
% 153.93/23.12  | | ALPHA: (8) implies:
% 153.93/23.12  | |   (9)  op(e0, e0) = e2
% 153.93/23.12  | | 
% 153.93/23.12  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #1097.
% 153.93/23.12  | | 
% 153.93/23.12  | End of split
% 153.93/23.12  | 
% 153.93/23.12  End of proof
% 153.93/23.12  
% 153.93/23.12  Sub-proof #775 shows that the following formulas are inconsistent:
% 153.93/23.12  ----------------------------------------------------------------
% 153.93/23.12    (1)  all_56_11 = e2 & op(e1, e0) = e2
% 153.93/23.12    (2)  all_56_11 = e3
% 153.93/23.12    (3)   ~ (e3 = e2)
% 153.93/23.12  
% 153.93/23.12  Begin of proof
% 153.93/23.12  | 
% 153.93/23.12  | ALPHA: (1) implies:
% 153.93/23.12  |   (4)  all_56_11 = e2
% 153.93/23.12  | 
% 153.93/23.12  | COMBINE_EQS: (2), (4) imply:
% 153.93/23.12  |   (5)  e3 = e2
% 153.93/23.12  | 
% 153.93/23.12  | REDUCE: (3), (5) imply:
% 153.93/23.12  |   (6)  $false
% 153.93/23.12  | 
% 153.93/23.12  | CLOSE: (6) is inconsistent.
% 153.93/23.12  | 
% 153.93/23.12  End of proof
% 153.93/23.12  
% 153.93/23.12  Sub-proof #776 shows that the following formulas are inconsistent:
% 153.93/23.12  ----------------------------------------------------------------
% 153.93/23.12    (1)  all_56_9 = e2
% 153.93/23.12    (2)  all_56_9 = e0
% 153.93/23.12    (3)   ~ (e2 = e0)
% 153.93/23.12  
% 153.93/23.12  Begin of proof
% 153.93/23.12  | 
% 153.93/23.12  | COMBINE_EQS: (1), (2) imply:
% 153.93/23.12  |   (4)  e2 = e0
% 153.93/23.12  | 
% 153.93/23.12  | SIMP: (4) implies:
% 153.93/23.12  |   (5)  e2 = e0
% 153.93/23.12  | 
% 153.93/23.12  | REDUCE: (3), (5) imply:
% 153.93/23.12  |   (6)  $false
% 153.93/23.12  | 
% 153.93/23.12  | CLOSE: (6) is inconsistent.
% 153.93/23.12  | 
% 153.93/23.12  End of proof
% 153.93/23.12  
% 153.93/23.12  Sub-proof #777 shows that the following formulas are inconsistent:
% 153.93/23.12  ----------------------------------------------------------------
% 153.93/23.12    (1)   ~ (e3 = e1)
% 153.93/23.12    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.93/23.12         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.93/23.12    (3)   ~ (e2 = e0)
% 153.93/23.12    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.12           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.12    (5)  all_56_12 = e0 & op(e0, e3) = e0
% 153.93/23.12    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.93/23.12         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.93/23.12    (7)   ~ (e1 = e0)
% 153.93/23.12    (8)   ~ (e3 = e2)
% 153.93/23.12    (9)  op(e3, e3) = e3
% 153.93/23.12    (10)   ~ (e2 = e1)
% 153.93/23.12    (11)  all_56_6 = e3
% 153.93/23.12    (12)  op(e2, e3) = all_52_1
% 153.93/23.12  
% 153.93/23.12  Begin of proof
% 153.93/23.12  | 
% 153.93/23.12  | ALPHA: (5) implies:
% 153.93/23.12  |   (13)  all_56_12 = e0
% 153.93/23.12  | 
% 153.93/23.12  | BETA: splitting (2) gives:
% 153.93/23.13  | 
% 153.93/23.13  | Case 1:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (14)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 153.93/23.13  | |           e1)
% 153.93/23.13  | | 
% 153.93/23.13  | | BETA: splitting (14) gives:
% 153.93/23.13  | | 
% 153.93/23.13  | | Case 1:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (15)  all_56_0 = e1 & op(e3, e3) = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (15) implies:
% 153.93/23.13  | | |   (16)  op(e3, e3) = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (1), (4), (9), (16) are inconsistent by sub-proof #1178.
% 153.93/23.13  | | | 
% 153.93/23.13  | | Case 2:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (17)  all_56_2 = e1 & op(e2, e3) = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (17) implies:
% 153.93/23.13  | | |   (18)  op(e2, e3) = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | BETA: splitting (6) gives:
% 153.93/23.13  | | | 
% 153.93/23.13  | | | Case 1:
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | |   (19)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3)
% 153.93/23.13  | | | |           = e2)
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | | BETA: splitting (19) gives:
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | | Case 1:
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | |   (20)  all_56_0 = e2 & op(e3, e3) = e2
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | | ALPHA: (20) implies:
% 153.93/23.13  | | | | |   (21)  op(e3, e3) = e2
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | | REF_CLOSE: (4), (8), (9), (21) are inconsistent by sub-proof #1085.
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | Case 2:
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | |   (22)  all_56_2 = e2 & op(e2, e3) = e2
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | | ALPHA: (22) implies:
% 153.93/23.13  | | | | |   (23)  op(e2, e3) = e2
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | | REF_CLOSE: (4), (10), (12), (18), (23) are inconsistent by sub-proof
% 153.93/23.13  | | | | |            #842.
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | End of split
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | Case 2:
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | |   (24)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3)
% 153.93/23.13  | | | |           = e2)
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | | BETA: splitting (24) gives:
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | | Case 1:
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | |   (25)  all_56_6 = e2 & op(e1, e3) = e2
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | | REF_CLOSE: (8), (11), (25) are inconsistent by sub-proof #779.
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | Case 2:
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | |   (26)  all_56_12 = e2 & op(e0, e3) = e2
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | | ALPHA: (26) implies:
% 153.93/23.13  | | | | |   (27)  all_56_12 = e2
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | | REF_CLOSE: (3), (13), (27) are inconsistent by sub-proof #1119.
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | End of split
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | End of split
% 153.93/23.13  | | | 
% 153.93/23.13  | | End of split
% 153.93/23.13  | | 
% 153.93/23.13  | Case 2:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (28)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 153.93/23.13  | |           e1)
% 153.93/23.13  | | 
% 153.93/23.13  | | BETA: splitting (28) gives:
% 153.93/23.13  | | 
% 153.93/23.13  | | Case 1:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (29)  all_56_6 = e1 & op(e1, e3) = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (1), (11), (29) are inconsistent by sub-proof #792.
% 153.93/23.13  | | | 
% 153.93/23.13  | | Case 2:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (30)  all_56_12 = e1 & op(e0, e3) = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (30) implies:
% 153.93/23.13  | | |   (31)  all_56_12 = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (7), (13), (31) are inconsistent by sub-proof #1051.
% 153.93/23.13  | | | 
% 153.93/23.13  | | End of split
% 153.93/23.13  | | 
% 153.93/23.13  | End of split
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #778 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)  all_56_6 = e0 & op(e1, e3) = e0
% 153.93/23.13    (2)  all_56_6 = e3
% 153.93/23.13    (3)   ~ (e3 = e0)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | ALPHA: (1) implies:
% 153.93/23.13  |   (4)  all_56_6 = e0
% 153.93/23.13  | 
% 153.93/23.13  | COMBINE_EQS: (2), (4) imply:
% 153.93/23.13  |   (5)  e3 = e0
% 153.93/23.13  | 
% 153.93/23.13  | REDUCE: (3), (5) imply:
% 153.93/23.13  |   (6)  $false
% 153.93/23.13  | 
% 153.93/23.13  | CLOSE: (6) is inconsistent.
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #779 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)  all_56_6 = e2 & op(e1, e3) = e2
% 153.93/23.13    (2)  all_56_6 = e3
% 153.93/23.13    (3)   ~ (e3 = e2)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | ALPHA: (1) implies:
% 153.93/23.13  |   (4)  all_56_6 = e2
% 153.93/23.13  | 
% 153.93/23.13  | COMBINE_EQS: (2), (4) imply:
% 153.93/23.13  |   (5)  e3 = e2
% 153.93/23.13  | 
% 153.93/23.13  | REDUCE: (3), (5) imply:
% 153.93/23.13  |   (6)  $false
% 153.93/23.13  | 
% 153.93/23.13  | CLOSE: (6) is inconsistent.
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #780 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)   ~ (e3 = e1)
% 153.93/23.13    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.93/23.13         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.93/23.13    (3)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.93/23.13         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.93/23.13    (4)  op(e0, e0) = all_10_2
% 153.93/23.13    (5)   ~ (all_10_2 = e1)
% 153.93/23.13    (6)   ~ (e2 = e0)
% 153.93/23.13    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.13    (8)  op(e0, e0) = e3
% 153.93/23.13    (9)  op(e3, e3) = e2
% 153.93/23.13    (10)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.93/23.13              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.93/23.13                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.93/23.13                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.93/23.13    (11)   ~ (e3 = e0)
% 153.93/23.13    (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.93/23.13          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.93/23.13    (13)   ~ (e1 = e0)
% 153.93/23.13    (14)  all_56_13 = e3
% 153.93/23.13    (15)   ~ (e3 = e2)
% 153.93/23.13    (16)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.93/23.13          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 153.93/23.13            e2)
% 153.93/23.13    (17)   ~ (all_10_2 = e2)
% 153.93/23.13    (18)   ~ (e2 = e1)
% 153.93/23.13    (19)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.93/23.13          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 153.93/23.13            e1)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | BETA: splitting (16) gives:
% 153.93/23.13  | 
% 153.93/23.13  | Case 1:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (20)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 153.93/23.13  | |           e2)
% 153.93/23.13  | | 
% 153.93/23.13  | | BETA: splitting (20) gives:
% 153.93/23.13  | | 
% 153.93/23.13  | | Case 1:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (21)  all_56_12 = e2 & op(e0, e3) = e2
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (21) implies:
% 153.93/23.13  | | |   (22)  all_56_12 = e2
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (11), (12), (13), (15), (18),
% 153.93/23.13  | | |            (22) are inconsistent by sub-proof #781.
% 153.93/23.13  | | | 
% 153.93/23.13  | | Case 2:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (23)  all_56_13 = e2 & op(e0, e2) = e2
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (14), (15), (23) are inconsistent by sub-proof #847.
% 153.93/23.13  | | | 
% 153.93/23.13  | | End of split
% 153.93/23.13  | | 
% 153.93/23.13  | Case 2:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (24)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 153.93/23.13  | |           e2)
% 153.93/23.13  | | 
% 153.93/23.13  | | BETA: splitting (24) gives:
% 153.93/23.13  | | 
% 153.93/23.13  | | Case 1:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (25)  all_56_14 = e2 & op(e0, e1) = e2
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (25) implies:
% 153.93/23.13  | | |   (26)  all_56_14 = e2
% 153.93/23.13  | | | 
% 153.93/23.13  | | | BETA: splitting (10) gives:
% 153.93/23.13  | | | 
% 153.93/23.13  | | | Case 1:
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | |   (27)  all_56_15 = e0 & op(e0, e0) = e0
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | | ALPHA: (27) implies:
% 153.93/23.13  | | | |   (28)  op(e0, e0) = e0
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | | REF_CLOSE: (7), (8), (11), (28) are inconsistent by sub-proof #1143.
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | Case 2:
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | |   (29)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2,
% 153.93/23.13  | | | |               e0) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)) &
% 153.93/23.13  | | | |         ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 153.93/23.13  | | | |               e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0))
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | | ALPHA: (29) implies:
% 153.93/23.13  | | | |   (30)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0,
% 153.93/23.13  | | | |             e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | | REF_CLOSE: (1), (4), (5), (6), (7), (11), (13), (14), (18), (19), (26),
% 153.93/23.13  | | | |            (30) are inconsistent by sub-proof #1098.
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | End of split
% 153.93/23.13  | | | 
% 153.93/23.13  | | Case 2:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (31)  all_56_15 = e2 & op(e0, e0) = e2
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (31) implies:
% 153.93/23.13  | | |   (32)  op(e0, e0) = e2
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (4), (7), (17), (32) are inconsistent by sub-proof #1097.
% 153.93/23.13  | | | 
% 153.93/23.13  | | End of split
% 153.93/23.13  | | 
% 153.93/23.13  | End of split
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #781 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)   ~ (e3 = e1)
% 153.93/23.13    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.93/23.13         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.93/23.13    (3)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.93/23.13         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.93/23.13    (4)   ~ (e2 = e0)
% 153.93/23.13    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.13    (6)  op(e3, e3) = e2
% 153.93/23.13    (7)   ~ (e3 = e0)
% 153.93/23.13    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.93/23.13         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.93/23.13    (9)   ~ (e1 = e0)
% 153.93/23.13    (10)   ~ (e3 = e2)
% 153.93/23.13    (11)  all_56_12 = e2
% 153.93/23.13    (12)   ~ (e2 = e1)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | BETA: splitting (8) gives:
% 153.93/23.13  | 
% 153.93/23.13  | Case 1:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (13)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 153.93/23.13  | |           e0)
% 153.93/23.13  | | 
% 153.93/23.13  | | BETA: splitting (13) gives:
% 153.93/23.13  | | 
% 153.93/23.13  | | Case 1:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (14)  all_56_0 = e0 & op(e3, e3) = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (14) implies:
% 153.93/23.13  | | |   (15)  op(e3, e3) = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (4), (5), (6), (15) are inconsistent by sub-proof #1073.
% 153.93/23.13  | | | 
% 153.93/23.13  | | Case 2:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (16)  all_56_2 = e0 & op(e2, e3) = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (16) implies:
% 153.93/23.13  | | |   (17)  all_56_2 = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | BETA: splitting (2) gives:
% 153.93/23.13  | | | 
% 153.93/23.13  | | | Case 1:
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | |   (18)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3)
% 153.93/23.13  | | | |           = e1)
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | | REF_CLOSE: (5), (6), (9), (12), (17), (18) are inconsistent by sub-proof
% 153.93/23.13  | | | |            #1059.
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | Case 2:
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | |   (19)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3)
% 153.93/23.13  | | | |           = e1)
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | | BETA: splitting (19) gives:
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | | Case 1:
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | |   (20)  all_56_6 = e1 & op(e1, e3) = e1
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | | ALPHA: (20) implies:
% 153.93/23.13  | | | | |   (21)  all_56_6 = e1
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | | BETA: splitting (3) gives:
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | | Case 1:
% 153.93/23.13  | | | | | | 
% 153.93/23.13  | | | | | |   (22)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2,
% 153.93/23.13  | | | | | |             e3) = e3)
% 153.93/23.13  | | | | | | 
% 153.93/23.13  | | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 153.93/23.13  | | | | | |            (22) are inconsistent by sub-proof #786.
% 153.93/23.13  | | | | | | 
% 153.93/23.13  | | | | | Case 2:
% 153.93/23.13  | | | | | | 
% 153.93/23.13  | | | | | |   (23)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0,
% 153.93/23.13  | | | | | |             e3) = e3)
% 153.93/23.13  | | | | | | 
% 153.93/23.13  | | | | | | BETA: splitting (23) gives:
% 153.93/23.13  | | | | | | 
% 153.93/23.13  | | | | | | Case 1:
% 153.93/23.13  | | | | | | | 
% 153.93/23.13  | | | | | | |   (24)  all_56_6 = e3 & op(e1, e3) = e3
% 153.93/23.13  | | | | | | | 
% 153.93/23.13  | | | | | | | REF_CLOSE: (1), (21), (24) are inconsistent by sub-proof #785.
% 153.93/23.13  | | | | | | | 
% 153.93/23.13  | | | | | | Case 2:
% 153.93/23.13  | | | | | | | 
% 153.93/23.13  | | | | | | |   (25)  all_56_12 = e3 & op(e0, e3) = e3
% 153.93/23.13  | | | | | | | 
% 153.93/23.13  | | | | | | | ALPHA: (25) implies:
% 153.93/23.13  | | | | | | |   (26)  all_56_12 = e3
% 153.93/23.13  | | | | | | | 
% 153.93/23.13  | | | | | | | REF_CLOSE: (10), (11), (26) are inconsistent by sub-proof #869.
% 153.93/23.13  | | | | | | | 
% 153.93/23.13  | | | | | | End of split
% 153.93/23.13  | | | | | | 
% 153.93/23.13  | | | | | End of split
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | Case 2:
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | |   (27)  all_56_12 = e1 & op(e0, e3) = e1
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | | REF_CLOSE: (11), (12), (27) are inconsistent by sub-proof #789.
% 153.93/23.13  | | | | | 
% 153.93/23.13  | | | | End of split
% 153.93/23.13  | | | | 
% 153.93/23.13  | | | End of split
% 153.93/23.13  | | | 
% 153.93/23.13  | | End of split
% 153.93/23.13  | | 
% 153.93/23.13  | Case 2:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (28)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 153.93/23.13  | |           e0)
% 153.93/23.13  | | 
% 153.93/23.13  | | BETA: splitting (28) gives:
% 153.93/23.13  | | 
% 153.93/23.13  | | Case 1:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (29)  all_56_6 = e0 & op(e1, e3) = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (29) implies:
% 153.93/23.13  | | |   (30)  all_56_6 = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (12), (30) are
% 153.93/23.13  | | |            inconsistent by sub-proof #782.
% 153.93/23.13  | | | 
% 153.93/23.13  | | Case 2:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (31)  all_56_12 = e0 & op(e0, e3) = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (4), (11), (31) are inconsistent by sub-proof #871.
% 153.93/23.13  | | | 
% 153.93/23.13  | | End of split
% 153.93/23.13  | | 
% 153.93/23.13  | End of split
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #782 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)   ~ (e3 = e1)
% 153.93/23.13    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.93/23.13         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.93/23.13    (3)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 153.93/23.13         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.93/23.13    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.13    (5)  all_56_6 = e0
% 153.93/23.13    (6)  op(e3, e3) = e2
% 153.93/23.13    (7)   ~ (e3 = e0)
% 153.93/23.13    (8)   ~ (e1 = e0)
% 153.93/23.13    (9)   ~ (e3 = e2)
% 153.93/23.13    (10)  all_56_12 = e2
% 153.93/23.13    (11)   ~ (e2 = e1)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | BETA: splitting (3) gives:
% 153.93/23.13  | 
% 153.93/23.13  | Case 1:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (12)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 153.93/23.13  | |           e3)
% 153.93/23.13  | | 
% 153.93/23.13  | | BETA: splitting (12) gives:
% 153.93/23.13  | | 
% 153.93/23.13  | | Case 1:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (13)  all_56_0 = e3 & op(e3, e3) = e3
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (13) implies:
% 153.93/23.13  | | |   (14)  op(e3, e3) = e3
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (4), (6), (9), (14) are inconsistent by sub-proof #1085.
% 153.93/23.13  | | | 
% 153.93/23.13  | | Case 2:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (15)  all_56_2 = e3 & op(e2, e3) = e3
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (15) implies:
% 153.93/23.13  | | |   (16)  all_56_2 = e3
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (11), (16) are inconsistent
% 153.93/23.13  | | |            by sub-proof #788.
% 153.93/23.13  | | | 
% 153.93/23.13  | | End of split
% 153.93/23.13  | | 
% 153.93/23.13  | Case 2:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (17)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 153.93/23.13  | |           e3)
% 153.93/23.13  | | 
% 153.93/23.13  | | REF_CLOSE: (5), (7), (9), (10), (17) are inconsistent by sub-proof #783.
% 153.93/23.13  | | 
% 153.93/23.13  | End of split
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #783 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 153.93/23.13    (2)  all_56_6 = e0
% 153.93/23.13    (3)   ~ (e3 = e0)
% 153.93/23.13    (4)   ~ (e3 = e2)
% 153.93/23.13    (5)  all_56_12 = e2
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | BETA: splitting (1) gives:
% 153.93/23.13  | 
% 153.93/23.13  | Case 1:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (6)  all_56_6 = e3 & op(e1, e3) = e3
% 153.93/23.13  | | 
% 153.93/23.13  | | ALPHA: (6) implies:
% 153.93/23.13  | |   (7)  all_56_6 = e3
% 153.93/23.13  | | 
% 153.93/23.13  | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #784.
% 153.93/23.13  | | 
% 153.93/23.13  | Case 2:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (8)  all_56_12 = e3 & op(e0, e3) = e3
% 153.93/23.13  | | 
% 153.93/23.13  | | ALPHA: (8) implies:
% 153.93/23.13  | |   (9)  all_56_12 = e3
% 153.93/23.13  | | 
% 153.93/23.13  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #869.
% 153.93/23.13  | | 
% 153.93/23.13  | End of split
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #784 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)  all_56_6 = e3
% 153.93/23.13    (2)  all_56_6 = e0
% 153.93/23.13    (3)   ~ (e3 = e0)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | COMBINE_EQS: (1), (2) imply:
% 153.93/23.13  |   (4)  e3 = e0
% 153.93/23.13  | 
% 153.93/23.13  | SIMP: (4) implies:
% 153.93/23.13  |   (5)  e3 = e0
% 153.93/23.13  | 
% 153.93/23.13  | REDUCE: (3), (5) imply:
% 153.93/23.13  |   (6)  $false
% 153.93/23.13  | 
% 153.93/23.13  | CLOSE: (6) is inconsistent.
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #785 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)  all_56_6 = e3 & op(e1, e3) = e3
% 153.93/23.13    (2)  all_56_6 = e1
% 153.93/23.13    (3)   ~ (e3 = e1)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | ALPHA: (1) implies:
% 153.93/23.13  |   (4)  all_56_6 = e3
% 153.93/23.13  | 
% 153.93/23.13  | COMBINE_EQS: (2), (4) imply:
% 153.93/23.13  |   (5)  e3 = e1
% 153.93/23.13  | 
% 153.93/23.13  | SIMP: (5) implies:
% 153.93/23.13  |   (6)  e3 = e1
% 153.93/23.13  | 
% 153.93/23.13  | REDUCE: (3), (6) imply:
% 153.93/23.13  |   (7)  $false
% 153.93/23.13  | 
% 153.93/23.13  | CLOSE: (7) is inconsistent.
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #786 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)   ~ (e3 = e1)
% 153.93/23.13    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.93/23.13         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.93/23.13    (3)   ~ (e2 = e0)
% 153.93/23.13    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.13    (5)  op(e3, e3) = e2
% 153.93/23.13    (6)   ~ (e3 = e0)
% 153.93/23.13    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.93/23.13         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.93/23.13    (8)   ~ (e1 = e0)
% 153.93/23.13    (9)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 153.93/23.13    (10)   ~ (e3 = e2)
% 153.93/23.13    (11)  all_56_12 = e2
% 153.93/23.13    (12)   ~ (e2 = e1)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | BETA: splitting (9) gives:
% 153.93/23.13  | 
% 153.93/23.13  | Case 1:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (13)  all_56_0 = e3 & op(e3, e3) = e3
% 153.93/23.13  | | 
% 153.93/23.13  | | ALPHA: (13) implies:
% 153.93/23.13  | |   (14)  op(e3, e3) = e3
% 153.93/23.13  | | 
% 153.93/23.13  | | REF_CLOSE: (4), (5), (10), (14) are inconsistent by sub-proof #1085.
% 153.93/23.13  | | 
% 153.93/23.13  | Case 2:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (15)  all_56_2 = e3 & op(e2, e3) = e3
% 153.93/23.13  | | 
% 153.93/23.13  | | ALPHA: (15) implies:
% 153.93/23.13  | |   (16)  all_56_2 = e3
% 153.93/23.13  | | 
% 153.93/23.13  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (16) are
% 153.93/23.13  | |            inconsistent by sub-proof #787.
% 153.93/23.13  | | 
% 153.93/23.13  | End of split
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #787 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)   ~ (e3 = e1)
% 153.93/23.13    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.93/23.13         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.93/23.13    (3)   ~ (e2 = e0)
% 153.93/23.13    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.13    (5)  op(e3, e3) = e2
% 153.93/23.13    (6)   ~ (e3 = e0)
% 153.93/23.13    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.93/23.13         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.93/23.13    (8)   ~ (e1 = e0)
% 153.93/23.13    (9)  all_56_12 = e2
% 153.93/23.13    (10)   ~ (e2 = e1)
% 153.93/23.13    (11)  all_56_2 = e3
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | BETA: splitting (7) gives:
% 153.93/23.13  | 
% 153.93/23.13  | Case 1:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 153.93/23.13  | |           e0)
% 153.93/23.13  | | 
% 153.93/23.13  | | BETA: splitting (12) gives:
% 153.93/23.13  | | 
% 153.93/23.13  | | Case 1:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (13)  all_56_0 = e0 & op(e3, e3) = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (13) implies:
% 153.93/23.13  | | |   (14)  op(e3, e3) = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (3), (4), (5), (14) are inconsistent by sub-proof #1073.
% 153.93/23.13  | | | 
% 153.93/23.13  | | Case 2:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (15)  all_56_2 = e0 & op(e2, e3) = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (6), (11), (15) are inconsistent by sub-proof #932.
% 153.93/23.13  | | | 
% 153.93/23.13  | | End of split
% 153.93/23.13  | | 
% 153.93/23.13  | Case 2:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 153.93/23.13  | |           e0)
% 153.93/23.13  | | 
% 153.93/23.13  | | BETA: splitting (16) gives:
% 153.93/23.13  | | 
% 153.93/23.13  | | Case 1:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (17)  all_56_6 = e0 & op(e1, e3) = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (17) implies:
% 153.93/23.13  | | |   (18)  all_56_6 = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (11), (18) are inconsistent
% 153.93/23.13  | | |            by sub-proof #788.
% 153.93/23.13  | | | 
% 153.93/23.13  | | Case 2:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (19)  all_56_12 = e0 & op(e0, e3) = e0
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (3), (9), (19) are inconsistent by sub-proof #871.
% 153.93/23.13  | | | 
% 153.93/23.13  | | End of split
% 153.93/23.13  | | 
% 153.93/23.13  | End of split
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #788 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)   ~ (e3 = e1)
% 153.93/23.13    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.93/23.13         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.93/23.13    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.13           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.13    (4)  all_56_6 = e0
% 153.93/23.13    (5)  op(e3, e3) = e2
% 153.93/23.13    (6)   ~ (e1 = e0)
% 153.93/23.13    (7)  all_56_12 = e2
% 153.93/23.13    (8)   ~ (e2 = e1)
% 153.93/23.13    (9)  all_56_2 = e3
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | BETA: splitting (2) gives:
% 153.93/23.13  | 
% 153.93/23.13  | Case 1:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (10)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 153.93/23.13  | |           e1)
% 153.93/23.13  | | 
% 153.93/23.13  | | BETA: splitting (10) gives:
% 153.93/23.13  | | 
% 153.93/23.13  | | Case 1:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (11)  all_56_0 = e1 & op(e3, e3) = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (11) implies:
% 153.93/23.13  | | |   (12)  op(e3, e3) = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | GROUND_INST: instantiating (3) with e1, e2, e3, e3, simplifying with (5),
% 153.93/23.13  | | |              (12) gives:
% 153.93/23.13  | | |   (13)  e2 = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REDUCE: (8), (13) imply:
% 153.93/23.13  | | |   (14)  $false
% 153.93/23.13  | | | 
% 153.93/23.13  | | | CLOSE: (14) is inconsistent.
% 153.93/23.13  | | | 
% 153.93/23.13  | | Case 2:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (15)  all_56_2 = e1 & op(e2, e3) = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (1), (9), (15) are inconsistent by sub-proof #791.
% 153.93/23.13  | | | 
% 153.93/23.13  | | End of split
% 153.93/23.13  | | 
% 153.93/23.13  | Case 2:
% 153.93/23.13  | | 
% 153.93/23.13  | |   (16)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 153.93/23.13  | |           e1)
% 153.93/23.13  | | 
% 153.93/23.13  | | BETA: splitting (16) gives:
% 153.93/23.13  | | 
% 153.93/23.13  | | Case 1:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (17)  all_56_6 = e1 & op(e1, e3) = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | ALPHA: (17) implies:
% 153.93/23.13  | | |   (18)  all_56_6 = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (4), (6), (18) are inconsistent by sub-proof #790.
% 153.93/23.13  | | | 
% 153.93/23.13  | | Case 2:
% 153.93/23.13  | | | 
% 153.93/23.13  | | |   (19)  all_56_12 = e1 & op(e0, e3) = e1
% 153.93/23.13  | | | 
% 153.93/23.13  | | | REF_CLOSE: (7), (8), (19) are inconsistent by sub-proof #789.
% 153.93/23.13  | | | 
% 153.93/23.13  | | End of split
% 153.93/23.13  | | 
% 153.93/23.13  | End of split
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #789 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)  all_56_12 = e1 & op(e0, e3) = e1
% 153.93/23.13    (2)  all_56_12 = e2
% 153.93/23.13    (3)   ~ (e2 = e1)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | ALPHA: (1) implies:
% 153.93/23.13  |   (4)  all_56_12 = e1
% 153.93/23.13  | 
% 153.93/23.13  | COMBINE_EQS: (2), (4) imply:
% 153.93/23.13  |   (5)  e2 = e1
% 153.93/23.13  | 
% 153.93/23.13  | REDUCE: (3), (5) imply:
% 153.93/23.13  |   (6)  $false
% 153.93/23.13  | 
% 153.93/23.13  | CLOSE: (6) is inconsistent.
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #790 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)  all_56_6 = e1
% 153.93/23.13    (2)  all_56_6 = e0
% 153.93/23.13    (3)   ~ (e1 = e0)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | COMBINE_EQS: (1), (2) imply:
% 153.93/23.13  |   (4)  e1 = e0
% 153.93/23.13  | 
% 153.93/23.13  | SIMP: (4) implies:
% 153.93/23.13  |   (5)  e1 = e0
% 153.93/23.13  | 
% 153.93/23.13  | REDUCE: (3), (5) imply:
% 153.93/23.13  |   (6)  $false
% 153.93/23.13  | 
% 153.93/23.13  | CLOSE: (6) is inconsistent.
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #791 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)  all_56_2 = e1 & op(e2, e3) = e1
% 153.93/23.13    (2)  all_56_2 = e3
% 153.93/23.13    (3)   ~ (e3 = e1)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | ALPHA: (1) implies:
% 153.93/23.13  |   (4)  all_56_2 = e1
% 153.93/23.13  | 
% 153.93/23.13  | COMBINE_EQS: (2), (4) imply:
% 153.93/23.13  |   (5)  e3 = e1
% 153.93/23.13  | 
% 153.93/23.13  | REDUCE: (3), (5) imply:
% 153.93/23.13  |   (6)  $false
% 153.93/23.13  | 
% 153.93/23.13  | CLOSE: (6) is inconsistent.
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #792 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)  all_56_6 = e1 & op(e1, e3) = e1
% 153.93/23.13    (2)  all_56_6 = e3
% 153.93/23.13    (3)   ~ (e3 = e1)
% 153.93/23.13  
% 153.93/23.13  Begin of proof
% 153.93/23.13  | 
% 153.93/23.13  | ALPHA: (1) implies:
% 153.93/23.13  |   (4)  all_56_6 = e1
% 153.93/23.13  | 
% 153.93/23.13  | COMBINE_EQS: (2), (4) imply:
% 153.93/23.13  |   (5)  e3 = e1
% 153.93/23.13  | 
% 153.93/23.13  | REDUCE: (3), (5) imply:
% 153.93/23.13  |   (6)  $false
% 153.93/23.13  | 
% 153.93/23.13  | CLOSE: (6) is inconsistent.
% 153.93/23.13  | 
% 153.93/23.13  End of proof
% 153.93/23.13  
% 153.93/23.13  Sub-proof #793 shows that the following formulas are inconsistent:
% 153.93/23.13  ----------------------------------------------------------------
% 153.93/23.13    (1)  op(e0, e1) = all_52_11
% 153.93/23.13    (2)   ~ (all_52_13 = e1)
% 153.93/23.13    (3)   ~ (all_52_7 = all_52_11)
% 153.93/23.13    (4)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 153.93/23.13    (5)   ~ (e3 = e1)
% 153.93/23.13    (6)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.93/23.13         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.93/23.13    (7)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.93/23.13         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.93/23.13    (8)  op(e2, e2) = e1
% 153.93/23.13    (9)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.93/23.13         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.93/23.13    (10)  op(e3, e2) = all_52_4
% 153.93/23.13    (11)   ~ (all_52_4 = all_52_7)
% 153.93/23.13    (12)  all_56_5 = e3
% 153.93/23.13    (13)  op(e0, e2) = all_52_7
% 153.93/23.13    (14)   ~ (all_52_3 = all_52_7)
% 153.93/23.13    (15)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.93/23.13          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.93/23.13    (16)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 153.93/23.13          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.93/23.13    (17)   ~ (e2 = e0)
% 153.93/23.13    (18)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.13            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.13    (19)  all_56_7 = e3
% 153.93/23.13    (20)  all_54_1 = all_52_4
% 153.93/23.13    (21)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.93/23.13          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.93/23.13    (22)   ~ (all_52_1 = all_52_13)
% 153.93/23.13    (23)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 153.93/23.13          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 153.93/23.13    (24)  ( ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 153.93/23.13            all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e2,
% 153.93/23.13              e1) = all_20_1 & $i(all_20_1))
% 153.93/23.13    (25)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 153.93/23.13    (26)   ~ (all_52_7 = e1)
% 153.93/23.14    (27)   ~ (all_52_3 = all_52_11)
% 153.93/23.14    (28)   ~ (all_52_11 = e3)
% 153.93/23.14    (29)   ~ (all_52_1 = all_52_9)
% 153.93/23.14    (30)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.93/23.14              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.93/23.14                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.93/23.14                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.93/23.14    (31)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.93/23.14          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.93/23.14    (32)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 153.93/23.14          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 153.93/23.14            e3)
% 153.93/23.14    (33)  op(e3, e0) = all_52_12
% 153.93/23.14    (34)   ~ (e3 = e0)
% 153.93/23.14    (35)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.93/23.14          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.93/23.14    (36)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.93/23.14          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.93/23.14    (37)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.93/23.14          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.93/23.14    (38)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 153.93/23.14          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 153.93/23.14    (39)  op(e1, e2) = all_52_6
% 153.93/23.14    (40)   ~ (all_52_12 = e3)
% 153.93/23.14    (41)  op(e2, e0) = all_52_13
% 153.93/23.14    (42)   ~ (all_52_1 = all_52_3)
% 153.93/23.14    (43)  op(e0, e3) = all_52_3
% 153.93/23.14    (44)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.93/23.14    (45)  ( ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0 & op(e2, e1) =
% 153.93/23.14            all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e0) & op(e2,
% 153.93/23.14              e1) = all_38_1 & $i(all_38_1))
% 153.93/23.14    (46)   ~ (all_52_4 = all_52_6)
% 153.93/23.14    (47)  op(e2, e1) = all_52_9
% 153.93/23.14    (48)   ~ (e1 = e0)
% 153.93/23.14    (49)   ~ (all_52_1 = e1)
% 153.93/23.14    (50)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.93/23.14          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.93/23.14    (51)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.93/23.14              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.93/23.14            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.93/23.14                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.93/23.14              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.93/23.14          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.93/23.14              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.93/23.14            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.93/23.14                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.93/23.14              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.93/23.14          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.93/23.14              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.93/23.14            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.93/23.14                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.93/23.14              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.93/23.14          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.93/23.14              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.93/23.14            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.93/23.14                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.93/23.14                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.93/23.14                $i(all_57_14))))
% 153.93/23.14    (52)   ~ (all_52_9 = e1)
% 153.93/23.14    (53)   ~ (all_52_4 = e1)
% 153.93/23.14    (54)   ~ (e3 = e2)
% 153.93/23.14    (55)  all_54_4 = all_52_1
% 153.93/23.14    (56)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.93/23.14          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.93/23.14    (57)  op(e2, e1) = e3
% 153.93/23.14    (58)  all_54_13 = all_52_7
% 153.93/23.14    (59)  op(e3, e1) = all_52_8
% 153.93/23.14    (60)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.93/23.14          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.93/23.14    (61)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.93/23.14          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.93/23.14    (62)  op(e3, e3) = e3
% 153.93/23.14    (63)   ~ (all_52_6 = all_52_7)
% 153.93/23.14    (64)   ~ (e2 = e1)
% 153.93/23.14    (65)   ~ (all_52_8 = all_52_9)
% 153.93/23.14    (66)  op(e1, e3) = all_52_2
% 153.93/23.14    (67)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.93/23.14              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.93/23.14            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.93/23.14            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.93/23.14            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.14            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.93/23.14            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.93/23.14            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.93/23.14            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.93/23.14            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.93/23.14            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.14            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.93/23.14            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.14            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.93/23.14            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.93/23.14            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.14            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.93/23.14            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.93/23.14            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.93/23.14            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.93/23.14            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.93/23.14            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.14            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.93/23.14            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.93/23.14            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.14            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.93/23.14            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.14            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.14            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.14            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.93/23.14            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.93/23.14            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.93/23.14            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.14            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.14            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.14            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.14            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.14            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.93/23.14            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.14            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.14            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.93/23.14            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.93/23.14            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.14            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.93/23.14            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.93/23.14            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.14            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.93/23.14            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.93/23.14              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.93/23.14            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.14            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.93/23.14              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.93/23.14            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.93/23.14            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.93/23.14                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.93/23.14                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.14                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.14                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.14                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.93/23.14                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.93/23.14                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.93/23.14              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.93/23.14                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.93/23.14                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.93/23.14                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.93/23.14                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.93/23.14                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.93/23.14                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.93/23.14                $i(all_57_7))))
% 153.93/23.14    (68)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.93/23.14          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 153.93/23.14            e1)
% 153.93/23.14    (69)  op(e1, e2) = e3
% 153.93/23.14    (70)  op(e2, e3) = all_52_1
% 153.93/23.14  
% 153.93/23.14  Begin of proof
% 153.93/23.14  | 
% 153.93/23.14  | BETA: splitting (32) gives:
% 153.93/23.14  | 
% 153.93/23.14  | Case 1:
% 153.93/23.14  | | 
% 153.93/23.14  | |   (71)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 153.93/23.14  | |           e3)
% 153.93/23.14  | | 
% 153.93/23.14  | | BETA: splitting (71) gives:
% 153.93/23.14  | | 
% 153.93/23.14  | | Case 1:
% 153.93/23.14  | | | 
% 153.93/23.14  | | |   (72)  all_56_12 = e3 & op(e0, e3) = e3
% 153.93/23.14  | | | 
% 153.93/23.14  | | | ALPHA: (72) implies:
% 153.93/23.14  | | |   (73)  all_56_12 = e3
% 153.93/23.14  | | | 
% 153.93/23.14  | | | BETA: splitting (6) gives:
% 153.93/23.14  | | | 
% 153.93/23.14  | | | Case 1:
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | |   (74)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3)
% 153.93/23.14  | | | |           = e1)
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | | REF_CLOSE: (5), (18), (49), (62), (70), (74) are inconsistent by
% 153.93/23.14  | | | |            sub-proof #1176.
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | Case 2:
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | |   (75)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3)
% 153.93/23.14  | | | |           = e1)
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | | REF_CLOSE: (5), (17), (18), (34), (35), (38), (48), (54), (62), (64),
% 153.93/23.14  | | | |            (66), (73), (75) are inconsistent by sub-proof #991.
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | End of split
% 153.93/23.14  | | | 
% 153.93/23.14  | | Case 2:
% 153.93/23.14  | | | 
% 153.93/23.14  | | |   (76)  all_56_13 = e3 & op(e0, e2) = e3
% 153.93/23.14  | | | 
% 153.93/23.14  | | | ALPHA: (76) implies:
% 153.93/23.14  | | |   (77)  all_56_13 = e3
% 153.93/23.14  | | | 
% 153.93/23.14  | | | REF_CLOSE: (8), (9), (17), (18), (19), (34), (48), (54), (56), (64), (77)
% 153.93/23.14  | | |            are inconsistent by sub-proof #846.
% 153.93/23.14  | | | 
% 153.93/23.14  | | End of split
% 153.93/23.14  | | 
% 153.93/23.14  | Case 2:
% 153.93/23.14  | | 
% 153.93/23.14  | |   (78)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 153.93/23.14  | |           e3)
% 153.93/23.14  | | 
% 153.93/23.14  | | BETA: splitting (78) gives:
% 153.93/23.14  | | 
% 153.93/23.14  | | Case 1:
% 153.93/23.14  | | | 
% 153.93/23.14  | | |   (79)  all_56_14 = e3 & op(e0, e1) = e3
% 153.93/23.14  | | | 
% 153.93/23.14  | | | ALPHA: (79) implies:
% 153.93/23.14  | | |   (80)  op(e0, e1) = e3
% 153.93/23.14  | | | 
% 153.93/23.14  | | | REF_CLOSE: (1), (18), (28), (80) are inconsistent by sub-proof #1147.
% 153.93/23.14  | | | 
% 153.93/23.14  | | Case 2:
% 153.93/23.14  | | | 
% 153.93/23.14  | | |   (81)  all_56_15 = e3 & op(e0, e0) = e3
% 153.93/23.14  | | | 
% 153.93/23.14  | | | ALPHA: (81) implies:
% 153.93/23.14  | | |   (82)  all_56_15 = e3
% 153.93/23.14  | | |   (83)  op(e0, e0) = e3
% 153.93/23.14  | | | 
% 153.93/23.14  | | | GROUND_INST: instantiating (18) with all_52_6, e3, e2, e1, simplifying
% 153.93/23.14  | | |              with (39), (69) gives:
% 153.93/23.14  | | |   (84)  all_52_6 = e3
% 153.93/23.14  | | | 
% 153.93/23.14  | | | GROUND_INST: instantiating (18) with all_52_9, e3, e1, e2, simplifying
% 153.93/23.14  | | |              with (47), (57) gives:
% 153.93/23.14  | | |   (85)  all_52_9 = e3
% 153.93/23.14  | | | 
% 153.93/23.14  | | | REDUCE: (29), (85) imply:
% 153.93/23.14  | | |   (86)   ~ (all_52_1 = e3)
% 153.93/23.14  | | | 
% 153.93/23.14  | | | REDUCE: (46), (84) imply:
% 153.93/23.14  | | |   (87)   ~ (all_52_4 = e3)
% 153.93/23.14  | | | 
% 153.93/23.14  | | | REDUCE: (63), (84) imply:
% 153.93/23.14  | | |   (88)   ~ (all_52_7 = e3)
% 153.93/23.14  | | | 
% 153.93/23.14  | | | SIMP: (88) implies:
% 153.93/23.14  | | |   (89)   ~ (all_52_7 = e3)
% 153.93/23.14  | | | 
% 153.93/23.14  | | | REDUCE: (65), (85) imply:
% 153.93/23.14  | | |   (90)   ~ (all_52_8 = e3)
% 153.93/23.14  | | | 
% 153.93/23.14  | | | BETA: splitting (24) gives:
% 153.93/23.14  | | | 
% 153.93/23.14  | | | Case 1:
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | |   (91)   ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 153.93/23.14  | | | |         all_20_1 & $i(all_20_0) & $i(all_20_1)
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | | ALPHA: (91) implies:
% 153.93/23.14  | | | |   (92)   ~ (all_20_0 = e0)
% 153.93/23.14  | | | |   (93)  op(e2, e1) = all_20_1
% 153.93/23.14  | | | |   (94)  op(all_20_1, e2) = all_20_0
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | | BETA: splitting (45) gives:
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | | Case 1:
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | |   (95)   ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0 & op(e2, e1)
% 153.93/23.14  | | | | |         = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | | ALPHA: (95) implies:
% 153.93/23.14  | | | | |   (96)  op(e2, e1) = all_38_1
% 153.93/23.14  | | | | |   (97)  op(all_38_1, e2) = all_38_0
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | | BETA: splitting (51) gives:
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | | Case 1:
% 153.93/23.14  | | | | | | 
% 153.93/23.14  | | | | | |   (98)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2,
% 153.93/23.14  | | | | | |                 e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 153.93/23.14  | | | | | |               all_57_12 & $i(all_57_12))) & ((all_57_1 = e1 & op(e1,
% 153.93/23.14  | | | | | |                 e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 153.93/23.14  | | | | | |               all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 153.93/23.14  | | | | | |                 e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 153.93/23.14  | | | | | |               all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 153.93/23.14  | | | | | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 153.93/23.14  | | | | | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.14  | | | | | |               $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) |
% 153.93/23.14  | | | | | |             ( ~ (all_57_14 = e2) & op(e1, e1) = all_57_14 &
% 153.93/23.14  | | | | | |               $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0) |
% 153.93/23.14  | | | | | |             ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.93/23.14  | | | | | |               $i(all_57_15))))
% 153.93/23.14  | | | | | | 
% 153.93/23.14  | | | | | | BETA: splitting (98) gives:
% 153.93/23.14  | | | | | | 
% 153.93/23.14  | | | | | | Case 1:
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | |   (99)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 &
% 153.93/23.14  | | | | | | |             op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 153.93/23.14  | | | | | | |             all_57_12 & $i(all_57_12))) & ((all_57_1 = e1 & op(e1,
% 153.93/23.14  | | | | | | |               e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 153.93/23.14  | | | | | | |             all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 153.93/23.14  | | | | | | |               e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 153.93/23.14  | | | | | | |             all_57_15 & $i(all_57_15)))
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | | ALPHA: (99) implies:
% 153.93/23.14  | | | | | | |   (100)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3)
% 153.93/23.14  | | | | | | |            & op(e0, e0) = all_57_15 & $i(all_57_15))
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | | BETA: splitting (100) gives:
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | | Case 1:
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | |   (101)  all_57_2 = e0 & op(e0, e3) = e0
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | ALPHA: (101) implies:
% 153.93/23.14  | | | | | | | |   (102)  op(e0, e3) = e0
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | GROUND_INST: instantiating (18) with all_52_3, e0, e3, e0,
% 153.93/23.14  | | | | | | | |              simplifying with (43), (102) gives:
% 153.93/23.14  | | | | | | | |   (103)  all_52_3 = e0
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | GROUND_INST: instantiating (18) with e3, all_38_1, e1, e2,
% 153.93/23.14  | | | | | | | |              simplifying with (57), (96) gives:
% 153.93/23.14  | | | | | | | |   (104)  all_38_1 = e3
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | GROUND_INST: instantiating (18) with all_20_1, all_38_1, e1, e2,
% 153.93/23.14  | | | | | | | |              simplifying with (93), (96) gives:
% 153.93/23.14  | | | | | | | |   (105)  all_38_1 = all_20_1
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | GROUND_INST: instantiating (18) with all_52_4, all_38_0, e2, e3,
% 153.93/23.14  | | | | | | | |              simplifying with (10) gives:
% 153.93/23.14  | | | | | | | |   (106)  all_52_4 = all_38_0 |  ~ (op(e3, e2) = all_38_0)
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | GROUND_INST: instantiating (18) with all_20_0, all_38_0, e2,
% 153.93/23.14  | | | | | | | |              all_20_1, simplifying with (94) gives:
% 153.93/23.14  | | | | | | | |   (107)  all_38_0 = all_20_0 |  ~ (op(all_20_1, e2) = all_38_0)
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | COMBINE_EQS: (104), (105) imply:
% 153.93/23.14  | | | | | | | |   (108)  all_20_1 = e3
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | REDUCE: (14), (103) imply:
% 153.93/23.14  | | | | | | | |   (109)   ~ (all_52_7 = e0)
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | SIMP: (109) implies:
% 153.93/23.14  | | | | | | | |   (110)   ~ (all_52_7 = e0)
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | REDUCE: (97), (104) imply:
% 153.93/23.14  | | | | | | | |   (111)  op(e3, e2) = all_38_0
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | BETA: splitting (44) gives:
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | Case 1:
% 153.93/23.14  | | | | | | | | | 
% 153.93/23.14  | | | | | | | | |   (112)  all_54_13 = e3
% 153.93/23.14  | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | REF_CLOSE: (58), (89), (112) are inconsistent by sub-proof
% 153.93/23.14  | | | | | | | | |            #845.
% 153.93/23.14  | | | | | | | | | 
% 153.93/23.14  | | | | | | | | Case 2:
% 153.93/23.14  | | | | | | | | | 
% 153.93/23.14  | | | | | | | | |   (113)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.93/23.14  | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | BETA: splitting (113) gives:
% 153.93/23.14  | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | Case 1:
% 153.93/23.14  | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | |   (114)  all_54_13 = e2
% 153.93/23.14  | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | COMBINE_EQS: (58), (114) imply:
% 153.93/23.14  | | | | | | | | | |   (115)  all_52_7 = e2
% 153.93/23.14  | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | SIMP: (115) implies:
% 153.93/23.14  | | | | | | | | | |   (116)  all_52_7 = e2
% 153.93/23.14  | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | REDUCE: (11), (116) imply:
% 153.93/23.14  | | | | | | | | | |   (117)   ~ (all_52_4 = e2)
% 153.93/23.14  | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | BETA: splitting (25) gives:
% 153.93/23.14  | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | Case 1:
% 153.93/23.14  | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | |   (118)  all_54_1 = e3
% 153.93/23.14  | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | REF_CLOSE: (20), (87), (118) are inconsistent by sub-proof
% 153.93/23.14  | | | | | | | | | | |            #988.
% 153.93/23.14  | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | Case 2:
% 153.93/23.14  | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | |   (119)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 153.93/23.14  | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | BETA: splitting (107) gives:
% 153.93/23.14  | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | Case 1:
% 153.93/23.14  | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | |   (120)   ~ (op(all_20_1, e2) = all_38_0)
% 153.93/23.14  | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | REDUCE: (108), (120) imply:
% 153.93/23.14  | | | | | | | | | | | |   (121)   ~ (op(e3, e2) = all_38_0)
% 153.93/23.14  | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | PRED_UNIFY: (111), (121) imply:
% 153.93/23.14  | | | | | | | | | | | |   (122)  $false
% 153.93/23.14  | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | CLOSE: (122) is inconsistent.
% 153.93/23.14  | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | Case 2:
% 153.93/23.14  | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | |   (123)  all_38_0 = all_20_0
% 153.93/23.14  | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | BETA: splitting (119) gives:
% 153.93/23.14  | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | Case 1:
% 153.93/23.14  | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | |   (124)  all_54_1 = e2
% 153.93/23.14  | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | COMBINE_EQS: (20), (124) imply:
% 153.93/23.14  | | | | | | | | | | | | |   (125)  all_52_4 = e2
% 153.93/23.14  | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | REDUCE: (117), (125) imply:
% 153.93/23.14  | | | | | | | | | | | | |   (126)  $false
% 153.93/23.14  | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | CLOSE: (126) is inconsistent.
% 153.93/23.14  | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | Case 2:
% 153.93/23.14  | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | |   (127)  all_54_1 = e1 | all_54_1 = e0
% 153.93/23.14  | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | BETA: splitting (106) gives:
% 153.93/23.14  | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | Case 1:
% 153.93/23.14  | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | |   (128)   ~ (op(e3, e2) = all_38_0)
% 153.93/23.14  | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | PRED_UNIFY: (111), (128) imply:
% 153.93/23.14  | | | | | | | | | | | | | |   (129)  $false
% 153.93/23.14  | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | CLOSE: (129) is inconsistent.
% 153.93/23.14  | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | Case 2:
% 153.93/23.14  | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | |   (130)  all_52_4 = all_38_0
% 153.93/23.14  | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | COMBINE_EQS: (123), (130) imply:
% 153.93/23.14  | | | | | | | | | | | | | |   (131)  all_52_4 = all_20_0
% 153.93/23.14  | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | COMBINE_EQS: (20), (131) imply:
% 153.93/23.14  | | | | | | | | | | | | | |   (132)  all_54_1 = all_20_0
% 153.93/23.14  | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | REDUCE: (53), (131) imply:
% 153.93/23.14  | | | | | | | | | | | | | |   (133)   ~ (all_20_0 = e1)
% 153.93/23.14  | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 153.93/23.14  | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | Case 1:
% 153.93/23.14  | | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | |   (134)  all_54_1 = e1
% 153.93/23.14  | | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | | COMBINE_EQS: (132), (134) imply:
% 153.93/23.14  | | | | | | | | | | | | | | |   (135)  all_20_0 = e1
% 153.93/23.14  | | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | | REDUCE: (133), (135) imply:
% 153.93/23.14  | | | | | | | | | | | | | | |   (136)  $false
% 153.93/23.14  | | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | | CLOSE: (136) is inconsistent.
% 153.93/23.14  | | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | Case 2:
% 153.93/23.14  | | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | |   (137)  all_54_1 = e0
% 153.93/23.14  | | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | | COMBINE_EQS: (132), (137) imply:
% 153.93/23.14  | | | | | | | | | | | | | | |   (138)  all_20_0 = e0
% 153.93/23.14  | | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | | REDUCE: (92), (138) imply:
% 153.93/23.14  | | | | | | | | | | | | | | |   (139)  $false
% 153.93/23.14  | | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | | CLOSE: (139) is inconsistent.
% 153.93/23.14  | | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | | End of split
% 153.93/23.14  | | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | | End of split
% 153.93/23.14  | | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | | End of split
% 153.93/23.14  | | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | | End of split
% 153.93/23.14  | | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | End of split
% 153.93/23.14  | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | Case 2:
% 153.93/23.14  | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | |   (140)  all_54_13 = e1 | all_54_13 = e0
% 153.93/23.14  | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | | REF_CLOSE: (26), (58), (110), (140) are inconsistent by
% 153.93/23.14  | | | | | | | | | |            sub-proof #983.
% 153.93/23.14  | | | | | | | | | | 
% 153.93/23.14  | | | | | | | | | End of split
% 153.93/23.14  | | | | | | | | | 
% 153.93/23.14  | | | | | | | | End of split
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | Case 2:
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | |   (141)   ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 153.93/23.14  | | | | | | | |          $i(all_57_15)
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | ALPHA: (141) implies:
% 153.93/23.14  | | | | | | | |   (142)   ~ (all_57_15 = e3)
% 153.93/23.14  | | | | | | | |   (143)  op(e0, e0) = all_57_15
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | | REF_CLOSE: (18), (83), (142), (143) are inconsistent by
% 153.93/23.14  | | | | | | | |            sub-proof #1019.
% 153.93/23.14  | | | | | | | | 
% 153.93/23.14  | | | | | | | End of split
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | Case 2:
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | |   (144)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 &
% 153.93/23.14  | | | | | | |              op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3, e3)
% 153.93/23.14  | | | | | | |              = all_57_10 & $i(all_57_10))) & ((all_57_4 = e1 &
% 153.93/23.14  | | | | | | |              op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.93/23.14  | | | | | | |              = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 &
% 153.93/23.14  | | | | | | |              op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0)
% 153.93/23.14  | | | | | | |              = all_57_15 & $i(all_57_15)))
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | | ALPHA: (144) implies:
% 153.93/23.14  | | | | | | |   (145)  op(e2, e2) = e2
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | | REF_CLOSE: (8), (18), (64), (145) are inconsistent by sub-proof
% 153.93/23.14  | | | | | | |            #1158.
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | End of split
% 153.93/23.14  | | | | | | 
% 153.93/23.14  | | | | | Case 2:
% 153.93/23.14  | | | | | | 
% 153.93/23.14  | | | | | |   (146)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 &
% 153.93/23.14  | | | | | |                op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3)
% 153.93/23.14  | | | | | |                = all_57_10 & $i(all_57_10))) & ((all_57_7 = e2 &
% 153.93/23.14  | | | | | |                op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.93/23.14  | | | | | |                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 &
% 153.93/23.14  | | | | | |                op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0)
% 153.93/23.14  | | | | | |                = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 153.93/23.14  | | | | | |            op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | (
% 153.93/23.14  | | | | | |                ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.93/23.14  | | | | | |                $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2)
% 153.93/23.14  | | | | | |              | ( ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 &
% 153.93/23.14  | | | | | |                $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 153.93/23.14  | | | | | |              | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.93/23.14  | | | | | |                $i(all_57_14))))
% 153.93/23.14  | | | | | | 
% 153.93/23.14  | | | | | | BETA: splitting (146) gives:
% 153.93/23.14  | | | | | | 
% 153.93/23.14  | | | | | | Case 1:
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | |   (147)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 &
% 153.93/23.14  | | | | | | |              op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3, e3)
% 153.93/23.14  | | | | | | |              = all_57_10 & $i(all_57_10))) & ((all_57_7 = e2 &
% 153.93/23.14  | | | | | | |              op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.93/23.14  | | | | | | |              = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 &
% 153.93/23.14  | | | | | | |              op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0)
% 153.93/23.14  | | | | | | |              = all_57_15 & $i(all_57_15)))
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | | ALPHA: (147) implies:
% 153.93/23.14  | | | | | | |   (148)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1)
% 153.93/23.14  | | | | | | |            & op(e2, e2) = all_57_12 & $i(all_57_12))
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | | REF_CLOSE: (8), (18), (54), (57), (148) are inconsistent by
% 153.93/23.14  | | | | | | |            sub-proof #844.
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | Case 2:
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | |   (149)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 &
% 153.93/23.14  | | | | | | |              op(e3, e0) = e3) | ( ~ (all_57_10 = e0) & op(e3, e3)
% 153.93/23.14  | | | | | | |              = all_57_10 & $i(all_57_10))) & ((all_57_11 = e2 &
% 153.93/23.14  | | | | | | |              op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 153.93/23.14  | | | | | | |              = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 153.93/23.14  | | | | | | |              op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1)
% 153.93/23.14  | | | | | | |              = all_57_14 & $i(all_57_14)))
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | | ALPHA: (149) implies:
% 153.93/23.14  | | | | | | |   (150)  op(e0, e0) = e0
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | | REF_CLOSE: (18), (34), (83), (150) are inconsistent by sub-proof
% 153.93/23.14  | | | | | | |            #1143.
% 153.93/23.14  | | | | | | | 
% 153.93/23.14  | | | | | | End of split
% 153.93/23.14  | | | | | | 
% 153.93/23.14  | | | | | End of split
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | Case 2:
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | |   (151)   ~ (all_38_1 = e0) & op(e2, e1) = all_38_1 & $i(all_38_1)
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | | ALPHA: (151) implies:
% 153.93/23.14  | | | | |   (152)   ~ (all_38_1 = e0)
% 153.93/23.14  | | | | |   (153)  op(e2, e1) = all_38_1
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 153.93/23.14  | | | | |            (13), (14), (15), (16), (18), (19), (21), (22), (23), (26),
% 153.93/23.14  | | | | |            (27), (30), (31), (33), (34), (35), (36), (37), (39), (40),
% 153.93/23.14  | | | | |            (41), (42), (43), (44), (48), (49), (50), (51), (54), (55),
% 153.93/23.14  | | | | |            (56), (57), (58), (59), (60), (61), (63), (64), (66), (67),
% 153.93/23.14  | | | | |            (68), (70), (82), (83), (86), (87), (89), (90), (93),
% 153.93/23.14  | | | | |            (152), (153) are inconsistent by sub-proof #794.
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | End of split
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | Case 2:
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | |   (154)   ~ (all_20_1 = e3) & op(e2, e1) = all_20_1 & $i(all_20_1)
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | | ALPHA: (154) implies:
% 153.93/23.14  | | | |   (155)   ~ (all_20_1 = e3)
% 153.93/23.14  | | | |   (156)  op(e2, e1) = all_20_1
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | | BETA: splitting (45) gives:
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | | Case 1:
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | |   (157)   ~ (all_38_0 = e3) & op(all_38_1, e2) = all_38_0 & op(e2, e1)
% 153.93/23.14  | | | | |          = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | | ALPHA: (157) implies:
% 153.93/23.14  | | | | |   (158)  op(e2, e1) = all_38_1
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | | REF_CLOSE: (18), (57), (155), (156), (158) are inconsistent by
% 153.93/23.14  | | | | |            sub-proof #858.
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | Case 2:
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | |   (159)   ~ (all_38_1 = e0) & op(e2, e1) = all_38_1 & $i(all_38_1)
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | | ALPHA: (159) implies:
% 153.93/23.14  | | | | |   (160)   ~ (all_38_1 = e0)
% 153.93/23.14  | | | | |   (161)  op(e2, e1) = all_38_1
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 153.93/23.14  | | | | |            (13), (14), (15), (16), (18), (19), (21), (22), (23), (26),
% 153.93/23.14  | | | | |            (27), (30), (31), (33), (34), (35), (36), (37), (39), (40),
% 153.93/23.14  | | | | |            (41), (42), (43), (44), (48), (49), (50), (51), (54), (55),
% 153.93/23.14  | | | | |            (56), (57), (58), (59), (60), (61), (63), (64), (66), (67),
% 153.93/23.14  | | | | |            (68), (70), (82), (83), (86), (87), (89), (90), (156),
% 153.93/23.14  | | | | |            (160), (161) are inconsistent by sub-proof #794.
% 153.93/23.14  | | | | | 
% 153.93/23.14  | | | | End of split
% 153.93/23.14  | | | | 
% 153.93/23.14  | | | End of split
% 153.93/23.14  | | | 
% 153.93/23.14  | | End of split
% 153.93/23.14  | | 
% 153.93/23.14  | End of split
% 153.93/23.14  | 
% 153.93/23.14  End of proof
% 153.93/23.14  
% 153.93/23.14  Sub-proof #794 shows that the following formulas are inconsistent:
% 153.93/23.14  ----------------------------------------------------------------
% 153.93/23.14    (1)  op(e0, e1) = all_52_11
% 153.93/23.14    (2)   ~ (all_52_13 = e1)
% 153.93/23.14    (3)   ~ (all_52_7 = all_52_11)
% 153.93/23.14    (4)  all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 153.93/23.14    (5)   ~ (e3 = e1)
% 153.93/23.14    (6)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 153.93/23.14         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 153.93/23.14    (7)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.93/23.14         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.93/23.14    (8)  op(e2, e2) = e1
% 153.93/23.14    (9)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.93/23.14         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.93/23.14    (10)  op(e3, e2) = all_52_4
% 153.93/23.14    (11)  all_56_5 = e3
% 153.93/23.14    (12)  op(e0, e2) = all_52_7
% 153.93/23.14    (13)   ~ (all_52_3 = all_52_7)
% 153.93/23.14    (14)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.93/23.14          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.93/23.14    (15)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 153.93/23.14          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.93/23.14    (16)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.14            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.14    (17)  op(e0, e0) = e3
% 153.93/23.14    (18)  all_56_7 = e3
% 153.93/23.14    (19)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.93/23.14          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.93/23.14    (20)   ~ (all_52_1 = all_52_13)
% 153.93/23.15    (21)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2) |
% 153.93/23.15          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 153.93/23.15    (22)   ~ (all_52_7 = e1)
% 153.93/23.15    (23)   ~ (all_52_3 = all_52_11)
% 153.93/23.15    (24)  all_56_15 = e3
% 153.93/23.15    (25)   ~ (all_52_1 = e3)
% 153.93/23.15    (26)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.93/23.15              | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0)
% 153.93/23.15                = e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.93/23.15                op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.93/23.15    (27)   ~ (all_38_1 = e0)
% 153.93/23.15    (28)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 153.93/23.15          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 153.93/23.15    (29)   ~ (all_52_4 = e3)
% 153.93/23.15    (30)  op(e2, e1) = all_38_1
% 153.93/23.15    (31)  op(e3, e0) = all_52_12
% 153.93/23.15    (32)   ~ (all_52_7 = e3)
% 153.93/23.15    (33)   ~ (e3 = e0)
% 153.93/23.15    (34)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 153.93/23.15          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 153.93/23.15    (35)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 153.93/23.15          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.93/23.15    (36)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 153.93/23.15          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 153.93/23.15    (37)  op(e1, e2) = all_52_6
% 153.93/23.15    (38)   ~ (all_52_12 = e3)
% 153.93/23.15    (39)  op(e2, e0) = all_52_13
% 153.93/23.15    (40)   ~ (all_52_1 = all_52_3)
% 153.93/23.15    (41)  op(e0, e3) = all_52_3
% 153.93/23.15    (42)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.93/23.15    (43)   ~ (e1 = e0)
% 153.93/23.15    (44)   ~ (all_52_1 = e1)
% 153.93/23.15    (45)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2) |
% 153.93/23.15          (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 153.93/23.15    (46)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 153.93/23.15              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.93/23.15            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 153.93/23.15                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 153.93/23.15              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.93/23.15          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 153.93/23.15              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.93/23.15            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 153.93/23.15                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 153.93/23.15              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.93/23.15          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 153.93/23.15              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.93/23.15            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 153.93/23.15                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 153.93/23.15              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 153.93/23.15          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 153.93/23.15              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.93/23.15            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 153.93/23.15                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 153.93/23.15                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 153.93/23.15                $i(all_57_14))))
% 153.93/23.15    (47)  op(e2, e1) = all_20_1
% 153.93/23.15    (48)   ~ (e3 = e2)
% 153.93/23.15    (49)  all_54_4 = all_52_1
% 153.93/23.15    (50)   ~ (all_52_8 = e3)
% 153.93/23.15    (51)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.93/23.15          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.93/23.15    (52)  op(e2, e1) = e3
% 153.93/23.15    (53)  all_54_13 = all_52_7
% 153.93/23.15    (54)  op(e3, e1) = all_52_8
% 153.93/23.15    (55)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.93/23.15          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.93/23.15    (56)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 153.93/23.15          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 153.93/23.15    (57)   ~ (all_52_6 = all_52_7)
% 153.93/23.15    (58)   ~ (e2 = e1)
% 153.93/23.15    (59)  op(e1, e3) = all_52_2
% 153.93/23.15    (60)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.93/23.15              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.93/23.15            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.93/23.15            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.93/23.15            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.15            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.93/23.15            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.93/23.15            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.93/23.15            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.93/23.15            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.93/23.15            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.15            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.93/23.15            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.15            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.93/23.15            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.93/23.15            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.15            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.93/23.15            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.93/23.15            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.93/23.15            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.93/23.15            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.93/23.15            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.15            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.93/23.15            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.93/23.15            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.15            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.93/23.15            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.15            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.15            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.15            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.93/23.15            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.93/23.15            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.93/23.15            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.15            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.15            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.15            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.15            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.15            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.93/23.15            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.15            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.15            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.93/23.15            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.93/23.15            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.15            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.93/23.15            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.93/23.15            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.15            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.93/23.15            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.93/23.15              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.93/23.15            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.15            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.93/23.15              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.93/23.15            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.93/23.15            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.93/23.15                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.93/23.15                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.15                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.15                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.15                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.93/23.15                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.93/23.15                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.93/23.15              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.93/23.15                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.93/23.15                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.93/23.15                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.93/23.15                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.93/23.15                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.93/23.15                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.93/23.15                $i(all_57_7))))
% 153.93/23.15    (61)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 153.93/23.15          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 153.93/23.15            e1)
% 153.93/23.15    (62)  op(e2, e3) = all_52_1
% 153.93/23.15  
% 153.93/23.15  Begin of proof
% 153.93/23.15  | 
% 153.93/23.15  | BETA: splitting (46) gives:
% 153.93/23.15  | 
% 153.93/23.15  | Case 1:
% 153.93/23.15  | | 
% 153.93/23.15  | |   (63)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.93/23.15  | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.93/23.15  | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.93/23.15  | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.93/23.15  | |           ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.93/23.15  | |                 e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2 &
% 153.93/23.15  | |           op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 153.93/23.15  | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.93/23.15  | |           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 153.93/23.15  | |                 e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 153.93/23.15  | |                 e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 153.93/23.15  | |               $i(all_57_15))))
% 153.93/23.15  | | 
% 153.93/23.15  | | BETA: splitting (63) gives:
% 153.93/23.15  | | 
% 153.93/23.15  | | Case 1:
% 153.93/23.15  | | | 
% 153.93/23.15  | | |   (64)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 153.93/23.15  | | |             e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 153.93/23.15  | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 153.93/23.15  | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.93/23.15  | | |         ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.93/23.15  | | |               e0) = all_57_15 & $i(all_57_15)))
% 153.93/23.15  | | | 
% 153.93/23.15  | | | ALPHA: (64) implies:
% 153.93/23.15  | | |   (65)  op(e3, e3) = e3
% 153.93/23.15  | | |   (66)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0,
% 153.93/23.15  | | |             e0) = all_57_15 & $i(all_57_15))
% 153.93/23.15  | | |   (67)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 153.93/23.15  | | |             e1) = all_57_14 & $i(all_57_14))
% 153.93/23.15  | | |   (68)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2,
% 153.93/23.15  | | |             e2) = all_57_12 & $i(all_57_12))
% 153.93/23.15  | | | 
% 153.93/23.15  | | | BETA: splitting (66) gives:
% 153.93/23.15  | | | 
% 153.93/23.15  | | | Case 1:
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | |   (69)  all_57_2 = e0 & op(e0, e3) = e0
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | ALPHA: (69) implies:
% 153.93/23.15  | | | |   (70)  op(e0, e3) = e0
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | GROUND_INST: instantiating (16) with all_52_3, e0, e3, e0, simplifying
% 153.93/23.15  | | | |              with (41), (70) gives:
% 153.93/23.15  | | | |   (71)  all_52_3 = e0
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | GROUND_INST: instantiating (16) with e3, all_38_1, e1, e2, simplifying
% 153.93/23.15  | | | |              with (30), (52) gives:
% 153.93/23.15  | | | |   (72)  all_38_1 = e3
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | GROUND_INST: instantiating (16) with all_20_1, all_38_1, e1, e2,
% 153.93/23.15  | | | |              simplifying with (30), (47) gives:
% 153.93/23.15  | | | |   (73)  all_38_1 = all_20_1
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | COMBINE_EQS: (72), (73) imply:
% 153.93/23.15  | | | |   (74)  all_20_1 = e3
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | SIMP: (74) implies:
% 153.93/23.15  | | | |   (75)  all_20_1 = e3
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | REDUCE: (40), (71) imply:
% 153.93/23.15  | | | |   (76)   ~ (all_52_1 = e0)
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | REDUCE: (13), (71) imply:
% 153.93/23.15  | | | |   (77)   ~ (all_52_7 = e0)
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | SIMP: (77) implies:
% 153.93/23.15  | | | |   (78)   ~ (all_52_7 = e0)
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | REDUCE: (23), (71) imply:
% 153.93/23.15  | | | |   (79)   ~ (all_52_11 = e0)
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | SIMP: (79) implies:
% 153.93/23.15  | | | |   (80)   ~ (all_52_11 = e0)
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | BETA: splitting (4) gives:
% 153.93/23.15  | | | | 
% 153.93/23.15  | | | | Case 1:
% 153.93/23.15  | | | | | 
% 153.93/23.15  | | | | |   (81)  all_54_4 = e3
% 153.93/23.15  | | | | | 
% 153.93/23.15  | | | | | REF_CLOSE: (25), (49), (81) are inconsistent by sub-proof #843.
% 153.93/23.15  | | | | | 
% 153.93/23.15  | | | | Case 2:
% 153.93/23.15  | | | | | 
% 153.93/23.15  | | | | |   (82)   ~ (all_54_4 = e3)
% 153.93/23.15  | | | | |   (83)  all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 153.93/23.15  | | | | | 
% 153.93/23.15  | | | | | BETA: splitting (83) gives:
% 153.93/23.15  | | | | | 
% 153.93/23.15  | | | | | Case 1:
% 153.93/23.15  | | | | | | 
% 153.93/23.15  | | | | | |   (84)  all_54_4 = e2
% 153.93/23.15  | | | | | | 
% 153.93/23.15  | | | | | | COMBINE_EQS: (49), (84) imply:
% 153.93/23.15  | | | | | |   (85)  all_52_1 = e2
% 153.93/23.15  | | | | | | 
% 153.93/23.15  | | | | | | SIMP: (85) implies:
% 153.93/23.15  | | | | | |   (86)  all_52_1 = e2
% 153.93/23.15  | | | | | | 
% 153.93/23.15  | | | | | | REDUCE: (20), (86) imply:
% 153.93/23.15  | | | | | |   (87)   ~ (all_52_13 = e2)
% 153.93/23.15  | | | | | | 
% 153.93/23.15  | | | | | | SIMP: (87) implies:
% 153.93/23.15  | | | | | |   (88)   ~ (all_52_13 = e2)
% 153.93/23.15  | | | | | | 
% 153.93/23.15  | | | | | | REDUCE: (25), (86) imply:
% 153.93/23.15  | | | | | |   (89)   ~ (e3 = e2)
% 153.93/23.15  | | | | | | 
% 153.93/23.15  | | | | | | REDUCE: (76), (86) imply:
% 153.93/23.15  | | | | | |   (90)   ~ (e2 = e0)
% 153.93/23.15  | | | | | | 
% 153.93/23.15  | | | | | | REDUCE: (62), (86) imply:
% 153.93/23.15  | | | | | |   (91)  op(e2, e3) = e2
% 153.93/23.15  | | | | | | 
% 153.93/23.15  | | | | | | BETA: splitting (6) gives:
% 153.93/23.15  | | | | | | 
% 153.93/23.15  | | | | | | Case 1:
% 153.93/23.15  | | | | | | | 
% 153.93/23.15  | | | | | | |   (92)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 &
% 153.93/23.15  | | | | | | |           op(e2, e3) = e1)
% 153.93/23.15  | | | | | | | 
% 153.93/23.15  | | | | | | | REF_CLOSE: (5), (16), (58), (62), (65), (91), (92) are
% 153.93/23.15  | | | | | | |            inconsistent by sub-proof #841.
% 153.93/23.15  | | | | | | | 
% 153.93/23.15  | | | | | | Case 2:
% 153.93/23.15  | | | | | | | 
% 153.93/23.15  | | | | | | |   (93)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 &
% 153.93/23.15  | | | | | | |           op(e0, e3) = e1)
% 153.93/23.15  | | | | | | | 
% 153.93/23.15  | | | | | | | BETA: splitting (93) gives:
% 153.93/23.15  | | | | | | | 
% 153.93/23.15  | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | 
% 153.93/23.15  | | | | | | | |   (94)  all_56_6 = e1 & op(e1, e3) = e1
% 153.93/23.15  | | | | | | | | 
% 153.93/23.15  | | | | | | | | ALPHA: (94) implies:
% 153.93/23.15  | | | | | | | |   (95)  all_56_6 = e1
% 153.93/23.15  | | | | | | | |   (96)  op(e1, e3) = e1
% 153.93/23.15  | | | | | | | | 
% 153.93/23.15  | | | | | | | | BETA: splitting (61) gives:
% 153.93/23.15  | | | | | | | | 
% 153.93/23.15  | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | 
% 153.93/23.15  | | | | | | | | |   (97)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 &
% 153.93/23.15  | | | | | | | | |           op(e0, e2) = e1)
% 153.93/23.15  | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | BETA: splitting (97) gives:
% 153.93/23.15  | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | |   (98)  all_56_12 = e1 & op(e0, e3) = e1
% 153.93/23.15  | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | ALPHA: (98) implies:
% 153.93/23.15  | | | | | | | | | |   (99)  all_56_12 = e1
% 153.93/23.15  | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | BETA: splitting (34) gives:
% 153.93/23.15  | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | |   (100)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 153.93/23.15  | | | | | | | | | | |            & op(e2, e3) = e0)
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | REF_CLOSE: (16), (33), (62), (65), (76), (100) are
% 153.93/23.15  | | | | | | | | | | |            inconsistent by sub-proof #839.
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | |   (101)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 153.93/23.15  | | | | | | | | | | |            e0 & op(e0, e3) = e0)
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | REF_CLOSE: (16), (43), (59), (96), (99), (101) are
% 153.93/23.15  | | | | | | | | | | |            inconsistent by sub-proof #838.
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | End of split
% 153.93/23.15  | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | |   (102)  all_56_13 = e1 & op(e0, e2) = e1
% 153.93/23.15  | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | ALPHA: (102) implies:
% 153.93/23.15  | | | | | | | | | |   (103)  all_56_13 = e1
% 153.93/23.15  | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | BETA: splitting (45) gives:
% 153.93/23.15  | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | |   (104)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 153.93/23.15  | | | | | | | | | | |            & op(e1, e2) = e2)
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | BETA: splitting (104) gives:
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | |   (105)  all_56_6 = e2 & op(e1, e3) = e2
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | REF_CLOSE: (58), (95), (105) are inconsistent by sub-proof
% 153.93/23.15  | | | | | | | | | | | |            #837.
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | |   (106)  all_56_7 = e2 & op(e1, e2) = e2
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | REF_CLOSE: (16), (22), (32), (37), (42), (53), (57), (78),
% 153.93/23.15  | | | | | | | | | | | |            (106) are inconsistent by sub-proof #835.
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | End of split
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | |   (107)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 153.93/23.15  | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | BETA: splitting (107) gives:
% 153.93/23.15  | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | |   (108)  all_56_8 = e2 & op(e1, e1) = e2
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | ALPHA: (108) implies:
% 153.93/23.15  | | | | | | | | | | | |   (109)  op(e1, e1) = e2
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | BETA: splitting (42) gives:
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | |   (110)  all_54_13 = e3
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | REF_CLOSE: (32), (53), (110) are inconsistent by sub-proof
% 153.93/23.15  | | | | | | | | | | | | |            #845.
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | |   (111)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | BETA: splitting (9) gives:
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | |   (112)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 153.93/23.15  | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 153.93/23.15  | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (10), (12), (16), (17), (18), (29),
% 153.93/23.15  | | | | | | | | | | | | | |            (31), (33), (38), (39), (43), (48), (50), (51),
% 153.93/23.15  | | | | | | | | | | | | | |            (52), (54), (58), (60), (65), (66), (68), (78),
% 153.93/23.15  | | | | | | | | | | | | | |            (88), (90), (109), (112) are inconsistent by
% 153.93/23.15  | | | | | | | | | | | | | |            sub-proof #818.
% 153.93/23.15  | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | |   (113)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 153.93/23.15  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 153.93/23.15  | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | REF_CLOSE: (16), (22), (37), (53), (57), (58), (78), (103),
% 153.93/23.15  | | | | | | | | | | | | | |            (111), (113) are inconsistent by sub-proof #817.
% 153.93/23.15  | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | End of split
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | End of split
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | |   (114)  all_56_11 = e2 & op(e1, e0) = e2
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | ALPHA: (114) implies:
% 153.93/23.15  | | | | | | | | | | | |   (115)  all_56_11 = e2
% 153.93/23.15  | | | | | | | | | | | |   (116)  op(e1, e0) = e2
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | BETA: splitting (42) gives:
% 153.93/23.15  | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | |   (117)  all_54_13 = e3
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | REF_CLOSE: (32), (53), (117) are inconsistent by sub-proof
% 153.93/23.15  | | | | | | | | | | | | |            #845.
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | |   (118)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | BETA: splitting (9) gives:
% 153.93/23.15  | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | |   (119)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 153.93/23.15  | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 153.93/23.15  | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | BETA: splitting (119) gives:
% 153.93/23.15  | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | |   (120)  all_56_1 = e2 & op(e3, e2) = e2
% 153.93/23.15  | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | ALPHA: (120) implies:
% 153.93/23.15  | | | | | | | | | | | | | | |   (121)  all_56_1 = e2
% 153.93/23.15  | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 153.93/23.15  | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | |   (122)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.15  | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 153.93/23.15  | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 153.93/23.15  | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.93/23.15  | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.15  | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.93/23.15  | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 153.93/23.15  | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.93/23.15  | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 153.93/23.15  | | | | | | | | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 153.93/23.15  | | | | | | | | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 153.93/23.15  | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.93/23.15  | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 153.93/23.15  | | | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 153.93/23.15  | | | | | | | | | | | | | | | |              e2) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.93/23.15  | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 153.93/23.15  | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 153.93/23.15  | | | | | | | | | | | | | | | |            = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.93/23.15  | | | | | | | | | | | | | | | |            = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.93/23.15  | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.93/23.15  | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 153.93/23.15  | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | |   (123)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.15  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 153.93/23.15  | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 153.93/23.15  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.93/23.15  | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.15  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 153.93/23.15  | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 153.93/23.15  | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | BETA: splitting (123) gives:
% 153.93/23.15  | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | |   (124)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.15  | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 153.93/23.15  | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 153.93/23.15  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.93/23.15  | | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (66), (67), (124) are inconsistent by
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            sub-proof #814.
% 153.93/23.15  | | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | |   (125)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.15  | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 153.93/23.15  | | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (66), (68), (125) are inconsistent by
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            sub-proof #831.
% 153.93/23.15  | | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | End of split
% 153.93/23.15  | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | |   (126)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.93/23.15  | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.93/23.15  | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 153.93/23.15  | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.93/23.15  | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 153.93/23.15  | | | | | | | | | | | | | | | | |            = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.93/23.15  | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.93/23.15  | | | | | | | | | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 153.93/23.15  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 153.93/23.15  | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 153.93/23.15  | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 153.93/23.15  | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (16), (17), (29), (48), (50), (54), (65),
% 153.93/23.15  | | | | | | | | | | | | | | | | |            (126) are inconsistent by sub-proof #829.
% 153.93/23.15  | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | End of split
% 153.93/23.15  | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | |   (127)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 153.93/23.15  | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.15  | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 153.93/23.15  | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 153.93/23.15  | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.93/23.15  | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 153.93/23.15  | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.93/23.15  | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 153.93/23.15  | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.93/23.15  | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 153.93/23.15  | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 153.93/23.15  | | | | | | | | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.93/23.15  | | | | | | | | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 153.93/23.15  | | | | | | | | | | | | | | | |            = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 153.93/23.15  | | | | | | | | | | | | | | | |            = e2 & $i(all_57_9) & $i(all_57_12)) |
% 153.93/23.15  | | | | | | | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 153.93/23.15  | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 153.93/23.15  | | | | | | | | | | | | | | | |          | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 153.93/23.15  | | | | | | | | | | | | | | | |              = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.15  | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 153.93/23.15  | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.93/23.15  | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.93/23.15  | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.93/23.15  | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.93/23.15  | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.93/23.15  | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.15  | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 153.93/23.15  | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.93/23.15  | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.15  | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.93/23.15  | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 153.93/23.15  | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 153.93/23.15  | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.93/23.15  | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.93/23.15  | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.93/23.15  | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.93/23.15  | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 153.93/23.15  | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 153.93/23.15  | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 153.93/23.15  | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.93/23.15  | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.93/23.15  | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.93/23.15  | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 153.93/23.15  | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | |   (128)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 153.93/23.15  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.93/23.15  | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 153.93/23.15  | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 153.93/23.15  | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.93/23.15  | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 153.93/23.15  | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.93/23.15  | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 153.93/23.15  | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 153.93/23.15  | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.93/23.15  | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 153.93/23.15  | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 153.93/23.15  | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.15  | | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | |   (129)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 153.93/23.15  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 153.93/23.15  | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 153.93/23.15  | | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (48), (50), (52), (54), (129) are
% 153.93/23.15  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 153.93/23.15  | | | | | | | | | | | | | | | | | | 
% 153.93/23.15  | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.15  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | |   (130)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (17), (31), (38), (130) are
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1020.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | |   (131)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 153.93/23.16  | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 153.93/23.16  | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 153.93/23.16  | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.93/23.16  | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 153.93/23.16  | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 153.93/23.16  | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 153.93/23.16  | | | | | | | | | | | | | | | | |            e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 153.93/23.16  | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.93/23.16  | | | | | | | | | | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 153.93/23.16  | | | | | | | | | | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 153.93/23.16  | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.93/23.16  | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 153.93/23.16  | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 153.93/23.16  | | | | | | | | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.93/23.16  | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 153.93/23.16  | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.93/23.16  | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.93/23.16  | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 153.93/23.16  | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 153.93/23.16  | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.93/23.16  | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | BETA: splitting (131) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | |   (132)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 153.93/23.16  | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.93/23.16  | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (33), (65), (132) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            sub-proof #975.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | |   (133)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |   (134)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |          $i(all_57_13)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |   (135)  op(e2, e0) = e2
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (39), (88), (135) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            sub-proof #1156.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |   (136)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |                & $i(all_57_7))))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |   (137)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |   (138)  op(e1, e0) = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (58), (116), (138) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            sub-proof #1125.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |   (139)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |          ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |                e1) = all_57_6 & op(e0, e1) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_7)))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |   (140)  op(e0, e0) = all_57_15
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |   (141)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |   (142)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |   (143)  all_56_9 = e1 & op(e3, e0) = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |   (144)  all_56_9 = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (12), (14), (16), (17), (18), (24),
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            (33), (43), (48), (51), (55), (58), (62), (65),
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            (76), (78), (90), (115), (121), (140), (141),
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            (144) are inconsistent by sub-proof #811.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |   (145)  all_56_10 = e1 & op(e2, e0) = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (16), (39), (145) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #810.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |   (146)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (17), (58), (116), (146) are
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #809.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | |   (147)  all_56_3 = e2 & op(e2, e2) = e2
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 153.93/23.16  | | | | | | | | | | | | | | |   (148)  op(e2, e2) = e2
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (58), (148) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | |            sub-proof #1158.
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | |   (149)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 153.93/23.16  | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | REF_CLOSE: (16), (22), (37), (53), (57), (58), (78), (103),
% 153.93/23.16  | | | | | | | | | | | | | |            (118), (149) are inconsistent by sub-proof #817.
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | 
% 153.93/23.16  | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | 
% 153.93/23.16  | | | | | | | | |   (150)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1
% 153.93/23.16  | | | | | | | | |            & op(e0, e0) = e1)
% 153.93/23.16  | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | BETA: splitting (150) gives:
% 153.93/23.16  | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | |   (151)  all_56_14 = e1 & op(e0, e1) = e1
% 153.93/23.16  | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | ALPHA: (151) implies:
% 153.93/23.16  | | | | | | | | | |   (152)  op(e0, e1) = e1
% 153.93/23.16  | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | BETA: splitting (45) gives:
% 153.93/23.16  | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | |   (153)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2
% 153.93/23.16  | | | | | | | | | | |            & op(e1, e2) = e2)
% 153.93/23.16  | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | BETA: splitting (153) gives:
% 153.93/23.16  | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | |   (154)  all_56_6 = e2 & op(e1, e3) = e2
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | REF_CLOSE: (58), (95), (154) are inconsistent by sub-proof
% 153.93/23.16  | | | | | | | | | | | |            #837.
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | |   (155)  all_56_7 = e2 & op(e1, e2) = e2
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | REF_CLOSE: (16), (22), (32), (37), (42), (53), (57), (78),
% 153.93/23.16  | | | | | | | | | | | |            (155) are inconsistent by sub-proof #835.
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | |   (156)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 =
% 153.93/23.16  | | | | | | | | | | |            e2 & op(e1, e0) = e2)
% 153.93/23.16  | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | BETA: splitting (156) gives:
% 153.93/23.16  | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | |   (157)  all_56_8 = e2 & op(e1, e1) = e2
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | ALPHA: (157) implies:
% 153.93/23.16  | | | | | | | | | | | |   (158)  op(e1, e1) = e2
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | BETA: splitting (42) gives:
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | |   (159)  all_54_13 = e3
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | REF_CLOSE: (32), (53), (159) are inconsistent by sub-proof
% 153.93/23.16  | | | | | | | | | | | | |            #845.
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | |   (160)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | BETA: splitting (56) gives:
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | |   (161)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0
% 153.93/23.16  | | | | | | | | | | | | | |            & op(e1, e2) = e0)
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | |   (162)  all_56_6 = e0 & op(e1, e3) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 153.93/23.16  | | | | | | | | | | | | | | |   (163)  op(e1, e3) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | REF_CLOSE: (16), (43), (59), (96), (163) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | |            sub-proof #1127.
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | |   (164)  all_56_7 = e0 & op(e1, e2) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | REF_CLOSE: (18), (33), (164) are inconsistent by sub-proof
% 153.93/23.16  | | | | | | | | | | | | | | |            #1151.
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | |   (165)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 =
% 153.93/23.16  | | | | | | | | | | | | | |            e0 & op(e1, e0) = e0)
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | |   (166)  all_56_8 = e0 & op(e1, e1) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 153.93/23.16  | | | | | | | | | | | | | | |   (167)  op(e1, e1) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | REF_CLOSE: (16), (90), (158), (167) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | |            sub-proof #1006.
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | |   (168)  all_56_11 = e0 & op(e1, e0) = e0
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 153.93/23.16  | | | | | | | | | | | | | | |   (169)  all_56_11 = e0
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | |   (170)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 153.93/23.16  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | BETA: splitting (170) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | |   (171)  all_56_9 = e1 & op(e3, e0) = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | ALPHA: (171) implies:
% 153.93/23.16  | | | | | | | | | | | | | | | | |   (172)  all_56_9 = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (8), (9), (10), (11), (12), (15),
% 153.93/23.16  | | | | | | | | | | | | | | | | |            (16), (17), (18), (19), (22), (29), (31), (33),
% 153.93/23.16  | | | | | | | | | | | | | | | | |            (37), (38), (39), (43), (48), (50), (51), (52),
% 153.93/23.16  | | | | | | | | | | | | | | | | |            (53), (54), (57), (58), (60), (65), (66), (68),
% 153.93/23.16  | | | | | | | | | | | | | | | | |            (78), (80), (88), (90), (158), (160), (172) are
% 153.93/23.16  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #806.
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | |   (173)  all_56_10 = e1 & op(e2, e0) = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (16), (39), (173) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | | | |            sub-proof #810.
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | |   (174)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 153.93/23.16  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | BETA: splitting (174) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | |   (175)  all_56_11 = e1 & op(e1, e0) = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | REF_CLOSE: (43), (169), (175) are inconsistent by sub-proof
% 153.93/23.16  | | | | | | | | | | | | | | | | |            #805.
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | |   (176)  all_56_15 = e1 & op(e0, e0) = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | ALPHA: (176) implies:
% 153.93/23.16  | | | | | | | | | | | | | | | | |   (177)  op(e0, e0) = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (17), (177) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | | | |            sub-proof #1022.
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | |   (178)  all_56_11 = e2 & op(e1, e0) = e2
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | ALPHA: (178) implies:
% 153.93/23.16  | | | | | | | | | | | |   (179)  all_56_11 = e2
% 153.93/23.16  | | | | | | | | | | | |   (180)  op(e1, e0) = e2
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | BETA: splitting (42) gives:
% 153.93/23.16  | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | |   (181)  all_54_13 = e3
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | REF_CLOSE: (32), (53), (181) are inconsistent by sub-proof
% 153.93/23.16  | | | | | | | | | | | | |            #845.
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | |   (182)   ~ (all_54_13 = e3)
% 153.93/23.16  | | | | | | | | | | | | |   (183)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | BETA: splitting (183) gives:
% 153.93/23.16  | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | |   (184)  all_54_13 = e2
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | COMBINE_EQS: (53), (184) imply:
% 153.93/23.16  | | | | | | | | | | | | | |   (185)  all_52_7 = e2
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | SIMP: (185) implies:
% 153.93/23.16  | | | | | | | | | | | | | |   (186)  all_52_7 = e2
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | REDUCE: (3), (186) imply:
% 153.93/23.16  | | | | | | | | | | | | | |   (187)   ~ (all_52_11 = e2)
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | SIMP: (187) implies:
% 153.93/23.16  | | | | | | | | | | | | | |   (188)   ~ (all_52_11 = e2)
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 153.93/23.16  | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | |   (189)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 153.93/23.16  | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | |   (190)  all_56_9 = e1 & op(e3, e0) = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 153.93/23.16  | | | | | | | | | | | | | | | |   (191)  all_56_9 = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | |   (192)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2
% 153.93/23.16  | | | | | | | | | | | | | | | | |            & op(e2, e1) = e2)
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | |   (193)  all_56_4 = e2 & op(e3, e1) = e2
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 153.93/23.16  | | | | | | | | | | | | | | | | | |   (194)  all_56_4 = e2
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | BETA: splitting (60) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |   (195)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |   (196)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |   (197)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (66), (67), (197) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            sub-proof #814.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |   (198)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (66), (68), (198) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            sub-proof #831.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |   (199)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |   (200)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |   (201)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (201) implies:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |   (202)  op(e1, e1) = e2
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (11), (15), (16), (33), (80), (90), (194),
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            (202) are inconsistent by sub-proof #908.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |   (203)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |          all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (203) implies:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |   (204)  op(e3, e2) = e3
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (16), (29), (204) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1166.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |   (205)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (205) gives:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |   (206)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (206) implies:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |   (207)  op(e3, e3) = e2
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (19), (28), (33), (36), (43), (48),
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            (58), (90), (194), (207) are inconsistent by
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1062.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |   (208)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (48), (50), (54), (208) are
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #830.
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.16  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |   (209)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_9) & $i(all_57_12)) |
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |          | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |              = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.93/23.16  | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |   (210)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |   (211)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (48), (50), (52), (54), (211) are
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #828.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |   (212)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (17), (31), (38), (212) are
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #1020.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |   (213)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |   (214)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (33), (65), (214) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            sub-proof #975.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |   (215)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |   (216)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_13)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |   (217)  op(e2, e0) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (39), (88), (217) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1156.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |   (218)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_7))))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |   (219)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (219) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |   (220)  op(e1, e0) = e1
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (58), (180), (220) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1125.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |   (221)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_6 & op(e0, e1) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_7)))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |   (222)  op(e0, e0) = all_57_15
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |   (223)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | |   (224)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e2)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (225)  all_56_1 = e2 & op(e3, e2) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (226)  all_56_1 = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (11), (12), (14), (16), (17), (18), (24),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |            (33), (43), (48), (51), (55), (58), (62), (65),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |            (76), (78), (90), (179), (191), (222), (223),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |            (226) are inconsistent by sub-proof #811.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (227)  all_56_3 = e2 & op(e2, e2) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (227) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (228)  op(e2, e2) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (16), (58), (228) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1158.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | |   (229)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | |            e2 & op(e0, e2) = e2)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (230)  all_56_7 = e2 & op(e1, e2) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (230) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (231)  op(e1, e2) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (22), (37), (53), (57), (78), (183), (231)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |            are inconsistent by sub-proof #836.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (232)  all_56_13 = e2 & op(e0, e2) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (232) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | |   (233)  all_56_13 = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (14) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (234)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (235)  all_56_2 = e0 & op(e2, e3) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (62), (76), (235) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #840.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (236)  all_56_3 = e0 & op(e2, e2) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (237)  op(e2, e2) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (12), (16), (17), (43), (58), (78), (80),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (237) are inconsistent by sub-proof
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #802.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | |   (238)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (239)  all_56_5 = e0 & op(e2, e1) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (239) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (240)  op(e2, e1) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (27), (30), (240) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #801.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (241)  all_56_10 = e0 & op(e2, e0) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (241) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (242)  all_56_10 = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (243)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (244)  all_56_1 = e0 & op(e3, e2) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (245)  all_56_1 = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (246)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (246) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (247)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_0)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (247) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (248)   ~ (all_57_15 = e3)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (222), (248) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1019.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (249)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) = e0 & $i(all_57_3))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (249) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (250)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_1)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (251)   ~ (all_57_15 = e3)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (17), (222), (251) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1019.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (252)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_3)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (253)  op(e3, e3) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (19), (33), (48), (50), (54), (191),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (253) are inconsistent by sub-proof #808.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (254)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (255)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_4)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (256)  op(e1, e1) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (8), (9), (10), (11), (12), (15),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (16), (17), (18), (19), (22), (29), (31), (33),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (37), (38), (39), (43), (48), (50), (51), (52),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (53), (54), (57), (58), (60), (65), (66), (68),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (80), (88), (90), (183), (191), (233),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (245), (256) are inconsistent by sub-proof #807.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (257)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_7))
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (43), (152), (257) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #800.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (258)  all_56_3 = e0 & op(e2, e2) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (258) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (259)  op(e2, e2) = e0
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (12), (16), (17), (43), (58), (78), (80),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (222), (223), (259) are inconsistent by sub-proof
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #802.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (260)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 =
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e2) = e0)
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (12), (16), (18), (24), (33), (48), (55),
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (78), (179), (191), (242), (260) are inconsistent
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            by sub-proof #812.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | |   (261)  all_56_5 = e2 & op(e2, e1) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | |   (262)  op(e2, e1) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (48), (52), (262) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | | | |            sub-proof #1135.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | |   (263)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 =
% 153.93/23.17  | | | | | | | | | | | | | | | | |            e2 & op(e0, e1) = e2)
% 153.93/23.17  | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | BETA: splitting (263) gives:
% 153.93/23.17  | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | Case 1:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | |   (264)  all_56_8 = e2 & op(e1, e1) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | ALPHA: (264) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | |   (265)  op(e1, e1) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (7), (8), (9), (10), (11), (12), (15),
% 153.93/23.17  | | | | | | | | | | | | | | | | | |            (16), (17), (18), (19), (22), (29), (31), (33),
% 153.93/23.17  | | | | | | | | | | | | | | | | | |            (37), (38), (39), (43), (48), (50), (51), (52),
% 153.93/23.17  | | | | | | | | | | | | | | | | | |            (53), (54), (57), (58), (60), (65), (66), (68),
% 153.93/23.17  | | | | | | | | | | | | | | | | | |            (78), (80), (88), (90), (183), (191), (265) are
% 153.93/23.17  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #806.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | |   (266)  all_56_14 = e2 & op(e0, e1) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | ALPHA: (266) implies:
% 153.93/23.17  | | | | | | | | | | | | | | | | | |   (267)  op(e0, e1) = e2
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (188), (267) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | | | |            sub-proof #1092.
% 153.93/23.17  | | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | |   (268)  all_56_10 = e1 & op(e2, e0) = e1
% 153.93/23.17  | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | | REF_CLOSE: (2), (16), (39), (268) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | | | |            sub-proof #810.
% 153.93/23.17  | | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | |   (269)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 153.93/23.17  | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 153.93/23.17  | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | | REF_CLOSE: (5), (16), (17), (58), (180), (269) are
% 153.93/23.17  | | | | | | | | | | | | | | |            inconsistent by sub-proof #809.
% 153.93/23.17  | | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | |   (270)  all_54_13 = e1 | all_54_13 = e0
% 153.93/23.17  | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | | REF_CLOSE: (22), (53), (78), (270) are inconsistent by
% 153.93/23.17  | | | | | | | | | | | | | |            sub-proof #983.
% 153.93/23.17  | | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | |   (271)  all_56_15 = e1 & op(e0, e0) = e1
% 153.93/23.17  | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | ALPHA: (271) implies:
% 153.93/23.17  | | | | | | | | | |   (272)  op(e0, e0) = e1
% 153.93/23.17  | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | | REF_CLOSE: (5), (16), (17), (272) are inconsistent by
% 153.93/23.17  | | | | | | | | | |            sub-proof #1022.
% 153.93/23.17  | | | | | | | | | | 
% 153.93/23.17  | | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | | 
% 153.93/23.17  | | | | | | | | End of split
% 153.93/23.17  | | | | | | | | 
% 153.93/23.17  | | | | | | | Case 2:
% 153.93/23.17  | | | | | | | | 
% 153.93/23.17  | | | | | | | |   (273)  all_56_12 = e1 & op(e0, e3) = e1
% 153.93/23.17  | | | | | | | | 
% 153.93/23.17  | | | | | | | | ALPHA: (273) implies:
% 153.93/23.17  | | | | | | | |   (274)  all_56_12 = e1
% 153.93/23.17  | | | | | | | | 
% 153.93/23.17  | | | | | | | | REF_CLOSE: (1), (12), (16), (17), (26), (33), (43), (78), (80),
% 153.93/23.17  | | | | | | | |            (274) are inconsistent by sub-proof #797.
% 153.93/23.17  | | | | | | | | 
% 153.93/23.17  | | | | | | | End of split
% 153.93/23.17  | | | | | | | 
% 153.93/23.17  | | | | | | End of split
% 153.93/23.17  | | | | | | 
% 153.93/23.17  | | | | | Case 2:
% 153.93/23.17  | | | | | | 
% 153.93/23.17  | | | | | |   (275)  all_54_4 = e1 | all_54_4 = e0
% 153.93/23.17  | | | | | | 
% 153.93/23.17  | | | | | | REF_CLOSE: (44), (49), (76), (275) are inconsistent by sub-proof
% 153.93/23.17  | | | | | |            #795.
% 153.93/23.17  | | | | | | 
% 153.93/23.17  | | | | | End of split
% 153.93/23.17  | | | | | 
% 153.93/23.17  | | | | End of split
% 153.93/23.17  | | | | 
% 153.93/23.17  | | | Case 2:
% 153.93/23.17  | | | | 
% 153.93/23.17  | | | |   (276)   ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)
% 153.93/23.17  | | | | 
% 153.93/23.17  | | | | ALPHA: (276) implies:
% 153.93/23.17  | | | |   (277)   ~ (all_57_15 = e3)
% 153.93/23.17  | | | |   (278)  op(e0, e0) = all_57_15
% 153.93/23.17  | | | | 
% 153.93/23.17  | | | | REF_CLOSE: (16), (17), (277), (278) are inconsistent by sub-proof #1019.
% 153.93/23.17  | | | | 
% 153.93/23.17  | | | End of split
% 153.93/23.17  | | | 
% 153.93/23.17  | | Case 2:
% 153.93/23.17  | | | 
% 153.93/23.17  | | |   (279)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) =
% 153.93/23.17  | | |              e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.17  | | |              $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 153.93/23.17  | | |              (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14))) &
% 153.93/23.17  | | |          ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) &
% 153.93/23.17  | | |              op(e0, e0) = all_57_15 & $i(all_57_15)))
% 153.93/23.17  | | | 
% 153.93/23.17  | | | ALPHA: (279) implies:
% 153.93/23.17  | | |   (280)  op(e2, e2) = e2
% 153.93/23.17  | | | 
% 153.93/23.17  | | | REF_CLOSE: (8), (16), (58), (280) are inconsistent by sub-proof #1158.
% 153.93/23.17  | | | 
% 153.93/23.17  | | End of split
% 153.93/23.17  | | 
% 153.93/23.17  | Case 2:
% 153.93/23.17  | | 
% 153.93/23.17  | |   (281)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.93/23.17  | |                e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.93/23.17  | |                $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.93/23.17  | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.93/23.17  | |            ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) &
% 153.93/23.17  | |                op(e0, e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0 &
% 153.93/23.17  | |            op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 153.93/23.17  | |                (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 153.93/23.17  | |            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 153.93/23.17  | |                op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 &
% 153.93/23.17  | |                op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 153.93/23.17  | |                all_57_14 & $i(all_57_14))))
% 153.93/23.17  | | 
% 153.93/23.17  | | BETA: splitting (281) gives:
% 153.93/23.17  | | 
% 153.93/23.17  | | Case 1:
% 153.93/23.17  | | | 
% 153.93/23.17  | | |   (282)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 153.93/23.17  | | |              e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 153.93/23.17  | | |              $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 153.93/23.17  | | |              (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.93/23.17  | | |          ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) &
% 153.93/23.17  | | |              op(e0, e0) = all_57_15 & $i(all_57_15)))
% 153.93/23.17  | | | 
% 153.93/23.17  | | | ALPHA: (282) implies:
% 153.93/23.17  | | |   (283)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 153.93/23.17  | | |              e2) = all_57_12 & $i(all_57_12))
% 153.93/23.17  | | | 
% 153.93/23.17  | | | REF_CLOSE: (8), (16), (48), (52), (283) are inconsistent by sub-proof
% 153.93/23.17  | | |            #844.
% 153.93/23.17  | | | 
% 153.93/23.17  | | Case 2:
% 153.93/23.17  | | | 
% 153.93/23.17  | | |   (284)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 153.93/23.17  | | |              e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 153.93/23.17  | | |              $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 153.93/23.17  | | |              (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 153.93/23.17  | | |          ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 153.93/23.17  | | |              op(e1, e1) = all_57_14 & $i(all_57_14)))
% 153.93/23.17  | | | 
% 153.93/23.17  | | | ALPHA: (284) implies:
% 153.93/23.17  | | |   (285)  op(e0, e0) = e0
% 153.93/23.17  | | | 
% 153.93/23.17  | | | REF_CLOSE: (16), (17), (33), (285) are inconsistent by sub-proof #1143.
% 153.93/23.17  | | | 
% 153.93/23.17  | | End of split
% 153.93/23.17  | | 
% 153.93/23.17  | End of split
% 153.93/23.17  | 
% 153.93/23.17  End of proof
% 153.93/23.17  
% 153.93/23.17  Sub-proof #795 shows that the following formulas are inconsistent:
% 153.93/23.17  ----------------------------------------------------------------
% 153.93/23.17    (1)  all_54_4 = e1 | all_54_4 = e0
% 153.93/23.17    (2)  all_54_4 = all_52_1
% 153.93/23.17    (3)   ~ (all_52_1 = e1)
% 153.93/23.17    (4)   ~ (all_52_1 = e0)
% 153.93/23.17  
% 153.93/23.17  Begin of proof
% 153.93/23.17  | 
% 153.93/23.17  | BETA: splitting (1) gives:
% 153.93/23.17  | 
% 153.93/23.17  | Case 1:
% 153.93/23.17  | | 
% 153.93/23.17  | |   (5)  all_54_4 = e1
% 153.93/23.17  | | 
% 153.93/23.17  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1174.
% 153.93/23.17  | | 
% 153.93/23.17  | Case 2:
% 153.93/23.17  | | 
% 153.93/23.17  | |   (6)  all_54_4 = e0
% 153.93/23.17  | | 
% 153.93/23.17  | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #796.
% 153.93/23.17  | | 
% 153.93/23.17  | End of split
% 153.93/23.17  | 
% 153.93/23.17  End of proof
% 153.93/23.17  
% 153.93/23.17  Sub-proof #796 shows that the following formulas are inconsistent:
% 153.93/23.17  ----------------------------------------------------------------
% 153.93/23.17    (1)  all_54_4 = all_52_1
% 153.93/23.17    (2)  all_54_4 = e0
% 153.93/23.17    (3)   ~ (all_52_1 = e0)
% 153.93/23.17  
% 153.93/23.17  Begin of proof
% 153.93/23.17  | 
% 153.93/23.17  | COMBINE_EQS: (1), (2) imply:
% 153.93/23.17  |   (4)  all_52_1 = e0
% 153.93/23.17  | 
% 153.93/23.17  | SIMP: (4) implies:
% 153.93/23.17  |   (5)  all_52_1 = e0
% 153.93/23.17  | 
% 153.93/23.17  | REDUCE: (3), (5) imply:
% 153.93/23.17  |   (6)  $false
% 153.93/23.17  | 
% 153.93/23.17  | CLOSE: (6) is inconsistent.
% 153.93/23.17  | 
% 153.93/23.17  End of proof
% 153.93/23.17  
% 153.93/23.17  Sub-proof #797 shows that the following formulas are inconsistent:
% 153.93/23.17  ----------------------------------------------------------------
% 153.93/23.17    (1)  op(e0, e1) = all_52_11
% 153.93/23.17    (2)  op(e0, e2) = all_52_7
% 153.93/23.17    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.17           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.17    (4)  op(e0, e0) = e3
% 153.93/23.17    (5)  all_56_12 = e1
% 153.93/23.17    (6)  (all_56_15 = e0 & op(e0, e0) = e0) | (((all_56_9 = e0 & op(e3, e0) = e0)
% 153.93/23.17             | (all_56_10 = e0 & op(e2, e0) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 153.93/23.17               e0)) & ((all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 &
% 153.93/23.17               op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)))
% 153.93/23.17    (7)   ~ (e3 = e0)
% 153.93/23.17    (8)   ~ (all_52_11 = e0)
% 153.93/23.17    (9)   ~ (all_52_7 = e0)
% 153.93/23.17    (10)   ~ (e1 = e0)
% 153.93/23.17  
% 153.93/23.17  Begin of proof
% 153.93/23.17  | 
% 153.93/23.17  | BETA: splitting (6) gives:
% 153.93/23.17  | 
% 153.93/23.17  | Case 1:
% 153.93/23.17  | | 
% 153.93/23.17  | |   (11)  all_56_15 = e0 & op(e0, e0) = e0
% 153.93/23.17  | | 
% 153.93/23.17  | | ALPHA: (11) implies:
% 153.93/23.17  | |   (12)  op(e0, e0) = e0
% 153.93/23.17  | | 
% 153.93/23.17  | | REF_CLOSE: (3), (4), (7), (12) are inconsistent by sub-proof #1143.
% 153.93/23.17  | | 
% 153.93/23.17  | Case 2:
% 153.93/23.17  | | 
% 153.93/23.18  | |   (13)  ((all_56_9 = e0 & op(e3, e0) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.93/23.18  | |             e0) | (all_56_11 = e0 & op(e1, e0) = e0)) & ((all_56_12 = e0 &
% 153.93/23.18  | |             op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.93/23.18  | |           (all_56_14 = e0 & op(e0, e1) = e0))
% 153.93/23.18  | | 
% 153.93/23.18  | | ALPHA: (13) implies:
% 153.93/23.18  | |   (14)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 153.93/23.18  | |           e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (1), (2), (3), (5), (8), (9), (10), (14) are inconsistent by
% 153.93/23.18  | |            sub-proof #798.
% 153.93/23.18  | | 
% 153.93/23.18  | End of split
% 153.93/23.18  | 
% 153.93/23.18  End of proof
% 153.93/23.18  
% 153.93/23.18  Sub-proof #798 shows that the following formulas are inconsistent:
% 153.93/23.18  ----------------------------------------------------------------
% 153.93/23.18    (1)  op(e0, e1) = all_52_11
% 153.93/23.18    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 153.93/23.18         (all_56_14 = e0 & op(e0, e1) = e0)
% 153.93/23.18    (3)  op(e0, e2) = all_52_7
% 153.93/23.18    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.18    (5)  all_56_12 = e1
% 153.93/23.18    (6)   ~ (all_52_11 = e0)
% 153.93/23.18    (7)   ~ (all_52_7 = e0)
% 153.93/23.18    (8)   ~ (e1 = e0)
% 153.93/23.18  
% 153.93/23.18  Begin of proof
% 153.93/23.18  | 
% 153.93/23.18  | BETA: splitting (2) gives:
% 153.93/23.18  | 
% 153.93/23.18  | Case 1:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (9)  all_56_12 = e0 & op(e0, e3) = e0
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (5), (8), (9) are inconsistent by sub-proof #1103.
% 153.93/23.18  | | 
% 153.93/23.18  | Case 2:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (10)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 153.93/23.18  | |           e0)
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (1), (3), (4), (6), (7), (10) are inconsistent by sub-proof #799.
% 153.93/23.18  | | 
% 153.93/23.18  | End of split
% 153.93/23.18  | 
% 153.93/23.18  End of proof
% 153.93/23.18  
% 153.93/23.18  Sub-proof #799 shows that the following formulas are inconsistent:
% 153.93/23.18  ----------------------------------------------------------------
% 153.93/23.18    (1)  op(e0, e1) = all_52_11
% 153.93/23.18    (2)  op(e0, e2) = all_52_7
% 153.93/23.18    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.18    (4)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.93/23.18    (5)   ~ (all_52_11 = e0)
% 153.93/23.18    (6)   ~ (all_52_7 = e0)
% 153.93/23.18  
% 153.93/23.18  Begin of proof
% 153.93/23.18  | 
% 153.93/23.18  | BETA: splitting (4) gives:
% 153.93/23.18  | 
% 153.93/23.18  | Case 1:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (7)  all_56_13 = e0 & op(e0, e2) = e0
% 153.93/23.18  | | 
% 153.93/23.18  | | ALPHA: (7) implies:
% 153.93/23.18  | |   (8)  op(e0, e2) = e0
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #1036.
% 153.93/23.18  | | 
% 153.93/23.18  | Case 2:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (9)  all_56_14 = e0 & op(e0, e1) = e0
% 153.93/23.18  | | 
% 153.93/23.18  | | ALPHA: (9) implies:
% 153.93/23.18  | |   (10)  op(e0, e1) = e0
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #1124.
% 153.93/23.18  | | 
% 153.93/23.18  | End of split
% 153.93/23.18  | 
% 153.93/23.18  End of proof
% 153.93/23.18  
% 153.93/23.18  Sub-proof #800 shows that the following formulas are inconsistent:
% 153.93/23.18  ----------------------------------------------------------------
% 153.93/23.18    (1)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.93/23.18             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.93/23.18           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 153.93/23.18           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 153.93/23.18             e1) = e0 & $i(all_57_7))
% 153.93/23.18    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.18    (3)  op(e0, e1) = e1
% 153.93/23.18    (4)   ~ (e1 = e0)
% 153.93/23.18  
% 153.93/23.18  Begin of proof
% 153.93/23.18  | 
% 153.93/23.18  | BETA: splitting (1) gives:
% 153.93/23.18  | 
% 153.93/23.18  | Case 1:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (5)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.93/23.18  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.93/23.18  | |        $i(all_57_6)
% 153.93/23.18  | | 
% 153.93/23.18  | | ALPHA: (5) implies:
% 153.93/23.18  | |   (6)  op(e0, e1) = e0
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #899.
% 153.93/23.18  | | 
% 153.93/23.18  | Case 2:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (7)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.93/23.18  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.93/23.18  | |        $i(all_57_7)
% 153.93/23.18  | | 
% 153.93/23.18  | | ALPHA: (7) implies:
% 153.93/23.18  | |   (8)  op(e0, e1) = e0
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #899.
% 153.93/23.18  | | 
% 153.93/23.18  | End of split
% 153.93/23.18  | 
% 153.93/23.18  End of proof
% 153.93/23.18  
% 153.93/23.18  Sub-proof #801 shows that the following formulas are inconsistent:
% 153.93/23.18  ----------------------------------------------------------------
% 153.93/23.18    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.18    (2)  op(e2, e1) = all_38_1
% 153.93/23.18    (3)  op(e2, e1) = e0
% 153.93/23.18    (4)   ~ (all_38_1 = e0)
% 153.93/23.18  
% 153.93/23.18  Begin of proof
% 153.93/23.18  | 
% 153.93/23.18  | GROUND_INST: instantiating (1) with e0, all_38_1, e1, e2, simplifying with
% 153.93/23.18  |              (2), (3) gives:
% 153.93/23.18  |   (5)  all_38_1 = e0
% 153.93/23.18  | 
% 153.93/23.18  | REDUCE: (4), (5) imply:
% 153.93/23.18  |   (6)  $false
% 153.93/23.18  | 
% 153.93/23.18  | CLOSE: (6) is inconsistent.
% 153.93/23.18  | 
% 153.93/23.18  End of proof
% 153.93/23.18  
% 153.93/23.18  Sub-proof #802 shows that the following formulas are inconsistent:
% 153.93/23.18  ----------------------------------------------------------------
% 153.93/23.18    (1)  op(e0, e1) = all_52_11
% 153.93/23.18    (2)  op(e0, e2) = all_52_7
% 153.93/23.18    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.18    (4)  op(e0, e0) = e3
% 153.93/23.18    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.93/23.18             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.18           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 153.93/23.18           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.93/23.18             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.93/23.18           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.93/23.18           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.93/23.18           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 153.93/23.18           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 153.93/23.18           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 153.93/23.18           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.93/23.18         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.93/23.18             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.93/23.18           $i(all_57_7))
% 153.93/23.18    (6)   ~ (all_52_11 = e0)
% 153.93/23.18    (7)   ~ (all_52_7 = e0)
% 153.93/23.18    (8)   ~ (e1 = e0)
% 153.93/23.18    (9)  op(e0, e0) = all_57_15
% 153.93/23.18    (10)   ~ (e2 = e1)
% 153.93/23.18    (11)  op(e2, e2) = e0
% 153.93/23.18  
% 153.93/23.18  Begin of proof
% 153.93/23.18  | 
% 153.93/23.18  | BETA: splitting (5) gives:
% 153.93/23.18  | 
% 153.93/23.18  | Case 1:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (12)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 153.93/23.18  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 153.93/23.18  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.93/23.18  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 153.93/23.18  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 153.93/23.18  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 153.93/23.18  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 153.93/23.18  | |           $i(all_57_3))
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12) are
% 153.93/23.18  | |            inconsistent by sub-proof #825.
% 153.93/23.18  | | 
% 153.93/23.18  | Case 2:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (13)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.93/23.18  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.93/23.18  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.93/23.18  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.93/23.18  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.93/23.18  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.93/23.18  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.93/23.18  | |           $i(all_57_7))
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (11), (13) are inconsistent by
% 153.93/23.18  | |            sub-proof #803.
% 153.93/23.18  | | 
% 153.93/23.18  | End of split
% 153.93/23.18  | 
% 153.93/23.18  End of proof
% 153.93/23.18  
% 153.93/23.18  Sub-proof #803 shows that the following formulas are inconsistent:
% 153.93/23.18  ----------------------------------------------------------------
% 153.93/23.18    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.93/23.18             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.93/23.18           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 153.93/23.18           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 153.93/23.18             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.93/23.18           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 153.93/23.18           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.93/23.18    (2)  op(e0, e1) = all_52_11
% 153.93/23.18    (3)  op(e0, e2) = all_52_7
% 153.93/23.18    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.18    (5)   ~ (all_52_11 = e0)
% 153.93/23.18    (6)   ~ (all_52_7 = e0)
% 153.93/23.18    (7)   ~ (e1 = e0)
% 153.93/23.18    (8)  op(e2, e2) = e0
% 153.93/23.18  
% 153.93/23.18  Begin of proof
% 153.93/23.18  | 
% 153.93/23.18  | BETA: splitting (1) gives:
% 153.93/23.18  | 
% 153.93/23.18  | Case 1:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (9)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 153.93/23.18  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.93/23.18  | |        $i(all_57_4)
% 153.93/23.18  | | 
% 153.93/23.18  | | ALPHA: (9) implies:
% 153.93/23.18  | |   (10)  op(e0, e2) = e0
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #1036.
% 153.93/23.18  | | 
% 153.93/23.18  | Case 2:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (11)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 153.93/23.18  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 153.93/23.18  | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 153.93/23.18  | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2,
% 153.93/23.18  | |             e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (2), (4), (5), (7), (8), (11) are inconsistent by sub-proof #804.
% 153.93/23.18  | | 
% 153.93/23.18  | End of split
% 153.93/23.18  | 
% 153.93/23.18  End of proof
% 153.93/23.18  
% 153.93/23.18  Sub-proof #804 shows that the following formulas are inconsistent:
% 153.93/23.18  ----------------------------------------------------------------
% 153.93/23.18    (1)  op(e0, e1) = all_52_11
% 153.93/23.18    (2)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.93/23.18             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.93/23.18           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 153.93/23.18           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 153.93/23.18             e1) = e0 & $i(all_57_7))
% 153.93/23.18    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.18           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.18    (4)   ~ (all_52_11 = e0)
% 153.93/23.18    (5)   ~ (e1 = e0)
% 153.93/23.18    (6)  op(e2, e2) = e0
% 153.93/23.18  
% 153.93/23.18  Begin of proof
% 153.93/23.18  | 
% 153.93/23.18  | BETA: splitting (2) gives:
% 153.93/23.18  | 
% 153.93/23.18  | Case 1:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (7)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.93/23.18  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.93/23.18  | |        $i(all_57_6)
% 153.93/23.18  | | 
% 153.93/23.18  | | ALPHA: (7) implies:
% 153.93/23.18  | |   (8)  op(e0, e1) = e0
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1124.
% 153.93/23.18  | | 
% 153.93/23.18  | Case 2:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (9)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 153.93/23.18  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.93/23.18  | |        $i(all_57_7)
% 153.93/23.18  | | 
% 153.93/23.18  | | ALPHA: (9) implies:
% 153.93/23.18  | |   (10)  op(e2, e2) = e1
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #853.
% 153.93/23.18  | | 
% 153.93/23.18  | End of split
% 153.93/23.18  | 
% 153.93/23.18  End of proof
% 153.93/23.18  
% 153.93/23.18  Sub-proof #805 shows that the following formulas are inconsistent:
% 153.93/23.18  ----------------------------------------------------------------
% 153.93/23.18    (1)  all_56_11 = e1 & op(e1, e0) = e1
% 153.93/23.18    (2)  all_56_11 = e0
% 153.93/23.18    (3)   ~ (e1 = e0)
% 153.93/23.18  
% 153.93/23.18  Begin of proof
% 153.93/23.18  | 
% 153.93/23.18  | ALPHA: (1) implies:
% 153.93/23.18  |   (4)  all_56_11 = e1
% 153.93/23.18  | 
% 153.93/23.18  | COMBINE_EQS: (2), (4) imply:
% 153.93/23.18  |   (5)  e1 = e0
% 153.93/23.18  | 
% 153.93/23.18  | REDUCE: (3), (5) imply:
% 153.93/23.18  |   (6)  $false
% 153.93/23.18  | 
% 153.93/23.18  | CLOSE: (6) is inconsistent.
% 153.93/23.18  | 
% 153.93/23.18  End of proof
% 153.93/23.18  
% 153.93/23.18  Sub-proof #806 shows that the following formulas are inconsistent:
% 153.93/23.18  ----------------------------------------------------------------
% 153.93/23.18    (1)  op(e0, e1) = all_52_11
% 153.93/23.18    (2)   ~ (e3 = e1)
% 153.93/23.18    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.93/23.18         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.93/23.18    (4)  all_56_9 = e1
% 153.93/23.18    (5)  op(e2, e2) = e1
% 153.93/23.18    (6)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.93/23.18         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.93/23.18    (7)  op(e3, e2) = all_52_4
% 153.93/23.18    (8)  all_56_5 = e3
% 153.93/23.18    (9)  op(e1, e1) = e2
% 153.93/23.18    (10)  op(e0, e2) = all_52_7
% 153.93/23.18    (11)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 153.93/23.18          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.93/23.18    (12)   ~ (e2 = e0)
% 153.93/23.18    (13)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.18    (14)  op(e0, e0) = e3
% 153.93/23.18    (15)  all_56_7 = e3
% 153.93/23.18    (16)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.93/23.18          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.93/23.18    (17)   ~ (all_52_7 = e1)
% 153.93/23.18    (18)   ~ (all_52_13 = e2)
% 153.93/23.18    (19)   ~ (all_52_4 = e3)
% 153.93/23.18    (20)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 153.93/23.18            all_57_12 & $i(all_57_12))
% 153.93/23.18    (21)  op(e3, e0) = all_52_12
% 153.93/23.18    (22)   ~ (e3 = e0)
% 153.93/23.18    (23)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 153.93/23.18            all_57_15 & $i(all_57_15))
% 153.93/23.18    (24)   ~ (all_52_11 = e0)
% 153.93/23.18    (25)  op(e1, e2) = all_52_6
% 153.93/23.18    (26)   ~ (all_52_12 = e3)
% 153.93/23.18    (27)  op(e2, e0) = all_52_13
% 153.93/23.18    (28)   ~ (all_52_7 = e0)
% 153.93/23.18    (29)   ~ (e1 = e0)
% 153.93/23.18    (30)   ~ (e3 = e2)
% 153.93/23.18    (31)   ~ (all_52_8 = e3)
% 153.93/23.18    (32)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.93/23.18          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.93/23.18    (33)  op(e2, e1) = e3
% 153.93/23.18    (34)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.93/23.18    (35)  all_54_13 = all_52_7
% 153.93/23.18    (36)  op(e3, e1) = all_52_8
% 153.93/23.18    (37)  op(e3, e3) = e3
% 153.93/23.18    (38)   ~ (all_52_6 = all_52_7)
% 153.93/23.18    (39)   ~ (e2 = e1)
% 153.93/23.18    (40)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.93/23.18              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.93/23.18            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.93/23.18            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.93/23.18            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.18            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.93/23.18            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.93/23.18            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.93/23.18            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.93/23.18            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.93/23.18            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.18            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.93/23.18            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.18            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.93/23.18            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.93/23.18            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.18            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.93/23.18            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.93/23.18            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.93/23.18            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.93/23.18            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.93/23.18            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.18            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.93/23.18            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.93/23.18            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.18            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.93/23.18            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.18            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.18            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.18            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.93/23.18            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.93/23.18            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.93/23.18            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.18            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.18            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.18            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.18            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.18            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.93/23.18            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.18            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.18            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.93/23.18            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.93/23.18            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.18            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.93/23.18            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.93/23.18            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.18            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.93/23.18            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.93/23.18              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.93/23.18            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.18            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.93/23.18              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.93/23.18            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.93/23.18            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.93/23.18                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.93/23.18                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.18                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.18                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.18                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.93/23.18                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.93/23.18                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.93/23.18              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.93/23.18                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.93/23.18                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.93/23.18                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.93/23.18                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.93/23.18                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.93/23.18                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.93/23.18                $i(all_57_7))))
% 153.93/23.18  
% 153.93/23.18  Begin of proof
% 153.93/23.18  | 
% 153.93/23.18  | BETA: splitting (6) gives:
% 153.93/23.18  | 
% 153.93/23.18  | Case 1:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (41)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 153.93/23.18  | |           e2)
% 153.93/23.18  | | 
% 153.93/23.18  | | REF_CLOSE: (2), (5), (7), (9), (10), (12), (13), (14), (15), (18), (19),
% 153.93/23.18  | |            (20), (21), (22), (23), (26), (27), (28), (29), (30), (31), (32),
% 153.93/23.18  | |            (33), (36), (37), (39), (40), (41) are inconsistent by sub-proof
% 153.93/23.18  | |            #818.
% 153.93/23.18  | | 
% 153.93/23.18  | Case 2:
% 153.93/23.18  | | 
% 153.93/23.18  | |   (42)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 153.93/23.18  | |           e2)
% 153.93/23.18  | | 
% 153.93/23.18  | | BETA: splitting (42) gives:
% 153.93/23.18  | | 
% 153.93/23.18  | | Case 1:
% 153.93/23.18  | | | 
% 153.93/23.18  | | |   (43)  all_56_7 = e2 & op(e1, e2) = e2
% 153.93/23.18  | | | 
% 153.93/23.18  | | | ALPHA: (43) implies:
% 153.93/23.18  | | |   (44)  op(e1, e2) = e2
% 153.93/23.18  | | | 
% 153.93/23.18  | | | REF_CLOSE: (13), (17), (25), (28), (34), (35), (38), (44) are inconsistent
% 153.93/23.18  | | |            by sub-proof #836.
% 153.93/23.18  | | | 
% 153.93/23.18  | | Case 2:
% 153.93/23.18  | | | 
% 153.93/23.18  | | |   (45)  all_56_13 = e2 & op(e0, e2) = e2
% 153.93/23.18  | | | 
% 153.93/23.18  | | | ALPHA: (45) implies:
% 153.93/23.18  | | |   (46)  all_56_13 = e2
% 153.93/23.18  | | | 
% 153.93/23.18  | | | BETA: splitting (32) gives:
% 153.93/23.18  | | | 
% 153.93/23.18  | | | Case 1:
% 153.93/23.18  | | | | 
% 153.93/23.18  | | | |   (47)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2)
% 153.93/23.18  | | | |           = e0)
% 153.93/23.18  | | | | 
% 153.93/23.18  | | | | BETA: splitting (47) gives:
% 153.93/23.18  | | | | 
% 153.93/23.18  | | | | Case 1:
% 153.93/23.18  | | | | | 
% 153.93/23.18  | | | | |   (48)  all_56_1 = e0 & op(e3, e2) = e0
% 153.93/23.18  | | | | | 
% 153.93/23.18  | | | | | ALPHA: (48) implies:
% 153.93/23.18  | | | | |   (49)  all_56_1 = e0
% 153.93/23.18  | | | | | 
% 153.93/23.18  | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 153.93/23.18  | | | | |            (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 153.93/23.18  | | | | |            (22), (23), (24), (25), (26), (27), (28), (29), (30), (31),
% 153.93/23.18  | | | | |            (32), (33), (34), (35), (36), (37), (38), (39), (40), (46),
% 153.93/23.18  | | | | |            (49) are inconsistent by sub-proof #807.
% 153.93/23.18  | | | | | 
% 153.93/23.18  | | | | Case 2:
% 153.93/23.18  | | | | | 
% 153.93/23.18  | | | | |   (50)  all_56_3 = e0 & op(e2, e2) = e0
% 153.93/23.18  | | | | | 
% 153.93/23.18  | | | | | ALPHA: (50) implies:
% 153.93/23.18  | | | | |   (51)  op(e2, e2) = e0
% 153.93/23.18  | | | | | 
% 153.93/23.18  | | | | | REF_CLOSE: (5), (13), (29), (51) are inconsistent by sub-proof #853.
% 153.93/23.18  | | | | | 
% 153.93/23.18  | | | | End of split
% 153.93/23.18  | | | | 
% 153.93/23.18  | | | Case 2:
% 153.93/23.18  | | | | 
% 153.93/23.18  | | | |   (52)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2)
% 153.93/23.18  | | | |           = e0)
% 153.93/23.18  | | | | 
% 153.93/23.18  | | | | REF_CLOSE: (10), (13), (15), (22), (28), (52) are inconsistent by
% 153.93/23.18  | | | |            sub-proof #820.
% 153.93/23.18  | | | | 
% 153.93/23.18  | | | End of split
% 153.93/23.18  | | | 
% 153.93/23.18  | | End of split
% 153.93/23.18  | | 
% 153.93/23.18  | End of split
% 153.93/23.18  | 
% 153.93/23.18  End of proof
% 153.93/23.18  
% 153.93/23.18  Sub-proof #807 shows that the following formulas are inconsistent:
% 153.93/23.18  ----------------------------------------------------------------
% 153.93/23.18    (1)  op(e0, e1) = all_52_11
% 153.93/23.18    (2)  all_56_13 = e2
% 153.93/23.18    (3)   ~ (e3 = e1)
% 153.93/23.18    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 153.93/23.18         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 153.93/23.18    (5)  all_56_9 = e1
% 153.93/23.18    (6)  op(e2, e2) = e1
% 153.93/23.18    (7)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 153.93/23.18         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.93/23.18    (8)  op(e3, e2) = all_52_4
% 153.93/23.18    (9)  all_56_5 = e3
% 153.93/23.18    (10)  op(e1, e1) = e2
% 153.93/23.18    (11)  op(e0, e2) = all_52_7
% 153.93/23.18    (12)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 153.93/23.18          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 153.93/23.18    (13)   ~ (e2 = e0)
% 153.93/23.18    (14)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.18            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.18    (15)  op(e0, e0) = e3
% 153.93/23.18    (16)  all_56_7 = e3
% 153.93/23.18    (17)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.93/23.18          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.93/23.18    (18)   ~ (all_52_7 = e1)
% 153.93/23.18    (19)   ~ (all_52_13 = e2)
% 153.93/23.18    (20)   ~ (all_52_4 = e3)
% 153.93/23.18    (21)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 153.93/23.18            all_57_12 & $i(all_57_12))
% 153.93/23.18    (22)  op(e3, e0) = all_52_12
% 153.93/23.18    (23)   ~ (e3 = e0)
% 153.93/23.18    (24)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 153.93/23.18            all_57_15 & $i(all_57_15))
% 153.93/23.18    (25)   ~ (all_52_11 = e0)
% 153.93/23.18    (26)  op(e1, e2) = all_52_6
% 153.93/23.18    (27)   ~ (all_52_12 = e3)
% 153.93/23.18    (28)  op(e2, e0) = all_52_13
% 153.93/23.18    (29)   ~ (all_52_7 = e0)
% 153.93/23.18    (30)   ~ (e1 = e0)
% 153.93/23.18    (31)   ~ (e3 = e2)
% 153.93/23.18    (32)   ~ (all_52_8 = e3)
% 153.93/23.18    (33)  all_56_1 = e0
% 153.93/23.18    (34)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.93/23.18          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.93/23.18    (35)  op(e2, e1) = e3
% 153.93/23.18    (36)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.93/23.18    (37)  all_54_13 = all_52_7
% 153.93/23.18    (38)  op(e3, e1) = all_52_8
% 153.93/23.18    (39)  op(e3, e3) = e3
% 153.93/23.18    (40)   ~ (all_52_6 = all_52_7)
% 153.93/23.18    (41)   ~ (e2 = e1)
% 153.93/23.18    (42)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.93/23.18              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.93/23.18            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.93/23.18            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.93/23.18            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.18            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.93/23.18            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.93/23.18            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.93/23.18            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.93/23.18            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.93/23.18            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.18            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.93/23.18            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.18            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.93/23.18            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.93/23.18            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.18            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.93/23.18            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.93/23.18            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.93/23.18            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.93/23.18            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.93/23.18            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.18            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.93/23.18            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.93/23.18            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.18            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.93/23.18            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.18            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.18            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.18            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.93/23.18            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.93/23.18            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.93/23.18            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.18            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.19            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.19            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.19            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.19            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.93/23.19            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.19            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.19            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.93/23.19            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.93/23.19            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.19            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.93/23.19            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.93/23.19            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.19            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.93/23.19            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.93/23.19              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.93/23.19            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.19            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.93/23.19              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.93/23.19            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.93/23.19            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.93/23.19                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.93/23.19                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.19                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.19                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.19                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.93/23.19                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.93/23.19                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.93/23.19              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.93/23.19                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.93/23.19                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.93/23.19                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.93/23.19                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.93/23.19                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.93/23.19                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.93/23.19                $i(all_57_7))))
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | BETA: splitting (4) gives:
% 153.93/23.19  | 
% 153.93/23.19  | Case 1:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (43)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) =
% 153.93/23.19  | |           e2)
% 153.93/23.19  | | 
% 153.93/23.19  | | BETA: splitting (43) gives:
% 153.93/23.19  | | 
% 153.93/23.19  | | Case 1:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (44)  all_56_0 = e2 & op(e3, e3) = e2
% 153.93/23.19  | | | 
% 153.93/23.19  | | | ALPHA: (44) implies:
% 153.93/23.19  | | |   (45)  op(e3, e3) = e2
% 153.93/23.19  | | | 
% 153.93/23.19  | | | REF_CLOSE: (3), (5), (14), (17), (23), (31), (32), (33), (38), (45) are
% 153.93/23.19  | | |            inconsistent by sub-proof #808.
% 153.93/23.19  | | | 
% 153.93/23.19  | | Case 2:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (46)  all_56_1 = e2 & op(e3, e2) = e2
% 153.93/23.19  | | | 
% 153.93/23.19  | | | REF_CLOSE: (3), (6), (8), (10), (11), (13), (14), (15), (16), (19), (20),
% 153.93/23.19  | | |            (21), (22), (23), (24), (27), (28), (29), (30), (31), (32),
% 153.93/23.19  | | |            (34), (35), (38), (39), (41), (42), (46) are inconsistent by
% 153.93/23.19  | | |            sub-proof #819.
% 153.93/23.19  | | | 
% 153.93/23.19  | | End of split
% 153.93/23.19  | | 
% 153.93/23.19  | Case 2:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (47)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 153.93/23.19  | |           e2)
% 153.93/23.19  | | 
% 153.93/23.19  | | BETA: splitting (47) gives:
% 153.93/23.19  | | 
% 153.93/23.19  | | Case 1:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (48)  all_56_4 = e2 & op(e3, e1) = e2
% 153.93/23.19  | | | 
% 153.93/23.19  | | | ALPHA: (48) implies:
% 153.93/23.19  | | |   (49)  all_56_4 = e2
% 153.93/23.19  | | | 
% 153.93/23.19  | | | REF_CLOSE: (1), (9), (10), (12), (13), (14), (23), (25), (49) are
% 153.93/23.19  | | |            inconsistent by sub-proof #908.
% 153.93/23.19  | | | 
% 153.93/23.19  | | Case 2:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (50)  all_56_9 = e2 & op(e3, e0) = e2
% 153.93/23.19  | | | 
% 153.93/23.19  | | | ALPHA: (50) implies:
% 153.93/23.19  | | |   (51)  all_56_9 = e2
% 153.93/23.19  | | | 
% 153.93/23.19  | | | COMBINE_EQS: (5), (51) imply:
% 153.93/23.19  | | |   (52)  e2 = e1
% 153.93/23.19  | | | 
% 153.93/23.19  | | | SIMP: (52) implies:
% 153.93/23.19  | | |   (53)  e2 = e1
% 153.93/23.19  | | | 
% 153.93/23.19  | | | COMBINE_EQS: (2), (53) imply:
% 153.93/23.19  | | |   (54)  all_56_13 = e1
% 153.93/23.19  | | | 
% 153.93/23.19  | | | BETA: splitting (7) gives:
% 153.93/23.19  | | | 
% 153.93/23.19  | | | Case 1:
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | |   (55)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2)
% 153.93/23.19  | | | |           = e2)
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | REF_CLOSE: (3), (6), (8), (10), (11), (13), (14), (15), (16), (19),
% 153.93/23.19  | | | |            (20), (21), (22), (23), (24), (27), (28), (29), (30), (31),
% 153.93/23.19  | | | |            (32), (34), (35), (38), (39), (41), (42), (55) are
% 153.93/23.19  | | | |            inconsistent by sub-proof #818.
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | Case 2:
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | |   (56)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2)
% 153.93/23.19  | | | |           = e2)
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | REF_CLOSE: (14), (18), (26), (29), (36), (37), (40), (41), (54), (56)
% 153.93/23.19  | | | |            are inconsistent by sub-proof #817.
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | End of split
% 153.93/23.19  | | | 
% 153.93/23.19  | | End of split
% 153.93/23.19  | | 
% 153.93/23.19  | End of split
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #808 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)   ~ (e3 = e1)
% 153.93/23.19    (2)  all_56_9 = e1
% 153.93/23.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.19    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 153.93/23.19         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 153.93/23.19    (5)  op(e3, e3) = e2
% 153.93/23.19    (6)   ~ (e3 = e0)
% 153.93/23.19    (7)   ~ (e3 = e2)
% 153.93/23.19    (8)   ~ (all_52_8 = e3)
% 153.93/23.19    (9)  all_56_1 = e0
% 153.93/23.19    (10)  op(e3, e1) = all_52_8
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | BETA: splitting (4) gives:
% 153.93/23.19  | 
% 153.93/23.19  | Case 1:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 153.93/23.19  | |           e3)
% 153.93/23.19  | | 
% 153.93/23.19  | | BETA: splitting (11) gives:
% 153.93/23.19  | | 
% 153.93/23.19  | | Case 1:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (12)  all_56_0 = e3 & op(e3, e3) = e3
% 153.93/23.19  | | | 
% 153.93/23.19  | | | ALPHA: (12) implies:
% 153.93/23.19  | | |   (13)  op(e3, e3) = e3
% 153.93/23.19  | | | 
% 153.93/23.19  | | | REF_CLOSE: (3), (5), (7), (13) are inconsistent by sub-proof #1085.
% 153.93/23.19  | | | 
% 153.93/23.19  | | Case 2:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (14)  all_56_1 = e3 & op(e3, e2) = e3
% 153.93/23.19  | | | 
% 153.93/23.19  | | | ALPHA: (14) implies:
% 153.93/23.19  | | |   (15)  all_56_1 = e3
% 153.93/23.19  | | | 
% 153.93/23.19  | | | COMBINE_EQS: (9), (15) imply:
% 153.93/23.19  | | |   (16)  e3 = e0
% 153.93/23.19  | | | 
% 153.93/23.19  | | | REDUCE: (6), (16) imply:
% 153.93/23.19  | | |   (17)  $false
% 153.93/23.19  | | | 
% 153.93/23.19  | | | CLOSE: (17) is inconsistent.
% 153.93/23.19  | | | 
% 153.93/23.19  | | End of split
% 153.93/23.19  | | 
% 153.93/23.19  | Case 2:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (18)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 153.93/23.19  | |           e3)
% 153.93/23.19  | | 
% 153.93/23.19  | | BETA: splitting (18) gives:
% 153.93/23.19  | | 
% 153.93/23.19  | | Case 1:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (19)  all_56_4 = e3 & op(e3, e1) = e3
% 153.93/23.19  | | | 
% 153.93/23.19  | | | ALPHA: (19) implies:
% 153.93/23.19  | | |   (20)  op(e3, e1) = e3
% 153.93/23.19  | | | 
% 153.93/23.19  | | | REF_CLOSE: (3), (8), (10), (20) are inconsistent by sub-proof #1164.
% 153.93/23.19  | | | 
% 153.93/23.19  | | Case 2:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (21)  all_56_9 = e3 & op(e3, e0) = e3
% 153.93/23.19  | | | 
% 153.93/23.19  | | | REF_CLOSE: (1), (2), (21) are inconsistent by sub-proof #942.
% 153.93/23.19  | | | 
% 153.93/23.19  | | End of split
% 153.93/23.19  | | 
% 153.93/23.19  | End of split
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #809 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 153.93/23.19    (2)   ~ (e3 = e1)
% 153.93/23.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.19    (4)  op(e0, e0) = e3
% 153.93/23.19    (5)  op(e1, e0) = e2
% 153.93/23.19    (6)   ~ (e2 = e1)
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | BETA: splitting (1) gives:
% 153.93/23.19  | 
% 153.93/23.19  | Case 1:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (7)  all_56_11 = e1 & op(e1, e0) = e1
% 153.93/23.19  | | 
% 153.93/23.19  | | ALPHA: (7) implies:
% 153.93/23.19  | |   (8)  op(e1, e0) = e1
% 153.93/23.19  | | 
% 153.93/23.19  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #1125.
% 153.93/23.19  | | 
% 153.93/23.19  | Case 2:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (9)  all_56_15 = e1 & op(e0, e0) = e1
% 153.93/23.19  | | 
% 153.93/23.19  | | ALPHA: (9) implies:
% 153.93/23.19  | |   (10)  op(e0, e0) = e1
% 153.93/23.19  | | 
% 153.93/23.19  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #1022.
% 153.93/23.19  | | 
% 153.93/23.19  | End of split
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #810 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)  all_56_10 = e1 & op(e2, e0) = e1
% 153.93/23.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.19    (3)  op(e2, e0) = all_52_13
% 153.93/23.19    (4)   ~ (all_52_13 = e1)
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | ALPHA: (1) implies:
% 153.93/23.19  |   (5)  op(e2, e0) = e1
% 153.93/23.19  | 
% 153.93/23.19  | GROUND_INST: instantiating (2) with all_52_13, e1, e0, e2, simplifying with
% 153.93/23.19  |              (3), (5) gives:
% 153.93/23.19  |   (6)  all_52_13 = e1
% 153.93/23.19  | 
% 153.93/23.19  | REDUCE: (4), (6) imply:
% 153.93/23.19  |   (7)  $false
% 153.93/23.19  | 
% 153.93/23.19  | CLOSE: (7) is inconsistent.
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #811 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)   ~ (all_52_1 = e0)
% 153.93/23.19    (2)   ~ (e3 = e1)
% 153.93/23.19    (3)  all_56_9 = e1
% 153.93/23.19    (4)  all_56_11 = e2
% 153.93/23.19    (5)  all_56_5 = e3
% 153.93/23.19    (6)  op(e0, e2) = all_52_7
% 153.93/23.19    (7)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.93/23.19         (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 153.93/23.19    (8)   ~ (e2 = e0)
% 153.93/23.19    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.19    (10)  op(e0, e0) = e3
% 153.93/23.19    (11)  all_56_7 = e3
% 153.93/23.19    (12)  all_56_15 = e3
% 153.93/23.19    (13)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 153.93/23.19              e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.19            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 153.93/23.19             ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 153.93/23.19              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 153.93/23.19            (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.93/23.19            all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.93/23.19            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 153.93/23.19            = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 153.93/23.19          (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 153.93/23.19              e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 153.93/23.19            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 153.93/23.19             ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 153.93/23.19              e1) = e0 & $i(all_57_7))
% 153.93/23.19    (14)   ~ (e3 = e0)
% 153.93/23.19    (15)   ~ (all_52_7 = e0)
% 153.93/23.19    (16)   ~ (e1 = e0)
% 153.93/23.19    (17)  all_56_1 = e2
% 153.93/23.19    (18)  op(e0, e0) = all_57_15
% 153.93/23.19    (19)   ~ (e3 = e2)
% 153.93/23.19    (20)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.93/23.19          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.93/23.19    (21)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.93/23.19          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.93/23.19    (22)  op(e3, e3) = e3
% 153.93/23.19    (23)   ~ (e2 = e1)
% 153.93/23.19    (24)  op(e2, e3) = all_52_1
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | BETA: splitting (7) gives:
% 153.93/23.19  | 
% 153.93/23.19  | Case 1:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (25)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 153.93/23.19  | |           e0)
% 153.93/23.19  | | 
% 153.93/23.19  | | BETA: splitting (25) gives:
% 153.93/23.19  | | 
% 153.93/23.19  | | Case 1:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (26)  all_56_2 = e0 & op(e2, e3) = e0
% 153.93/23.19  | | | 
% 153.93/23.19  | | | REF_CLOSE: (1), (9), (24), (26) are inconsistent by sub-proof #840.
% 153.93/23.19  | | | 
% 153.93/23.19  | | Case 2:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (27)  all_56_3 = e0 & op(e2, e2) = e0
% 153.93/23.19  | | | 
% 153.93/23.19  | | | ALPHA: (27) implies:
% 153.93/23.19  | | |   (28)  op(e2, e2) = e0
% 153.93/23.19  | | | 
% 153.93/23.19  | | | REF_CLOSE: (2), (6), (9), (10), (13), (15), (16), (18), (22), (23), (28)
% 153.93/23.19  | | |            are inconsistent by sub-proof #822.
% 153.93/23.19  | | | 
% 153.93/23.19  | | End of split
% 153.93/23.19  | | 
% 153.93/23.19  | Case 2:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (29)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) =
% 153.93/23.19  | |           e0)
% 153.93/23.19  | | 
% 153.93/23.19  | | BETA: splitting (29) gives:
% 153.93/23.19  | | 
% 153.93/23.19  | | Case 1:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (30)  all_56_5 = e0 & op(e2, e1) = e0
% 153.93/23.19  | | | 
% 153.93/23.19  | | | REF_CLOSE: (5), (14), (30) are inconsistent by sub-proof #910.
% 153.93/23.19  | | | 
% 153.93/23.19  | | Case 2:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (31)  all_56_10 = e0 & op(e2, e0) = e0
% 153.93/23.19  | | | 
% 153.93/23.19  | | | ALPHA: (31) implies:
% 153.93/23.19  | | |   (32)  all_56_10 = e0
% 153.93/23.19  | | | 
% 153.93/23.19  | | | BETA: splitting (20) gives:
% 153.93/23.19  | | | 
% 153.93/23.19  | | | Case 1:
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | |   (33)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2)
% 153.93/23.19  | | | |           = e0)
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | REF_CLOSE: (2), (6), (8), (9), (10), (13), (15), (16), (17), (18), (22),
% 153.93/23.19  | | | |            (23), (33) are inconsistent by sub-proof #821.
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | Case 2:
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | |   (34)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2)
% 153.93/23.19  | | | |           = e0)
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | REF_CLOSE: (2), (3), (4), (6), (9), (11), (12), (14), (15), (19), (21),
% 153.93/23.19  | | | |            (32), (34) are inconsistent by sub-proof #812.
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | End of split
% 153.93/23.19  | | | 
% 153.93/23.19  | | End of split
% 153.93/23.19  | | 
% 153.93/23.19  | End of split
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #812 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)   ~ (e3 = e1)
% 153.93/23.19    (2)  all_56_9 = e1
% 153.93/23.19    (3)  all_56_11 = e2
% 153.93/23.19    (4)  op(e0, e2) = all_52_7
% 153.93/23.19    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.19    (6)  all_56_7 = e3
% 153.93/23.19    (7)  all_56_10 = e0
% 153.93/23.19    (8)  all_56_15 = e3
% 153.93/23.19    (9)   ~ (e3 = e0)
% 153.93/23.19    (10)   ~ (all_52_7 = e0)
% 153.93/23.19    (11)   ~ (e3 = e2)
% 153.93/23.19    (12)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) = e3) |
% 153.93/23.19          (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 153.93/23.19    (13)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | BETA: splitting (13) gives:
% 153.93/23.19  | 
% 153.93/23.19  | Case 1:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (14)  all_56_7 = e0 & op(e1, e2) = e0
% 153.93/23.19  | | 
% 153.93/23.19  | | ALPHA: (14) implies:
% 153.93/23.19  | |   (15)  all_56_7 = e0
% 153.93/23.19  | | 
% 153.93/23.19  | | COMBINE_EQS: (6), (15) imply:
% 153.93/23.19  | |   (16)  e3 = e0
% 153.93/23.19  | | 
% 153.93/23.19  | | COMBINE_EQS: (8), (16) imply:
% 153.93/23.19  | |   (17)  all_56_15 = e0
% 153.93/23.19  | | 
% 153.93/23.19  | | BETA: splitting (12) gives:
% 153.93/23.19  | | 
% 153.93/23.19  | | Case 1:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (18)  (all_56_9 = e3 & op(e3, e0) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 153.93/23.19  | | |           e3)
% 153.93/23.19  | | | 
% 153.93/23.19  | | | BETA: splitting (18) gives:
% 153.93/23.19  | | | 
% 153.93/23.19  | | | Case 1:
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | |   (19)  all_56_9 = e3 & op(e3, e0) = e3
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | REF_CLOSE: (1), (2), (19) are inconsistent by sub-proof #942.
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | Case 2:
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | |   (20)  all_56_10 = e3 & op(e2, e0) = e3
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | REF_CLOSE: (7), (9), (20) are inconsistent by sub-proof #813.
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | End of split
% 153.93/23.19  | | | 
% 153.93/23.19  | | Case 2:
% 153.93/23.19  | | | 
% 153.93/23.19  | | |   (21)  (all_56_11 = e3 & op(e1, e0) = e3) | (all_56_15 = e3 & op(e0, e0)
% 153.93/23.19  | | |           = e3)
% 153.93/23.19  | | | 
% 153.93/23.19  | | | BETA: splitting (21) gives:
% 153.93/23.19  | | | 
% 153.93/23.19  | | | Case 1:
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | |   (22)  all_56_11 = e3 & op(e1, e0) = e3
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | ALPHA: (22) implies:
% 153.93/23.19  | | | |   (23)  all_56_11 = e3
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | COMBINE_EQS: (3), (23) imply:
% 153.93/23.19  | | | |   (24)  e3 = e2
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | REDUCE: (11), (24) imply:
% 153.93/23.19  | | | |   (25)  $false
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | CLOSE: (25) is inconsistent.
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | Case 2:
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | |   (26)  all_56_15 = e3 & op(e0, e0) = e3
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | COMBINE_EQS: (8), (17) imply:
% 153.93/23.19  | | | |   (27)  e3 = e0
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | REDUCE: (9), (16) imply:
% 153.93/23.19  | | | |   (28)  $false
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | | CLOSE: (28) is inconsistent.
% 153.93/23.19  | | | | 
% 153.93/23.19  | | | End of split
% 153.93/23.19  | | | 
% 153.93/23.19  | | End of split
% 153.93/23.19  | | 
% 153.93/23.19  | Case 2:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (29)  all_56_13 = e0 & op(e0, e2) = e0
% 153.93/23.19  | | 
% 153.93/23.19  | | ALPHA: (29) implies:
% 153.93/23.19  | |   (30)  op(e0, e2) = e0
% 153.93/23.19  | | 
% 153.93/23.19  | | REF_CLOSE: (4), (5), (10), (30) are inconsistent by sub-proof #1036.
% 153.93/23.19  | | 
% 153.93/23.19  | End of split
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #813 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)  all_56_10 = e3 & op(e2, e0) = e3
% 153.93/23.19    (2)  all_56_10 = e0
% 153.93/23.19    (3)   ~ (e3 = e0)
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | ALPHA: (1) implies:
% 153.93/23.19  |   (4)  all_56_10 = e3
% 153.93/23.19  | 
% 153.93/23.19  | COMBINE_EQS: (2), (4) imply:
% 153.93/23.19  |   (5)  e3 = e0
% 153.93/23.19  | 
% 153.93/23.19  | REDUCE: (3), (5) imply:
% 153.93/23.19  |   (6)  $false
% 153.93/23.19  | 
% 153.93/23.19  | CLOSE: (6) is inconsistent.
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #814 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.93/23.19             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.93/23.19           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.93/23.19           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.93/23.19           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.19           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 153.93/23.19    (2)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 153.93/23.19           all_57_14 & $i(all_57_14))
% 153.93/23.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.19    (4)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 153.93/23.19           all_57_15 & $i(all_57_15))
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | BETA: splitting (1) gives:
% 153.93/23.19  | 
% 153.93/23.19  | Case 1:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (5)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.93/23.19  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.93/23.19  | |        all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 153.93/23.19  | | 
% 153.93/23.19  | | ALPHA: (5) implies:
% 153.93/23.19  | |   (6)   ~ (all_57_1 = e1)
% 153.93/23.19  | |   (7)  op(e1, e1) = e3
% 153.93/23.19  | | 
% 153.93/23.19  | | REF_CLOSE: (2), (3), (6), (7) are inconsistent by sub-proof #815.
% 153.93/23.19  | | 
% 153.93/23.19  | Case 2:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (8)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 153.93/23.19  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.93/23.19  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 153.93/23.19  | | 
% 153.93/23.19  | | ALPHA: (8) implies:
% 153.93/23.19  | |   (9)   ~ (all_57_2 = e0)
% 153.93/23.19  | |   (10)  op(e0, e0) = e3
% 153.93/23.19  | | 
% 153.93/23.19  | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #833.
% 153.93/23.19  | | 
% 153.93/23.19  | End of split
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #815 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)  (all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1) =
% 153.93/23.19           all_57_14 & $i(all_57_14))
% 153.93/23.19    (2)   ~ (all_57_1 = e1)
% 153.93/23.19    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.19    (4)  op(e1, e1) = e3
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | BETA: splitting (1) gives:
% 153.93/23.19  | 
% 153.93/23.19  | Case 1:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (5)  all_57_1 = e1 & op(e1, e3) = e1
% 153.93/23.19  | | 
% 153.93/23.19  | | ALPHA: (5) implies:
% 153.93/23.19  | |   (6)  all_57_1 = e1
% 153.93/23.19  | | 
% 153.93/23.19  | | REDUCE: (2), (6) imply:
% 153.93/23.19  | |   (7)  $false
% 153.93/23.19  | | 
% 153.93/23.19  | | CLOSE: (7) is inconsistent.
% 153.93/23.19  | | 
% 153.93/23.19  | Case 2:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (8)   ~ (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14)
% 153.93/23.19  | | 
% 153.93/23.19  | | ALPHA: (8) implies:
% 153.93/23.19  | |   (9)   ~ (all_57_14 = e3)
% 153.93/23.19  | |   (10)  op(e1, e1) = all_57_14
% 153.93/23.19  | | 
% 153.93/23.19  | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #816.
% 153.93/23.19  | | 
% 153.93/23.19  | End of split
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #816 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.19    (2)  op(e1, e1) = all_57_14
% 153.93/23.19    (3)  op(e1, e1) = e3
% 153.93/23.19    (4)   ~ (all_57_14 = e3)
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | GROUND_INST: instantiating (1) with e3, all_57_14, e1, e1, simplifying with
% 153.93/23.19  |              (2), (3) gives:
% 153.93/23.19  |   (5)  all_57_14 = e3
% 153.93/23.19  | 
% 153.93/23.19  | REDUCE: (4), (5) imply:
% 153.93/23.19  |   (6)  $false
% 153.93/23.19  | 
% 153.93/23.19  | CLOSE: (6) is inconsistent.
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #817 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 153.93/23.19    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.19    (3)   ~ (all_52_7 = e1)
% 153.93/23.19    (4)  all_56_13 = e1
% 153.93/23.19    (5)  op(e1, e2) = all_52_6
% 153.93/23.19    (6)   ~ (all_52_7 = e0)
% 153.93/23.19    (7)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 153.93/23.19    (8)  all_54_13 = all_52_7
% 153.93/23.19    (9)   ~ (all_52_6 = all_52_7)
% 153.93/23.19    (10)   ~ (e2 = e1)
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | BETA: splitting (1) gives:
% 153.93/23.19  | 
% 153.93/23.19  | Case 1:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (11)  all_56_7 = e2 & op(e1, e2) = e2
% 153.93/23.19  | | 
% 153.93/23.19  | | ALPHA: (11) implies:
% 153.93/23.19  | |   (12)  op(e1, e2) = e2
% 153.93/23.19  | | 
% 153.93/23.19  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (12) are inconsistent by
% 153.93/23.19  | |            sub-proof #836.
% 153.93/23.19  | | 
% 153.93/23.19  | Case 2:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (13)  all_56_13 = e2 & op(e0, e2) = e2
% 153.93/23.19  | | 
% 153.93/23.19  | | ALPHA: (13) implies:
% 153.93/23.19  | |   (14)  all_56_13 = e2
% 153.93/23.19  | | 
% 153.93/23.19  | | REF_CLOSE: (4), (10), (14) are inconsistent by sub-proof #1110.
% 153.93/23.19  | | 
% 153.93/23.19  | End of split
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #818 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)   ~ (e3 = e1)
% 153.93/23.19    (2)  op(e2, e2) = e1
% 153.93/23.19    (3)  op(e3, e2) = all_52_4
% 153.93/23.19    (4)  op(e1, e1) = e2
% 153.93/23.19    (5)  op(e0, e2) = all_52_7
% 153.93/23.19    (6)   ~ (e2 = e0)
% 153.93/23.19    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.19           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.19    (8)  op(e0, e0) = e3
% 153.93/23.19    (9)  all_56_7 = e3
% 153.93/23.19    (10)   ~ (all_52_13 = e2)
% 153.93/23.19    (11)   ~ (all_52_4 = e3)
% 153.93/23.19    (12)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 153.93/23.19            all_57_12 & $i(all_57_12))
% 153.93/23.19    (13)  op(e3, e0) = all_52_12
% 153.93/23.19    (14)   ~ (e3 = e0)
% 153.93/23.19    (15)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 153.93/23.19            all_57_15 & $i(all_57_15))
% 153.93/23.19    (16)   ~ (all_52_12 = e3)
% 153.93/23.19    (17)  op(e2, e0) = all_52_13
% 153.93/23.19    (18)   ~ (all_52_7 = e0)
% 153.93/23.19    (19)   ~ (e1 = e0)
% 153.93/23.19    (20)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 153.93/23.19    (21)   ~ (e3 = e2)
% 153.93/23.19    (22)   ~ (all_52_8 = e3)
% 153.93/23.19    (23)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.93/23.19          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.93/23.19    (24)  op(e2, e1) = e3
% 153.93/23.19    (25)  op(e3, e1) = all_52_8
% 153.93/23.19    (26)  op(e3, e3) = e3
% 153.93/23.19    (27)   ~ (e2 = e1)
% 153.93/23.19    (28)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.93/23.19              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.93/23.19            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.93/23.19            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.93/23.19            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.19            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.93/23.19            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.93/23.19            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.93/23.19            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.93/23.19            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.93/23.19            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.19            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.93/23.19            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.19            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.93/23.19            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.93/23.19            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.19            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.93/23.19            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.93/23.19            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.93/23.19            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.93/23.19            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.93/23.19            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.19            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.93/23.19            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.93/23.19            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.19            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.93/23.19            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.19            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.19            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.19            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.93/23.19            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.93/23.19            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.93/23.19            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.19            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.19            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.19            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.19            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.19            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.93/23.19            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.19            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.19            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.93/23.19            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.93/23.19            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.19            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.93/23.19            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.93/23.19            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.19            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.93/23.19            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.93/23.19              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.93/23.19            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.19            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.93/23.19              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.93/23.19            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.93/23.19            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.93/23.19                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.93/23.19                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.19                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.19                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.19                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.93/23.19                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.93/23.19                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.93/23.19              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.93/23.19                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.93/23.19                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.93/23.19                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.93/23.19                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.93/23.19                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.93/23.19                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.93/23.19                $i(all_57_7))))
% 153.93/23.19  
% 153.93/23.19  Begin of proof
% 153.93/23.19  | 
% 153.93/23.19  | BETA: splitting (20) gives:
% 153.93/23.19  | 
% 153.93/23.19  | Case 1:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (29)  all_56_1 = e2 & op(e3, e2) = e2
% 153.93/23.19  | | 
% 153.93/23.19  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 153.93/23.19  | |            (13), (14), (15), (16), (17), (18), (19), (21), (22), (23), (24),
% 153.93/23.19  | |            (25), (26), (27), (28), (29) are inconsistent by sub-proof #819.
% 153.93/23.19  | | 
% 153.93/23.19  | Case 2:
% 153.93/23.19  | | 
% 153.93/23.19  | |   (30)  all_56_3 = e2 & op(e2, e2) = e2
% 153.93/23.19  | | 
% 153.93/23.19  | | ALPHA: (30) implies:
% 153.93/23.19  | |   (31)  op(e2, e2) = e2
% 153.93/23.19  | | 
% 153.93/23.19  | | REF_CLOSE: (2), (7), (27), (31) are inconsistent by sub-proof #1158.
% 153.93/23.19  | | 
% 153.93/23.19  | End of split
% 153.93/23.19  | 
% 153.93/23.19  End of proof
% 153.93/23.19  
% 153.93/23.19  Sub-proof #819 shows that the following formulas are inconsistent:
% 153.93/23.19  ----------------------------------------------------------------
% 153.93/23.19    (1)   ~ (e3 = e1)
% 153.93/23.19    (2)  op(e2, e2) = e1
% 153.93/23.19    (3)  op(e3, e2) = all_52_4
% 153.93/23.19    (4)  op(e1, e1) = e2
% 153.93/23.19    (5)  op(e0, e2) = all_52_7
% 153.93/23.19    (6)   ~ (e2 = e0)
% 153.93/23.20    (7)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 153.93/23.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 153.93/23.20    (8)  op(e0, e0) = e3
% 153.93/23.20    (9)  all_56_7 = e3
% 153.93/23.20    (10)   ~ (all_52_13 = e2)
% 153.93/23.20    (11)   ~ (all_52_4 = e3)
% 153.93/23.20    (12)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 153.93/23.20            all_57_12 & $i(all_57_12))
% 153.93/23.20    (13)  op(e3, e0) = all_52_12
% 153.93/23.20    (14)   ~ (e3 = e0)
% 153.93/23.20    (15)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 153.93/23.20            all_57_15 & $i(all_57_15))
% 153.93/23.20    (16)   ~ (all_52_12 = e3)
% 153.93/23.20    (17)  op(e2, e0) = all_52_13
% 153.93/23.20    (18)   ~ (all_52_7 = e0)
% 153.93/23.20    (19)   ~ (e1 = e0)
% 153.93/23.20    (20)  all_56_1 = e2 & op(e3, e2) = e2
% 153.93/23.20    (21)   ~ (e3 = e2)
% 153.93/23.20    (22)   ~ (all_52_8 = e3)
% 153.93/23.20    (23)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 153.93/23.20          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 153.93/23.20    (24)  op(e2, e1) = e3
% 153.93/23.20    (25)  op(e3, e1) = all_52_8
% 153.93/23.20    (26)  op(e3, e3) = e3
% 153.93/23.20    (27)   ~ (e2 = e1)
% 153.93/23.20    (28)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 153.93/23.20              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.93/23.20            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 153.93/23.20            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 153.93/23.20            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 153.93/23.20            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 153.93/23.20            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 153.93/23.20            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.93/23.20            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 153.93/23.20            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.93/23.20            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.20            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 153.93/23.20            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.20            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 153.93/23.20            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 153.93/23.20            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 153.93/23.20            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.93/23.20            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 153.93/23.20            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.93/23.20            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 153.93/23.20            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 153.93/23.20            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 153.93/23.20            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 153.93/23.20            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 153.93/23.20            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.20            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 153.93/23.20            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.20            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.20            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.20            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 153.93/23.20            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 153.93/23.20            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 153.93/23.20            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 153.93/23.20            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.20            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.20            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.20            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.20            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.93/23.20            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 153.93/23.20            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.20            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.93/23.20            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 153.93/23.20            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.20            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.93/23.20            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 153.93/23.20            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.20            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 153.93/23.20            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 153.93/23.20              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 153.93/23.20            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 153.93/23.20            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 153.93/23.20              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 153.93/23.20            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 153.93/23.20            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 153.93/23.20                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.93/23.20                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.20                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 153.93/23.20                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 153.93/23.20                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 153.93/23.20                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 153.93/23.20                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 153.93/23.20              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 153.93/23.20                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 153.93/23.20                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.93/23.20                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 153.93/23.20                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 153.93/23.20                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.93/23.20                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.93/23.20                $i(all_57_7))))
% 153.93/23.20  
% 153.93/23.20  Begin of proof
% 153.93/23.20  | 
% 153.93/23.20  | ALPHA: (20) implies:
% 153.93/23.20  |   (29)  all_56_1 = e2
% 153.93/23.20  | 
% 153.93/23.20  | BETA: splitting (28) gives:
% 153.93/23.20  | 
% 153.93/23.20  | Case 1:
% 153.93/23.20  | | 
% 153.93/23.20  | |   (30)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 153.93/23.20  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 153.93/23.20  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 153.93/23.20  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 153.93/23.20  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 153.93/23.20  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 153.93/23.20  | |         (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 153.93/23.20  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 153.93/23.20  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 153.93/23.20  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 153.93/23.20  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 153.93/23.20  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) |
% 153.93/23.20  | |         (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 153.93/23.20  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 153.93/23.20  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 153.93/23.20  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 153.93/23.20  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 153.93/23.20  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 153.93/23.20  | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 153.93/23.20  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 153.93/23.20  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 153.93/23.20  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 153.93/23.20  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 153.93/23.20  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 153.93/23.20  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 153.93/23.20  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 153.93/23.20  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.93/23.20  | | 
% 153.93/23.20  | | BETA: splitting (30) gives:
% 153.93/23.20  | | 
% 153.93/23.20  | | Case 1:
% 153.93/23.20  | | | 
% 153.93/23.20  | | |   (31)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.93/23.20  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.93/23.20  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.93/23.20  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 153.93/23.20  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 153.93/23.20  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 153.93/23.20  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 153.93/23.20  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 153.93/23.20  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 153.93/23.20  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 153.93/23.20  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 153.93/23.20  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 153.93/23.20  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 153.93/23.20  | | | 
% 153.93/23.20  | | | BETA: splitting (31) gives:
% 153.93/23.20  | | | 
% 153.93/23.20  | | | Case 1:
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | |   (32)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.93/23.20  | | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.93/23.20  | | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.93/23.20  | | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~
% 153.93/23.20  | | | |           (all_57_2 = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 153.93/23.20  | | | |           op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.93/23.20  | | | |           e3 & $i(all_57_2) & $i(all_57_12))
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | | BETA: splitting (32) gives:
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | | Case 1:
% 153.93/23.20  | | | | | 
% 153.93/23.20  | | | | |   (33)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 153.93/23.20  | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.93/23.20  | | | | |         op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 153.93/23.20  | | | | |         $i(all_57_12)
% 153.93/23.20  | | | | | 
% 153.93/23.20  | | | | | ALPHA: (33) implies:
% 153.93/23.20  | | | | |   (34)  op(e1, e1) = e3
% 153.93/23.20  | | | | | 
% 153.93/23.20  | | | | | REF_CLOSE: (4), (7), (21), (34) are inconsistent by sub-proof #834.
% 153.93/23.20  | | | | | 
% 153.93/23.20  | | | | Case 2:
% 153.93/23.20  | | | | | 
% 153.93/23.20  | | | | |   (35)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 153.93/23.20  | | | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 153.93/23.20  | | | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 153.93/23.20  | | | | |         $i(all_57_12)
% 153.93/23.20  | | | | | 
% 153.93/23.20  | | | | | ALPHA: (35) implies:
% 153.93/23.20  | | | | |   (36)   ~ (all_57_2 = e0)
% 153.93/23.20  | | | | | 
% 153.93/23.20  | | | | | REF_CLOSE: (7), (8), (15), (36) are inconsistent by sub-proof #833.
% 153.93/23.20  | | | | | 
% 153.93/23.20  | | | | End of split
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | Case 2:
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | |   (37)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 153.93/23.20  | | | |           (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 153.93/23.20  | | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 153.93/23.20  | | | |           $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 153.93/23.20  | | | |           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 153.93/23.20  | | | |           op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) =
% 153.93/23.20  | | | |           e3 & $i(all_57_2) & $i(all_57_14))
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | | REF_CLOSE: (7), (12), (15), (37) are inconsistent by sub-proof #831.
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | End of split
% 153.93/23.20  | | | 
% 153.93/23.20  | | Case 2:
% 153.93/23.20  | | | 
% 153.93/23.20  | | |   (38)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 153.93/23.20  | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 153.93/23.20  | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 153.93/23.20  | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5
% 153.93/23.20  | | |             = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 153.93/23.20  | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 153.93/23.20  | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 153.93/23.20  | | |           &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 153.93/23.20  | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 153.93/23.20  | | |           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 =
% 153.93/23.20  | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 153.93/23.20  | | |           & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 153.93/23.20  | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 153.93/23.20  | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 153.93/23.20  | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 153.93/23.20  | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 153.93/23.20  | | | 
% 153.93/23.20  | | | REF_CLOSE: (3), (7), (8), (11), (21), (22), (25), (26), (38) are
% 153.93/23.20  | | |            inconsistent by sub-proof #829.
% 153.93/23.20  | | | 
% 153.93/23.20  | | End of split
% 153.93/23.20  | | 
% 153.93/23.20  | Case 2:
% 153.93/23.20  | | 
% 153.93/23.20  | |   (39)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 153.93/23.20  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 153.93/23.20  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 153.93/23.20  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 153.93/23.20  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 153.93/23.20  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 153.93/23.20  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 153.93/23.20  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 153.93/23.20  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 153.93/23.20  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.93/23.20  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.20  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 153.93/23.20  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 153.93/23.20  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 153.93/23.20  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.93/23.20  | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 153.93/23.20  | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.93/23.20  | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 153.93/23.20  | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.93/23.20  | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.93/23.20  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 153.93/23.20  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 153.93/23.20  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 153.93/23.20  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 153.93/23.20  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 153.93/23.20  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 153.93/23.20  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 153.93/23.20  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 153.93/23.20  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 153.93/23.20  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 153.93/23.20  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 153.93/23.20  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 153.93/23.20  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 153.93/23.20  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 153.93/23.20  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 153.93/23.20  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 153.93/23.20  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 153.93/23.20  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.93/23.20  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 153.93/23.20  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.93/23.20  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 153.93/23.20  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 153.93/23.20  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 153.93/23.20  | |               $i(all_57_7))))
% 153.93/23.20  | | 
% 153.93/23.20  | | BETA: splitting (39) gives:
% 153.93/23.20  | | 
% 153.93/23.20  | | Case 1:
% 153.93/23.20  | | | 
% 153.93/23.20  | | |   (40)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.93/23.20  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.20  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.20  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 153.93/23.20  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 153.93/23.20  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.20  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 153.93/23.20  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 153.93/23.20  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 153.93/23.20  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 153.93/23.20  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 153.93/23.20  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 153.93/23.20  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 153.93/23.20  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 153.93/23.20  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 153.93/23.20  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 153.93/23.20  | | |           $i(all_57_13))
% 153.93/23.20  | | | 
% 153.93/23.20  | | | BETA: splitting (40) gives:
% 153.93/23.20  | | | 
% 153.93/23.20  | | | Case 1:
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | |   (41)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.93/23.20  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 153.93/23.20  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.20  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 153.93/23.20  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 153.93/23.20  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 153.93/23.20  | | | |           e2 & $i(all_57_6) & $i(all_57_12))
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | | REF_CLOSE: (7), (21), (22), (24), (25), (41) are inconsistent by
% 153.93/23.20  | | | |            sub-proof #828.
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | Case 2:
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | |   (42)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 153.93/23.20  | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 153.93/23.20  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 153.93/23.20  | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 153.93/23.20  | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 153.93/23.20  | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 153.93/23.20  | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 153.93/23.20  | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 153.93/23.20  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 153.93/23.20  | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | | REF_CLOSE: (1), (7), (8), (13), (16), (42) are inconsistent by sub-proof
% 153.93/23.20  | | | |            #1020.
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | End of split
% 153.93/23.20  | | | 
% 153.93/23.20  | | Case 2:
% 153.93/23.20  | | | 
% 153.93/23.20  | | |   (43)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.93/23.20  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.20  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.93/23.20  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 153.93/23.20  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 153.93/23.20  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 153.93/23.20  | | |           $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0
% 153.93/23.20  | | |           &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 153.93/23.20  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 153.93/23.20  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 153.93/23.20  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 153.93/23.20  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 153.93/23.20  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 153.93/23.20  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 153.93/23.20  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 153.93/23.20  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 153.93/23.20  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 153.93/23.20  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 153.93/23.20  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 153.93/23.20  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 153.93/23.20  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 153.93/23.20  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 153.93/23.20  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 153.93/23.20  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 153.93/23.20  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 153.93/23.20  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 153.93/23.20  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 153.93/23.20  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 153.93/23.20  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 153.93/23.20  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 153.93/23.20  | | | 
% 153.93/23.20  | | | BETA: splitting (43) gives:
% 153.93/23.20  | | | 
% 153.93/23.20  | | | Case 1:
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | |   (44)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 153.93/23.20  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 153.93/23.20  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 153.93/23.20  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 153.93/23.20  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 153.93/23.20  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 153.93/23.20  | | | |           e1 & $i(all_57_9) & $i(all_57_14))
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | | REF_CLOSE: (7), (14), (26), (44) are inconsistent by sub-proof #975.
% 153.93/23.20  | | | | 
% 153.93/23.20  | | | Case 2:
% 153.93/23.20  | | | | 
% 154.02/23.20  | | | |   (45)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 154.02/23.20  | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.02/23.20  | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 154.02/23.20  | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 154.02/23.20  | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 154.02/23.20  | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 154.02/23.20  | | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 154.02/23.20  | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 154.02/23.20  | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 154.02/23.20  | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.20  | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 154.02/23.20  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 154.02/23.20  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 154.02/23.20  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.02/23.20  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 154.02/23.20  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 154.02/23.20  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.02/23.20  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 154.02/23.20  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.02/23.20  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 154.02/23.20  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 154.02/23.20  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.02/23.20  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 154.02/23.20  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 154.02/23.20  | | | | 
% 154.02/23.20  | | | | BETA: splitting (45) gives:
% 154.02/23.20  | | | | 
% 154.02/23.20  | | | | Case 1:
% 154.02/23.20  | | | | | 
% 154.02/23.20  | | | | |   (46)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 154.02/23.20  | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.02/23.20  | | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 154.02/23.20  | | | | |         $i(all_57_13)
% 154.02/23.20  | | | | | 
% 154.02/23.20  | | | | | ALPHA: (46) implies:
% 154.02/23.20  | | | | |   (47)  op(e2, e0) = e2
% 154.02/23.20  | | | | | 
% 154.02/23.20  | | | | | REF_CLOSE: (7), (10), (17), (47) are inconsistent by sub-proof #1156.
% 154.02/23.20  | | | | | 
% 154.02/23.20  | | | | Case 2:
% 154.02/23.20  | | | | | 
% 154.02/23.20  | | | | |   (48)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 154.02/23.20  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 154.02/23.20  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 154.02/23.20  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.02/23.20  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.02/23.20  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 154.02/23.20  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 154.02/23.20  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 154.02/23.20  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.02/23.20  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 154.02/23.20  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 154.02/23.20  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.02/23.20  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 154.02/23.20  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 154.02/23.20  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.02/23.20  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.02/23.20  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 154.02/23.20  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.02/23.20  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.02/23.20  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 154.02/23.20  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.20  | | | | |               $i(all_57_7))))
% 154.02/23.20  | | | | | 
% 154.02/23.20  | | | | | BETA: splitting (48) gives:
% 154.02/23.20  | | | | | 
% 154.02/23.20  | | | | | Case 1:
% 154.02/23.20  | | | | | | 
% 154.02/23.20  | | | | | |   (49)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 154.02/23.20  | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 154.02/23.20  | | | | | |         & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 154.02/23.20  | | | | | |         $i(all_57_14)
% 154.02/23.20  | | | | | | 
% 154.02/23.20  | | | | | | ALPHA: (49) implies:
% 154.02/23.20  | | | | | |   (50)  op(e2, e2) = e0
% 154.02/23.20  | | | | | | 
% 154.02/23.20  | | | | | | REF_CLOSE: (2), (7), (19), (50) are inconsistent by sub-proof #853.
% 154.02/23.20  | | | | | | 
% 154.02/23.20  | | | | | Case 2:
% 154.02/23.20  | | | | | | 
% 154.02/23.20  | | | | | |   (51)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 154.02/23.20  | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.02/23.20  | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 154.02/23.20  | | | | | |               e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 154.02/23.20  | | | | | |             = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1,
% 154.02/23.20  | | | | | |               e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 154.02/23.20  | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.02/23.20  | | | | | |             (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 154.02/23.20  | | | | | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.02/23.20  | | | | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 154.02/23.20  | | | | | |             (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 154.02/23.20  | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.02/23.20  | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.02/23.20  | | | | | |             (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 154.02/23.20  | | | | | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.02/23.20  | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.02/23.20  | | | | | |             (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 154.02/23.20  | | | | | |             & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.20  | | | | | |             $i(all_57_7)))
% 154.02/23.20  | | | | | | 
% 154.02/23.20  | | | | | | ALPHA: (51) implies:
% 154.02/23.20  | | | | | |   (52)  op(e0, e0) = all_57_15
% 154.02/23.20  | | | | | |   (53)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.02/23.20  | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 154.02/23.20  | | | | | |           & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 154.02/23.20  | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 154.02/23.20  | | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 154.02/23.20  | | | | | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.02/23.20  | | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 154.02/23.20  | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 154.02/23.20  | | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.02/23.20  | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 154.02/23.20  | | | | | |           & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.02/23.20  | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 154.02/23.20  | | | | | |           & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 154.02/23.20  | | | | | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.02/23.20  | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 154.02/23.20  | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.02/23.20  | | | | | | 
% 154.02/23.20  | | | | | | BETA: splitting (23) gives:
% 154.02/23.20  | | | | | | 
% 154.02/23.20  | | | | | | Case 1:
% 154.02/23.20  | | | | | | | 
% 154.02/23.20  | | | | | | |   (54)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 &
% 154.02/23.20  | | | | | | |           op(e2, e2) = e0)
% 154.02/23.20  | | | | | | | 
% 154.02/23.20  | | | | | | | REF_CLOSE: (1), (5), (6), (7), (8), (18), (19), (26), (27), (29),
% 154.02/23.20  | | | | | | |            (52), (53), (54) are inconsistent by sub-proof #821.
% 154.02/23.20  | | | | | | | 
% 154.02/23.20  | | | | | | Case 2:
% 154.02/23.20  | | | | | | | 
% 154.02/23.20  | | | | | | |   (55)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 &
% 154.02/23.20  | | | | | | |           op(e0, e2) = e0)
% 154.02/23.20  | | | | | | | 
% 154.02/23.20  | | | | | | | REF_CLOSE: (5), (7), (9), (14), (18), (55) are inconsistent by
% 154.02/23.20  | | | | | | |            sub-proof #820.
% 154.02/23.20  | | | | | | | 
% 154.02/23.20  | | | | | | End of split
% 154.02/23.20  | | | | | | 
% 154.02/23.20  | | | | | End of split
% 154.02/23.20  | | | | | 
% 154.02/23.20  | | | | End of split
% 154.02/23.20  | | | | 
% 154.02/23.20  | | | End of split
% 154.02/23.20  | | | 
% 154.02/23.20  | | End of split
% 154.02/23.20  | | 
% 154.02/23.20  | End of split
% 154.02/23.20  | 
% 154.02/23.20  End of proof
% 154.02/23.20  
% 154.02/23.20  Sub-proof #820 shows that the following formulas are inconsistent:
% 154.02/23.20  ----------------------------------------------------------------
% 154.02/23.20    (1)  op(e0, e2) = all_52_7
% 154.02/23.20    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.20    (3)  all_56_7 = e3
% 154.02/23.20    (4)   ~ (e3 = e0)
% 154.02/23.20    (5)   ~ (all_52_7 = e0)
% 154.02/23.20    (6)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.02/23.20  
% 154.02/23.20  Begin of proof
% 154.02/23.20  | 
% 154.02/23.20  | BETA: splitting (6) gives:
% 154.02/23.20  | 
% 154.02/23.20  | Case 1:
% 154.02/23.20  | | 
% 154.02/23.20  | |   (7)  all_56_7 = e0 & op(e1, e2) = e0
% 154.02/23.20  | | 
% 154.02/23.20  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #1151.
% 154.02/23.20  | | 
% 154.02/23.20  | Case 2:
% 154.02/23.20  | | 
% 154.02/23.20  | |   (8)  all_56_13 = e0 & op(e0, e2) = e0
% 154.02/23.20  | | 
% 154.02/23.20  | | ALPHA: (8) implies:
% 154.02/23.20  | |   (9)  op(e0, e2) = e0
% 154.02/23.20  | | 
% 154.02/23.20  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #1036.
% 154.02/23.20  | | 
% 154.02/23.20  | End of split
% 154.02/23.20  | 
% 154.02/23.20  End of proof
% 154.02/23.20  
% 154.02/23.20  Sub-proof #821 shows that the following formulas are inconsistent:
% 154.02/23.20  ----------------------------------------------------------------
% 154.02/23.20    (1)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 154.02/23.20    (2)   ~ (e3 = e1)
% 154.02/23.20    (3)  op(e0, e2) = all_52_7
% 154.02/23.20    (4)   ~ (e2 = e0)
% 154.02/23.20    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.20           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.20    (6)  op(e0, e0) = e3
% 154.02/23.20    (7)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.02/23.20             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.20           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.02/23.20           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.02/23.20             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.02/23.20           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.20           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 154.02/23.20           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 154.02/23.20           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.02/23.20           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 154.02/23.20           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 154.02/23.20         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.02/23.20             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.20           $i(all_57_7))
% 154.02/23.20    (8)   ~ (all_52_7 = e0)
% 154.02/23.20    (9)   ~ (e1 = e0)
% 154.02/23.20    (10)  all_56_1 = e2
% 154.02/23.20    (11)  op(e0, e0) = all_57_15
% 154.02/23.20    (12)  op(e3, e3) = e3
% 154.02/23.20    (13)   ~ (e2 = e1)
% 154.02/23.20  
% 154.02/23.20  Begin of proof
% 154.02/23.20  | 
% 154.02/23.20  | BETA: splitting (1) gives:
% 154.02/23.20  | 
% 154.02/23.20  | Case 1:
% 154.02/23.20  | | 
% 154.02/23.20  | |   (14)  all_56_1 = e0 & op(e3, e2) = e0
% 154.02/23.20  | | 
% 154.02/23.20  | | REF_CLOSE: (4), (10), (14) are inconsistent by sub-proof #924.
% 154.02/23.20  | | 
% 154.02/23.20  | Case 2:
% 154.02/23.20  | | 
% 154.02/23.20  | |   (15)  all_56_3 = e0 & op(e2, e2) = e0
% 154.02/23.20  | | 
% 154.02/23.20  | | ALPHA: (15) implies:
% 154.02/23.20  | |   (16)  op(e2, e2) = e0
% 154.02/23.20  | | 
% 154.02/23.20  | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (12), (13), (16) are
% 154.02/23.20  | |            inconsistent by sub-proof #822.
% 154.02/23.20  | | 
% 154.02/23.20  | End of split
% 154.02/23.20  | 
% 154.02/23.20  End of proof
% 154.02/23.20  
% 154.02/23.20  Sub-proof #822 shows that the following formulas are inconsistent:
% 154.02/23.20  ----------------------------------------------------------------
% 154.02/23.20    (1)   ~ (e3 = e1)
% 154.02/23.21    (2)  op(e0, e2) = all_52_7
% 154.02/23.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.21    (4)  op(e0, e0) = e3
% 154.02/23.21    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.02/23.21             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.21           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.02/23.21           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.02/23.21             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.02/23.21           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.21           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 154.02/23.21           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 154.02/23.21           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.02/23.21           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 154.02/23.21           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 154.02/23.21         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.02/23.21             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.21           $i(all_57_7))
% 154.02/23.21    (6)   ~ (all_52_7 = e0)
% 154.02/23.21    (7)   ~ (e1 = e0)
% 154.02/23.21    (8)  op(e0, e0) = all_57_15
% 154.02/23.21    (9)  op(e3, e3) = e3
% 154.02/23.21    (10)   ~ (e2 = e1)
% 154.02/23.21    (11)  op(e2, e2) = e0
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (5) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (12)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 154.02/23.21  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 154.02/23.21  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 154.02/23.21  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 154.02/23.21  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 154.02/23.21  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 154.02/23.21  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.02/23.21  | |           $i(all_57_3))
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (12) are
% 154.02/23.21  | |            inconsistent by sub-proof #825.
% 154.02/23.21  | | 
% 154.02/23.21  | Case 2:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (13)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 154.02/23.21  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 154.02/23.21  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.02/23.21  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 154.02/23.21  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 154.02/23.21  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 154.02/23.21  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.21  | |           $i(all_57_7))
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (1), (2), (3), (6), (7), (9), (11), (13) are inconsistent by
% 154.02/23.21  | |            sub-proof #823.
% 154.02/23.21  | | 
% 154.02/23.21  | End of split
% 154.02/23.21  | 
% 154.02/23.21  End of proof
% 154.02/23.21  
% 154.02/23.21  Sub-proof #823 shows that the following formulas are inconsistent:
% 154.02/23.21  ----------------------------------------------------------------
% 154.02/23.21    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 154.02/23.21             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.02/23.21           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 154.02/23.21           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 154.02/23.21             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.02/23.21           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 154.02/23.21           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.02/23.21    (2)   ~ (e3 = e1)
% 154.02/23.21    (3)  op(e0, e2) = all_52_7
% 154.02/23.21    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.21    (5)   ~ (all_52_7 = e0)
% 154.02/23.21    (6)   ~ (e1 = e0)
% 154.02/23.21    (7)  op(e3, e3) = e3
% 154.02/23.21    (8)  op(e2, e2) = e0
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (1) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (9)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 154.02/23.21  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.02/23.21  | |        $i(all_57_4)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (9) implies:
% 154.02/23.21  | |   (10)  op(e0, e2) = e0
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #1036.
% 154.02/23.21  | | 
% 154.02/23.21  | Case 2:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (11)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 154.02/23.21  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 154.02/23.21  | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.02/23.21  | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2,
% 154.02/23.21  | |             e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (2), (4), (6), (7), (8), (11) are inconsistent by sub-proof #824.
% 154.02/23.21  | | 
% 154.02/23.21  | End of split
% 154.02/23.21  | 
% 154.02/23.21  End of proof
% 154.02/23.21  
% 154.02/23.21  Sub-proof #824 shows that the following formulas are inconsistent:
% 154.02/23.21  ----------------------------------------------------------------
% 154.02/23.21    (1)   ~ (e3 = e1)
% 154.02/23.21    (2)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.02/23.21             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.02/23.21           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 154.02/23.21           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 154.02/23.21             e1) = e0 & $i(all_57_7))
% 154.02/23.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.21    (4)   ~ (e1 = e0)
% 154.02/23.21    (5)  op(e3, e3) = e3
% 154.02/23.21    (6)  op(e2, e2) = e0
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (2) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (7)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.02/23.21  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.02/23.21  | |        $i(all_57_6)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (7) implies:
% 154.02/23.21  | |   (8)  op(e3, e3) = e1
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1178.
% 154.02/23.21  | | 
% 154.02/23.21  | Case 2:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (9)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.02/23.21  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.21  | |        $i(all_57_7)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (9) implies:
% 154.02/23.21  | |   (10)  op(e2, e2) = e1
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #853.
% 154.02/23.21  | | 
% 154.02/23.21  | End of split
% 154.02/23.21  | 
% 154.02/23.21  End of proof
% 154.02/23.21  
% 154.02/23.21  Sub-proof #825 shows that the following formulas are inconsistent:
% 154.02/23.21  ----------------------------------------------------------------
% 154.02/23.21    (1)  op(e0, e2) = all_52_7
% 154.02/23.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.21    (3)  op(e0, e0) = e3
% 154.02/23.21    (4)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.02/23.21             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.21           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.02/23.21           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.02/23.21             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.02/23.21           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.21           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.02/23.21    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.02/23.21             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.21           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.02/23.21           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.02/23.21             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.02/23.21           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.21           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 154.02/23.21           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 154.02/23.21           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.02/23.21           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 154.02/23.21           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 154.02/23.21         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.02/23.21             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.21           $i(all_57_7))
% 154.02/23.21    (6)   ~ (all_52_7 = e0)
% 154.02/23.21    (7)   ~ (e1 = e0)
% 154.02/23.21    (8)  op(e0, e0) = all_57_15
% 154.02/23.21    (9)   ~ (e2 = e1)
% 154.02/23.21    (10)  op(e2, e2) = e0
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (4) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (11)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 154.02/23.21  | |           = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 154.02/23.21  | |         & $i(all_57_0)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (11) implies:
% 154.02/23.21  | |   (12)   ~ (all_57_15 = e3)
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (2), (3), (8), (12) are inconsistent by sub-proof #1019.
% 154.02/23.21  | | 
% 154.02/23.21  | Case 2:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (13)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 154.02/23.21  | |             = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 154.02/23.21  | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.02/23.21  | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 154.02/23.21  | |             e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.02/23.21  | | 
% 154.02/23.21  | | BETA: splitting (13) gives:
% 154.02/23.21  | | 
% 154.02/23.21  | | Case 1:
% 154.02/23.21  | | | 
% 154.02/23.21  | | |   (14)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.02/23.21  | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.02/23.21  | | |         op(e0, e3) = e0 & $i(all_57_1)
% 154.02/23.21  | | | 
% 154.02/23.21  | | | ALPHA: (14) implies:
% 154.02/23.21  | | |   (15)   ~ (all_57_15 = e3)
% 154.02/23.21  | | | 
% 154.02/23.21  | | | REF_CLOSE: (2), (3), (8), (15) are inconsistent by sub-proof #1019.
% 154.02/23.21  | | | 
% 154.02/23.21  | | Case 2:
% 154.02/23.21  | | | 
% 154.02/23.21  | | |   (16)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.02/23.21  | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 154.02/23.21  | | |         op(e0, e2) = e0 & $i(all_57_3)
% 154.02/23.21  | | | 
% 154.02/23.21  | | | ALPHA: (16) implies:
% 154.02/23.21  | | |   (17)  op(e3, e3) = e2
% 154.02/23.21  | | | 
% 154.02/23.21  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (17) are
% 154.02/23.21  | | |            inconsistent by sub-proof #826.
% 154.02/23.21  | | | 
% 154.02/23.21  | | End of split
% 154.02/23.21  | | 
% 154.02/23.21  | End of split
% 154.02/23.21  | 
% 154.02/23.21  End of proof
% 154.02/23.21  
% 154.02/23.21  Sub-proof #826 shows that the following formulas are inconsistent:
% 154.02/23.21  ----------------------------------------------------------------
% 154.02/23.21    (1)  op(e0, e2) = all_52_7
% 154.02/23.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.21    (3)  op(e0, e0) = e3
% 154.02/23.21    (4)  op(e3, e3) = e2
% 154.02/23.21    (5)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.02/23.21             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.21           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.02/23.21           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.02/23.21             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.02/23.21           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.21           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 154.02/23.21           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 154.02/23.21           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.02/23.21           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 154.02/23.21           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 154.02/23.21         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.02/23.21             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.21           $i(all_57_7))
% 154.02/23.21    (6)   ~ (all_52_7 = e0)
% 154.02/23.21    (7)   ~ (e1 = e0)
% 154.02/23.21    (8)  op(e0, e0) = all_57_15
% 154.02/23.21    (9)   ~ (e2 = e1)
% 154.02/23.21    (10)  op(e2, e2) = e0
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (5) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (11)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 154.02/23.21  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 154.02/23.21  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 154.02/23.21  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 154.02/23.21  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 154.02/23.21  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 154.02/23.21  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.02/23.21  | |           $i(all_57_3))
% 154.02/23.21  | | 
% 154.02/23.21  | | BETA: splitting (11) gives:
% 154.02/23.21  | | 
% 154.02/23.21  | | Case 1:
% 154.02/23.21  | | | 
% 154.02/23.21  | | |   (12)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.02/23.21  | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 154.02/23.21  | | |         op(e0, e3) = e0 & $i(all_57_0)
% 154.02/23.21  | | | 
% 154.02/23.21  | | | ALPHA: (12) implies:
% 154.02/23.21  | | |   (13)   ~ (all_57_15 = e3)
% 154.02/23.21  | | | 
% 154.02/23.21  | | | REF_CLOSE: (2), (3), (8), (13) are inconsistent by sub-proof #1019.
% 154.02/23.21  | | | 
% 154.02/23.21  | | Case 2:
% 154.02/23.21  | | | 
% 154.02/23.21  | | |   (14)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.02/23.21  | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.02/23.21  | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 154.02/23.21  | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 154.02/23.21  | | |           & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.02/23.21  | | | 
% 154.02/23.21  | | | BETA: splitting (14) gives:
% 154.02/23.21  | | | 
% 154.02/23.21  | | | Case 1:
% 154.02/23.21  | | | | 
% 154.02/23.21  | | | |   (15)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.02/23.21  | | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.02/23.21  | | | |         op(e0, e3) = e0 & $i(all_57_1)
% 154.02/23.21  | | | | 
% 154.02/23.21  | | | | ALPHA: (15) implies:
% 154.02/23.21  | | | |   (16)   ~ (all_57_15 = e3)
% 154.02/23.21  | | | | 
% 154.02/23.21  | | | | REF_CLOSE: (2), (3), (8), (16) are inconsistent by sub-proof #1019.
% 154.02/23.21  | | | | 
% 154.02/23.21  | | | Case 2:
% 154.02/23.21  | | | | 
% 154.02/23.21  | | | |   (17)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.02/23.21  | | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 154.02/23.21  | | | |         op(e0, e2) = e0 & $i(all_57_3)
% 154.02/23.21  | | | | 
% 154.02/23.21  | | | | ALPHA: (17) implies:
% 154.02/23.21  | | | |   (18)  op(e0, e2) = e0
% 154.02/23.21  | | | | 
% 154.02/23.21  | | | | REF_CLOSE: (1), (2), (6), (18) are inconsistent by sub-proof #1036.
% 154.02/23.21  | | | | 
% 154.02/23.21  | | | End of split
% 154.02/23.21  | | | 
% 154.02/23.21  | | End of split
% 154.02/23.21  | | 
% 154.02/23.21  | Case 2:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (19)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 154.02/23.21  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 154.02/23.21  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.02/23.21  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 154.02/23.21  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 154.02/23.21  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 154.02/23.21  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.21  | |           $i(all_57_7))
% 154.02/23.21  | | 
% 154.02/23.21  | | BETA: splitting (19) gives:
% 154.02/23.21  | | 
% 154.02/23.21  | | Case 1:
% 154.02/23.21  | | | 
% 154.02/23.21  | | |   (20)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.02/23.21  | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 154.02/23.21  | | |         op(e0, e2) = e0 & $i(all_57_4)
% 154.02/23.21  | | | 
% 154.02/23.21  | | | ALPHA: (20) implies:
% 154.02/23.21  | | |   (21)  op(e0, e2) = e0
% 154.02/23.21  | | | 
% 154.02/23.21  | | | REF_CLOSE: (1), (2), (6), (21) are inconsistent by sub-proof #1036.
% 154.02/23.21  | | | 
% 154.02/23.21  | | Case 2:
% 154.02/23.21  | | | 
% 154.02/23.21  | | |   (22)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 154.02/23.21  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 154.02/23.21  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 154.02/23.21  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 154.02/23.21  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.02/23.21  | | | 
% 154.02/23.21  | | | REF_CLOSE: (2), (4), (7), (9), (10), (22) are inconsistent by sub-proof
% 154.02/23.21  | | |            #827.
% 154.02/23.21  | | | 
% 154.02/23.21  | | End of split
% 154.02/23.21  | | 
% 154.02/23.21  | End of split
% 154.02/23.21  | 
% 154.02/23.21  End of proof
% 154.02/23.21  
% 154.02/23.21  Sub-proof #827 shows that the following formulas are inconsistent:
% 154.02/23.21  ----------------------------------------------------------------
% 154.02/23.21    (1)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.02/23.21             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.02/23.21           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 154.02/23.21           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 154.02/23.21             e1) = e0 & $i(all_57_7))
% 154.02/23.21    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.21    (3)  op(e3, e3) = e2
% 154.02/23.21    (4)   ~ (e1 = e0)
% 154.02/23.21    (5)   ~ (e2 = e1)
% 154.02/23.21    (6)  op(e2, e2) = e0
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (1) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (7)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.02/23.21  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.02/23.21  | |        $i(all_57_6)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (7) implies:
% 154.02/23.21  | |   (8)  op(e3, e3) = e1
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1074.
% 154.02/23.21  | | 
% 154.02/23.21  | Case 2:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (9)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.02/23.21  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.21  | |        $i(all_57_7)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (9) implies:
% 154.02/23.21  | |   (10)  op(e2, e2) = e1
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #853.
% 154.02/23.21  | | 
% 154.02/23.21  | End of split
% 154.02/23.21  | 
% 154.02/23.21  End of proof
% 154.02/23.21  
% 154.02/23.21  Sub-proof #828 shows that the following formulas are inconsistent:
% 154.02/23.21  ----------------------------------------------------------------
% 154.02/23.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.21    (2)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.02/23.21             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.02/23.21           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 154.02/23.21           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 154.02/23.21           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 154.02/23.21           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 154.02/23.21    (3)   ~ (e3 = e2)
% 154.02/23.21    (4)   ~ (all_52_8 = e3)
% 154.02/23.21    (5)  op(e2, e1) = e3
% 154.02/23.21    (6)  op(e3, e1) = all_52_8
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (2) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (7)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.02/23.21  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.02/23.21  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (7) implies:
% 154.02/23.21  | |   (8)  op(e3, e1) = e3
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #1164.
% 154.02/23.21  | | 
% 154.02/23.21  | Case 2:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (9)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 154.02/23.21  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 154.02/23.21  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (9) implies:
% 154.02/23.21  | |   (10)  op(e2, e1) = e2
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #1135.
% 154.02/23.21  | | 
% 154.02/23.21  | End of split
% 154.02/23.21  | 
% 154.02/23.21  End of proof
% 154.02/23.21  
% 154.02/23.21  Sub-proof #829 shows that the following formulas are inconsistent:
% 154.02/23.21  ----------------------------------------------------------------
% 154.02/23.21    (1)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 154.02/23.21             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.02/23.21           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 154.02/23.21           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 154.02/23.21           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 154.02/23.21           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 154.02/23.21           all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3)
% 154.02/23.21           = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 154.02/23.21           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 154.02/23.21           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) =
% 154.02/23.21           all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 154.02/23.21           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &
% 154.02/23.21            ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2,
% 154.02/23.21             e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.02/23.21    (2)  op(e3, e2) = all_52_4
% 154.02/23.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.21    (4)  op(e0, e0) = e3
% 154.02/23.21    (5)   ~ (all_52_4 = e3)
% 154.02/23.21    (6)   ~ (e3 = e2)
% 154.02/23.21    (7)   ~ (all_52_8 = e3)
% 154.02/23.21    (8)  op(e3, e1) = all_52_8
% 154.02/23.21    (9)  op(e3, e3) = e3
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (1) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (10)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 154.02/23.21  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.02/23.21  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 154.02/23.21  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 154.02/23.21  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 154.02/23.21  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #863.
% 154.02/23.21  | | 
% 154.02/23.21  | Case 2:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (11)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 154.02/23.21  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 154.02/23.21  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 154.02/23.21  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 154.02/23.21  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.02/23.21  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 154.02/23.21  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 154.02/23.21  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 154.02/23.21  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.02/23.21  | | 
% 154.02/23.21  | | BETA: splitting (11) gives:
% 154.02/23.21  | | 
% 154.02/23.21  | | Case 1:
% 154.02/23.21  | | | 
% 154.02/23.21  | | |   (12)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.02/23.21  | | |         (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 154.02/23.21  | | |         op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 154.02/23.21  | | |         $i(all_57_14)
% 154.02/23.21  | | | 
% 154.02/23.21  | | | ALPHA: (12) implies:
% 154.02/23.21  | | |   (13)  op(e3, e3) = e2
% 154.02/23.21  | | | 
% 154.02/23.21  | | | REF_CLOSE: (3), (6), (9), (13) are inconsistent by sub-proof #1085.
% 154.02/23.21  | | | 
% 154.02/23.21  | | Case 2:
% 154.02/23.21  | | | 
% 154.02/23.21  | | |   (14)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 154.02/23.21  | | |           (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.02/23.21  | | |           op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 154.02/23.21  | | |           $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7
% 154.02/23.21  | | |             = e2) &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3,
% 154.02/23.21  | | |             e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 154.02/23.21  | | |           $i(all_57_7) & $i(all_57_10))
% 154.02/23.21  | | | 
% 154.02/23.21  | | | REF_CLOSE: (3), (4), (6), (7), (8), (14) are inconsistent by sub-proof
% 154.02/23.21  | | |            #830.
% 154.02/23.21  | | | 
% 154.02/23.21  | | End of split
% 154.02/23.21  | | 
% 154.02/23.21  | End of split
% 154.02/23.21  | 
% 154.02/23.21  End of proof
% 154.02/23.21  
% 154.02/23.21  Sub-proof #830 shows that the following formulas are inconsistent:
% 154.02/23.21  ----------------------------------------------------------------
% 154.02/23.21    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.21    (2)  op(e0, e0) = e3
% 154.02/23.21    (3)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 154.02/23.21             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.02/23.21           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 154.02/23.21           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 154.02/23.21           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 154.02/23.21           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.02/23.21    (4)   ~ (e3 = e2)
% 154.02/23.21    (5)   ~ (all_52_8 = e3)
% 154.02/23.21    (6)  op(e3, e1) = all_52_8
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (3) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 154.02/23.21  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.02/23.21  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (7) implies:
% 154.02/23.21  | |   (8)  op(e0, e0) = e2
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #1087.
% 154.02/23.21  | | 
% 154.02/23.21  | Case 2:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 154.02/23.21  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 154.02/23.21  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (9) implies:
% 154.02/23.21  | |   (10)  op(e3, e1) = e3
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #1164.
% 154.02/23.21  | | 
% 154.02/23.21  | End of split
% 154.02/23.21  | 
% 154.02/23.21  End of proof
% 154.02/23.21  
% 154.02/23.21  Sub-proof #831 shows that the following formulas are inconsistent:
% 154.02/23.21  ----------------------------------------------------------------
% 154.02/23.21    (1)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 154.02/23.21             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.02/23.21           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 154.02/23.21           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 154.02/23.21             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 154.02/23.21             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 154.02/23.21    (2)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 154.02/23.21           all_57_12 & $i(all_57_12))
% 154.02/23.21    (3)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 154.02/23.21           all_57_15 & $i(all_57_15))
% 154.02/23.21    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (1) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (5)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 154.02/23.21  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.02/23.21  | |        op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (5) implies:
% 154.02/23.21  | |   (6)  all_57_12 = e3
% 154.02/23.21  | |   (7)   ~ (all_57_0 = e2)
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #832.
% 154.02/23.21  | | 
% 154.02/23.21  | Case 2:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (8)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 154.02/23.21  | |          e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 154.02/23.21  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (8) implies:
% 154.02/23.21  | |   (9)   ~ (all_57_2 = e0)
% 154.02/23.21  | |   (10)  op(e0, e0) = e3
% 154.02/23.21  | | 
% 154.02/23.21  | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #833.
% 154.02/23.21  | | 
% 154.02/23.21  | End of split
% 154.02/23.21  | 
% 154.02/23.21  End of proof
% 154.02/23.21  
% 154.02/23.21  Sub-proof #832 shows that the following formulas are inconsistent:
% 154.02/23.21  ----------------------------------------------------------------
% 154.02/23.21    (1)  (all_57_0 = e2 & op(e2, e3) = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) =
% 154.02/23.21           all_57_12 & $i(all_57_12))
% 154.02/23.21    (2)   ~ (all_57_0 = e2)
% 154.02/23.21    (3)  all_57_12 = e3
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (1) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (4)  all_57_0 = e2 & op(e2, e3) = e2
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (4) implies:
% 154.02/23.21  | |   (5)  all_57_0 = e2
% 154.02/23.21  | | 
% 154.02/23.21  | | REDUCE: (2), (5) imply:
% 154.02/23.21  | |   (6)  $false
% 154.02/23.21  | | 
% 154.02/23.21  | | CLOSE: (6) is inconsistent.
% 154.02/23.21  | | 
% 154.02/23.21  | Case 2:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (7)   ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12)
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (7) implies:
% 154.02/23.21  | |   (8)   ~ (all_57_12 = e3)
% 154.02/23.21  | | 
% 154.02/23.21  | | REDUCE: (3), (8) imply:
% 154.02/23.21  | |   (9)  $false
% 154.02/23.21  | | 
% 154.02/23.21  | | CLOSE: (9) is inconsistent.
% 154.02/23.21  | | 
% 154.02/23.21  | End of split
% 154.02/23.21  | 
% 154.02/23.21  End of proof
% 154.02/23.21  
% 154.02/23.21  Sub-proof #833 shows that the following formulas are inconsistent:
% 154.02/23.21  ----------------------------------------------------------------
% 154.02/23.21    (1)  (all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) =
% 154.02/23.21           all_57_15 & $i(all_57_15))
% 154.02/23.21    (2)   ~ (all_57_2 = e0)
% 154.02/23.21    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.21           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.21    (4)  op(e0, e0) = e3
% 154.02/23.21  
% 154.02/23.21  Begin of proof
% 154.02/23.21  | 
% 154.02/23.21  | BETA: splitting (1) gives:
% 154.02/23.21  | 
% 154.02/23.21  | Case 1:
% 154.02/23.21  | | 
% 154.02/23.21  | |   (5)  all_57_2 = e0 & op(e0, e3) = e0
% 154.02/23.21  | | 
% 154.02/23.21  | | ALPHA: (5) implies:
% 154.02/23.22  | |   (6)  all_57_2 = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | REDUCE: (2), (6) imply:
% 154.02/23.22  | |   (7)  $false
% 154.02/23.22  | | 
% 154.02/23.22  | | CLOSE: (7) is inconsistent.
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (8)   ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (8) implies:
% 154.02/23.22  | |   (9)   ~ (all_57_15 = e3)
% 154.02/23.22  | |   (10)  op(e0, e0) = all_57_15
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #1019.
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #834 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (2)  op(e1, e1) = e3
% 154.02/23.22    (3)  op(e1, e1) = e2
% 154.02/23.22    (4)   ~ (e3 = e2)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | GROUND_INST: instantiating (1) with e3, e2, e1, e1, simplifying with (2), (3)
% 154.02/23.22  |              gives:
% 154.02/23.22  |   (5)  e3 = e2
% 154.02/23.22  | 
% 154.02/23.22  | REDUCE: (4), (5) imply:
% 154.02/23.22  |   (6)  $false
% 154.02/23.22  | 
% 154.02/23.22  | CLOSE: (6) is inconsistent.
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #835 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (2)   ~ (all_52_7 = e1)
% 154.02/23.22    (3)  all_56_7 = e2 & op(e1, e2) = e2
% 154.02/23.22    (4)   ~ (all_52_7 = e3)
% 154.02/23.22    (5)  op(e1, e2) = all_52_6
% 154.02/23.22    (6)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.02/23.22    (7)   ~ (all_52_7 = e0)
% 154.02/23.22    (8)  all_54_13 = all_52_7
% 154.02/23.22    (9)   ~ (all_52_6 = all_52_7)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | ALPHA: (3) implies:
% 154.02/23.22  |   (10)  op(e1, e2) = e2
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (6) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (11)  all_54_13 = e3
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (4), (8), (11) are inconsistent by sub-proof #845.
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (12)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (1), (2), (5), (7), (8), (9), (10), (12) are inconsistent by
% 154.02/23.22  | |            sub-proof #836.
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #836 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (2)   ~ (all_52_7 = e1)
% 154.02/23.22    (3)  op(e1, e2) = all_52_6
% 154.02/23.22    (4)  op(e1, e2) = e2
% 154.02/23.22    (5)   ~ (all_52_7 = e0)
% 154.02/23.22    (6)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.02/23.22    (7)  all_54_13 = all_52_7
% 154.02/23.22    (8)   ~ (all_52_6 = all_52_7)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (6) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (9)  all_54_13 = e2
% 154.02/23.22  | | 
% 154.02/23.22  | | COMBINE_EQS: (7), (9) imply:
% 154.02/23.22  | |   (10)  all_52_7 = e2
% 154.02/23.22  | | 
% 154.02/23.22  | | SIMP: (10) implies:
% 154.02/23.22  | |   (11)  all_52_7 = e2
% 154.02/23.22  | | 
% 154.02/23.22  | | REDUCE: (8), (11) imply:
% 154.02/23.22  | |   (12)   ~ (all_52_6 = e2)
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (1), (3), (4), (12) are inconsistent by sub-proof #1171.
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (13)  all_54_13 = e1 | all_54_13 = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (2), (5), (7), (13) are inconsistent by sub-proof #983.
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #837 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  all_56_6 = e2 & op(e1, e3) = e2
% 154.02/23.22    (2)  all_56_6 = e1
% 154.02/23.22    (3)   ~ (e2 = e1)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | ALPHA: (1) implies:
% 154.02/23.22  |   (4)  all_56_6 = e2
% 154.02/23.22  | 
% 154.02/23.22  | COMBINE_EQS: (2), (4) imply:
% 154.02/23.22  |   (5)  e2 = e1
% 154.02/23.22  | 
% 154.02/23.22  | REDUCE: (3), (5) imply:
% 154.02/23.22  |   (6)  $false
% 154.02/23.22  | 
% 154.02/23.22  | CLOSE: (6) is inconsistent.
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #838 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (2)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.02/23.22    (3)  all_56_12 = e1
% 154.02/23.22    (4)  op(e1, e3) = e1
% 154.02/23.22    (5)   ~ (e1 = e0)
% 154.02/23.22    (6)  op(e1, e3) = all_52_2
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (2) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (7)  all_56_6 = e0 & op(e1, e3) = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (7) implies:
% 154.02/23.22  | |   (8)  op(e1, e3) = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (1), (4), (5), (6), (8) are inconsistent by sub-proof #1127.
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (9)  all_56_12 = e0 & op(e0, e3) = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (9) implies:
% 154.02/23.22  | |   (10)  all_56_12 = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #1051.
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #839 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 154.02/23.22    (2)   ~ (all_52_1 = e0)
% 154.02/23.22    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (4)   ~ (e3 = e0)
% 154.02/23.22    (5)  op(e3, e3) = e3
% 154.02/23.22    (6)  op(e2, e3) = all_52_1
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (1) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (7) implies:
% 154.02/23.22  | |   (8)  op(e3, e3) = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1141.
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (9)  all_56_2 = e0 & op(e2, e3) = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #840.
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #840 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  all_56_2 = e0 & op(e2, e3) = e0
% 154.02/23.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (3)  op(e2, e3) = all_52_1
% 154.02/23.22    (4)   ~ (all_52_1 = e0)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | ALPHA: (1) implies:
% 154.02/23.22  |   (5)  op(e2, e3) = e0
% 154.02/23.22  | 
% 154.02/23.22  | GROUND_INST: instantiating (2) with all_52_1, e0, e3, e2, simplifying with
% 154.02/23.22  |              (3), (5) gives:
% 154.02/23.22  |   (6)  all_52_1 = e0
% 154.02/23.22  | 
% 154.02/23.22  | REDUCE: (4), (6) imply:
% 154.02/23.22  |   (7)  $false
% 154.02/23.22  | 
% 154.02/23.22  | CLOSE: (7) is inconsistent.
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #841 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)   ~ (e3 = e1)
% 154.02/23.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (3)  op(e2, e3) = e2
% 154.02/23.22    (4)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 154.02/23.22    (5)  op(e3, e3) = e3
% 154.02/23.22    (6)   ~ (e2 = e1)
% 154.02/23.22    (7)  op(e2, e3) = all_52_1
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (4) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (8)  all_56_0 = e1 & op(e3, e3) = e1
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (8) implies:
% 154.02/23.22  | |   (9)  op(e3, e3) = e1
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #1178.
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (10)  all_56_2 = e1 & op(e2, e3) = e1
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (10) implies:
% 154.02/23.22  | |   (11)  op(e2, e3) = e1
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (2), (3), (6), (7), (11) are inconsistent by sub-proof #842.
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #842 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (2)  op(e2, e3) = e2
% 154.02/23.22    (3)  op(e2, e3) = e1
% 154.02/23.22    (4)   ~ (e2 = e1)
% 154.02/23.22    (5)  op(e2, e3) = all_52_1
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | GROUND_INST: instantiating (1) with all_52_1, e1, e3, e2, simplifying with
% 154.02/23.22  |              (3), (5) gives:
% 154.02/23.22  |   (6)  all_52_1 = e1
% 154.02/23.22  | 
% 154.02/23.22  | GROUND_INST: instantiating (1) with all_52_1, e2, e3, e2, simplifying with
% 154.02/23.22  |              (2), (5) gives:
% 154.02/23.22  |   (7)  all_52_1 = e2
% 154.02/23.22  | 
% 154.02/23.22  | COMBINE_EQS: (6), (7) imply:
% 154.02/23.22  |   (8)  e2 = e1
% 154.02/23.22  | 
% 154.02/23.22  | SIMP: (8) implies:
% 154.02/23.22  |   (9)  e2 = e1
% 154.02/23.22  | 
% 154.02/23.22  | REDUCE: (4), (9) imply:
% 154.02/23.22  |   (10)  $false
% 154.02/23.22  | 
% 154.02/23.22  | CLOSE: (10) is inconsistent.
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #843 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  all_54_4 = all_52_1
% 154.02/23.22    (2)  all_54_4 = e3
% 154.02/23.22    (3)   ~ (all_52_1 = e3)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | COMBINE_EQS: (1), (2) imply:
% 154.02/23.22  |   (4)  all_52_1 = e3
% 154.02/23.22  | 
% 154.02/23.22  | SIMP: (4) implies:
% 154.02/23.22  |   (5)  all_52_1 = e3
% 154.02/23.22  | 
% 154.02/23.22  | REDUCE: (3), (5) imply:
% 154.02/23.22  |   (6)  $false
% 154.02/23.22  | 
% 154.02/23.22  | CLOSE: (6) is inconsistent.
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #844 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  op(e2, e2) = e1
% 154.02/23.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (3)  (all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2) =
% 154.02/23.22           all_57_12 & $i(all_57_12))
% 154.02/23.22    (4)   ~ (e3 = e2)
% 154.02/23.22    (5)  op(e2, e1) = e3
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (3) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (6)  all_57_7 = e2 & op(e2, e1) = e2
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (6) implies:
% 154.02/23.22  | |   (7)  op(e2, e1) = e2
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #1135.
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (8)   ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12)
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (8) implies:
% 154.02/23.22  | |   (9)   ~ (all_57_12 = e1)
% 154.02/23.22  | |   (10)  op(e2, e2) = all_57_12
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (1), (2), (9), (10) are inconsistent by sub-proof #1014.
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #845 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  all_54_13 = all_52_7
% 154.02/23.22    (2)  all_54_13 = e3
% 154.02/23.22    (3)   ~ (all_52_7 = e3)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | COMBINE_EQS: (1), (2) imply:
% 154.02/23.22  |   (4)  all_52_7 = e3
% 154.02/23.22  | 
% 154.02/23.22  | SIMP: (4) implies:
% 154.02/23.22  |   (5)  all_52_7 = e3
% 154.02/23.22  | 
% 154.02/23.22  | REDUCE: (3), (5) imply:
% 154.02/23.22  |   (6)  $false
% 154.02/23.22  | 
% 154.02/23.22  | CLOSE: (6) is inconsistent.
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #846 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  op(e2, e2) = e1
% 154.02/23.22    (2)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 154.02/23.22         (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 154.02/23.22    (3)   ~ (e2 = e0)
% 154.02/23.22    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (5)  all_56_7 = e3
% 154.02/23.22    (6)   ~ (e3 = e0)
% 154.02/23.22    (7)   ~ (e1 = e0)
% 154.02/23.22    (8)  all_56_13 = e3
% 154.02/23.22    (9)   ~ (e3 = e2)
% 154.02/23.22    (10)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.02/23.22          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.02/23.22    (11)   ~ (e2 = e1)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (10) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 154.02/23.22  | |           e0)
% 154.02/23.22  | | 
% 154.02/23.22  | | BETA: splitting (12) gives:
% 154.02/23.22  | | 
% 154.02/23.22  | | Case 1:
% 154.02/23.22  | | | 
% 154.02/23.22  | | |   (13)  all_56_1 = e0 & op(e3, e2) = e0
% 154.02/23.22  | | | 
% 154.02/23.22  | | | ALPHA: (13) implies:
% 154.02/23.22  | | |   (14)  all_56_1 = e0
% 154.02/23.22  | | | 
% 154.02/23.22  | | | BETA: splitting (2) gives:
% 154.02/23.22  | | | 
% 154.02/23.22  | | | Case 1:
% 154.02/23.22  | | | | 
% 154.02/23.22  | | | |   (15)  (all_56_1 = e2 & op(e3, e2) = e2) | (all_56_3 = e2 & op(e2, e2)
% 154.02/23.22  | | | |           = e2)
% 154.02/23.22  | | | | 
% 154.02/23.22  | | | | BETA: splitting (15) gives:
% 154.02/23.22  | | | | 
% 154.02/23.22  | | | | Case 1:
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | |   (16)  all_56_1 = e2 & op(e3, e2) = e2
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | | REF_CLOSE: (3), (14), (16) are inconsistent by sub-proof #848.
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | Case 2:
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | |   (17)  all_56_3 = e2 & op(e2, e2) = e2
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | | ALPHA: (17) implies:
% 154.02/23.22  | | | | |   (18)  op(e2, e2) = e2
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | | REF_CLOSE: (1), (4), (11), (18) are inconsistent by sub-proof #1158.
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | End of split
% 154.02/23.22  | | | | 
% 154.02/23.22  | | | Case 2:
% 154.02/23.22  | | | | 
% 154.02/23.22  | | | |   (19)  (all_56_7 = e2 & op(e1, e2) = e2) | (all_56_13 = e2 & op(e0, e2)
% 154.02/23.22  | | | |           = e2)
% 154.02/23.22  | | | | 
% 154.02/23.22  | | | | BETA: splitting (19) gives:
% 154.02/23.22  | | | | 
% 154.02/23.22  | | | | Case 1:
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | |   (20)  all_56_7 = e2 & op(e1, e2) = e2
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | | REF_CLOSE: (5), (9), (20) are inconsistent by sub-proof #1128.
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | Case 2:
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | |   (21)  all_56_13 = e2 & op(e0, e2) = e2
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | | REF_CLOSE: (8), (9), (21) are inconsistent by sub-proof #847.
% 154.02/23.22  | | | | | 
% 154.02/23.22  | | | | End of split
% 154.02/23.22  | | | | 
% 154.02/23.22  | | | End of split
% 154.02/23.22  | | | 
% 154.02/23.22  | | Case 2:
% 154.02/23.22  | | | 
% 154.02/23.22  | | |   (22)  all_56_3 = e0 & op(e2, e2) = e0
% 154.02/23.22  | | | 
% 154.02/23.22  | | | ALPHA: (22) implies:
% 154.02/23.22  | | |   (23)  op(e2, e2) = e0
% 154.02/23.22  | | | 
% 154.02/23.22  | | | REF_CLOSE: (1), (4), (7), (23) are inconsistent by sub-proof #853.
% 154.02/23.22  | | | 
% 154.02/23.22  | | End of split
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (24)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 154.02/23.22  | |           e0)
% 154.02/23.22  | | 
% 154.02/23.22  | | BETA: splitting (24) gives:
% 154.02/23.22  | | 
% 154.02/23.22  | | Case 1:
% 154.02/23.22  | | | 
% 154.02/23.22  | | |   (25)  all_56_7 = e0 & op(e1, e2) = e0
% 154.02/23.22  | | | 
% 154.02/23.22  | | | REF_CLOSE: (5), (6), (25) are inconsistent by sub-proof #1151.
% 154.02/23.22  | | | 
% 154.02/23.22  | | Case 2:
% 154.02/23.22  | | | 
% 154.02/23.22  | | |   (26)  all_56_13 = e0 & op(e0, e2) = e0
% 154.02/23.22  | | | 
% 154.02/23.22  | | | REF_CLOSE: (6), (8), (26) are inconsistent by sub-proof #1102.
% 154.02/23.22  | | | 
% 154.02/23.22  | | End of split
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #847 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  all_56_13 = e2 & op(e0, e2) = e2
% 154.02/23.22    (2)  all_56_13 = e3
% 154.02/23.22    (3)   ~ (e3 = e2)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | ALPHA: (1) implies:
% 154.02/23.22  |   (4)  all_56_13 = e2
% 154.02/23.22  | 
% 154.02/23.22  | COMBINE_EQS: (2), (4) imply:
% 154.02/23.22  |   (5)  e3 = e2
% 154.02/23.22  | 
% 154.02/23.22  | REDUCE: (3), (5) imply:
% 154.02/23.22  |   (6)  $false
% 154.02/23.22  | 
% 154.02/23.22  | CLOSE: (6) is inconsistent.
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #848 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  all_56_1 = e2 & op(e3, e2) = e2
% 154.02/23.22    (2)  all_56_1 = e0
% 154.02/23.22    (3)   ~ (e2 = e0)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | ALPHA: (1) implies:
% 154.02/23.22  |   (4)  all_56_1 = e2
% 154.02/23.22  | 
% 154.02/23.22  | COMBINE_EQS: (2), (4) imply:
% 154.02/23.22  |   (5)  e2 = e0
% 154.02/23.22  | 
% 154.02/23.22  | SIMP: (5) implies:
% 154.02/23.22  |   (6)  e2 = e0
% 154.02/23.22  | 
% 154.02/23.22  | REDUCE: (3), (6) imply:
% 154.02/23.22  |   (7)  $false
% 154.02/23.22  | 
% 154.02/23.22  | CLOSE: (7) is inconsistent.
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #849 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)   ~ (e3 = e1)
% 154.02/23.22    (2)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 154.02/23.22    (3)  op(e2, e2) = e1
% 154.02/23.22    (4)  op(e3, e2) = all_52_4
% 154.02/23.22    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (6)   ~ (all_52_4 = e3)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (2) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (7)  all_56_1 = e3 & op(e3, e2) = e3
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (7) implies:
% 154.02/23.22  | |   (8)  op(e3, e2) = e3
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #1166.
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (9)  all_56_3 = e3 & op(e2, e2) = e3
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (9) implies:
% 154.02/23.22  | |   (10)  op(e2, e2) = e3
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #1136.
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #850 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  op(e0, e1) = all_52_11
% 154.02/23.22    (2)  op(e0, e2) = all_52_7
% 154.02/23.22    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (4)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.02/23.22             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.22           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.02/23.22           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.02/23.22             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.02/23.22           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.22           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 154.02/23.22           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 154.02/23.22           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.02/23.22           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 154.02/23.22           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 154.02/23.22         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.02/23.22             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.22           $i(all_57_7))
% 154.02/23.22    (5)   ~ (all_52_11 = e0)
% 154.02/23.22    (6)  op(e0, e3) = all_52_3
% 154.02/23.22    (7)   ~ (all_52_7 = e0)
% 154.02/23.22    (8)   ~ (e3 = e2)
% 154.02/23.22    (9)   ~ (all_52_3 = e0)
% 154.02/23.22    (10)  op(e3, e3) = e3
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (4) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (11)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 154.02/23.22  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 154.02/23.22  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 154.02/23.22  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 154.02/23.22  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 154.02/23.22  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 154.02/23.22  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.02/23.22  | |           $i(all_57_3))
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (3), (6), (8), (9), (10), (11) are inconsistent by sub-proof
% 154.02/23.22  | |            #852.
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (12)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 154.02/23.22  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 154.02/23.22  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.02/23.22  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 154.02/23.22  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 154.02/23.22  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 154.02/23.22  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.22  | |           $i(all_57_7))
% 154.02/23.22  | | 
% 154.02/23.22  | | BETA: splitting (12) gives:
% 154.02/23.22  | | 
% 154.02/23.22  | | Case 1:
% 154.02/23.22  | | | 
% 154.02/23.22  | | |   (13)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.02/23.22  | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 154.02/23.22  | | |         op(e0, e2) = e0 & $i(all_57_4)
% 154.02/23.22  | | | 
% 154.02/23.22  | | | ALPHA: (13) implies:
% 154.02/23.22  | | |   (14)  op(e0, e2) = e0
% 154.02/23.22  | | | 
% 154.02/23.22  | | | REF_CLOSE: (2), (3), (7), (14) are inconsistent by sub-proof #1036.
% 154.02/23.22  | | | 
% 154.02/23.22  | | Case 2:
% 154.02/23.22  | | | 
% 154.02/23.22  | | |   (15)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 154.02/23.22  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 154.02/23.22  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 154.02/23.22  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 154.02/23.22  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.02/23.22  | | | 
% 154.02/23.22  | | | REF_CLOSE: (1), (3), (5), (15) are inconsistent by sub-proof #851.
% 154.02/23.22  | | | 
% 154.02/23.22  | | End of split
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #851 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.02/23.22             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.02/23.22           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 154.02/23.22           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 154.02/23.22             e1) = e0 & $i(all_57_7))
% 154.02/23.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (3)  op(e0, e1) = all_52_11
% 154.02/23.22    (4)   ~ (all_52_11 = e0)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (1) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (5)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.02/23.22  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.02/23.22  | |        $i(all_57_6)
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (5) implies:
% 154.02/23.22  | |   (6)  op(e0, e1) = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #1124.
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (7)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.02/23.22  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.22  | |        $i(all_57_7)
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (7) implies:
% 154.02/23.22  | |   (8)  op(e0, e1) = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1124.
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #852 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (2)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.02/23.22             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.22           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.02/23.22           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.02/23.22             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.02/23.22           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.22           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.02/23.22    (3)  op(e0, e3) = all_52_3
% 154.02/23.22    (4)   ~ (e3 = e2)
% 154.02/23.22    (5)   ~ (all_52_3 = e0)
% 154.02/23.22    (6)  op(e3, e3) = e3
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (2) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (7)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.02/23.22  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.22  | |        $i(all_57_0)
% 154.02/23.22  | | 
% 154.02/23.22  | | ALPHA: (7) implies:
% 154.02/23.22  | |   (8)  op(e0, e3) = e0
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1142.
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (9)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 154.02/23.22  | |            = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0
% 154.02/23.22  | |          & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 154.02/23.22  | |            e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.22  | |          all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.02/23.22  | | 
% 154.02/23.22  | | BETA: splitting (9) gives:
% 154.02/23.22  | | 
% 154.02/23.22  | | Case 1:
% 154.02/23.22  | | | 
% 154.02/23.22  | | |   (10)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.02/23.22  | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.02/23.22  | | |         op(e0, e3) = e0 & $i(all_57_1)
% 154.02/23.22  | | | 
% 154.02/23.22  | | | ALPHA: (10) implies:
% 154.02/23.22  | | |   (11)  op(e0, e3) = e0
% 154.02/23.22  | | | 
% 154.02/23.22  | | | REF_CLOSE: (1), (3), (5), (11) are inconsistent by sub-proof #1142.
% 154.02/23.22  | | | 
% 154.02/23.22  | | Case 2:
% 154.02/23.22  | | | 
% 154.02/23.22  | | |   (12)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.02/23.22  | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 154.02/23.22  | | |         op(e0, e2) = e0 & $i(all_57_3)
% 154.02/23.22  | | | 
% 154.02/23.22  | | | ALPHA: (12) implies:
% 154.02/23.22  | | |   (13)  op(e3, e3) = e2
% 154.02/23.22  | | | 
% 154.02/23.22  | | | REF_CLOSE: (1), (4), (6), (13) are inconsistent by sub-proof #1085.
% 154.02/23.22  | | | 
% 154.02/23.22  | | End of split
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #853 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (2)  op(e2, e2) = e1
% 154.02/23.22    (3)  op(e2, e2) = e0
% 154.02/23.22    (4)   ~ (e1 = e0)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | GROUND_INST: instantiating (1) with e1, e0, e2, e2, simplifying with (2), (3)
% 154.02/23.22  |              gives:
% 154.02/23.22  |   (5)  e1 = e0
% 154.02/23.22  | 
% 154.02/23.22  | REDUCE: (4), (5) imply:
% 154.02/23.22  |   (6)  $false
% 154.02/23.22  | 
% 154.02/23.22  | CLOSE: (6) is inconsistent.
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #854 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (2)  op(e2, e0) = e3
% 154.02/23.22    (3)  op(e2, e0) = e2
% 154.02/23.22    (4)   ~ (e3 = e2)
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | GROUND_INST: instantiating (1) with e3, e2, e0, e2, simplifying with (2), (3)
% 154.02/23.22  |              gives:
% 154.02/23.22  |   (5)  e3 = e2
% 154.02/23.22  | 
% 154.02/23.22  | REDUCE: (4), (5) imply:
% 154.02/23.22  |   (6)  $false
% 154.02/23.22  | 
% 154.02/23.22  | CLOSE: (6) is inconsistent.
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #855 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.22    (1)  op(e0, e2) = all_52_7
% 154.02/23.22    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.22           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.22    (3)  ( ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 & op(e2, e1) = all_20_1
% 154.02/23.22           & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e2, e1) =
% 154.02/23.22           all_20_1 & $i(all_20_1))
% 154.02/23.22    (4)   ~ (all_57_12 = e0)
% 154.02/23.22    (5)  op(e2, e1) = all_38_1
% 154.02/23.22    (6)   ~ (all_52_6 = e0)
% 154.02/23.22    (7)  op(e1, e2) = all_52_6
% 154.02/23.22    (8)  op(e2, e2) = all_57_12
% 154.02/23.22    (9)   ~ (all_52_7 = e0)
% 154.02/23.22    (10)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.02/23.22          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.02/23.22    (11)  op(e2, e1) = e3
% 154.02/23.22  
% 154.02/23.22  Begin of proof
% 154.02/23.22  | 
% 154.02/23.22  | BETA: splitting (10) gives:
% 154.02/23.22  | 
% 154.02/23.22  | Case 1:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 154.02/23.22  | |           e0)
% 154.02/23.22  | | 
% 154.02/23.22  | | BETA: splitting (12) gives:
% 154.02/23.22  | | 
% 154.02/23.22  | | Case 1:
% 154.02/23.22  | | | 
% 154.02/23.22  | | |   (13)  all_56_1 = e0 & op(e3, e2) = e0
% 154.02/23.22  | | | 
% 154.02/23.22  | | | REF_CLOSE: (2), (3), (5), (11), (13) are inconsistent by sub-proof #857.
% 154.02/23.22  | | | 
% 154.02/23.22  | | Case 2:
% 154.02/23.22  | | | 
% 154.02/23.22  | | |   (14)  all_56_3 = e0 & op(e2, e2) = e0
% 154.02/23.22  | | | 
% 154.02/23.22  | | | ALPHA: (14) implies:
% 154.02/23.22  | | |   (15)  op(e2, e2) = e0
% 154.02/23.22  | | | 
% 154.02/23.22  | | | REF_CLOSE: (2), (4), (8), (15) are inconsistent by sub-proof #856.
% 154.02/23.22  | | | 
% 154.02/23.22  | | End of split
% 154.02/23.22  | | 
% 154.02/23.22  | Case 2:
% 154.02/23.22  | | 
% 154.02/23.22  | |   (16)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 154.02/23.22  | |           e0)
% 154.02/23.22  | | 
% 154.02/23.22  | | REF_CLOSE: (1), (2), (6), (7), (9), (16) are inconsistent by sub-proof
% 154.02/23.22  | |            #1028.
% 154.02/23.22  | | 
% 154.02/23.22  | End of split
% 154.02/23.22  | 
% 154.02/23.22  End of proof
% 154.02/23.22  
% 154.02/23.22  Sub-proof #856 shows that the following formulas are inconsistent:
% 154.02/23.22  ----------------------------------------------------------------
% 154.02/23.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (2)  op(e2, e2) = all_57_12
% 154.02/23.23    (3)  op(e2, e2) = e0
% 154.02/23.23    (4)   ~ (all_57_12 = e0)
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | GROUND_INST: instantiating (1) with e0, all_57_12, e2, e2, simplifying with
% 154.02/23.23  |              (2), (3) gives:
% 154.02/23.23  |   (5)  all_57_12 = e0
% 154.02/23.23  | 
% 154.02/23.23  | REDUCE: (4), (5) imply:
% 154.02/23.23  |   (6)  $false
% 154.02/23.23  | 
% 154.02/23.23  | CLOSE: (6) is inconsistent.
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #857 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (2)  ( ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 & op(e2, e1) = all_20_1
% 154.02/23.23           & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e3) & op(e2, e1) =
% 154.02/23.23           all_20_1 & $i(all_20_1))
% 154.02/23.23    (3)  all_56_1 = e0 & op(e3, e2) = e0
% 154.02/23.23    (4)  op(e2, e1) = all_38_1
% 154.02/23.23    (5)  op(e2, e1) = e3
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | ALPHA: (3) implies:
% 154.02/23.23  |   (6)  op(e3, e2) = e0
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (2) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (7)   ~ (all_20_0 = e0) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 154.02/23.23  | |        all_20_1 & $i(all_20_0) & $i(all_20_1)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (7) implies:
% 154.02/23.23  | |   (8)   ~ (all_20_0 = e0)
% 154.02/23.23  | |   (9)  op(e2, e1) = all_20_1
% 154.02/23.23  | |   (10)  op(all_20_1, e2) = all_20_0
% 154.02/23.23  | | 
% 154.02/23.23  | | GROUND_INST: instantiating (1) with all_20_1, all_38_1, e1, e2, simplifying
% 154.02/23.23  | |              with (4), (9) gives:
% 154.02/23.23  | |   (11)  all_38_1 = all_20_1
% 154.02/23.23  | | 
% 154.02/23.23  | | GROUND_INST: instantiating (1) with e3, all_38_1, e1, e2, simplifying with
% 154.02/23.23  | |              (4), (5) gives:
% 154.02/23.23  | |   (12)  all_38_1 = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | GROUND_INST: instantiating (1) with e0, all_20_0, e2, e3, simplifying with
% 154.02/23.23  | |              (6) gives:
% 154.02/23.23  | |   (13)  all_20_0 = e0 |  ~ (op(e3, e2) = all_20_0)
% 154.02/23.23  | | 
% 154.02/23.23  | | COMBINE_EQS: (11), (12) imply:
% 154.02/23.23  | |   (14)  all_20_1 = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REDUCE: (10), (14) imply:
% 154.02/23.23  | |   (15)  op(e3, e2) = all_20_0
% 154.02/23.23  | | 
% 154.02/23.23  | | BETA: splitting (13) gives:
% 154.02/23.23  | | 
% 154.02/23.23  | | Case 1:
% 154.02/23.23  | | | 
% 154.02/23.23  | | |   (16)   ~ (op(e3, e2) = all_20_0)
% 154.02/23.23  | | | 
% 154.02/23.23  | | | PRED_UNIFY: (15), (16) imply:
% 154.02/23.23  | | |   (17)  $false
% 154.02/23.23  | | | 
% 154.02/23.23  | | | CLOSE: (17) is inconsistent.
% 154.02/23.23  | | | 
% 154.02/23.23  | | Case 2:
% 154.02/23.23  | | | 
% 154.02/23.23  | | |   (18)  all_20_0 = e0
% 154.02/23.23  | | | 
% 154.02/23.23  | | | REDUCE: (8), (18) imply:
% 154.02/23.23  | | |   (19)  $false
% 154.02/23.23  | | | 
% 154.02/23.23  | | | CLOSE: (19) is inconsistent.
% 154.02/23.23  | | | 
% 154.02/23.23  | | End of split
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (20)   ~ (all_20_1 = e3) & op(e2, e1) = all_20_1 & $i(all_20_1)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (20) implies:
% 154.02/23.23  | |   (21)   ~ (all_20_1 = e3)
% 154.02/23.23  | |   (22)  op(e2, e1) = all_20_1
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (1), (4), (5), (21), (22) are inconsistent by sub-proof #858.
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #858 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (2)  op(e2, e1) = all_38_1
% 154.02/23.23    (3)   ~ (all_20_1 = e3)
% 154.02/23.23    (4)  op(e2, e1) = all_20_1
% 154.02/23.23    (5)  op(e2, e1) = e3
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | GROUND_INST: instantiating (1) with e3, all_38_1, e1, e2, simplifying with
% 154.02/23.23  |              (2), (5) gives:
% 154.02/23.23  |   (6)  all_38_1 = e3
% 154.02/23.23  | 
% 154.02/23.23  | GROUND_INST: instantiating (1) with all_20_1, all_38_1, e1, e2, simplifying
% 154.02/23.23  |              with (2), (4) gives:
% 154.02/23.23  |   (7)  all_38_1 = all_20_1
% 154.02/23.23  | 
% 154.02/23.23  | COMBINE_EQS: (6), (7) imply:
% 154.02/23.23  |   (8)  all_20_1 = e3
% 154.02/23.23  | 
% 154.02/23.23  | SIMP: (8) implies:
% 154.02/23.23  |   (9)  all_20_1 = e3
% 154.02/23.23  | 
% 154.02/23.23  | REDUCE: (3), (9) imply:
% 154.02/23.23  |   (10)  $false
% 154.02/23.23  | 
% 154.02/23.23  | CLOSE: (10) is inconsistent.
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #859 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (2)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 154.02/23.23             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.02/23.23           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 154.02/23.23           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 154.02/23.23           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 154.02/23.23           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 154.02/23.23           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 154.02/23.23           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 154.02/23.23           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.02/23.23    (3)  op(e3, e0) = all_52_12
% 154.02/23.23    (4)   ~ (all_52_12 = e3)
% 154.02/23.23    (5)   ~ (e1 = e0)
% 154.02/23.23    (6)  op(e0, e0) = e0
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (2) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (7)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 154.02/23.23  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.02/23.23  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (7) implies:
% 154.02/23.23  | |   (8)  op(e0, e0) = e1
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #1040.
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (9)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 154.02/23.23  | |            = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) =
% 154.02/23.23  | |          e0 & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 154.02/23.23  | |        (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 154.02/23.23  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 154.02/23.23  | |          e0 & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #1081.
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #860 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)   ~ (e3 = e1)
% 154.02/23.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (3)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.02/23.23             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.02/23.23           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 154.02/23.23           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 154.02/23.23           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 154.02/23.23           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 154.02/23.23    (4)   ~ (all_52_8 = e3)
% 154.02/23.23    (5)  op(e3, e1) = all_52_8
% 154.02/23.23    (6)  op(e3, e3) = e3
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (3) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (7)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.02/23.23  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.02/23.23  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (7) implies:
% 154.02/23.23  | |   (8)  op(e3, e1) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #1164.
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (9)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 154.02/23.23  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 154.02/23.23  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (9) implies:
% 154.02/23.23  | |   (10)  op(e3, e3) = e1
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (1), (2), (6), (10) are inconsistent by sub-proof #1178.
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #861 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)  op(e0, e0) = all_10_2
% 154.02/23.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (3)   ~ (e3 = e2)
% 154.02/23.23    (4)   ~ (all_52_8 = e3)
% 154.02/23.23    (5)   ~ (all_10_2 = e2)
% 154.02/23.23    (6)  op(e3, e1) = all_52_8
% 154.02/23.23    (7)  op(e3, e3) = e3
% 154.02/23.23    (8)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 154.02/23.23             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 154.02/23.23           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 154.02/23.23           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 154.02/23.23             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 154.02/23.23             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 154.02/23.23           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.02/23.23           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 154.02/23.23           $i(all_57_7) & $i(all_57_10))
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (8) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (9)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 154.02/23.23  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 154.02/23.23  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (9) implies:
% 154.02/23.23  | |   (10)  op(e3, e3) = e2
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (2), (3), (7), (10) are inconsistent by sub-proof #1085.
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (11)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 154.02/23.23  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.02/23.23  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 154.02/23.23  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 154.02/23.23  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 154.02/23.23  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (1), (2), (4), (5), (6), (11) are inconsistent by sub-proof #862.
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #862 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)  op(e0, e0) = all_10_2
% 154.02/23.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (3)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 154.02/23.23             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.02/23.23           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 154.02/23.23           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 154.02/23.23           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 154.02/23.23           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.02/23.23    (4)   ~ (all_52_8 = e3)
% 154.02/23.23    (5)   ~ (all_10_2 = e2)
% 154.02/23.23    (6)  op(e3, e1) = all_52_8
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (3) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 154.02/23.23  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.02/23.23  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (7) implies:
% 154.02/23.23  | |   (8)  op(e0, e0) = e2
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1097.
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 154.02/23.23  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 154.02/23.23  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (9) implies:
% 154.02/23.23  | |   (10)  op(e3, e1) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #1164.
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #863 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 154.02/23.23             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.02/23.23           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 154.02/23.23           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 154.02/23.23           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 154.02/23.23           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 154.02/23.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (3)  op(e3, e2) = all_52_4
% 154.02/23.23    (4)   ~ (all_52_4 = e3)
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (1) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (5)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 154.02/23.23  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.02/23.23  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (5) implies:
% 154.02/23.23  | |   (6)  op(e3, e2) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #1166.
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (7)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 154.02/23.23  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 154.02/23.23  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (7) implies:
% 154.02/23.23  | |   (8)  op(e3, e2) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1166.
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #864 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)   ~ (e3 = e1)
% 154.02/23.23    (2)  op(e2, e2) = e1
% 154.02/23.23    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (4)   ~ (e3 = e0)
% 154.02/23.23    (5)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 154.02/23.23             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.02/23.23           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 154.02/23.23           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 154.02/23.23             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 154.02/23.23             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 154.02/23.23    (6)  op(e0, e0) = e0
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (5) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (7)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 154.02/23.23  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.02/23.23  | |        op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (7) implies:
% 154.02/23.23  | |   (8)  op(e2, e2) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1136.
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (9)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 154.02/23.23  | |          e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 154.02/23.23  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (9) implies:
% 154.02/23.23  | |   (10)  op(e0, e0) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #1143.
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #865 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)  op(e1, e1) = all_4_2
% 154.02/23.23    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (3)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 154.02/23.23             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.02/23.23           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 154.02/23.23           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 154.02/23.23           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 154.02/23.23           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 154.02/23.23    (4)   ~ (e3 = e0)
% 154.02/23.23    (5)   ~ (all_4_2 = e3)
% 154.02/23.23    (6)  op(e0, e0) = e0
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (3) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (7)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 154.02/23.23  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.02/23.23  | |        all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (7) implies:
% 154.02/23.23  | |   (8)  op(e1, e1) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1078.
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (9)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 154.02/23.23  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 154.02/23.23  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (9) implies:
% 154.02/23.23  | |   (10)  op(e0, e0) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #1143.
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #866 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)  all_54_5 = e1 | all_54_5 = e0
% 154.02/23.23    (2)  all_54_5 = all_6_2
% 154.02/23.23    (3)   ~ (all_6_2 = e1)
% 154.02/23.23    (4)   ~ (all_6_2 = e0)
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (1) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (5)  all_54_5 = e1
% 154.02/23.23  | | 
% 154.02/23.23  | | COMBINE_EQS: (2), (5) imply:
% 154.02/23.23  | |   (6)  all_6_2 = e1
% 154.02/23.23  | | 
% 154.02/23.23  | | SIMP: (6) implies:
% 154.02/23.23  | |   (7)  all_6_2 = e1
% 154.02/23.23  | | 
% 154.02/23.23  | | REDUCE: (3), (7) imply:
% 154.02/23.23  | |   (8)  $false
% 154.02/23.23  | | 
% 154.02/23.23  | | CLOSE: (8) is inconsistent.
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (9)  all_54_5 = e0
% 154.02/23.23  | | 
% 154.02/23.23  | | COMBINE_EQS: (2), (9) imply:
% 154.02/23.23  | |   (10)  all_6_2 = e0
% 154.02/23.23  | | 
% 154.02/23.23  | | SIMP: (10) implies:
% 154.02/23.23  | |   (11)  all_6_2 = e0
% 154.02/23.23  | | 
% 154.02/23.23  | | REDUCE: (4), (11) imply:
% 154.02/23.23  | |   (12)  $false
% 154.02/23.23  | | 
% 154.02/23.23  | | CLOSE: (12) is inconsistent.
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #867 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)   ~ (e3 = e1)
% 154.02/23.23    (2)  all_56_6 = e2
% 154.02/23.23    (3)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 154.02/23.23         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 154.02/23.23    (4)   ~ (e2 = e0)
% 154.02/23.23    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (6)   ~ (e3 = e0)
% 154.02/23.23    (7)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 154.02/23.23         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.02/23.23    (8)  op(e3, e3) = e1
% 154.02/23.23    (9)   ~ (e1 = e0)
% 154.02/23.23    (10)   ~ (e3 = e2)
% 154.02/23.23    (11)  all_56_12 = e2
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (3) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (12)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 154.02/23.23  | |           e3)
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12) are
% 154.02/23.23  | |            inconsistent by sub-proof #870.
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (13)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 154.02/23.23  | |           e3)
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (2), (10), (11), (13) are inconsistent by sub-proof #868.
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #868 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 154.02/23.23    (2)  all_56_6 = e2
% 154.02/23.23    (3)   ~ (e3 = e2)
% 154.02/23.23    (4)  all_56_12 = e2
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (1) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (5)  all_56_6 = e3 & op(e1, e3) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (5) implies:
% 154.02/23.23  | |   (6)  all_56_6 = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #1057.
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (7)  all_56_12 = e3 & op(e0, e3) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (7) implies:
% 154.02/23.23  | |   (8)  all_56_12 = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #869.
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #869 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)  all_56_12 = e3
% 154.02/23.23    (2)  all_56_12 = e2
% 154.02/23.23    (3)   ~ (e3 = e2)
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | COMBINE_EQS: (1), (2) imply:
% 154.02/23.23  |   (4)  e3 = e2
% 154.02/23.23  | 
% 154.02/23.23  | SIMP: (4) implies:
% 154.02/23.23  |   (5)  e3 = e2
% 154.02/23.23  | 
% 154.02/23.23  | REDUCE: (3), (5) imply:
% 154.02/23.23  |   (6)  $false
% 154.02/23.23  | 
% 154.02/23.23  | CLOSE: (6) is inconsistent.
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #870 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)   ~ (e3 = e1)
% 154.02/23.23    (2)  all_56_6 = e2
% 154.02/23.23    (3)   ~ (e2 = e0)
% 154.02/23.23    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (5)   ~ (e3 = e0)
% 154.02/23.23    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 154.02/23.23         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.02/23.23    (7)  op(e3, e3) = e1
% 154.02/23.23    (8)   ~ (e1 = e0)
% 154.02/23.23    (9)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 154.02/23.23    (10)  all_56_12 = e2
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | BETA: splitting (9) gives:
% 154.02/23.23  | 
% 154.02/23.23  | Case 1:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (11)  all_56_0 = e3 & op(e3, e3) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (11) implies:
% 154.02/23.23  | |   (12)  op(e3, e3) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | REF_CLOSE: (1), (4), (7), (12) are inconsistent by sub-proof #1178.
% 154.02/23.23  | | 
% 154.02/23.23  | Case 2:
% 154.02/23.23  | | 
% 154.02/23.23  | |   (13)  all_56_2 = e3 & op(e2, e3) = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | ALPHA: (13) implies:
% 154.02/23.23  | |   (14)  all_56_2 = e3
% 154.02/23.23  | | 
% 154.02/23.23  | | BETA: splitting (6) gives:
% 154.02/23.23  | | 
% 154.02/23.23  | | Case 1:
% 154.02/23.23  | | | 
% 154.02/23.23  | | |   (15)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 154.02/23.23  | | |           e0)
% 154.02/23.23  | | | 
% 154.02/23.23  | | | REF_CLOSE: (4), (5), (7), (8), (14), (15) are inconsistent by sub-proof
% 154.02/23.23  | | |            #931.
% 154.02/23.23  | | | 
% 154.02/23.23  | | Case 2:
% 154.02/23.23  | | | 
% 154.02/23.23  | | |   (16)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 154.02/23.23  | | |           e0)
% 154.02/23.23  | | | 
% 154.02/23.23  | | | BETA: splitting (16) gives:
% 154.02/23.23  | | | 
% 154.02/23.23  | | | Case 1:
% 154.02/23.23  | | | | 
% 154.02/23.23  | | | |   (17)  all_56_6 = e0 & op(e1, e3) = e0
% 154.02/23.23  | | | | 
% 154.02/23.23  | | | | REF_CLOSE: (2), (3), (17) are inconsistent by sub-proof #1054.
% 154.02/23.23  | | | | 
% 154.02/23.23  | | | Case 2:
% 154.02/23.23  | | | | 
% 154.02/23.23  | | | |   (18)  all_56_12 = e0 & op(e0, e3) = e0
% 154.02/23.23  | | | | 
% 154.02/23.23  | | | | REF_CLOSE: (3), (10), (18) are inconsistent by sub-proof #871.
% 154.02/23.23  | | | | 
% 154.02/23.23  | | | End of split
% 154.02/23.23  | | | 
% 154.02/23.23  | | End of split
% 154.02/23.23  | | 
% 154.02/23.23  | End of split
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #871 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)  all_56_12 = e0 & op(e0, e3) = e0
% 154.02/23.23    (2)  all_56_12 = e2
% 154.02/23.23    (3)   ~ (e2 = e0)
% 154.02/23.23  
% 154.02/23.23  Begin of proof
% 154.02/23.23  | 
% 154.02/23.23  | ALPHA: (1) implies:
% 154.02/23.23  |   (4)  all_56_12 = e0
% 154.02/23.23  | 
% 154.02/23.23  | COMBINE_EQS: (2), (4) imply:
% 154.02/23.23  |   (5)  e2 = e0
% 154.02/23.23  | 
% 154.02/23.23  | REDUCE: (3), (5) imply:
% 154.02/23.23  |   (6)  $false
% 154.02/23.23  | 
% 154.02/23.23  | CLOSE: (6) is inconsistent.
% 154.02/23.23  | 
% 154.02/23.23  End of proof
% 154.02/23.23  
% 154.02/23.23  Sub-proof #872 shows that the following formulas are inconsistent:
% 154.02/23.23  ----------------------------------------------------------------
% 154.02/23.23    (1)  op(e0, e1) = all_52_11
% 154.02/23.23    (2)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 154.02/23.23         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 154.02/23.23    (3)   ~ (all_52_7 = all_52_11)
% 154.02/23.23    (4)   ~ (e3 = e1)
% 154.02/23.23    (5)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 154.02/23.23         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 154.02/23.23    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 154.02/23.23         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 154.02/23.23    (7)  op(e3, e1) = all_34_1
% 154.02/23.23    (8)   ~ (all_52_11 = all_10_2)
% 154.02/23.23    (9)  all_56_6 = e2
% 154.02/23.23    (10)   ~ (all_52_2 = all_52_6)
% 154.02/23.23    (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 154.02/23.23          (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 154.02/23.23    (12)  op(e0, e0) = all_10_2
% 154.02/23.23    (13)  op(e3, e2) = all_52_4
% 154.02/23.23    (14)   ~ (all_52_4 = all_52_7)
% 154.02/23.23    (15)  op(e0, e2) = all_52_7
% 154.02/23.23    (16)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.02/23.23    (17)   ~ (all_52_3 = all_52_7)
% 154.02/23.23    (18)  all_54_14 = all_52_11
% 154.02/23.23    (19)   ~ (all_52_4 = e2)
% 154.02/23.23    (20)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.02/23.23          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 154.02/23.23    (21)  op(e1, e1) = all_4_2
% 154.02/23.23    (22)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 154.02/23.23          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 154.02/23.23    (23)   ~ (all_52_4 = all_52_12)
% 154.02/23.23    (24)   ~ (e2 = e0)
% 154.02/23.23    (25)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 154.02/23.23          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 154.02/23.23    (26)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.23            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.23    (27)  all_54_1 = all_52_4
% 154.02/23.23    (28)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 154.02/23.23          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 154.02/23.23    (29)  all_56_4 = e2
% 154.02/23.23    (30)  ( ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0 & op(e3, e1) =
% 154.02/23.23            all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3,
% 154.02/23.23              e1) = all_22_1 & $i(all_22_1))
% 154.02/23.23    (31)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.02/23.23    (32)   ~ (all_52_3 = e2)
% 154.02/23.23    (33)   ~ (all_52_3 = all_52_11)
% 154.02/23.23    (34)  all_54_10 = all_4_2
% 154.02/23.23    (35)  op(e0, e0) = e2
% 154.02/23.23    (36)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 154.02/23.23          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 154.02/23.23    (37)   ~ (all_52_13 = e2)
% 154.02/23.23    (38)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 154.02/23.23    (39)  op(e3, e0) = all_52_12
% 154.02/23.23    (40)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 154.02/23.23          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.02/23.23    (41)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 154.02/23.23          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 154.02/23.23    (42)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 154.02/23.24          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 154.02/23.24    (43)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 154.02/23.24          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 154.02/23.24    (44)  op(e3, e3) = e1
% 154.02/23.24    (45)  op(e1, e2) = all_52_6
% 154.02/23.24    (46)  op(e2, e0) = all_52_13
% 154.02/23.24    (47)   ~ (all_52_1 = all_52_3)
% 154.02/23.24    (48)   ~ (all_52_9 = e2)
% 154.02/23.24    (49)   ~ (all_52_3 = e1)
% 154.02/23.24    (50)  op(e0, e3) = all_52_3
% 154.02/23.24    (51)   ~ (all_52_7 = e2)
% 154.02/23.24    (52)   ~ (all_4_2 = e2)
% 154.02/23.24    (53)  all_54_12 = all_52_3
% 154.02/23.24    (54)   ~ (all_52_4 = all_52_6)
% 154.02/23.24    (55)  op(e2, e1) = all_52_9
% 154.02/23.24    (56)   ~ (e1 = e0)
% 154.02/23.24    (57)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 154.02/23.24              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 154.02/23.24            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 154.02/23.24                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 154.02/23.24              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.02/23.24          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 154.02/23.24              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.02/23.24            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 154.02/23.24                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 154.02/23.24              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.02/23.24          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 154.02/23.24              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.02/23.24            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 154.02/23.24                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 154.02/23.24              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.02/23.24          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 154.02/23.24              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.02/23.24            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 154.02/23.24                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 154.02/23.24                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.02/23.24                $i(all_57_14))))
% 154.02/23.24    (58)  op(e3, e1) = e2
% 154.02/23.24    (59)   ~ (all_52_4 = e1)
% 154.02/23.24    (60)   ~ (all_4_2 = e3)
% 154.02/23.24    (61)   ~ (e3 = e2)
% 154.02/23.24    (62)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.02/23.24          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.02/23.24    (63)   ~ (all_52_2 = e1)
% 154.02/23.24    (64)   ~ (all_52_6 = all_52_7)
% 154.02/23.24    (65)   ~ (e2 = e1)
% 154.02/23.24    (66)   ~ (all_52_11 = all_4_2)
% 154.02/23.24    (67)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.02/23.24    (68)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.02/23.24          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.02/23.24    (69)  op(e1, e3) = all_52_2
% 154.02/23.24    (70)   ~ (all_52_11 = e2)
% 154.02/23.24    (71)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 154.02/23.24              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.02/23.24            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 154.02/23.24            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 154.02/23.24            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 154.02/23.24            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 154.02/23.24            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 154.02/23.24            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.02/23.24            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 154.02/23.24            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 154.02/23.24            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 154.02/23.24            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 154.02/23.24            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.02/23.24            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 154.02/23.24            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 154.02/23.24            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.02/23.24            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 154.02/23.24            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 154.02/23.24            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.24            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 154.02/23.24            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 154.02/23.24            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.02/23.24            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 154.02/23.24            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 154.02/23.24            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 154.02/23.24            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 154.02/23.24            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 154.02/23.24            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 154.02/23.24            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.24            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 154.02/23.24            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 154.02/23.24            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 154.02/23.24            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 154.02/23.24            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 154.02/23.24            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.24            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 154.02/23.24            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.24            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 154.02/23.24            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 154.02/23.24            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.24            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 154.02/23.24            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 154.02/23.24            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 154.02/23.24            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 154.02/23.24            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 154.02/23.24            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 154.02/23.24            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 154.02/23.24            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 154.02/23.24              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 154.02/23.24            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 154.02/23.24            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 154.02/23.24              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 154.02/23.24            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 154.02/23.24            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 154.02/23.24                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 154.02/23.24                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.24                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 154.02/23.24                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 154.02/23.24                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 154.02/23.24                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 154.02/23.24                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 154.02/23.24              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 154.02/23.24                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 154.02/23.24                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.02/23.24                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 154.02/23.24                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 154.02/23.24                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 154.02/23.24                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.24                $i(all_57_7))))
% 154.02/23.24    (72)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 154.02/23.24          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 154.02/23.24    (73)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.02/23.24          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 154.02/23.24            e1)
% 154.02/23.24    (74)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 154.02/23.24          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 154.02/23.24    (75)  op(e2, e3) = all_52_1
% 154.02/23.24    (76)   ~ (all_52_1 = e2)
% 154.02/23.24  
% 154.02/23.24  Begin of proof
% 154.02/23.24  | 
% 154.02/23.24  | BETA: splitting (30) gives:
% 154.02/23.24  | 
% 154.02/23.24  | Case 1:
% 154.02/23.24  | | 
% 154.02/23.24  | |   (77)   ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0 & op(e3, e1) =
% 154.02/23.24  | |         all_22_1 & $i(all_22_0) & $i(all_22_1)
% 154.02/23.24  | | 
% 154.02/23.24  | | ALPHA: (77) implies:
% 154.02/23.24  | |   (78)  op(e3, e1) = all_22_1
% 154.02/23.24  | | 
% 154.02/23.24  | | BETA: splitting (57) gives:
% 154.02/23.24  | | 
% 154.02/23.24  | | Case 1:
% 154.02/23.24  | | | 
% 154.02/23.24  | | |   (79)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 154.02/23.24  | | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 154.02/23.24  | | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 154.02/23.24  | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14)))
% 154.02/23.24  | | |           & ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) &
% 154.02/23.24  | | |               op(e0, e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2
% 154.02/23.24  | | |           & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 154.02/23.24  | | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10)))
% 154.02/23.24  | | |           & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) &
% 154.02/23.24  | | |               op(e1, e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 &
% 154.02/23.24  | | |               op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 154.02/23.24  | | |               all_57_15 & $i(all_57_15))))
% 154.02/23.24  | | | 
% 154.02/23.24  | | | BETA: splitting (79) gives:
% 154.02/23.24  | | | 
% 154.02/23.24  | | | Case 1:
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | |   (80)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3)
% 154.02/23.24  | | | |             = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 154.02/23.24  | | | |             $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 154.02/23.24  | | | |             (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14)))
% 154.02/23.24  | | | |         & ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) &
% 154.02/23.24  | | | |             op(e0, e0) = all_57_15 & $i(all_57_15)))
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | | ALPHA: (80) implies:
% 154.02/23.24  | | | |   (81)  op(e3, e3) = e3
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | | REF_CLOSE: (4), (26), (44), (81) are inconsistent by sub-proof #1178.
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | Case 2:
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | |   (82)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2)
% 154.02/23.24  | | | |             = e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.02/23.24  | | | |             $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 154.02/23.24  | | | |             (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14)))
% 154.02/23.24  | | | |         & ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) &
% 154.02/23.24  | | | |             op(e0, e0) = all_57_15 & $i(all_57_15)))
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | | ALPHA: (82) implies:
% 154.02/23.24  | | | |   (83)  op(e2, e2) = e2
% 154.02/23.24  | | | |   (84)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) &
% 154.02/23.24  | | | |           op(e0, e0) = all_57_15 & $i(all_57_15))
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | | BETA: splitting (84) gives:
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | | Case 1:
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | |   (85)  all_57_5 = e0 & op(e0, e2) = e0
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | ALPHA: (85) implies:
% 154.02/23.24  | | | | |   (86)  all_57_5 = e0
% 154.02/23.24  | | | | |   (87)  op(e0, e2) = e0
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | GROUND_INST: instantiating (26) with all_52_7, e0, e2, e0, simplifying
% 154.02/23.24  | | | | |              with (15), (87) gives:
% 154.02/23.24  | | | | |   (88)  all_52_7 = e0
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | GROUND_INST: instantiating (26) with e2, all_34_1, e1, e3, simplifying
% 154.02/23.24  | | | | |              with (7), (58) gives:
% 154.02/23.24  | | | | |   (89)  all_34_1 = e2
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | GROUND_INST: instantiating (26) with all_22_1, all_34_1, e1, e3,
% 154.02/23.24  | | | | |              simplifying with (7), (78) gives:
% 154.02/23.24  | | | | |   (90)  all_34_1 = all_22_1
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | COMBINE_EQS: (89), (90) imply:
% 154.02/23.24  | | | | |   (91)  all_22_1 = e2
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | SIMP: (91) implies:
% 154.02/23.24  | | | | |   (92)  all_22_1 = e2
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REDUCE: (17), (88) imply:
% 154.02/23.24  | | | | |   (93)   ~ (all_52_3 = e0)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REDUCE: (14), (88) imply:
% 154.02/23.24  | | | | |   (94)   ~ (all_52_4 = e0)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REDUCE: (64), (88) imply:
% 154.02/23.24  | | | | |   (95)   ~ (all_52_6 = e0)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REDUCE: (3), (88) imply:
% 154.02/23.24  | | | | |   (96)   ~ (all_52_11 = e0)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | SIMP: (96) implies:
% 154.02/23.24  | | | | |   (97)   ~ (all_52_11 = e0)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REDUCE: (51), (88) imply:
% 154.02/23.24  | | | | |   (98)   ~ (e2 = e0)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 154.02/23.24  | | | | |            (16), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 154.02/23.24  | | | | |            (27), (28), (29), (31), (32), (33), (34), (35), (36), (37),
% 154.02/23.24  | | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 154.02/23.24  | | | | |            (48), (49), (50), (52), (53), (54), (55), (56), (57), (59),
% 154.02/23.24  | | | | |            (60), (62), (63), (65), (66), (67), (68), (69), (70), (71),
% 154.02/23.24  | | | | |            (72), (73), (74), (75), (76), (78), (83), (86), (92), (93),
% 154.02/23.24  | | | | |            (94), (95), (97) are inconsistent by sub-proof #874.
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | Case 2:
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | |   (99)   ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | ALPHA: (99) implies:
% 154.02/23.24  | | | | |   (100)   ~ (all_57_15 = e2)
% 154.02/23.24  | | | | |   (101)  op(e0, e0) = all_57_15
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REF_CLOSE: (26), (35), (100), (101) are inconsistent by sub-proof
% 154.02/23.24  | | | | |            #901.
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | End of split
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | End of split
% 154.02/23.24  | | | 
% 154.02/23.24  | | Case 2:
% 154.02/23.24  | | | 
% 154.02/23.24  | | |   (102)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1)
% 154.02/23.24  | | |                = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.02/23.24  | | |                $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 154.02/23.24  | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12)))
% 154.02/23.24  | | |            & ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) &
% 154.02/23.24  | | |                op(e0, e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0
% 154.02/23.24  | | |            & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 154.02/23.24  | | |                (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10)))
% 154.02/23.24  | | |            & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 154.02/23.24  | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1
% 154.02/23.24  | | |                & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 154.02/23.24  | | |                all_57_14 & $i(all_57_14))))
% 154.02/23.24  | | | 
% 154.02/23.24  | | | REF_CLOSE: (7), (24), (26), (35), (44), (58), (61), (78), (102) are
% 154.02/23.24  | | |            inconsistent by sub-proof #873.
% 154.02/23.24  | | | 
% 154.02/23.24  | | End of split
% 154.02/23.24  | | 
% 154.02/23.24  | Case 2:
% 154.02/23.24  | | 
% 154.02/23.24  | |   (103)   ~ (all_22_1 = e0) & op(e3, e1) = all_22_1 & $i(all_22_1)
% 154.02/23.24  | | 
% 154.02/23.24  | | ALPHA: (103) implies:
% 154.02/23.24  | |   (104)   ~ (all_22_1 = e0)
% 154.02/23.24  | |   (105)  op(e3, e1) = all_22_1
% 154.02/23.24  | | 
% 154.02/23.24  | | BETA: splitting (57) gives:
% 154.02/23.24  | | 
% 154.02/23.24  | | Case 1:
% 154.02/23.24  | | | 
% 154.02/23.24  | | |   (106)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3)
% 154.02/23.24  | | |                = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 154.02/23.24  | | |                $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 154.02/23.24  | | |                (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14)))
% 154.02/23.24  | | |            & ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) &
% 154.02/23.24  | | |                op(e0, e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2
% 154.02/23.24  | | |            & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 154.02/23.24  | | |                (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10)))
% 154.02/23.24  | | |            & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) &
% 154.02/23.24  | | |                op(e1, e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0
% 154.02/23.24  | | |                & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 154.02/23.24  | | |                all_57_15 & $i(all_57_15))))
% 154.02/23.24  | | | 
% 154.02/23.24  | | | BETA: splitting (106) gives:
% 154.02/23.24  | | | 
% 154.02/23.24  | | | Case 1:
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | |   (107)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3)
% 154.02/23.24  | | | |              = e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 154.02/23.24  | | | |              $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 154.02/23.24  | | | |              (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14)))
% 154.02/23.24  | | | |          & ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) &
% 154.02/23.24  | | | |              op(e0, e0) = all_57_15 & $i(all_57_15)))
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | | ALPHA: (107) implies:
% 154.02/23.24  | | | |   (108)  op(e3, e3) = e3
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | | REF_CLOSE: (4), (26), (44), (108) are inconsistent by sub-proof #1178.
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | Case 2:
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | |   (109)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2)
% 154.02/23.24  | | | |              = e3) | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.02/23.24  | | | |              $i(all_57_10))) & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~
% 154.02/23.24  | | | |              (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14)))
% 154.02/23.24  | | | |          & ((all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) &
% 154.02/23.24  | | | |              op(e0, e0) = all_57_15 & $i(all_57_15)))
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | | ALPHA: (109) implies:
% 154.02/23.24  | | | |   (110)  op(e2, e2) = e2
% 154.02/23.24  | | | |   (111)  (all_57_5 = e0 & op(e0, e2) = e0) | ( ~ (all_57_15 = e2) &
% 154.02/23.24  | | | |            op(e0, e0) = all_57_15 & $i(all_57_15))
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | | BETA: splitting (111) gives:
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | | Case 1:
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | |   (112)  all_57_5 = e0 & op(e0, e2) = e0
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | ALPHA: (112) implies:
% 154.02/23.24  | | | | |   (113)  all_57_5 = e0
% 154.02/23.24  | | | | |   (114)  op(e0, e2) = e0
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | GROUND_INST: instantiating (26) with all_52_7, e0, e2, e0, simplifying
% 154.02/23.24  | | | | |              with (15), (114) gives:
% 154.02/23.24  | | | | |   (115)  all_52_7 = e0
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | GROUND_INST: instantiating (26) with e2, all_34_1, e1, e3, simplifying
% 154.02/23.24  | | | | |              with (7), (58) gives:
% 154.02/23.24  | | | | |   (116)  all_34_1 = e2
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | GROUND_INST: instantiating (26) with all_22_1, all_34_1, e1, e3,
% 154.02/23.24  | | | | |              simplifying with (7), (105) gives:
% 154.02/23.24  | | | | |   (117)  all_34_1 = all_22_1
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | COMBINE_EQS: (116), (117) imply:
% 154.02/23.24  | | | | |   (118)  all_22_1 = e2
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REDUCE: (17), (115) imply:
% 154.02/23.24  | | | | |   (119)   ~ (all_52_3 = e0)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REDUCE: (14), (115) imply:
% 154.02/23.24  | | | | |   (120)   ~ (all_52_4 = e0)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REDUCE: (64), (115) imply:
% 154.02/23.24  | | | | |   (121)   ~ (all_52_6 = e0)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REDUCE: (3), (115) imply:
% 154.02/23.24  | | | | |   (122)   ~ (all_52_11 = e0)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | SIMP: (122) implies:
% 154.02/23.24  | | | | |   (123)   ~ (all_52_11 = e0)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 154.02/23.24  | | | | |            (16), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 154.02/23.24  | | | | |            (27), (28), (29), (31), (32), (33), (34), (35), (36), (37),
% 154.02/23.24  | | | | |            (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 154.02/23.24  | | | | |            (48), (49), (50), (52), (53), (54), (55), (56), (57), (59),
% 154.02/23.24  | | | | |            (60), (62), (63), (65), (66), (67), (68), (69), (70), (71),
% 154.02/23.24  | | | | |            (72), (73), (74), (75), (76), (105), (110), (113), (118),
% 154.02/23.24  | | | | |            (119), (120), (121), (123) are inconsistent by sub-proof
% 154.02/23.24  | | | | |            #874.
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | Case 2:
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | |   (124)   ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | ALPHA: (124) implies:
% 154.02/23.24  | | | | |   (125)   ~ (all_57_15 = e2)
% 154.02/23.24  | | | | |   (126)  op(e0, e0) = all_57_15
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | | REF_CLOSE: (26), (35), (125), (126) are inconsistent by sub-proof
% 154.02/23.24  | | | | |            #901.
% 154.02/23.24  | | | | | 
% 154.02/23.24  | | | | End of split
% 154.02/23.24  | | | | 
% 154.02/23.24  | | | End of split
% 154.02/23.24  | | | 
% 154.02/23.24  | | Case 2:
% 154.02/23.24  | | | 
% 154.02/23.24  | | |   (127)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1)
% 154.02/23.24  | | |                = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.02/23.24  | | |                $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 154.02/23.24  | | |                (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12)))
% 154.02/23.24  | | |            & ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) &
% 154.02/23.24  | | |                op(e0, e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0
% 154.02/23.24  | | |            & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 154.02/23.24  | | |                (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10)))
% 154.02/23.24  | | |            & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 154.02/23.24  | | |                op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1
% 154.02/23.24  | | |                & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 154.02/23.24  | | |                all_57_14 & $i(all_57_14))))
% 154.02/23.24  | | | 
% 154.02/23.24  | | | REF_CLOSE: (7), (24), (26), (35), (44), (58), (61), (105), (127) are
% 154.02/23.24  | | |            inconsistent by sub-proof #873.
% 154.02/23.24  | | | 
% 154.02/23.24  | | End of split
% 154.02/23.24  | | 
% 154.02/23.24  | End of split
% 154.02/23.24  | 
% 154.02/23.24  End of proof
% 154.02/23.24  
% 154.02/23.24  Sub-proof #873 shows that the following formulas are inconsistent:
% 154.02/23.24  ----------------------------------------------------------------
% 154.02/23.24    (1)  op(e3, e1) = all_34_1
% 154.02/23.24    (2)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 154.02/23.24             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.02/23.24           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 154.02/23.24               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 154.02/23.24             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.02/23.24         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 154.02/23.24             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.02/23.24           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 154.02/23.24               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 154.02/23.24             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 154.02/23.24    (3)   ~ (e2 = e0)
% 154.02/23.24    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.24           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.24    (5)  op(e0, e0) = e2
% 154.02/23.24    (6)  op(e3, e1) = all_22_1
% 154.02/23.24    (7)  op(e3, e3) = e1
% 154.02/23.24    (8)  op(e3, e1) = e2
% 154.02/23.24    (9)   ~ (e3 = e2)
% 154.02/23.24  
% 154.02/23.24  Begin of proof
% 154.02/23.24  | 
% 154.02/23.24  | BETA: splitting (2) gives:
% 154.02/23.24  | 
% 154.02/23.24  | Case 1:
% 154.02/23.24  | | 
% 154.02/23.24  | |   (10)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 154.02/23.24  | |             e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.02/23.24  | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 154.02/23.24  | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 154.02/23.24  | |         ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) & op(e0,
% 154.02/23.24  | |               e0) = all_57_15 & $i(all_57_15)))
% 154.02/23.24  | | 
% 154.02/23.24  | | ALPHA: (10) implies:
% 154.02/23.24  | |   (11)  (all_57_6 = e3 & op(e3, e1) = e3) | ( ~ (all_57_10 = e1) & op(e3,
% 154.02/23.24  | |             e3) = all_57_10 & $i(all_57_10))
% 154.02/23.24  | | 
% 154.02/23.24  | | BETA: splitting (11) gives:
% 154.02/23.24  | | 
% 154.02/23.24  | | Case 1:
% 154.02/23.24  | | | 
% 154.02/23.24  | | |   (12)  all_57_6 = e3 & op(e3, e1) = e3
% 154.02/23.24  | | | 
% 154.02/23.24  | | | ALPHA: (12) implies:
% 154.02/23.24  | | |   (13)  op(e3, e1) = e3
% 154.02/23.24  | | | 
% 154.02/23.24  | | | REF_CLOSE: (1), (4), (6), (8), (9), (13) are inconsistent by sub-proof
% 154.02/23.24  | | |            #912.
% 154.02/23.24  | | | 
% 154.02/23.24  | | Case 2:
% 154.02/23.24  | | | 
% 154.02/23.24  | | |   (14)   ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10)
% 154.02/23.24  | | | 
% 154.02/23.24  | | | ALPHA: (14) implies:
% 154.02/23.24  | | |   (15)   ~ (all_57_10 = e1)
% 154.02/23.24  | | |   (16)  op(e3, e3) = all_57_10
% 154.02/23.24  | | | 
% 154.02/23.24  | | | REF_CLOSE: (4), (7), (15), (16) are inconsistent by sub-proof #893.
% 154.02/23.24  | | | 
% 154.02/23.24  | | End of split
% 154.02/23.24  | | 
% 154.02/23.24  | Case 2:
% 154.02/23.24  | | 
% 154.02/23.24  | |   (17)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) =
% 154.02/23.24  | |             e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.02/23.24  | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 154.02/23.24  | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 154.02/23.24  | |         ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 154.02/23.24  | |               e1) = all_57_14 & $i(all_57_14)))
% 154.02/23.24  | | 
% 154.02/23.24  | | ALPHA: (17) implies:
% 154.02/23.24  | |   (18)  op(e0, e0) = e0
% 154.02/23.24  | | 
% 154.02/23.24  | | REF_CLOSE: (3), (4), (5), (18) are inconsistent by sub-proof #1043.
% 154.02/23.24  | | 
% 154.02/23.24  | End of split
% 154.02/23.24  | 
% 154.02/23.24  End of proof
% 154.02/23.24  
% 154.02/23.24  Sub-proof #874 shows that the following formulas are inconsistent:
% 154.02/23.24  ----------------------------------------------------------------
% 154.02/23.24    (1)  op(e0, e1) = all_52_11
% 154.02/23.24    (2)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3 & op(e2, e1) = e3) |
% 154.02/23.24         (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 154.02/23.24    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 154.02/23.24         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 154.02/23.24    (4)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 154.02/23.24         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 154.02/23.24    (5)  op(e3, e1) = all_34_1
% 154.02/23.24    (6)   ~ (all_52_11 = all_10_2)
% 154.02/23.24    (7)  all_56_6 = e2
% 154.02/23.24    (8)   ~ (all_52_2 = all_52_6)
% 154.02/23.24    (9)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 154.02/23.24         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 154.02/23.24    (10)  op(e0, e0) = all_10_2
% 154.02/23.24    (11)  op(e3, e2) = all_52_4
% 154.02/23.24    (12)  all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.02/23.24    (13)  all_54_14 = all_52_11
% 154.02/23.24    (14)   ~ (all_52_4 = e2)
% 154.02/23.24    (15)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.02/23.24          (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 154.02/23.24    (16)  op(e1, e1) = all_4_2
% 154.02/23.24    (17)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 154.02/23.24          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 154.02/23.24    (18)   ~ (all_52_4 = all_52_12)
% 154.02/23.24    (19)   ~ (e2 = e0)
% 154.02/23.24    (20)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 154.02/23.24          (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 154.02/23.24    (21)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.24            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.24    (22)  all_54_1 = all_52_4
% 154.02/23.24    (23)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 154.02/23.24          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 154.02/23.24    (24)  all_56_4 = e2
% 154.02/23.24    (25)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.02/23.24    (26)   ~ (all_52_3 = e2)
% 154.02/23.24    (27)   ~ (all_52_3 = all_52_11)
% 154.02/23.24    (28)  all_54_10 = all_4_2
% 154.02/23.24    (29)  op(e0, e0) = e2
% 154.02/23.24    (30)  op(e3, e1) = all_22_1
% 154.02/23.24    (31)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 154.02/23.24          (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 154.02/23.24    (32)   ~ (all_52_13 = e2)
% 154.02/23.24    (33)  all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 154.02/23.24    (34)  op(e3, e0) = all_52_12
% 154.02/23.24    (35)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 154.02/23.24          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.02/23.24    (36)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 = e1 & op(e2, e0) = e1) |
% 154.02/23.24          (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 154.02/23.24    (37)   ~ (all_52_11 = e0)
% 154.02/23.24    (38)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 154.02/23.24          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 154.02/23.24    (39)   ~ (all_52_6 = e0)
% 154.02/23.24    (40)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 154.02/23.24          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 154.02/23.24    (41)  op(e3, e3) = e1
% 154.02/23.24    (42)  op(e1, e2) = all_52_6
% 154.02/23.24    (43)  op(e2, e0) = all_52_13
% 154.02/23.24    (44)   ~ (all_52_1 = all_52_3)
% 154.02/23.24    (45)   ~ (all_52_9 = e2)
% 154.02/23.24    (46)   ~ (all_52_3 = e1)
% 154.02/23.24    (47)  op(e0, e3) = all_52_3
% 154.02/23.24    (48)   ~ (all_4_2 = e2)
% 154.02/23.24    (49)  all_54_12 = all_52_3
% 154.02/23.24    (50)   ~ (all_52_4 = all_52_6)
% 154.02/23.24    (51)  op(e2, e2) = e2
% 154.02/23.24    (52)  op(e2, e1) = all_52_9
% 154.02/23.24    (53)   ~ (e1 = e0)
% 154.02/23.25    (54)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 154.02/23.25              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 154.02/23.25            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 154.02/23.25                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 154.02/23.25              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.02/23.25          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 154.02/23.25              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.02/23.25            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 154.02/23.25                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 154.02/23.25              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.02/23.25          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 154.02/23.25              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.02/23.25            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 154.02/23.25                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 154.02/23.25              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.02/23.25          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 154.02/23.25              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.02/23.25            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 154.02/23.25                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 154.02/23.25                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.02/23.25                $i(all_57_14))))
% 154.02/23.25    (55)  all_57_5 = e0
% 154.02/23.25    (56)   ~ (all_52_4 = e1)
% 154.02/23.25    (57)   ~ (all_4_2 = e3)
% 154.02/23.25    (58)  all_22_1 = e2
% 154.02/23.25    (59)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.02/23.25          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.02/23.25    (60)   ~ (all_52_3 = e0)
% 154.02/23.25    (61)   ~ (all_52_2 = e1)
% 154.02/23.25    (62)   ~ (e2 = e1)
% 154.02/23.25    (63)   ~ (all_52_11 = all_4_2)
% 154.02/23.25    (64)   ~ (all_52_4 = e0)
% 154.02/23.25    (65)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.02/23.25    (66)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.02/23.25          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.02/23.25    (67)  op(e1, e3) = all_52_2
% 154.02/23.25    (68)   ~ (all_52_11 = e2)
% 154.02/23.25    (69)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 154.02/23.25              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.02/23.25            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 154.02/23.25            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 154.02/23.25            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 154.02/23.25            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 154.02/23.25            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 154.02/23.25            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.02/23.25            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 154.02/23.25            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 154.02/23.25            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 154.02/23.25            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 154.02/23.25            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.02/23.25            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 154.02/23.25            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 154.02/23.25            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.02/23.25            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 154.02/23.25            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 154.02/23.25            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.25            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 154.02/23.25            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 154.02/23.25            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.02/23.25            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 154.02/23.25            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 154.02/23.25            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 154.02/23.25            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 154.02/23.25            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 154.02/23.25            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 154.02/23.25            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.25            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 154.02/23.25            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 154.02/23.25            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 154.02/23.25            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 154.02/23.25            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 154.02/23.25            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.25            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 154.02/23.25            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.25            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 154.02/23.25            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 154.02/23.25            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.25            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 154.02/23.25            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 154.02/23.25            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 154.02/23.25            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 154.02/23.25            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 154.02/23.25            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 154.02/23.25            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 154.02/23.25            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 154.02/23.25              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 154.02/23.25            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 154.02/23.25            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 154.02/23.25              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 154.02/23.25            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 154.02/23.25            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 154.02/23.25                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 154.02/23.25                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.25                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 154.02/23.25                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 154.02/23.25                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 154.02/23.25                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 154.02/23.25                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 154.02/23.25              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 154.02/23.25                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 154.02/23.25                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.02/23.25                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 154.02/23.25                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 154.02/23.25                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 154.02/23.25                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.25                $i(all_57_7))))
% 154.02/23.25    (70)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 154.02/23.25          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 154.02/23.25    (71)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.02/23.25          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 154.02/23.25            e1)
% 154.02/23.25    (72)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3 & op(e1, e2) = e3) |
% 154.02/23.25          (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 = e3 & op(e1, e0) = e3)
% 154.02/23.25    (73)  op(e2, e3) = all_52_1
% 154.02/23.25    (74)   ~ (all_52_1 = e2)
% 154.02/23.25  
% 154.02/23.25  Begin of proof
% 154.02/23.25  | 
% 154.02/23.25  | REDUCE: (30), (58) imply:
% 154.02/23.25  |   (75)  op(e3, e1) = e2
% 154.02/23.25  | 
% 154.02/23.25  | BETA: splitting (25) gives:
% 154.02/23.25  | 
% 154.02/23.25  | Case 1:
% 154.02/23.25  | | 
% 154.02/23.25  | |   (76)  all_54_1 = e3
% 154.02/23.25  | | 
% 154.02/23.25  | | COMBINE_EQS: (22), (76) imply:
% 154.02/23.25  | |   (77)  all_52_4 = e3
% 154.02/23.25  | | 
% 154.02/23.25  | | REDUCE: (50), (77) imply:
% 154.02/23.25  | |   (78)   ~ (all_52_6 = e3)
% 154.02/23.25  | | 
% 154.02/23.25  | | SIMP: (78) implies:
% 154.02/23.25  | |   (79)   ~ (all_52_6 = e3)
% 154.02/23.25  | | 
% 154.02/23.25  | | REDUCE: (18), (77) imply:
% 154.02/23.25  | |   (80)   ~ (all_52_12 = e3)
% 154.02/23.25  | | 
% 154.02/23.25  | | SIMP: (80) implies:
% 154.02/23.25  | |   (81)   ~ (all_52_12 = e3)
% 154.02/23.25  | | 
% 154.02/23.25  | | REDUCE: (14), (77) imply:
% 154.02/23.25  | |   (82)   ~ (e3 = e2)
% 154.02/23.25  | | 
% 154.02/23.25  | | REDUCE: (56), (77) imply:
% 154.02/23.25  | |   (83)   ~ (e3 = e1)
% 154.02/23.25  | | 
% 154.02/23.25  | | REDUCE: (64), (77) imply:
% 154.02/23.25  | |   (84)   ~ (e3 = e0)
% 154.02/23.25  | | 
% 154.02/23.25  | | BETA: splitting (70) gives:
% 154.02/23.25  | | 
% 154.02/23.25  | | Case 1:
% 154.02/23.25  | | | 
% 154.02/23.25  | | |   (85)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 154.02/23.25  | | |           e3)
% 154.02/23.25  | | | 
% 154.02/23.25  | | | BETA: splitting (85) gives:
% 154.02/23.25  | | | 
% 154.02/23.25  | | | Case 1:
% 154.02/23.25  | | | | 
% 154.02/23.25  | | | |   (86)  all_56_1 = e3 & op(e3, e2) = e3
% 154.02/23.25  | | | | 
% 154.02/23.25  | | | | ALPHA: (86) implies:
% 154.02/23.25  | | | |   (87)  all_56_1 = e3
% 154.02/23.25  | | | | 
% 154.02/23.25  | | | | BETA: splitting (38) gives:
% 154.02/23.25  | | | | 
% 154.02/23.25  | | | | Case 1:
% 154.02/23.25  | | | | | 
% 154.02/23.25  | | | | |   (88)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3,
% 154.02/23.25  | | | | |             e2) = e0)
% 154.02/23.25  | | | | | 
% 154.02/23.25  | | | | | REF_CLOSE: (11), (21), (41), (53), (64), (88) are inconsistent by
% 154.02/23.25  | | | | |            sub-proof #937.
% 154.02/23.25  | | | | | 
% 154.02/23.25  | | | | Case 2:
% 154.02/23.25  | | | | | 
% 154.02/23.25  | | | | |   (89)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3,
% 154.02/23.25  | | | | |             e0) = e0)
% 154.02/23.25  | | | | | 
% 154.02/23.25  | | | | | BETA: splitting (89) gives:
% 154.02/23.25  | | | | | 
% 154.02/23.25  | | | | | Case 1:
% 154.02/23.25  | | | | | | 
% 154.02/23.25  | | | | | |   (90)  all_56_4 = e0 & op(e3, e1) = e0
% 154.02/23.25  | | | | | | 
% 154.02/23.25  | | | | | | ALPHA: (90) implies:
% 154.02/23.25  | | | | | |   (91)  all_56_4 = e0
% 154.02/23.25  | | | | | | 
% 154.02/23.25  | | | | | | REF_CLOSE: (19), (24), (91) are inconsistent by sub-proof #936.
% 154.02/23.25  | | | | | | 
% 154.02/23.25  | | | | | Case 2:
% 154.02/23.25  | | | | | | 
% 154.02/23.25  | | | | | |   (92)  all_56_9 = e0 & op(e3, e0) = e0
% 154.02/23.25  | | | | | | 
% 154.02/23.25  | | | | | | ALPHA: (92) implies:
% 154.02/23.25  | | | | | |   (93)  all_56_9 = e0
% 154.02/23.25  | | | | | | 
% 154.02/23.25  | | | | | | BETA: splitting (66) gives:
% 154.02/23.25  | | | | | | 
% 154.02/23.25  | | | | | | Case 1:
% 154.02/23.25  | | | | | | | 
% 154.02/23.25  | | | | | | |   (94)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 &
% 154.02/23.25  | | | | | | |           op(e2, e2) = e1)
% 154.02/23.25  | | | | | | | 
% 154.02/23.25  | | | | | | | REF_CLOSE: (21), (51), (62), (83), (87), (94) are inconsistent by
% 154.02/23.25  | | | | | | |            sub-proof #935.
% 154.02/23.25  | | | | | | | 
% 154.02/23.25  | | | | | | Case 2:
% 154.02/23.25  | | | | | | | 
% 154.02/23.25  | | | | | | |   (95)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 &
% 154.02/23.25  | | | | | | |           op(e0, e2) = e1)
% 154.02/23.25  | | | | | | | 
% 154.02/23.25  | | | | | | | BETA: splitting (95) gives:
% 154.02/23.25  | | | | | | | 
% 154.02/23.25  | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | 
% 154.02/23.25  | | | | | | | |   (96)  all_56_7 = e1 & op(e1, e2) = e1
% 154.02/23.25  | | | | | | | | 
% 154.02/23.25  | | | | | | | | ALPHA: (96) implies:
% 154.02/23.25  | | | | | | | |   (97)  op(e1, e2) = e1
% 154.02/23.25  | | | | | | | | 
% 154.02/23.25  | | | | | | | | BETA: splitting (71) gives:
% 154.02/23.25  | | | | | | | | 
% 154.02/23.25  | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | 
% 154.02/23.25  | | | | | | | | |   (98)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 &
% 154.02/23.25  | | | | | | | | |           op(e0, e2) = e1)
% 154.02/23.25  | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | BETA: splitting (98) gives:
% 154.02/23.25  | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | |   (99)  all_56_12 = e1 & op(e0, e3) = e1
% 154.02/23.25  | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | ALPHA: (99) implies:
% 154.02/23.25  | | | | | | | | | |   (100)  all_56_12 = e1
% 154.02/23.25  | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | REF_CLOSE: (7), (9), (19), (21), (35), (40), (41), (42),
% 154.02/23.25  | | | | | | | | | |            (51), (53), (59), (62), (66), (70), (79), (82),
% 154.02/23.25  | | | | | | | | | |            (83), (84), (87), (100) are inconsistent by
% 154.02/23.25  | | | | | | | | | |            sub-proof #918.
% 154.02/23.25  | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | |   (101)  all_56_13 = e1 & op(e0, e2) = e1
% 154.02/23.25  | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | REF_CLOSE: (11), (19), (21), (39), (42), (51), (53), (59),
% 154.02/23.25  | | | | | | | | | |            (64), (101) are inconsistent by sub-proof #1010.
% 154.02/23.25  | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | End of split
% 154.02/23.25  | | | | | | | | | 
% 154.02/23.25  | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | 
% 154.02/23.25  | | | | | | | | |   (102)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1
% 154.02/23.25  | | | | | | | | |            & op(e0, e0) = e1)
% 154.02/23.25  | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | BETA: splitting (102) gives:
% 154.02/23.25  | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | |   (103)  all_56_14 = e1 & op(e0, e1) = e1
% 154.02/23.25  | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | ALPHA: (103) implies:
% 154.02/23.25  | | | | | | | | | |   (104)  op(e0, e1) = e1
% 154.02/23.25  | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | BETA: splitting (65) gives:
% 154.02/23.25  | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | |   (105)  all_54_12 = e3
% 154.02/23.25  | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | COMBINE_EQS: (49), (105) imply:
% 154.02/23.25  | | | | | | | | | | |   (106)  all_52_3 = e3
% 154.02/23.25  | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | SIMP: (106) implies:
% 154.02/23.25  | | | | | | | | | | |   (107)  all_52_3 = e3
% 154.02/23.25  | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | REDUCE: (44), (107) imply:
% 154.02/23.25  | | | | | | | | | | |   (108)   ~ (all_52_1 = e3)
% 154.02/23.25  | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | REDUCE: (27), (107) imply:
% 154.02/23.25  | | | | | | | | | | |   (109)   ~ (all_52_11 = e3)
% 154.02/23.25  | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | SIMP: (109) implies:
% 154.02/23.25  | | | | | | | | | | |   (110)   ~ (all_52_11 = e3)
% 154.02/23.25  | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | BETA: splitting (72) gives:
% 154.02/23.25  | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | |   (111)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_7 = e3
% 154.02/23.25  | | | | | | | | | | | |            & op(e1, e2) = e3)
% 154.02/23.25  | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | BETA: splitting (111) gives:
% 154.02/23.25  | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | |   (112)  all_56_6 = e3 & op(e1, e3) = e3
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | REF_CLOSE: (7), (19), (21), (42), (51), (53), (59), (62),
% 154.02/23.25  | | | | | | | | | | | | |            (66), (70), (79), (82), (83), (84), (87), (112)
% 154.02/23.25  | | | | | | | | | | | | |            are inconsistent by sub-proof #920.
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | |   (113)  all_56_7 = e3 & op(e1, e2) = e3
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | REF_CLOSE: (21), (42), (79), (113) are inconsistent by
% 154.02/23.25  | | | | | | | | | | | | |            sub-proof #925.
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | End of split
% 154.02/23.25  | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | |   (114)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_11 =
% 154.02/23.25  | | | | | | | | | | | |            e3 & op(e1, e0) = e3)
% 154.02/23.25  | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | BETA: splitting (114) gives:
% 154.02/23.25  | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | |   (115)  all_56_8 = e3 & op(e1, e1) = e3
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | ALPHA: (115) implies:
% 154.02/23.25  | | | | | | | | | | | | |   (116)  op(e1, e1) = e3
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | REF_CLOSE: (16), (21), (57), (116) are inconsistent by
% 154.02/23.25  | | | | | | | | | | | | |            sub-proof #1078.
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | |   (117)  all_56_11 = e3 & op(e1, e0) = e3
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | ALPHA: (117) implies:
% 154.02/23.25  | | | | | | | | | | | | |   (118)  all_56_11 = e3
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | BETA: splitting (9) gives:
% 154.02/23.25  | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | |   (119)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3
% 154.02/23.25  | | | | | | | | | | | | | |            & op(e2, e3) = e3)
% 154.02/23.25  | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | REF_CLOSE: (21), (41), (73), (83), (108), (119) are
% 154.02/23.25  | | | | | | | | | | | | | |            inconsistent by sub-proof #916.
% 154.02/23.25  | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | |   (120)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 =
% 154.02/23.25  | | | | | | | | | | | | | |            e3 & op(e0, e3) = e3)
% 154.02/23.25  | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | BETA: splitting (120) gives:
% 154.02/23.25  | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | |   (121)  all_56_6 = e3 & op(e1, e3) = e3
% 154.02/23.25  | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | REF_CLOSE: (7), (19), (21), (42), (51), (53), (59), (62),
% 154.02/23.25  | | | | | | | | | | | | | | |            (66), (70), (79), (82), (83), (84), (87), (121)
% 154.02/23.25  | | | | | | | | | | | | | | |            are inconsistent by sub-proof #920.
% 154.02/23.25  | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | |   (122)  all_56_12 = e3 & op(e0, e3) = e3
% 154.02/23.25  | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | ALPHA: (122) implies:
% 154.02/23.25  | | | | | | | | | | | | | | |   (123)  all_56_12 = e3
% 154.02/23.25  | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | |   (124)  (all_56_9 = e1 & op(e3, e0) = e1) | (all_56_10 =
% 154.02/23.25  | | | | | | | | | | | | | | | |            e1 & op(e2, e0) = e1)
% 154.02/23.25  | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | BETA: splitting (124) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | |   (125)  all_56_9 = e1 & op(e3, e0) = e1
% 154.02/23.25  | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | |   (126)  all_56_9 = e1
% 154.02/23.25  | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (11), (19), (21), (23), (38), (41), (53),
% 154.02/23.25  | | | | | | | | | | | | | | | | |            (62), (64), (82), (83), (84), (126) are
% 154.02/23.25  | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #913.
% 154.02/23.25  | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | |   (127)  all_56_10 = e1 & op(e2, e0) = e1
% 154.02/23.25  | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | |   (128)  all_56_10 = e1
% 154.02/23.25  | | | | | | | | | | | | | | | | |   (129)  op(e2, e0) = e1
% 154.02/23.25  | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | BETA: splitting (2) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | |   (130)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_5 = e3
% 154.02/23.25  | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e3)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | |   (131)  all_56_4 = e3 & op(e3, e1) = e3
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | |   (132)  op(e3, e1) = e3
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (21), (30), (75), (82), (132) are
% 154.02/23.25  | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | |   (133)  all_56_5 = e3 & op(e2, e1) = e3
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | |   (134)  all_56_5 = e3
% 154.02/23.25  | | | | | | | | | | | | | | | | | | |   (135)  op(e2, e1) = e3
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | BETA: splitting (15) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | |   (136)  (all_56_2 = e0 & op(e2, e3) = e0) | (all_56_3 = e0
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | |            & op(e2, e2) = e0)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | BETA: splitting (136) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | |   (137)  all_56_2 = e0 & op(e2, e3) = e0
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | ALPHA: (137) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | |   (138)  all_56_2 = e0
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | BETA: splitting (69) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |   (139)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1,
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |              e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |          (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1,
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |              e2) = e1 & op(e1, e1) = all_57_14 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (139) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |   (140)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |   (141)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e1, e3) = all_57_1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (73), (74), (141) are inconsistent by
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1180.
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |   (142)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & $i(all_57_0) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_2) & $i(all_57_14))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (142) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (143)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = all_57_14 & $i(all_57_0) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_14)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (143) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (144)  op(e1, e3) = e1
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (21), (42), (67), (97), (144) are
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #911.
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (145)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (146)  op(e0, e0) = e3
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (29), (82), (146) are inconsistent by
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1087.
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |   (147)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e1, e2) = e1 & op(e1, e1) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |          (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (147) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |   (148)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_10))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (148) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (149)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (150)  op(e1, e1) = e2
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (17), (19), (21), (24), (37), (84), (134),
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            (150) are inconsistent by sub-proof #908.
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (151)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_10 = e2) & op(e3, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (152)   ~ (all_57_5 = e0)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (152) imply:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (153)  $false
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (153) is inconsistent.
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |   (154)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |              e1) = all_57_14 & $i(all_57_3) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (154) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (155)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1,
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (156)  op(e3, e3) = e2
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (9), (21), (53), (62), (82), (83), (84),
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            (138), (156) are inconsistent by sub-proof #1055.
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |   (157)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = all_57_7 & $i(all_57_7) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10))
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (158)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (159)   ~ (all_57_5 = e0)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (55), (159) imply:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (160)  $false
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (160) is inconsistent.
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (161)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = all_57_7 & $i(all_57_7) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |   (162)  op(e2, e2) = e1
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (20), (21), (32), (43), (45), (52), (62),
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | |            (138), (162) are inconsistent by sub-proof #1154.
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |   (163)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13)) | (all_57_10 = e0
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0)
% 154.02/23.25  | | | | | | | | | | | | | | | | | | | | | |            = all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |            = e2 & $i(all_57_9) & $i(all_57_12)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |          (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |          | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |              = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |   (164)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_12 = e1) & op(e2, e2) = all_57_12 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0,
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |          (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & $i(all_57_10) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_13))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (164) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |   (165)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2,
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |              e2) = all_57_12 & op(e2, e1) = e2 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6) & $i(all_57_12))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (165) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (166)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_10)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (166) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (167)  op(e3, e1) = e3
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (21), (30), (75), (82), (167) are
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #912.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (168)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (169)  op(e2, e1) = e2
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (82), (135), (169) are inconsistent by
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1135.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |   (170)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_13 = e1) & op(e3, e3) = all_57_10 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (29), (34), (62), (81), (170) are
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #976.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |   (171)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            e0 &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            = all_57_11 & op(e1, e1) = all_57_14 & op(e1,
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |              e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |          (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |            ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (171) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |   (172)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |          | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |              = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_9) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (173)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e0) = all_57_9 & op(e2, e2) = all_57_12 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (174)  op(e3, e3) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19), (21), (31), (53), (62), (82), (83),
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            (87), (93), (174) are inconsistent by sub-proof
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            #905.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (175)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (176)  op(e3, e3) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (19), (21), (31), (53), (62), (82), (83),
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            (87), (93), (176) are inconsistent by sub-proof
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            #905.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |   (177)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |              e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e0) = all_57_13 & $i(all_57_12) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e0 & op(e2, e0) = all_57_11 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |            all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                  e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e2) & op(e3, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                e2 & op(e0, e2) = e0 & $i(all_57_4)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                  = e3) &  ~ (all_57_15 = e1) & op(e3, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e2, e2) = e1 & op(e2, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | |                all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (177) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (178)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = all_57_13 & $i(all_57_12) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_13)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (178) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (179)  op(e2, e0) = e2
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (43), (62), (129), (179) are inconsistent by
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #904.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |   (180)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e1, e0) = e1 & $i(all_57_11) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                 ~ (all_57_15 = e3) & op(e1, e3) = all_57_1
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                  e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                  e1) & op(e3, e3) = e1 & op(e3, e1) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                  = e2) &  ~ (all_57_15 = e1) & op(e2, e2) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | |                & $i(all_57_7))))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (180) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (181)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (182)  op(e2, e2) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (51), (182) are inconsistent by
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1145.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (183)  op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |          ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_0)) | (all_57_2 = e0 & all_57_14 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e2) & op(e3, e3) = e2 & op(e3,
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                e2) = all_57_3 & op(e0, e2) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_3)) | (all_57_5 = e0 & all_57_14 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |                e1) = all_57_6 & op(e0, e1) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              op(e0, e1) = e0 & $i(all_57_7)))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (183) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (184)  op(e0, e0) = all_57_15
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |   (185)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |          (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (33) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (186)  all_54_14 = e3
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (110), (186) are inconsistent by sub-proof
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |            #903.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (187)   ~ (all_54_14 = e3)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | |   (188)  all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (189)  all_54_14 = e2
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (68), (189) are inconsistent by sub-proof
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #902.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (190)   ~ (all_54_14 = e2)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (191)  all_54_14 = e1 | all_54_14 = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (17) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (192)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            & op(e2, e1) = e0)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (24), (84), (134), (192) are inconsistent by
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #909.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (193)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e0 & op(e0, e1) = e0)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (194)  all_56_8 = e0 & op(e1, e1) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (194) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (195)  op(e1, e1) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (196)  all_54_14 = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (13), (196) imply:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (197)  all_52_11 = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (197) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (198)  all_52_11 = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (63), (198) imply:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (199)   ~ (all_4_2 = e1)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (199) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (200)   ~ (all_4_2 = e1)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (198) imply:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (201)   ~ (e3 = e1)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (68), (198) imply:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (202)   ~ (e2 = e1)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (203)  all_54_10 = e3
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (57), (203) are inconsistent by sub-proof
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #1173.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (204)   ~ (all_54_10 = e3)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (205)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (206)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (29), (47), (60), (184), (206) are
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #900.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (207)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (208)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_4)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (208) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (209)  op(e1, e1) = e2
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (195), (209) are inconsistent by
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #1006.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (210)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |              e1) = e0 & $i(all_57_7))
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (211)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_6)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (212)  op(e0, e1) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (53), (104), (212) are inconsistent by
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #899.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (213)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |          $i(all_57_7)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (214)  op(e2, e2) = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (6), (10), (16), (21), (28), (41), (48),
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (54), (57), (61), (62), (67), (69), (83), (200),
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            (205), (214) are inconsistent by sub-proof #887.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (215)  all_54_14 = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (37), (215) are inconsistent by sub-proof
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            #886.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (216)  all_56_14 = e0 & op(e0, e1) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |   (217)  op(e0, e1) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (53), (104), (217) are inconsistent by
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |            sub-proof #899.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | |   (218)  all_56_3 = e0 & op(e2, e2) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | ALPHA: (218) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | |   (219)  op(e2, e2) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (19), (21), (51), (219) are inconsistent by
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | |            sub-proof #1145.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | |   (220)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | |            e0 & op(e2, e0) = e0)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | |   (221)  all_56_5 = e0 & op(e2, e1) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (84), (134), (221) are inconsistent by sub-proof
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | |            #885.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | |   (222)  all_56_10 = e0 & op(e2, e0) = e0
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (128), (222) are inconsistent by sub-proof
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | |            #884.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | |   (223)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 =
% 154.02/23.26  | | | | | | | | | | | | | | | | | |            e3 & op(e0, e1) = e3)
% 154.02/23.26  | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (21), (57), (110), (223) are
% 154.02/23.26  | | | | | | | | | | | | | | | | | |            inconsistent by sub-proof #883.
% 154.02/23.26  | | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | |   (224)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 =
% 154.02/23.26  | | | | | | | | | | | | | | | |            e1 & op(e0, e0) = e1)
% 154.02/23.26  | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 154.02/23.26  | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | Case 1:
% 154.02/23.26  | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | |   (225)  all_56_11 = e1 & op(e1, e0) = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | ALPHA: (225) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | |   (226)  all_56_11 = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (118), (226) imply:
% 154.02/23.26  | | | | | | | | | | | | | | | | |   (227)  e3 = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | COMBINE_EQS: (123), (227) imply:
% 154.02/23.26  | | | | | | | | | | | | | | | | |   (228)  all_56_12 = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (19), (21), (35), (40), (41), (42),
% 154.02/23.26  | | | | | | | | | | | | | | | | |            (51), (53), (59), (62), (66), (70), (79), (82),
% 154.02/23.26  | | | | | | | | | | | | | | | | |            (83), (84), (87), (228) are inconsistent by
% 154.02/23.26  | | | | | | | | | | | | | | | | |            sub-proof #918.
% 154.02/23.26  | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | |   (229)  all_56_15 = e1 & op(e0, e0) = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | ALPHA: (229) implies:
% 154.02/23.26  | | | | | | | | | | | | | | | | |   (230)  op(e0, e0) = e1
% 154.02/23.26  | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | | REF_CLOSE: (21), (29), (62), (230) are inconsistent by
% 154.02/23.26  | | | | | | | | | | | | | | | | |            sub-proof #978.
% 154.02/23.26  | | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | |   (231)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.02/23.26  | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | | REF_CLOSE: (26), (46), (49), (60), (231) are inconsistent by
% 154.02/23.26  | | | | | | | | | | |            sub-proof #881.
% 154.02/23.26  | | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | |   (232)  all_56_15 = e1 & op(e0, e0) = e1
% 154.02/23.26  | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | ALPHA: (232) implies:
% 154.02/23.26  | | | | | | | | | |   (233)  op(e0, e0) = e1
% 154.02/23.26  | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | | REF_CLOSE: (21), (29), (62), (233) are inconsistent by
% 154.02/23.26  | | | | | | | | | |            sub-proof #978.
% 154.02/23.26  | | | | | | | | | | 
% 154.02/23.26  | | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | | 
% 154.02/23.26  | | | | | | | | End of split
% 154.02/23.26  | | | | | | | | 
% 154.02/23.26  | | | | | | | Case 2:
% 154.02/23.26  | | | | | | | | 
% 154.02/23.26  | | | | | | | |   (234)  all_56_13 = e1 & op(e0, e2) = e1
% 154.02/23.26  | | | | | | | | 
% 154.02/23.26  | | | | | | | | REF_CLOSE: (11), (19), (21), (39), (42), (51), (53), (59), (64),
% 154.02/23.26  | | | | | | | |            (234) are inconsistent by sub-proof #1010.
% 154.02/23.26  | | | | | | | | 
% 154.02/23.26  | | | | | | | End of split
% 154.02/23.26  | | | | | | | 
% 154.02/23.26  | | | | | | End of split
% 154.02/23.26  | | | | | | 
% 154.02/23.26  | | | | | End of split
% 154.02/23.26  | | | | | 
% 154.02/23.26  | | | | End of split
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | Case 2:
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | |   (235)  all_56_3 = e3 & op(e2, e2) = e3
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | | ALPHA: (235) implies:
% 154.02/23.26  | | | |   (236)  op(e2, e2) = e3
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | | REF_CLOSE: (21), (51), (82), (236) are inconsistent by sub-proof #1179.
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | End of split
% 154.02/23.26  | | | 
% 154.02/23.26  | | Case 2:
% 154.02/23.26  | | | 
% 154.02/23.26  | | |   (237)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2)
% 154.02/23.26  | | |            = e3)
% 154.02/23.26  | | | 
% 154.02/23.26  | | | BETA: splitting (237) gives:
% 154.02/23.26  | | | 
% 154.02/23.26  | | | Case 1:
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | |   (238)  all_56_7 = e3 & op(e1, e2) = e3
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | | REF_CLOSE: (21), (42), (79), (238) are inconsistent by sub-proof #925.
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | Case 2:
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | |   (239)  all_56_13 = e3 & op(e0, e2) = e3
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | | ALPHA: (239) implies:
% 154.02/23.26  | | | |   (240)  all_56_13 = e3
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | | BETA: splitting (23) gives:
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | | Case 1:
% 154.02/23.26  | | | | | 
% 154.02/23.26  | | | | |   (241)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3,
% 154.02/23.26  | | | | |              e2) = e3)
% 154.02/23.26  | | | | | 
% 154.02/23.26  | | | | | REF_CLOSE: (19), (21), (41), (51), (53), (59), (62), (66), (83), (84),
% 154.02/23.26  | | | | |            (240), (241) are inconsistent by sub-proof #876.
% 154.02/23.26  | | | | | 
% 154.02/23.26  | | | | Case 2:
% 154.02/23.26  | | | | | 
% 154.02/23.26  | | | | |   (242)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3,
% 154.02/23.26  | | | | |              e0) = e3)
% 154.02/23.26  | | | | | 
% 154.02/23.26  | | | | | BETA: splitting (242) gives:
% 154.02/23.26  | | | | | 
% 154.02/23.26  | | | | | Case 1:
% 154.02/23.26  | | | | | | 
% 154.02/23.26  | | | | | |   (243)  all_56_4 = e3 & op(e3, e1) = e3
% 154.02/23.26  | | | | | | 
% 154.02/23.26  | | | | | | ALPHA: (243) implies:
% 154.02/23.26  | | | | | |   (244)  op(e3, e1) = e3
% 154.02/23.26  | | | | | | 
% 154.02/23.26  | | | | | | REF_CLOSE: (5), (21), (30), (75), (82), (244) are inconsistent by
% 154.02/23.26  | | | | | |            sub-proof #912.
% 154.02/23.26  | | | | | | 
% 154.02/23.26  | | | | | Case 2:
% 154.02/23.26  | | | | | | 
% 154.02/23.26  | | | | | |   (245)  all_56_9 = e3 & op(e3, e0) = e3
% 154.02/23.26  | | | | | | 
% 154.02/23.26  | | | | | | ALPHA: (245) implies:
% 154.02/23.26  | | | | | |   (246)  op(e3, e0) = e3
% 154.02/23.26  | | | | | | 
% 154.02/23.26  | | | | | | REF_CLOSE: (21), (34), (81), (246) are inconsistent by sub-proof
% 154.02/23.26  | | | | | |            #1082.
% 154.02/23.26  | | | | | | 
% 154.02/23.26  | | | | | End of split
% 154.02/23.26  | | | | | 
% 154.02/23.26  | | | | End of split
% 154.02/23.26  | | | | 
% 154.02/23.26  | | | End of split
% 154.02/23.26  | | | 
% 154.02/23.26  | | End of split
% 154.02/23.26  | | 
% 154.02/23.26  | Case 2:
% 154.02/23.26  | | 
% 154.02/23.26  | |   (247)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.02/23.26  | | 
% 154.02/23.26  | | REF_CLOSE: (14), (22), (56), (64), (247) are inconsistent by sub-proof #875.
% 154.02/23.26  | | 
% 154.02/23.26  | End of split
% 154.02/23.26  | 
% 154.02/23.26  End of proof
% 154.02/23.26  
% 154.02/23.26  Sub-proof #875 shows that the following formulas are inconsistent:
% 154.02/23.26  ----------------------------------------------------------------
% 154.02/23.26    (1)   ~ (all_52_4 = e2)
% 154.02/23.26    (2)  all_54_1 = all_52_4
% 154.02/23.26    (3)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.02/23.26    (4)   ~ (all_52_4 = e1)
% 154.02/23.26    (5)   ~ (all_52_4 = e0)
% 154.02/23.26  
% 154.02/23.26  Begin of proof
% 154.02/23.26  | 
% 154.02/23.26  | BETA: splitting (3) gives:
% 154.02/23.26  | 
% 154.02/23.26  | Case 1:
% 154.02/23.26  | | 
% 154.02/23.26  | |   (6)  all_54_1 = e2
% 154.02/23.26  | | 
% 154.02/23.26  | | COMBINE_EQS: (2), (6) imply:
% 154.02/23.26  | |   (7)  all_52_4 = e2
% 154.02/23.26  | | 
% 154.02/23.26  | | REDUCE: (1), (7) imply:
% 154.02/23.26  | |   (8)  $false
% 154.02/23.26  | | 
% 154.02/23.26  | | CLOSE: (8) is inconsistent.
% 154.02/23.26  | | 
% 154.02/23.26  | Case 2:
% 154.02/23.26  | | 
% 154.02/23.26  | |   (9)  all_54_1 = e1 | all_54_1 = e0
% 154.02/23.26  | | 
% 154.02/23.26  | | BETA: splitting (9) gives:
% 154.02/23.26  | | 
% 154.02/23.26  | | Case 1:
% 154.02/23.26  | | | 
% 154.02/23.26  | | |   (10)  all_54_1 = e1
% 154.02/23.26  | | | 
% 154.02/23.26  | | | COMBINE_EQS: (2), (10) imply:
% 154.02/23.26  | | |   (11)  all_52_4 = e1
% 154.02/23.26  | | | 
% 154.02/23.26  | | | REDUCE: (4), (11) imply:
% 154.02/23.26  | | |   (12)  $false
% 154.02/23.26  | | | 
% 154.02/23.26  | | | CLOSE: (12) is inconsistent.
% 154.02/23.26  | | | 
% 154.02/23.26  | | Case 2:
% 154.02/23.26  | | | 
% 154.02/23.26  | | |   (13)  all_54_1 = e0
% 154.02/23.26  | | | 
% 154.02/23.26  | | | COMBINE_EQS: (2), (13) imply:
% 154.02/23.26  | | |   (14)  all_52_4 = e0
% 154.02/23.26  | | | 
% 154.02/23.26  | | | REDUCE: (5), (14) imply:
% 154.02/23.26  | | |   (15)  $false
% 154.02/23.26  | | | 
% 154.02/23.26  | | | CLOSE: (15) is inconsistent.
% 154.02/23.26  | | | 
% 154.02/23.26  | | End of split
% 154.02/23.26  | | 
% 154.02/23.26  | End of split
% 154.02/23.26  | 
% 154.02/23.26  End of proof
% 154.02/23.26  
% 154.02/23.26  Sub-proof #876 shows that the following formulas are inconsistent:
% 154.02/23.26  ----------------------------------------------------------------
% 154.02/23.26    (1)   ~ (e3 = e1)
% 154.02/23.26    (2)   ~ (e2 = e0)
% 154.02/23.26    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.26    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3)
% 154.02/23.26    (5)   ~ (e3 = e0)
% 154.02/23.26    (6)  op(e3, e3) = e1
% 154.02/23.26    (7)  op(e2, e2) = e2
% 154.02/23.26    (8)   ~ (e1 = e0)
% 154.02/23.26    (9)  all_56_13 = e3
% 154.02/23.26    (10)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.02/23.26          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.02/23.26    (11)   ~ (e2 = e1)
% 154.02/23.26    (12)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.02/23.26          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.02/23.26  
% 154.02/23.26  Begin of proof
% 154.02/23.26  | 
% 154.02/23.26  | BETA: splitting (4) gives:
% 154.02/23.26  | 
% 154.02/23.26  | Case 1:
% 154.02/23.26  | | 
% 154.02/23.26  | |   (13)  all_56_0 = e3 & op(e3, e3) = e3
% 154.02/23.26  | | 
% 154.02/23.26  | | ALPHA: (13) implies:
% 154.02/23.26  | |   (14)  op(e3, e3) = e3
% 154.02/23.26  | | 
% 154.02/23.26  | | REF_CLOSE: (1), (3), (6), (14) are inconsistent by sub-proof #1178.
% 154.02/23.26  | | 
% 154.02/23.26  | Case 2:
% 154.02/23.26  | | 
% 154.02/23.26  | |   (15)  all_56_1 = e3 & op(e3, e2) = e3
% 154.02/23.26  | | 
% 154.02/23.26  | | ALPHA: (15) implies:
% 154.02/23.26  | |   (16)  all_56_1 = e3
% 154.02/23.26  | | 
% 154.02/23.26  | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (12), (16) are
% 154.02/23.26  | |            inconsistent by sub-proof #877.
% 154.02/23.26  | | 
% 154.02/23.26  | End of split
% 154.02/23.26  | 
% 154.02/23.26  End of proof
% 154.02/23.26  
% 154.02/23.26  Sub-proof #877 shows that the following formulas are inconsistent:
% 154.02/23.26  ----------------------------------------------------------------
% 154.02/23.26    (1)   ~ (e3 = e1)
% 154.02/23.26    (2)   ~ (e2 = e0)
% 154.02/23.26    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.26           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.26    (4)   ~ (e3 = e0)
% 154.02/23.26    (5)  op(e2, e2) = e2
% 154.02/23.26    (6)   ~ (e1 = e0)
% 154.02/23.26    (7)  all_56_13 = e3
% 154.02/23.27    (8)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.02/23.27         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.02/23.27    (9)   ~ (e2 = e1)
% 154.02/23.27    (10)  all_56_1 = e3
% 154.02/23.27    (11)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.02/23.27          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | BETA: splitting (11) gives:
% 154.02/23.27  | 
% 154.02/23.27  | Case 1:
% 154.02/23.27  | | 
% 154.02/23.27  | |   (12)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) =
% 154.02/23.27  | |           e1)
% 154.02/23.27  | | 
% 154.02/23.27  | | REF_CLOSE: (1), (3), (5), (9), (10), (12) are inconsistent by sub-proof
% 154.02/23.27  | |            #935.
% 154.02/23.27  | | 
% 154.02/23.27  | Case 2:
% 154.02/23.27  | | 
% 154.02/23.27  | |   (13)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 154.02/23.27  | |           e1)
% 154.02/23.27  | | 
% 154.02/23.27  | | BETA: splitting (13) gives:
% 154.02/23.27  | | 
% 154.02/23.27  | | Case 1:
% 154.02/23.27  | | | 
% 154.02/23.27  | | |   (14)  all_56_7 = e1 & op(e1, e2) = e1
% 154.02/23.27  | | | 
% 154.02/23.27  | | | ALPHA: (14) implies:
% 154.02/23.27  | | |   (15)  all_56_7 = e1
% 154.02/23.27  | | | 
% 154.02/23.27  | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (15) are inconsistent
% 154.02/23.27  | | |            by sub-proof #879.
% 154.02/23.27  | | | 
% 154.02/23.27  | | Case 2:
% 154.02/23.27  | | | 
% 154.02/23.27  | | |   (16)  all_56_13 = e1 & op(e0, e2) = e1
% 154.02/23.27  | | | 
% 154.02/23.27  | | | REF_CLOSE: (1), (7), (16) are inconsistent by sub-proof #878.
% 154.02/23.27  | | | 
% 154.02/23.27  | | End of split
% 154.02/23.27  | | 
% 154.02/23.27  | End of split
% 154.02/23.27  | 
% 154.02/23.27  End of proof
% 154.02/23.27  
% 154.02/23.27  Sub-proof #878 shows that the following formulas are inconsistent:
% 154.02/23.27  ----------------------------------------------------------------
% 154.02/23.27    (1)  all_56_13 = e1 & op(e0, e2) = e1
% 154.02/23.27    (2)  all_56_13 = e3
% 154.02/23.27    (3)   ~ (e3 = e1)
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | ALPHA: (1) implies:
% 154.02/23.27  |   (4)  all_56_13 = e1
% 154.02/23.27  | 
% 154.02/23.27  | COMBINE_EQS: (2), (4) imply:
% 154.02/23.27  |   (5)  e3 = e1
% 154.02/23.27  | 
% 154.02/23.27  | REDUCE: (3), (5) imply:
% 154.02/23.27  |   (6)  $false
% 154.02/23.27  | 
% 154.02/23.27  | CLOSE: (6) is inconsistent.
% 154.02/23.27  | 
% 154.02/23.27  End of proof
% 154.02/23.27  
% 154.02/23.27  Sub-proof #879 shows that the following formulas are inconsistent:
% 154.02/23.27  ----------------------------------------------------------------
% 154.02/23.27    (1)  all_56_7 = e1
% 154.02/23.27    (2)   ~ (e2 = e0)
% 154.02/23.27    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.27    (4)   ~ (e3 = e0)
% 154.02/23.27    (5)  op(e2, e2) = e2
% 154.02/23.27    (6)   ~ (e1 = e0)
% 154.02/23.27    (7)  all_56_13 = e3
% 154.02/23.27    (8)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.02/23.27         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.02/23.27    (9)  all_56_1 = e3
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | BETA: splitting (8) gives:
% 154.02/23.27  | 
% 154.02/23.27  | Case 1:
% 154.02/23.27  | | 
% 154.02/23.27  | |   (10)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 154.02/23.27  | |           e0)
% 154.02/23.27  | | 
% 154.02/23.27  | | REF_CLOSE: (2), (3), (4), (5), (9), (10) are inconsistent by sub-proof
% 154.02/23.27  | |            #1113.
% 154.02/23.27  | | 
% 154.02/23.27  | Case 2:
% 154.02/23.27  | | 
% 154.02/23.27  | |   (11)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 154.02/23.27  | |           e0)
% 154.02/23.27  | | 
% 154.02/23.27  | | BETA: splitting (11) gives:
% 154.02/23.27  | | 
% 154.02/23.27  | | Case 1:
% 154.02/23.27  | | | 
% 154.02/23.27  | | |   (12)  all_56_7 = e0 & op(e1, e2) = e0
% 154.02/23.27  | | | 
% 154.02/23.27  | | | REF_CLOSE: (1), (6), (12) are inconsistent by sub-proof #880.
% 154.02/23.27  | | | 
% 154.02/23.27  | | Case 2:
% 154.02/23.27  | | | 
% 154.02/23.27  | | |   (13)  all_56_13 = e0 & op(e0, e2) = e0
% 154.02/23.27  | | | 
% 154.02/23.27  | | | REF_CLOSE: (4), (7), (13) are inconsistent by sub-proof #1102.
% 154.02/23.27  | | | 
% 154.02/23.27  | | End of split
% 154.02/23.27  | | 
% 154.02/23.27  | End of split
% 154.02/23.27  | 
% 154.02/23.27  End of proof
% 154.02/23.27  
% 154.02/23.27  Sub-proof #880 shows that the following formulas are inconsistent:
% 154.02/23.27  ----------------------------------------------------------------
% 154.02/23.27    (1)  all_56_7 = e0 & op(e1, e2) = e0
% 154.02/23.27    (2)  all_56_7 = e1
% 154.02/23.27    (3)   ~ (e1 = e0)
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | ALPHA: (1) implies:
% 154.02/23.27  |   (4)  all_56_7 = e0
% 154.02/23.27  | 
% 154.02/23.27  | COMBINE_EQS: (2), (4) imply:
% 154.02/23.27  |   (5)  e1 = e0
% 154.02/23.27  | 
% 154.02/23.27  | REDUCE: (3), (5) imply:
% 154.02/23.27  |   (6)  $false
% 154.02/23.27  | 
% 154.02/23.27  | CLOSE: (6) is inconsistent.
% 154.02/23.27  | 
% 154.02/23.27  End of proof
% 154.02/23.27  
% 154.02/23.27  Sub-proof #881 shows that the following formulas are inconsistent:
% 154.02/23.27  ----------------------------------------------------------------
% 154.02/23.27    (1)   ~ (all_52_3 = e2)
% 154.02/23.27    (2)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.02/23.27    (3)   ~ (all_52_3 = e1)
% 154.02/23.27    (4)  all_54_12 = all_52_3
% 154.02/23.27    (5)   ~ (all_52_3 = e0)
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | BETA: splitting (2) gives:
% 154.02/23.27  | 
% 154.02/23.27  | Case 1:
% 154.02/23.27  | | 
% 154.02/23.27  | |   (6)  all_54_12 = e2
% 154.02/23.27  | | 
% 154.02/23.27  | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #882.
% 154.02/23.27  | | 
% 154.02/23.27  | Case 2:
% 154.02/23.27  | | 
% 154.02/23.27  | |   (7)  all_54_12 = e1 | all_54_12 = e0
% 154.02/23.27  | | 
% 154.02/23.27  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1090.
% 154.02/23.27  | | 
% 154.02/23.27  | End of split
% 154.02/23.27  | 
% 154.02/23.27  End of proof
% 154.02/23.27  
% 154.02/23.27  Sub-proof #882 shows that the following formulas are inconsistent:
% 154.02/23.27  ----------------------------------------------------------------
% 154.02/23.27    (1)  all_54_12 = all_52_3
% 154.02/23.27    (2)  all_54_12 = e2
% 154.02/23.27    (3)   ~ (all_52_3 = e2)
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | COMBINE_EQS: (1), (2) imply:
% 154.02/23.27  |   (4)  all_52_3 = e2
% 154.02/23.27  | 
% 154.02/23.27  | SIMP: (4) implies:
% 154.02/23.27  |   (5)  all_52_3 = e2
% 154.02/23.27  | 
% 154.02/23.27  | REDUCE: (3), (5) imply:
% 154.02/23.27  |   (6)  $false
% 154.02/23.27  | 
% 154.02/23.27  | CLOSE: (6) is inconsistent.
% 154.02/23.27  | 
% 154.02/23.27  End of proof
% 154.02/23.27  
% 154.02/23.27  Sub-proof #883 shows that the following formulas are inconsistent:
% 154.02/23.27  ----------------------------------------------------------------
% 154.02/23.27    (1)  op(e0, e1) = all_52_11
% 154.02/23.27    (2)  op(e1, e1) = all_4_2
% 154.02/23.27    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.27    (4)   ~ (all_52_11 = e3)
% 154.02/23.27    (5)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 154.02/23.27    (6)   ~ (all_4_2 = e3)
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | BETA: splitting (5) gives:
% 154.02/23.27  | 
% 154.02/23.27  | Case 1:
% 154.02/23.27  | | 
% 154.02/23.27  | |   (7)  all_56_8 = e3 & op(e1, e1) = e3
% 154.02/23.27  | | 
% 154.02/23.27  | | ALPHA: (7) implies:
% 154.02/23.27  | |   (8)  op(e1, e1) = e3
% 154.02/23.27  | | 
% 154.02/23.27  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #1078.
% 154.02/23.27  | | 
% 154.02/23.27  | Case 2:
% 154.02/23.27  | | 
% 154.02/23.27  | |   (9)  all_56_14 = e3 & op(e0, e1) = e3
% 154.02/23.27  | | 
% 154.02/23.27  | | ALPHA: (9) implies:
% 154.02/23.27  | |   (10)  op(e0, e1) = e3
% 154.02/23.27  | | 
% 154.02/23.27  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1147.
% 154.02/23.27  | | 
% 154.02/23.27  | End of split
% 154.02/23.27  | 
% 154.02/23.27  End of proof
% 154.02/23.27  
% 154.02/23.27  Sub-proof #884 shows that the following formulas are inconsistent:
% 154.02/23.27  ----------------------------------------------------------------
% 154.02/23.27    (1)  all_56_10 = e0 & op(e2, e0) = e0
% 154.02/23.27    (2)  all_56_10 = e1
% 154.02/23.27    (3)   ~ (e1 = e0)
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | ALPHA: (1) implies:
% 154.02/23.27  |   (4)  all_56_10 = e0
% 154.02/23.27  | 
% 154.02/23.27  | COMBINE_EQS: (2), (4) imply:
% 154.02/23.27  |   (5)  e1 = e0
% 154.02/23.27  | 
% 154.02/23.27  | REDUCE: (3), (5) imply:
% 154.02/23.27  |   (6)  $false
% 154.02/23.27  | 
% 154.02/23.27  | CLOSE: (6) is inconsistent.
% 154.02/23.27  | 
% 154.02/23.27  End of proof
% 154.02/23.27  
% 154.02/23.27  Sub-proof #885 shows that the following formulas are inconsistent:
% 154.02/23.27  ----------------------------------------------------------------
% 154.02/23.27    (1)  all_56_5 = e0 & op(e2, e1) = e0
% 154.02/23.27    (2)  all_56_5 = e3
% 154.02/23.27    (3)   ~ (e3 = e0)
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | ALPHA: (1) implies:
% 154.02/23.27  |   (4)  all_56_5 = e0
% 154.02/23.27  | 
% 154.02/23.27  | COMBINE_EQS: (2), (4) imply:
% 154.02/23.27  |   (5)  e3 = e0
% 154.02/23.27  | 
% 154.02/23.27  | SIMP: (5) implies:
% 154.02/23.27  |   (6)  e3 = e0
% 154.02/23.27  | 
% 154.02/23.27  | REDUCE: (3), (6) imply:
% 154.02/23.27  |   (7)  $false
% 154.02/23.27  | 
% 154.02/23.27  | CLOSE: (7) is inconsistent.
% 154.02/23.27  | 
% 154.02/23.27  End of proof
% 154.02/23.27  
% 154.02/23.27  Sub-proof #886 shows that the following formulas are inconsistent:
% 154.02/23.27  ----------------------------------------------------------------
% 154.02/23.27    (1)  all_54_14 = all_52_11
% 154.02/23.27    (2)  all_54_14 = e0
% 154.02/23.27    (3)   ~ (all_52_11 = e0)
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | COMBINE_EQS: (1), (2) imply:
% 154.02/23.27  |   (4)  all_52_11 = e0
% 154.02/23.27  | 
% 154.02/23.27  | SIMP: (4) implies:
% 154.02/23.27  |   (5)  all_52_11 = e0
% 154.02/23.27  | 
% 154.02/23.27  | REDUCE: (3), (5) imply:
% 154.02/23.27  |   (6)  $false
% 154.02/23.27  | 
% 154.02/23.27  | CLOSE: (6) is inconsistent.
% 154.02/23.27  | 
% 154.02/23.27  End of proof
% 154.02/23.27  
% 154.02/23.27  Sub-proof #887 shows that the following formulas are inconsistent:
% 154.02/23.27  ----------------------------------------------------------------
% 154.02/23.27    (1)  op(e0, e1) = all_52_11
% 154.02/23.27    (2)   ~ (e3 = e1)
% 154.02/23.27    (3)   ~ (all_52_11 = all_10_2)
% 154.02/23.27    (4)   ~ (all_4_2 = e1)
% 154.02/23.27    (5)  op(e2, e2) = e1
% 154.02/23.27    (6)  op(e0, e0) = all_10_2
% 154.02/23.27    (7)  op(e1, e1) = all_4_2
% 154.02/23.27    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.27    (9)  all_54_10 = all_4_2
% 154.02/23.27    (10)  op(e3, e3) = e1
% 154.02/23.27    (11)   ~ (all_4_2 = e2)
% 154.02/23.27    (12)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 154.02/23.27              ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 154.02/23.27            ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 154.02/23.27                = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 154.02/23.27              | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.02/23.27          (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 154.02/23.27              ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.02/23.27            ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 154.02/23.27                = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 154.02/23.27              | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.02/23.27          (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 154.02/23.27              ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.02/23.27            ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 154.02/23.27                = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 154.02/23.27              | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.02/23.27          (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 154.02/23.27              ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.02/23.27            ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 154.02/23.27                  e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 154.02/23.27                  e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.02/23.27                $i(all_57_14))))
% 154.02/23.27    (13)  all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 154.02/23.27    (14)   ~ (all_4_2 = e3)
% 154.02/23.27    (15)   ~ (all_52_2 = e1)
% 154.02/23.27    (16)   ~ (e2 = e1)
% 154.02/23.27    (17)  op(e1, e3) = all_52_2
% 154.02/23.27    (18)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 154.02/23.27              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.02/23.27            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 154.02/23.27            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 154.02/23.27            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 154.02/23.27            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 154.02/23.27            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 154.02/23.27            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.02/23.27            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 154.02/23.27            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 154.02/23.27            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 154.02/23.27            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 154.02/23.27            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.02/23.27            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 154.02/23.27            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 154.02/23.27            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.02/23.27            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 154.02/23.27            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 154.02/23.27            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.27            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 154.02/23.27            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 154.02/23.27            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.02/23.27            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 154.02/23.27            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 154.02/23.27            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 154.02/23.27            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 154.02/23.27            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 154.02/23.27            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 154.02/23.27            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.27            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 154.02/23.27            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 154.02/23.27            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 154.02/23.27            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 154.02/23.27            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 154.02/23.27            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.27            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 154.02/23.27            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.27            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 154.02/23.27            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 154.02/23.27            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.27            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 154.02/23.27            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 154.02/23.27            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 154.02/23.27            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 154.02/23.27            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 154.02/23.27            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 154.02/23.27            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 154.02/23.27            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 154.02/23.27              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 154.02/23.27            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 154.02/23.27            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 154.02/23.27              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 154.02/23.27            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 154.02/23.27            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 154.02/23.27                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 154.02/23.27                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.27                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 154.02/23.27                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 154.02/23.27                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 154.02/23.27                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 154.02/23.27                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 154.02/23.27              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 154.02/23.27                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 154.02/23.27                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.02/23.27                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 154.02/23.27                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 154.02/23.27                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 154.02/23.27                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.27                $i(all_57_7))))
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | BETA: splitting (13) gives:
% 154.02/23.27  | 
% 154.02/23.27  | Case 1:
% 154.02/23.27  | | 
% 154.02/23.27  | |   (19)  all_54_10 = e2
% 154.02/23.27  | | 
% 154.02/23.27  | | REF_CLOSE: (9), (11), (19) are inconsistent by sub-proof #1168.
% 154.02/23.27  | | 
% 154.02/23.27  | Case 2:
% 154.02/23.27  | | 
% 154.02/23.27  | |   (20)   ~ (all_54_10 = e2)
% 154.02/23.27  | |   (21)  all_54_10 = e1 | all_54_10 = e0
% 154.02/23.27  | | 
% 154.02/23.27  | | BETA: splitting (12) gives:
% 154.02/23.27  | | 
% 154.02/23.27  | | Case 1:
% 154.02/23.27  | | | 
% 154.02/23.27  | | |   (22)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) =
% 154.02/23.27  | | |               e2) | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 &
% 154.02/23.27  | | |               $i(all_57_12))) & ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~
% 154.02/23.27  | | |               (all_57_14 = e3) & op(e1, e1) = all_57_14 & $i(all_57_14)))
% 154.02/23.27  | | |           & ((all_57_2 = e0 & op(e0, e3) = e0) | ( ~ (all_57_15 = e3) &
% 154.02/23.27  | | |               op(e0, e0) = all_57_15 & $i(all_57_15)))) | (all_57_12 = e2
% 154.02/23.27  | | |           & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) | ( ~
% 154.02/23.27  | | |               (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10)))
% 154.02/23.27  | | |           & ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) &
% 154.02/23.27  | | |               op(e1, e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 &
% 154.02/23.27  | | |               op(e0, e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) =
% 154.02/23.27  | | |               all_57_15 & $i(all_57_15))))
% 154.02/23.27  | | | 
% 154.02/23.27  | | | REF_CLOSE: (2), (5), (8), (10), (16), (22) are inconsistent by sub-proof
% 154.02/23.27  | | |            #898.
% 154.02/23.27  | | | 
% 154.02/23.27  | | Case 2:
% 154.02/23.27  | | | 
% 154.02/23.27  | | |   (23)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) =
% 154.02/23.27  | | |               e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.02/23.27  | | |               $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 154.02/23.27  | | |               (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12)))
% 154.02/23.27  | | |           & ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) &
% 154.02/23.27  | | |               op(e0, e0) = all_57_15 & $i(all_57_15)))) | (all_57_15 = e0
% 154.02/23.27  | | |           & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) | ( ~
% 154.02/23.27  | | |               (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10)))
% 154.02/23.27  | | |           & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 154.02/23.27  | | |               op(e2, e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1
% 154.02/23.27  | | |               & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 154.02/23.27  | | |               all_57_14 & $i(all_57_14))))
% 154.02/23.27  | | | 
% 154.02/23.27  | | | BETA: splitting (23) gives:
% 154.02/23.27  | | | 
% 154.02/23.27  | | | Case 1:
% 154.02/23.27  | | | | 
% 154.02/23.27  | | | |   (24)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1)
% 154.02/23.27  | | | |             = e3) | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 &
% 154.02/23.27  | | | |             $i(all_57_10))) & ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~
% 154.02/23.27  | | | |             (all_57_12 = e1) & op(e2, e2) = all_57_12 & $i(all_57_12)))
% 154.02/23.27  | | | |         & ((all_57_8 = e0 & op(e0, e1) = e0) | ( ~ (all_57_15 = e1) &
% 154.02/23.27  | | | |             op(e0, e0) = all_57_15 & $i(all_57_15)))
% 154.02/23.27  | | | | 
% 154.02/23.27  | | | | ALPHA: (24) implies:
% 154.02/23.27  | | | |   (25)  op(e1, e1) = e1
% 154.02/23.27  | | | | 
% 154.02/23.27  | | | | REF_CLOSE: (4), (7), (8), (9), (21), (25) are inconsistent by sub-proof
% 154.02/23.27  | | | |            #897.
% 154.02/23.27  | | | | 
% 154.02/23.27  | | | Case 2:
% 154.02/23.27  | | | | 
% 154.02/23.27  | | | |   (26)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0)
% 154.02/23.27  | | | |             = e3) | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 &
% 154.02/23.27  | | | |             $i(all_57_10))) & ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~
% 154.02/23.27  | | | |             (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12)))
% 154.02/23.27  | | | |         & ((all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 154.02/23.27  | | | |             op(e1, e1) = all_57_14 & $i(all_57_14)))
% 154.02/23.27  | | | | 
% 154.02/23.27  | | | | ALPHA: (26) implies:
% 154.02/23.27  | | | |   (27)  all_57_15 = e0
% 154.02/23.27  | | | |   (28)  op(e0, e0) = e0
% 154.02/23.27  | | | |   (29)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) &
% 154.02/23.27  | | | |           op(e1, e1) = all_57_14 & $i(all_57_14))
% 154.02/23.27  | | | |   (30)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) &
% 154.02/23.27  | | | |           op(e2, e2) = all_57_12 & $i(all_57_12))
% 154.02/23.27  | | | | 
% 154.02/23.27  | | | | BETA: splitting (21) gives:
% 154.02/23.27  | | | | 
% 154.02/23.27  | | | | Case 1:
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | |   (31)  all_54_10 = e1
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | REF_CLOSE: (4), (9), (31) are inconsistent by sub-proof #1167.
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | Case 2:
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | |   (32)  all_54_10 = e0
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | COMBINE_EQS: (9), (32) imply:
% 154.02/23.27  | | | | |   (33)  all_4_2 = e0
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | SIMP: (33) implies:
% 154.02/23.27  | | | | |   (34)  all_4_2 = e0
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | REDUCE: (14), (34) imply:
% 154.02/23.27  | | | | |   (35)   ~ (e3 = e0)
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | SIMP: (35) implies:
% 154.02/23.27  | | | | |   (36)   ~ (e3 = e0)
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | REDUCE: (11), (34) imply:
% 154.02/23.27  | | | | |   (37)   ~ (e2 = e0)
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | SIMP: (37) implies:
% 154.02/23.27  | | | | |   (38)   ~ (e2 = e0)
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | REDUCE: (4), (34) imply:
% 154.02/23.27  | | | | |   (39)   ~ (e1 = e0)
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | SIMP: (39) implies:
% 154.02/23.27  | | | | |   (40)   ~ (e1 = e0)
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | REDUCE: (7), (34) imply:
% 154.02/23.27  | | | | |   (41)  op(e1, e1) = e0
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | BETA: splitting (29) gives:
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | | Case 1:
% 154.02/23.27  | | | | | | 
% 154.02/23.27  | | | | | |   (42)  all_57_13 = e1 & op(e1, e0) = e1
% 154.02/23.27  | | | | | | 
% 154.02/23.27  | | | | | | ALPHA: (42) implies:
% 154.02/23.27  | | | | | |   (43)  all_57_13 = e1
% 154.02/23.27  | | | | | | 
% 154.02/23.27  | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (8), (10), (15), (16), (17),
% 154.02/23.27  | | | | | |            (18), (27), (28), (30), (36), (38), (40), (41), (43) are
% 154.02/23.27  | | | | | |            inconsistent by sub-proof #888.
% 154.02/23.27  | | | | | | 
% 154.02/23.27  | | | | | Case 2:
% 154.02/23.27  | | | | | | 
% 154.02/23.27  | | | | | |   (44)   ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14)
% 154.02/23.27  | | | | | | 
% 154.02/23.27  | | | | | | ALPHA: (44) implies:
% 154.02/23.27  | | | | | |   (45)   ~ (all_57_14 = e0)
% 154.02/23.27  | | | | | |   (46)  op(e1, e1) = all_57_14
% 154.02/23.27  | | | | | | 
% 154.02/23.27  | | | | | | REF_CLOSE: (8), (41), (45), (46) are inconsistent by sub-proof
% 154.02/23.27  | | | | | |            #1026.
% 154.02/23.27  | | | | | | 
% 154.02/23.27  | | | | | End of split
% 154.02/23.27  | | | | | 
% 154.02/23.27  | | | | End of split
% 154.02/23.27  | | | | 
% 154.02/23.27  | | | End of split
% 154.02/23.27  | | | 
% 154.02/23.27  | | End of split
% 154.02/23.27  | | 
% 154.02/23.27  | End of split
% 154.02/23.27  | 
% 154.02/23.27  End of proof
% 154.02/23.27  
% 154.02/23.27  Sub-proof #888 shows that the following formulas are inconsistent:
% 154.02/23.27  ----------------------------------------------------------------
% 154.02/23.27    (1)  op(e0, e1) = all_52_11
% 154.02/23.27    (2)   ~ (e3 = e1)
% 154.02/23.27    (3)   ~ (all_52_11 = all_10_2)
% 154.02/23.27    (4)  op(e2, e2) = e1
% 154.02/23.27    (5)  op(e0, e0) = all_10_2
% 154.02/23.27    (6)  all_57_13 = e1
% 154.02/23.27    (7)   ~ (e2 = e0)
% 154.02/23.27    (8)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 154.02/23.27           all_57_12 & $i(all_57_12))
% 154.02/23.27    (9)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.02/23.27           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.02/23.27    (10)  op(e1, e1) = e0
% 154.02/23.27    (11)   ~ (e3 = e0)
% 154.02/23.27    (12)  all_57_15 = e0
% 154.02/23.27    (13)  op(e3, e3) = e1
% 154.02/23.27    (14)   ~ (e1 = e0)
% 154.02/23.27    (15)   ~ (all_52_2 = e1)
% 154.02/23.27    (16)   ~ (e2 = e1)
% 154.02/23.27    (17)  op(e0, e0) = e0
% 154.02/23.27    (18)  op(e1, e3) = all_52_2
% 154.02/23.27    (19)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 154.02/23.27              e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.02/23.27            all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 154.02/23.27            = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 154.02/23.27            op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 154.02/23.27            op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 154.02/23.27            all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 154.02/23.27            = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.02/23.27            all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15
% 154.02/23.27            = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 &
% 154.02/23.27            op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 154.02/23.27            $i(all_57_2) & $i(all_57_14)) | (all_57_3 = e3 & all_57_14 = e2 &  ~
% 154.02/23.27            (all_57_4 = e1) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.02/23.27            op(e3, e2) = e3 & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 154.02/23.27            $i(all_57_4) & $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 154.02/23.27            (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 &
% 154.02/23.27            op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 154.02/23.27            $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2 &  ~
% 154.02/23.27            (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.27            all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 154.02/23.27            $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0)
% 154.02/23.27            &  ~ (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.02/23.27            op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 154.02/23.27            $i(all_57_14)) | (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2)
% 154.02/23.27            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 154.02/23.27            op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 154.02/23.27            $i(all_57_10)) | (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 154.02/23.27            &  ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 154.02/23.27            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.27            $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3)
% 154.02/23.27            &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 154.02/23.27            op(e2, e2) = all_57_12 & op(e2, e1) = e2 & $i(all_57_6) &
% 154.02/23.27            $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0)
% 154.02/23.27            &  ~ (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 154.02/23.27            op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.02/23.27            $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0)
% 154.02/23.27            &  ~ (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.27            op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 154.02/23.27            $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0)
% 154.02/23.27            &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.27            op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 154.02/23.27            $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3)
% 154.02/23.27            &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 154.02/23.27            op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 154.02/23.27            $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3)
% 154.02/23.27            &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 154.02/23.27            op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9) &
% 154.02/23.27            $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 =
% 154.02/23.27              e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2
% 154.02/23.27            & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 154.02/23.27            $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 =
% 154.02/23.27              e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 154.02/23.27            & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 154.02/23.27            $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2
% 154.02/23.27                = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 154.02/23.27                op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.02/23.27                $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 =
% 154.02/23.27                  e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) =
% 154.02/23.27                e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 154.02/23.27                = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 154.02/23.27                & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 154.02/23.27              (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 154.02/23.27                  = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 154.02/23.27                e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.02/23.27                (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 154.02/23.27                  e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 154.02/23.27                e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 154.02/23.27                op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.27                $i(all_57_7))))
% 154.02/23.27  
% 154.02/23.27  Begin of proof
% 154.02/23.27  | 
% 154.02/23.27  | BETA: splitting (19) gives:
% 154.02/23.27  | 
% 154.02/23.27  | Case 1:
% 154.02/23.27  | | 
% 154.02/23.28  | |   (20)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 154.02/23.28  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.02/23.28  | |           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 154.02/23.28  | |         (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 154.02/23.28  | |             = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 154.02/23.28  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) |
% 154.02/23.28  | |         (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 154.02/23.28  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 154.02/23.28  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 154.02/23.28  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 154.02/23.28  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 154.02/23.28  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)) |
% 154.02/23.28  | |         (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10
% 154.02/23.28  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.02/23.28  | |           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) |
% 154.02/23.28  | |         (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 154.02/23.28  | |             = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 154.02/23.28  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)) |
% 154.02/23.28  | |         (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14
% 154.02/23.28  | |             = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) =
% 154.02/23.28  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) |
% 154.02/23.28  | |         (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 154.02/23.28  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.02/23.28  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 154.02/23.28  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 154.02/23.28  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 154.02/23.28  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.02/23.28  | | 
% 154.02/23.28  | | BETA: splitting (20) gives:
% 154.02/23.28  | | 
% 154.02/23.28  | | Case 1:
% 154.02/23.28  | | | 
% 154.02/23.28  | | |   (21)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.02/23.28  | | |           (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.02/23.28  | | |           op(e1, e3) = all_57_1 & op(e1, e1) = e3 & $i(all_57_1) &
% 154.02/23.28  | | |           $i(all_57_12)) | (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2
% 154.02/23.28  | | |             = e0) &  ~ (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) =
% 154.02/23.28  | | |           all_57_12 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 &
% 154.02/23.28  | | |           $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 & all_57_12 = e3
% 154.02/23.28  | | |           &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3) =
% 154.02/23.28  | | |           all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) =
% 154.02/23.28  | | |           all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 &
% 154.02/23.28  | | |           all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) &
% 154.02/23.28  | | |           op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2
% 154.02/23.28  | | |           & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 154.02/23.28  | | | 
% 154.02/23.28  | | | REF_CLOSE: (9), (10), (11), (15), (17), (18), (21) are inconsistent by
% 154.02/23.28  | | |            sub-proof #895.
% 154.02/23.28  | | | 
% 154.02/23.28  | | Case 2:
% 154.02/23.28  | | | 
% 154.02/23.28  | | |   (22)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.02/23.28  | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 154.02/23.28  | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 154.02/23.28  | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5
% 154.02/23.28  | | |             = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3,
% 154.02/23.28  | | |             e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 154.02/23.28  | | |           $i(all_57_5) & $i(all_57_10)) | (all_57_4 = e1 & all_57_10 = e2
% 154.02/23.28  | | |           &  ~ (all_57_3 = e3) &  ~ (all_57_14 = e2) & op(e3, e3) = e2 &
% 154.02/23.28  | | |           op(e3, e2) = all_57_3 & op(e1, e2) = e1 & op(e1, e1) = all_57_14
% 154.02/23.28  | | |           & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1 & all_57_15 =
% 154.02/23.28  | | |           e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1
% 154.02/23.28  | | |           & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 154.02/23.28  | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 154.02/23.28  | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.02/23.28  | | |           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) =
% 154.02/23.28  | | |           all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.02/23.28  | | | 
% 154.02/23.28  | | | BETA: splitting (22) gives:
% 154.02/23.28  | | | 
% 154.02/23.28  | | | Case 1:
% 154.02/23.28  | | | | 
% 154.02/23.28  | | | |   (23)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.02/23.28  | | | |           (all_57_10 = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 &
% 154.02/23.28  | | | |           op(e1, e2) = all_57_4 & op(e1, e1) = e2 & $i(all_57_4) &
% 154.02/23.28  | | | |           $i(all_57_10)) | (all_57_3 = e3 & all_57_15 = e2 &  ~
% 154.02/23.28  | | | |           (all_57_5 = e0) &  ~ (all_57_10 = e2) & op(e3, e3) = all_57_10
% 154.02/23.28  | | | |           & op(e3, e2) = e3 & op(e0, e2) = all_57_5 & op(e0, e0) = e2 &
% 154.02/23.28  | | | |           $i(all_57_5) & $i(all_57_10))
% 154.02/23.28  | | | | 
% 154.02/23.28  | | | | REF_CLOSE: (7), (9), (10), (17), (23) are inconsistent by sub-proof
% 154.02/23.28  | | | |            #894.
% 154.02/23.28  | | | | 
% 154.02/23.28  | | | Case 2:
% 154.02/23.28  | | | | 
% 154.02/23.28  | | | |   (24)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.02/23.28  | | | |           (all_57_14 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 154.02/23.28  | | | |           op(e1, e2) = e1 & op(e1, e1) = all_57_14 & $i(all_57_3) &
% 154.02/23.28  | | | |           $i(all_57_14)) | (all_57_4 = e1 & all_57_15 = e2 &  ~
% 154.02/23.28  | | | |           (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1, e2) = e1 &
% 154.02/23.28  | | | |           op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0, e0) =
% 154.02/23.28  | | | |           e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 &
% 154.02/23.28  | | | |           all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 154.02/23.28  | | | |           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 154.02/23.28  | | | |           op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.02/23.28  | | | | 
% 154.02/23.28  | | | | REF_CLOSE: (7), (9), (13), (16), (17), (24) are inconsistent by
% 154.02/23.28  | | | |            sub-proof #892.
% 154.02/23.28  | | | | 
% 154.02/23.28  | | | End of split
% 154.02/23.28  | | | 
% 154.02/23.28  | | End of split
% 154.02/23.28  | | 
% 154.02/23.28  | Case 2:
% 154.02/23.28  | | 
% 154.02/23.28  | |   (25)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10
% 154.02/23.28  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.02/23.28  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) |
% 154.02/23.28  | |         (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12
% 154.02/23.28  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 154.02/23.28  | |           all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)) |
% 154.02/23.28  | |         (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12
% 154.02/23.28  | |             = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.02/23.28  | |           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) |
% 154.02/23.28  | |         (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 154.02/23.28  | |           (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.02/23.28  | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 154.02/23.28  | |           $i(all_57_11)) | (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 =
% 154.02/23.28  | |             e0) &  ~ (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0)
% 154.02/23.28  | |           = e3 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 154.02/23.28  | |           $i(all_57_13)) | (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 =
% 154.02/23.28  | |             e3) &  ~ (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 154.02/23.28  | |           all_57_9 & op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9)
% 154.02/23.28  | |           & $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 154.02/23.28  | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 154.02/23.28  | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_9)
% 154.02/23.28  | |           & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0 &  ~
% 154.02/23.28  | |           (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) = all_57_12 &
% 154.02/23.28  | |           op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) = all_57_13 &
% 154.02/23.28  | |           $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1
% 154.02/23.28  | |           &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 154.02/23.28  | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) = e1
% 154.02/23.28  | |           & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15 &
% 154.02/23.28  | |           $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 =
% 154.02/23.28  | |                 e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2,
% 154.02/23.28  | |                 e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 154.02/23.28  | |               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 154.02/23.28  | |               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 154.02/23.28  | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3
% 154.02/23.28  | |                 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.02/23.28  | |               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 154.02/23.28  | |               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) &
% 154.02/23.28  | |               op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.02/23.28  | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6
% 154.02/23.28  | |                 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 154.02/23.28  | |               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 154.02/23.28  | |               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 154.02/23.28  | |               op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.02/23.28  | |               $i(all_57_7))))
% 154.02/23.28  | | 
% 154.02/23.28  | | BETA: splitting (25) gives:
% 154.02/23.28  | | 
% 154.02/23.28  | | Case 1:
% 154.02/23.28  | | | 
% 154.11/23.28  | | |   (26)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 154.11/23.28  | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 154.11/23.28  | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.11/23.28  | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6
% 154.11/23.28  | | |             = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 154.11/23.28  | | |           all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 154.11/23.28  | | |           $i(all_57_6) & $i(all_57_12)) | (all_57_7 = e2 & all_57_15 = e1
% 154.11/23.28  | | |           &  ~ (all_57_8 = e0) &  ~ (all_57_12 = e1) & op(e2, e2) =
% 154.11/23.28  | | |           all_57_12 & op(e2, e1) = e2 & op(e0, e1) = all_57_8 & op(e0, e0)
% 154.11/23.28  | | |           = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9 = e3 &
% 154.11/23.28  | | |           all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 154.11/23.28  | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 154.11/23.28  | | |           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 154.11/23.28  | | |         (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 154.11/23.28  | | |           (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.11/23.28  | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 154.11/23.28  | | |           $i(all_57_13))
% 154.11/23.28  | | | 
% 154.11/23.28  | | | BETA: splitting (26) gives:
% 154.11/23.28  | | | 
% 154.11/23.28  | | | Case 1:
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | |   (27)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 154.11/23.28  | | | |           (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 154.11/23.28  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.11/23.28  | | | |           $i(all_57_10)) | (all_57_7 = e2 & all_57_10 = e1 &  ~
% 154.11/23.28  | | | |           (all_57_6 = e3) &  ~ (all_57_12 = e1) & op(e3, e3) = e1 &
% 154.11/23.28  | | | |           op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 & op(e2, e1) =
% 154.11/23.28  | | | |           e2 & $i(all_57_6) & $i(all_57_12))
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | | REF_CLOSE: (4), (9), (14), (17), (27) are inconsistent by sub-proof
% 154.11/23.28  | | | |            #891.
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | Case 2:
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | |   (28)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~
% 154.11/23.28  | | | |           (all_57_12 = e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 &
% 154.11/23.28  | | | |           op(e0, e1) = all_57_8 & op(e0, e0) = e1 & $i(all_57_8) &
% 154.11/23.28  | | | |           $i(all_57_12)) | (all_57_9 = e3 & all_57_12 = e0 &  ~
% 154.11/23.28  | | | |           (all_57_10 = e0) &  ~ (all_57_11 = e2) & op(e3, e3) =
% 154.11/23.28  | | | |           all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0) =
% 154.11/23.28  | | | |           all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 154.11/23.28  | | | |           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 154.11/23.28  | | | |           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 &
% 154.11/23.28  | | | |           op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | | REF_CLOSE: (6), (8), (9), (14), (17), (28) are inconsistent by sub-proof
% 154.11/23.28  | | | |            #889.
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | End of split
% 154.11/23.28  | | | 
% 154.11/23.28  | | Case 2:
% 154.11/23.28  | | | 
% 154.11/23.28  | | |   (29)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 154.11/23.28  | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 154.11/23.28  | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 154.11/23.28  | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9
% 154.11/23.28  | | |             = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 & op(e3, e0) =
% 154.11/23.28  | | |           all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) = e1 &
% 154.11/23.28  | | |           $i(all_57_9) & $i(all_57_14)) | (all_57_11 = e2 & all_57_14 = e0
% 154.11/23.28  | | |           &  ~ (all_57_12 = e0) &  ~ (all_57_13 = e1) & op(e2, e2) =
% 154.11/23.28  | | |           all_57_12 & op(e2, e0) = e2 & op(e1, e1) = e0 & op(e1, e0) =
% 154.11/23.28  | | |           all_57_13 & $i(all_57_12) & $i(all_57_13)) | (all_57_12 = e0 &
% 154.11/23.28  | | |           all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 = e0) &
% 154.11/23.28  | | |           op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 154.11/23.28  | | |           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) |
% 154.11/23.28  | | |         (op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 154.11/23.28  | | |               all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) &
% 154.11/23.28  | | |               op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.11/23.28  | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 154.11/23.28  | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 154.11/23.28  | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1))
% 154.11/23.28  | | |             | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.11/23.28  | | |               (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 154.11/23.28  | | |               op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 154.11/23.28  | | |               = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2)
% 154.11/23.28  | | |               = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.11/23.28  | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.11/23.28  | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 &
% 154.11/23.28  | | |               op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 154.11/23.28  | | |             (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 154.11/23.28  | | |               (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 154.11/23.28  | | |               op(e0, e1) = e0 & $i(all_57_7))))
% 154.11/23.28  | | | 
% 154.11/23.28  | | | BETA: splitting (29) gives:
% 154.11/23.28  | | | 
% 154.11/23.28  | | | Case 1:
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | |   (30)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~
% 154.11/23.28  | | | |           (all_57_12 = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 &
% 154.11/23.28  | | | |           op(e2, e2) = all_57_12 & op(e2, e0) = e2 & $i(all_57_9) &
% 154.11/23.28  | | | |           $i(all_57_12)) | (all_57_10 = e0 & all_57_13 = e1 &  ~
% 154.11/23.28  | | | |           (all_57_9 = e3) &  ~ (all_57_14 = e0) & op(e3, e3) = e0 &
% 154.11/23.28  | | | |           op(e3, e0) = all_57_9 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 154.11/23.28  | | | |           e1 & $i(all_57_9) & $i(all_57_14))
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | | REF_CLOSE: (9), (13), (14), (30) are inconsistent by sub-proof #956.
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | Case 2:
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | |   (31)  (all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 154.11/23.28  | | | |           (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.11/23.28  | | | |           op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 154.11/23.28  | | | |           $i(all_57_13)) | (all_57_12 = e0 & all_57_13 = e1 &  ~
% 154.11/23.28  | | | |           (all_57_11 = e2) &  ~ (all_57_14 = e0) & op(e2, e2) = e0 &
% 154.11/23.28  | | | |           op(e2, e0) = all_57_11 & op(e1, e1) = all_57_14 & op(e1, e0) =
% 154.11/23.28  | | | |           e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0, e0) = all_57_15
% 154.11/23.28  | | | |           & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 &  ~
% 154.11/23.28  | | | |               (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 154.11/23.28  | | | |               all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.11/23.28  | | | |               $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 154.11/23.28  | | | |               (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) =
% 154.11/23.28  | | | |               all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 154.11/23.28  | | | |               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.11/23.28  | | | |               (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 154.11/23.28  | | | |               op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 154.11/23.28  | | | |             (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.11/23.28  | | | |               (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 154.11/23.28  | | | |               & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.11/23.28  | | | |               all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 154.11/23.28  | | | |               & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 154.11/23.28  | | | |               e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.11/23.28  | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 154.11/23.28  | | | |               op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))))
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | | BETA: splitting (31) gives:
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | | Case 1:
% 154.11/23.28  | | | | | 
% 154.11/23.28  | | | | |   (32)  all_57_11 = e2 & all_57_14 = e0 &  ~ (all_57_12 = e0) &  ~
% 154.11/23.28  | | | | |         (all_57_13 = e1) & op(e2, e2) = all_57_12 & op(e2, e0) = e2 &
% 154.11/23.28  | | | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_12) &
% 154.11/23.28  | | | | |         $i(all_57_13)
% 154.11/23.28  | | | | | 
% 154.11/23.28  | | | | | ALPHA: (32) implies:
% 154.11/23.28  | | | | |   (33)   ~ (all_57_13 = e1)
% 154.11/23.28  | | | | | 
% 154.11/23.28  | | | | | REDUCE: (6), (33) imply:
% 154.11/23.28  | | | | |   (34)  $false
% 154.11/23.28  | | | | | 
% 154.11/23.28  | | | | | CLOSE: (34) is inconsistent.
% 154.11/23.28  | | | | | 
% 154.11/23.28  | | | | Case 2:
% 154.11/23.28  | | | | | 
% 154.11/23.28  | | | | |   (35)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 154.11/23.28  | | | | |           (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 154.11/23.28  | | | | |           & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 154.11/23.28  | | | | |           $i(all_57_14)) | (op(e0, e0) = all_57_15 & $i(all_57_15) &
% 154.11/23.28  | | | | |           ((all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.11/23.28  | | | | |               (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 154.11/23.28  | | | | |               e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 154.11/23.28  | | | | |               all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 154.11/23.28  | | | | |                 e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.11/23.28  | | | | |                 e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 154.11/23.28  | | | | |               = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 154.11/23.28  | | | | |                 e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.11/23.28  | | | | |               $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 154.11/23.28  | | | | |               (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 154.11/23.28  | | | | |               all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.11/23.28  | | | | |               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.11/23.28  | | | | |               (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 154.11/23.28  | | | | |               & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.11/23.28  | | | | |               $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.11/23.28  | | | | |               (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 154.11/23.28  | | | | |               & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.11/23.28  | | | | |               $i(all_57_7))))
% 154.11/23.28  | | | | | 
% 154.11/23.28  | | | | | BETA: splitting (35) gives:
% 154.11/23.28  | | | | | 
% 154.11/23.28  | | | | | Case 1:
% 154.11/23.28  | | | | | | 
% 154.11/23.28  | | | | | |   (36)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 154.11/23.28  | | | | | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11
% 154.11/23.28  | | | | | |         & op(e1, e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) &
% 154.11/23.28  | | | | | |         $i(all_57_14)
% 154.11/23.28  | | | | | | 
% 154.11/23.28  | | | | | | ALPHA: (36) implies:
% 154.11/23.28  | | | | | |   (37)   ~ (all_57_14 = e0)
% 154.11/23.28  | | | | | |   (38)  op(e1, e1) = all_57_14
% 154.11/23.28  | | | | | | 
% 154.11/23.28  | | | | | | REF_CLOSE: (9), (10), (37), (38) are inconsistent by sub-proof
% 154.11/23.28  | | | | | |            #1026.
% 154.11/23.28  | | | | | | 
% 154.11/23.28  | | | | | Case 2:
% 154.11/23.28  | | | | | | 
% 154.11/23.28  | | | | | |   (39)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 &
% 154.11/23.28  | | | | | |             all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.11/23.28  | | | | | |               e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0,
% 154.11/23.28  | | | | | |               e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14
% 154.11/23.28  | | | | | |             = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1,
% 154.11/23.28  | | | | | |               e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 154.11/23.28  | | | | | |             $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.11/23.28  | | | | | |             (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 154.11/23.28  | | | | | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.11/23.28  | | | | | |             $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~
% 154.11/23.28  | | | | | |             (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) =
% 154.11/23.28  | | | | | |             all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.11/23.28  | | | | | |             $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.11/23.28  | | | | | |             (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 154.11/23.28  | | | | | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.11/23.28  | | | | | |             $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.11/23.28  | | | | | |             (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 154.11/23.28  | | | | | |             & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.11/23.28  | | | | | |             $i(all_57_7)))
% 154.11/23.28  | | | | | | 
% 154.11/23.28  | | | | | | ALPHA: (39) implies:
% 154.11/23.28  | | | | | |   (40)  op(e0, e0) = all_57_15
% 154.11/23.28  | | | | | |   (41)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.11/23.28  | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3
% 154.11/23.28  | | | | | |           & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 154.11/23.28  | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3)
% 154.11/23.28  | | | | | |           & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) =
% 154.11/23.28  | | | | | |           e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.11/23.28  | | | | | |           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 &
% 154.11/23.28  | | | | | |           op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 154.11/23.28  | | | | | |         (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.11/23.28  | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2
% 154.11/23.28  | | | | | |           & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.11/23.28  | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1)
% 154.11/23.28  | | | | | |           & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 154.11/23.28  | | | | | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.11/23.28  | | | | | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 &
% 154.11/23.28  | | | | | |           op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.11/23.28  | | | | | | 
% 154.11/23.28  | | | | | | BETA: splitting (41) gives:
% 154.11/23.28  | | | | | | 
% 154.11/23.28  | | | | | | Case 1:
% 154.11/23.28  | | | | | | | 
% 154.11/23.28  | | | | | | |   (42)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.11/23.28  | | | | | | |           (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 154.11/23.28  | | | | | | |           e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0 &
% 154.11/23.28  | | | | | | |           all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 154.11/23.28  | | | | | | |             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.11/23.28  | | | | | | |             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10
% 154.11/23.28  | | | | | | |           = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3,
% 154.11/23.28  | | | | | | |             e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.11/23.28  | | | | | | |           $i(all_57_3))
% 154.11/23.28  | | | | | | | 
% 154.11/23.28  | | | | | | | BETA: splitting (42) gives:
% 154.11/23.28  | | | | | | | 
% 154.11/23.28  | | | | | | | Case 1:
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | |   (43)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.11/23.28  | | | | | | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) =
% 154.11/23.28  | | | | | | | |         e3 & op(e0, e3) = e0 & $i(all_57_0)
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | | ALPHA: (43) implies:
% 154.11/23.28  | | | | | | | |   (44)  op(e2, e2) = e3
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | | REF_CLOSE: (2), (4), (9), (44) are inconsistent by sub-proof
% 154.11/23.28  | | | | | | | |            #1136.
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | Case 2:
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | |   (45)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.11/23.28  | | | | | | | |           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 154.11/23.28  | | | | | | | |             e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) |
% 154.11/23.28  | | | | | | | |         (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 154.11/23.28  | | | | | | | |           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.28  | | | | | | | |           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | | BETA: splitting (45) gives:
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | | Case 1:
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | |   (46)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.11/23.28  | | | | | | | | |         ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1,
% 154.11/23.28  | | | | | | | | |           e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | | ALPHA: (46) implies:
% 154.11/23.28  | | | | | | | | |   (47)  op(e1, e1) = e3
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | | REF_CLOSE: (9), (10), (11), (47) are inconsistent by sub-proof
% 154.11/23.28  | | | | | | | | |            #896.
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | Case 2:
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | |   (48)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 154.11/23.28  | | | | | | | | |         ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.28  | | | | | | | | |         all_57_3 & op(e0, e2) = e0 & $i(all_57_3)
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | | ALPHA: (48) implies:
% 154.11/23.28  | | | | | | | | |   (49)  op(e3, e3) = e2
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | | REF_CLOSE: (9), (13), (16), (49) are inconsistent by sub-proof
% 154.11/23.28  | | | | | | | | |            #1074.
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | End of split
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | End of split
% 154.11/23.28  | | | | | | | 
% 154.11/23.28  | | | | | | Case 2:
% 154.11/23.28  | | | | | | | 
% 154.11/23.28  | | | | | | |   (50)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.11/23.28  | | | | | | |           (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 154.11/23.28  | | | | | | |           e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.11/23.28  | | | | | | |           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.11/23.28  | | | | | | |             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 154.11/23.28  | | | | | | |             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12
% 154.11/23.28  | | | | | | |           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 154.11/23.28  | | | | | | |             e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.11/23.28  | | | | | | |           $i(all_57_7))
% 154.11/23.28  | | | | | | | 
% 154.11/23.28  | | | | | | | BETA: splitting (50) gives:
% 154.11/23.28  | | | | | | | 
% 154.11/23.28  | | | | | | | Case 1:
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | |   (51)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.11/23.28  | | | | | | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 154.11/23.28  | | | | | | | |         e2 & op(e0, e2) = e0 & $i(all_57_4)
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | | ALPHA: (51) implies:
% 154.11/23.28  | | | | | | | |   (52)   ~ (all_57_15 = e2)
% 154.11/23.28  | | | | | | | |   (53)  op(e1, e1) = e2
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | | REDUCE: (12), (52) imply:
% 154.11/23.28  | | | | | | | |   (54)   ~ (e2 = e0)
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | | GROUND_INST: instantiating (9) with e0, e2, e1, e1, simplifying
% 154.11/23.28  | | | | | | | |              with (10), (53) gives:
% 154.11/23.28  | | | | | | | |   (55)  e2 = e0
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | | REDUCE: (7), (55) imply:
% 154.11/23.28  | | | | | | | |   (56)  $false
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | | CLOSE: (56) is inconsistent.
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | Case 2:
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | |   (57)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 154.11/23.28  | | | | | | | |           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 154.11/23.28  | | | | | | | |           all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8
% 154.11/23.28  | | | | | | | |           = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 154.11/23.28  | | | | | | | |           (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 154.11/23.28  | | | | | | | |           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | | BETA: splitting (57) gives:
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | | Case 1:
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | |   (58)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 154.11/23.28  | | | | | | | | |         ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 154.11/23.28  | | | | | | | | |         all_57_6 & op(e0, e1) = e0 & $i(all_57_6)
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | | ALPHA: (58) implies:
% 154.11/23.28  | | | | | | | | |   (59)  op(e0, e1) = e0
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | | REF_CLOSE: (1), (3), (5), (9), (17), (59) are inconsistent by
% 154.11/23.28  | | | | | | | | |            sub-proof #1034.
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | Case 2:
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | |   (60)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 154.11/23.28  | | | | | | | | |         ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 154.11/23.28  | | | | | | | | |         all_57_7 & op(e0, e1) = e0 & $i(all_57_7)
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | | ALPHA: (60) implies:
% 154.11/23.28  | | | | | | | | |   (61)  op(e0, e1) = e0
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | | REF_CLOSE: (1), (3), (5), (9), (17), (61) are inconsistent by
% 154.11/23.28  | | | | | | | | |            sub-proof #1034.
% 154.11/23.28  | | | | | | | | | 
% 154.11/23.28  | | | | | | | | End of split
% 154.11/23.28  | | | | | | | | 
% 154.11/23.28  | | | | | | | End of split
% 154.11/23.28  | | | | | | | 
% 154.11/23.28  | | | | | | End of split
% 154.11/23.28  | | | | | | 
% 154.11/23.28  | | | | | End of split
% 154.11/23.28  | | | | | 
% 154.11/23.28  | | | | End of split
% 154.11/23.28  | | | | 
% 154.11/23.28  | | | End of split
% 154.11/23.28  | | | 
% 154.11/23.28  | | End of split
% 154.11/23.28  | | 
% 154.11/23.28  | End of split
% 154.11/23.28  | 
% 154.11/23.28  End of proof
% 154.11/23.28  
% 154.11/23.28  Sub-proof #889 shows that the following formulas are inconsistent:
% 154.11/23.28  ----------------------------------------------------------------
% 154.11/23.28    (1)  all_57_13 = e1
% 154.11/23.28    (2)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 154.11/23.28           all_57_12 & $i(all_57_12))
% 154.11/23.28    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.28    (4)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 154.11/23.28             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.11/23.28           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 154.11/23.28           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 154.11/23.28           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 154.11/23.28           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 154.11/23.28           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 154.11/23.28           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 154.11/23.28           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.11/23.28    (5)   ~ (e1 = e0)
% 154.11/23.28    (6)  op(e0, e0) = e0
% 154.11/23.28  
% 154.11/23.28  Begin of proof
% 154.11/23.28  | 
% 154.11/23.28  | BETA: splitting (4) gives:
% 154.11/23.28  | 
% 154.11/23.28  | Case 1:
% 154.11/23.28  | | 
% 154.11/23.28  | |   (7)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 154.11/23.28  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.11/23.28  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 154.11/23.28  | | 
% 154.11/23.28  | | ALPHA: (7) implies:
% 154.11/23.28  | |   (8)  op(e0, e0) = e1
% 154.11/23.28  | | 
% 154.11/23.28  | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #1040.
% 154.11/23.28  | | 
% 154.11/23.28  | Case 2:
% 154.11/23.28  | | 
% 154.11/23.28  | |   (9)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 154.11/23.28  | |            = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) =
% 154.11/23.28  | |          e0 & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 154.11/23.28  | |        (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 154.11/23.28  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 154.11/23.28  | |          e0 & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.11/23.28  | | 
% 154.11/23.28  | | BETA: splitting (9) gives:
% 154.11/23.28  | | 
% 154.11/23.28  | | Case 1:
% 154.11/23.28  | | | 
% 154.11/23.28  | | |   (10)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~
% 154.11/23.28  | | |         (all_57_11 = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.11/23.28  | | |         op(e2, e2) = e0 & op(e2, e0) = all_57_11 & $i(all_57_10) &
% 154.11/23.28  | | |         $i(all_57_11)
% 154.11/23.28  | | | 
% 154.11/23.28  | | | ALPHA: (10) implies:
% 154.11/23.28  | | |   (11)  all_57_12 = e0
% 154.11/23.28  | | |   (12)   ~ (all_57_11 = e2)
% 154.11/23.28  | | | 
% 154.11/23.28  | | | REF_CLOSE: (2), (11), (12) are inconsistent by sub-proof #890.
% 154.11/23.28  | | | 
% 154.11/23.28  | | Case 2:
% 154.11/23.28  | | | 
% 154.11/23.28  | | |   (13)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~
% 154.11/23.28  | | |         (all_57_13 = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 &
% 154.11/23.28  | | |         op(e1, e1) = e0 & op(e1, e0) = all_57_13 & $i(all_57_10) &
% 154.11/23.28  | | |         $i(all_57_13)
% 154.11/23.28  | | | 
% 154.11/23.28  | | | ALPHA: (13) implies:
% 154.11/23.28  | | |   (14)   ~ (all_57_13 = e1)
% 154.11/23.28  | | | 
% 154.11/23.28  | | | REDUCE: (1), (14) imply:
% 154.11/23.28  | | |   (15)  $false
% 154.11/23.28  | | | 
% 154.11/23.28  | | | CLOSE: (15) is inconsistent.
% 154.11/23.28  | | | 
% 154.11/23.28  | | End of split
% 154.11/23.28  | | 
% 154.11/23.28  | End of split
% 154.11/23.28  | 
% 154.11/23.28  End of proof
% 154.11/23.28  
% 154.11/23.28  Sub-proof #890 shows that the following formulas are inconsistent:
% 154.11/23.28  ----------------------------------------------------------------
% 154.11/23.28    (1)  (all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2) =
% 154.11/23.28           all_57_12 & $i(all_57_12))
% 154.11/23.28    (2)   ~ (all_57_11 = e2)
% 154.11/23.28    (3)  all_57_12 = e0
% 154.11/23.28  
% 154.11/23.28  Begin of proof
% 154.11/23.28  | 
% 154.11/23.28  | BETA: splitting (1) gives:
% 154.11/23.28  | 
% 154.11/23.28  | Case 1:
% 154.11/23.28  | | 
% 154.11/23.28  | |   (4)  all_57_11 = e2 & op(e2, e0) = e2
% 154.11/23.28  | | 
% 154.11/23.28  | | ALPHA: (4) implies:
% 154.11/23.28  | |   (5)  all_57_11 = e2
% 154.11/23.28  | | 
% 154.11/23.28  | | REDUCE: (2), (5) imply:
% 154.11/23.28  | |   (6)  $false
% 154.11/23.28  | | 
% 154.11/23.28  | | CLOSE: (6) is inconsistent.
% 154.11/23.28  | | 
% 154.11/23.28  | Case 2:
% 154.11/23.28  | | 
% 154.11/23.28  | |   (7)   ~ (all_57_12 = e0) & op(e2, e2) = all_57_12 & $i(all_57_12)
% 154.11/23.28  | | 
% 154.11/23.28  | | ALPHA: (7) implies:
% 154.11/23.28  | |   (8)   ~ (all_57_12 = e0)
% 154.11/23.28  | | 
% 154.11/23.28  | | REDUCE: (3), (8) imply:
% 154.11/23.28  | |   (9)  $false
% 154.11/23.28  | | 
% 154.11/23.28  | | CLOSE: (9) is inconsistent.
% 154.11/23.28  | | 
% 154.11/23.28  | End of split
% 154.11/23.28  | 
% 154.11/23.28  End of proof
% 154.11/23.28  
% 154.11/23.28  Sub-proof #891 shows that the following formulas are inconsistent:
% 154.11/23.28  ----------------------------------------------------------------
% 154.11/23.28    (1)  op(e2, e2) = e1
% 154.11/23.28    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.28           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.28    (3)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.11/23.28             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.11/23.28           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 154.11/23.28           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 154.11/23.28           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 154.11/23.28           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 154.11/23.28    (4)   ~ (e1 = e0)
% 154.11/23.28    (5)  op(e0, e0) = e0
% 154.11/23.28  
% 154.11/23.28  Begin of proof
% 154.11/23.28  | 
% 154.11/23.28  | BETA: splitting (3) gives:
% 154.11/23.28  | 
% 154.11/23.28  | Case 1:
% 154.11/23.28  | | 
% 154.11/23.29  | |   (6)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.11/23.29  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.11/23.29  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 154.11/23.29  | | 
% 154.11/23.29  | | ALPHA: (6) implies:
% 154.11/23.29  | |   (7)  op(e0, e0) = e1
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #1040.
% 154.11/23.29  | | 
% 154.11/23.29  | Case 2:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (8)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 154.11/23.29  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 154.11/23.29  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 154.11/23.29  | | 
% 154.11/23.29  | | ALPHA: (8) implies:
% 154.11/23.29  | |   (9)   ~ (all_57_12 = e1)
% 154.11/23.29  | |   (10)  op(e2, e2) = all_57_12
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (1), (2), (9), (10) are inconsistent by sub-proof #1014.
% 154.11/23.29  | | 
% 154.11/23.29  | End of split
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #892 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)   ~ (e2 = e0)
% 154.11/23.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (3)  op(e3, e3) = e1
% 154.11/23.29    (4)   ~ (e2 = e1)
% 154.11/23.29    (5)  op(e0, e0) = e0
% 154.11/23.29    (6)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 154.11/23.29             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 154.11/23.29           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 154.11/23.29           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 154.11/23.29             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 154.11/23.29             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 154.11/23.29           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.11/23.29           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 154.11/23.29           $i(all_57_7) & $i(all_57_10))
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | BETA: splitting (6) gives:
% 154.11/23.29  | 
% 154.11/23.29  | Case 1:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (7)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 154.11/23.29  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 154.11/23.29  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 154.11/23.29  | | 
% 154.11/23.29  | | ALPHA: (7) implies:
% 154.11/23.29  | |   (8)  op(e3, e3) = e2
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1074.
% 154.11/23.29  | | 
% 154.11/23.29  | Case 2:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (9)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 154.11/23.29  | |            = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.11/23.29  | |          all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 154.11/23.29  | |        (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 154.11/23.29  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 154.11/23.29  | |          e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.11/23.29  | | 
% 154.11/23.29  | | BETA: splitting (9) gives:
% 154.11/23.29  | | 
% 154.11/23.29  | | Case 1:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (10)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~
% 154.11/23.29  | | |         (all_57_14 = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 &
% 154.11/23.29  | | |         op(e0, e2) = all_57_5 & op(e0, e0) = e2 & $i(all_57_5) &
% 154.11/23.29  | | |         $i(all_57_14)
% 154.11/23.29  | | | 
% 154.11/23.29  | | | ALPHA: (10) implies:
% 154.11/23.29  | | |   (11)  op(e0, e0) = e2
% 154.11/23.29  | | | 
% 154.11/23.29  | | | REF_CLOSE: (1), (2), (5), (11) are inconsistent by sub-proof #1043.
% 154.11/23.29  | | | 
% 154.11/23.29  | | Case 2:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (12)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 154.11/23.29  | | |         (all_57_10 = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 &
% 154.11/23.29  | | |         op(e2, e2) = e1 & op(e2, e1) = all_57_7 & $i(all_57_7) &
% 154.11/23.29  | | |         $i(all_57_10)
% 154.11/23.29  | | | 
% 154.11/23.29  | | | ALPHA: (12) implies:
% 154.11/23.29  | | |   (13)   ~ (all_57_10 = e1)
% 154.11/23.29  | | |   (14)  op(e3, e3) = all_57_10
% 154.11/23.29  | | | 
% 154.11/23.29  | | | REF_CLOSE: (2), (3), (13), (14) are inconsistent by sub-proof #893.
% 154.11/23.29  | | | 
% 154.11/23.29  | | End of split
% 154.11/23.29  | | 
% 154.11/23.29  | End of split
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #893 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (2)  op(e3, e3) = all_57_10
% 154.11/23.29    (3)  op(e3, e3) = e1
% 154.11/23.29    (4)   ~ (all_57_10 = e1)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | GROUND_INST: instantiating (1) with e1, all_57_10, e3, e3, simplifying with
% 154.11/23.29  |              (2), (3) gives:
% 154.11/23.29  |   (5)  all_57_10 = e1
% 154.11/23.29  | 
% 154.11/23.29  | REDUCE: (4), (5) imply:
% 154.11/23.29  |   (6)  $false
% 154.11/23.29  | 
% 154.11/23.29  | CLOSE: (6) is inconsistent.
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #894 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)   ~ (e2 = e0)
% 154.11/23.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (3)  op(e1, e1) = e0
% 154.11/23.29    (4)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 154.11/23.29             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.11/23.29           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 154.11/23.29           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 154.11/23.29           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 154.11/23.29           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 154.11/23.29    (5)  op(e0, e0) = e0
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | BETA: splitting (4) gives:
% 154.11/23.29  | 
% 154.11/23.29  | Case 1:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (6)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 154.11/23.29  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.11/23.29  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 154.11/23.29  | | 
% 154.11/23.29  | | ALPHA: (6) implies:
% 154.11/23.29  | |   (7)  op(e1, e1) = e2
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #1006.
% 154.11/23.29  | | 
% 154.11/23.29  | Case 2:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (8)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 154.11/23.29  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 154.11/23.29  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 154.11/23.29  | | 
% 154.11/23.29  | | ALPHA: (8) implies:
% 154.11/23.29  | |   (9)  op(e0, e0) = e2
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #1043.
% 154.11/23.29  | | 
% 154.11/23.29  | End of split
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #895 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (2)  op(e1, e1) = e0
% 154.11/23.29    (3)   ~ (e3 = e0)
% 154.11/23.29    (4)   ~ (all_52_2 = e1)
% 154.11/23.29    (5)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 154.11/23.29             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.11/23.29           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 154.11/23.29           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 154.11/23.29           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 154.11/23.29           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 154.11/23.29           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 154.11/23.29           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 154.11/23.29           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 154.11/23.29           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 154.11/23.29           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 154.11/23.29           $i(all_57_14))
% 154.11/23.29    (6)  op(e0, e0) = e0
% 154.11/23.29    (7)  op(e1, e3) = all_52_2
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | BETA: splitting (5) gives:
% 154.11/23.29  | 
% 154.11/23.29  | Case 1:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (8)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 154.11/23.29  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.11/23.29  | |          all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 154.11/23.29  | |        (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 154.11/23.29  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 154.11/23.29  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 154.11/23.29  | | 
% 154.11/23.29  | | BETA: splitting (8) gives:
% 154.11/23.29  | | 
% 154.11/23.29  | | Case 1:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (9)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 154.11/23.29  | | |          = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.11/23.29  | | |        all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 154.11/23.29  | | | 
% 154.11/23.29  | | | ALPHA: (9) implies:
% 154.11/23.29  | | |   (10)  op(e1, e1) = e3
% 154.11/23.29  | | | 
% 154.11/23.29  | | | REF_CLOSE: (1), (2), (3), (10) are inconsistent by sub-proof #896.
% 154.11/23.29  | | | 
% 154.11/23.29  | | Case 2:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (11)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 154.11/23.29  | | |         (all_57_12 = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 &
% 154.11/23.29  | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 154.11/23.29  | | |         $i(all_57_12)
% 154.11/23.29  | | | 
% 154.11/23.29  | | | ALPHA: (11) implies:
% 154.11/23.29  | | |   (12)  op(e0, e0) = e3
% 154.11/23.29  | | | 
% 154.11/23.29  | | | REF_CLOSE: (1), (3), (6), (12) are inconsistent by sub-proof #1143.
% 154.11/23.29  | | | 
% 154.11/23.29  | | End of split
% 154.11/23.29  | | 
% 154.11/23.29  | Case 2:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (13)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 154.11/23.29  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) =
% 154.11/23.29  | |           e1 & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 154.11/23.29  | |         (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 154.11/23.29  | |             = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 154.11/23.29  | |           all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (1), (3), (4), (6), (7), (13) are inconsistent by sub-proof
% 154.11/23.29  | |            #1045.
% 154.11/23.29  | | 
% 154.11/23.29  | End of split
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #896 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (2)  op(e1, e1) = e3
% 154.11/23.29    (3)  op(e1, e1) = e0
% 154.11/23.29    (4)   ~ (e3 = e0)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | GROUND_INST: instantiating (1) with e3, e0, e1, e1, simplifying with (2), (3)
% 154.11/23.29  |              gives:
% 154.11/23.29  |   (5)  e3 = e0
% 154.11/23.29  | 
% 154.11/23.29  | REDUCE: (4), (5) imply:
% 154.11/23.29  |   (6)  $false
% 154.11/23.29  | 
% 154.11/23.29  | CLOSE: (6) is inconsistent.
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #897 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)  all_54_10 = e1 | all_54_10 = e0
% 154.11/23.29    (2)   ~ (all_4_2 = e1)
% 154.11/23.29    (3)  op(e1, e1) = all_4_2
% 154.11/23.29    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (5)  all_54_10 = all_4_2
% 154.11/23.29    (6)  op(e1, e1) = e1
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | BETA: splitting (1) gives:
% 154.11/23.29  | 
% 154.11/23.29  | Case 1:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (7)  all_54_10 = e1
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #1167.
% 154.11/23.29  | | 
% 154.11/23.29  | Case 2:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (8)  all_54_10 = e0
% 154.11/23.29  | | 
% 154.11/23.29  | | COMBINE_EQS: (5), (8) imply:
% 154.11/23.29  | |   (9)  all_4_2 = e0
% 154.11/23.29  | | 
% 154.11/23.29  | | SIMP: (9) implies:
% 154.11/23.29  | |   (10)  all_4_2 = e0
% 154.11/23.29  | | 
% 154.11/23.29  | | REDUCE: (2), (10) imply:
% 154.11/23.29  | |   (11)   ~ (e1 = e0)
% 154.11/23.29  | | 
% 154.11/23.29  | | SIMP: (11) implies:
% 154.11/23.29  | |   (12)   ~ (e1 = e0)
% 154.11/23.29  | | 
% 154.11/23.29  | | REDUCE: (3), (10) imply:
% 154.11/23.29  | |   (13)  op(e1, e1) = e0
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (4), (6), (12), (13) are inconsistent by sub-proof #1038.
% 154.11/23.29  | | 
% 154.11/23.29  | End of split
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #898 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)   ~ (e3 = e1)
% 154.11/23.29    (2)  op(e2, e2) = e1
% 154.11/23.29    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (4)  op(e3, e3) = e1
% 154.11/23.29    (5)  (all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2) |
% 154.11/23.29             ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 154.11/23.29           ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1, e1)
% 154.11/23.29               = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0, e3) = e0)
% 154.11/23.29             | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.11/23.29         (all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3) |
% 154.11/23.29             ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.11/23.29           ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1)
% 154.11/23.29               = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0, e2) = e0)
% 154.11/23.29             | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 & $i(all_57_15))))
% 154.11/23.29    (6)   ~ (e2 = e1)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | BETA: splitting (5) gives:
% 154.11/23.29  | 
% 154.11/23.29  | Case 1:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (7)  all_57_10 = e3 & op(e3, e3) = e3 & ((all_57_0 = e2 & op(e2, e3) = e2)
% 154.11/23.29  | |          | ( ~ (all_57_12 = e3) & op(e2, e2) = all_57_12 & $i(all_57_12))) &
% 154.11/23.29  | |        ((all_57_1 = e1 & op(e1, e3) = e1) | ( ~ (all_57_14 = e3) & op(e1,
% 154.11/23.29  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_2 = e0 & op(e0,
% 154.11/23.29  | |              e3) = e0) | ( ~ (all_57_15 = e3) & op(e0, e0) = all_57_15 &
% 154.11/23.29  | |            $i(all_57_15)))
% 154.11/23.29  | | 
% 154.11/23.29  | | ALPHA: (7) implies:
% 154.11/23.29  | |   (8)  op(e3, e3) = e3
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1178.
% 154.11/23.29  | | 
% 154.11/23.29  | Case 2:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (9)  all_57_12 = e2 & op(e2, e2) = e2 & ((all_57_3 = e3 & op(e3, e2) = e3)
% 154.11/23.29  | |          | ( ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.11/23.29  | |        ((all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1,
% 154.11/23.29  | |              e1) = all_57_14 & $i(all_57_14))) & ((all_57_5 = e0 & op(e0,
% 154.11/23.29  | |              e2) = e0) | ( ~ (all_57_15 = e2) & op(e0, e0) = all_57_15 &
% 154.11/23.29  | |            $i(all_57_15)))
% 154.11/23.29  | | 
% 154.11/23.29  | | ALPHA: (9) implies:
% 154.11/23.29  | |   (10)  op(e2, e2) = e2
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #1158.
% 154.11/23.29  | | 
% 154.11/23.29  | End of split
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #899 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (2)  op(e0, e1) = e1
% 154.11/23.29    (3)  op(e0, e1) = e0
% 154.11/23.29    (4)   ~ (e1 = e0)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | GROUND_INST: instantiating (1) with e1, e0, e1, e0, simplifying with (2), (3)
% 154.11/23.29  |              gives:
% 154.11/23.29  |   (5)  e1 = e0
% 154.11/23.29  | 
% 154.11/23.29  | REDUCE: (4), (5) imply:
% 154.11/23.29  |   (6)  $false
% 154.11/23.29  | 
% 154.11/23.29  | CLOSE: (6) is inconsistent.
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #900 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (2)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.11/23.29             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.11/23.29           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.11/23.29           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.11/23.29             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.11/23.29           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.29           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.11/23.29    (3)  op(e0, e0) = e2
% 154.11/23.29    (4)  op(e0, e3) = all_52_3
% 154.11/23.29    (5)  op(e0, e0) = all_57_15
% 154.11/23.29    (6)   ~ (all_52_3 = e0)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | BETA: splitting (2) gives:
% 154.11/23.29  | 
% 154.11/23.29  | Case 1:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (7)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.11/23.29  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.11/23.29  | |        $i(all_57_0)
% 154.11/23.29  | | 
% 154.11/23.29  | | ALPHA: (7) implies:
% 154.11/23.29  | |   (8)  op(e0, e3) = e0
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #1142.
% 154.11/23.29  | | 
% 154.11/23.29  | Case 2:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (9)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 154.11/23.29  | |            = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0
% 154.11/23.29  | |          & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 154.11/23.29  | |            e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.29  | |          all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.11/23.29  | | 
% 154.11/23.29  | | BETA: splitting (9) gives:
% 154.11/23.29  | | 
% 154.11/23.29  | | Case 1:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (10)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.11/23.29  | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.11/23.29  | | |         op(e0, e3) = e0 & $i(all_57_1)
% 154.11/23.29  | | | 
% 154.11/23.29  | | | ALPHA: (10) implies:
% 154.11/23.29  | | |   (11)  op(e0, e3) = e0
% 154.11/23.29  | | | 
% 154.11/23.29  | | | REF_CLOSE: (1), (4), (6), (11) are inconsistent by sub-proof #1142.
% 154.11/23.29  | | | 
% 154.11/23.29  | | Case 2:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (12)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.11/23.29  | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 154.11/23.29  | | |         op(e0, e2) = e0 & $i(all_57_3)
% 154.11/23.29  | | | 
% 154.11/23.29  | | | ALPHA: (12) implies:
% 154.11/23.29  | | |   (13)   ~ (all_57_15 = e2)
% 154.11/23.29  | | | 
% 154.11/23.29  | | | REF_CLOSE: (1), (3), (5), (13) are inconsistent by sub-proof #901.
% 154.11/23.29  | | | 
% 154.11/23.29  | | End of split
% 154.11/23.29  | | 
% 154.11/23.29  | End of split
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #901 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (2)  op(e0, e0) = all_57_15
% 154.11/23.29    (3)  op(e0, e0) = e2
% 154.11/23.29    (4)   ~ (all_57_15 = e2)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | GROUND_INST: instantiating (1) with e2, all_57_15, e0, e0, simplifying with
% 154.11/23.29  |              (2), (3) gives:
% 154.11/23.29  |   (5)  all_57_15 = e2
% 154.11/23.29  | 
% 154.11/23.29  | REDUCE: (4), (5) imply:
% 154.11/23.29  |   (6)  $false
% 154.11/23.29  | 
% 154.11/23.29  | CLOSE: (6) is inconsistent.
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #902 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)  all_54_14 = all_52_11
% 154.11/23.29    (2)  all_54_14 = e2
% 154.11/23.29    (3)   ~ (all_52_11 = e2)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.29  |   (4)  all_52_11 = e2
% 154.11/23.29  | 
% 154.11/23.29  | SIMP: (4) implies:
% 154.11/23.29  |   (5)  all_52_11 = e2
% 154.11/23.29  | 
% 154.11/23.29  | REDUCE: (3), (5) imply:
% 154.11/23.29  |   (6)  $false
% 154.11/23.29  | 
% 154.11/23.29  | CLOSE: (6) is inconsistent.
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #903 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)  all_54_14 = all_52_11
% 154.11/23.29    (2)  all_54_14 = e3
% 154.11/23.29    (3)   ~ (all_52_11 = e3)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.29  |   (4)  all_52_11 = e3
% 154.11/23.29  | 
% 154.11/23.29  | SIMP: (4) implies:
% 154.11/23.29  |   (5)  all_52_11 = e3
% 154.11/23.29  | 
% 154.11/23.29  | REDUCE: (3), (5) imply:
% 154.11/23.29  |   (6)  $false
% 154.11/23.29  | 
% 154.11/23.29  | CLOSE: (6) is inconsistent.
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #904 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)  op(e2, e0) = e1
% 154.11/23.29    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (3)  op(e2, e0) = e2
% 154.11/23.29    (4)  op(e2, e0) = all_52_13
% 154.11/23.29    (5)   ~ (e2 = e1)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | GROUND_INST: instantiating (2) with all_52_13, e1, e0, e2, simplifying with
% 154.11/23.29  |              (1), (4) gives:
% 154.11/23.29  |   (6)  all_52_13 = e1
% 154.11/23.29  | 
% 154.11/23.29  | GROUND_INST: instantiating (2) with all_52_13, e2, e0, e2, simplifying with
% 154.11/23.29  |              (3), (4) gives:
% 154.11/23.29  |   (7)  all_52_13 = e2
% 154.11/23.29  | 
% 154.11/23.29  | COMBINE_EQS: (6), (7) imply:
% 154.11/23.29  |   (8)  e2 = e1
% 154.11/23.29  | 
% 154.11/23.29  | REDUCE: (5), (8) imply:
% 154.11/23.29  |   (9)  $false
% 154.11/23.29  | 
% 154.11/23.29  | CLOSE: (9) is inconsistent.
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #905 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)  op(e3, e3) = e0
% 154.11/23.29    (2)   ~ (e3 = e1)
% 154.11/23.29    (3)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 154.11/23.29         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 154.11/23.29    (4)   ~ (e2 = e0)
% 154.11/23.29    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (6)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 154.11/23.29         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 154.11/23.29    (7)   ~ (e1 = e0)
% 154.11/23.29    (8)  all_56_9 = e0
% 154.11/23.29    (9)   ~ (e3 = e2)
% 154.11/23.29    (10)   ~ (e2 = e1)
% 154.11/23.29    (11)  all_56_1 = e3
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | BETA: splitting (6) gives:
% 154.11/23.29  | 
% 154.11/23.29  | Case 1:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 154.11/23.29  | |           e1)
% 154.11/23.29  | | 
% 154.11/23.29  | | BETA: splitting (12) gives:
% 154.11/23.29  | | 
% 154.11/23.29  | | Case 1:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (13)  all_56_0 = e1 & op(e3, e3) = e1
% 154.11/23.29  | | | 
% 154.11/23.29  | | | ALPHA: (13) implies:
% 154.11/23.29  | | |   (14)  op(e3, e3) = e1
% 154.11/23.29  | | | 
% 154.11/23.29  | | | REF_CLOSE: (1), (5), (7), (14) are inconsistent by sub-proof #957.
% 154.11/23.29  | | | 
% 154.11/23.29  | | Case 2:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (15)  all_56_1 = e1 & op(e3, e2) = e1
% 154.11/23.29  | | | 
% 154.11/23.29  | | | REF_CLOSE: (2), (11), (15) are inconsistent by sub-proof #1112.
% 154.11/23.29  | | | 
% 154.11/23.29  | | End of split
% 154.11/23.29  | | 
% 154.11/23.29  | Case 2:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (16)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 154.11/23.29  | |           e1)
% 154.11/23.29  | | 
% 154.11/23.29  | | BETA: splitting (16) gives:
% 154.11/23.29  | | 
% 154.11/23.29  | | Case 1:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (17)  all_56_4 = e1 & op(e3, e1) = e1
% 154.11/23.29  | | | 
% 154.11/23.29  | | | ALPHA: (17) implies:
% 154.11/23.29  | | |   (18)  all_56_4 = e1
% 154.11/23.29  | | | 
% 154.11/23.29  | | | BETA: splitting (3) gives:
% 154.11/23.29  | | | 
% 154.11/23.29  | | | Case 1:
% 154.11/23.29  | | | | 
% 154.11/23.29  | | | |   (19)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2)
% 154.11/23.29  | | | |           = e2)
% 154.11/23.29  | | | | 
% 154.11/23.29  | | | | BETA: splitting (19) gives:
% 154.11/23.29  | | | | 
% 154.11/23.29  | | | | Case 1:
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | |   (20)  all_56_0 = e2 & op(e3, e3) = e2
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | | ALPHA: (20) implies:
% 154.11/23.29  | | | | |   (21)  op(e3, e3) = e2
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | | REF_CLOSE: (1), (4), (5), (21) are inconsistent by sub-proof #1073.
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | Case 2:
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | |   (22)  all_56_1 = e2 & op(e3, e2) = e2
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | | REF_CLOSE: (9), (11), (22) are inconsistent by sub-proof #907.
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | End of split
% 154.11/23.29  | | | | 
% 154.11/23.29  | | | Case 2:
% 154.11/23.29  | | | | 
% 154.11/23.29  | | | |   (23)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0)
% 154.11/23.29  | | | |           = e2)
% 154.11/23.29  | | | | 
% 154.11/23.29  | | | | BETA: splitting (23) gives:
% 154.11/23.29  | | | | 
% 154.11/23.29  | | | | Case 1:
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | |   (24)  all_56_4 = e2 & op(e3, e1) = e2
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | | ALPHA: (24) implies:
% 154.11/23.29  | | | | |   (25)  all_56_4 = e2
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | | REF_CLOSE: (10), (18), (25) are inconsistent by sub-proof #980.
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | Case 2:
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | |   (26)  all_56_9 = e2 & op(e3, e0) = e2
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | | REF_CLOSE: (4), (8), (26) are inconsistent by sub-proof #906.
% 154.11/23.29  | | | | | 
% 154.11/23.29  | | | | End of split
% 154.11/23.29  | | | | 
% 154.11/23.29  | | | End of split
% 154.11/23.29  | | | 
% 154.11/23.29  | | Case 2:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (27)  all_56_9 = e1 & op(e3, e0) = e1
% 154.11/23.29  | | | 
% 154.11/23.29  | | | ALPHA: (27) implies:
% 154.11/23.29  | | |   (28)  all_56_9 = e1
% 154.11/23.29  | | | 
% 154.11/23.29  | | | REF_CLOSE: (7), (8), (28) are inconsistent by sub-proof #946.
% 154.11/23.29  | | | 
% 154.11/23.29  | | End of split
% 154.11/23.29  | | 
% 154.11/23.29  | End of split
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #906 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)  all_56_9 = e2 & op(e3, e0) = e2
% 154.11/23.29    (2)  all_56_9 = e0
% 154.11/23.29    (3)   ~ (e2 = e0)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | ALPHA: (1) implies:
% 154.11/23.29  |   (4)  all_56_9 = e2
% 154.11/23.29  | 
% 154.11/23.29  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.29  |   (5)  e2 = e0
% 154.11/23.29  | 
% 154.11/23.29  | REDUCE: (3), (5) imply:
% 154.11/23.29  |   (6)  $false
% 154.11/23.29  | 
% 154.11/23.29  | CLOSE: (6) is inconsistent.
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #907 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)  all_56_1 = e2 & op(e3, e2) = e2
% 154.11/23.29    (2)  all_56_1 = e3
% 154.11/23.29    (3)   ~ (e3 = e2)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | ALPHA: (1) implies:
% 154.11/23.29  |   (4)  all_56_1 = e2
% 154.11/23.29  | 
% 154.11/23.29  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.29  |   (5)  e3 = e2
% 154.11/23.29  | 
% 154.11/23.29  | REDUCE: (3), (5) imply:
% 154.11/23.29  |   (6)  $false
% 154.11/23.29  | 
% 154.11/23.29  | CLOSE: (6) is inconsistent.
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #908 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)  op(e0, e1) = all_52_11
% 154.11/23.29    (2)  all_56_5 = e3
% 154.11/23.29    (3)  op(e1, e1) = e2
% 154.11/23.29    (4)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0) |
% 154.11/23.29         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) = e0)
% 154.11/23.29    (5)   ~ (e2 = e0)
% 154.11/23.29    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.29           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.29    (7)  all_56_4 = e2
% 154.11/23.29    (8)   ~ (e3 = e0)
% 154.11/23.29    (9)   ~ (all_52_11 = e0)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | BETA: splitting (4) gives:
% 154.11/23.29  | 
% 154.11/23.29  | Case 1:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (10)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) =
% 154.11/23.29  | |           e0)
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (2), (5), (7), (8), (10) are inconsistent by sub-proof #909.
% 154.11/23.29  | | 
% 154.11/23.29  | Case 2:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (11)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 154.11/23.29  | |           e0)
% 154.11/23.29  | | 
% 154.11/23.29  | | BETA: splitting (11) gives:
% 154.11/23.29  | | 
% 154.11/23.29  | | Case 1:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (12)  all_56_8 = e0 & op(e1, e1) = e0
% 154.11/23.29  | | | 
% 154.11/23.29  | | | ALPHA: (12) implies:
% 154.11/23.29  | | |   (13)  op(e1, e1) = e0
% 154.11/23.29  | | | 
% 154.11/23.29  | | | REF_CLOSE: (3), (5), (6), (13) are inconsistent by sub-proof #1006.
% 154.11/23.29  | | | 
% 154.11/23.29  | | Case 2:
% 154.11/23.29  | | | 
% 154.11/23.29  | | |   (14)  all_56_14 = e0 & op(e0, e1) = e0
% 154.11/23.29  | | | 
% 154.11/23.29  | | | ALPHA: (14) implies:
% 154.11/23.29  | | |   (15)  op(e0, e1) = e0
% 154.11/23.29  | | | 
% 154.11/23.29  | | | REF_CLOSE: (1), (6), (9), (15) are inconsistent by sub-proof #1124.
% 154.11/23.29  | | | 
% 154.11/23.29  | | End of split
% 154.11/23.29  | | 
% 154.11/23.29  | End of split
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #909 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_5 = e0 & op(e2, e1) = e0)
% 154.11/23.29    (2)  all_56_5 = e3
% 154.11/23.29    (3)   ~ (e2 = e0)
% 154.11/23.29    (4)  all_56_4 = e2
% 154.11/23.29    (5)   ~ (e3 = e0)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | BETA: splitting (1) gives:
% 154.11/23.29  | 
% 154.11/23.29  | Case 1:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (6)  all_56_4 = e0 & op(e3, e1) = e0
% 154.11/23.29  | | 
% 154.11/23.29  | | ALPHA: (6) implies:
% 154.11/23.29  | |   (7)  all_56_4 = e0
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #936.
% 154.11/23.29  | | 
% 154.11/23.29  | Case 2:
% 154.11/23.29  | | 
% 154.11/23.29  | |   (8)  all_56_5 = e0 & op(e2, e1) = e0
% 154.11/23.29  | | 
% 154.11/23.29  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #910.
% 154.11/23.29  | | 
% 154.11/23.29  | End of split
% 154.11/23.29  | 
% 154.11/23.29  End of proof
% 154.11/23.29  
% 154.11/23.29  Sub-proof #910 shows that the following formulas are inconsistent:
% 154.11/23.29  ----------------------------------------------------------------
% 154.11/23.29    (1)  all_56_5 = e0 & op(e2, e1) = e0
% 154.11/23.29    (2)  all_56_5 = e3
% 154.11/23.29    (3)   ~ (e3 = e0)
% 154.11/23.29  
% 154.11/23.29  Begin of proof
% 154.11/23.29  | 
% 154.11/23.29  | ALPHA: (1) implies:
% 154.11/23.29  |   (4)  all_56_5 = e0
% 154.11/23.29  | 
% 154.11/23.29  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.29  |   (5)  e3 = e0
% 154.11/23.29  | 
% 154.11/23.29  | REDUCE: (3), (5) imply:
% 154.11/23.30  |   (6)  $false
% 154.11/23.30  | 
% 154.11/23.30  | CLOSE: (6) is inconsistent.
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #911 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)   ~ (all_52_2 = all_52_6)
% 154.11/23.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (3)  op(e1, e3) = e1
% 154.11/23.30    (4)  op(e1, e2) = all_52_6
% 154.11/23.30    (5)  op(e1, e2) = e1
% 154.11/23.30    (6)  op(e1, e3) = all_52_2
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | GROUND_INST: instantiating (2) with all_52_6, e1, e2, e1, simplifying with
% 154.11/23.30  |              (4), (5) gives:
% 154.11/23.30  |   (7)  all_52_6 = e1
% 154.11/23.30  | 
% 154.11/23.30  | GROUND_INST: instantiating (2) with all_52_2, e1, e3, e1, simplifying with
% 154.11/23.30  |              (3), (6) gives:
% 154.11/23.30  |   (8)  all_52_2 = e1
% 154.11/23.30  | 
% 154.11/23.30  | REDUCE: (1), (7), (8) imply:
% 154.11/23.30  |   (9)  $false
% 154.11/23.30  | 
% 154.11/23.30  | CLOSE: (9) is inconsistent.
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #912 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)  op(e3, e1) = all_34_1
% 154.11/23.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (3)  op(e3, e1) = e3
% 154.11/23.30    (4)  op(e3, e1) = all_22_1
% 154.11/23.30    (5)  op(e3, e1) = e2
% 154.11/23.30    (6)   ~ (e3 = e2)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | GROUND_INST: instantiating (2) with e2, all_22_1, e1, e3, simplifying with
% 154.11/23.30  |              (4), (5) gives:
% 154.11/23.30  |   (7)  all_22_1 = e2
% 154.11/23.30  | 
% 154.11/23.30  | GROUND_INST: instantiating (2) with all_22_1, all_34_1, e1, e3, simplifying
% 154.11/23.30  |              with (1), (4) gives:
% 154.11/23.30  |   (8)  all_34_1 = all_22_1
% 154.11/23.30  | 
% 154.11/23.30  | GROUND_INST: instantiating (2) with e3, all_34_1, e1, e3, simplifying with
% 154.11/23.30  |              (1), (3) gives:
% 154.11/23.30  |   (9)  all_34_1 = e3
% 154.11/23.30  | 
% 154.11/23.30  | COMBINE_EQS: (8), (9) imply:
% 154.11/23.30  |   (10)  all_22_1 = e3
% 154.11/23.30  | 
% 154.11/23.30  | SIMP: (10) implies:
% 154.11/23.30  |   (11)  all_22_1 = e3
% 154.11/23.30  | 
% 154.11/23.30  | COMBINE_EQS: (7), (11) imply:
% 154.11/23.30  |   (12)  e3 = e2
% 154.11/23.30  | 
% 154.11/23.30  | REDUCE: (6), (12) imply:
% 154.11/23.30  |   (13)  $false
% 154.11/23.30  | 
% 154.11/23.30  | CLOSE: (13) is inconsistent.
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #913 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)   ~ (e3 = e1)
% 154.11/23.30    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 154.11/23.30         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 154.11/23.30    (3)  all_56_9 = e1
% 154.11/23.30    (4)  op(e3, e2) = all_52_4
% 154.11/23.30    (5)   ~ (e2 = e0)
% 154.11/23.30    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (7)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 154.11/23.30         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 154.11/23.30    (8)   ~ (e3 = e0)
% 154.11/23.30    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 154.11/23.30         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 154.11/23.30    (10)  op(e3, e3) = e1
% 154.11/23.30    (11)   ~ (e1 = e0)
% 154.11/23.30    (12)   ~ (e3 = e2)
% 154.11/23.30    (13)   ~ (e2 = e1)
% 154.11/23.30    (14)   ~ (all_52_4 = e0)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | BETA: splitting (9) gives:
% 154.11/23.30  | 
% 154.11/23.30  | Case 1:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (15)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 154.11/23.30  | |           e0)
% 154.11/23.30  | | 
% 154.11/23.30  | | REF_CLOSE: (4), (6), (10), (11), (14), (15) are inconsistent by sub-proof
% 154.11/23.30  | |            #937.
% 154.11/23.30  | | 
% 154.11/23.30  | Case 2:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (16)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 154.11/23.30  | |           e0)
% 154.11/23.30  | | 
% 154.11/23.30  | | BETA: splitting (16) gives:
% 154.11/23.30  | | 
% 154.11/23.30  | | Case 1:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (17)  all_56_4 = e0 & op(e3, e1) = e0
% 154.11/23.30  | | | 
% 154.11/23.30  | | | ALPHA: (17) implies:
% 154.11/23.30  | | |   (18)  all_56_4 = e0
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (12), (13), (18) are
% 154.11/23.30  | | |            inconsistent by sub-proof #914.
% 154.11/23.30  | | | 
% 154.11/23.30  | | Case 2:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (19)  all_56_9 = e0 & op(e3, e0) = e0
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (3), (11), (19) are inconsistent by sub-proof #1063.
% 154.11/23.30  | | | 
% 154.11/23.30  | | End of split
% 154.11/23.30  | | 
% 154.11/23.30  | End of split
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #914 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)   ~ (e3 = e1)
% 154.11/23.30    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 154.11/23.30         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 154.11/23.30    (3)  all_56_9 = e1
% 154.11/23.30    (4)  all_56_4 = e0
% 154.11/23.30    (5)   ~ (e2 = e0)
% 154.11/23.30    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (7)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 154.11/23.30         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 154.11/23.30    (8)   ~ (e3 = e0)
% 154.11/23.30    (9)  op(e3, e3) = e1
% 154.11/23.30    (10)   ~ (e3 = e2)
% 154.11/23.30    (11)   ~ (e2 = e1)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | BETA: splitting (7) gives:
% 154.11/23.30  | 
% 154.11/23.30  | Case 1:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (12)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 154.11/23.30  | |           e3)
% 154.11/23.30  | | 
% 154.11/23.30  | | BETA: splitting (12) gives:
% 154.11/23.30  | | 
% 154.11/23.30  | | Case 1:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (13)  all_56_0 = e3 & op(e3, e3) = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | ALPHA: (13) implies:
% 154.11/23.30  | | |   (14)  op(e3, e3) = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (1), (6), (9), (14) are inconsistent by sub-proof #1178.
% 154.11/23.30  | | | 
% 154.11/23.30  | | Case 2:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (15)  all_56_1 = e3 & op(e3, e2) = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | ALPHA: (15) implies:
% 154.11/23.30  | | |   (16)  all_56_1 = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (2), (3), (4), (5), (6), (9), (10), (11), (16) are inconsistent
% 154.11/23.30  | | |            by sub-proof #947.
% 154.11/23.30  | | | 
% 154.11/23.30  | | End of split
% 154.11/23.30  | | 
% 154.11/23.30  | Case 2:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (17)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 154.11/23.30  | |           e3)
% 154.11/23.30  | | 
% 154.11/23.30  | | BETA: splitting (17) gives:
% 154.11/23.30  | | 
% 154.11/23.30  | | Case 1:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (18)  all_56_4 = e3 & op(e3, e1) = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (4), (8), (18) are inconsistent by sub-proof #915.
% 154.11/23.30  | | | 
% 154.11/23.30  | | Case 2:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (19)  all_56_9 = e3 & op(e3, e0) = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | ALPHA: (19) implies:
% 154.11/23.30  | | |   (20)  all_56_9 = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (1), (3), (20) are inconsistent by sub-proof #1064.
% 154.11/23.30  | | | 
% 154.11/23.30  | | End of split
% 154.11/23.30  | | 
% 154.11/23.30  | End of split
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #915 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)  all_56_4 = e3 & op(e3, e1) = e3
% 154.11/23.30    (2)  all_56_4 = e0
% 154.11/23.30    (3)   ~ (e3 = e0)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | ALPHA: (1) implies:
% 154.11/23.30  |   (4)  all_56_4 = e3
% 154.11/23.30  | 
% 154.11/23.30  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.30  |   (5)  e3 = e0
% 154.11/23.30  | 
% 154.11/23.30  | SIMP: (5) implies:
% 154.11/23.30  |   (6)  e3 = e0
% 154.11/23.30  | 
% 154.11/23.30  | REDUCE: (3), (6) imply:
% 154.11/23.30  |   (7)  $false
% 154.11/23.30  | 
% 154.11/23.30  | CLOSE: (7) is inconsistent.
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #916 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)   ~ (e3 = e1)
% 154.11/23.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (3)   ~ (all_52_1 = e3)
% 154.11/23.30    (4)  op(e3, e3) = e1
% 154.11/23.30    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 154.11/23.30    (6)  op(e2, e3) = all_52_1
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | BETA: splitting (5) gives:
% 154.11/23.30  | 
% 154.11/23.30  | Case 1:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (7)  all_56_0 = e3 & op(e3, e3) = e3
% 154.11/23.30  | | 
% 154.11/23.30  | | ALPHA: (7) implies:
% 154.11/23.30  | |   (8)  op(e3, e3) = e3
% 154.11/23.30  | | 
% 154.11/23.30  | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #1178.
% 154.11/23.30  | | 
% 154.11/23.30  | Case 2:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (9)  all_56_2 = e3 & op(e2, e3) = e3
% 154.11/23.30  | | 
% 154.11/23.30  | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #917.
% 154.11/23.30  | | 
% 154.11/23.30  | End of split
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #917 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)  all_56_2 = e3 & op(e2, e3) = e3
% 154.11/23.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (3)  op(e2, e3) = all_52_1
% 154.11/23.30    (4)   ~ (all_52_1 = e3)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | ALPHA: (1) implies:
% 154.11/23.30  |   (5)  op(e2, e3) = e3
% 154.11/23.30  | 
% 154.11/23.30  | GROUND_INST: instantiating (2) with all_52_1, e3, e3, e2, simplifying with
% 154.11/23.30  |              (3), (5) gives:
% 154.11/23.30  |   (6)  all_52_1 = e3
% 154.11/23.30  | 
% 154.11/23.30  | REDUCE: (4), (6) imply:
% 154.11/23.30  |   (7)  $false
% 154.11/23.30  | 
% 154.11/23.30  | CLOSE: (7) is inconsistent.
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #918 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)   ~ (e3 = e1)
% 154.11/23.30    (2)  all_56_6 = e2
% 154.11/23.30    (3)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 154.11/23.30         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 154.11/23.30    (4)   ~ (e2 = e0)
% 154.11/23.30    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (6)  all_56_12 = e1
% 154.11/23.30    (7)   ~ (e3 = e0)
% 154.11/23.30    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 154.11/23.30         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.11/23.30    (9)   ~ (all_52_6 = e3)
% 154.11/23.30    (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 154.11/23.30          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 154.11/23.30    (11)  op(e3, e3) = e1
% 154.11/23.30    (12)  op(e1, e2) = all_52_6
% 154.11/23.30    (13)  op(e2, e2) = e2
% 154.11/23.30    (14)   ~ (e1 = e0)
% 154.11/23.30    (15)   ~ (e3 = e2)
% 154.11/23.30    (16)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.11/23.30          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.11/23.30    (17)   ~ (e2 = e1)
% 154.11/23.30    (18)  all_56_1 = e3
% 154.11/23.30    (19)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.11/23.30          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.11/23.30    (20)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 154.11/23.30          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | BETA: splitting (3) gives:
% 154.11/23.30  | 
% 154.11/23.30  | Case 1:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (21)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) =
% 154.11/23.30  | |           e3)
% 154.11/23.30  | | 
% 154.11/23.30  | | REF_CLOSE: (1), (4), (5), (6), (7), (8), (10), (11), (14), (15), (17), (21)
% 154.11/23.30  | |            are inconsistent by sub-proof #927.
% 154.11/23.30  | | 
% 154.11/23.30  | Case 2:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (22)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) =
% 154.11/23.30  | |           e3)
% 154.11/23.30  | | 
% 154.11/23.30  | | BETA: splitting (22) gives:
% 154.11/23.30  | | 
% 154.11/23.30  | | Case 1:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (23)  all_56_6 = e3 & op(e1, e3) = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (12), (13), (14), (15), (16),
% 154.11/23.30  | | |            (17), (18), (19), (20), (23) are inconsistent by sub-proof
% 154.11/23.30  | | |            #920.
% 154.11/23.30  | | | 
% 154.11/23.30  | | Case 2:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (24)  all_56_12 = e3 & op(e0, e3) = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (1), (6), (24) are inconsistent by sub-proof #919.
% 154.11/23.30  | | | 
% 154.11/23.30  | | End of split
% 154.11/23.30  | | 
% 154.11/23.30  | End of split
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #919 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)  all_56_12 = e3 & op(e0, e3) = e3
% 154.11/23.30    (2)  all_56_12 = e1
% 154.11/23.30    (3)   ~ (e3 = e1)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | ALPHA: (1) implies:
% 154.11/23.30  |   (4)  all_56_12 = e3
% 154.11/23.30  | 
% 154.11/23.30  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.30  |   (5)  e3 = e1
% 154.11/23.30  | 
% 154.11/23.30  | REDUCE: (3), (5) imply:
% 154.11/23.30  |   (6)  $false
% 154.11/23.30  | 
% 154.11/23.30  | CLOSE: (6) is inconsistent.
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #920 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)   ~ (e3 = e1)
% 154.11/23.30    (2)  all_56_6 = e2
% 154.11/23.30    (3)   ~ (e2 = e0)
% 154.11/23.30    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (5)   ~ (e3 = e0)
% 154.11/23.30    (6)  all_56_6 = e3 & op(e1, e3) = e3
% 154.11/23.30    (7)   ~ (all_52_6 = e3)
% 154.11/23.30    (8)  op(e1, e2) = all_52_6
% 154.11/23.30    (9)  op(e2, e2) = e2
% 154.11/23.30    (10)   ~ (e1 = e0)
% 154.11/23.30    (11)   ~ (e3 = e2)
% 154.11/23.30    (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.11/23.30          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.11/23.30    (13)   ~ (e2 = e1)
% 154.11/23.30    (14)  all_56_1 = e3
% 154.11/23.30    (15)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.11/23.30          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.11/23.30    (16)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 154.11/23.30          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | ALPHA: (6) implies:
% 154.11/23.30  |   (17)  all_56_6 = e3
% 154.11/23.30  | 
% 154.11/23.30  | COMBINE_EQS: (2), (17) imply:
% 154.11/23.30  |   (18)  e3 = e2
% 154.11/23.30  | 
% 154.11/23.30  | COMBINE_EQS: (14), (18) imply:
% 154.11/23.30  |   (19)  all_56_1 = e2
% 154.11/23.30  | 
% 154.11/23.30  | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (15),
% 154.11/23.30  |            (16), (19) are inconsistent by sub-proof #921.
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #921 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)   ~ (e3 = e1)
% 154.11/23.30    (2)   ~ (e2 = e0)
% 154.11/23.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (4)   ~ (e3 = e0)
% 154.11/23.30    (5)   ~ (all_52_6 = e3)
% 154.11/23.30    (6)  op(e1, e2) = all_52_6
% 154.11/23.30    (7)  op(e2, e2) = e2
% 154.11/23.30    (8)   ~ (e1 = e0)
% 154.11/23.30    (9)  all_56_1 = e2
% 154.11/23.30    (10)   ~ (e3 = e2)
% 154.11/23.30    (11)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.11/23.30          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.11/23.30    (12)   ~ (e2 = e1)
% 154.11/23.30    (13)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.11/23.30          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.11/23.30    (14)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 154.11/23.30          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | BETA: splitting (14) gives:
% 154.11/23.30  | 
% 154.11/23.30  | Case 1:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (15)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 154.11/23.30  | |           e3)
% 154.11/23.30  | | 
% 154.11/23.30  | | REF_CLOSE: (3), (7), (9), (10), (15) are inconsistent by sub-proof #926.
% 154.11/23.30  | | 
% 154.11/23.30  | Case 2:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (16)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 154.11/23.30  | |           e3)
% 154.11/23.30  | | 
% 154.11/23.30  | | BETA: splitting (16) gives:
% 154.11/23.30  | | 
% 154.11/23.30  | | Case 1:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (17)  all_56_7 = e3 & op(e1, e2) = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (3), (5), (6), (17) are inconsistent by sub-proof #925.
% 154.11/23.30  | | | 
% 154.11/23.30  | | Case 2:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (18)  all_56_13 = e3 & op(e0, e2) = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | ALPHA: (18) implies:
% 154.11/23.30  | | |   (19)  all_56_13 = e3
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (11), (12), (13), (19) are
% 154.11/23.30  | | |            inconsistent by sub-proof #922.
% 154.11/23.30  | | | 
% 154.11/23.30  | | End of split
% 154.11/23.30  | | 
% 154.11/23.30  | End of split
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #922 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)   ~ (e3 = e1)
% 154.11/23.30    (2)   ~ (e2 = e0)
% 154.11/23.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (4)   ~ (e3 = e0)
% 154.11/23.30    (5)  op(e2, e2) = e2
% 154.11/23.30    (6)   ~ (e1 = e0)
% 154.11/23.30    (7)  all_56_1 = e2
% 154.11/23.30    (8)  all_56_13 = e3
% 154.11/23.30    (9)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.11/23.30         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.11/23.30    (10)   ~ (e2 = e1)
% 154.11/23.30    (11)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.11/23.30          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | BETA: splitting (9) gives:
% 154.11/23.30  | 
% 154.11/23.30  | Case 1:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 154.11/23.30  | |           e0)
% 154.11/23.30  | | 
% 154.11/23.30  | | BETA: splitting (12) gives:
% 154.11/23.30  | | 
% 154.11/23.30  | | Case 1:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (13)  all_56_1 = e0 & op(e3, e2) = e0
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (2), (7), (13) are inconsistent by sub-proof #924.
% 154.11/23.30  | | | 
% 154.11/23.30  | | Case 2:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (14)  all_56_3 = e0 & op(e2, e2) = e0
% 154.11/23.30  | | | 
% 154.11/23.30  | | | ALPHA: (14) implies:
% 154.11/23.30  | | |   (15)  op(e2, e2) = e0
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (2), (3), (5), (15) are inconsistent by sub-proof #1145.
% 154.11/23.30  | | | 
% 154.11/23.30  | | End of split
% 154.11/23.30  | | 
% 154.11/23.30  | Case 2:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (16)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 154.11/23.30  | |           e0)
% 154.11/23.30  | | 
% 154.11/23.30  | | BETA: splitting (16) gives:
% 154.11/23.30  | | 
% 154.11/23.30  | | Case 1:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (17)  all_56_7 = e0 & op(e1, e2) = e0
% 154.11/23.30  | | | 
% 154.11/23.30  | | | ALPHA: (17) implies:
% 154.11/23.30  | | |   (18)  all_56_7 = e0
% 154.11/23.30  | | | 
% 154.11/23.30  | | | BETA: splitting (11) gives:
% 154.11/23.30  | | | 
% 154.11/23.30  | | | Case 1:
% 154.11/23.30  | | | | 
% 154.11/23.30  | | | |   (19)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2)
% 154.11/23.30  | | | |           = e1)
% 154.11/23.30  | | | | 
% 154.11/23.30  | | | | BETA: splitting (19) gives:
% 154.11/23.30  | | | | 
% 154.11/23.30  | | | | Case 1:
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | |   (20)  all_56_1 = e1 & op(e3, e2) = e1
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | | REF_CLOSE: (7), (10), (20) are inconsistent by sub-proof #923.
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | Case 2:
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | |   (21)  all_56_3 = e1 & op(e2, e2) = e1
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | | ALPHA: (21) implies:
% 154.11/23.30  | | | | |   (22)  op(e2, e2) = e1
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | | REF_CLOSE: (3), (5), (10), (22) are inconsistent by sub-proof #1158.
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | End of split
% 154.11/23.30  | | | | 
% 154.11/23.30  | | | Case 2:
% 154.11/23.30  | | | | 
% 154.11/23.30  | | | |   (23)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2)
% 154.11/23.30  | | | |           = e1)
% 154.11/23.30  | | | | 
% 154.11/23.30  | | | | BETA: splitting (23) gives:
% 154.11/23.30  | | | | 
% 154.11/23.30  | | | | Case 1:
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | |   (24)  all_56_7 = e1 & op(e1, e2) = e1
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | | REF_CLOSE: (6), (18), (24) are inconsistent by sub-proof #1111.
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | Case 2:
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | |   (25)  all_56_13 = e1 & op(e0, e2) = e1
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | | ALPHA: (25) implies:
% 154.11/23.30  | | | | |   (26)  all_56_13 = e1
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | | REF_CLOSE: (1), (8), (26) are inconsistent by sub-proof #1121.
% 154.11/23.30  | | | | | 
% 154.11/23.30  | | | | End of split
% 154.11/23.30  | | | | 
% 154.11/23.30  | | | End of split
% 154.11/23.30  | | | 
% 154.11/23.30  | | Case 2:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (27)  all_56_13 = e0 & op(e0, e2) = e0
% 154.11/23.30  | | | 
% 154.11/23.30  | | | ALPHA: (27) implies:
% 154.11/23.30  | | |   (28)  all_56_13 = e0
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (4), (8), (28) are inconsistent by sub-proof #1094.
% 154.11/23.30  | | | 
% 154.11/23.30  | | End of split
% 154.11/23.30  | | 
% 154.11/23.30  | End of split
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #923 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)  all_56_1 = e1 & op(e3, e2) = e1
% 154.11/23.30    (2)  all_56_1 = e2
% 154.11/23.30    (3)   ~ (e2 = e1)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | ALPHA: (1) implies:
% 154.11/23.30  |   (4)  all_56_1 = e1
% 154.11/23.30  | 
% 154.11/23.30  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.30  |   (5)  e2 = e1
% 154.11/23.30  | 
% 154.11/23.30  | REDUCE: (3), (5) imply:
% 154.11/23.30  |   (6)  $false
% 154.11/23.30  | 
% 154.11/23.30  | CLOSE: (6) is inconsistent.
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #924 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)  all_56_1 = e0 & op(e3, e2) = e0
% 154.11/23.30    (2)  all_56_1 = e2
% 154.11/23.30    (3)   ~ (e2 = e0)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | ALPHA: (1) implies:
% 154.11/23.30  |   (4)  all_56_1 = e0
% 154.11/23.30  | 
% 154.11/23.30  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.30  |   (5)  e2 = e0
% 154.11/23.30  | 
% 154.11/23.30  | REDUCE: (3), (5) imply:
% 154.11/23.30  |   (6)  $false
% 154.11/23.30  | 
% 154.11/23.30  | CLOSE: (6) is inconsistent.
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #925 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)  all_56_7 = e3 & op(e1, e2) = e3
% 154.11/23.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (3)  op(e1, e2) = all_52_6
% 154.11/23.30    (4)   ~ (all_52_6 = e3)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | ALPHA: (1) implies:
% 154.11/23.30  |   (5)  op(e1, e2) = e3
% 154.11/23.30  | 
% 154.11/23.30  | GROUND_INST: instantiating (2) with all_52_6, e3, e2, e1, simplifying with
% 154.11/23.30  |              (3), (5) gives:
% 154.11/23.30  |   (6)  all_52_6 = e3
% 154.11/23.30  | 
% 154.11/23.30  | REDUCE: (4), (6) imply:
% 154.11/23.30  |   (7)  $false
% 154.11/23.30  | 
% 154.11/23.30  | CLOSE: (7) is inconsistent.
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #926 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 154.11/23.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (3)  op(e2, e2) = e2
% 154.11/23.30    (4)  all_56_1 = e2
% 154.11/23.30    (5)   ~ (e3 = e2)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | BETA: splitting (1) gives:
% 154.11/23.30  | 
% 154.11/23.30  | Case 1:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (6)  all_56_1 = e3 & op(e3, e2) = e3
% 154.11/23.30  | | 
% 154.11/23.30  | | ALPHA: (6) implies:
% 154.11/23.30  | |   (7)  all_56_1 = e3
% 154.11/23.30  | | 
% 154.11/23.30  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #950.
% 154.11/23.30  | | 
% 154.11/23.30  | Case 2:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (8)  all_56_3 = e3 & op(e2, e2) = e3
% 154.11/23.30  | | 
% 154.11/23.30  | | ALPHA: (8) implies:
% 154.11/23.30  | |   (9)  op(e2, e2) = e3
% 154.11/23.30  | | 
% 154.11/23.30  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1179.
% 154.11/23.30  | | 
% 154.11/23.30  | End of split
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #927 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)   ~ (e3 = e1)
% 154.11/23.30    (2)   ~ (e2 = e0)
% 154.11/23.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (4)  all_56_12 = e1
% 154.11/23.30    (5)   ~ (e3 = e0)
% 154.11/23.30    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 154.11/23.30         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.11/23.30    (7)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 154.11/23.30         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 154.11/23.30    (8)  op(e3, e3) = e1
% 154.11/23.30    (9)   ~ (e1 = e0)
% 154.11/23.30    (10)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3)
% 154.11/23.30    (11)   ~ (e3 = e2)
% 154.11/23.30    (12)   ~ (e2 = e1)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | BETA: splitting (10) gives:
% 154.11/23.30  | 
% 154.11/23.30  | Case 1:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (13)  all_56_0 = e3 & op(e3, e3) = e3
% 154.11/23.30  | | 
% 154.11/23.30  | | ALPHA: (13) implies:
% 154.11/23.30  | |   (14)  op(e3, e3) = e3
% 154.11/23.30  | | 
% 154.11/23.30  | | REF_CLOSE: (1), (3), (8), (14) are inconsistent by sub-proof #1178.
% 154.11/23.30  | | 
% 154.11/23.30  | Case 2:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (15)  all_56_2 = e3 & op(e2, e3) = e3
% 154.11/23.30  | | 
% 154.11/23.30  | | ALPHA: (15) implies:
% 154.11/23.30  | |   (16)  all_56_2 = e3
% 154.11/23.30  | | 
% 154.11/23.30  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (16) are
% 154.11/23.30  | |            inconsistent by sub-proof #928.
% 154.11/23.30  | | 
% 154.11/23.30  | End of split
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #928 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)   ~ (e2 = e0)
% 154.11/23.30    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (3)  all_56_12 = e1
% 154.11/23.30    (4)   ~ (e3 = e0)
% 154.11/23.30    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 154.11/23.30         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.11/23.30    (6)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 154.11/23.30         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 154.11/23.30    (7)  op(e3, e3) = e1
% 154.11/23.30    (8)   ~ (e1 = e0)
% 154.11/23.30    (9)   ~ (e3 = e2)
% 154.11/23.30    (10)   ~ (e2 = e1)
% 154.11/23.30    (11)  all_56_2 = e3
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | BETA: splitting (6) gives:
% 154.11/23.30  | 
% 154.11/23.30  | Case 1:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (12)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) =
% 154.11/23.30  | |           e2)
% 154.11/23.30  | | 
% 154.11/23.30  | | REF_CLOSE: (2), (7), (9), (10), (11), (12) are inconsistent by sub-proof
% 154.11/23.30  | |            #933.
% 154.11/23.30  | | 
% 154.11/23.30  | Case 2:
% 154.11/23.30  | | 
% 154.11/23.30  | |   (13)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) =
% 154.11/23.30  | |           e2)
% 154.11/23.30  | | 
% 154.11/23.30  | | BETA: splitting (13) gives:
% 154.11/23.30  | | 
% 154.11/23.30  | | Case 1:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (14)  all_56_6 = e2 & op(e1, e3) = e2
% 154.11/23.30  | | | 
% 154.11/23.30  | | | ALPHA: (14) implies:
% 154.11/23.30  | | |   (15)  all_56_6 = e2
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (15) are inconsistent
% 154.11/23.30  | | |            by sub-proof #930.
% 154.11/23.30  | | | 
% 154.11/23.30  | | Case 2:
% 154.11/23.30  | | | 
% 154.11/23.30  | | |   (16)  all_56_12 = e2 & op(e0, e3) = e2
% 154.11/23.30  | | | 
% 154.11/23.30  | | | REF_CLOSE: (3), (10), (16) are inconsistent by sub-proof #929.
% 154.11/23.30  | | | 
% 154.11/23.30  | | End of split
% 154.11/23.30  | | 
% 154.11/23.30  | End of split
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #929 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)  all_56_12 = e2 & op(e0, e3) = e2
% 154.11/23.30    (2)  all_56_12 = e1
% 154.11/23.30    (3)   ~ (e2 = e1)
% 154.11/23.30  
% 154.11/23.30  Begin of proof
% 154.11/23.30  | 
% 154.11/23.30  | ALPHA: (1) implies:
% 154.11/23.30  |   (4)  all_56_12 = e2
% 154.11/23.30  | 
% 154.11/23.30  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.30  |   (5)  e2 = e1
% 154.11/23.30  | 
% 154.11/23.30  | REDUCE: (3), (5) imply:
% 154.11/23.30  |   (6)  $false
% 154.11/23.30  | 
% 154.11/23.30  | CLOSE: (6) is inconsistent.
% 154.11/23.30  | 
% 154.11/23.30  End of proof
% 154.11/23.30  
% 154.11/23.30  Sub-proof #930 shows that the following formulas are inconsistent:
% 154.11/23.30  ----------------------------------------------------------------
% 154.11/23.30    (1)  all_56_6 = e2
% 154.11/23.30    (2)   ~ (e2 = e0)
% 154.11/23.30    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.30           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.30    (4)  all_56_12 = e1
% 154.11/23.30    (5)   ~ (e3 = e0)
% 154.11/23.31    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 154.11/23.31         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.11/23.31    (7)  op(e3, e3) = e1
% 154.11/23.31    (8)   ~ (e1 = e0)
% 154.11/23.31    (9)  all_56_2 = e3
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (6) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 154.11/23.31  | |           e0)
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (3), (5), (7), (8), (9), (10) are inconsistent by sub-proof #931.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (11)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 154.11/23.31  | |           e0)
% 154.11/23.31  | | 
% 154.11/23.31  | | BETA: splitting (11) gives:
% 154.11/23.31  | | 
% 154.11/23.31  | | Case 1:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (12)  all_56_6 = e0 & op(e1, e3) = e0
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (1), (2), (12) are inconsistent by sub-proof #1054.
% 154.11/23.31  | | | 
% 154.11/23.31  | | Case 2:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (13)  all_56_12 = e0 & op(e0, e3) = e0
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (4), (8), (13) are inconsistent by sub-proof #1103.
% 154.11/23.31  | | | 
% 154.11/23.31  | | End of split
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #931 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 154.11/23.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (3)   ~ (e3 = e0)
% 154.11/23.31    (4)  op(e3, e3) = e1
% 154.11/23.31    (5)   ~ (e1 = e0)
% 154.11/23.31    (6)  all_56_2 = e3
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (1) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (7) implies:
% 154.11/23.31  | |   (8)  op(e3, e3) = e0
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #957.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (9)  all_56_2 = e0 & op(e2, e3) = e0
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #932.
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #932 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  all_56_2 = e0 & op(e2, e3) = e0
% 154.11/23.31    (2)  all_56_2 = e3
% 154.11/23.31    (3)   ~ (e3 = e0)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | ALPHA: (1) implies:
% 154.11/23.31  |   (4)  all_56_2 = e0
% 154.11/23.31  | 
% 154.11/23.31  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.31  |   (5)  e3 = e0
% 154.11/23.31  | 
% 154.11/23.31  | REDUCE: (3), (5) imply:
% 154.11/23.31  |   (6)  $false
% 154.11/23.31  | 
% 154.11/23.31  | CLOSE: (6) is inconsistent.
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #933 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 154.11/23.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (3)  op(e3, e3) = e1
% 154.11/23.31    (4)   ~ (e3 = e2)
% 154.11/23.31    (5)   ~ (e2 = e1)
% 154.11/23.31    (6)  all_56_2 = e3
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (1) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (7) implies:
% 154.11/23.31  | |   (8)  op(e3, e3) = e2
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1074.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (9)  all_56_2 = e2 & op(e2, e3) = e2
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #934.
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #934 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  all_56_2 = e2 & op(e2, e3) = e2
% 154.11/23.31    (2)  all_56_2 = e3
% 154.11/23.31    (3)   ~ (e3 = e2)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | ALPHA: (1) implies:
% 154.11/23.31  |   (4)  all_56_2 = e2
% 154.11/23.31  | 
% 154.11/23.31  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.31  |   (5)  e3 = e2
% 154.11/23.31  | 
% 154.11/23.31  | REDUCE: (3), (5) imply:
% 154.11/23.31  |   (6)  $false
% 154.11/23.31  | 
% 154.11/23.31  | CLOSE: (6) is inconsistent.
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #935 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)   ~ (e3 = e1)
% 154.11/23.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (3)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 154.11/23.31    (4)  op(e2, e2) = e2
% 154.11/23.31    (5)   ~ (e2 = e1)
% 154.11/23.31    (6)  all_56_1 = e3
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (3) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (7)  all_56_1 = e1 & op(e3, e2) = e1
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #1112.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (8)  all_56_3 = e1 & op(e2, e2) = e1
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (8) implies:
% 154.11/23.31  | |   (9)  op(e2, e2) = e1
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #1158.
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #936 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  all_56_4 = e2
% 154.11/23.31    (2)  all_56_4 = e0
% 154.11/23.31    (3)   ~ (e2 = e0)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.31  |   (4)  e2 = e0
% 154.11/23.31  | 
% 154.11/23.31  | SIMP: (4) implies:
% 154.11/23.31  |   (5)  e2 = e0
% 154.11/23.31  | 
% 154.11/23.31  | REDUCE: (3), (5) imply:
% 154.11/23.31  |   (6)  $false
% 154.11/23.31  | 
% 154.11/23.31  | CLOSE: (6) is inconsistent.
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #937 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  op(e3, e2) = all_52_4
% 154.11/23.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 154.11/23.31    (4)  op(e3, e3) = e1
% 154.11/23.31    (5)   ~ (e1 = e0)
% 154.11/23.31    (6)   ~ (all_52_4 = e0)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (3) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (7) implies:
% 154.11/23.31  | |   (8)  op(e3, e3) = e0
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #957.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (9)  all_56_1 = e0 & op(e3, e2) = e0
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (1), (2), (6), (9) are inconsistent by sub-proof #1013.
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #938 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2)
% 154.11/23.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (3)  op(e3, e3) = e1
% 154.11/23.31    (4)   ~ (e2 = e1)
% 154.11/23.31    (5)  op(e2, e3) = all_52_1
% 154.11/23.31    (6)   ~ (all_52_1 = e2)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (1) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (7) implies:
% 154.11/23.31  | |   (8)  op(e3, e3) = e2
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1074.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (9)  all_56_2 = e2 & op(e2, e3) = e2
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (9) implies:
% 154.11/23.31  | |   (10)  op(e2, e3) = e2
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1181.
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #939 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 154.11/23.31    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (3)   ~ (all_52_14 = e1)
% 154.11/23.31    (4)  op(e1, e0) = all_52_14
% 154.11/23.31    (5)   ~ (all_57_15 = e1)
% 154.11/23.31    (6)  op(e0, e0) = all_57_15
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (1) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (7)  all_56_11 = e1 & op(e1, e0) = e1
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (7) implies:
% 154.11/23.31  | |   (8)  op(e1, e0) = e1
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #961.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (9)  all_56_15 = e1 & op(e0, e0) = e1
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (9) implies:
% 154.11/23.31  | |   (10)  op(e0, e0) = e1
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #940.
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #940 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (2)  op(e0, e0) = all_57_15
% 154.11/23.31    (3)  op(e0, e0) = e1
% 154.11/23.31    (4)   ~ (all_57_15 = e1)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | GROUND_INST: instantiating (1) with e1, all_57_15, e0, e0, simplifying with
% 154.11/23.31  |              (2), (3) gives:
% 154.11/23.31  |   (5)  all_57_15 = e1
% 154.11/23.31  | 
% 154.11/23.31  | REDUCE: (4), (5) imply:
% 154.11/23.31  |   (6)  $false
% 154.11/23.31  | 
% 154.11/23.31  | CLOSE: (6) is inconsistent.
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #941 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)   ~ (e3 = e1)
% 154.11/23.31    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 154.11/23.31         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 154.11/23.31    (3)  all_56_9 = e1
% 154.11/23.31    (4)   ~ (e2 = e0)
% 154.11/23.31    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 154.11/23.31         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 154.11/23.31    (7)  all_56_4 = e2
% 154.11/23.31    (8)   ~ (e3 = e0)
% 154.11/23.31    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 154.11/23.31         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 154.11/23.31    (10)  op(e3, e3) = e1
% 154.11/23.31    (11)   ~ (e1 = e0)
% 154.11/23.31    (12)   ~ (e3 = e2)
% 154.11/23.31    (13)   ~ (e2 = e1)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (6) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (14)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 154.11/23.31  | |           e3)
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (11), (12), (13), (14)
% 154.11/23.31  | |            are inconsistent by sub-proof #944.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (15)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 154.11/23.31  | |           e3)
% 154.11/23.31  | | 
% 154.11/23.31  | | BETA: splitting (15) gives:
% 154.11/23.31  | | 
% 154.11/23.31  | | Case 1:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (16)  all_56_4 = e3 & op(e3, e1) = e3
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (7), (12), (16) are inconsistent by sub-proof #943.
% 154.11/23.31  | | | 
% 154.11/23.31  | | Case 2:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (17)  all_56_9 = e3 & op(e3, e0) = e3
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (1), (3), (17) are inconsistent by sub-proof #942.
% 154.11/23.31  | | | 
% 154.11/23.31  | | End of split
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #942 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  all_56_9 = e3 & op(e3, e0) = e3
% 154.11/23.31    (2)  all_56_9 = e1
% 154.11/23.31    (3)   ~ (e3 = e1)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | ALPHA: (1) implies:
% 154.11/23.31  |   (4)  all_56_9 = e3
% 154.11/23.31  | 
% 154.11/23.31  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.31  |   (5)  e3 = e1
% 154.11/23.31  | 
% 154.11/23.31  | REDUCE: (3), (5) imply:
% 154.11/23.31  |   (6)  $false
% 154.11/23.31  | 
% 154.11/23.31  | CLOSE: (6) is inconsistent.
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #943 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  all_56_4 = e3 & op(e3, e1) = e3
% 154.11/23.31    (2)  all_56_4 = e2
% 154.11/23.31    (3)   ~ (e3 = e2)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | ALPHA: (1) implies:
% 154.11/23.31  |   (4)  all_56_4 = e3
% 154.11/23.31  | 
% 154.11/23.31  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.31  |   (5)  e3 = e2
% 154.11/23.31  | 
% 154.11/23.31  | REDUCE: (3), (5) imply:
% 154.11/23.31  |   (6)  $false
% 154.11/23.31  | 
% 154.11/23.31  | CLOSE: (6) is inconsistent.
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #944 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)   ~ (e3 = e1)
% 154.11/23.31    (2)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 154.11/23.31         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 154.11/23.31    (3)  all_56_9 = e1
% 154.11/23.31    (4)   ~ (e2 = e0)
% 154.11/23.31    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (6)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3)
% 154.11/23.31    (7)   ~ (e3 = e0)
% 154.11/23.31    (8)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 154.11/23.31         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 154.11/23.31    (9)  op(e3, e3) = e1
% 154.11/23.31    (10)   ~ (e1 = e0)
% 154.11/23.31    (11)   ~ (e3 = e2)
% 154.11/23.31    (12)   ~ (e2 = e1)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (6) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (13)  all_56_0 = e3 & op(e3, e3) = e3
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (13) implies:
% 154.11/23.31  | |   (14)  op(e3, e3) = e3
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (1), (5), (9), (14) are inconsistent by sub-proof #1178.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (15)  all_56_1 = e3 & op(e3, e2) = e3
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (15) implies:
% 154.11/23.31  | |   (16)  all_56_1 = e3
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (16) are
% 154.11/23.31  | |            inconsistent by sub-proof #945.
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #945 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 154.11/23.31         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 154.11/23.31    (2)  all_56_9 = e1
% 154.11/23.31    (3)   ~ (e2 = e0)
% 154.11/23.31    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (5)   ~ (e3 = e0)
% 154.11/23.31    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 154.11/23.31         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 154.11/23.31    (7)  op(e3, e3) = e1
% 154.11/23.31    (8)   ~ (e1 = e0)
% 154.11/23.31    (9)   ~ (e3 = e2)
% 154.11/23.31    (10)   ~ (e2 = e1)
% 154.11/23.31    (11)  all_56_1 = e3
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (6) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (12)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) =
% 154.11/23.31  | |           e0)
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (4), (5), (7), (8), (11), (12) are inconsistent by sub-proof
% 154.11/23.31  | |            #951.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (13)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) =
% 154.11/23.31  | |           e0)
% 154.11/23.31  | | 
% 154.11/23.31  | | BETA: splitting (13) gives:
% 154.11/23.31  | | 
% 154.11/23.31  | | Case 1:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (14)  all_56_4 = e0 & op(e3, e1) = e0
% 154.11/23.31  | | | 
% 154.11/23.31  | | | ALPHA: (14) implies:
% 154.11/23.31  | | |   (15)  all_56_4 = e0
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (1), (2), (3), (4), (7), (9), (10), (11), (15) are inconsistent
% 154.11/23.31  | | |            by sub-proof #947.
% 154.11/23.31  | | | 
% 154.11/23.31  | | Case 2:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (16)  all_56_9 = e0 & op(e3, e0) = e0
% 154.11/23.31  | | | 
% 154.11/23.31  | | | ALPHA: (16) implies:
% 154.11/23.31  | | |   (17)  all_56_9 = e0
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (2), (8), (17) are inconsistent by sub-proof #946.
% 154.11/23.31  | | | 
% 154.11/23.31  | | End of split
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #946 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  all_56_9 = e1
% 154.11/23.31    (2)  all_56_9 = e0
% 154.11/23.31    (3)   ~ (e1 = e0)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.31  |   (4)  e1 = e0
% 154.11/23.31  | 
% 154.11/23.31  | SIMP: (4) implies:
% 154.11/23.31  |   (5)  e1 = e0
% 154.11/23.31  | 
% 154.11/23.31  | REDUCE: (3), (5) imply:
% 154.11/23.31  |   (6)  $false
% 154.11/23.31  | 
% 154.11/23.31  | CLOSE: (6) is inconsistent.
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #947 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2) |
% 154.11/23.31         (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) = e2)
% 154.11/23.31    (2)  all_56_9 = e1
% 154.11/23.31    (3)  all_56_4 = e0
% 154.11/23.31    (4)   ~ (e2 = e0)
% 154.11/23.31    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (6)  op(e3, e3) = e1
% 154.11/23.31    (7)   ~ (e3 = e2)
% 154.11/23.31    (8)   ~ (e2 = e1)
% 154.11/23.31    (9)  all_56_1 = e3
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (1) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (10)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) =
% 154.11/23.31  | |           e2)
% 154.11/23.31  | | 
% 154.11/23.31  | | BETA: splitting (10) gives:
% 154.11/23.31  | | 
% 154.11/23.31  | | Case 1:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (11)  all_56_0 = e2 & op(e3, e3) = e2
% 154.11/23.31  | | | 
% 154.11/23.31  | | | ALPHA: (11) implies:
% 154.11/23.31  | | |   (12)  op(e3, e3) = e2
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (5), (6), (8), (12) are inconsistent by sub-proof #1074.
% 154.11/23.31  | | | 
% 154.11/23.31  | | Case 2:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (13)  all_56_1 = e2 & op(e3, e2) = e2
% 154.11/23.31  | | | 
% 154.11/23.31  | | | ALPHA: (13) implies:
% 154.11/23.31  | | |   (14)  all_56_1 = e2
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (7), (9), (14) are inconsistent by sub-proof #950.
% 154.11/23.31  | | | 
% 154.11/23.31  | | End of split
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (15)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_9 = e2 & op(e3, e0) =
% 154.11/23.31  | |           e2)
% 154.11/23.31  | | 
% 154.11/23.31  | | BETA: splitting (15) gives:
% 154.11/23.31  | | 
% 154.11/23.31  | | Case 1:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (16)  all_56_4 = e2 & op(e3, e1) = e2
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (3), (4), (16) are inconsistent by sub-proof #949.
% 154.11/23.31  | | | 
% 154.11/23.31  | | Case 2:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (17)  all_56_9 = e2 & op(e3, e0) = e2
% 154.11/23.31  | | | 
% 154.11/23.31  | | | ALPHA: (17) implies:
% 154.11/23.31  | | |   (18)  all_56_9 = e2
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (2), (8), (18) are inconsistent by sub-proof #948.
% 154.11/23.31  | | | 
% 154.11/23.31  | | End of split
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #948 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  all_56_9 = e2
% 154.11/23.31    (2)  all_56_9 = e1
% 154.11/23.31    (3)   ~ (e2 = e1)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.31  |   (4)  e2 = e1
% 154.11/23.31  | 
% 154.11/23.31  | SIMP: (4) implies:
% 154.11/23.31  |   (5)  e2 = e1
% 154.11/23.31  | 
% 154.11/23.31  | REDUCE: (3), (5) imply:
% 154.11/23.31  |   (6)  $false
% 154.11/23.31  | 
% 154.11/23.31  | CLOSE: (6) is inconsistent.
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #949 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  all_56_4 = e2 & op(e3, e1) = e2
% 154.11/23.31    (2)  all_56_4 = e0
% 154.11/23.31    (3)   ~ (e2 = e0)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | ALPHA: (1) implies:
% 154.11/23.31  |   (4)  all_56_4 = e2
% 154.11/23.31  | 
% 154.11/23.31  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.31  |   (5)  e2 = e0
% 154.11/23.31  | 
% 154.11/23.31  | REDUCE: (3), (5) imply:
% 154.11/23.31  |   (6)  $false
% 154.11/23.31  | 
% 154.11/23.31  | CLOSE: (6) is inconsistent.
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #950 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  all_56_1 = e3
% 154.11/23.31    (2)  all_56_1 = e2
% 154.11/23.31    (3)   ~ (e3 = e2)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.31  |   (4)  e3 = e2
% 154.11/23.31  | 
% 154.11/23.31  | SIMP: (4) implies:
% 154.11/23.31  |   (5)  e3 = e2
% 154.11/23.31  | 
% 154.11/23.31  | REDUCE: (3), (5) imply:
% 154.11/23.31  |   (6)  $false
% 154.11/23.31  | 
% 154.11/23.31  | CLOSE: (6) is inconsistent.
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #951 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (2)   ~ (e3 = e0)
% 154.11/23.31    (3)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 154.11/23.31    (4)  op(e3, e3) = e1
% 154.11/23.31    (5)   ~ (e1 = e0)
% 154.11/23.31    (6)  all_56_1 = e3
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (3) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (7) implies:
% 154.11/23.31  | |   (8)  op(e3, e3) = e0
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #957.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (9)  all_56_1 = e0 & op(e3, e2) = e0
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (9) implies:
% 154.11/23.31  | |   (10)  all_56_1 = e0
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #1065.
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #952 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (2)  op(e0, e0) = e3
% 154.11/23.31    (3)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.11/23.31             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.11/23.31           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.11/23.31           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.11/23.31             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.11/23.31           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.31           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.11/23.31    (4)  op(e3, e3) = e1
% 154.11/23.31    (5)  op(e0, e0) = all_57_15
% 154.11/23.31    (6)   ~ (e2 = e1)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (3) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (7)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.11/23.31  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.11/23.31  | |        $i(all_57_0)
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (7) implies:
% 154.11/23.31  | |   (8)   ~ (all_57_15 = e3)
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1019.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (9)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 154.11/23.31  | |            = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0
% 154.11/23.31  | |          & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 154.11/23.31  | |            e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.31  | |          all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.11/23.31  | | 
% 154.11/23.31  | | BETA: splitting (9) gives:
% 154.11/23.31  | | 
% 154.11/23.31  | | Case 1:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (10)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.11/23.31  | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.11/23.31  | | |         op(e0, e3) = e0 & $i(all_57_1)
% 154.11/23.31  | | | 
% 154.11/23.31  | | | ALPHA: (10) implies:
% 154.11/23.31  | | |   (11)   ~ (all_57_15 = e3)
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (1), (2), (5), (11) are inconsistent by sub-proof #1019.
% 154.11/23.31  | | | 
% 154.11/23.31  | | Case 2:
% 154.11/23.31  | | | 
% 154.11/23.31  | | |   (12)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.11/23.31  | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 154.11/23.31  | | |         op(e0, e2) = e0 & $i(all_57_3)
% 154.11/23.31  | | | 
% 154.11/23.31  | | | ALPHA: (12) implies:
% 154.11/23.31  | | |   (13)  op(e3, e3) = e2
% 154.11/23.31  | | | 
% 154.11/23.31  | | | REF_CLOSE: (1), (4), (6), (13) are inconsistent by sub-proof #1074.
% 154.11/23.31  | | | 
% 154.11/23.31  | | End of split
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #953 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (2)  op(e0, e0) = e3
% 154.11/23.31    (3)  op(e3, e3) = e1
% 154.11/23.31    (4)  op(e2, e2) = e2
% 154.11/23.31    (5)   ~ (e3 = e2)
% 154.11/23.31    (6)   ~ (e2 = e1)
% 154.11/23.31    (7)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 154.11/23.31             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 154.11/23.31           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 154.11/23.31           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 154.11/23.31             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 154.11/23.31             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 154.11/23.31           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.11/23.31           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 154.11/23.31           $i(all_57_7) & $i(all_57_10))
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (7) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (8)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 154.11/23.31  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 154.11/23.31  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (8) implies:
% 154.11/23.31  | |   (9)  op(e3, e3) = e2
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #1074.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (10)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 154.11/23.31  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.11/23.31  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 154.11/23.31  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 154.11/23.31  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 154.11/23.31  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (1), (2), (4), (5), (6), (10) are inconsistent by sub-proof
% 154.11/23.31  | |            #1023.
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #954 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)  op(e0, e1) = all_52_11
% 154.11/23.31    (2)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.11/23.31             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.11/23.31           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 154.11/23.31           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 154.11/23.31             e1) = e0 & $i(all_57_7))
% 154.11/23.31    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (4)   ~ (all_52_11 = e0)
% 154.11/23.31    (5)  op(e2, e2) = e2
% 154.11/23.31    (6)   ~ (e2 = e1)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (2) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (7)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.11/23.31  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.11/23.31  | |        $i(all_57_6)
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (7) implies:
% 154.11/23.31  | |   (8)  op(e0, e1) = e0
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1124.
% 154.11/23.31  | | 
% 154.11/23.31  | Case 2:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (9)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.11/23.31  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.11/23.31  | |        $i(all_57_7)
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (9) implies:
% 154.11/23.31  | |   (10)  op(e2, e2) = e1
% 154.11/23.31  | | 
% 154.11/23.31  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1158.
% 154.11/23.31  | | 
% 154.11/23.31  | End of split
% 154.11/23.31  | 
% 154.11/23.31  End of proof
% 154.11/23.31  
% 154.11/23.31  Sub-proof #955 shows that the following formulas are inconsistent:
% 154.11/23.31  ----------------------------------------------------------------
% 154.11/23.31    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.31           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.31    (2)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.11/23.31             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.11/23.31           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.11/23.31           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.11/23.31             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.11/23.31           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.31           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.11/23.31    (3)  op(e3, e3) = e1
% 154.11/23.31    (4)  op(e0, e3) = all_52_3
% 154.11/23.31    (5)   ~ (all_52_3 = e0)
% 154.11/23.31    (6)   ~ (e2 = e1)
% 154.11/23.31  
% 154.11/23.31  Begin of proof
% 154.11/23.31  | 
% 154.11/23.31  | BETA: splitting (2) gives:
% 154.11/23.31  | 
% 154.11/23.31  | Case 1:
% 154.11/23.31  | | 
% 154.11/23.31  | |   (7)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.11/23.31  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.11/23.31  | |        $i(all_57_0)
% 154.11/23.31  | | 
% 154.11/23.31  | | ALPHA: (7) implies:
% 154.11/23.32  | |   (8)  op(e0, e3) = e0
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1142.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (9)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 154.11/23.32  | |            = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0
% 154.11/23.32  | |          & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 154.11/23.32  | |            e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.32  | |          all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.11/23.32  | | 
% 154.11/23.32  | | BETA: splitting (9) gives:
% 154.11/23.32  | | 
% 154.11/23.32  | | Case 1:
% 154.11/23.32  | | | 
% 154.11/23.32  | | |   (10)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.11/23.32  | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.11/23.32  | | |         op(e0, e3) = e0 & $i(all_57_1)
% 154.11/23.32  | | | 
% 154.11/23.32  | | | ALPHA: (10) implies:
% 154.11/23.32  | | |   (11)  op(e0, e3) = e0
% 154.11/23.32  | | | 
% 154.11/23.32  | | | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #1142.
% 154.11/23.32  | | | 
% 154.11/23.32  | | Case 2:
% 154.11/23.32  | | | 
% 154.11/23.32  | | |   (12)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.11/23.32  | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 154.11/23.32  | | |         op(e0, e2) = e0 & $i(all_57_3)
% 154.11/23.32  | | | 
% 154.11/23.32  | | | ALPHA: (12) implies:
% 154.11/23.32  | | |   (13)  op(e3, e3) = e2
% 154.11/23.32  | | | 
% 154.11/23.32  | | | REF_CLOSE: (1), (3), (6), (13) are inconsistent by sub-proof #1074.
% 154.11/23.32  | | | 
% 154.11/23.32  | | End of split
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #956 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 =
% 154.11/23.32             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 154.11/23.32           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 154.11/23.32         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 154.11/23.32             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 154.11/23.32           all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 154.11/23.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (3)  op(e3, e3) = e1
% 154.11/23.32    (4)   ~ (e1 = e0)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (1) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (5)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12
% 154.11/23.32  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 154.11/23.32  | |        all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (5) implies:
% 154.11/23.32  | |   (6)  op(e3, e3) = e0
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #957.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (7)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14
% 154.11/23.32  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 154.11/23.32  | |        all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (7) implies:
% 154.11/23.32  | |   (8)  op(e3, e3) = e0
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #957.
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #957 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (2)  op(e3, e3) = e1
% 154.11/23.32    (3)  op(e3, e3) = e0
% 154.11/23.32    (4)   ~ (e1 = e0)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | GROUND_INST: instantiating (1) with e0, e1, e3, e3, simplifying with (2), (3)
% 154.11/23.32  |              gives:
% 154.11/23.32  |   (5)  e1 = e0
% 154.11/23.32  | 
% 154.11/23.32  | REDUCE: (4), (5) imply:
% 154.11/23.32  |   (6)  $false
% 154.11/23.32  | 
% 154.11/23.32  | CLOSE: (6) is inconsistent.
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #958 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)   ~ (all_57_13 = e1)
% 154.11/23.32    (2)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 154.11/23.32             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.11/23.32           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 154.11/23.32               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 154.11/23.32             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.11/23.32         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 154.11/23.32             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.11/23.32           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 154.11/23.32               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 154.11/23.32             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 154.11/23.32    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (4)  op(e1, e1) = e0
% 154.11/23.32    (5)   ~ (e1 = e0)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (2) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (6)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3)
% 154.11/23.32  | |          | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.11/23.32  | |        ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 154.11/23.32  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 154.11/23.32  | |              e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 154.11/23.32  | |            $i(all_57_15)))
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (6) implies:
% 154.11/23.32  | |   (7)  op(e1, e1) = e1
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1038.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (8)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3)
% 154.11/23.32  | |          | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.11/23.32  | |        ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 154.11/23.32  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 154.11/23.32  | |              e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.11/23.32  | |            $i(all_57_14)))
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (8) implies:
% 154.11/23.32  | |   (9)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1,
% 154.11/23.32  | |            e1) = all_57_14 & $i(all_57_14))
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #959.
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #959 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  (all_57_13 = e1 & op(e1, e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) =
% 154.11/23.32           all_57_14 & $i(all_57_14))
% 154.11/23.32    (2)   ~ (all_57_13 = e1)
% 154.11/23.32    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (4)  op(e1, e1) = e0
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (1) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (5)  all_57_13 = e1 & op(e1, e0) = e1
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (5) implies:
% 154.11/23.32  | |   (6)  all_57_13 = e1
% 154.11/23.32  | | 
% 154.11/23.32  | | REDUCE: (2), (6) imply:
% 154.11/23.32  | |   (7)  $false
% 154.11/23.32  | | 
% 154.11/23.32  | | CLOSE: (7) is inconsistent.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (8)   ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14)
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (8) implies:
% 154.11/23.32  | |   (9)   ~ (all_57_14 = e0)
% 154.11/23.32  | |   (10)  op(e1, e1) = all_57_14
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #1026.
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #960 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  (all_56_11 = e1 & op(e1, e0) = e1) | (all_56_15 = e1 & op(e0, e0) = e1)
% 154.11/23.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (3)   ~ (all_52_14 = e1)
% 154.11/23.32    (4)  op(e1, e0) = all_52_14
% 154.11/23.32    (5)   ~ (e1 = e0)
% 154.11/23.32    (6)  op(e0, e0) = e0
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (1) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (7)  all_56_11 = e1 & op(e1, e0) = e1
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (7) implies:
% 154.11/23.32  | |   (8)  op(e1, e0) = e1
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #961.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (9)  all_56_15 = e1 & op(e0, e0) = e1
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (9) implies:
% 154.11/23.32  | |   (10)  op(e0, e0) = e1
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1040.
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #961 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (2)  op(e1, e0) = all_52_14
% 154.11/23.32    (3)  op(e1, e0) = e1
% 154.11/23.32    (4)   ~ (all_52_14 = e1)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | GROUND_INST: instantiating (1) with all_52_14, e1, e0, e1, simplifying with
% 154.11/23.32  |              (2), (3) gives:
% 154.11/23.32  |   (5)  all_52_14 = e1
% 154.11/23.32  | 
% 154.11/23.32  | REDUCE: (4), (5) imply:
% 154.11/23.32  |   (6)  $false
% 154.11/23.32  | 
% 154.11/23.32  | CLOSE: (6) is inconsistent.
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #962 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (2)  (all_56_5 = e0 & op(e2, e1) = e0) | (all_56_10 = e0 & op(e2, e0) = e0)
% 154.11/23.32    (3)  all_56_10 = e1
% 154.11/23.32    (4)  op(e2, e1) = all_52_9
% 154.11/23.32    (5)   ~ (e1 = e0)
% 154.11/23.32    (6)   ~ (all_52_9 = e0)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (2) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (7)  all_56_5 = e0 & op(e2, e1) = e0
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (1), (4), (6), (7) are inconsistent by sub-proof #1144.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (8)  all_56_10 = e0 & op(e2, e0) = e0
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (8) implies:
% 154.11/23.32  | |   (9)  all_56_10 = e0
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #963.
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #963 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  all_56_10 = e1
% 154.11/23.32    (2)  all_56_10 = e0
% 154.11/23.32    (3)   ~ (e1 = e0)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.32  |   (4)  e1 = e0
% 154.11/23.32  | 
% 154.11/23.32  | SIMP: (4) implies:
% 154.11/23.32  |   (5)  e1 = e0
% 154.11/23.32  | 
% 154.11/23.32  | REDUCE: (3), (5) imply:
% 154.11/23.32  |   (6)  $false
% 154.11/23.32  | 
% 154.11/23.32  | CLOSE: (6) is inconsistent.
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #964 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  all_56_9 = e3
% 154.11/23.32    (2)  all_56_9 = e2
% 154.11/23.32    (3)   ~ (e3 = e2)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.32  |   (4)  e3 = e2
% 154.11/23.32  | 
% 154.11/23.32  | SIMP: (4) implies:
% 154.11/23.32  |   (5)  e3 = e2
% 154.11/23.32  | 
% 154.11/23.32  | REDUCE: (3), (5) imply:
% 154.11/23.32  |   (6)  $false
% 154.11/23.32  | 
% 154.11/23.32  | CLOSE: (6) is inconsistent.
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #965 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (2)  ( ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0 & op(e3, e1) = all_22_1
% 154.11/23.32           & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e0) & op(e3, e1) =
% 154.11/23.32           all_22_1 & $i(all_22_1))
% 154.11/23.32    (3)  ( ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0 & op(e3, e1) = all_34_1
% 154.11/23.32           & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e2) & op(e3, e1) =
% 154.11/23.32           all_34_1 & $i(all_34_1))
% 154.11/23.32    (4)  op(e3, e1) = e2
% 154.11/23.32    (5)  op(e2, e3) = e0
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (3) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (6)   ~ (all_34_0 = e0) & op(all_34_1, e3) = all_34_0 & op(e3, e1) =
% 154.11/23.32  | |        all_34_1 & $i(all_34_0) & $i(all_34_1)
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (6) implies:
% 154.11/23.32  | |   (7)   ~ (all_34_0 = e0)
% 154.11/23.32  | |   (8)  op(e3, e1) = all_34_1
% 154.11/23.32  | |   (9)  op(all_34_1, e3) = all_34_0
% 154.11/23.32  | | 
% 154.11/23.32  | | BETA: splitting (2) gives:
% 154.11/23.32  | | 
% 154.11/23.32  | | Case 1:
% 154.11/23.32  | | | 
% 154.11/23.32  | | |   (10)   ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0 & op(e3, e1) =
% 154.11/23.32  | | |         all_22_1 & $i(all_22_0) & $i(all_22_1)
% 154.11/23.32  | | | 
% 154.11/23.32  | | | ALPHA: (10) implies:
% 154.11/23.32  | | |   (11)  op(e3, e1) = all_22_1
% 154.11/23.32  | | | 
% 154.11/23.32  | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (11) are inconsistent by
% 154.11/23.32  | | |            sub-proof #967.
% 154.11/23.32  | | | 
% 154.11/23.32  | | Case 2:
% 154.11/23.32  | | | 
% 154.11/23.32  | | |   (12)   ~ (all_22_1 = e0) & op(e3, e1) = all_22_1 & $i(all_22_1)
% 154.11/23.32  | | | 
% 154.11/23.32  | | | ALPHA: (12) implies:
% 154.11/23.32  | | |   (13)  op(e3, e1) = all_22_1
% 154.11/23.32  | | | 
% 154.11/23.32  | | | REF_CLOSE: (1), (4), (5), (7), (8), (9), (13) are inconsistent by
% 154.11/23.32  | | |            sub-proof #967.
% 154.11/23.32  | | | 
% 154.11/23.32  | | End of split
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (14)   ~ (all_34_1 = e2) & op(e3, e1) = all_34_1 & $i(all_34_1)
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (14) implies:
% 154.11/23.32  | |   (15)   ~ (all_34_1 = e2)
% 154.11/23.32  | |   (16)  op(e3, e1) = all_34_1
% 154.11/23.32  | | 
% 154.11/23.32  | | BETA: splitting (2) gives:
% 154.11/23.32  | | 
% 154.11/23.32  | | Case 1:
% 154.11/23.32  | | | 
% 154.11/23.32  | | |   (17)   ~ (all_22_0 = e2) & op(all_22_1, e3) = all_22_0 & op(e3, e1) =
% 154.11/23.32  | | |         all_22_1 & $i(all_22_0) & $i(all_22_1)
% 154.11/23.32  | | | 
% 154.11/23.32  | | | ALPHA: (17) implies:
% 154.11/23.32  | | |   (18)  op(e3, e1) = all_22_1
% 154.11/23.32  | | | 
% 154.11/23.32  | | | REF_CLOSE: (1), (4), (15), (16), (18) are inconsistent by sub-proof #966.
% 154.11/23.32  | | | 
% 154.11/23.32  | | Case 2:
% 154.11/23.32  | | | 
% 154.11/23.32  | | |   (19)   ~ (all_22_1 = e0) & op(e3, e1) = all_22_1 & $i(all_22_1)
% 154.11/23.32  | | | 
% 154.11/23.32  | | | ALPHA: (19) implies:
% 154.11/23.32  | | |   (20)  op(e3, e1) = all_22_1
% 154.11/23.32  | | | 
% 154.11/23.32  | | | REF_CLOSE: (1), (4), (15), (16), (20) are inconsistent by sub-proof #966.
% 154.11/23.32  | | | 
% 154.11/23.32  | | End of split
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #966 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  op(e3, e1) = all_34_1
% 154.11/23.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (3)  op(e3, e1) = all_22_1
% 154.11/23.32    (4)  op(e3, e1) = e2
% 154.11/23.32    (5)   ~ (all_34_1 = e2)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | GROUND_INST: instantiating (2) with all_22_1, all_34_1, e1, e3, simplifying
% 154.11/23.32  |              with (1), (3) gives:
% 154.11/23.32  |   (6)  all_34_1 = all_22_1
% 154.11/23.32  | 
% 154.11/23.32  | GROUND_INST: instantiating (2) with e2, all_34_1, e1, e3, simplifying with
% 154.11/23.32  |              (1), (4) gives:
% 154.11/23.32  |   (7)  all_34_1 = e2
% 154.11/23.32  | 
% 154.11/23.32  | COMBINE_EQS: (6), (7) imply:
% 154.11/23.32  |   (8)  all_22_1 = e2
% 154.11/23.32  | 
% 154.11/23.32  | REDUCE: (5), (7) imply:
% 154.11/23.32  |   (9)  $false
% 154.11/23.32  | 
% 154.11/23.32  | CLOSE: (9) is inconsistent.
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #967 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  op(e3, e1) = all_34_1
% 154.11/23.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (3)   ~ (all_34_0 = e0)
% 154.11/23.32    (4)  op(e3, e1) = all_22_1
% 154.11/23.32    (5)  op(e3, e1) = e2
% 154.11/23.32    (6)  op(e2, e3) = e0
% 154.11/23.32    (7)  op(all_34_1, e3) = all_34_0
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | GROUND_INST: instantiating (2) with all_22_1, all_34_1, e1, e3, simplifying
% 154.11/23.32  |              with (1), (4) gives:
% 154.11/23.32  |   (8)  all_34_1 = all_22_1
% 154.11/23.32  | 
% 154.11/23.32  | GROUND_INST: instantiating (2) with e2, all_34_1, e1, e3, simplifying with
% 154.11/23.32  |              (1), (5) gives:
% 154.11/23.32  |   (9)  all_34_1 = e2
% 154.11/23.32  | 
% 154.11/23.32  | GROUND_INST: instantiating (2) with e0, all_34_0, e3, e2, simplifying with (6)
% 154.11/23.32  |              gives:
% 154.11/23.32  |   (10)  all_34_0 = e0 |  ~ (op(e2, e3) = all_34_0)
% 154.11/23.32  | 
% 154.11/23.32  | COMBINE_EQS: (8), (9) imply:
% 154.11/23.32  |   (11)  all_22_1 = e2
% 154.11/23.32  | 
% 154.11/23.32  | REDUCE: (7), (9) imply:
% 154.11/23.32  |   (12)  op(e2, e3) = all_34_0
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (10) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (13)   ~ (op(e2, e3) = all_34_0)
% 154.11/23.32  | | 
% 154.11/23.32  | | PRED_UNIFY: (12), (13) imply:
% 154.11/23.32  | |   (14)  $false
% 154.11/23.32  | | 
% 154.11/23.32  | | CLOSE: (14) is inconsistent.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (15)  all_34_0 = e0
% 154.11/23.32  | | 
% 154.11/23.32  | | REDUCE: (3), (15) imply:
% 154.11/23.32  | |   (16)  $false
% 154.11/23.32  | | 
% 154.11/23.32  | | CLOSE: (16) is inconsistent.
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #968 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  op(e3, e2) = all_52_4
% 154.11/23.32    (2)   ~ (all_52_4 = e2)
% 154.11/23.32    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (4)  op(e3, e3) = e1
% 154.11/23.32    (5)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_1 = e2 & op(e3, e2) = e2)
% 154.11/23.32    (6)   ~ (e2 = e1)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (5) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (7)  all_56_0 = e2 & op(e3, e3) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (7) implies:
% 154.11/23.32  | |   (8)  op(e3, e3) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #1074.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (9)  all_56_1 = e2 & op(e3, e2) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (1), (2), (3), (9) are inconsistent by sub-proof #969.
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #969 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  all_56_1 = e2 & op(e3, e2) = e2
% 154.11/23.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (3)  op(e3, e2) = all_52_4
% 154.11/23.32    (4)   ~ (all_52_4 = e2)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | ALPHA: (1) implies:
% 154.11/23.32  |   (5)  op(e3, e2) = e2
% 154.11/23.32  | 
% 154.11/23.32  | GROUND_INST: instantiating (2) with all_52_4, e2, e2, e3, simplifying with
% 154.11/23.32  |              (3), (5) gives:
% 154.11/23.32  |   (6)  all_52_4 = e2
% 154.11/23.32  | 
% 154.11/23.32  | REDUCE: (4), (6) imply:
% 154.11/23.32  |   (7)  $false
% 154.11/23.32  | 
% 154.11/23.32  | CLOSE: (7) is inconsistent.
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #970 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  all_56_9 = e1 & op(e3, e0) = e1
% 154.11/23.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (3)  op(e3, e0) = all_52_12
% 154.11/23.32    (4)   ~ (all_52_12 = e1)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | ALPHA: (1) implies:
% 154.11/23.32  |   (5)  op(e3, e0) = e1
% 154.11/23.32  | 
% 154.11/23.32  | GROUND_INST: instantiating (2) with all_52_12, e1, e0, e3, simplifying with
% 154.11/23.32  |              (3), (5) gives:
% 154.11/23.32  |   (6)  all_52_12 = e1
% 154.11/23.32  | 
% 154.11/23.32  | REDUCE: (4), (6) imply:
% 154.11/23.32  |   (7)  $false
% 154.11/23.32  | 
% 154.11/23.32  | CLOSE: (7) is inconsistent.
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #971 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)   ~ (e2 = e0)
% 154.11/23.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (3)  op(e3, e3) = e1
% 154.11/23.32    (4)  op(e2, e2) = e2
% 154.11/23.32    (5)   ~ (e2 = e1)
% 154.11/23.32    (6)  op(e0, e0) = e0
% 154.11/23.32    (7)  (all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 154.11/23.32             e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 154.11/23.32           op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)) | (all_57_4 = e1
% 154.11/23.32           & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 = e2) & op(e1,
% 154.11/23.32             e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) = all_57_5 & op(e0,
% 154.11/23.32             e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6 = e3 & all_57_12
% 154.11/23.32           = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) & op(e3, e3) =
% 154.11/23.32           all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 154.11/23.32           $i(all_57_7) & $i(all_57_10))
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (7) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (8)  all_57_4 = e1 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_14 =
% 154.11/23.32  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e1, e2) = e1 &
% 154.11/23.32  | |        op(e1, e1) = all_57_14 & $i(all_57_3) & $i(all_57_14)
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (8) implies:
% 154.11/23.32  | |   (9)  op(e3, e3) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1074.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (10)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14
% 154.11/23.32  | |             = e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.11/23.32  | |           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) |
% 154.11/23.32  | |         (all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10
% 154.11/23.32  | |             = e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) =
% 154.11/23.32  | |           e1 & op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (1), (2), (4), (5), (6), (10) are inconsistent by sub-proof
% 154.11/23.32  | |            #1041.
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #972 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  op(e0, e1) = all_52_11
% 154.11/23.32    (2)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_14 = e2 & op(e0, e1) = e2)
% 154.11/23.32    (3)  op(e1, e1) = all_4_2
% 154.11/23.32    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (5)   ~ (all_4_2 = e2)
% 154.11/23.32    (6)   ~ (all_52_11 = e2)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (2) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (7)  all_56_8 = e2 & op(e1, e1) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (7) implies:
% 154.11/23.32  | |   (8)  op(e1, e1) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1169.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (9)  all_56_14 = e2 & op(e0, e1) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (9) implies:
% 154.11/23.32  | |   (10)  op(e0, e1) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #1092.
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #973 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)   ~ (all_52_14 = e2)
% 154.11/23.32    (2)  op(e1, e1) = all_4_2
% 154.11/23.32    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (4)  op(e1, e0) = all_52_14
% 154.11/23.32    (5)   ~ (all_4_2 = e2)
% 154.11/23.32    (6)  (all_56_8 = e2 & op(e1, e1) = e2) | (all_56_11 = e2 & op(e1, e0) = e2)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (6) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (7)  all_56_8 = e2 & op(e1, e1) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (7) implies:
% 154.11/23.32  | |   (8)  op(e1, e1) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1169.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (9)  all_56_11 = e2 & op(e1, e0) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (9) implies:
% 154.11/23.32  | |   (10)  op(e1, e0) = e2
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #974.
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #974 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (2)  op(e1, e0) = all_52_14
% 154.11/23.32    (3)  op(e1, e0) = e2
% 154.11/23.32    (4)   ~ (all_52_14 = e2)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | GROUND_INST: instantiating (1) with all_52_14, e2, e0, e1, simplifying with
% 154.11/23.32  |              (2), (3) gives:
% 154.11/23.32  |   (5)  all_52_14 = e2
% 154.11/23.32  | 
% 154.11/23.32  | REDUCE: (4), (5) imply:
% 154.11/23.32  |   (6)  $false
% 154.11/23.32  | 
% 154.11/23.32  | CLOSE: (6) is inconsistent.
% 154.11/23.32  | 
% 154.11/23.32  End of proof
% 154.11/23.32  
% 154.11/23.32  Sub-proof #975 shows that the following formulas are inconsistent:
% 154.11/23.32  ----------------------------------------------------------------
% 154.11/23.32    (1)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 =
% 154.11/23.32             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 154.11/23.32           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 154.11/23.32         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 154.11/23.32             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 154.11/23.32           all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 154.11/23.32    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.32           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.32    (3)  op(e3, e3) = e3
% 154.11/23.32    (4)   ~ (e3 = e0)
% 154.11/23.32  
% 154.11/23.32  Begin of proof
% 154.11/23.32  | 
% 154.11/23.32  | BETA: splitting (1) gives:
% 154.11/23.32  | 
% 154.11/23.32  | Case 1:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (5)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12
% 154.11/23.32  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 154.11/23.32  | |        all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (5) implies:
% 154.11/23.32  | |   (6)  op(e3, e3) = e0
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #1141.
% 154.11/23.32  | | 
% 154.11/23.32  | Case 2:
% 154.11/23.32  | | 
% 154.11/23.32  | |   (7)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14
% 154.11/23.32  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 154.11/23.32  | |        all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 154.11/23.32  | | 
% 154.11/23.32  | | ALPHA: (7) implies:
% 154.11/23.32  | |   (8)  op(e3, e3) = e0
% 154.11/23.32  | | 
% 154.11/23.32  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1141.
% 154.11/23.32  | | 
% 154.11/23.32  | End of split
% 154.11/23.33  | 
% 154.11/23.33  End of proof
% 154.11/23.33  
% 154.11/23.33  Sub-proof #976 shows that the following formulas are inconsistent:
% 154.11/23.33  ----------------------------------------------------------------
% 154.11/23.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.33    (2)  op(e0, e0) = e2
% 154.11/23.33    (3)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 154.11/23.33             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.11/23.33           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 154.11/23.33           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 154.11/23.33           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 154.11/23.33           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 154.11/23.33           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 154.11/23.33           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 154.11/23.33           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.11/23.33    (4)  op(e3, e0) = all_52_12
% 154.11/23.33    (5)   ~ (all_52_12 = e3)
% 154.11/23.33    (6)   ~ (e2 = e1)
% 154.11/23.33  
% 154.11/23.33  Begin of proof
% 154.11/23.33  | 
% 154.11/23.33  | BETA: splitting (3) gives:
% 154.11/23.33  | 
% 154.11/23.33  | Case 1:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (7)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 154.11/23.33  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.11/23.33  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 154.11/23.33  | | 
% 154.11/23.33  | | ALPHA: (7) implies:
% 154.11/23.33  | |   (8)  op(e0, e0) = e1
% 154.11/23.33  | | 
% 154.11/23.33  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #978.
% 154.11/23.33  | | 
% 154.11/23.33  | Case 2:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (9)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 154.11/23.33  | |            = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) =
% 154.11/23.33  | |          e0 & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 154.11/23.33  | |        (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 154.11/23.33  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 154.11/23.33  | |          e0 & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.11/23.33  | | 
% 154.11/23.33  | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1081.
% 154.11/23.33  | | 
% 154.11/23.33  | End of split
% 154.11/23.33  | 
% 154.11/23.33  End of proof
% 154.11/23.33  
% 154.11/23.33  Sub-proof #977 shows that the following formulas are inconsistent:
% 154.11/23.33  ----------------------------------------------------------------
% 154.11/23.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.33    (2)  op(e0, e0) = e2
% 154.11/23.33    (3)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.11/23.33             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.11/23.33           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 154.11/23.33           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 154.11/23.33           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 154.11/23.33           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 154.11/23.33    (4)   ~ (all_52_9 = e2)
% 154.11/23.33    (5)  op(e2, e1) = all_52_9
% 154.11/23.33    (6)   ~ (e2 = e1)
% 154.11/23.33  
% 154.11/23.33  Begin of proof
% 154.11/23.33  | 
% 154.11/23.33  | BETA: splitting (3) gives:
% 154.11/23.33  | 
% 154.11/23.33  | Case 1:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (7)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.11/23.33  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.11/23.33  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 154.11/23.33  | | 
% 154.11/23.33  | | ALPHA: (7) implies:
% 154.11/23.33  | |   (8)  op(e0, e0) = e1
% 154.11/23.33  | | 
% 154.11/23.33  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #978.
% 154.11/23.33  | | 
% 154.11/23.33  | Case 2:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (9)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 154.11/23.33  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 154.11/23.33  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 154.11/23.33  | | 
% 154.11/23.33  | | ALPHA: (9) implies:
% 154.11/23.33  | |   (10)  op(e2, e1) = e2
% 154.11/23.33  | | 
% 154.11/23.33  | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #1157.
% 154.11/23.33  | | 
% 154.11/23.33  | End of split
% 154.11/23.33  | 
% 154.11/23.33  End of proof
% 154.11/23.33  
% 154.11/23.33  Sub-proof #978 shows that the following formulas are inconsistent:
% 154.11/23.33  ----------------------------------------------------------------
% 154.11/23.33    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.33    (2)  op(e0, e0) = e2
% 154.11/23.33    (3)  op(e0, e0) = e1
% 154.11/23.33    (4)   ~ (e2 = e1)
% 154.11/23.33  
% 154.11/23.33  Begin of proof
% 154.11/23.33  | 
% 154.11/23.33  | GROUND_INST: instantiating (1) with e1, e2, e0, e0, simplifying with (2), (3)
% 154.11/23.33  |              gives:
% 154.11/23.33  |   (5)  e2 = e1
% 154.11/23.33  | 
% 154.11/23.33  | REDUCE: (4), (5) imply:
% 154.11/23.33  |   (6)  $false
% 154.11/23.33  | 
% 154.11/23.33  | CLOSE: (6) is inconsistent.
% 154.11/23.33  | 
% 154.11/23.33  End of proof
% 154.11/23.33  
% 154.11/23.33  Sub-proof #979 shows that the following formulas are inconsistent:
% 154.11/23.33  ----------------------------------------------------------------
% 154.11/23.33    (1)  op(e3, e0) = e1
% 154.11/23.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.33    (3)  all_40_2 = e2
% 154.11/23.33    (4)   ~ (all_40_2 = e2) | ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0 &
% 154.11/23.33           op(e0, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 154.11/23.33             e3) & op(e0, e2) = all_40_1 & $i(all_40_1))
% 154.11/23.33    (5)  all_56_13 = e3 & op(e0, e2) = e3
% 154.11/23.33  
% 154.11/23.33  Begin of proof
% 154.11/23.33  | 
% 154.11/23.33  | ALPHA: (5) implies:
% 154.11/23.33  |   (6)  op(e0, e2) = e3
% 154.11/23.33  | 
% 154.11/23.33  | BETA: splitting (4) gives:
% 154.11/23.33  | 
% 154.11/23.33  | Case 1:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (7)   ~ (all_40_2 = e2)
% 154.11/23.33  | | 
% 154.11/23.33  | | REDUCE: (3), (7) imply:
% 154.11/23.33  | |   (8)  $false
% 154.11/23.33  | | 
% 154.11/23.33  | | CLOSE: (8) is inconsistent.
% 154.11/23.33  | | 
% 154.11/23.33  | Case 2:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (9)  ( ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0 & op(e0, e2) =
% 154.11/23.33  | |          all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e3) &
% 154.11/23.33  | |          op(e0, e2) = all_40_1 & $i(all_40_1))
% 154.11/23.33  | | 
% 154.11/23.33  | | BETA: splitting (9) gives:
% 154.11/23.33  | | 
% 154.11/23.33  | | Case 1:
% 154.11/23.33  | | | 
% 154.11/23.33  | | |   (10)   ~ (all_40_0 = e1) & op(all_40_1, e0) = all_40_0 & op(e0, e2) =
% 154.11/23.33  | | |         all_40_1 & $i(all_40_0) & $i(all_40_1)
% 154.11/23.33  | | | 
% 154.11/23.33  | | | ALPHA: (10) implies:
% 154.11/23.33  | | |   (11)   ~ (all_40_0 = e1)
% 154.11/23.33  | | |   (12)  op(e0, e2) = all_40_1
% 154.11/23.33  | | |   (13)  op(all_40_1, e0) = all_40_0
% 154.11/23.33  | | | 
% 154.11/23.33  | | | GROUND_INST: instantiating (2) with e3, all_40_1, e2, e0, simplifying with
% 154.11/23.33  | | |              (6), (12) gives:
% 154.11/23.33  | | |   (14)  all_40_1 = e3
% 154.11/23.33  | | | 
% 154.11/23.33  | | | GROUND_INST: instantiating (2) with e1, all_40_0, e0, e3, simplifying with
% 154.11/23.33  | | |              (1) gives:
% 154.11/23.33  | | |   (15)  all_40_0 = e1 |  ~ (op(e3, e0) = all_40_0)
% 154.11/23.33  | | | 
% 154.11/23.33  | | | REDUCE: (13), (14) imply:
% 154.11/23.33  | | |   (16)  op(e3, e0) = all_40_0
% 154.11/23.33  | | | 
% 154.11/23.33  | | | BETA: splitting (15) gives:
% 154.11/23.33  | | | 
% 154.11/23.33  | | | Case 1:
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | |   (17)   ~ (op(e3, e0) = all_40_0)
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | PRED_UNIFY: (16), (17) imply:
% 154.11/23.33  | | | |   (18)  $false
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | CLOSE: (18) is inconsistent.
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | Case 2:
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | |   (19)  all_40_0 = e1
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | REDUCE: (11), (19) imply:
% 154.11/23.33  | | | |   (20)  $false
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | CLOSE: (20) is inconsistent.
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | End of split
% 154.11/23.33  | | | 
% 154.11/23.33  | | Case 2:
% 154.11/23.33  | | | 
% 154.11/23.33  | | |   (21)   ~ (all_40_1 = e3) & op(e0, e2) = all_40_1 & $i(all_40_1)
% 154.11/23.33  | | | 
% 154.11/23.33  | | | ALPHA: (21) implies:
% 154.11/23.33  | | |   (22)   ~ (all_40_1 = e3)
% 154.11/23.33  | | |   (23)  op(e0, e2) = all_40_1
% 154.11/23.33  | | | 
% 154.11/23.33  | | | GROUND_INST: instantiating (2) with e3, all_40_1, e2, e0, simplifying with
% 154.11/23.33  | | |              (6), (23) gives:
% 154.11/23.33  | | |   (24)  all_40_1 = e3
% 154.11/23.33  | | | 
% 154.11/23.33  | | | REDUCE: (22), (24) imply:
% 154.11/23.33  | | |   (25)  $false
% 154.11/23.33  | | | 
% 154.11/23.33  | | | CLOSE: (25) is inconsistent.
% 154.11/23.33  | | | 
% 154.11/23.33  | | End of split
% 154.11/23.33  | | 
% 154.11/23.33  | End of split
% 154.11/23.33  | 
% 154.11/23.33  End of proof
% 154.11/23.33  
% 154.11/23.33  Sub-proof #980 shows that the following formulas are inconsistent:
% 154.11/23.33  ----------------------------------------------------------------
% 154.11/23.33    (1)  all_56_4 = e2
% 154.11/23.33    (2)  all_56_4 = e1
% 154.11/23.33    (3)   ~ (e2 = e1)
% 154.11/23.33  
% 154.11/23.33  Begin of proof
% 154.11/23.33  | 
% 154.11/23.33  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.33  |   (4)  e2 = e1
% 154.11/23.33  | 
% 154.11/23.33  | SIMP: (4) implies:
% 154.11/23.33  |   (5)  e2 = e1
% 154.11/23.33  | 
% 154.11/23.33  | REDUCE: (3), (5) imply:
% 154.11/23.33  |   (6)  $false
% 154.11/23.33  | 
% 154.11/23.33  | CLOSE: (6) is inconsistent.
% 154.11/23.33  | 
% 154.11/23.33  End of proof
% 154.11/23.33  
% 154.11/23.33  Sub-proof #981 shows that the following formulas are inconsistent:
% 154.11/23.33  ----------------------------------------------------------------
% 154.11/23.33    (1)  op(e0, e1) = all_52_11
% 154.11/23.33    (2)   ~ (all_52_7 = all_52_11)
% 154.11/23.33    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 154.11/23.33         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 154.11/23.33    (4)  all_56_6 = e2
% 154.11/23.33    (5)  op(e3, e2) = all_52_4
% 154.11/23.33    (6)   ~ (all_52_4 = all_52_7)
% 154.11/23.33    (7)  op(e0, e2) = all_52_7
% 154.11/23.33    (8)   ~ (all_52_4 = e2)
% 154.11/23.33    (9)   ~ (all_52_4 = all_52_12)
% 154.11/23.33    (10)   ~ (e2 = e0)
% 154.11/23.33    (11)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.33            (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.33    (12)  all_54_1 = all_52_4
% 154.11/23.33    (13)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 154.11/23.33          (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 154.11/23.33    (14)  all_56_4 = e2
% 154.11/23.33    (15)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.11/23.33    (16)   ~ (all_52_7 = e1)
% 154.11/23.33    (17)  op(e0, e0) = e2
% 154.11/23.33    (18)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 154.11/23.33          | (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) =
% 154.11/23.33            e3)
% 154.11/23.33    (19)  op(e3, e0) = all_52_12
% 154.11/23.33    (20)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 154.11/23.33          (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.11/23.33    (21)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 154.11/23.33          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 154.11/23.33    (22)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 154.11/23.33          (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 154.11/23.33    (23)   ~ (all_52_12 = e3)
% 154.11/23.33    (24)   ~ (all_52_7 = e2)
% 154.11/23.33    (25)  all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.11/23.33    (26)  op(e2, e2) = e2
% 154.11/23.33    (27)   ~ (all_52_7 = e0)
% 154.11/23.33    (28)   ~ (e1 = e0)
% 154.11/23.33    (29)   ~ (all_52_4 = e1)
% 154.11/23.33    (30)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.11/23.33          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.11/23.33    (31)  all_54_13 = all_52_7
% 154.11/23.33    (32)  all_56_7 = e3 & op(e1, e2) = e3
% 154.11/23.33    (33)  op(e3, e3) = e3
% 154.11/23.33    (34)   ~ (e2 = e1)
% 154.11/23.33    (35)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.11/23.33          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.11/23.33    (36)  op(e1, e3) = all_52_2
% 154.11/23.33    (37)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 154.11/23.33          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 154.11/23.33  
% 154.11/23.33  Begin of proof
% 154.11/23.33  | 
% 154.11/23.33  | ALPHA: (32) implies:
% 154.11/23.33  |   (38)  all_56_7 = e3
% 154.11/23.33  | 
% 154.11/23.33  | BETA: splitting (25) gives:
% 154.11/23.33  | 
% 154.11/23.33  | Case 1:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (39)  all_54_13 = e3
% 154.11/23.33  | | 
% 154.11/23.33  | | COMBINE_EQS: (31), (39) imply:
% 154.11/23.33  | |   (40)  all_52_7 = e3
% 154.11/23.33  | | 
% 154.11/23.33  | | SIMP: (40) implies:
% 154.11/23.33  | |   (41)  all_52_7 = e3
% 154.11/23.33  | | 
% 154.11/23.33  | | REDUCE: (6), (41) imply:
% 154.11/23.33  | |   (42)   ~ (all_52_4 = e3)
% 154.11/23.33  | | 
% 154.11/23.33  | | REDUCE: (2), (41) imply:
% 154.11/23.33  | |   (43)   ~ (all_52_11 = e3)
% 154.11/23.33  | | 
% 154.11/23.33  | | SIMP: (43) implies:
% 154.11/23.33  | |   (44)   ~ (all_52_11 = e3)
% 154.11/23.33  | | 
% 154.11/23.33  | | REDUCE: (24), (41) imply:
% 154.11/23.33  | |   (45)   ~ (e3 = e2)
% 154.11/23.33  | | 
% 154.11/23.33  | | REDUCE: (16), (41) imply:
% 154.11/23.33  | |   (46)   ~ (e3 = e1)
% 154.11/23.33  | | 
% 154.11/23.33  | | REDUCE: (27), (41) imply:
% 154.11/23.33  | |   (47)   ~ (e3 = e0)
% 154.11/23.33  | | 
% 154.11/23.33  | | BETA: splitting (30) gives:
% 154.11/23.33  | | 
% 154.11/23.33  | | Case 1:
% 154.11/23.33  | | | 
% 154.11/23.33  | | |   (48)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 154.11/23.33  | | |           e0)
% 154.11/23.33  | | | 
% 154.11/23.33  | | | BETA: splitting (48) gives:
% 154.11/23.33  | | | 
% 154.11/23.33  | | | Case 1:
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | |   (49)  all_56_1 = e0 & op(e3, e2) = e0
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | ALPHA: (49) implies:
% 154.11/23.33  | | | |   (50)  all_56_1 = e0
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | BETA: splitting (35) gives:
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | Case 1:
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | |   (51)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2,
% 154.11/23.33  | | | | |             e2) = e1)
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | | REF_CLOSE: (11), (26), (28), (34), (50), (51) are inconsistent by
% 154.11/23.33  | | | | |            sub-proof #997.
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | Case 2:
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | |   (52)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0,
% 154.11/23.33  | | | | |             e2) = e1)
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | | BETA: splitting (52) gives:
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | | Case 1:
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | |   (53)  all_56_7 = e1 & op(e1, e2) = e1
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | REF_CLOSE: (38), (46), (53) are inconsistent by sub-proof #1126.
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | Case 2:
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | |   (54)  all_56_13 = e1 & op(e0, e2) = e1
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | ALPHA: (54) implies:
% 154.11/23.33  | | | | | |   (55)  all_56_13 = e1
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | BETA: splitting (18) gives:
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | Case 1:
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | |   (56)  (all_56_12 = e3 & op(e0, e3) = e3) | (all_56_13 = e3 &
% 154.11/23.33  | | | | | | |           op(e0, e2) = e3)
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | | BETA: splitting (56) gives:
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | | Case 1:
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | |   (57)  all_56_12 = e3 & op(e0, e3) = e3
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | | ALPHA: (57) implies:
% 154.11/23.33  | | | | | | | |   (58)  all_56_12 = e3
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | | BETA: splitting (3) gives:
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | | Case 1:
% 154.11/23.33  | | | | | | | | | 
% 154.11/23.33  | | | | | | | | |   (59)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 &
% 154.11/23.33  | | | | | | | | |           op(e2, e3) = e1)
% 154.11/23.33  | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | BETA: splitting (59) gives:
% 154.11/23.33  | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | Case 1:
% 154.11/23.33  | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | |   (60)  all_56_0 = e1 & op(e3, e3) = e1
% 154.11/23.33  | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | ALPHA: (60) implies:
% 154.11/23.33  | | | | | | | | | |   (61)  op(e3, e3) = e1
% 154.11/23.33  | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | REF_CLOSE: (5), (11), (13), (14), (19), (23), (42), (45),
% 154.11/23.33  | | | | | | | | | |            (46), (61) are inconsistent by sub-proof #998.
% 154.11/23.33  | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | Case 2:
% 154.11/23.33  | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | |   (62)  all_56_2 = e1 & op(e2, e3) = e1
% 154.11/23.33  | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | ALPHA: (62) implies:
% 154.11/23.33  | | | | | | | | | |   (63)  all_56_2 = e1
% 154.11/23.33  | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | BETA: splitting (20) gives:
% 154.11/23.33  | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | Case 1:
% 154.11/23.33  | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | |   (64)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0
% 154.11/23.33  | | | | | | | | | | |           & op(e2, e3) = e0)
% 154.11/23.33  | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | | REF_CLOSE: (11), (28), (33), (47), (63), (64) are
% 154.11/23.33  | | | | | | | | | | |            inconsistent by sub-proof #995.
% 154.11/23.33  | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | Case 2:
% 154.11/23.33  | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | |   (65)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 =
% 154.11/23.33  | | | | | | | | | | |           e0 & op(e0, e3) = e0)
% 154.11/23.33  | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | | BETA: splitting (65) gives:
% 154.11/23.33  | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | | Case 1:
% 154.11/23.33  | | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | | |   (66)  all_56_6 = e0 & op(e1, e3) = e0
% 154.11/23.33  | | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | | | REF_CLOSE: (4), (10), (66) are inconsistent by sub-proof
% 154.11/23.33  | | | | | | | | | | | |            #1054.
% 154.11/23.33  | | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | | Case 2:
% 154.11/23.33  | | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | | |   (67)  all_56_12 = e0 & op(e0, e3) = e0
% 154.11/23.33  | | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | | | ALPHA: (67) implies:
% 154.11/23.33  | | | | | | | | | | | |   (68)  all_56_12 = e0
% 154.11/23.33  | | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | | | REF_CLOSE: (47), (58), (68) are inconsistent by sub-proof
% 154.11/23.33  | | | | | | | | | | | |            #1052.
% 154.11/23.33  | | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | | End of split
% 154.11/23.33  | | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | | End of split
% 154.11/23.33  | | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | End of split
% 154.11/23.33  | | | | | | | | | 
% 154.11/23.33  | | | | | | | | Case 2:
% 154.11/23.33  | | | | | | | | | 
% 154.11/23.33  | | | | | | | | |   (69)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 &
% 154.11/23.33  | | | | | | | | |           op(e0, e3) = e1)
% 154.11/23.33  | | | | | | | | | 
% 154.11/23.33  | | | | | | | | | REF_CLOSE: (10), (11), (20), (22), (28), (33), (34), (36),
% 154.11/23.33  | | | | | | | | |            (45), (46), (47), (58), (69) are inconsistent by
% 154.11/23.33  | | | | | | | | |            sub-proof #991.
% 154.11/23.33  | | | | | | | | | 
% 154.11/23.33  | | | | | | | | End of split
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | Case 2:
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | |   (70)  all_56_13 = e3 & op(e0, e2) = e3
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | | ALPHA: (70) implies:
% 154.11/23.33  | | | | | | | |   (71)  all_56_13 = e3
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | | REF_CLOSE: (46), (55), (71) are inconsistent by sub-proof #1121.
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | End of split
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | Case 2:
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | |   (72)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 &
% 154.11/23.33  | | | | | | |           op(e0, e0) = e3)
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | | REF_CLOSE: (1), (11), (17), (44), (45), (72) are inconsistent by
% 154.11/23.33  | | | | | | |            sub-proof #990.
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | End of split
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | End of split
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | End of split
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | Case 2:
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | |   (73)  all_56_3 = e0 & op(e2, e2) = e0
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | ALPHA: (73) implies:
% 154.11/23.33  | | | |   (74)  op(e2, e2) = e0
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | REF_CLOSE: (10), (11), (26), (74) are inconsistent by sub-proof #1145.
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | End of split
% 154.11/23.33  | | | 
% 154.11/23.33  | | Case 2:
% 154.11/23.33  | | | 
% 154.11/23.33  | | |   (75)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 154.11/23.33  | | |           e0)
% 154.11/23.33  | | | 
% 154.11/23.33  | | | BETA: splitting (75) gives:
% 154.11/23.33  | | | 
% 154.11/23.33  | | | Case 1:
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | |   (76)  all_56_7 = e0 & op(e1, e2) = e0
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | ALPHA: (76) implies:
% 154.11/23.33  | | | |   (77)  all_56_7 = e0
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | BETA: splitting (37) gives:
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | Case 1:
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | |   (78)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2,
% 154.11/23.33  | | | | |             e2) = e3)
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | | REF_CLOSE: (5), (11), (26), (42), (45), (78) are inconsistent by
% 154.11/23.33  | | | | |            sub-proof #1165.
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | Case 2:
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | |   (79)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0,
% 154.11/23.33  | | | | |             e2) = e3)
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | | BETA: splitting (79) gives:
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | | Case 1:
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | REF_CLOSE: (32), (47), (77) are inconsistent by sub-proof #989.
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | Case 2:
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | |   (80)  all_56_13 = e3 & op(e0, e2) = e3
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | ALPHA: (80) implies:
% 154.11/23.33  | | | | | |   (81)  all_56_13 = e3
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | REF_CLOSE: (8), (9), (11), (12), (14), (15), (19), (21), (26), (29),
% 154.11/23.33  | | | | | |            (33), (34), (35), (42), (46), (77), (81) are inconsistent
% 154.11/23.33  | | | | | |            by sub-proof #985.
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | End of split
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | End of split
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | Case 2:
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | |   (82)  all_56_13 = e0 & op(e0, e2) = e0
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | ALPHA: (82) implies:
% 154.11/23.33  | | | |   (83)  op(e0, e2) = e0
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | REF_CLOSE: (7), (11), (27), (83) are inconsistent by sub-proof #1036.
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | End of split
% 154.11/23.33  | | | 
% 154.11/23.33  | | End of split
% 154.11/23.33  | | 
% 154.11/23.33  | Case 2:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (84)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.11/23.33  | | 
% 154.11/23.33  | | REF_CLOSE: (16), (24), (27), (31), (84) are inconsistent by sub-proof #982.
% 154.11/23.33  | | 
% 154.11/23.33  | End of split
% 154.11/23.33  | 
% 154.11/23.33  End of proof
% 154.11/23.33  
% 154.11/23.33  Sub-proof #982 shows that the following formulas are inconsistent:
% 154.11/23.33  ----------------------------------------------------------------
% 154.11/23.33    (1)   ~ (all_52_7 = e1)
% 154.11/23.33    (2)   ~ (all_52_7 = e2)
% 154.11/23.33    (3)   ~ (all_52_7 = e0)
% 154.11/23.33    (4)  all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 154.11/23.33    (5)  all_54_13 = all_52_7
% 154.11/23.33  
% 154.11/23.33  Begin of proof
% 154.11/23.33  | 
% 154.11/23.33  | BETA: splitting (4) gives:
% 154.11/23.33  | 
% 154.11/23.33  | Case 1:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (6)  all_54_13 = e2
% 154.11/23.33  | | 
% 154.11/23.33  | | COMBINE_EQS: (5), (6) imply:
% 154.11/23.33  | |   (7)  all_52_7 = e2
% 154.11/23.33  | | 
% 154.11/23.33  | | REDUCE: (2), (7) imply:
% 154.11/23.33  | |   (8)  $false
% 154.11/23.33  | | 
% 154.11/23.33  | | CLOSE: (8) is inconsistent.
% 154.11/23.33  | | 
% 154.11/23.33  | Case 2:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (9)  all_54_13 = e1 | all_54_13 = e0
% 154.11/23.33  | | 
% 154.11/23.33  | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #983.
% 154.11/23.33  | | 
% 154.11/23.33  | End of split
% 154.11/23.33  | 
% 154.11/23.33  End of proof
% 154.11/23.33  
% 154.11/23.33  Sub-proof #983 shows that the following formulas are inconsistent:
% 154.11/23.33  ----------------------------------------------------------------
% 154.11/23.33    (1)  all_54_13 = e1 | all_54_13 = e0
% 154.11/23.33    (2)  all_54_13 = all_52_7
% 154.11/23.33    (3)   ~ (all_52_7 = e1)
% 154.11/23.33    (4)   ~ (all_52_7 = e0)
% 154.11/23.33  
% 154.11/23.33  Begin of proof
% 154.11/23.33  | 
% 154.11/23.33  | BETA: splitting (1) gives:
% 154.11/23.33  | 
% 154.11/23.33  | Case 1:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (5)  all_54_13 = e1
% 154.11/23.33  | | 
% 154.11/23.33  | | COMBINE_EQS: (2), (5) imply:
% 154.11/23.33  | |   (6)  all_52_7 = e1
% 154.11/23.33  | | 
% 154.11/23.33  | | SIMP: (6) implies:
% 154.11/23.33  | |   (7)  all_52_7 = e1
% 154.11/23.33  | | 
% 154.11/23.33  | | REDUCE: (3), (7) imply:
% 154.11/23.33  | |   (8)  $false
% 154.11/23.33  | | 
% 154.11/23.33  | | CLOSE: (8) is inconsistent.
% 154.11/23.33  | | 
% 154.11/23.33  | Case 2:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (9)  all_54_13 = e0
% 154.11/23.33  | | 
% 154.11/23.33  | | REF_CLOSE: (2), (4), (9) are inconsistent by sub-proof #984.
% 154.11/23.33  | | 
% 154.11/23.33  | End of split
% 154.11/23.33  | 
% 154.11/23.33  End of proof
% 154.11/23.33  
% 154.11/23.33  Sub-proof #984 shows that the following formulas are inconsistent:
% 154.11/23.33  ----------------------------------------------------------------
% 154.11/23.33    (1)  all_54_13 = all_52_7
% 154.11/23.33    (2)  all_54_13 = e0
% 154.11/23.33    (3)   ~ (all_52_7 = e0)
% 154.11/23.33  
% 154.11/23.33  Begin of proof
% 154.11/23.33  | 
% 154.11/23.33  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.33  |   (4)  all_52_7 = e0
% 154.11/23.33  | 
% 154.11/23.33  | SIMP: (4) implies:
% 154.11/23.33  |   (5)  all_52_7 = e0
% 154.11/23.33  | 
% 154.11/23.33  | REDUCE: (3), (5) imply:
% 154.11/23.33  |   (6)  $false
% 154.11/23.33  | 
% 154.11/23.33  | CLOSE: (6) is inconsistent.
% 154.11/23.33  | 
% 154.11/23.33  End of proof
% 154.11/23.33  
% 154.11/23.33  Sub-proof #985 shows that the following formulas are inconsistent:
% 154.11/23.33  ----------------------------------------------------------------
% 154.11/23.33    (1)   ~ (e3 = e1)
% 154.11/23.33    (2)   ~ (all_52_4 = e2)
% 154.11/23.33    (3)   ~ (all_52_4 = all_52_12)
% 154.11/23.33    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.33    (5)  all_54_1 = all_52_4
% 154.11/23.33    (6)  all_56_4 = e2
% 154.11/23.33    (7)  all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.11/23.33    (8)   ~ (all_52_4 = e3)
% 154.11/23.33    (9)  op(e3, e0) = all_52_12
% 154.11/23.33    (10)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 154.11/23.33          (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 154.11/23.33    (11)  op(e2, e2) = e2
% 154.11/23.33    (12)   ~ (all_52_4 = e1)
% 154.11/23.33    (13)  all_56_13 = e3
% 154.11/23.33    (14)  all_56_7 = e0
% 154.11/23.33    (15)  op(e3, e3) = e3
% 154.11/23.33    (16)   ~ (e2 = e1)
% 154.11/23.33    (17)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.11/23.33          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.11/23.33  
% 154.11/23.33  Begin of proof
% 154.11/23.33  | 
% 154.11/23.33  | BETA: splitting (7) gives:
% 154.11/23.33  | 
% 154.11/23.33  | Case 1:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (18)  all_54_1 = e3
% 154.11/23.33  | | 
% 154.11/23.33  | | REF_CLOSE: (5), (8), (18) are inconsistent by sub-proof #988.
% 154.11/23.33  | | 
% 154.11/23.33  | Case 2:
% 154.11/23.33  | | 
% 154.11/23.33  | |   (19)   ~ (all_54_1 = e3)
% 154.11/23.33  | |   (20)  all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 154.11/23.33  | | 
% 154.11/23.33  | | BETA: splitting (20) gives:
% 154.11/23.33  | | 
% 154.11/23.33  | | Case 1:
% 154.11/23.33  | | | 
% 154.11/23.33  | | |   (21)  all_54_1 = e2
% 154.11/23.33  | | | 
% 154.11/23.33  | | | COMBINE_EQS: (5), (21) imply:
% 154.11/23.33  | | |   (22)  all_52_4 = e2
% 154.11/23.33  | | | 
% 154.11/23.33  | | | REDUCE: (2), (22) imply:
% 154.11/23.33  | | |   (23)  $false
% 154.11/23.33  | | | 
% 154.11/23.33  | | | CLOSE: (23) is inconsistent.
% 154.11/23.33  | | | 
% 154.11/23.33  | | Case 2:
% 154.11/23.33  | | | 
% 154.11/23.33  | | |   (24)   ~ (all_54_1 = e2)
% 154.11/23.33  | | |   (25)  all_54_1 = e1 | all_54_1 = e0
% 154.11/23.33  | | | 
% 154.11/23.33  | | | BETA: splitting (25) gives:
% 154.11/23.33  | | | 
% 154.11/23.33  | | | Case 1:
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | |   (26)  all_54_1 = e1
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | COMBINE_EQS: (5), (26) imply:
% 154.11/23.33  | | | |   (27)  all_52_4 = e1
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | REDUCE: (12), (27) imply:
% 154.11/23.33  | | | |   (28)  $false
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | CLOSE: (28) is inconsistent.
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | Case 2:
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | |   (29)  all_54_1 = e0
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | COMBINE_EQS: (5), (29) imply:
% 154.11/23.33  | | | |   (30)  all_52_4 = e0
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | REDUCE: (3), (30) imply:
% 154.11/23.33  | | | |   (31)   ~ (all_52_12 = e0)
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | SIMP: (31) implies:
% 154.11/23.33  | | | |   (32)   ~ (all_52_12 = e0)
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | REDUCE: (8), (30) imply:
% 154.11/23.33  | | | |   (33)   ~ (e3 = e0)
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | SIMP: (33) implies:
% 154.11/23.33  | | | |   (34)   ~ (e3 = e0)
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | REDUCE: (2), (30) imply:
% 154.11/23.33  | | | |   (35)   ~ (e2 = e0)
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | SIMP: (35) implies:
% 154.11/23.33  | | | |   (36)   ~ (e2 = e0)
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | REDUCE: (12), (30) imply:
% 154.11/23.33  | | | |   (37)   ~ (e1 = e0)
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | SIMP: (37) implies:
% 154.11/23.33  | | | |   (38)   ~ (e1 = e0)
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | BETA: splitting (10) gives:
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | | Case 1:
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | |   (39)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3,
% 154.11/23.33  | | | | |             e2) = e0)
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | | BETA: splitting (39) gives:
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | | Case 1:
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | |   (40)  all_56_0 = e0 & op(e3, e3) = e0
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | ALPHA: (40) implies:
% 154.11/23.33  | | | | | |   (41)  op(e3, e3) = e0
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | REF_CLOSE: (4), (15), (34), (41) are inconsistent by sub-proof
% 154.11/23.33  | | | | | |            #1141.
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | Case 2:
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | |   (42)  all_56_1 = e0 & op(e3, e2) = e0
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | ALPHA: (42) implies:
% 154.11/23.33  | | | | | |   (43)  all_56_1 = e0
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | BETA: splitting (17) gives:
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | Case 1:
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | |   (44)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 &
% 154.11/23.33  | | | | | | |           op(e2, e2) = e1)
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | | REF_CLOSE: (4), (11), (16), (38), (43), (44) are inconsistent by
% 154.11/23.33  | | | | | | |            sub-proof #997.
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | Case 2:
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | |   (45)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 &
% 154.11/23.33  | | | | | | |           op(e0, e2) = e1)
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | | BETA: splitting (45) gives:
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | | Case 1:
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | |   (46)  all_56_7 = e1 & op(e1, e2) = e1
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | | ALPHA: (46) implies:
% 154.11/23.33  | | | | | | | |   (47)  all_56_7 = e1
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | | REF_CLOSE: (14), (38), (47) are inconsistent by sub-proof #987.
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | Case 2:
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | |   (48)  all_56_13 = e1 & op(e0, e2) = e1
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | | ALPHA: (48) implies:
% 154.11/23.33  | | | | | | | |   (49)  all_56_13 = e1
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | | REF_CLOSE: (1), (13), (49) are inconsistent by sub-proof #1121.
% 154.11/23.33  | | | | | | | | 
% 154.11/23.33  | | | | | | | End of split
% 154.11/23.33  | | | | | | | 
% 154.11/23.33  | | | | | | End of split
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | End of split
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | Case 2:
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | |   (50)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3,
% 154.11/23.33  | | | | |             e0) = e0)
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | | BETA: splitting (50) gives:
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | | Case 1:
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | |   (51)  all_56_4 = e0 & op(e3, e1) = e0
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | REF_CLOSE: (6), (36), (51) are inconsistent by sub-proof #1070.
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | Case 2:
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | |   (52)  all_56_9 = e0 & op(e3, e0) = e0
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | | REF_CLOSE: (4), (9), (32), (52) are inconsistent by sub-proof #986.
% 154.11/23.33  | | | | | | 
% 154.11/23.33  | | | | | End of split
% 154.11/23.33  | | | | | 
% 154.11/23.33  | | | | End of split
% 154.11/23.33  | | | | 
% 154.11/23.33  | | | End of split
% 154.11/23.33  | | | 
% 154.11/23.33  | | End of split
% 154.11/23.33  | | 
% 154.11/23.33  | End of split
% 154.11/23.33  | 
% 154.11/23.33  End of proof
% 154.11/23.33  
% 154.11/23.33  Sub-proof #986 shows that the following formulas are inconsistent:
% 154.11/23.33  ----------------------------------------------------------------
% 154.11/23.33    (1)  all_56_9 = e0 & op(e3, e0) = e0
% 154.11/23.33    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.33           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.33    (3)  op(e3, e0) = all_52_12
% 154.11/23.34    (4)   ~ (all_52_12 = e0)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | ALPHA: (1) implies:
% 154.11/23.34  |   (5)  op(e3, e0) = e0
% 154.11/23.34  | 
% 154.11/23.34  | GROUND_INST: instantiating (2) with all_52_12, e0, e0, e3, simplifying with
% 154.11/23.34  |              (3), (5) gives:
% 154.11/23.34  |   (6)  all_52_12 = e0
% 154.11/23.34  | 
% 154.11/23.34  | REDUCE: (4), (6) imply:
% 154.11/23.34  |   (7)  $false
% 154.11/23.34  | 
% 154.11/23.34  | CLOSE: (7) is inconsistent.
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #987 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)  all_56_7 = e1
% 154.11/23.34    (2)  all_56_7 = e0
% 154.11/23.34    (3)   ~ (e1 = e0)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.34  |   (4)  e1 = e0
% 154.11/23.34  | 
% 154.11/23.34  | SIMP: (4) implies:
% 154.11/23.34  |   (5)  e1 = e0
% 154.11/23.34  | 
% 154.11/23.34  | REDUCE: (3), (5) imply:
% 154.11/23.34  |   (6)  $false
% 154.11/23.34  | 
% 154.11/23.34  | CLOSE: (6) is inconsistent.
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #988 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)  all_54_1 = all_52_4
% 154.11/23.34    (2)  all_54_1 = e3
% 154.11/23.34    (3)   ~ (all_52_4 = e3)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.34  |   (4)  all_52_4 = e3
% 154.11/23.34  | 
% 154.11/23.34  | SIMP: (4) implies:
% 154.11/23.34  |   (5)  all_52_4 = e3
% 154.11/23.34  | 
% 154.11/23.34  | REDUCE: (3), (5) imply:
% 154.11/23.34  |   (6)  $false
% 154.11/23.34  | 
% 154.11/23.34  | CLOSE: (6) is inconsistent.
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #989 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)  all_56_7 = e3 & op(e1, e2) = e3
% 154.11/23.34    (2)  all_56_7 = e0
% 154.11/23.34    (3)   ~ (e3 = e0)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | ALPHA: (1) implies:
% 154.11/23.34  |   (4)  all_56_7 = e3
% 154.11/23.34  | 
% 154.11/23.34  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.34  |   (5)  e3 = e0
% 154.11/23.34  | 
% 154.11/23.34  | SIMP: (5) implies:
% 154.11/23.34  |   (6)  e3 = e0
% 154.11/23.34  | 
% 154.11/23.34  | REDUCE: (3), (6) imply:
% 154.11/23.34  |   (7)  $false
% 154.11/23.34  | 
% 154.11/23.34  | CLOSE: (7) is inconsistent.
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #990 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)  op(e0, e1) = all_52_11
% 154.11/23.34    (2)  (all_56_14 = e3 & op(e0, e1) = e3) | (all_56_15 = e3 & op(e0, e0) = e3)
% 154.11/23.34    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.34    (4)  op(e0, e0) = e2
% 154.11/23.34    (5)   ~ (all_52_11 = e3)
% 154.11/23.34    (6)   ~ (e3 = e2)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | BETA: splitting (2) gives:
% 154.11/23.34  | 
% 154.11/23.34  | Case 1:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (7)  all_56_14 = e3 & op(e0, e1) = e3
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (7) implies:
% 154.11/23.34  | |   (8)  op(e0, e1) = e3
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1147.
% 154.11/23.34  | | 
% 154.11/23.34  | Case 2:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (9)  all_56_15 = e3 & op(e0, e0) = e3
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (9) implies:
% 154.11/23.34  | |   (10)  op(e0, e0) = e3
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #1087.
% 154.11/23.34  | | 
% 154.11/23.34  | End of split
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #991 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)   ~ (e3 = e1)
% 154.11/23.34    (2)   ~ (e2 = e0)
% 154.11/23.34    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.34    (4)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 154.11/23.34    (5)   ~ (e3 = e0)
% 154.11/23.34    (6)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 154.11/23.34         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.11/23.34    (7)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2, e3) = e2) |
% 154.11/23.34         (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0, e3) = e2)
% 154.11/23.34    (8)   ~ (e1 = e0)
% 154.11/23.34    (9)   ~ (e3 = e2)
% 154.11/23.34    (10)  op(e3, e3) = e3
% 154.11/23.34    (11)   ~ (e2 = e1)
% 154.11/23.34    (12)  all_56_12 = e3
% 154.11/23.34    (13)  op(e1, e3) = all_52_2
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | BETA: splitting (4) gives:
% 154.11/23.34  | 
% 154.11/23.34  | Case 1:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (14)  all_56_6 = e1 & op(e1, e3) = e1
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (14) implies:
% 154.11/23.34  | |   (15)  all_56_6 = e1
% 154.11/23.34  | |   (16)  op(e1, e3) = e1
% 154.11/23.34  | | 
% 154.11/23.34  | | BETA: splitting (6) gives:
% 154.11/23.34  | | 
% 154.11/23.34  | | Case 1:
% 154.11/23.34  | | | 
% 154.11/23.34  | | |   (17)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 154.11/23.34  | | |           e0)
% 154.11/23.34  | | | 
% 154.11/23.34  | | | BETA: splitting (17) gives:
% 154.11/23.34  | | | 
% 154.11/23.34  | | | Case 1:
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | |   (18)  all_56_0 = e0 & op(e3, e3) = e0
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | | ALPHA: (18) implies:
% 154.11/23.34  | | | |   (19)  op(e3, e3) = e0
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | | REF_CLOSE: (3), (5), (10), (19) are inconsistent by sub-proof #1141.
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | Case 2:
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | |   (20)  all_56_2 = e0 & op(e2, e3) = e0
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | | ALPHA: (20) implies:
% 154.11/23.34  | | | |   (21)  all_56_2 = e0
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | | BETA: splitting (7) gives:
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | | Case 1:
% 154.11/23.34  | | | | | 
% 154.11/23.34  | | | | |   (22)  (all_56_0 = e2 & op(e3, e3) = e2) | (all_56_2 = e2 & op(e2,
% 154.11/23.34  | | | | |             e3) = e2)
% 154.11/23.34  | | | | | 
% 154.11/23.34  | | | | | BETA: splitting (22) gives:
% 154.11/23.34  | | | | | 
% 154.11/23.34  | | | | | Case 1:
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | |   (23)  all_56_0 = e2 & op(e3, e3) = e2
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | | ALPHA: (23) implies:
% 154.11/23.34  | | | | | |   (24)  op(e3, e3) = e2
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | | REF_CLOSE: (3), (9), (10), (24) are inconsistent by sub-proof #1085.
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | Case 2:
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | |   (25)  all_56_2 = e2 & op(e2, e3) = e2
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | | REF_CLOSE: (2), (21), (25) are inconsistent by sub-proof #994.
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | End of split
% 154.11/23.34  | | | | | 
% 154.11/23.34  | | | | Case 2:
% 154.11/23.34  | | | | | 
% 154.11/23.34  | | | | |   (26)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_12 = e2 & op(e0,
% 154.11/23.34  | | | | |             e3) = e2)
% 154.11/23.34  | | | | | 
% 154.11/23.34  | | | | | BETA: splitting (26) gives:
% 154.11/23.34  | | | | | 
% 154.11/23.34  | | | | | Case 1:
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | |   (27)  all_56_6 = e2 & op(e1, e3) = e2
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | | ALPHA: (27) implies:
% 154.11/23.34  | | | | | |   (28)  all_56_6 = e2
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | | REF_CLOSE: (11), (15), (28) are inconsistent by sub-proof #1172.
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | Case 2:
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | |   (29)  all_56_12 = e2 & op(e0, e3) = e2
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | | REF_CLOSE: (9), (12), (29) are inconsistent by sub-proof #993.
% 154.11/23.34  | | | | | | 
% 154.11/23.34  | | | | | End of split
% 154.11/23.34  | | | | | 
% 154.11/23.34  | | | | End of split
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | End of split
% 154.11/23.34  | | | 
% 154.11/23.34  | | Case 2:
% 154.11/23.34  | | | 
% 154.11/23.34  | | |   (30)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 154.11/23.34  | | |           e0)
% 154.11/23.34  | | | 
% 154.11/23.34  | | | BETA: splitting (30) gives:
% 154.11/23.34  | | | 
% 154.11/23.34  | | | Case 1:
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | |   (31)  all_56_6 = e0 & op(e1, e3) = e0
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | | ALPHA: (31) implies:
% 154.11/23.34  | | | |   (32)  op(e1, e3) = e0
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | | REF_CLOSE: (3), (8), (13), (16), (32) are inconsistent by sub-proof
% 154.11/23.34  | | | |            #1127.
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | Case 2:
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | |   (33)  all_56_12 = e0 & op(e0, e3) = e0
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | | ALPHA: (33) implies:
% 154.11/23.34  | | | |   (34)  all_56_12 = e0
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | | REF_CLOSE: (5), (12), (34) are inconsistent by sub-proof #1052.
% 154.11/23.34  | | | | 
% 154.11/23.34  | | | End of split
% 154.11/23.34  | | | 
% 154.11/23.34  | | End of split
% 154.11/23.34  | | 
% 154.11/23.34  | Case 2:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (35)  all_56_12 = e1 & op(e0, e3) = e1
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (1), (12), (35) are inconsistent by sub-proof #992.
% 154.11/23.34  | | 
% 154.11/23.34  | End of split
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #992 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)  all_56_12 = e1 & op(e0, e3) = e1
% 154.11/23.34    (2)  all_56_12 = e3
% 154.11/23.34    (3)   ~ (e3 = e1)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | ALPHA: (1) implies:
% 154.11/23.34  |   (4)  all_56_12 = e1
% 154.11/23.34  | 
% 154.11/23.34  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.34  |   (5)  e3 = e1
% 154.11/23.34  | 
% 154.11/23.34  | REDUCE: (3), (5) imply:
% 154.11/23.34  |   (6)  $false
% 154.11/23.34  | 
% 154.11/23.34  | CLOSE: (6) is inconsistent.
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #993 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)  all_56_12 = e2 & op(e0, e3) = e2
% 154.11/23.34    (2)  all_56_12 = e3
% 154.11/23.34    (3)   ~ (e3 = e2)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | ALPHA: (1) implies:
% 154.11/23.34  |   (4)  all_56_12 = e2
% 154.11/23.34  | 
% 154.11/23.34  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.34  |   (5)  e3 = e2
% 154.11/23.34  | 
% 154.11/23.34  | REDUCE: (3), (5) imply:
% 154.11/23.34  |   (6)  $false
% 154.11/23.34  | 
% 154.11/23.34  | CLOSE: (6) is inconsistent.
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #994 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)  all_56_2 = e2 & op(e2, e3) = e2
% 154.11/23.34    (2)  all_56_2 = e0
% 154.11/23.34    (3)   ~ (e2 = e0)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | ALPHA: (1) implies:
% 154.11/23.34  |   (4)  all_56_2 = e2
% 154.11/23.34  | 
% 154.11/23.34  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.34  |   (5)  e2 = e0
% 154.11/23.34  | 
% 154.11/23.34  | SIMP: (5) implies:
% 154.11/23.34  |   (6)  e2 = e0
% 154.11/23.34  | 
% 154.11/23.34  | REDUCE: (3), (6) imply:
% 154.11/23.34  |   (7)  $false
% 154.11/23.34  | 
% 154.11/23.34  | CLOSE: (7) is inconsistent.
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #995 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0)
% 154.11/23.34    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.34    (3)   ~ (e3 = e0)
% 154.11/23.34    (4)  all_56_2 = e1
% 154.11/23.34    (5)   ~ (e1 = e0)
% 154.11/23.34    (6)  op(e3, e3) = e3
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | BETA: splitting (1) gives:
% 154.11/23.34  | 
% 154.11/23.34  | Case 1:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (7) implies:
% 154.11/23.34  | |   (8)  op(e3, e3) = e0
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #1141.
% 154.11/23.34  | | 
% 154.11/23.34  | Case 2:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (9)  all_56_2 = e0 & op(e2, e3) = e0
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #996.
% 154.11/23.34  | | 
% 154.11/23.34  | End of split
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #996 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)  all_56_2 = e0 & op(e2, e3) = e0
% 154.11/23.34    (2)  all_56_2 = e1
% 154.11/23.34    (3)   ~ (e1 = e0)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | ALPHA: (1) implies:
% 154.11/23.34  |   (4)  all_56_2 = e0
% 154.11/23.34  | 
% 154.11/23.34  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.34  |   (5)  e1 = e0
% 154.11/23.34  | 
% 154.11/23.34  | REDUCE: (3), (5) imply:
% 154.11/23.34  |   (6)  $false
% 154.11/23.34  | 
% 154.11/23.34  | CLOSE: (6) is inconsistent.
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #997 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.34    (2)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1)
% 154.11/23.34    (3)  op(e2, e2) = e2
% 154.11/23.34    (4)   ~ (e1 = e0)
% 154.11/23.34    (5)  all_56_1 = e0
% 154.11/23.34    (6)   ~ (e2 = e1)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | BETA: splitting (2) gives:
% 154.11/23.34  | 
% 154.11/23.34  | Case 1:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (7)  all_56_1 = e1 & op(e3, e2) = e1
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (7) implies:
% 154.11/23.34  | |   (8)  all_56_1 = e1
% 154.11/23.34  | | 
% 154.11/23.34  | | COMBINE_EQS: (5), (8) imply:
% 154.11/23.34  | |   (9)  e1 = e0
% 154.11/23.34  | | 
% 154.11/23.34  | | REDUCE: (4), (9) imply:
% 154.11/23.34  | |   (10)  $false
% 154.11/23.34  | | 
% 154.11/23.34  | | CLOSE: (10) is inconsistent.
% 154.11/23.34  | | 
% 154.11/23.34  | Case 2:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (11)  all_56_3 = e1 & op(e2, e2) = e1
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (11) implies:
% 154.11/23.34  | |   (12)  op(e2, e2) = e1
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (1), (3), (6), (12) are inconsistent by sub-proof #1158.
% 154.11/23.34  | | 
% 154.11/23.34  | End of split
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #998 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)   ~ (e3 = e1)
% 154.11/23.34    (2)  op(e3, e2) = all_52_4
% 154.11/23.34    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.34    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 154.11/23.34         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 154.11/23.34    (5)  all_56_4 = e2
% 154.11/23.34    (6)   ~ (all_52_4 = e3)
% 154.11/23.34    (7)  op(e3, e0) = all_52_12
% 154.11/23.34    (8)  op(e3, e3) = e1
% 154.11/23.34    (9)   ~ (all_52_12 = e3)
% 154.11/23.34    (10)   ~ (e3 = e2)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | BETA: splitting (4) gives:
% 154.11/23.34  | 
% 154.11/23.34  | Case 1:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (11)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) =
% 154.11/23.34  | |           e3)
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (1), (2), (3), (6), (8), (11) are inconsistent by sub-proof #999.
% 154.11/23.34  | | 
% 154.11/23.34  | Case 2:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (12)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) =
% 154.11/23.34  | |           e3)
% 154.11/23.34  | | 
% 154.11/23.34  | | BETA: splitting (12) gives:
% 154.11/23.34  | | 
% 154.11/23.34  | | Case 1:
% 154.11/23.34  | | | 
% 154.11/23.34  | | |   (13)  all_56_4 = e3 & op(e3, e1) = e3
% 154.11/23.34  | | | 
% 154.11/23.34  | | | ALPHA: (13) implies:
% 154.11/23.34  | | |   (14)  all_56_4 = e3
% 154.11/23.34  | | | 
% 154.11/23.34  | | | REF_CLOSE: (5), (10), (14) are inconsistent by sub-proof #1068.
% 154.11/23.34  | | | 
% 154.11/23.34  | | Case 2:
% 154.11/23.34  | | | 
% 154.11/23.34  | | |   (15)  all_56_9 = e3 & op(e3, e0) = e3
% 154.11/23.34  | | | 
% 154.11/23.34  | | | ALPHA: (15) implies:
% 154.11/23.34  | | |   (16)  op(e3, e0) = e3
% 154.11/23.34  | | | 
% 154.11/23.34  | | | REF_CLOSE: (3), (7), (9), (16) are inconsistent by sub-proof #1082.
% 154.11/23.34  | | | 
% 154.11/23.34  | | End of split
% 154.11/23.34  | | 
% 154.11/23.34  | End of split
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #999 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)   ~ (e3 = e1)
% 154.11/23.34    (2)  op(e3, e2) = all_52_4
% 154.11/23.34    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.34    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3)
% 154.11/23.34    (5)   ~ (all_52_4 = e3)
% 154.11/23.34    (6)  op(e3, e3) = e1
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | BETA: splitting (4) gives:
% 154.11/23.34  | 
% 154.11/23.34  | Case 1:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (7)  all_56_0 = e3 & op(e3, e3) = e3
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (7) implies:
% 154.11/23.34  | |   (8)  op(e3, e3) = e3
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #1178.
% 154.11/23.34  | | 
% 154.11/23.34  | Case 2:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (9)  all_56_1 = e3 & op(e3, e2) = e3
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (9) implies:
% 154.11/23.34  | |   (10)  op(e3, e2) = e3
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #1166.
% 154.11/23.34  | | 
% 154.11/23.34  | End of split
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #1000 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.34    (2)  op(e0, e0) = e2
% 154.11/23.34    (3)  op(e2, e2) = e2
% 154.11/23.34    (4)   ~ (e3 = e2)
% 154.11/23.34    (5)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 154.11/23.34             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.11/23.34           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 154.11/23.34           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 154.11/23.34           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 154.11/23.34           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)) | (all_57_1 = e1 &
% 154.11/23.34           all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 = e3) & op(e2, e3)
% 154.11/23.34           = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 & op(e1, e1) = all_57_14
% 154.11/23.34           & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1 & all_57_15 = e3 &  ~
% 154.11/23.34           (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) =
% 154.11/23.34           all_57_14 & op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 154.11/23.34           $i(all_57_14))
% 154.11/23.34    (6)  op(e2, e3) = all_52_1
% 154.11/23.34    (7)   ~ (all_52_1 = e2)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | BETA: splitting (5) gives:
% 154.11/23.34  | 
% 154.11/23.34  | Case 1:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (8)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12
% 154.11/23.34  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.11/23.34  | |          all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) |
% 154.11/23.34  | |        (all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12
% 154.11/23.34  | |            = e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 154.11/23.34  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (1), (6), (7), (8) are inconsistent by sub-proof #1180.
% 154.11/23.34  | | 
% 154.11/23.34  | Case 2:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (9)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14
% 154.11/23.34  | |            = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1
% 154.11/23.34  | |          & op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) |
% 154.11/23.34  | |        (all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14
% 154.11/23.34  | |            = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 154.11/23.34  | |          all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 154.11/23.34  | | 
% 154.11/23.34  | | BETA: splitting (9) gives:
% 154.11/23.34  | | 
% 154.11/23.34  | | Case 1:
% 154.11/23.34  | | | 
% 154.11/23.34  | | |   (10)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.11/23.34  | | |         (all_57_14 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 154.11/23.34  | | |         op(e1, e3) = e1 & op(e1, e1) = all_57_14 & $i(all_57_0) &
% 154.11/23.34  | | |         $i(all_57_14)
% 154.11/23.34  | | | 
% 154.11/23.34  | | | ALPHA: (10) implies:
% 154.11/23.34  | | |   (11)  op(e2, e2) = e3
% 154.11/23.34  | | | 
% 154.11/23.34  | | | REF_CLOSE: (1), (3), (4), (11) are inconsistent by sub-proof #1179.
% 154.11/23.34  | | | 
% 154.11/23.34  | | Case 2:
% 154.11/23.34  | | | 
% 154.11/23.34  | | |   (12)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~
% 154.11/23.34  | | |         (all_57_14 = e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 &
% 154.11/23.34  | | |         op(e0, e3) = all_57_2 & op(e0, e0) = e3 & $i(all_57_2) &
% 154.11/23.34  | | |         $i(all_57_14)
% 154.11/23.34  | | | 
% 154.11/23.34  | | | ALPHA: (12) implies:
% 154.11/23.34  | | |   (13)  op(e0, e0) = e3
% 154.11/23.34  | | | 
% 154.11/23.34  | | | REF_CLOSE: (1), (2), (4), (13) are inconsistent by sub-proof #1087.
% 154.11/23.34  | | | 
% 154.11/23.34  | | End of split
% 154.11/23.34  | | 
% 154.11/23.34  | End of split
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #1001 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)  (all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3) |
% 154.11/23.34             ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.11/23.34           ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2, e2)
% 154.11/23.34               = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0, e1) = e0)
% 154.11/23.34             | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 & $i(all_57_15)))) |
% 154.11/23.34         (all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3) |
% 154.11/23.34             ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.11/23.34           ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2, e2)
% 154.11/23.34               = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1, e0) = e1)
% 154.11/23.34             | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 & $i(all_57_14))))
% 154.11/23.34    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.34    (3)  op(e0, e0) = e3
% 154.11/23.34    (4)  op(e1, e1) = e0
% 154.11/23.34    (5)   ~ (e3 = e0)
% 154.11/23.34    (6)   ~ (e1 = e0)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | BETA: splitting (1) gives:
% 154.11/23.34  | 
% 154.11/23.34  | Case 1:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (7)  all_57_14 = e1 & op(e1, e1) = e1 & ((all_57_6 = e3 & op(e3, e1) = e3)
% 154.11/23.34  | |          | ( ~ (all_57_10 = e1) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.11/23.34  | |        ((all_57_7 = e2 & op(e2, e1) = e2) | ( ~ (all_57_12 = e1) & op(e2,
% 154.11/23.34  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_8 = e0 & op(e0,
% 154.11/23.34  | |              e1) = e0) | ( ~ (all_57_15 = e1) & op(e0, e0) = all_57_15 &
% 154.11/23.34  | |            $i(all_57_15)))
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (7) implies:
% 154.11/23.34  | |   (8)  op(e1, e1) = e1
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1038.
% 154.11/23.34  | | 
% 154.11/23.34  | Case 2:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (9)  all_57_15 = e0 & op(e0, e0) = e0 & ((all_57_9 = e3 & op(e3, e0) = e3)
% 154.11/23.34  | |          | ( ~ (all_57_10 = e0) & op(e3, e3) = all_57_10 & $i(all_57_10))) &
% 154.11/23.34  | |        ((all_57_11 = e2 & op(e2, e0) = e2) | ( ~ (all_57_12 = e0) & op(e2,
% 154.11/23.34  | |              e2) = all_57_12 & $i(all_57_12))) & ((all_57_13 = e1 & op(e1,
% 154.11/23.34  | |              e0) = e1) | ( ~ (all_57_14 = e0) & op(e1, e1) = all_57_14 &
% 154.11/23.34  | |            $i(all_57_14)))
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (9) implies:
% 154.11/23.34  | |   (10)  op(e0, e0) = e0
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #1143.
% 154.11/23.34  | | 
% 154.11/23.34  | End of split
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #1002 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)  (all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~ (all_57_14 =
% 154.11/23.34             e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1, e1) =
% 154.11/23.34           all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)) | (op(e0,
% 154.11/23.34             e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12 = e3 & 
% 154.11/23.34               ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) = all_57_0 &
% 154.11/23.34               op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) | (all_57_2 = e0
% 154.11/23.34               & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 = e3) &
% 154.11/23.34               op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 154.11/23.34               $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 154.11/23.34                 e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.34               all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 &
% 154.11/23.34               all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1,
% 154.11/23.34                 e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.11/23.34               $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 =
% 154.11/23.34                 e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) =
% 154.11/23.34               all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 &
% 154.11/23.34               all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2,
% 154.11/23.34                 e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.11/23.34               $i(all_57_7))))
% 154.11/23.34    (2)   ~ (e2 = e0)
% 154.11/23.34    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.34    (4)  op(e0, e0) = e3
% 154.11/23.34    (5)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 154.11/23.34           all_57_14 & $i(all_57_14))
% 154.11/23.34    (6)  all_57_3 = e3
% 154.11/23.34    (7)  op(e0, e1) = e2
% 154.11/23.34    (8)  op(e2, e2) = e2
% 154.11/23.34    (9)  op(e1, e0) = e2
% 154.11/23.34    (10)   ~ (e3 = e2)
% 154.11/23.34    (11)   ~ (e2 = e1)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | BETA: splitting (1) gives:
% 154.11/23.34  | 
% 154.11/23.34  | Case 1:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (12)  all_57_12 = e0 & all_57_13 = e1 &  ~ (all_57_11 = e2) &  ~
% 154.11/23.34  | |         (all_57_14 = e0) & op(e2, e2) = e0 & op(e2, e0) = all_57_11 & op(e1,
% 154.11/23.34  | |           e1) = all_57_14 & op(e1, e0) = e1 & $i(all_57_11) & $i(all_57_14)
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (12) implies:
% 154.11/23.34  | |   (13)  op(e1, e0) = e1
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (3), (9), (11), (13) are inconsistent by sub-proof #1125.
% 154.11/23.34  | | 
% 154.11/23.34  | Case 2:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (14)  op(e0, e0) = all_57_15 & $i(all_57_15) & ((all_57_2 = e0 & all_57_12
% 154.11/23.34  | |             = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 = e3) & op(e2, e3) =
% 154.11/23.34  | |             all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 & $i(all_57_0)) |
% 154.11/23.34  | |           (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.11/23.34  | |             (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.11/23.34  | |             op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 154.11/23.34  | |             e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 154.11/23.34  | |             & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) |
% 154.11/23.34  | |           (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.11/23.34  | |             (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 154.11/23.34  | |             op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 =
% 154.11/23.34  | |             e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 154.11/23.34  | |             & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 154.11/23.34  | |           (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~
% 154.11/23.34  | |             (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 &
% 154.11/23.34  | |             op(e0, e1) = e0 & $i(all_57_7)))
% 154.11/23.34  | | 
% 154.11/23.34  | | ALPHA: (14) implies:
% 154.11/23.34  | |   (15)  op(e0, e0) = all_57_15
% 154.11/23.34  | |   (16)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 154.11/23.34  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 154.11/23.34  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 154.11/23.34  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 154.11/23.34  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 154.11/23.34  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 154.11/23.34  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.11/23.34  | |           $i(all_57_3)) | (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 =
% 154.11/23.34  | |             e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) =
% 154.11/23.34  | |           e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10
% 154.11/23.34  | |           = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1
% 154.11/23.34  | |           & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 154.11/23.34  | |         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15
% 154.11/23.34  | |             = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) =
% 154.11/23.34  | |           e0 & $i(all_57_7))
% 154.11/23.34  | | 
% 154.11/23.34  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (15), (16) are
% 154.11/23.34  | |            inconsistent by sub-proof #1003.
% 154.11/23.34  | | 
% 154.11/23.34  | End of split
% 154.11/23.34  | 
% 154.11/23.34  End of proof
% 154.11/23.34  
% 154.11/23.34  Sub-proof #1003 shows that the following formulas are inconsistent:
% 154.11/23.34  ----------------------------------------------------------------
% 154.11/23.34    (1)   ~ (e2 = e0)
% 154.11/23.34    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.34           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.34    (3)  op(e0, e0) = e3
% 154.11/23.34    (4)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 154.11/23.34           all_57_14 & $i(all_57_14))
% 154.11/23.34    (5)  all_57_3 = e3
% 154.11/23.34    (6)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.11/23.34             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.11/23.34           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.11/23.34           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.11/23.34             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.11/23.34           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.34           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 154.11/23.34           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 154.11/23.34           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.11/23.34           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 154.11/23.34           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 154.11/23.34         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.11/23.34             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.11/23.34           $i(all_57_7))
% 154.11/23.34    (7)  op(e0, e1) = e2
% 154.11/23.34    (8)  op(e2, e2) = e2
% 154.11/23.34    (9)  op(e0, e0) = all_57_15
% 154.11/23.34    (10)   ~ (e3 = e2)
% 154.11/23.34    (11)   ~ (e2 = e1)
% 154.11/23.34  
% 154.11/23.34  Begin of proof
% 154.11/23.34  | 
% 154.11/23.34  | BETA: splitting (6) gives:
% 154.11/23.34  | 
% 154.11/23.34  | Case 1:
% 154.11/23.34  | | 
% 154.11/23.34  | |   (12)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 154.11/23.34  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 154.11/23.34  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 154.11/23.34  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 154.11/23.34  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 154.11/23.34  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 154.11/23.34  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.11/23.34  | |           $i(all_57_3))
% 154.11/23.34  | | 
% 154.11/23.34  | | BETA: splitting (12) gives:
% 154.11/23.34  | | 
% 154.11/23.34  | | Case 1:
% 154.11/23.34  | | | 
% 154.11/23.34  | | |   (13)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.11/23.34  | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 154.11/23.34  | | |         op(e0, e3) = e0 & $i(all_57_0)
% 154.11/23.34  | | | 
% 154.11/23.34  | | | ALPHA: (13) implies:
% 154.11/23.34  | | |   (14)  op(e2, e2) = e3
% 154.11/23.34  | | | 
% 154.11/23.34  | | | REF_CLOSE: (2), (8), (10), (14) are inconsistent by sub-proof #1179.
% 154.11/23.34  | | | 
% 154.11/23.34  | | Case 2:
% 154.11/23.34  | | | 
% 154.11/23.34  | | |   (15)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.11/23.34  | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.11/23.34  | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 154.11/23.34  | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 154.11/23.34  | | |           & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.11/23.34  | | | 
% 154.11/23.34  | | | BETA: splitting (15) gives:
% 154.11/23.34  | | | 
% 154.11/23.34  | | | Case 1:
% 154.11/23.34  | | | | 
% 154.11/23.35  | | | |   (16)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.11/23.35  | | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.11/23.35  | | | |         op(e0, e3) = e0 & $i(all_57_1)
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | | ALPHA: (16) implies:
% 154.11/23.35  | | | |   (17)   ~ (all_57_15 = e3)
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | | REF_CLOSE: (2), (3), (9), (17) are inconsistent by sub-proof #1019.
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | Case 2:
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | |   (18)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.11/23.35  | | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 154.11/23.35  | | | |         op(e0, e2) = e0 & $i(all_57_3)
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | | ALPHA: (18) implies:
% 154.11/23.35  | | | |   (19)   ~ (all_57_3 = e3)
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | | REDUCE: (5), (19) imply:
% 154.11/23.35  | | | |   (20)  $false
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | | CLOSE: (20) is inconsistent.
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | End of split
% 154.11/23.35  | | | 
% 154.11/23.35  | | End of split
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (21)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 154.11/23.35  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 154.11/23.35  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.11/23.35  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 154.11/23.35  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 154.11/23.35  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 154.11/23.35  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.11/23.35  | |           $i(all_57_7))
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (1), (2), (4), (7), (8), (11), (21) are inconsistent by sub-proof
% 154.11/23.35  | |            #1004.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1004 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 154.11/23.35             e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.11/23.35           $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) & 
% 154.11/23.35           ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0,
% 154.11/23.35             e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.11/23.35           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) =
% 154.11/23.35           all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.11/23.35    (2)   ~ (e2 = e0)
% 154.11/23.35    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (4)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 154.11/23.35           all_57_14 & $i(all_57_14))
% 154.11/23.35    (5)  op(e0, e1) = e2
% 154.11/23.35    (6)  op(e2, e2) = e2
% 154.11/23.35    (7)   ~ (e2 = e1)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (1) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (8)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 =
% 154.11/23.35  | |          e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) = e0 &
% 154.11/23.35  | |        $i(all_57_4)
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (8) implies:
% 154.11/23.35  | |   (9)  all_57_14 = e2
% 154.11/23.35  | |   (10)   ~ (all_57_4 = e1)
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (4), (9), (10) are inconsistent by sub-proof #1005.
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (11)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15
% 154.11/23.35  | |             = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) =
% 154.11/23.35  | |           e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~
% 154.11/23.35  | |           (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2,
% 154.11/23.35  | |             e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (2), (3), (5), (6), (7), (11) are inconsistent by sub-proof
% 154.11/23.35  | |            #1007.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1005 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)  (all_57_4 = e1 & op(e1, e2) = e1) | ( ~ (all_57_14 = e2) & op(e1, e1) =
% 154.11/23.35           all_57_14 & $i(all_57_14))
% 154.11/23.35    (2)   ~ (all_57_4 = e1)
% 154.11/23.35    (3)  all_57_14 = e2
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (1) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (4)  all_57_4 = e1 & op(e1, e2) = e1
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (4) implies:
% 154.11/23.35  | |   (5)  all_57_4 = e1
% 154.11/23.35  | | 
% 154.11/23.35  | | REDUCE: (2), (5) imply:
% 154.11/23.35  | |   (6)  $false
% 154.11/23.35  | | 
% 154.11/23.35  | | CLOSE: (6) is inconsistent.
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (7)   ~ (all_57_14 = e2) & op(e1, e1) = all_57_14 & $i(all_57_14)
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (7) implies:
% 154.11/23.35  | |   (8)   ~ (all_57_14 = e2)
% 154.11/23.35  | | 
% 154.11/23.35  | | REDUCE: (3), (8) imply:
% 154.11/23.35  | |   (9)  $false
% 154.11/23.35  | | 
% 154.11/23.35  | | CLOSE: (9) is inconsistent.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1006 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (2)  op(e1, e1) = e2
% 154.11/23.35    (3)  op(e1, e1) = e0
% 154.11/23.35    (4)   ~ (e2 = e0)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | GROUND_INST: instantiating (1) with e0, e2, e1, e1, simplifying with (2), (3)
% 154.11/23.35  |              gives:
% 154.11/23.35  |   (5)  e2 = e0
% 154.11/23.35  | 
% 154.11/23.35  | REDUCE: (4), (5) imply:
% 154.11/23.35  |   (6)  $false
% 154.11/23.35  | 
% 154.11/23.35  | CLOSE: (6) is inconsistent.
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1007 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.11/23.35             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.11/23.35           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 154.11/23.35           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 154.11/23.35             e1) = e0 & $i(all_57_7))
% 154.11/23.35    (2)   ~ (e2 = e0)
% 154.11/23.35    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (4)  op(e0, e1) = e2
% 154.11/23.35    (5)  op(e2, e2) = e2
% 154.11/23.35    (6)   ~ (e2 = e1)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (1) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (7)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.11/23.35  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.11/23.35  | |        $i(all_57_6)
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (7) implies:
% 154.11/23.35  | |   (8)  op(e0, e1) = e0
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1008.
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (9)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.11/23.35  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.11/23.35  | |        $i(all_57_7)
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (9) implies:
% 154.11/23.35  | |   (10)  op(e2, e2) = e1
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1158.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1008 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (2)  op(e0, e1) = e2
% 154.11/23.35    (3)  op(e0, e1) = e0
% 154.11/23.35    (4)   ~ (e2 = e0)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | GROUND_INST: instantiating (1) with e2, e0, e1, e0, simplifying with (2), (3)
% 154.11/23.35  |              gives:
% 154.11/23.35  |   (5)  e2 = e0
% 154.11/23.35  | 
% 154.11/23.35  | REDUCE: (4), (5) imply:
% 154.11/23.35  |   (6)  $false
% 154.11/23.35  | 
% 154.11/23.35  | CLOSE: (6) is inconsistent.
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1009 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)   ~ (all_52_6 = e1)
% 154.11/23.35    (2)  op(e3, e2) = all_52_4
% 154.11/23.35    (3)   ~ (e2 = e0)
% 154.11/23.35    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (5)   ~ (all_52_6 = e0)
% 154.11/23.35    (6)  op(e1, e2) = all_52_6
% 154.11/23.35    (7)  op(e2, e2) = e2
% 154.11/23.35    (8)   ~ (e1 = e0)
% 154.11/23.35    (9)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.11/23.35         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.11/23.35    (10)   ~ (all_52_4 = e0)
% 154.11/23.35    (11)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (11) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (12)  all_56_7 = e1 & op(e1, e2) = e1
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (12) implies:
% 154.11/23.35  | |   (13)  op(e1, e2) = e1
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (1), (4), (6), (13) are inconsistent by sub-proof #1042.
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (14)  all_56_13 = e1 & op(e0, e2) = e1
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (14) are
% 154.11/23.35  | |            inconsistent by sub-proof #1010.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1010 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)  all_56_13 = e1 & op(e0, e2) = e1
% 154.11/23.35    (2)  op(e3, e2) = all_52_4
% 154.11/23.35    (3)   ~ (e2 = e0)
% 154.11/23.35    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (5)   ~ (all_52_6 = e0)
% 154.11/23.35    (6)  op(e1, e2) = all_52_6
% 154.11/23.35    (7)  op(e2, e2) = e2
% 154.11/23.35    (8)   ~ (e1 = e0)
% 154.11/23.35    (9)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.11/23.35         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.11/23.35    (10)   ~ (all_52_4 = e0)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | ALPHA: (1) implies:
% 154.11/23.35  |   (11)  all_56_13 = e1
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (9) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 154.11/23.35  | |           e0)
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (2), (3), (4), (7), (10), (12) are inconsistent by sub-proof
% 154.11/23.35  | |            #1012.
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (13)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 154.11/23.35  | |           e0)
% 154.11/23.35  | | 
% 154.11/23.35  | | BETA: splitting (13) gives:
% 154.11/23.35  | | 
% 154.11/23.35  | | Case 1:
% 154.11/23.35  | | | 
% 154.11/23.35  | | |   (14)  all_56_7 = e0 & op(e1, e2) = e0
% 154.11/23.35  | | | 
% 154.11/23.35  | | | REF_CLOSE: (4), (5), (6), (14) are inconsistent by sub-proof #1029.
% 154.11/23.35  | | | 
% 154.11/23.35  | | Case 2:
% 154.11/23.35  | | | 
% 154.11/23.35  | | |   (15)  all_56_13 = e0 & op(e0, e2) = e0
% 154.11/23.35  | | | 
% 154.11/23.35  | | | REF_CLOSE: (8), (11), (15) are inconsistent by sub-proof #1011.
% 154.11/23.35  | | | 
% 154.11/23.35  | | End of split
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1011 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)  all_56_13 = e0 & op(e0, e2) = e0
% 154.11/23.35    (2)  all_56_13 = e1
% 154.11/23.35    (3)   ~ (e1 = e0)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | ALPHA: (1) implies:
% 154.11/23.35  |   (4)  all_56_13 = e0
% 154.11/23.35  | 
% 154.11/23.35  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.35  |   (5)  e1 = e0
% 154.11/23.35  | 
% 154.11/23.35  | SIMP: (5) implies:
% 154.11/23.35  |   (6)  e1 = e0
% 154.11/23.35  | 
% 154.11/23.35  | REDUCE: (3), (6) imply:
% 154.11/23.35  |   (7)  $false
% 154.11/23.35  | 
% 154.11/23.35  | CLOSE: (7) is inconsistent.
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1012 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 154.11/23.35    (2)  op(e3, e2) = all_52_4
% 154.11/23.35    (3)   ~ (e2 = e0)
% 154.11/23.35    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (5)  op(e2, e2) = e2
% 154.11/23.35    (6)   ~ (all_52_4 = e0)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (1) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (7)  all_56_1 = e0 & op(e3, e2) = e0
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (2), (4), (6), (7) are inconsistent by sub-proof #1013.
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (8)  all_56_3 = e0 & op(e2, e2) = e0
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (8) implies:
% 154.11/23.35  | |   (9)  op(e2, e2) = e0
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #1145.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1013 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)  all_56_1 = e0 & op(e3, e2) = e0
% 154.11/23.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (3)  op(e3, e2) = all_52_4
% 154.11/23.35    (4)   ~ (all_52_4 = e0)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | ALPHA: (1) implies:
% 154.11/23.35  |   (5)  op(e3, e2) = e0
% 154.11/23.35  | 
% 154.11/23.35  | GROUND_INST: instantiating (2) with all_52_4, e0, e2, e3, simplifying with
% 154.11/23.35  |              (3), (5) gives:
% 154.11/23.35  |   (6)  all_52_4 = e0
% 154.11/23.35  | 
% 154.11/23.35  | REDUCE: (4), (6) imply:
% 154.11/23.35  |   (7)  $false
% 154.11/23.35  | 
% 154.11/23.35  | CLOSE: (7) is inconsistent.
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1014 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (2)  op(e2, e2) = all_57_12
% 154.11/23.35    (3)  op(e2, e2) = e1
% 154.11/23.35    (4)   ~ (all_57_12 = e1)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | GROUND_INST: instantiating (1) with e1, all_57_12, e2, e2, simplifying with
% 154.11/23.35  |              (2), (3) gives:
% 154.11/23.35  |   (5)  all_57_12 = e1
% 154.11/23.35  | 
% 154.11/23.35  | REDUCE: (4), (5) imply:
% 154.11/23.35  |   (6)  $false
% 154.11/23.35  | 
% 154.11/23.35  | CLOSE: (6) is inconsistent.
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1015 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)  all_56_11 = e2
% 154.11/23.35    (2)  ( ~ (all_44_0 = e0) & op(all_44_1, e3) = all_44_0 & op(e3, e2) = all_44_1
% 154.11/23.35           & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e1) & op(e3, e2) =
% 154.11/23.35           all_44_1 & $i(all_44_1))
% 154.11/23.35    (3)   ~ (e2 = e0)
% 154.11/23.35    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (5)   ~ (all_52_6 = e0)
% 154.11/23.35    (6)  op(e1, e2) = all_52_6
% 154.11/23.35    (7)  op(e3, e2) = e1
% 154.11/23.35    (8)  op(e1, e1) = e1
% 154.11/23.35    (9)   ~ (e1 = e0)
% 154.11/23.35    (10)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 154.11/23.35          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (2) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (11)   ~ (all_44_0 = e0) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 154.11/23.35  | |         all_44_1 & $i(all_44_0) & $i(all_44_1)
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (11) implies:
% 154.11/23.35  | |   (12)   ~ (all_44_0 = e0)
% 154.11/23.35  | |   (13)  op(e3, e2) = all_44_1
% 154.11/23.35  | |   (14)  op(all_44_1, e3) = all_44_0
% 154.11/23.35  | | 
% 154.11/23.35  | | BETA: splitting (10) gives:
% 154.11/23.35  | | 
% 154.11/23.35  | | Case 1:
% 154.11/23.35  | | | 
% 154.11/23.35  | | |   (15)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) =
% 154.11/23.35  | | |           e0)
% 154.11/23.35  | | | 
% 154.11/23.35  | | | BETA: splitting (15) gives:
% 154.11/23.35  | | | 
% 154.11/23.35  | | | Case 1:
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | |   (16)  all_56_6 = e0 & op(e1, e3) = e0
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | | ALPHA: (16) implies:
% 154.11/23.35  | | | |   (17)  op(e1, e3) = e0
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | | REF_CLOSE: (4), (7), (12), (13), (14), (17) are inconsistent by
% 154.11/23.35  | | | |            sub-proof #1017.
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | Case 2:
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | |   (18)  all_56_7 = e0 & op(e1, e2) = e0
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | | REF_CLOSE: (4), (5), (6), (18) are inconsistent by sub-proof #1029.
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | End of split
% 154.11/23.35  | | | 
% 154.11/23.35  | | Case 2:
% 154.11/23.35  | | | 
% 154.11/23.35  | | |   (19)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 154.11/23.35  | | |           e0)
% 154.11/23.35  | | | 
% 154.11/23.35  | | | BETA: splitting (19) gives:
% 154.11/23.35  | | | 
% 154.11/23.35  | | | Case 1:
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | |   (20)  all_56_8 = e0 & op(e1, e1) = e0
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | | ALPHA: (20) implies:
% 154.11/23.35  | | | |   (21)  op(e1, e1) = e0
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | | REF_CLOSE: (4), (8), (9), (21) are inconsistent by sub-proof #1038.
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | Case 2:
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | |   (22)  all_56_11 = e0 & op(e1, e0) = e0
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | | REF_CLOSE: (1), (3), (22) are inconsistent by sub-proof #1149.
% 154.11/23.35  | | | | 
% 154.11/23.35  | | | End of split
% 154.11/23.35  | | | 
% 154.11/23.35  | | End of split
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (23)   ~ (all_44_1 = e1) & op(e3, e2) = all_44_1 & $i(all_44_1)
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (4), (7), (23) are inconsistent by sub-proof #1016.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1016 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)   ~ (all_44_1 = e1) & op(e3, e2) = all_44_1 & $i(all_44_1)
% 154.11/23.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (3)  op(e3, e2) = e1
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | ALPHA: (1) implies:
% 154.11/23.35  |   (4)   ~ (all_44_1 = e1)
% 154.11/23.35  |   (5)  op(e3, e2) = all_44_1
% 154.11/23.35  | 
% 154.11/23.35  | GROUND_INST: instantiating (2) with e1, all_44_1, e2, e3, simplifying with
% 154.11/23.35  |              (3), (5) gives:
% 154.11/23.35  |   (6)  all_44_1 = e1
% 154.11/23.35  | 
% 154.11/23.35  | REDUCE: (4), (6) imply:
% 154.11/23.35  |   (7)  $false
% 154.11/23.35  | 
% 154.11/23.35  | CLOSE: (7) is inconsistent.
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1017 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)   ~ (all_44_0 = e0)
% 154.11/23.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (3)  op(e1, e3) = e0
% 154.11/23.35    (4)  op(all_44_1, e3) = all_44_0
% 154.11/23.35    (5)  op(e3, e2) = e1
% 154.11/23.35    (6)  op(e3, e2) = all_44_1
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | GROUND_INST: instantiating (2) with e1, all_44_1, e2, e3, simplifying with
% 154.11/23.35  |              (5), (6) gives:
% 154.11/23.35  |   (7)  all_44_1 = e1
% 154.11/23.35  | 
% 154.11/23.35  | GROUND_INST: instantiating (2) with e0, all_44_0, e3, e1, simplifying with (3)
% 154.11/23.35  |              gives:
% 154.11/23.35  |   (8)  all_44_0 = e0 |  ~ (op(e1, e3) = all_44_0)
% 154.11/23.35  | 
% 154.11/23.35  | REDUCE: (4), (7) imply:
% 154.11/23.35  |   (9)  op(e1, e3) = all_44_0
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (8) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (10)   ~ (op(e1, e3) = all_44_0)
% 154.11/23.35  | | 
% 154.11/23.35  | | PRED_UNIFY: (9), (10) imply:
% 154.11/23.35  | |   (11)  $false
% 154.11/23.35  | | 
% 154.11/23.35  | | CLOSE: (11) is inconsistent.
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (12)  all_44_0 = e0
% 154.11/23.35  | | 
% 154.11/23.35  | | REDUCE: (1), (12) imply:
% 154.11/23.35  | |   (13)  $false
% 154.11/23.35  | | 
% 154.11/23.35  | | CLOSE: (13) is inconsistent.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1018 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3, e3) =
% 154.11/23.35           all_57_10 & $i(all_57_10))
% 154.11/23.35    (2)   ~ (all_57_3 = e3)
% 154.11/23.35    (3)  all_57_10 = e2
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (1) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (4)  all_57_3 = e3 & op(e3, e2) = e3
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (4) implies:
% 154.11/23.35  | |   (5)  all_57_3 = e3
% 154.11/23.35  | | 
% 154.11/23.35  | | REDUCE: (2), (5) imply:
% 154.11/23.35  | |   (6)  $false
% 154.11/23.35  | | 
% 154.11/23.35  | | CLOSE: (6) is inconsistent.
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (7)   ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10)
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (7) implies:
% 154.11/23.35  | |   (8)   ~ (all_57_10 = e2)
% 154.11/23.35  | | 
% 154.11/23.35  | | REDUCE: (3), (8) imply:
% 154.11/23.35  | |   (9)  $false
% 154.11/23.35  | | 
% 154.11/23.35  | | CLOSE: (9) is inconsistent.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1019 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (2)  op(e0, e0) = all_57_15
% 154.11/23.35    (3)  op(e0, e0) = e3
% 154.11/23.35    (4)   ~ (all_57_15 = e3)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | GROUND_INST: instantiating (1) with e3, all_57_15, e0, e0, simplifying with
% 154.11/23.35  |              (2), (3) gives:
% 154.11/23.35  |   (5)  all_57_15 = e3
% 154.11/23.35  | 
% 154.11/23.35  | REDUCE: (4), (5) imply:
% 154.11/23.35  |   (6)  $false
% 154.11/23.35  | 
% 154.11/23.35  | CLOSE: (6) is inconsistent.
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1020 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)   ~ (e3 = e1)
% 154.11/23.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (3)  op(e0, e0) = e3
% 154.11/23.35    (4)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 154.11/23.35             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.11/23.35           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 154.11/23.35           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 154.11/23.35           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 154.11/23.35           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 154.11/23.35           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 154.11/23.35           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 154.11/23.35           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.11/23.35    (5)  op(e3, e0) = all_52_12
% 154.11/23.35    (6)   ~ (all_52_12 = e3)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (4) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (7)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 154.11/23.35  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.11/23.35  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (7) implies:
% 154.11/23.35  | |   (8)  op(e0, e0) = e1
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1022.
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (9)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 154.11/23.35  | |            = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) =
% 154.11/23.35  | |          e0 & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 154.11/23.35  | |        (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 154.11/23.35  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 154.11/23.35  | |          e0 & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #1081.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1021 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)   ~ (e3 = e1)
% 154.11/23.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (3)  op(e0, e0) = e3
% 154.11/23.35    (4)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.11/23.35             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.11/23.35           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 154.11/23.35           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 154.11/23.35           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 154.11/23.35           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 154.11/23.35    (5)   ~ (all_52_9 = e2)
% 154.11/23.35    (6)  op(e2, e1) = all_52_9
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (4) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (7)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.11/23.35  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.11/23.35  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (7) implies:
% 154.11/23.35  | |   (8)  op(e0, e0) = e1
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1022.
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (9)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 154.11/23.35  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 154.11/23.35  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (9) implies:
% 154.11/23.35  | |   (10)  op(e2, e1) = e2
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1157.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1022 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (2)  op(e0, e0) = e3
% 154.11/23.35    (3)  op(e0, e0) = e1
% 154.11/23.35    (4)   ~ (e3 = e1)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | GROUND_INST: instantiating (1) with e1, e3, e0, e0, simplifying with (2), (3)
% 154.11/23.35  |              gives:
% 154.11/23.35  |   (5)  e3 = e1
% 154.11/23.35  | 
% 154.11/23.35  | REDUCE: (4), (5) imply:
% 154.11/23.35  |   (6)  $false
% 154.11/23.35  | 
% 154.11/23.35  | CLOSE: (6) is inconsistent.
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1023 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (2)  op(e0, e0) = e3
% 154.11/23.35    (3)  op(e2, e2) = e2
% 154.11/23.35    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 154.11/23.35             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.11/23.35           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 154.11/23.35           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 154.11/23.35           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 154.11/23.35           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.11/23.35    (5)   ~ (e3 = e2)
% 154.11/23.35    (6)   ~ (e2 = e1)
% 154.11/23.35  
% 154.11/23.35  Begin of proof
% 154.11/23.35  | 
% 154.11/23.35  | BETA: splitting (4) gives:
% 154.11/23.35  | 
% 154.11/23.35  | Case 1:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 154.11/23.35  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.11/23.35  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (7) implies:
% 154.11/23.35  | |   (8)  op(e0, e0) = e2
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1087.
% 154.11/23.35  | | 
% 154.11/23.35  | Case 2:
% 154.11/23.35  | | 
% 154.11/23.35  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 154.11/23.35  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 154.11/23.35  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 154.11/23.35  | | 
% 154.11/23.35  | | ALPHA: (9) implies:
% 154.11/23.35  | |   (10)  op(e2, e2) = e1
% 154.11/23.35  | | 
% 154.11/23.35  | | REF_CLOSE: (1), (3), (6), (10) are inconsistent by sub-proof #1158.
% 154.11/23.35  | | 
% 154.11/23.35  | End of split
% 154.11/23.35  | 
% 154.11/23.35  End of proof
% 154.11/23.35  
% 154.11/23.35  Sub-proof #1024 shows that the following formulas are inconsistent:
% 154.11/23.35  ----------------------------------------------------------------
% 154.11/23.35    (1)  op(e1, e1) = all_4_2
% 154.11/23.35    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.35           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.35    (3)  op(e0, e0) = e3
% 154.11/23.35    (4)  op(e1, e1) = e1
% 154.11/23.35    (5)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 154.11/23.35             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.11/23.35           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 154.11/23.35           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 154.11/23.35           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 154.11/23.35           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 154.11/23.35    (6)   ~ (e3 = e2)
% 154.11/23.36    (7)   ~ (e2 = e1)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | BETA: splitting (5) gives:
% 154.11/23.36  | 
% 154.11/23.36  | Case 1:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (8)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 154.11/23.36  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.11/23.36  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (8) implies:
% 154.11/23.36  | |   (9)  op(e1, e1) = e2
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (1), (2), (4), (7), (9) are inconsistent by sub-proof #1044.
% 154.11/23.36  | | 
% 154.11/23.36  | Case 2:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (10)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10
% 154.11/23.36  | |           = e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 154.11/23.36  | |         all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (10) implies:
% 154.11/23.36  | |   (11)  op(e0, e0) = e2
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (2), (3), (6), (11) are inconsistent by sub-proof #1087.
% 154.11/23.36  | | 
% 154.11/23.36  | End of split
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1025 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 154.11/23.36             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.11/23.36           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 154.11/23.36           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 154.11/23.36             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 154.11/23.36             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 154.11/23.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (3)  op(e1, e3) = all_52_2
% 154.11/23.36    (4)   ~ (all_52_2 = e1)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | BETA: splitting (1) gives:
% 154.11/23.36  | 
% 154.11/23.36  | Case 1:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (5)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 154.11/23.36  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.11/23.36  | |        op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (5) implies:
% 154.11/23.36  | |   (6)  op(e1, e3) = e1
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #1046.
% 154.11/23.36  | | 
% 154.11/23.36  | Case 2:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (7)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 154.11/23.36  | |          e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 154.11/23.36  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (7) implies:
% 154.11/23.36  | |   (8)  op(e1, e3) = e1
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1046.
% 154.11/23.36  | | 
% 154.11/23.36  | End of split
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1026 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (2)  op(e1, e1) = all_57_14
% 154.11/23.36    (3)  op(e1, e1) = e0
% 154.11/23.36    (4)   ~ (all_57_14 = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | GROUND_INST: instantiating (1) with e0, all_57_14, e1, e1, simplifying with
% 154.11/23.36  |              (2), (3) gives:
% 154.11/23.36  |   (5)  all_57_14 = e0
% 154.11/23.36  | 
% 154.11/23.36  | REDUCE: (4), (5) imply:
% 154.11/23.36  |   (6)  $false
% 154.11/23.36  | 
% 154.11/23.36  | CLOSE: (6) is inconsistent.
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1027 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)  op(e3, e2) = all_52_4
% 154.11/23.36    (2)  op(e0, e2) = all_52_7
% 154.11/23.36    (3)   ~ (e2 = e0)
% 154.11/23.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (5)  op(e3, e3) = e2
% 154.11/23.36    (6)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3, e3) =
% 154.11/23.36           all_57_10 & $i(all_57_10))
% 154.11/23.36    (7)   ~ (e3 = e0)
% 154.11/23.36    (8)   ~ (all_52_6 = e0)
% 154.11/23.36    (9)  op(e1, e2) = all_52_6
% 154.11/23.36    (10)  op(e2, e2) = e2
% 154.11/23.36    (11)   ~ (all_52_7 = e0)
% 154.11/23.36    (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.11/23.36          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | BETA: splitting (12) gives:
% 154.11/23.36  | 
% 154.11/23.36  | Case 1:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (13)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 154.11/23.36  | |           e0)
% 154.11/23.36  | | 
% 154.11/23.36  | | BETA: splitting (13) gives:
% 154.11/23.36  | | 
% 154.11/23.36  | | Case 1:
% 154.11/23.36  | | | 
% 154.11/23.36  | | |   (14)  all_56_1 = e0 & op(e3, e2) = e0
% 154.11/23.36  | | | 
% 154.11/23.36  | | | ALPHA: (14) implies:
% 154.11/23.36  | | |   (15)  op(e3, e2) = e0
% 154.11/23.36  | | | 
% 154.11/23.36  | | | REF_CLOSE: (1), (4), (5), (6), (7), (15) are inconsistent by sub-proof
% 154.11/23.36  | | |            #1030.
% 154.11/23.36  | | | 
% 154.11/23.36  | | Case 2:
% 154.11/23.36  | | | 
% 154.11/23.36  | | |   (16)  all_56_3 = e0 & op(e2, e2) = e0
% 154.11/23.36  | | | 
% 154.11/23.36  | | | ALPHA: (16) implies:
% 154.11/23.36  | | |   (17)  op(e2, e2) = e0
% 154.11/23.36  | | | 
% 154.11/23.36  | | | REF_CLOSE: (3), (4), (10), (17) are inconsistent by sub-proof #1145.
% 154.11/23.36  | | | 
% 154.11/23.36  | | End of split
% 154.11/23.36  | | 
% 154.11/23.36  | Case 2:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (18)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 154.11/23.36  | |           e0)
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (2), (4), (8), (9), (11), (18) are inconsistent by sub-proof
% 154.11/23.36  | |            #1028.
% 154.11/23.36  | | 
% 154.11/23.36  | End of split
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1028 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)  op(e0, e2) = all_52_7
% 154.11/23.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (3)   ~ (all_52_6 = e0)
% 154.11/23.36    (4)  op(e1, e2) = all_52_6
% 154.11/23.36    (5)   ~ (all_52_7 = e0)
% 154.11/23.36    (6)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | BETA: splitting (6) gives:
% 154.11/23.36  | 
% 154.11/23.36  | Case 1:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (7)  all_56_7 = e0 & op(e1, e2) = e0
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #1029.
% 154.11/23.36  | | 
% 154.11/23.36  | Case 2:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (8)  all_56_13 = e0 & op(e0, e2) = e0
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (8) implies:
% 154.11/23.36  | |   (9)  op(e0, e2) = e0
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #1036.
% 154.11/23.36  | | 
% 154.11/23.36  | End of split
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1029 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)  all_56_7 = e0 & op(e1, e2) = e0
% 154.11/23.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (3)  op(e1, e2) = all_52_6
% 154.11/23.36    (4)   ~ (all_52_6 = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | ALPHA: (1) implies:
% 154.11/23.36  |   (5)  op(e1, e2) = e0
% 154.11/23.36  | 
% 154.11/23.36  | GROUND_INST: instantiating (2) with all_52_6, e0, e2, e1, simplifying with
% 154.11/23.36  |              (3), (5) gives:
% 154.11/23.36  |   (6)  all_52_6 = e0
% 154.11/23.36  | 
% 154.11/23.36  | REDUCE: (4), (6) imply:
% 154.11/23.36  |   (7)  $false
% 154.11/23.36  | 
% 154.11/23.36  | CLOSE: (7) is inconsistent.
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1030 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)  op(e3, e2) = e0
% 154.11/23.36    (2)  op(e3, e2) = all_52_4
% 154.11/23.36    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (4)  op(e3, e3) = e2
% 154.11/23.36    (5)  (all_57_3 = e3 & op(e3, e2) = e3) | ( ~ (all_57_10 = e2) & op(e3, e3) =
% 154.11/23.36           all_57_10 & $i(all_57_10))
% 154.11/23.36    (6)   ~ (e3 = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | BETA: splitting (5) gives:
% 154.11/23.36  | 
% 154.11/23.36  | Case 1:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (7)  all_57_3 = e3 & op(e3, e2) = e3
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (7) implies:
% 154.11/23.36  | |   (8)  op(e3, e2) = e3
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (1), (2), (3), (6), (8) are inconsistent by sub-proof #1032.
% 154.11/23.36  | | 
% 154.11/23.36  | Case 2:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (9)   ~ (all_57_10 = e2) & op(e3, e3) = all_57_10 & $i(all_57_10)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (9) implies:
% 154.11/23.36  | |   (10)   ~ (all_57_10 = e2)
% 154.11/23.36  | |   (11)  op(e3, e3) = all_57_10
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (3), (4), (10), (11) are inconsistent by sub-proof #1031.
% 154.11/23.36  | | 
% 154.11/23.36  | End of split
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1031 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (2)  op(e3, e3) = all_57_10
% 154.11/23.36    (3)  op(e3, e3) = e2
% 154.11/23.36    (4)   ~ (all_57_10 = e2)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | GROUND_INST: instantiating (1) with e2, all_57_10, e3, e3, simplifying with
% 154.11/23.36  |              (2), (3) gives:
% 154.11/23.36  |   (5)  all_57_10 = e2
% 154.11/23.36  | 
% 154.11/23.36  | REDUCE: (4), (5) imply:
% 154.11/23.36  |   (6)  $false
% 154.11/23.36  | 
% 154.11/23.36  | CLOSE: (6) is inconsistent.
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1032 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)  op(e3, e2) = e0
% 154.11/23.36    (2)  op(e3, e2) = all_52_4
% 154.11/23.36    (3)  op(e3, e2) = e3
% 154.11/23.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (5)   ~ (e3 = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | GROUND_INST: instantiating (4) with all_52_4, e0, e2, e3, simplifying with
% 154.11/23.36  |              (1), (2) gives:
% 154.11/23.36  |   (6)  all_52_4 = e0
% 154.11/23.36  | 
% 154.11/23.36  | GROUND_INST: instantiating (4) with all_52_4, e3, e2, e3, simplifying with
% 154.11/23.36  |              (2), (3) gives:
% 154.11/23.36  |   (7)  all_52_4 = e3
% 154.11/23.36  | 
% 154.11/23.36  | COMBINE_EQS: (6), (7) imply:
% 154.11/23.36  |   (8)  e3 = e0
% 154.11/23.36  | 
% 154.11/23.36  | SIMP: (8) implies:
% 154.11/23.36  |   (9)  e3 = e0
% 154.11/23.36  | 
% 154.11/23.36  | REDUCE: (5), (9) imply:
% 154.11/23.36  |   (10)  $false
% 154.11/23.36  | 
% 154.11/23.36  | CLOSE: (10) is inconsistent.
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1033 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)  all_54_10 = all_4_2
% 154.11/23.36    (2)  all_54_10 = e0
% 154.11/23.36    (3)   ~ (all_4_2 = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.36  |   (4)  all_4_2 = e0
% 154.11/23.36  | 
% 154.11/23.36  | SIMP: (4) implies:
% 154.11/23.36  |   (5)  all_4_2 = e0
% 154.11/23.36  | 
% 154.11/23.36  | REDUCE: (3), (5) imply:
% 154.11/23.36  |   (6)  $false
% 154.11/23.36  | 
% 154.11/23.36  | CLOSE: (6) is inconsistent.
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1034 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)  op(e0, e1) = all_52_11
% 154.11/23.36    (2)   ~ (all_52_11 = all_10_2)
% 154.11/23.36    (3)  op(e0, e0) = all_10_2
% 154.11/23.36    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (5)  op(e0, e1) = e0
% 154.11/23.36    (6)  op(e0, e0) = e0
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | GROUND_INST: instantiating (4) with all_10_2, e0, e0, e0, simplifying with
% 154.11/23.36  |              (3), (6) gives:
% 154.11/23.36  |   (7)  all_10_2 = e0
% 154.11/23.36  | 
% 154.11/23.36  | GROUND_INST: instantiating (4) with all_52_11, e0, e1, e0, simplifying with
% 154.11/23.36  |              (1), (5) gives:
% 154.11/23.36  |   (8)  all_52_11 = e0
% 154.11/23.36  | 
% 154.11/23.36  | REDUCE: (2), (7), (8) imply:
% 154.11/23.36  |   (9)  $false
% 154.11/23.36  | 
% 154.11/23.36  | CLOSE: (9) is inconsistent.
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1035 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)  op(e0, e2) = all_52_7
% 154.11/23.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (3)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.11/23.36             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.11/23.36           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.11/23.36           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.11/23.36             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.11/23.36           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.36           all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.11/23.36    (4)  op(e0, e3) = all_52_3
% 154.11/23.36    (5)   ~ (all_52_7 = e0)
% 154.11/23.36    (6)   ~ (all_52_3 = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | BETA: splitting (3) gives:
% 154.11/23.36  | 
% 154.11/23.36  | Case 1:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (7)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.11/23.36  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.11/23.36  | |        $i(all_57_0)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (7) implies:
% 154.11/23.36  | |   (8)  op(e0, e3) = e0
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1142.
% 154.11/23.36  | | 
% 154.11/23.36  | Case 2:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (9)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15
% 154.11/23.36  | |            = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0
% 154.11/23.36  | |          & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 =
% 154.11/23.36  | |            e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.11/23.36  | |          all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.11/23.36  | | 
% 154.11/23.36  | | BETA: splitting (9) gives:
% 154.11/23.36  | | 
% 154.11/23.36  | | Case 1:
% 154.11/23.36  | | | 
% 154.11/23.36  | | |   (10)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.11/23.36  | | |         (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.11/23.36  | | |         op(e0, e3) = e0 & $i(all_57_1)
% 154.11/23.36  | | | 
% 154.11/23.36  | | | ALPHA: (10) implies:
% 154.11/23.36  | | |   (11)  op(e0, e3) = e0
% 154.11/23.36  | | | 
% 154.11/23.36  | | | REF_CLOSE: (2), (4), (6), (11) are inconsistent by sub-proof #1142.
% 154.11/23.36  | | | 
% 154.11/23.36  | | Case 2:
% 154.11/23.36  | | | 
% 154.11/23.36  | | |   (12)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~
% 154.11/23.36  | | |         (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 &
% 154.11/23.36  | | |         op(e0, e2) = e0 & $i(all_57_3)
% 154.11/23.36  | | | 
% 154.11/23.36  | | | ALPHA: (12) implies:
% 154.11/23.36  | | |   (13)  op(e0, e2) = e0
% 154.11/23.36  | | | 
% 154.11/23.36  | | | REF_CLOSE: (1), (2), (5), (13) are inconsistent by sub-proof #1036.
% 154.11/23.36  | | | 
% 154.11/23.36  | | End of split
% 154.11/23.36  | | 
% 154.11/23.36  | End of split
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1036 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (2)  op(e0, e2) = all_52_7
% 154.11/23.36    (3)  op(e0, e2) = e0
% 154.11/23.36    (4)   ~ (all_52_7 = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | GROUND_INST: instantiating (1) with all_52_7, e0, e2, e0, simplifying with
% 154.11/23.36  |              (2), (3) gives:
% 154.11/23.36  |   (5)  all_52_7 = e0
% 154.11/23.36  | 
% 154.11/23.36  | REDUCE: (4), (5) imply:
% 154.11/23.36  |   (6)  $false
% 154.11/23.36  | 
% 154.11/23.36  | CLOSE: (6) is inconsistent.
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1037 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 =
% 154.11/23.36             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 154.11/23.36           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 154.11/23.36         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 154.11/23.36             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 154.11/23.36           all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 154.11/23.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (3)  op(e3, e3) = e2
% 154.11/23.36    (4)   ~ (e2 = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | BETA: splitting (1) gives:
% 154.11/23.36  | 
% 154.11/23.36  | Case 1:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (5)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12
% 154.11/23.36  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 154.11/23.36  | |        all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (5) implies:
% 154.11/23.36  | |   (6)  op(e3, e3) = e0
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #1073.
% 154.11/23.36  | | 
% 154.11/23.36  | Case 2:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (7)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14
% 154.11/23.36  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 154.11/23.36  | |        all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (7) implies:
% 154.11/23.36  | |   (8)  op(e3, e3) = e0
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1073.
% 154.11/23.36  | | 
% 154.11/23.36  | End of split
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1038 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (2)  op(e1, e1) = e1
% 154.11/23.36    (3)  op(e1, e1) = e0
% 154.11/23.36    (4)   ~ (e1 = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | GROUND_INST: instantiating (1) with e0, e1, e1, e1, simplifying with (2), (3)
% 154.11/23.36  |              gives:
% 154.11/23.36  |   (5)  e1 = e0
% 154.11/23.36  | 
% 154.11/23.36  | REDUCE: (4), (5) imply:
% 154.11/23.36  |   (6)  $false
% 154.11/23.36  | 
% 154.11/23.36  | CLOSE: (6) is inconsistent.
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1039 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (2)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.11/23.36             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.11/23.36           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 154.11/23.36           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 154.11/23.36           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 154.11/23.36           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 154.11/23.36    (3)   ~ (all_52_9 = e2)
% 154.11/23.36    (4)  op(e2, e1) = all_52_9
% 154.11/23.36    (5)   ~ (e1 = e0)
% 154.11/23.36    (6)  op(e0, e0) = e0
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | BETA: splitting (2) gives:
% 154.11/23.36  | 
% 154.11/23.36  | Case 1:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (7)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.11/23.36  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.11/23.36  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (7) implies:
% 154.11/23.36  | |   (8)  op(e0, e0) = e1
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #1040.
% 154.11/23.36  | | 
% 154.11/23.36  | Case 2:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (9)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 154.11/23.36  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 154.11/23.36  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (9) implies:
% 154.11/23.36  | |   (10)  op(e2, e1) = e2
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1157.
% 154.11/23.36  | | 
% 154.11/23.36  | End of split
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1040 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (2)  op(e0, e0) = e1
% 154.11/23.36    (3)  op(e0, e0) = e0
% 154.11/23.36    (4)   ~ (e1 = e0)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | GROUND_INST: instantiating (1) with e0, e1, e0, e0, simplifying with (2), (3)
% 154.11/23.36  |              gives:
% 154.11/23.36  |   (5)  e1 = e0
% 154.11/23.36  | 
% 154.11/23.36  | REDUCE: (4), (5) imply:
% 154.11/23.36  |   (6)  $false
% 154.11/23.36  | 
% 154.11/23.36  | CLOSE: (6) is inconsistent.
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1041 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)   ~ (e2 = e0)
% 154.11/23.36    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (3)  op(e2, e2) = e2
% 154.11/23.36    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 154.11/23.36             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.11/23.36           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 154.11/23.36           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 154.11/23.36           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 154.11/23.36           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.11/23.36    (5)   ~ (e2 = e1)
% 154.11/23.36    (6)  op(e0, e0) = e0
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | BETA: splitting (4) gives:
% 154.11/23.36  | 
% 154.11/23.36  | Case 1:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 154.11/23.36  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.11/23.36  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (7) implies:
% 154.11/23.36  | |   (8)  op(e0, e0) = e2
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #1043.
% 154.11/23.36  | | 
% 154.11/23.36  | Case 2:
% 154.11/23.36  | | 
% 154.11/23.36  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 154.11/23.36  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 154.11/23.36  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 154.11/23.36  | | 
% 154.11/23.36  | | ALPHA: (9) implies:
% 154.11/23.36  | |   (10)  op(e2, e2) = e1
% 154.11/23.36  | | 
% 154.11/23.36  | | REF_CLOSE: (2), (3), (5), (10) are inconsistent by sub-proof #1158.
% 154.11/23.36  | | 
% 154.11/23.36  | End of split
% 154.11/23.36  | 
% 154.11/23.36  End of proof
% 154.11/23.36  
% 154.11/23.36  Sub-proof #1042 shows that the following formulas are inconsistent:
% 154.11/23.36  ----------------------------------------------------------------
% 154.11/23.36    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.36           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.36    (2)  op(e1, e2) = all_52_6
% 154.11/23.36    (3)  op(e1, e2) = e1
% 154.11/23.36    (4)   ~ (all_52_6 = e1)
% 154.11/23.36  
% 154.11/23.36  Begin of proof
% 154.11/23.36  | 
% 154.11/23.36  | GROUND_INST: instantiating (1) with all_52_6, e1, e2, e1, simplifying with
% 154.11/23.36  |              (2), (3) gives:
% 154.11/23.37  |   (5)  all_52_6 = e1
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (4), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1043 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.37    (2)  op(e0, e0) = e2
% 154.11/23.37    (3)  op(e0, e0) = e0
% 154.11/23.37    (4)   ~ (e2 = e0)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | GROUND_INST: instantiating (1) with e2, e0, e0, e0, simplifying with (2), (3)
% 154.11/23.37  |              gives:
% 154.11/23.37  |   (5)  e2 = e0
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (4), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1044 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  op(e1, e1) = e2
% 154.11/23.37    (2)  op(e1, e1) = all_4_2
% 154.11/23.37    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.37    (4)  op(e1, e1) = e1
% 154.11/23.37    (5)   ~ (e2 = e1)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | GROUND_INST: instantiating (3) with all_4_2, e1, e1, e1, simplifying with (2),
% 154.11/23.37  |              (4) gives:
% 154.11/23.37  |   (6)  all_4_2 = e1
% 154.11/23.37  | 
% 154.11/23.37  | GROUND_INST: instantiating (3) with all_4_2, e2, e1, e1, simplifying with (1),
% 154.11/23.37  |              (2) gives:
% 154.11/23.37  |   (7)  all_4_2 = e2
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (6), (7) imply:
% 154.11/23.37  |   (8)  e2 = e1
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (5), (8) imply:
% 154.11/23.37  |   (9)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (9) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1045 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.37    (2)   ~ (e3 = e0)
% 154.11/23.37    (3)  (all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 154.11/23.37             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.11/23.37           op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)) | (all_57_1 = e1
% 154.11/23.37           & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 = e3) & op(e1,
% 154.11/23.37             e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) = all_57_2 & op(e0,
% 154.11/23.37             e0) = e3 & $i(all_57_2) & $i(all_57_14))
% 154.11/23.37    (4)   ~ (all_52_2 = e1)
% 154.11/23.37    (5)  op(e0, e0) = e0
% 154.11/23.37    (6)  op(e1, e3) = all_52_2
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | BETA: splitting (3) gives:
% 154.11/23.37  | 
% 154.11/23.37  | Case 1:
% 154.11/23.37  | | 
% 154.11/23.37  | |   (7)  all_57_1 = e1 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_14 =
% 154.11/23.37  | |          e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e1, e3) = e1 &
% 154.11/23.37  | |        op(e1, e1) = all_57_14 & $i(all_57_0) & $i(all_57_14)
% 154.11/23.37  | | 
% 154.11/23.37  | | ALPHA: (7) implies:
% 154.11/23.37  | |   (8)  op(e1, e3) = e1
% 154.11/23.37  | | 
% 154.11/23.37  | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #1046.
% 154.11/23.37  | | 
% 154.11/23.37  | Case 2:
% 154.11/23.37  | | 
% 154.11/23.37  | |   (9)  all_57_1 = e1 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_14 =
% 154.11/23.37  | |          e3) & op(e1, e3) = e1 & op(e1, e1) = all_57_14 & op(e0, e3) =
% 154.11/23.37  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_14)
% 154.11/23.37  | | 
% 154.11/23.37  | | ALPHA: (9) implies:
% 154.11/23.37  | |   (10)  op(e0, e0) = e3
% 154.11/23.37  | | 
% 154.11/23.37  | | REF_CLOSE: (1), (2), (5), (10) are inconsistent by sub-proof #1143.
% 154.11/23.37  | | 
% 154.11/23.37  | End of split
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1046 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.37    (2)  op(e1, e3) = all_52_2
% 154.11/23.37    (3)  op(e1, e3) = e1
% 154.11/23.37    (4)   ~ (all_52_2 = e1)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | GROUND_INST: instantiating (1) with all_52_2, e1, e3, e1, simplifying with
% 154.11/23.37  |              (2), (3) gives:
% 154.11/23.37  |   (5)  all_52_2 = e1
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (4), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1047 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  all_54_15 = all_10_2
% 154.11/23.37    (2)  all_54_15 = e1
% 154.11/23.37    (3)   ~ (all_10_2 = e1)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.37  |   (4)  all_10_2 = e1
% 154.11/23.37  | 
% 154.11/23.37  | SIMP: (4) implies:
% 154.11/23.37  |   (5)  all_10_2 = e1
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (3), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1048 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  all_54_15 = all_10_2
% 154.11/23.37    (2)  all_54_15 = e2
% 154.11/23.37    (3)   ~ (all_10_2 = e2)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.37  |   (4)  all_10_2 = e2
% 154.11/23.37  | 
% 154.11/23.37  | SIMP: (4) implies:
% 154.11/23.37  |   (5)  all_10_2 = e2
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (3), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1049 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  all_54_15 = all_10_2
% 154.11/23.37    (2)  all_54_15 = e3
% 154.11/23.37    (3)   ~ (all_10_2 = e3)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.37  |   (4)  all_10_2 = e3
% 154.11/23.37  | 
% 154.11/23.37  | SIMP: (4) implies:
% 154.11/23.37  |   (5)  all_10_2 = e3
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (3), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1050 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)   ~ (e3 = e1)
% 154.11/23.37    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 154.11/23.37         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 154.11/23.37    (3)  all_56_6 = e2
% 154.11/23.37    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 154.11/23.37         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 154.11/23.37    (5)   ~ (e2 = e0)
% 154.11/23.37    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.37    (7)  op(e3, e3) = e2
% 154.11/23.37    (8)   ~ (e3 = e0)
% 154.11/23.37    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) = e0) |
% 154.11/23.37         (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) = e0)
% 154.11/23.37    (10)   ~ (e1 = e0)
% 154.11/23.37    (11)   ~ (e3 = e2)
% 154.11/23.37    (12)   ~ (e2 = e1)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | BETA: splitting (9) gives:
% 154.11/23.37  | 
% 154.11/23.37  | Case 1:
% 154.11/23.37  | | 
% 154.11/23.37  | |   (13)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_2 = e0 & op(e2, e3) =
% 154.11/23.37  | |           e0)
% 154.11/23.37  | | 
% 154.11/23.37  | | BETA: splitting (13) gives:
% 154.11/23.37  | | 
% 154.11/23.37  | | Case 1:
% 154.11/23.37  | | | 
% 154.11/23.37  | | |   (14)  all_56_0 = e0 & op(e3, e3) = e0
% 154.11/23.37  | | | 
% 154.11/23.37  | | | ALPHA: (14) implies:
% 154.11/23.37  | | |   (15)  op(e3, e3) = e0
% 154.11/23.37  | | | 
% 154.11/23.37  | | | REF_CLOSE: (5), (6), (7), (15) are inconsistent by sub-proof #1073.
% 154.11/23.37  | | | 
% 154.11/23.37  | | Case 2:
% 154.11/23.37  | | | 
% 154.11/23.37  | | |   (16)  all_56_2 = e0 & op(e2, e3) = e0
% 154.11/23.37  | | | 
% 154.11/23.37  | | | ALPHA: (16) implies:
% 154.11/23.37  | | |   (17)  all_56_2 = e0
% 154.11/23.37  | | | 
% 154.11/23.37  | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (10), (11), (12), (17) are
% 154.11/23.37  | | |            inconsistent by sub-proof #1055.
% 154.11/23.37  | | | 
% 154.11/23.37  | | End of split
% 154.11/23.37  | | 
% 154.11/23.37  | Case 2:
% 154.11/23.37  | | 
% 154.11/23.37  | |   (18)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_12 = e0 & op(e0, e3) =
% 154.11/23.37  | |           e0)
% 154.11/23.37  | | 
% 154.11/23.37  | | BETA: splitting (18) gives:
% 154.11/23.37  | | 
% 154.11/23.37  | | Case 1:
% 154.11/23.37  | | | 
% 154.11/23.37  | | |   (19)  all_56_6 = e0 & op(e1, e3) = e0
% 154.11/23.37  | | | 
% 154.11/23.37  | | | REF_CLOSE: (3), (5), (19) are inconsistent by sub-proof #1054.
% 154.11/23.37  | | | 
% 154.11/23.37  | | Case 2:
% 154.11/23.37  | | | 
% 154.11/23.37  | | |   (20)  all_56_12 = e0 & op(e0, e3) = e0
% 154.11/23.37  | | | 
% 154.11/23.37  | | | ALPHA: (20) implies:
% 154.11/23.37  | | |   (21)  all_56_12 = e0
% 154.11/23.37  | | | 
% 154.11/23.37  | | | BETA: splitting (2) gives:
% 154.11/23.37  | | | 
% 154.11/23.37  | | | Case 1:
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | |   (22)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3)
% 154.11/23.37  | | | |           = e1)
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | | BETA: splitting (22) gives:
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | | Case 1:
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | |   (23)  all_56_0 = e1 & op(e3, e3) = e1
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | ALPHA: (23) implies:
% 154.11/23.37  | | | | |   (24)  op(e3, e3) = e1
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | REF_CLOSE: (6), (7), (12), (24) are inconsistent by sub-proof #1074.
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | Case 2:
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | |   (25)  all_56_2 = e1 & op(e2, e3) = e1
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | ALPHA: (25) implies:
% 154.11/23.37  | | | | |   (26)  all_56_2 = e1
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | BETA: splitting (4) gives:
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | Case 1:
% 154.11/23.37  | | | | | | 
% 154.11/23.37  | | | | | |   (27)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2,
% 154.11/23.37  | | | | | |             e3) = e3)
% 154.11/23.37  | | | | | | 
% 154.11/23.37  | | | | | | BETA: splitting (27) gives:
% 154.11/23.37  | | | | | | 
% 154.11/23.37  | | | | | | Case 1:
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | |   (28)  all_56_0 = e3 & op(e3, e3) = e3
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | | ALPHA: (28) implies:
% 154.11/23.37  | | | | | | |   (29)  op(e3, e3) = e3
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | | REF_CLOSE: (6), (7), (11), (29) are inconsistent by sub-proof
% 154.11/23.37  | | | | | | |            #1085.
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | Case 2:
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | |   (30)  all_56_2 = e3 & op(e2, e3) = e3
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | | ALPHA: (30) implies:
% 154.11/23.37  | | | | | | |   (31)  all_56_2 = e3
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | | REF_CLOSE: (1), (26), (31) are inconsistent by sub-proof #1053.
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | End of split
% 154.11/23.37  | | | | | | 
% 154.11/23.37  | | | | | Case 2:
% 154.11/23.37  | | | | | | 
% 154.11/23.37  | | | | | |   (32)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0,
% 154.11/23.37  | | | | | |             e3) = e3)
% 154.11/23.37  | | | | | | 
% 154.11/23.37  | | | | | | BETA: splitting (32) gives:
% 154.11/23.37  | | | | | | 
% 154.11/23.37  | | | | | | Case 1:
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | |   (33)  all_56_6 = e3 & op(e1, e3) = e3
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | | ALPHA: (33) implies:
% 154.11/23.37  | | | | | | |   (34)  all_56_6 = e3
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | | REF_CLOSE: (3), (11), (34) are inconsistent by sub-proof #1057.
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | Case 2:
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | |   (35)  all_56_12 = e3 & op(e0, e3) = e3
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | | ALPHA: (35) implies:
% 154.11/23.37  | | | | | | |   (36)  all_56_12 = e3
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | | REF_CLOSE: (8), (21), (36) are inconsistent by sub-proof #1052.
% 154.11/23.37  | | | | | | | 
% 154.11/23.37  | | | | | | End of split
% 154.11/23.37  | | | | | | 
% 154.11/23.37  | | | | | End of split
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | End of split
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | Case 2:
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | |   (37)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3)
% 154.11/23.37  | | | |           = e1)
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | | BETA: splitting (37) gives:
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | | Case 1:
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | |   (38)  all_56_6 = e1 & op(e1, e3) = e1
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | REF_CLOSE: (3), (12), (38) are inconsistent by sub-proof #1058.
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | Case 2:
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | |   (39)  all_56_12 = e1 & op(e0, e3) = e1
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | ALPHA: (39) implies:
% 154.11/23.37  | | | | |   (40)  all_56_12 = e1
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | REF_CLOSE: (10), (21), (40) are inconsistent by sub-proof #1051.
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | End of split
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | End of split
% 154.11/23.37  | | | 
% 154.11/23.37  | | End of split
% 154.11/23.37  | | 
% 154.11/23.37  | End of split
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1051 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  all_56_12 = e1
% 154.11/23.37    (2)  all_56_12 = e0
% 154.11/23.37    (3)   ~ (e1 = e0)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.37  |   (4)  e1 = e0
% 154.11/23.37  | 
% 154.11/23.37  | SIMP: (4) implies:
% 154.11/23.37  |   (5)  e1 = e0
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (3), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1052 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  all_56_12 = e3
% 154.11/23.37    (2)  all_56_12 = e0
% 154.11/23.37    (3)   ~ (e3 = e0)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.37  |   (4)  e3 = e0
% 154.11/23.37  | 
% 154.11/23.37  | SIMP: (4) implies:
% 154.11/23.37  |   (5)  e3 = e0
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (3), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1053 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  all_56_2 = e3
% 154.11/23.37    (2)  all_56_2 = e1
% 154.11/23.37    (3)   ~ (e3 = e1)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.37  |   (4)  e3 = e1
% 154.11/23.37  | 
% 154.11/23.37  | SIMP: (4) implies:
% 154.11/23.37  |   (5)  e3 = e1
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (3), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1054 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  all_56_6 = e0 & op(e1, e3) = e0
% 154.11/23.37    (2)  all_56_6 = e2
% 154.11/23.37    (3)   ~ (e2 = e0)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | ALPHA: (1) implies:
% 154.11/23.37  |   (4)  all_56_6 = e0
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.37  |   (5)  e2 = e0
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (3), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1055 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)   ~ (e3 = e1)
% 154.11/23.37    (2)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1) |
% 154.11/23.37         (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) = e1)
% 154.11/23.37    (3)  all_56_6 = e2
% 154.11/23.37    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3) = e3) |
% 154.11/23.37         (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3) = e3)
% 154.11/23.37    (5)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.37    (6)  op(e3, e3) = e2
% 154.11/23.37    (7)   ~ (e3 = e0)
% 154.11/23.37    (8)   ~ (e1 = e0)
% 154.11/23.37    (9)  all_56_2 = e0
% 154.11/23.37    (10)   ~ (e3 = e2)
% 154.11/23.37    (11)   ~ (e2 = e1)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | BETA: splitting (2) gives:
% 154.11/23.37  | 
% 154.11/23.37  | Case 1:
% 154.11/23.37  | | 
% 154.11/23.37  | |   (12)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) =
% 154.11/23.37  | |           e1)
% 154.11/23.37  | | 
% 154.11/23.37  | | REF_CLOSE: (5), (6), (8), (9), (11), (12) are inconsistent by sub-proof
% 154.11/23.37  | |            #1059.
% 154.11/23.37  | | 
% 154.11/23.37  | Case 2:
% 154.11/23.37  | | 
% 154.11/23.37  | |   (13)  (all_56_6 = e1 & op(e1, e3) = e1) | (all_56_12 = e1 & op(e0, e3) =
% 154.11/23.37  | |           e1)
% 154.11/23.37  | | 
% 154.11/23.37  | | BETA: splitting (13) gives:
% 154.11/23.37  | | 
% 154.11/23.37  | | Case 1:
% 154.11/23.37  | | | 
% 154.11/23.37  | | |   (14)  all_56_6 = e1 & op(e1, e3) = e1
% 154.11/23.37  | | | 
% 154.11/23.37  | | | REF_CLOSE: (3), (11), (14) are inconsistent by sub-proof #1058.
% 154.11/23.37  | | | 
% 154.11/23.37  | | Case 2:
% 154.11/23.37  | | | 
% 154.11/23.37  | | |   (15)  all_56_12 = e1 & op(e0, e3) = e1
% 154.11/23.37  | | | 
% 154.11/23.37  | | | ALPHA: (15) implies:
% 154.11/23.37  | | |   (16)  all_56_12 = e1
% 154.11/23.37  | | | 
% 154.11/23.37  | | | BETA: splitting (4) gives:
% 154.11/23.37  | | | 
% 154.11/23.37  | | | Case 1:
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | |   (17)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_2 = e3 & op(e2, e3)
% 154.11/23.37  | | | |           = e3)
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | | BETA: splitting (17) gives:
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | | Case 1:
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | |   (18)  all_56_0 = e3 & op(e3, e3) = e3
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | ALPHA: (18) implies:
% 154.11/23.37  | | | | |   (19)  op(e3, e3) = e3
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | REF_CLOSE: (5), (6), (10), (19) are inconsistent by sub-proof #1085.
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | Case 2:
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | |   (20)  all_56_2 = e3 & op(e2, e3) = e3
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | ALPHA: (20) implies:
% 154.11/23.37  | | | | |   (21)  all_56_2 = e3
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | REF_CLOSE: (7), (9), (21) are inconsistent by sub-proof #1137.
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | End of split
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | Case 2:
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | |   (22)  (all_56_6 = e3 & op(e1, e3) = e3) | (all_56_12 = e3 & op(e0, e3)
% 154.11/23.37  | | | |           = e3)
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | | BETA: splitting (22) gives:
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | | Case 1:
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | |   (23)  all_56_6 = e3 & op(e1, e3) = e3
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | ALPHA: (23) implies:
% 154.11/23.37  | | | | |   (24)  all_56_6 = e3
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | REF_CLOSE: (3), (10), (24) are inconsistent by sub-proof #1057.
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | Case 2:
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | |   (25)  all_56_12 = e3 & op(e0, e3) = e3
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | ALPHA: (25) implies:
% 154.11/23.37  | | | | |   (26)  all_56_12 = e3
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | | REF_CLOSE: (1), (16), (26) are inconsistent by sub-proof #1056.
% 154.11/23.37  | | | | | 
% 154.11/23.37  | | | | End of split
% 154.11/23.37  | | | | 
% 154.11/23.37  | | | End of split
% 154.11/23.37  | | | 
% 154.11/23.37  | | End of split
% 154.11/23.37  | | 
% 154.11/23.37  | End of split
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1056 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  all_56_12 = e3
% 154.11/23.37    (2)  all_56_12 = e1
% 154.11/23.37    (3)   ~ (e3 = e1)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.37  |   (4)  e3 = e1
% 154.11/23.37  | 
% 154.11/23.37  | SIMP: (4) implies:
% 154.11/23.37  |   (5)  e3 = e1
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (3), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1057 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  all_56_6 = e3
% 154.11/23.37    (2)  all_56_6 = e2
% 154.11/23.37    (3)   ~ (e3 = e2)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.37  |   (4)  e3 = e2
% 154.11/23.37  | 
% 154.11/23.37  | SIMP: (4) implies:
% 154.11/23.37  |   (5)  e3 = e2
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (3), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1058 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  all_56_6 = e1 & op(e1, e3) = e1
% 154.11/23.37    (2)  all_56_6 = e2
% 154.11/23.37    (3)   ~ (e2 = e1)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | ALPHA: (1) implies:
% 154.11/23.37  |   (4)  all_56_6 = e1
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (2), (4) imply:
% 154.11/23.37  |   (5)  e2 = e1
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (3), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1059 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.37    (2)  op(e3, e3) = e2
% 154.11/23.37    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 154.11/23.37    (4)   ~ (e1 = e0)
% 154.11/23.37    (5)  all_56_2 = e0
% 154.11/23.37    (6)   ~ (e2 = e1)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | BETA: splitting (3) gives:
% 154.11/23.37  | 
% 154.11/23.37  | Case 1:
% 154.11/23.37  | | 
% 154.11/23.37  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 154.11/23.37  | | 
% 154.11/23.37  | | ALPHA: (7) implies:
% 154.11/23.37  | |   (8)  op(e3, e3) = e1
% 154.11/23.37  | | 
% 154.11/23.37  | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #1074.
% 154.11/23.37  | | 
% 154.11/23.37  | Case 2:
% 154.11/23.37  | | 
% 154.11/23.37  | |   (9)  all_56_2 = e1 & op(e2, e3) = e1
% 154.11/23.37  | | 
% 154.11/23.37  | | ALPHA: (9) implies:
% 154.11/23.37  | |   (10)  all_56_2 = e1
% 154.11/23.37  | | 
% 154.11/23.37  | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #1060.
% 154.11/23.37  | | 
% 154.11/23.37  | End of split
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1060 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)  all_56_2 = e1
% 154.11/23.37    (2)  all_56_2 = e0
% 154.11/23.37    (3)   ~ (e1 = e0)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | COMBINE_EQS: (1), (2) imply:
% 154.11/23.37  |   (4)  e1 = e0
% 154.11/23.37  | 
% 154.11/23.37  | SIMP: (4) implies:
% 154.11/23.37  |   (5)  e1 = e0
% 154.11/23.37  | 
% 154.11/23.37  | REDUCE: (3), (5) imply:
% 154.11/23.37  |   (6)  $false
% 154.11/23.37  | 
% 154.11/23.37  | CLOSE: (6) is inconsistent.
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1061 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)   ~ (e3 = e1)
% 154.11/23.37    (2)  (all_56_4 = e2 & op(e3, e1) = e2) | (all_56_5 = e2 & op(e2, e1) = e2)
% 154.11/23.37    (3)   ~ (e2 = e0)
% 154.11/23.37    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.37    (5)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 154.11/23.37         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 154.11/23.37    (6)  op(e3, e3) = e2
% 154.11/23.37    (7)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 154.11/23.37         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 154.11/23.37    (8)   ~ (e3 = e0)
% 154.11/23.37    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 154.11/23.37         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 154.11/23.37    (10)   ~ (all_52_9 = e2)
% 154.11/23.37    (11)  op(e2, e1) = all_52_9
% 154.11/23.37    (12)   ~ (e1 = e0)
% 154.11/23.37    (13)   ~ (e3 = e2)
% 154.11/23.37    (14)   ~ (e2 = e1)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | BETA: splitting (2) gives:
% 154.11/23.37  | 
% 154.11/23.37  | Case 1:
% 154.11/23.37  | | 
% 154.11/23.37  | |   (15)  all_56_4 = e2 & op(e3, e1) = e2
% 154.11/23.37  | | 
% 154.11/23.37  | | ALPHA: (15) implies:
% 154.11/23.37  | |   (16)  all_56_4 = e2
% 154.11/23.37  | | 
% 154.11/23.37  | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (12), (13), (14), (16)
% 154.11/23.37  | |            are inconsistent by sub-proof #1062.
% 154.11/23.37  | | 
% 154.11/23.37  | Case 2:
% 154.11/23.37  | | 
% 154.11/23.37  | |   (17)  all_56_5 = e2 & op(e2, e1) = e2
% 154.11/23.37  | | 
% 154.11/23.37  | | ALPHA: (17) implies:
% 154.11/23.37  | |   (18)  op(e2, e1) = e2
% 154.11/23.37  | | 
% 154.11/23.37  | | REF_CLOSE: (4), (10), (11), (18) are inconsistent by sub-proof #1157.
% 154.11/23.37  | | 
% 154.11/23.37  | End of split
% 154.11/23.37  | 
% 154.11/23.37  End of proof
% 154.11/23.37  
% 154.11/23.37  Sub-proof #1062 shows that the following formulas are inconsistent:
% 154.11/23.37  ----------------------------------------------------------------
% 154.11/23.37    (1)   ~ (e3 = e1)
% 154.11/23.37    (2)   ~ (e2 = e0)
% 154.11/23.37    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.11/23.37           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.11/23.37    (4)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3, e2) = e3) |
% 154.11/23.37         (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3, e0) = e3)
% 154.11/23.37    (5)  all_56_4 = e2
% 154.11/23.37    (6)  op(e3, e3) = e2
% 154.11/23.37    (7)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) = e1) |
% 154.11/23.37         (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) = e1)
% 154.11/23.37    (8)   ~ (e3 = e0)
% 154.11/23.37    (9)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0) |
% 154.11/23.37         (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0) = e0)
% 154.11/23.37    (10)   ~ (e1 = e0)
% 154.11/23.37    (11)   ~ (e3 = e2)
% 154.11/23.37    (12)   ~ (e2 = e1)
% 154.11/23.37  
% 154.11/23.37  Begin of proof
% 154.11/23.37  | 
% 154.11/23.37  | BETA: splitting (7) gives:
% 154.11/23.37  | 
% 154.11/23.37  | Case 1:
% 154.11/23.37  | | 
% 154.11/23.37  | |   (13)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_1 = e1 & op(e3, e2) =
% 154.11/23.37  | |           e1)
% 154.11/23.37  | | 
% 154.11/23.37  | | BETA: splitting (13) gives:
% 154.11/23.37  | | 
% 154.11/23.37  | | Case 1:
% 154.11/23.37  | | | 
% 154.24/23.37  | | |   (14)  all_56_0 = e1 & op(e3, e3) = e1
% 154.24/23.37  | | | 
% 154.24/23.37  | | | ALPHA: (14) implies:
% 154.24/23.37  | | |   (15)  op(e3, e3) = e1
% 154.24/23.37  | | | 
% 154.24/23.37  | | | REF_CLOSE: (3), (6), (12), (15) are inconsistent by sub-proof #1074.
% 154.24/23.37  | | | 
% 154.24/23.37  | | Case 2:
% 154.24/23.37  | | | 
% 154.24/23.37  | | |   (16)  all_56_1 = e1 & op(e3, e2) = e1
% 154.24/23.37  | | | 
% 154.24/23.37  | | | ALPHA: (16) implies:
% 154.24/23.37  | | |   (17)  all_56_1 = e1
% 154.24/23.37  | | | 
% 154.24/23.37  | | | BETA: splitting (9) gives:
% 154.24/23.37  | | | 
% 154.24/23.37  | | | Case 1:
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | |   (18)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2)
% 154.24/23.37  | | | |           = e0)
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | | REF_CLOSE: (2), (3), (6), (10), (17), (18) are inconsistent by sub-proof
% 154.24/23.37  | | | |            #1071.
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | Case 2:
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | |   (19)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0)
% 154.24/23.37  | | | |           = e0)
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | | BETA: splitting (19) gives:
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | | Case 1:
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | |   (20)  all_56_4 = e0 & op(e3, e1) = e0
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | | REF_CLOSE: (2), (5), (20) are inconsistent by sub-proof #1070.
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | Case 2:
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | |   (21)  all_56_9 = e0 & op(e3, e0) = e0
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | | ALPHA: (21) implies:
% 154.24/23.37  | | | | |   (22)  all_56_9 = e0
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | | BETA: splitting (4) gives:
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | | Case 1:
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | |   (23)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3,
% 154.24/23.37  | | | | | |             e2) = e3)
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | | BETA: splitting (23) gives:
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | | Case 1:
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | |   (24)  all_56_0 = e3 & op(e3, e3) = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | ALPHA: (24) implies:
% 154.24/23.37  | | | | | | |   (25)  op(e3, e3) = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | REF_CLOSE: (3), (6), (11), (25) are inconsistent by sub-proof
% 154.24/23.37  | | | | | | |            #1085.
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | Case 2:
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | |   (26)  all_56_1 = e3 & op(e3, e2) = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | ALPHA: (26) implies:
% 154.24/23.37  | | | | | | |   (27)  all_56_1 = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | REF_CLOSE: (1), (17), (27) are inconsistent by sub-proof #1069.
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | End of split
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | Case 2:
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | |   (28)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3,
% 154.24/23.37  | | | | | |             e0) = e3)
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | | BETA: splitting (28) gives:
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | | Case 1:
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | |   (29)  all_56_4 = e3 & op(e3, e1) = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | ALPHA: (29) implies:
% 154.24/23.37  | | | | | | |   (30)  all_56_4 = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | REF_CLOSE: (5), (11), (30) are inconsistent by sub-proof #1068.
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | Case 2:
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | |   (31)  all_56_9 = e3 & op(e3, e0) = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | ALPHA: (31) implies:
% 154.24/23.37  | | | | | | |   (32)  all_56_9 = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | REF_CLOSE: (8), (22), (32) are inconsistent by sub-proof #1067.
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | End of split
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | End of split
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | End of split
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | End of split
% 154.24/23.37  | | | 
% 154.24/23.37  | | End of split
% 154.24/23.37  | | 
% 154.24/23.37  | Case 2:
% 154.24/23.37  | | 
% 154.24/23.37  | |   (33)  (all_56_4 = e1 & op(e3, e1) = e1) | (all_56_9 = e1 & op(e3, e0) =
% 154.24/23.37  | |           e1)
% 154.24/23.37  | | 
% 154.24/23.37  | | BETA: splitting (33) gives:
% 154.24/23.37  | | 
% 154.24/23.37  | | Case 1:
% 154.24/23.37  | | | 
% 154.24/23.37  | | |   (34)  all_56_4 = e1 & op(e3, e1) = e1
% 154.24/23.37  | | | 
% 154.24/23.37  | | | REF_CLOSE: (5), (12), (34) are inconsistent by sub-proof #1066.
% 154.24/23.37  | | | 
% 154.24/23.37  | | Case 2:
% 154.24/23.37  | | | 
% 154.24/23.37  | | |   (35)  all_56_9 = e1 & op(e3, e0) = e1
% 154.24/23.37  | | | 
% 154.24/23.37  | | | ALPHA: (35) implies:
% 154.24/23.37  | | |   (36)  all_56_9 = e1
% 154.24/23.37  | | | 
% 154.24/23.37  | | | BETA: splitting (9) gives:
% 154.24/23.37  | | | 
% 154.24/23.37  | | | Case 1:
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | |   (37)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2)
% 154.24/23.37  | | | |           = e0)
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | | BETA: splitting (37) gives:
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | | Case 1:
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | |   (38)  all_56_0 = e0 & op(e3, e3) = e0
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | | ALPHA: (38) implies:
% 154.24/23.37  | | | | |   (39)  op(e3, e3) = e0
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | | REF_CLOSE: (2), (3), (6), (39) are inconsistent by sub-proof #1073.
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | Case 2:
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | |   (40)  all_56_1 = e0 & op(e3, e2) = e0
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | | ALPHA: (40) implies:
% 154.24/23.37  | | | | |   (41)  all_56_1 = e0
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | | BETA: splitting (4) gives:
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | | Case 1:
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | |   (42)  (all_56_0 = e3 & op(e3, e3) = e3) | (all_56_1 = e3 & op(e3,
% 154.24/23.37  | | | | | |             e2) = e3)
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | | BETA: splitting (42) gives:
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | | Case 1:
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | |   (43)  all_56_0 = e3 & op(e3, e3) = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | ALPHA: (43) implies:
% 154.24/23.37  | | | | | | |   (44)  op(e3, e3) = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | REF_CLOSE: (3), (6), (11), (44) are inconsistent by sub-proof
% 154.24/23.37  | | | | | | |            #1085.
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | Case 2:
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | |   (45)  all_56_1 = e3 & op(e3, e2) = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | ALPHA: (45) implies:
% 154.24/23.37  | | | | | | |   (46)  all_56_1 = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | REF_CLOSE: (8), (41), (46) are inconsistent by sub-proof #1065.
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | End of split
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | Case 2:
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | |   (47)  (all_56_4 = e3 & op(e3, e1) = e3) | (all_56_9 = e3 & op(e3,
% 154.24/23.37  | | | | | |             e0) = e3)
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | | BETA: splitting (47) gives:
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | | Case 1:
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | |   (48)  all_56_4 = e3 & op(e3, e1) = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | ALPHA: (48) implies:
% 154.24/23.37  | | | | | | |   (49)  all_56_4 = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | REF_CLOSE: (5), (11), (49) are inconsistent by sub-proof #1068.
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | Case 2:
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | |   (50)  all_56_9 = e3 & op(e3, e0) = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | ALPHA: (50) implies:
% 154.24/23.37  | | | | | | |   (51)  all_56_9 = e3
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | | REF_CLOSE: (1), (36), (51) are inconsistent by sub-proof #1064.
% 154.24/23.37  | | | | | | | 
% 154.24/23.37  | | | | | | End of split
% 154.24/23.37  | | | | | | 
% 154.24/23.37  | | | | | End of split
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | End of split
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | Case 2:
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | |   (52)  (all_56_4 = e0 & op(e3, e1) = e0) | (all_56_9 = e0 & op(e3, e0)
% 154.24/23.37  | | | |           = e0)
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | | BETA: splitting (52) gives:
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | | Case 1:
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | |   (53)  all_56_4 = e0 & op(e3, e1) = e0
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | | REF_CLOSE: (2), (5), (53) are inconsistent by sub-proof #1070.
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | Case 2:
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | |   (54)  all_56_9 = e0 & op(e3, e0) = e0
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | | REF_CLOSE: (10), (36), (54) are inconsistent by sub-proof #1063.
% 154.24/23.37  | | | | | 
% 154.24/23.37  | | | | End of split
% 154.24/23.37  | | | | 
% 154.24/23.37  | | | End of split
% 154.24/23.37  | | | 
% 154.24/23.37  | | End of split
% 154.24/23.37  | | 
% 154.24/23.37  | End of split
% 154.24/23.37  | 
% 154.24/23.37  End of proof
% 154.24/23.37  
% 154.24/23.37  Sub-proof #1063 shows that the following formulas are inconsistent:
% 154.24/23.37  ----------------------------------------------------------------
% 154.24/23.37    (1)  all_56_9 = e0 & op(e3, e0) = e0
% 154.24/23.37    (2)  all_56_9 = e1
% 154.24/23.37    (3)   ~ (e1 = e0)
% 154.24/23.37  
% 154.24/23.37  Begin of proof
% 154.24/23.37  | 
% 154.24/23.37  | ALPHA: (1) implies:
% 154.24/23.37  |   (4)  all_56_9 = e0
% 154.24/23.37  | 
% 154.24/23.37  | COMBINE_EQS: (2), (4) imply:
% 154.24/23.37  |   (5)  e1 = e0
% 154.24/23.37  | 
% 154.24/23.37  | REDUCE: (3), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1064 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  all_56_9 = e3
% 154.24/23.38    (2)  all_56_9 = e1
% 154.24/23.38    (3)   ~ (e3 = e1)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | COMBINE_EQS: (1), (2) imply:
% 154.24/23.38  |   (4)  e3 = e1
% 154.24/23.38  | 
% 154.24/23.38  | SIMP: (4) implies:
% 154.24/23.38  |   (5)  e3 = e1
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (3), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1065 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  all_56_1 = e3
% 154.24/23.38    (2)  all_56_1 = e0
% 154.24/23.38    (3)   ~ (e3 = e0)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | COMBINE_EQS: (1), (2) imply:
% 154.24/23.38  |   (4)  e3 = e0
% 154.24/23.38  | 
% 154.24/23.38  | SIMP: (4) implies:
% 154.24/23.38  |   (5)  e3 = e0
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (3), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1066 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  all_56_4 = e1 & op(e3, e1) = e1
% 154.24/23.38    (2)  all_56_4 = e2
% 154.24/23.38    (3)   ~ (e2 = e1)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | ALPHA: (1) implies:
% 154.24/23.38  |   (4)  all_56_4 = e1
% 154.24/23.38  | 
% 154.24/23.38  | COMBINE_EQS: (2), (4) imply:
% 154.24/23.38  |   (5)  e2 = e1
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (3), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1067 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  all_56_9 = e3
% 154.24/23.38    (2)  all_56_9 = e0
% 154.24/23.38    (3)   ~ (e3 = e0)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | COMBINE_EQS: (1), (2) imply:
% 154.24/23.38  |   (4)  e3 = e0
% 154.24/23.38  | 
% 154.24/23.38  | SIMP: (4) implies:
% 154.24/23.38  |   (5)  e3 = e0
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (3), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1068 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  all_56_4 = e3
% 154.24/23.38    (2)  all_56_4 = e2
% 154.24/23.38    (3)   ~ (e3 = e2)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | COMBINE_EQS: (1), (2) imply:
% 154.24/23.38  |   (4)  e3 = e2
% 154.24/23.38  | 
% 154.24/23.38  | SIMP: (4) implies:
% 154.24/23.38  |   (5)  e3 = e2
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (3), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1069 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  all_56_1 = e3
% 154.24/23.38    (2)  all_56_1 = e1
% 154.24/23.38    (3)   ~ (e3 = e1)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | COMBINE_EQS: (1), (2) imply:
% 154.24/23.38  |   (4)  e3 = e1
% 154.24/23.38  | 
% 154.24/23.38  | SIMP: (4) implies:
% 154.24/23.38  |   (5)  e3 = e1
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (3), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1070 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  all_56_4 = e0 & op(e3, e1) = e0
% 154.24/23.38    (2)  all_56_4 = e2
% 154.24/23.38    (3)   ~ (e2 = e0)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | ALPHA: (1) implies:
% 154.24/23.38  |   (4)  all_56_4 = e0
% 154.24/23.38  | 
% 154.24/23.38  | COMBINE_EQS: (2), (4) imply:
% 154.24/23.38  |   (5)  e2 = e0
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (3), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1071 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  all_56_1 = e1
% 154.24/23.38    (2)   ~ (e2 = e0)
% 154.24/23.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (4)  op(e3, e3) = e2
% 154.24/23.38    (5)  (all_56_0 = e0 & op(e3, e3) = e0) | (all_56_1 = e0 & op(e3, e2) = e0)
% 154.24/23.38    (6)   ~ (e1 = e0)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | BETA: splitting (5) gives:
% 154.24/23.38  | 
% 154.24/23.38  | Case 1:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (7)  all_56_0 = e0 & op(e3, e3) = e0
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (7) implies:
% 154.24/23.38  | |   (8)  op(e3, e3) = e0
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1073.
% 154.24/23.38  | | 
% 154.24/23.38  | Case 2:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (9)  all_56_1 = e0 & op(e3, e2) = e0
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #1072.
% 154.24/23.38  | | 
% 154.24/23.38  | End of split
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1072 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  all_56_1 = e0 & op(e3, e2) = e0
% 154.24/23.38    (2)  all_56_1 = e1
% 154.24/23.38    (3)   ~ (e1 = e0)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | ALPHA: (1) implies:
% 154.24/23.38  |   (4)  all_56_1 = e0
% 154.24/23.38  | 
% 154.24/23.38  | COMBINE_EQS: (2), (4) imply:
% 154.24/23.38  |   (5)  e1 = e0
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (3), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1073 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (2)  op(e3, e3) = e2
% 154.24/23.38    (3)  op(e3, e3) = e0
% 154.24/23.38    (4)   ~ (e2 = e0)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | GROUND_INST: instantiating (1) with e0, e2, e3, e3, simplifying with (2), (3)
% 154.24/23.38  |              gives:
% 154.24/23.38  |   (5)  e2 = e0
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (4), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1074 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (2)  op(e3, e3) = e2
% 154.24/23.38    (3)  op(e3, e3) = e1
% 154.24/23.38    (4)   ~ (e2 = e1)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | GROUND_INST: instantiating (1) with e1, e2, e3, e3, simplifying with (2), (3)
% 154.24/23.38  |              gives:
% 154.24/23.38  |   (5)  e2 = e1
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (4), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1075 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)   ~ (e3 = e1)
% 154.24/23.38    (2)  op(e1, e1) = all_4_2
% 154.24/23.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (4)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15 =
% 154.24/23.38             e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) = e0 &
% 154.24/23.38           $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) & 
% 154.24/23.38           ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0,
% 154.24/23.38             e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~
% 154.24/23.38           (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) =
% 154.24/23.38           all_57_3 & op(e0, e2) = e0 & $i(all_57_3)) | (all_57_5 = e0 & all_57_14
% 154.24/23.38           = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15 = e2) & op(e1, e2) = all_57_4
% 154.24/23.38           & op(e1, e1) = e2 & op(e0, e2) = e0 & $i(all_57_4)) | (all_57_8 = e0 &
% 154.24/23.38           all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3)
% 154.24/23.38           = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) |
% 154.24/23.38         (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.24/23.38             e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.24/23.38           $i(all_57_7))
% 154.24/23.38    (5)   ~ (all_4_2 = e2)
% 154.24/23.38    (6)  op(e2, e2) = e2
% 154.24/23.38    (7)   ~ (all_4_2 = e3)
% 154.24/23.38    (8)   ~ (e3 = e2)
% 154.24/23.38    (9)  op(e3, e3) = e3
% 154.24/23.38    (10)   ~ (e2 = e1)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | BETA: splitting (4) gives:
% 154.24/23.38  | 
% 154.24/23.38  | Case 1:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (11)  (all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~ (all_57_15
% 154.24/23.38  | |             = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 & op(e0, e3) =
% 154.24/23.38  | |           e0 & $i(all_57_0)) | (all_57_2 = e0 & all_57_14 = e3 &  ~
% 154.24/23.38  | |           (all_57_1 = e1) &  ~ (all_57_15 = e3) & op(e1, e3) = all_57_1 &
% 154.24/23.38  | |           op(e1, e1) = e3 & op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0
% 154.24/23.38  | |           & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) &
% 154.24/23.38  | |           op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.24/23.38  | |           $i(all_57_3))
% 154.24/23.38  | | 
% 154.24/23.38  | | BETA: splitting (11) gives:
% 154.24/23.38  | | 
% 154.24/23.38  | | Case 1:
% 154.24/23.38  | | | 
% 154.24/23.38  | | |   (12)  all_57_2 = e0 & all_57_12 = e3 &  ~ (all_57_0 = e2) &  ~
% 154.24/23.38  | | |         (all_57_15 = e3) & op(e2, e3) = all_57_0 & op(e2, e2) = e3 &
% 154.24/23.38  | | |         op(e0, e3) = e0 & $i(all_57_0)
% 154.24/23.38  | | | 
% 154.24/23.38  | | | ALPHA: (12) implies:
% 154.24/23.38  | | |   (13)  op(e2, e2) = e3
% 154.24/23.38  | | | 
% 154.24/23.38  | | | REF_CLOSE: (3), (6), (8), (13) are inconsistent by sub-proof #1179.
% 154.24/23.38  | | | 
% 154.24/23.38  | | Case 2:
% 154.24/23.38  | | | 
% 154.24/23.38  | | |   (14)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~
% 154.24/23.38  | | |           (all_57_15 = e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 &
% 154.24/23.38  | | |           op(e0, e3) = e0 & $i(all_57_1)) | (all_57_5 = e0 & all_57_10 =
% 154.24/23.38  | | |           e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 = e2) & op(e3, e3) = e2
% 154.24/23.38  | | |           & op(e3, e2) = all_57_3 & op(e0, e2) = e0 & $i(all_57_3))
% 154.24/23.38  | | | 
% 154.24/23.38  | | | REF_CLOSE: (2), (3), (7), (8), (9), (14) are inconsistent by sub-proof
% 154.24/23.38  | | |            #1077.
% 154.24/23.38  | | | 
% 154.24/23.38  | | End of split
% 154.24/23.38  | | 
% 154.24/23.38  | Case 2:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (15)  (all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_15
% 154.24/23.38  | |             = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 & op(e0, e2) =
% 154.24/23.38  | |           e0 & $i(all_57_4)) | (all_57_8 = e0 & all_57_10 = e1 &  ~
% 154.24/23.38  | |           (all_57_6 = e3) &  ~ (all_57_15 = e1) & op(e3, e3) = e1 & op(e3,
% 154.24/23.38  | |             e1) = all_57_6 & op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 =
% 154.24/23.38  | |           e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) &
% 154.24/23.38  | |           op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.24/23.38  | |           $i(all_57_7))
% 154.24/23.38  | | 
% 154.24/23.38  | | BETA: splitting (15) gives:
% 154.24/23.38  | | 
% 154.24/23.38  | | Case 1:
% 154.24/23.38  | | | 
% 154.24/23.38  | | |   (16)  all_57_5 = e0 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~
% 154.24/23.38  | | |         (all_57_15 = e2) & op(e1, e2) = all_57_4 & op(e1, e1) = e2 &
% 154.24/23.38  | | |         op(e0, e2) = e0 & $i(all_57_4)
% 154.24/23.38  | | | 
% 154.24/23.38  | | | ALPHA: (16) implies:
% 154.24/23.38  | | |   (17)  op(e1, e1) = e2
% 154.24/23.38  | | | 
% 154.24/23.38  | | | REF_CLOSE: (2), (3), (5), (17) are inconsistent by sub-proof #1169.
% 154.24/23.38  | | | 
% 154.24/23.38  | | Case 2:
% 154.24/23.38  | | | 
% 154.24/23.38  | | |   (18)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~
% 154.24/23.38  | | |           (all_57_15 = e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 &
% 154.24/23.38  | | |           op(e0, e1) = e0 & $i(all_57_6)) | (all_57_8 = e0 & all_57_12 =
% 154.24/23.38  | | |           e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 = e1) & op(e2, e2) = e1
% 154.24/23.38  | | |           & op(e2, e1) = all_57_7 & op(e0, e1) = e0 & $i(all_57_7))
% 154.24/23.38  | | | 
% 154.24/23.38  | | | REF_CLOSE: (1), (3), (6), (9), (10), (18) are inconsistent by sub-proof
% 154.24/23.38  | | |            #1076.
% 154.24/23.38  | | | 
% 154.24/23.38  | | End of split
% 154.24/23.38  | | 
% 154.24/23.38  | End of split
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1076 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)   ~ (e3 = e1)
% 154.24/23.38    (2)  (all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.24/23.38             e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.24/23.38           $i(all_57_6)) | (all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) & 
% 154.24/23.38           ~ (all_57_15 = e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0,
% 154.24/23.38             e1) = e0 & $i(all_57_7))
% 154.24/23.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (4)  op(e2, e2) = e2
% 154.24/23.38    (5)  op(e3, e3) = e3
% 154.24/23.38    (6)   ~ (e2 = e1)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | BETA: splitting (2) gives:
% 154.24/23.38  | 
% 154.24/23.38  | Case 1:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (7)  all_57_8 = e0 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_15 =
% 154.24/23.38  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e0, e1) = e0 &
% 154.24/23.38  | |        $i(all_57_6)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (7) implies:
% 154.24/23.38  | |   (8)  op(e3, e3) = e1
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1178.
% 154.24/23.38  | | 
% 154.24/23.38  | Case 2:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (9)  all_57_8 = e0 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_15 =
% 154.24/23.38  | |          e1) & op(e2, e2) = e1 & op(e2, e1) = all_57_7 & op(e0, e1) = e0 &
% 154.24/23.38  | |        $i(all_57_7)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (9) implies:
% 154.24/23.38  | |   (10)  op(e2, e2) = e1
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #1158.
% 154.24/23.38  | | 
% 154.24/23.38  | End of split
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1077 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  (all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 154.24/23.38             e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 154.24/23.38           $i(all_57_1)) | (all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) & 
% 154.24/23.38           ~ (all_57_15 = e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0,
% 154.24/23.38             e2) = e0 & $i(all_57_3))
% 154.24/23.38    (2)  op(e1, e1) = all_4_2
% 154.24/23.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (4)   ~ (all_4_2 = e3)
% 154.24/23.38    (5)   ~ (e3 = e2)
% 154.24/23.38    (6)  op(e3, e3) = e3
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | BETA: splitting (1) gives:
% 154.24/23.38  | 
% 154.24/23.38  | Case 1:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (7)  all_57_2 = e0 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_15 =
% 154.24/23.38  | |          e3) & op(e1, e3) = all_57_1 & op(e1, e1) = e3 & op(e0, e3) = e0 &
% 154.24/23.38  | |        $i(all_57_1)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (7) implies:
% 154.24/23.38  | |   (8)  op(e1, e1) = e3
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1078.
% 154.24/23.38  | | 
% 154.24/23.38  | Case 2:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (9)  all_57_5 = e0 & all_57_10 = e2 &  ~ (all_57_3 = e3) &  ~ (all_57_15 =
% 154.24/23.38  | |          e2) & op(e3, e3) = e2 & op(e3, e2) = all_57_3 & op(e0, e2) = e0 &
% 154.24/23.38  | |        $i(all_57_3)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (9) implies:
% 154.24/23.38  | |   (10)  op(e3, e3) = e2
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1085.
% 154.24/23.38  | | 
% 154.24/23.38  | End of split
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1078 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (2)  op(e1, e1) = all_4_2
% 154.24/23.38    (3)  op(e1, e1) = e3
% 154.24/23.38    (4)   ~ (all_4_2 = e3)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | GROUND_INST: instantiating (1) with all_4_2, e3, e1, e1, simplifying with (2),
% 154.24/23.38  |              (3) gives:
% 154.24/23.38  |   (5)  all_4_2 = e3
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (4), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1079 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)   ~ (all_14_2 = e0)
% 154.24/23.38    (2)  op(e3, e3) = all_14_2
% 154.24/23.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (4)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.24/23.38    (5)  all_54_0 = all_14_2
% 154.24/23.38    (6)   ~ (all_14_2 = e2)
% 154.24/23.38    (7)   ~ (all_14_2 = e1)
% 154.24/23.38    (8)  (all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12 =
% 154.24/23.38             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 154.24/23.38           all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)) |
% 154.24/23.38         (all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14 =
% 154.24/23.38             e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 154.24/23.38           all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14))
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | BETA: splitting (8) gives:
% 154.24/23.38  | 
% 154.24/23.38  | Case 1:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (9)  all_57_10 = e0 & all_57_11 = e2 &  ~ (all_57_9 = e3) &  ~ (all_57_12
% 154.24/23.38  | |          = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e2, e2) =
% 154.24/23.38  | |        all_57_12 & op(e2, e0) = e2 & $i(all_57_9) & $i(all_57_12)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (9) implies:
% 154.24/23.38  | |   (10)  op(e3, e3) = e0
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10) are inconsistent by
% 154.24/23.38  | |            sub-proof #1139.
% 154.24/23.38  | | 
% 154.24/23.38  | Case 2:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (11)  all_57_10 = e0 & all_57_13 = e1 &  ~ (all_57_9 = e3) &  ~ (all_57_14
% 154.24/23.38  | |           = e0) & op(e3, e3) = e0 & op(e3, e0) = all_57_9 & op(e1, e1) =
% 154.24/23.38  | |         all_57_14 & op(e1, e0) = e1 & $i(all_57_9) & $i(all_57_14)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (11) implies:
% 154.24/23.38  | |   (12)  op(e3, e3) = e0
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (12) are inconsistent by
% 154.24/23.38  | |            sub-proof #1139.
% 154.24/23.38  | | 
% 154.24/23.38  | End of split
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1080 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  op(e0, e0) = all_10_2
% 154.24/23.38    (2)   ~ (all_10_2 = e1)
% 154.24/23.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (4)  (all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 154.24/23.38             e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.24/23.38           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)) | (all_57_9
% 154.24/23.38           = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 = e2) &
% 154.24/23.38           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 & op(e2, e0)
% 154.24/23.38           = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 = e3 &
% 154.24/23.38           all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) & op(e3, e3)
% 154.24/23.38           = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0) =
% 154.24/23.38           all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.24/23.38    (5)  op(e3, e0) = all_52_12
% 154.24/23.38    (6)   ~ (all_52_12 = e3)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | BETA: splitting (4) gives:
% 154.24/23.38  | 
% 154.24/23.38  | Case 1:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (7)  all_57_7 = e2 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_12 =
% 154.24/23.38  | |          e1) & op(e2, e2) = all_57_12 & op(e2, e1) = e2 & op(e0, e1) =
% 154.24/23.38  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_12)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (7) implies:
% 154.24/23.38  | |   (8)  op(e0, e0) = e1
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #1116.
% 154.24/23.38  | | 
% 154.24/23.38  | Case 2:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (9)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 154.24/23.38  | |            = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) =
% 154.24/23.38  | |          e0 & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) |
% 154.24/23.38  | |        (all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 154.24/23.38  | |            = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) =
% 154.24/23.38  | |          e0 & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #1081.
% 154.24/23.38  | | 
% 154.24/23.38  | End of split
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1081 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  (all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11 =
% 154.24/23.38             e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0 &
% 154.24/23.38           op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)) | (all_57_9 =
% 154.24/23.38           e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13 = e1) &
% 154.24/23.38           op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0 & op(e1, e0)
% 154.24/23.38           = all_57_13 & $i(all_57_10) & $i(all_57_13))
% 154.24/23.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (3)  op(e3, e0) = all_52_12
% 154.24/23.38    (4)   ~ (all_52_12 = e3)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | BETA: splitting (1) gives:
% 154.24/23.38  | 
% 154.24/23.38  | Case 1:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (5)  all_57_9 = e3 & all_57_12 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_11
% 154.24/23.38  | |          = e2) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e2, e2) = e0
% 154.24/23.38  | |        & op(e2, e0) = all_57_11 & $i(all_57_10) & $i(all_57_11)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (5) implies:
% 154.24/23.38  | |   (6)  op(e3, e0) = e3
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #1082.
% 154.24/23.38  | | 
% 154.24/23.38  | Case 2:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (7)  all_57_9 = e3 & all_57_14 = e0 &  ~ (all_57_10 = e0) &  ~ (all_57_13
% 154.24/23.38  | |          = e1) & op(e3, e3) = all_57_10 & op(e3, e0) = e3 & op(e1, e1) = e0
% 154.24/23.38  | |        & op(e1, e0) = all_57_13 & $i(all_57_10) & $i(all_57_13)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (7) implies:
% 154.24/23.38  | |   (8)  op(e3, e0) = e3
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1082.
% 154.24/23.38  | | 
% 154.24/23.38  | End of split
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1082 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (2)  op(e3, e0) = all_52_12
% 154.24/23.38    (3)  op(e3, e0) = e3
% 154.24/23.38    (4)   ~ (all_52_12 = e3)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | GROUND_INST: instantiating (1) with all_52_12, e3, e0, e3, simplifying with
% 154.24/23.38  |              (2), (3) gives:
% 154.24/23.38  |   (5)  all_52_12 = e3
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (4), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1083 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (2)  (all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.24/23.38             e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.24/23.38           all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)) | (all_57_7
% 154.24/23.38           = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 = e1) &
% 154.24/23.38           op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) = all_57_12 &
% 154.24/23.38           op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12))
% 154.24/23.38    (3)   ~ (all_52_9 = e2)
% 154.24/23.38    (4)  op(e2, e1) = all_52_9
% 154.24/23.38    (5)   ~ (all_52_8 = e3)
% 154.24/23.38    (6)  op(e3, e1) = all_52_8
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | BETA: splitting (2) gives:
% 154.24/23.38  | 
% 154.24/23.38  | Case 1:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (7)  all_57_6 = e3 & all_57_15 = e1 &  ~ (all_57_8 = e0) &  ~ (all_57_10 =
% 154.24/23.38  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e0, e1) =
% 154.24/23.38  | |        all_57_8 & op(e0, e0) = e1 & $i(all_57_8) & $i(all_57_10)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (7) implies:
% 154.24/23.38  | |   (8)  op(e3, e1) = e3
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #1164.
% 154.24/23.38  | | 
% 154.24/23.38  | Case 2:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (9)  all_57_7 = e2 & all_57_10 = e1 &  ~ (all_57_6 = e3) &  ~ (all_57_12 =
% 154.24/23.38  | |          e1) & op(e3, e3) = e1 & op(e3, e1) = all_57_6 & op(e2, e2) =
% 154.24/23.38  | |        all_57_12 & op(e2, e1) = e2 & $i(all_57_6) & $i(all_57_12)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (9) implies:
% 154.24/23.38  | |   (10)  op(e2, e1) = e2
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1157.
% 154.24/23.38  | | 
% 154.24/23.38  | End of split
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1084 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  op(e0, e0) = all_10_2
% 154.24/23.38    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (3)  op(e2, e2) = e2
% 154.24/23.38    (4)  (all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 154.24/23.38             e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.24/23.38           all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)) | (all_57_6
% 154.24/23.38           = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 = e1) &
% 154.24/23.38           op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 & op(e2, e1)
% 154.24/23.38           = all_57_7 & $i(all_57_7) & $i(all_57_10))
% 154.24/23.38    (5)   ~ (all_10_2 = e2)
% 154.24/23.38    (6)   ~ (e2 = e1)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | BETA: splitting (4) gives:
% 154.24/23.38  | 
% 154.24/23.38  | Case 1:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (7)  all_57_4 = e1 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_14 =
% 154.24/23.38  | |          e2) & op(e1, e2) = e1 & op(e1, e1) = all_57_14 & op(e0, e2) =
% 154.24/23.38  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_14)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (7) implies:
% 154.24/23.38  | |   (8)  op(e0, e0) = e2
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1097.
% 154.24/23.38  | | 
% 154.24/23.38  | Case 2:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (9)  all_57_6 = e3 & all_57_12 = e1 &  ~ (all_57_7 = e2) &  ~ (all_57_10 =
% 154.24/23.38  | |          e1) & op(e3, e3) = all_57_10 & op(e3, e1) = e3 & op(e2, e2) = e1 &
% 154.24/23.38  | |        op(e2, e1) = all_57_7 & $i(all_57_7) & $i(all_57_10)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (9) implies:
% 154.24/23.38  | |   (10)  op(e2, e2) = e1
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #1158.
% 154.24/23.38  | | 
% 154.24/23.38  | End of split
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1085 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (2)  op(e3, e3) = e3
% 154.24/23.38    (3)  op(e3, e3) = e2
% 154.24/23.38    (4)   ~ (e3 = e2)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | GROUND_INST: instantiating (1) with e2, e3, e3, e3, simplifying with (2), (3)
% 154.24/23.38  |              gives:
% 154.24/23.38  |   (5)  e3 = e2
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (4), (5) imply:
% 154.24/23.38  |   (6)  $false
% 154.24/23.38  | 
% 154.24/23.38  | CLOSE: (6) is inconsistent.
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1086 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)  op(e3, e2) = all_52_4
% 154.24/23.38    (2)  op(e1, e1) = all_4_2
% 154.24/23.38    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (4)   ~ (all_52_4 = e3)
% 154.24/23.38    (5)   ~ (all_4_2 = e2)
% 154.24/23.38    (6)  (all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 154.24/23.38             e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.24/23.38           all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)) | (all_57_3
% 154.24/23.38           = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 = e2) &
% 154.24/23.38           op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) = all_57_5 &
% 154.24/23.38           op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10))
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | BETA: splitting (6) gives:
% 154.24/23.38  | 
% 154.24/23.38  | Case 1:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (7)  all_57_3 = e3 & all_57_14 = e2 &  ~ (all_57_4 = e1) &  ~ (all_57_10 =
% 154.24/23.38  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e1, e2) =
% 154.24/23.38  | |        all_57_4 & op(e1, e1) = e2 & $i(all_57_4) & $i(all_57_10)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (7) implies:
% 154.24/23.38  | |   (8)  op(e1, e1) = e2
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #1169.
% 154.24/23.38  | | 
% 154.24/23.38  | Case 2:
% 154.24/23.38  | | 
% 154.24/23.38  | |   (9)  all_57_3 = e3 & all_57_15 = e2 &  ~ (all_57_5 = e0) &  ~ (all_57_10 =
% 154.24/23.38  | |          e2) & op(e3, e3) = all_57_10 & op(e3, e2) = e3 & op(e0, e2) =
% 154.24/23.38  | |        all_57_5 & op(e0, e0) = e2 & $i(all_57_5) & $i(all_57_10)
% 154.24/23.38  | | 
% 154.24/23.38  | | ALPHA: (9) implies:
% 154.24/23.38  | |   (10)  op(e3, e2) = e3
% 154.24/23.38  | | 
% 154.24/23.38  | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1166.
% 154.24/23.38  | | 
% 154.24/23.38  | End of split
% 154.24/23.38  | 
% 154.24/23.38  End of proof
% 154.24/23.38  
% 154.24/23.38  Sub-proof #1087 shows that the following formulas are inconsistent:
% 154.24/23.38  ----------------------------------------------------------------
% 154.24/23.38    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.38           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.38    (2)  op(e0, e0) = e3
% 154.24/23.38    (3)  op(e0, e0) = e2
% 154.24/23.38    (4)   ~ (e3 = e2)
% 154.24/23.38  
% 154.24/23.38  Begin of proof
% 154.24/23.38  | 
% 154.24/23.38  | GROUND_INST: instantiating (1) with e2, e3, e0, e0, simplifying with (2), (3)
% 154.24/23.38  |              gives:
% 154.24/23.38  |   (5)  e3 = e2
% 154.24/23.38  | 
% 154.24/23.38  | REDUCE: (4), (5) imply:
% 154.24/23.39  |   (6)  $false
% 154.24/23.39  | 
% 154.24/23.39  | CLOSE: (6) is inconsistent.
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1088 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  op(e0, e1) = all_52_11
% 154.24/23.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.39    (3)   ~ (all_52_3 = all_52_11)
% 154.24/23.39    (4)   ~ (all_52_3 = e3)
% 154.24/23.39    (5)  op(e0, e1) = e2
% 154.24/23.39    (6)   ~ (all_52_3 = e1)
% 154.24/23.39    (7)  all_54_12 = all_52_3
% 154.24/23.39    (8)   ~ (all_52_3 = e0)
% 154.24/23.39    (9)  all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | BETA: splitting (9) gives:
% 154.24/23.39  | 
% 154.24/23.39  | Case 1:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (10)  all_54_12 = e3
% 154.24/23.39  | | 
% 154.24/23.39  | | REF_CLOSE: (4), (7), (10) are inconsistent by sub-proof #1093.
% 154.24/23.39  | | 
% 154.24/23.39  | Case 2:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (11)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.24/23.39  | | 
% 154.24/23.39  | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (11) are inconsistent by
% 154.24/23.39  | |            sub-proof #1089.
% 154.24/23.39  | | 
% 154.24/23.39  | End of split
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1089 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  op(e0, e1) = all_52_11
% 154.24/23.39    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.39    (3)   ~ (all_52_3 = all_52_11)
% 154.24/23.39    (4)  all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 154.24/23.39    (5)  op(e0, e1) = e2
% 154.24/23.39    (6)   ~ (all_52_3 = e1)
% 154.24/23.39    (7)  all_54_12 = all_52_3
% 154.24/23.39    (8)   ~ (all_52_3 = e0)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | BETA: splitting (4) gives:
% 154.24/23.39  | 
% 154.24/23.39  | Case 1:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (9)  all_54_12 = e2
% 154.24/23.39  | | 
% 154.24/23.39  | | COMBINE_EQS: (7), (9) imply:
% 154.24/23.39  | |   (10)  all_52_3 = e2
% 154.24/23.39  | | 
% 154.24/23.39  | | SIMP: (10) implies:
% 154.24/23.39  | |   (11)  all_52_3 = e2
% 154.24/23.39  | | 
% 154.24/23.39  | | REDUCE: (3), (11) imply:
% 154.24/23.39  | |   (12)   ~ (all_52_11 = e2)
% 154.24/23.39  | | 
% 154.24/23.39  | | SIMP: (12) implies:
% 154.24/23.39  | |   (13)   ~ (all_52_11 = e2)
% 154.24/23.39  | | 
% 154.24/23.39  | | REF_CLOSE: (1), (2), (5), (13) are inconsistent by sub-proof #1092.
% 154.24/23.39  | | 
% 154.24/23.39  | Case 2:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (14)  all_54_12 = e1 | all_54_12 = e0
% 154.24/23.39  | | 
% 154.24/23.39  | | REF_CLOSE: (6), (7), (8), (14) are inconsistent by sub-proof #1090.
% 154.24/23.39  | | 
% 154.24/23.39  | End of split
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1090 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  all_54_12 = e1 | all_54_12 = e0
% 154.24/23.39    (2)  all_54_12 = all_52_3
% 154.24/23.39    (3)   ~ (all_52_3 = e1)
% 154.24/23.39    (4)   ~ (all_52_3 = e0)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | BETA: splitting (1) gives:
% 154.24/23.39  | 
% 154.24/23.39  | Case 1:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (5)  all_54_12 = e1
% 154.24/23.39  | | 
% 154.24/23.39  | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1091.
% 154.24/23.39  | | 
% 154.24/23.39  | Case 2:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (6)  all_54_12 = e0
% 154.24/23.39  | | 
% 154.24/23.39  | | COMBINE_EQS: (2), (6) imply:
% 154.24/23.39  | |   (7)  all_52_3 = e0
% 154.24/23.39  | | 
% 154.24/23.39  | | SIMP: (7) implies:
% 154.24/23.39  | |   (8)  all_52_3 = e0
% 154.24/23.39  | | 
% 154.24/23.39  | | REDUCE: (4), (8) imply:
% 154.24/23.39  | |   (9)  $false
% 154.24/23.39  | | 
% 154.24/23.39  | | CLOSE: (9) is inconsistent.
% 154.24/23.39  | | 
% 154.24/23.39  | End of split
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1091 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  all_54_12 = all_52_3
% 154.24/23.39    (2)  all_54_12 = e1
% 154.24/23.39    (3)   ~ (all_52_3 = e1)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | COMBINE_EQS: (1), (2) imply:
% 154.24/23.39  |   (4)  all_52_3 = e1
% 154.24/23.39  | 
% 154.24/23.39  | SIMP: (4) implies:
% 154.24/23.39  |   (5)  all_52_3 = e1
% 154.24/23.39  | 
% 154.24/23.39  | REDUCE: (3), (5) imply:
% 154.24/23.39  |   (6)  $false
% 154.24/23.39  | 
% 154.24/23.39  | CLOSE: (6) is inconsistent.
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1092 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.39    (2)  op(e0, e1) = all_52_11
% 154.24/23.39    (3)  op(e0, e1) = e2
% 154.24/23.39    (4)   ~ (all_52_11 = e2)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | GROUND_INST: instantiating (1) with all_52_11, e2, e1, e0, simplifying with
% 154.24/23.39  |              (2), (3) gives:
% 154.24/23.39  |   (5)  all_52_11 = e2
% 154.24/23.39  | 
% 154.24/23.39  | REDUCE: (4), (5) imply:
% 154.24/23.39  |   (6)  $false
% 154.24/23.39  | 
% 154.24/23.39  | CLOSE: (6) is inconsistent.
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1093 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  all_54_12 = all_52_3
% 154.24/23.39    (2)  all_54_12 = e3
% 154.24/23.39    (3)   ~ (all_52_3 = e3)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | COMBINE_EQS: (1), (2) imply:
% 154.24/23.39  |   (4)  all_52_3 = e3
% 154.24/23.39  | 
% 154.24/23.39  | SIMP: (4) implies:
% 154.24/23.39  |   (5)  all_52_3 = e3
% 154.24/23.39  | 
% 154.24/23.39  | REDUCE: (3), (5) imply:
% 154.24/23.39  |   (6)  $false
% 154.24/23.39  | 
% 154.24/23.39  | CLOSE: (6) is inconsistent.
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1094 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  all_56_13 = e3
% 154.24/23.39    (2)  all_56_13 = e0
% 154.24/23.39    (3)   ~ (e3 = e0)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | COMBINE_EQS: (1), (2) imply:
% 154.24/23.39  |   (4)  e3 = e0
% 154.24/23.39  | 
% 154.24/23.39  | SIMP: (4) implies:
% 154.24/23.39  |   (5)  e3 = e0
% 154.24/23.39  | 
% 154.24/23.39  | REDUCE: (3), (5) imply:
% 154.24/23.39  |   (6)  $false
% 154.24/23.39  | 
% 154.24/23.39  | CLOSE: (6) is inconsistent.
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1095 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)   ~ (e3 = e1)
% 154.24/23.39    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 154.24/23.39         (all_56_14 = e0 & op(e0, e1) = e0)
% 154.24/23.39    (3)  op(e0, e0) = all_10_2
% 154.24/23.39    (4)  op(e0, e2) = all_52_7
% 154.24/23.39    (5)   ~ (all_52_3 = all_52_7)
% 154.24/23.39    (6)   ~ (all_10_2 = e1)
% 154.24/23.39    (7)   ~ (e2 = e0)
% 154.24/23.39    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.39    (9)  all_56_12 = e0 & op(e0, e3) = e0
% 154.24/23.39    (10)   ~ (e3 = e0)
% 154.24/23.39    (11)  op(e0, e3) = all_52_3
% 154.24/23.39    (12)  op(e2, e2) = e2
% 154.24/23.39    (13)   ~ (e1 = e0)
% 154.24/23.39    (14)  all_56_13 = e3
% 154.24/23.39    (15)   ~ (e3 = e2)
% 154.24/23.39    (16)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) = e2)
% 154.24/23.39          | (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 154.24/23.39            e2)
% 154.24/23.39    (17)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.24/23.39          (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.24/23.39    (18)   ~ (all_10_2 = e2)
% 154.24/23.39    (19)   ~ (e2 = e1)
% 154.24/23.39    (20)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.24/23.39          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.24/23.39    (21)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 154.24/23.39          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 154.24/23.39    (22)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.24/23.39          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 154.24/23.39            e1)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | ALPHA: (9) implies:
% 154.24/23.39  |   (23)  op(e0, e3) = e0
% 154.24/23.39  | 
% 154.24/23.39  | BETA: splitting (16) gives:
% 154.24/23.39  | 
% 154.24/23.39  | Case 1:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (24)  (all_56_12 = e2 & op(e0, e3) = e2) | (all_56_13 = e2 & op(e0, e2) =
% 154.24/23.39  | |           e2)
% 154.24/23.39  | | 
% 154.24/23.39  | | BETA: splitting (24) gives:
% 154.24/23.39  | | 
% 154.24/23.39  | | Case 1:
% 154.24/23.39  | | | 
% 154.24/23.39  | | |   (25)  all_56_12 = e2 & op(e0, e3) = e2
% 154.24/23.39  | | | 
% 154.24/23.39  | | | ALPHA: (25) implies:
% 154.24/23.39  | | |   (26)  all_56_12 = e2
% 154.24/23.39  | | | 
% 154.24/23.39  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (13), (14), (19),
% 154.24/23.39  | | |            (22), (23), (26) are inconsistent by sub-proof #1115.
% 154.24/23.39  | | | 
% 154.24/23.39  | | Case 2:
% 154.24/23.39  | | | 
% 154.24/23.39  | | |   (27)  all_56_13 = e2 & op(e0, e2) = e2
% 154.24/23.39  | | | 
% 154.24/23.39  | | | ALPHA: (27) implies:
% 154.24/23.39  | | |   (28)  all_56_13 = e2
% 154.24/23.39  | | | 
% 154.24/23.39  | | | REF_CLOSE: (1), (7), (8), (10), (12), (13), (15), (17), (19), (20), (21),
% 154.24/23.39  | | |            (28) are inconsistent by sub-proof #1104.
% 154.24/23.39  | | | 
% 154.24/23.39  | | End of split
% 154.24/23.39  | | 
% 154.24/23.39  | Case 2:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (29)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) =
% 154.24/23.39  | |           e2)
% 154.24/23.39  | | 
% 154.24/23.39  | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (10), (13), (14), (18), (19), (22),
% 154.24/23.39  | |            (29) are inconsistent by sub-proof #1096.
% 154.24/23.39  | | 
% 154.24/23.39  | End of split
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1096 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)   ~ (e3 = e1)
% 154.24/23.39    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 154.24/23.39         (all_56_14 = e0 & op(e0, e1) = e0)
% 154.24/23.39    (3)  op(e0, e0) = all_10_2
% 154.24/23.39    (4)   ~ (all_10_2 = e1)
% 154.24/23.39    (5)   ~ (e2 = e0)
% 154.24/23.39    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.39    (7)   ~ (e3 = e0)
% 154.24/23.39    (8)   ~ (e1 = e0)
% 154.24/23.39    (9)  all_56_13 = e3
% 154.24/23.39    (10)   ~ (all_10_2 = e2)
% 154.24/23.39    (11)   ~ (e2 = e1)
% 154.24/23.39    (12)  (all_56_14 = e2 & op(e0, e1) = e2) | (all_56_15 = e2 & op(e0, e0) = e2)
% 154.24/23.39    (13)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.24/23.39          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 154.24/23.39            e1)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | BETA: splitting (12) gives:
% 154.24/23.39  | 
% 154.24/23.39  | Case 1:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (14)  all_56_14 = e2 & op(e0, e1) = e2
% 154.24/23.39  | | 
% 154.24/23.39  | | ALPHA: (14) implies:
% 154.24/23.39  | |   (15)  all_56_14 = e2
% 154.24/23.39  | | 
% 154.24/23.39  | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (13), (15) are
% 154.24/23.39  | |            inconsistent by sub-proof #1098.
% 154.24/23.39  | | 
% 154.24/23.39  | Case 2:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (16)  all_56_15 = e2 & op(e0, e0) = e2
% 154.24/23.39  | | 
% 154.24/23.39  | | ALPHA: (16) implies:
% 154.24/23.39  | |   (17)  op(e0, e0) = e2
% 154.24/23.39  | | 
% 154.24/23.39  | | REF_CLOSE: (3), (6), (10), (17) are inconsistent by sub-proof #1097.
% 154.24/23.39  | | 
% 154.24/23.39  | End of split
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1097 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.39    (2)  op(e0, e0) = all_10_2
% 154.24/23.39    (3)  op(e0, e0) = e2
% 154.24/23.39    (4)   ~ (all_10_2 = e2)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | GROUND_INST: instantiating (1) with all_10_2, e2, e0, e0, simplifying with
% 154.24/23.39  |              (2), (3) gives:
% 154.24/23.39  |   (5)  all_10_2 = e2
% 154.24/23.39  | 
% 154.24/23.39  | REDUCE: (4), (5) imply:
% 154.24/23.39  |   (6)  $false
% 154.24/23.39  | 
% 154.24/23.39  | CLOSE: (6) is inconsistent.
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1098 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)   ~ (e3 = e1)
% 154.24/23.39    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 154.24/23.39         (all_56_14 = e0 & op(e0, e1) = e0)
% 154.24/23.39    (3)  op(e0, e0) = all_10_2
% 154.24/23.39    (4)   ~ (all_10_2 = e1)
% 154.24/23.39    (5)   ~ (e2 = e0)
% 154.24/23.39    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.39    (7)  all_56_14 = e2
% 154.24/23.39    (8)   ~ (e3 = e0)
% 154.24/23.39    (9)   ~ (e1 = e0)
% 154.24/23.39    (10)  all_56_13 = e3
% 154.24/23.39    (11)   ~ (e2 = e1)
% 154.24/23.39    (12)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.24/23.39          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 154.24/23.39            e1)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | BETA: splitting (12) gives:
% 154.24/23.39  | 
% 154.24/23.39  | Case 1:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (13)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 154.24/23.39  | |           e1)
% 154.24/23.39  | | 
% 154.24/23.39  | | BETA: splitting (13) gives:
% 154.24/23.39  | | 
% 154.24/23.39  | | Case 1:
% 154.24/23.39  | | | 
% 154.24/23.39  | | |   (14)  all_56_12 = e1 & op(e0, e3) = e1
% 154.24/23.39  | | | 
% 154.24/23.39  | | | ALPHA: (14) implies:
% 154.24/23.39  | | |   (15)  all_56_12 = e1
% 154.24/23.39  | | | 
% 154.24/23.39  | | | REF_CLOSE: (2), (5), (7), (8), (9), (10), (15) are inconsistent by
% 154.24/23.39  | | |            sub-proof #1100.
% 154.24/23.39  | | | 
% 154.24/23.39  | | Case 2:
% 154.24/23.39  | | | 
% 154.24/23.39  | | |   (16)  all_56_13 = e1 & op(e0, e2) = e1
% 154.24/23.39  | | | 
% 154.24/23.39  | | | ALPHA: (16) implies:
% 154.24/23.39  | | |   (17)  all_56_13 = e1
% 154.24/23.39  | | | 
% 154.24/23.39  | | | REF_CLOSE: (1), (10), (17) are inconsistent by sub-proof #1121.
% 154.24/23.39  | | | 
% 154.24/23.39  | | End of split
% 154.24/23.39  | | 
% 154.24/23.39  | Case 2:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (18)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 154.24/23.39  | |           e1)
% 154.24/23.39  | | 
% 154.24/23.39  | | BETA: splitting (18) gives:
% 154.24/23.39  | | 
% 154.24/23.39  | | Case 1:
% 154.24/23.39  | | | 
% 154.24/23.39  | | |   (19)  all_56_14 = e1 & op(e0, e1) = e1
% 154.24/23.39  | | | 
% 154.24/23.39  | | | ALPHA: (19) implies:
% 154.24/23.39  | | |   (20)  all_56_14 = e1
% 154.24/23.39  | | | 
% 154.24/23.39  | | | REF_CLOSE: (7), (11), (20) are inconsistent by sub-proof #1099.
% 154.24/23.39  | | | 
% 154.24/23.39  | | Case 2:
% 154.24/23.39  | | | 
% 154.24/23.39  | | |   (21)  all_56_15 = e1 & op(e0, e0) = e1
% 154.24/23.39  | | | 
% 154.24/23.39  | | | ALPHA: (21) implies:
% 154.24/23.39  | | |   (22)  op(e0, e0) = e1
% 154.24/23.39  | | | 
% 154.24/23.39  | | | REF_CLOSE: (3), (4), (6), (22) are inconsistent by sub-proof #1116.
% 154.24/23.39  | | | 
% 154.24/23.39  | | End of split
% 154.24/23.39  | | 
% 154.24/23.39  | End of split
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1099 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  all_56_14 = e2
% 154.24/23.39    (2)  all_56_14 = e1
% 154.24/23.39    (3)   ~ (e2 = e1)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | COMBINE_EQS: (1), (2) imply:
% 154.24/23.39  |   (4)  e2 = e1
% 154.24/23.39  | 
% 154.24/23.39  | SIMP: (4) implies:
% 154.24/23.39  |   (5)  e2 = e1
% 154.24/23.39  | 
% 154.24/23.39  | REDUCE: (3), (5) imply:
% 154.24/23.39  |   (6)  $false
% 154.24/23.39  | 
% 154.24/23.39  | CLOSE: (6) is inconsistent.
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1100 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 154.24/23.39         (all_56_14 = e0 & op(e0, e1) = e0)
% 154.24/23.39    (2)   ~ (e2 = e0)
% 154.24/23.39    (3)  all_56_14 = e2
% 154.24/23.39    (4)  all_56_12 = e1
% 154.24/23.39    (5)   ~ (e3 = e0)
% 154.24/23.39    (6)   ~ (e1 = e0)
% 154.24/23.39    (7)  all_56_13 = e3
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | BETA: splitting (1) gives:
% 154.24/23.39  | 
% 154.24/23.39  | Case 1:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (8)  all_56_12 = e0 & op(e0, e3) = e0
% 154.24/23.39  | | 
% 154.24/23.39  | | REF_CLOSE: (4), (6), (8) are inconsistent by sub-proof #1103.
% 154.24/23.39  | | 
% 154.24/23.39  | Case 2:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (9)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 154.24/23.39  | |          e0)
% 154.24/23.39  | | 
% 154.24/23.39  | | BETA: splitting (9) gives:
% 154.24/23.39  | | 
% 154.24/23.39  | | Case 1:
% 154.24/23.39  | | | 
% 154.24/23.39  | | |   (10)  all_56_13 = e0 & op(e0, e2) = e0
% 154.24/23.39  | | | 
% 154.24/23.39  | | | REF_CLOSE: (5), (7), (10) are inconsistent by sub-proof #1102.
% 154.24/23.39  | | | 
% 154.24/23.39  | | Case 2:
% 154.24/23.39  | | | 
% 154.24/23.39  | | |   (11)  all_56_14 = e0 & op(e0, e1) = e0
% 154.24/23.39  | | | 
% 154.24/23.39  | | | REF_CLOSE: (2), (3), (11) are inconsistent by sub-proof #1101.
% 154.24/23.39  | | | 
% 154.24/23.39  | | End of split
% 154.24/23.39  | | 
% 154.24/23.39  | End of split
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1101 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  all_56_14 = e0 & op(e0, e1) = e0
% 154.24/23.39    (2)  all_56_14 = e2
% 154.24/23.39    (3)   ~ (e2 = e0)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | ALPHA: (1) implies:
% 154.24/23.39  |   (4)  all_56_14 = e0
% 154.24/23.39  | 
% 154.24/23.39  | COMBINE_EQS: (2), (4) imply:
% 154.24/23.39  |   (5)  e2 = e0
% 154.24/23.39  | 
% 154.24/23.39  | REDUCE: (3), (5) imply:
% 154.24/23.39  |   (6)  $false
% 154.24/23.39  | 
% 154.24/23.39  | CLOSE: (6) is inconsistent.
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1102 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  all_56_13 = e0 & op(e0, e2) = e0
% 154.24/23.39    (2)  all_56_13 = e3
% 154.24/23.39    (3)   ~ (e3 = e0)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | ALPHA: (1) implies:
% 154.24/23.39  |   (4)  all_56_13 = e0
% 154.24/23.39  | 
% 154.24/23.39  | COMBINE_EQS: (2), (4) imply:
% 154.24/23.39  |   (5)  e3 = e0
% 154.24/23.39  | 
% 154.24/23.39  | REDUCE: (3), (5) imply:
% 154.24/23.39  |   (6)  $false
% 154.24/23.39  | 
% 154.24/23.39  | CLOSE: (6) is inconsistent.
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1103 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  all_56_12 = e0 & op(e0, e3) = e0
% 154.24/23.39    (2)  all_56_12 = e1
% 154.24/23.39    (3)   ~ (e1 = e0)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | ALPHA: (1) implies:
% 154.24/23.39  |   (4)  all_56_12 = e0
% 154.24/23.39  | 
% 154.24/23.39  | COMBINE_EQS: (2), (4) imply:
% 154.24/23.39  |   (5)  e1 = e0
% 154.24/23.39  | 
% 154.24/23.39  | REDUCE: (3), (5) imply:
% 154.24/23.39  |   (6)  $false
% 154.24/23.39  | 
% 154.24/23.39  | CLOSE: (6) is inconsistent.
% 154.24/23.39  | 
% 154.24/23.39  End of proof
% 154.24/23.39  
% 154.24/23.39  Sub-proof #1104 shows that the following formulas are inconsistent:
% 154.24/23.39  ----------------------------------------------------------------
% 154.24/23.39    (1)  all_56_13 = e2
% 154.24/23.39    (2)   ~ (e3 = e1)
% 154.24/23.39    (3)   ~ (e2 = e0)
% 154.24/23.39    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.24/23.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.24/23.39    (5)   ~ (e3 = e0)
% 154.24/23.39    (6)  op(e2, e2) = e2
% 154.24/23.39    (7)   ~ (e1 = e0)
% 154.24/23.39    (8)   ~ (e3 = e2)
% 154.24/23.39    (9)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.24/23.39         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.24/23.39    (10)   ~ (e2 = e1)
% 154.24/23.39    (11)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.24/23.39          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.24/23.39    (12)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 154.24/23.39          (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) = e3)
% 154.24/23.39  
% 154.24/23.39  Begin of proof
% 154.24/23.39  | 
% 154.24/23.39  | BETA: splitting (12) gives:
% 154.24/23.39  | 
% 154.24/23.39  | Case 1:
% 154.24/23.39  | | 
% 154.24/23.39  | |   (13)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 154.24/23.39  | |           e3)
% 154.24/23.39  | | 
% 154.24/23.39  | | BETA: splitting (13) gives:
% 154.24/23.39  | | 
% 154.24/23.39  | | Case 1:
% 154.24/23.39  | | | 
% 154.24/23.39  | | |   (14)  all_56_1 = e3 & op(e3, e2) = e3
% 154.24/23.39  | | | 
% 154.24/23.39  | | | ALPHA: (14) implies:
% 154.24/23.39  | | |   (15)  all_56_1 = e3
% 154.24/23.39  | | | 
% 154.24/23.39  | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (15) are
% 154.24/23.39  | | |            inconsistent by sub-proof #1108.
% 154.24/23.39  | | | 
% 154.24/23.39  | | Case 2:
% 154.24/23.39  | | | 
% 154.24/23.39  | | |   (16)  all_56_3 = e3 & op(e2, e2) = e3
% 154.24/23.39  | | | 
% 154.26/23.39  | | | ALPHA: (16) implies:
% 154.26/23.39  | | |   (17)  op(e2, e2) = e3
% 154.26/23.39  | | | 
% 154.26/23.39  | | | GROUND_INST: instantiating (4) with e2, e3, e2, e2, simplifying with (6),
% 154.26/23.39  | | |              (17) gives:
% 154.26/23.39  | | |   (18)  e3 = e2
% 154.26/23.39  | | | 
% 154.26/23.39  | | | REDUCE: (8), (18) imply:
% 154.26/23.39  | | |   (19)  $false
% 154.26/23.39  | | | 
% 154.26/23.39  | | | CLOSE: (19) is inconsistent.
% 154.26/23.39  | | | 
% 154.26/23.39  | | End of split
% 154.26/23.39  | | 
% 154.26/23.39  | Case 2:
% 154.26/23.39  | | 
% 154.26/23.39  | |   (20)  (all_56_7 = e3 & op(e1, e2) = e3) | (all_56_13 = e3 & op(e0, e2) =
% 154.26/23.39  | |           e3)
% 154.26/23.39  | | 
% 154.26/23.39  | | BETA: splitting (20) gives:
% 154.26/23.39  | | 
% 154.26/23.39  | | Case 1:
% 154.26/23.39  | | | 
% 154.26/23.39  | | |   (21)  all_56_7 = e3 & op(e1, e2) = e3
% 154.26/23.39  | | | 
% 154.26/23.39  | | | ALPHA: (21) implies:
% 154.26/23.39  | | |   (22)  all_56_7 = e3
% 154.26/23.39  | | | 
% 154.26/23.39  | | | BETA: splitting (9) gives:
% 154.26/23.39  | | | 
% 154.26/23.39  | | | Case 1:
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | |   (23)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2)
% 154.26/23.39  | | | |           = e0)
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | | BETA: splitting (23) gives:
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | | Case 1:
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | |   (24)  all_56_1 = e0 & op(e3, e2) = e0
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | ALPHA: (24) implies:
% 154.26/23.39  | | | | |   (25)  all_56_1 = e0
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | BETA: splitting (11) gives:
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | Case 1:
% 154.26/23.39  | | | | | | 
% 154.26/23.39  | | | | | |   (26)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2,
% 154.26/23.39  | | | | | |             e2) = e1)
% 154.26/23.39  | | | | | | 
% 154.26/23.39  | | | | | | BETA: splitting (26) gives:
% 154.26/23.39  | | | | | | 
% 154.26/23.39  | | | | | | Case 1:
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | |   (27)  all_56_1 = e1 & op(e3, e2) = e1
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | | ALPHA: (27) implies:
% 154.26/23.39  | | | | | | |   (28)  all_56_1 = e1
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | | REF_CLOSE: (7), (25), (28) are inconsistent by sub-proof #1107.
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | Case 2:
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | |   (29)  all_56_3 = e1 & op(e2, e2) = e1
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | | ALPHA: (29) implies:
% 154.26/23.39  | | | | | | |   (30)  op(e2, e2) = e1
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | | REF_CLOSE: (4), (6), (10), (30) are inconsistent by sub-proof
% 154.26/23.39  | | | | | | |            #1158.
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | End of split
% 154.26/23.39  | | | | | | 
% 154.26/23.39  | | | | | Case 2:
% 154.26/23.39  | | | | | | 
% 154.26/23.39  | | | | | |   (31)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0,
% 154.26/23.39  | | | | | |             e2) = e1)
% 154.26/23.39  | | | | | | 
% 154.26/23.39  | | | | | | BETA: splitting (31) gives:
% 154.26/23.39  | | | | | | 
% 154.26/23.39  | | | | | | Case 1:
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | |   (32)  all_56_7 = e1 & op(e1, e2) = e1
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | | ALPHA: (32) implies:
% 154.26/23.39  | | | | | | |   (33)  all_56_7 = e1
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | | REF_CLOSE: (2), (22), (33) are inconsistent by sub-proof #1106.
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | Case 2:
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | |   (34)  all_56_13 = e1 & op(e0, e2) = e1
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | | ALPHA: (34) implies:
% 154.26/23.39  | | | | | | |   (35)  all_56_13 = e1
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | | REF_CLOSE: (1), (10), (35) are inconsistent by sub-proof #1110.
% 154.26/23.39  | | | | | | | 
% 154.26/23.39  | | | | | | End of split
% 154.26/23.39  | | | | | | 
% 154.26/23.39  | | | | | End of split
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | Case 2:
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | |   (36)  all_56_3 = e0 & op(e2, e2) = e0
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | ALPHA: (36) implies:
% 154.26/23.39  | | | | |   (37)  op(e2, e2) = e0
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | REF_CLOSE: (3), (4), (6), (37) are inconsistent by sub-proof #1145.
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | End of split
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | Case 2:
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | |   (38)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2)
% 154.26/23.39  | | | |           = e0)
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | | BETA: splitting (38) gives:
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | | Case 1:
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | |   (39)  all_56_7 = e0 & op(e1, e2) = e0
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | REF_CLOSE: (5), (22), (39) are inconsistent by sub-proof #1151.
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | Case 2:
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | |   (40)  all_56_13 = e0 & op(e0, e2) = e0
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | REF_CLOSE: (1), (3), (40) are inconsistent by sub-proof #1109.
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | End of split
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | End of split
% 154.26/23.39  | | | 
% 154.26/23.39  | | Case 2:
% 154.26/23.39  | | | 
% 154.26/23.39  | | |   (41)  all_56_13 = e3 & op(e0, e2) = e3
% 154.26/23.39  | | | 
% 154.26/23.39  | | | ALPHA: (41) implies:
% 154.26/23.39  | | |   (42)  all_56_13 = e3
% 154.26/23.39  | | | 
% 154.26/23.39  | | | REF_CLOSE: (1), (8), (42) are inconsistent by sub-proof #1105.
% 154.26/23.39  | | | 
% 154.26/23.39  | | End of split
% 154.26/23.39  | | 
% 154.26/23.39  | End of split
% 154.26/23.39  | 
% 154.26/23.39  End of proof
% 154.26/23.39  
% 154.26/23.39  Sub-proof #1105 shows that the following formulas are inconsistent:
% 154.26/23.39  ----------------------------------------------------------------
% 154.26/23.39    (1)  all_56_13 = e3
% 154.26/23.39    (2)  all_56_13 = e2
% 154.26/23.39    (3)   ~ (e3 = e2)
% 154.26/23.39  
% 154.26/23.39  Begin of proof
% 154.26/23.39  | 
% 154.26/23.39  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.39  |   (4)  e3 = e2
% 154.26/23.39  | 
% 154.26/23.39  | SIMP: (4) implies:
% 154.26/23.39  |   (5)  e3 = e2
% 154.26/23.39  | 
% 154.26/23.39  | REDUCE: (3), (5) imply:
% 154.26/23.39  |   (6)  $false
% 154.26/23.39  | 
% 154.26/23.39  | CLOSE: (6) is inconsistent.
% 154.26/23.39  | 
% 154.26/23.39  End of proof
% 154.26/23.39  
% 154.26/23.39  Sub-proof #1106 shows that the following formulas are inconsistent:
% 154.26/23.39  ----------------------------------------------------------------
% 154.26/23.39    (1)  all_56_7 = e3
% 154.26/23.39    (2)  all_56_7 = e1
% 154.26/23.39    (3)   ~ (e3 = e1)
% 154.26/23.39  
% 154.26/23.39  Begin of proof
% 154.26/23.39  | 
% 154.26/23.39  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.39  |   (4)  e3 = e1
% 154.26/23.39  | 
% 154.26/23.39  | SIMP: (4) implies:
% 154.26/23.39  |   (5)  e3 = e1
% 154.26/23.39  | 
% 154.26/23.39  | REDUCE: (3), (5) imply:
% 154.26/23.39  |   (6)  $false
% 154.26/23.39  | 
% 154.26/23.39  | CLOSE: (6) is inconsistent.
% 154.26/23.39  | 
% 154.26/23.39  End of proof
% 154.26/23.39  
% 154.26/23.39  Sub-proof #1107 shows that the following formulas are inconsistent:
% 154.26/23.39  ----------------------------------------------------------------
% 154.26/23.39    (1)  all_56_1 = e1
% 154.26/23.39    (2)  all_56_1 = e0
% 154.26/23.39    (3)   ~ (e1 = e0)
% 154.26/23.39  
% 154.26/23.39  Begin of proof
% 154.26/23.39  | 
% 154.26/23.39  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.39  |   (4)  e1 = e0
% 154.26/23.39  | 
% 154.26/23.39  | SIMP: (4) implies:
% 154.26/23.39  |   (5)  e1 = e0
% 154.26/23.39  | 
% 154.26/23.39  | REDUCE: (3), (5) imply:
% 154.26/23.39  |   (6)  $false
% 154.26/23.39  | 
% 154.26/23.39  | CLOSE: (6) is inconsistent.
% 154.26/23.39  | 
% 154.26/23.39  End of proof
% 154.26/23.39  
% 154.26/23.39  Sub-proof #1108 shows that the following formulas are inconsistent:
% 154.26/23.39  ----------------------------------------------------------------
% 154.26/23.39    (1)  all_56_13 = e2
% 154.26/23.39    (2)   ~ (e3 = e1)
% 154.26/23.39    (3)   ~ (e2 = e0)
% 154.26/23.39    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.39           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.39    (5)   ~ (e3 = e0)
% 154.26/23.39    (6)  op(e2, e2) = e2
% 154.26/23.39    (7)   ~ (e1 = e0)
% 154.26/23.39    (8)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0) |
% 154.26/23.39         (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) = e0)
% 154.26/23.39    (9)   ~ (e2 = e1)
% 154.26/23.39    (10)  all_56_1 = e3
% 154.26/23.39    (11)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2) = e1) |
% 154.26/23.39          (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.26/23.39  
% 154.26/23.39  Begin of proof
% 154.26/23.39  | 
% 154.26/23.39  | BETA: splitting (8) gives:
% 154.26/23.39  | 
% 154.26/23.39  | Case 1:
% 154.26/23.39  | | 
% 154.26/23.39  | |   (12)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) =
% 154.26/23.39  | |           e0)
% 154.26/23.39  | | 
% 154.26/23.39  | | REF_CLOSE: (3), (4), (5), (6), (10), (12) are inconsistent by sub-proof
% 154.26/23.39  | |            #1113.
% 154.26/23.39  | | 
% 154.26/23.39  | Case 2:
% 154.26/23.39  | | 
% 154.26/23.39  | |   (13)  (all_56_7 = e0 & op(e1, e2) = e0) | (all_56_13 = e0 & op(e0, e2) =
% 154.26/23.39  | |           e0)
% 154.26/23.39  | | 
% 154.26/23.39  | | BETA: splitting (13) gives:
% 154.26/23.39  | | 
% 154.26/23.39  | | Case 1:
% 154.26/23.39  | | | 
% 154.26/23.39  | | |   (14)  all_56_7 = e0 & op(e1, e2) = e0
% 154.26/23.39  | | | 
% 154.26/23.39  | | | ALPHA: (14) implies:
% 154.26/23.39  | | |   (15)  all_56_7 = e0
% 154.26/23.39  | | | 
% 154.26/23.39  | | | BETA: splitting (11) gives:
% 154.26/23.39  | | | 
% 154.26/23.39  | | | Case 1:
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | |   (16)  (all_56_1 = e1 & op(e3, e2) = e1) | (all_56_3 = e1 & op(e2, e2)
% 154.26/23.39  | | | |           = e1)
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | | BETA: splitting (16) gives:
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | | Case 1:
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | |   (17)  all_56_1 = e1 & op(e3, e2) = e1
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | REF_CLOSE: (2), (10), (17) are inconsistent by sub-proof #1112.
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | Case 2:
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | |   (18)  all_56_3 = e1 & op(e2, e2) = e1
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | ALPHA: (18) implies:
% 154.26/23.39  | | | | |   (19)  op(e2, e2) = e1
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | GROUND_INST: instantiating (4) with e1, e2, e2, e2, simplifying with
% 154.26/23.39  | | | | |              (6), (19) gives:
% 154.26/23.39  | | | | |   (20)  e2 = e1
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | REDUCE: (9), (20) imply:
% 154.26/23.39  | | | | |   (21)  $false
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | CLOSE: (21) is inconsistent.
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | End of split
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | Case 2:
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | |   (22)  (all_56_7 = e1 & op(e1, e2) = e1) | (all_56_13 = e1 & op(e0, e2)
% 154.26/23.39  | | | |           = e1)
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | | BETA: splitting (22) gives:
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | | Case 1:
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | |   (23)  all_56_7 = e1 & op(e1, e2) = e1
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | REF_CLOSE: (7), (15), (23) are inconsistent by sub-proof #1111.
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | Case 2:
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | |   (24)  all_56_13 = e1 & op(e0, e2) = e1
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | ALPHA: (24) implies:
% 154.26/23.39  | | | | |   (25)  all_56_13 = e1
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | | REF_CLOSE: (1), (9), (25) are inconsistent by sub-proof #1110.
% 154.26/23.39  | | | | | 
% 154.26/23.39  | | | | End of split
% 154.26/23.39  | | | | 
% 154.26/23.39  | | | End of split
% 154.26/23.39  | | | 
% 154.26/23.39  | | Case 2:
% 154.26/23.39  | | | 
% 154.26/23.39  | | |   (26)  all_56_13 = e0 & op(e0, e2) = e0
% 154.26/23.39  | | | 
% 154.26/23.39  | | | REF_CLOSE: (1), (3), (26) are inconsistent by sub-proof #1109.
% 154.26/23.39  | | | 
% 154.26/23.39  | | End of split
% 154.26/23.39  | | 
% 154.26/23.39  | End of split
% 154.26/23.39  | 
% 154.26/23.39  End of proof
% 154.26/23.39  
% 154.26/23.39  Sub-proof #1109 shows that the following formulas are inconsistent:
% 154.26/23.39  ----------------------------------------------------------------
% 154.26/23.39    (1)  all_56_13 = e0 & op(e0, e2) = e0
% 154.26/23.39    (2)  all_56_13 = e2
% 154.26/23.40    (3)   ~ (e2 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | ALPHA: (1) implies:
% 154.26/23.40  |   (4)  all_56_13 = e0
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.40  |   (5)  e2 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1110 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_13 = e2
% 154.26/23.40    (2)  all_56_13 = e1
% 154.26/23.40    (3)   ~ (e2 = e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.40  |   (4)  e2 = e1
% 154.26/23.40  | 
% 154.26/23.40  | SIMP: (4) implies:
% 154.26/23.40  |   (5)  e2 = e1
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1111 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_7 = e1 & op(e1, e2) = e1
% 154.26/23.40    (2)  all_56_7 = e0
% 154.26/23.40    (3)   ~ (e1 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | ALPHA: (1) implies:
% 154.26/23.40  |   (4)  all_56_7 = e1
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.40  |   (5)  e1 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1112 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_1 = e1 & op(e3, e2) = e1
% 154.26/23.40    (2)  all_56_1 = e3
% 154.26/23.40    (3)   ~ (e3 = e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | ALPHA: (1) implies:
% 154.26/23.40  |   (4)  all_56_1 = e1
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.40  |   (5)  e3 = e1
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1113 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  (all_56_1 = e0 & op(e3, e2) = e0) | (all_56_3 = e0 & op(e2, e2) = e0)
% 154.26/23.40    (2)   ~ (e2 = e0)
% 154.26/23.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (4)   ~ (e3 = e0)
% 154.26/23.40    (5)  op(e2, e2) = e2
% 154.26/23.40    (6)  all_56_1 = e3
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | BETA: splitting (1) gives:
% 154.26/23.40  | 
% 154.26/23.40  | Case 1:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (7)  all_56_1 = e0 & op(e3, e2) = e0
% 154.26/23.40  | | 
% 154.26/23.40  | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #1114.
% 154.26/23.40  | | 
% 154.26/23.40  | Case 2:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (8)  all_56_3 = e0 & op(e2, e2) = e0
% 154.26/23.40  | | 
% 154.26/23.40  | | ALPHA: (8) implies:
% 154.26/23.40  | |   (9)  op(e2, e2) = e0
% 154.26/23.40  | | 
% 154.26/23.40  | | REF_CLOSE: (2), (3), (5), (9) are inconsistent by sub-proof #1145.
% 154.26/23.40  | | 
% 154.26/23.40  | End of split
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1114 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_1 = e0 & op(e3, e2) = e0
% 154.26/23.40    (2)  all_56_1 = e3
% 154.26/23.40    (3)   ~ (e3 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | ALPHA: (1) implies:
% 154.26/23.40  |   (4)  all_56_1 = e0
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.40  |   (5)  e3 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1115 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)   ~ (e3 = e1)
% 154.26/23.40    (2)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 154.26/23.40         (all_56_14 = e0 & op(e0, e1) = e0)
% 154.26/23.40    (3)  op(e0, e0) = all_10_2
% 154.26/23.40    (4)  op(e0, e2) = all_52_7
% 154.26/23.40    (5)   ~ (all_52_3 = all_52_7)
% 154.26/23.40    (6)   ~ (all_10_2 = e1)
% 154.26/23.40    (7)   ~ (e2 = e0)
% 154.26/23.40    (8)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (9)  op(e0, e3) = e0
% 154.26/23.40    (10)  op(e0, e3) = all_52_3
% 154.26/23.40    (11)   ~ (e1 = e0)
% 154.26/23.40    (12)  all_56_13 = e3
% 154.26/23.40    (13)  all_56_12 = e2
% 154.26/23.40    (14)   ~ (e2 = e1)
% 154.26/23.40    (15)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.26/23.40          | (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 154.26/23.40            e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | BETA: splitting (15) gives:
% 154.26/23.40  | 
% 154.26/23.40  | Case 1:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (16)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) =
% 154.26/23.40  | |           e1)
% 154.26/23.40  | | 
% 154.26/23.40  | | REF_CLOSE: (1), (12), (13), (14), (16) are inconsistent by sub-proof #1120.
% 154.26/23.40  | | 
% 154.26/23.40  | Case 2:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (17)  (all_56_14 = e1 & op(e0, e1) = e1) | (all_56_15 = e1 & op(e0, e0) =
% 154.26/23.40  | |           e1)
% 154.26/23.40  | | 
% 154.26/23.40  | | BETA: splitting (17) gives:
% 154.26/23.40  | | 
% 154.26/23.40  | | Case 1:
% 154.26/23.40  | | | 
% 154.26/23.40  | | |   (18)  all_56_14 = e1 & op(e0, e1) = e1
% 154.26/23.40  | | | 
% 154.26/23.40  | | | ALPHA: (18) implies:
% 154.26/23.40  | | |   (19)  all_56_14 = e1
% 154.26/23.40  | | | 
% 154.26/23.40  | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (13), (19) are
% 154.26/23.40  | | |            inconsistent by sub-proof #1117.
% 154.26/23.40  | | | 
% 154.26/23.40  | | Case 2:
% 154.26/23.40  | | | 
% 154.26/23.40  | | |   (20)  all_56_15 = e1 & op(e0, e0) = e1
% 154.26/23.40  | | | 
% 154.26/23.40  | | | ALPHA: (20) implies:
% 154.26/23.40  | | |   (21)  op(e0, e0) = e1
% 154.26/23.40  | | | 
% 154.26/23.40  | | | REF_CLOSE: (3), (6), (8), (21) are inconsistent by sub-proof #1116.
% 154.26/23.40  | | | 
% 154.26/23.40  | | End of split
% 154.26/23.40  | | 
% 154.26/23.40  | End of split
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1116 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (2)  op(e0, e0) = all_10_2
% 154.26/23.40    (3)  op(e0, e0) = e1
% 154.26/23.40    (4)   ~ (all_10_2 = e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | GROUND_INST: instantiating (1) with all_10_2, e1, e0, e0, simplifying with
% 154.26/23.40  |              (2), (3) gives:
% 154.26/23.40  |   (5)  all_10_2 = e1
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (4), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1117 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  (all_56_12 = e0 & op(e0, e3) = e0) | (all_56_13 = e0 & op(e0, e2) = e0) |
% 154.26/23.40         (all_56_14 = e0 & op(e0, e1) = e0)
% 154.26/23.40    (2)  op(e0, e2) = all_52_7
% 154.26/23.40    (3)   ~ (all_52_3 = all_52_7)
% 154.26/23.40    (4)   ~ (e2 = e0)
% 154.26/23.40    (5)  all_56_14 = e1
% 154.26/23.40    (6)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (7)  op(e0, e3) = e0
% 154.26/23.40    (8)  op(e0, e3) = all_52_3
% 154.26/23.40    (9)   ~ (e1 = e0)
% 154.26/23.40    (10)  all_56_12 = e2
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | BETA: splitting (1) gives:
% 154.26/23.40  | 
% 154.26/23.40  | Case 1:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (11)  all_56_12 = e0 & op(e0, e3) = e0
% 154.26/23.40  | | 
% 154.26/23.40  | | ALPHA: (11) implies:
% 154.26/23.40  | |   (12)  all_56_12 = e0
% 154.26/23.40  | | 
% 154.26/23.40  | | REF_CLOSE: (4), (10), (12) are inconsistent by sub-proof #1119.
% 154.26/23.40  | | 
% 154.26/23.40  | Case 2:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (13)  (all_56_13 = e0 & op(e0, e2) = e0) | (all_56_14 = e0 & op(e0, e1) =
% 154.26/23.40  | |           e0)
% 154.26/23.40  | | 
% 154.26/23.40  | | BETA: splitting (13) gives:
% 154.26/23.40  | | 
% 154.26/23.40  | | Case 1:
% 154.26/23.40  | | | 
% 154.26/23.40  | | |   (14)  all_56_13 = e0 & op(e0, e2) = e0
% 154.26/23.40  | | | 
% 154.26/23.40  | | | ALPHA: (14) implies:
% 154.26/23.40  | | |   (15)  op(e0, e2) = e0
% 154.26/23.40  | | | 
% 154.26/23.40  | | | REF_CLOSE: (2), (3), (6), (7), (8), (15) are inconsistent by sub-proof
% 154.26/23.40  | | |            #1123.
% 154.26/23.40  | | | 
% 154.26/23.40  | | Case 2:
% 154.26/23.40  | | | 
% 154.26/23.40  | | |   (16)  all_56_14 = e0 & op(e0, e1) = e0
% 154.26/23.40  | | | 
% 154.26/23.40  | | | REF_CLOSE: (5), (9), (16) are inconsistent by sub-proof #1118.
% 154.26/23.40  | | | 
% 154.26/23.40  | | End of split
% 154.26/23.40  | | 
% 154.26/23.40  | End of split
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1118 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_14 = e0 & op(e0, e1) = e0
% 154.26/23.40    (2)  all_56_14 = e1
% 154.26/23.40    (3)   ~ (e1 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | ALPHA: (1) implies:
% 154.26/23.40  |   (4)  all_56_14 = e0
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.40  |   (5)  e1 = e0
% 154.26/23.40  | 
% 154.26/23.40  | SIMP: (5) implies:
% 154.26/23.40  |   (6)  e1 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (6) imply:
% 154.26/23.40  |   (7)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (7) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1119 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_12 = e2
% 154.26/23.40    (2)  all_56_12 = e0
% 154.26/23.40    (3)   ~ (e2 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.40  |   (4)  e2 = e0
% 154.26/23.40  | 
% 154.26/23.40  | SIMP: (4) implies:
% 154.26/23.40  |   (5)  e2 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1120 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)   ~ (e3 = e1)
% 154.26/23.40    (2)  (all_56_12 = e1 & op(e0, e3) = e1) | (all_56_13 = e1 & op(e0, e2) = e1)
% 154.26/23.40    (3)  all_56_13 = e3
% 154.26/23.40    (4)  all_56_12 = e2
% 154.26/23.40    (5)   ~ (e2 = e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | BETA: splitting (2) gives:
% 154.26/23.40  | 
% 154.26/23.40  | Case 1:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (6)  all_56_12 = e1 & op(e0, e3) = e1
% 154.26/23.40  | | 
% 154.26/23.40  | | ALPHA: (6) implies:
% 154.26/23.40  | |   (7)  all_56_12 = e1
% 154.26/23.40  | | 
% 154.26/23.40  | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #1122.
% 154.26/23.40  | | 
% 154.26/23.40  | Case 2:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (8)  all_56_13 = e1 & op(e0, e2) = e1
% 154.26/23.40  | | 
% 154.26/23.40  | | ALPHA: (8) implies:
% 154.26/23.40  | |   (9)  all_56_13 = e1
% 154.26/23.40  | | 
% 154.26/23.40  | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #1121.
% 154.26/23.40  | | 
% 154.26/23.40  | End of split
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1121 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_13 = e3
% 154.26/23.40    (2)  all_56_13 = e1
% 154.26/23.40    (3)   ~ (e3 = e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.40  |   (4)  e3 = e1
% 154.26/23.40  | 
% 154.26/23.40  | SIMP: (4) implies:
% 154.26/23.40  |   (5)  e3 = e1
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1122 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_12 = e2
% 154.26/23.40    (2)  all_56_12 = e1
% 154.26/23.40    (3)   ~ (e2 = e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.40  |   (4)  e2 = e1
% 154.26/23.40  | 
% 154.26/23.40  | SIMP: (4) implies:
% 154.26/23.40  |   (5)  e2 = e1
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1123 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  op(e0, e2) = all_52_7
% 154.26/23.40    (2)   ~ (all_52_3 = all_52_7)
% 154.26/23.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (4)  op(e0, e3) = e0
% 154.26/23.40    (5)  op(e0, e3) = all_52_3
% 154.26/23.40    (6)  op(e0, e2) = e0
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | GROUND_INST: instantiating (3) with all_52_7, e0, e2, e0, simplifying with
% 154.26/23.40  |              (1), (6) gives:
% 154.26/23.40  |   (7)  all_52_7 = e0
% 154.26/23.40  | 
% 154.26/23.40  | GROUND_INST: instantiating (3) with all_52_3, e0, e3, e0, simplifying with
% 154.26/23.40  |              (4), (5) gives:
% 154.26/23.40  |   (8)  all_52_3 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (2), (7), (8) imply:
% 154.26/23.40  |   (9)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (9) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1124 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (2)  op(e0, e1) = all_52_11
% 154.26/23.40    (3)  op(e0, e1) = e0
% 154.26/23.40    (4)   ~ (all_52_11 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | GROUND_INST: instantiating (1) with all_52_11, e0, e1, e0, simplifying with
% 154.26/23.40  |              (2), (3) gives:
% 154.26/23.40  |   (5)  all_52_11 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (4), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1125 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (2)  op(e1, e0) = e2
% 154.26/23.40    (3)  op(e1, e0) = e1
% 154.26/23.40    (4)   ~ (e2 = e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | GROUND_INST: instantiating (1) with e2, e1, e0, e1, simplifying with (2), (3)
% 154.26/23.40  |              gives:
% 154.26/23.40  |   (5)  e2 = e1
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (4), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1126 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_7 = e1 & op(e1, e2) = e1
% 154.26/23.40    (2)  all_56_7 = e3
% 154.26/23.40    (3)   ~ (e3 = e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | ALPHA: (1) implies:
% 154.26/23.40  |   (4)  all_56_7 = e1
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.40  |   (5)  e3 = e1
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1127 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (2)  op(e1, e3) = e0
% 154.26/23.40    (3)  op(e1, e3) = e1
% 154.26/23.40    (4)   ~ (e1 = e0)
% 154.26/23.40    (5)  op(e1, e3) = all_52_2
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | GROUND_INST: instantiating (1) with all_52_2, e0, e3, e1, simplifying with
% 154.26/23.40  |              (2), (5) gives:
% 154.26/23.40  |   (6)  all_52_2 = e0
% 154.26/23.40  | 
% 154.26/23.40  | GROUND_INST: instantiating (1) with all_52_2, e1, e3, e1, simplifying with
% 154.26/23.40  |              (3), (5) gives:
% 154.26/23.40  |   (7)  all_52_2 = e1
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (6), (7) imply:
% 154.26/23.40  |   (8)  e1 = e0
% 154.26/23.40  | 
% 154.26/23.40  | SIMP: (8) implies:
% 154.26/23.40  |   (9)  e1 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (4), (9) imply:
% 154.26/23.40  |   (10)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (10) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1128 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_7 = e2 & op(e1, e2) = e2
% 154.26/23.40    (2)  all_56_7 = e3
% 154.26/23.40    (3)   ~ (e3 = e2)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | ALPHA: (1) implies:
% 154.26/23.40  |   (4)  all_56_7 = e2
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.40  |   (5)  e3 = e2
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1129 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_6 = e2 & op(e1, e3) = e2
% 154.26/23.40    (2)  all_56_6 = e0
% 154.26/23.40    (3)   ~ (e2 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | ALPHA: (1) implies:
% 154.26/23.40  |   (4)  all_56_6 = e2
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.40  |   (5)  e2 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1130 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_4 = e0 & op(e3, e1) = e0
% 154.26/23.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (3)  op(e3, e1) = all_52_8
% 154.26/23.40    (4)   ~ (all_52_8 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | ALPHA: (1) implies:
% 154.26/23.40  |   (5)  op(e3, e1) = e0
% 154.26/23.40  | 
% 154.26/23.40  | GROUND_INST: instantiating (2) with all_52_8, e0, e1, e3, simplifying with
% 154.26/23.40  |              (3), (5) gives:
% 154.26/23.40  |   (6)  all_52_8 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (4), (6) imply:
% 154.26/23.40  |   (7)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (7) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1131 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_10 = e1 & op(e2, e0) = e1
% 154.26/23.40    (2)  all_56_10 = e0
% 154.26/23.40    (3)   ~ (e1 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | ALPHA: (1) implies:
% 154.26/23.40  |   (4)  all_56_10 = e1
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.40  |   (5)  e1 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1132 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_10 = e2 & op(e2, e0) = e2
% 154.26/23.40    (2)  all_56_10 = e0
% 154.26/23.40    (3)   ~ (e2 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | ALPHA: (1) implies:
% 154.26/23.40  |   (4)  all_56_10 = e2
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.40  |   (5)  e2 = e0
% 154.26/23.40  | 
% 154.26/23.40  | SIMP: (5) implies:
% 154.26/23.40  |   (6)  e2 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (6) imply:
% 154.26/23.40  |   (7)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (7) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1133 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)   ~ (e3 = e1)
% 154.26/23.40    (2)  op(e2, e2) = e1
% 154.26/23.40    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (4)  all_56_10 = e0
% 154.26/23.40    (5)   ~ (e3 = e0)
% 154.26/23.40    (6)  op(e2, e1) = e2
% 154.26/23.40    (7)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) = e3) |
% 154.26/23.40         (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) = e3)
% 154.26/23.40    (8)  all_56_2 = e0
% 154.26/23.40    (9)   ~ (e3 = e2)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | BETA: splitting (7) gives:
% 154.26/23.40  | 
% 154.26/23.40  | Case 1:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (10)  (all_56_2 = e3 & op(e2, e3) = e3) | (all_56_3 = e3 & op(e2, e2) =
% 154.26/23.40  | |           e3)
% 154.26/23.40  | | 
% 154.26/23.40  | | BETA: splitting (10) gives:
% 154.26/23.40  | | 
% 154.26/23.40  | | Case 1:
% 154.26/23.40  | | | 
% 154.26/23.40  | | |   (11)  all_56_2 = e3 & op(e2, e3) = e3
% 154.26/23.40  | | | 
% 154.26/23.40  | | | ALPHA: (11) implies:
% 154.26/23.40  | | |   (12)  all_56_2 = e3
% 154.26/23.40  | | | 
% 154.26/23.40  | | | REF_CLOSE: (5), (8), (12) are inconsistent by sub-proof #1137.
% 154.26/23.40  | | | 
% 154.26/23.40  | | Case 2:
% 154.26/23.40  | | | 
% 154.26/23.40  | | |   (13)  all_56_3 = e3 & op(e2, e2) = e3
% 154.26/23.40  | | | 
% 154.26/23.40  | | | ALPHA: (13) implies:
% 154.26/23.40  | | |   (14)  op(e2, e2) = e3
% 154.26/23.40  | | | 
% 154.26/23.40  | | | REF_CLOSE: (1), (2), (3), (14) are inconsistent by sub-proof #1136.
% 154.26/23.40  | | | 
% 154.26/23.40  | | End of split
% 154.26/23.40  | | 
% 154.26/23.40  | Case 2:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (15)  (all_56_5 = e3 & op(e2, e1) = e3) | (all_56_10 = e3 & op(e2, e0) =
% 154.26/23.40  | |           e3)
% 154.26/23.40  | | 
% 154.26/23.40  | | BETA: splitting (15) gives:
% 154.26/23.40  | | 
% 154.26/23.40  | | Case 1:
% 154.26/23.40  | | | 
% 154.26/23.40  | | |   (16)  all_56_5 = e3 & op(e2, e1) = e3
% 154.26/23.40  | | | 
% 154.26/23.40  | | | ALPHA: (16) implies:
% 154.26/23.40  | | |   (17)  op(e2, e1) = e3
% 154.26/23.40  | | | 
% 154.26/23.40  | | | REF_CLOSE: (3), (6), (9), (17) are inconsistent by sub-proof #1135.
% 154.26/23.40  | | | 
% 154.26/23.40  | | Case 2:
% 154.26/23.40  | | | 
% 154.26/23.40  | | |   (18)  all_56_10 = e3 & op(e2, e0) = e3
% 154.26/23.40  | | | 
% 154.26/23.40  | | | ALPHA: (18) implies:
% 154.26/23.40  | | |   (19)  all_56_10 = e3
% 154.26/23.40  | | | 
% 154.26/23.40  | | | REF_CLOSE: (4), (5), (19) are inconsistent by sub-proof #1134.
% 154.26/23.40  | | | 
% 154.26/23.40  | | End of split
% 154.26/23.40  | | 
% 154.26/23.40  | End of split
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1134 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_10 = e3
% 154.26/23.40    (2)  all_56_10 = e0
% 154.26/23.40    (3)   ~ (e3 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.40  |   (4)  e3 = e0
% 154.26/23.40  | 
% 154.26/23.40  | SIMP: (4) implies:
% 154.26/23.40  |   (5)  e3 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1135 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (2)  op(e2, e1) = e3
% 154.26/23.40    (3)  op(e2, e1) = e2
% 154.26/23.40    (4)   ~ (e3 = e2)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | GROUND_INST: instantiating (1) with e3, e2, e1, e2, simplifying with (2), (3)
% 154.26/23.40  |              gives:
% 154.26/23.40  |   (5)  e3 = e2
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (4), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1136 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (2)  op(e2, e2) = e3
% 154.26/23.40    (3)  op(e2, e2) = e1
% 154.26/23.40    (4)   ~ (e3 = e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | GROUND_INST: instantiating (1) with e1, e3, e2, e2, simplifying with (2), (3)
% 154.26/23.40  |              gives:
% 154.26/23.40  |   (5)  e3 = e1
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (4), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1137 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  all_56_2 = e3
% 154.26/23.40    (2)  all_56_2 = e0
% 154.26/23.40    (3)   ~ (e3 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.40  |   (4)  e3 = e0
% 154.26/23.40  | 
% 154.26/23.40  | SIMP: (4) implies:
% 154.26/23.40  |   (5)  e3 = e0
% 154.26/23.40  | 
% 154.26/23.40  | REDUCE: (3), (5) imply:
% 154.26/23.40  |   (6)  $false
% 154.26/23.40  | 
% 154.26/23.40  | CLOSE: (6) is inconsistent.
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1138 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  op(e2, e2) = e1
% 154.26/23.40    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2)
% 154.26/23.40    (4)   ~ (e2 = e1)
% 154.26/23.40    (5)  op(e2, e3) = all_52_1
% 154.26/23.40    (6)   ~ (all_52_1 = e2)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | BETA: splitting (3) gives:
% 154.26/23.40  | 
% 154.26/23.40  | Case 1:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (7)  all_56_2 = e2 & op(e2, e3) = e2
% 154.26/23.40  | | 
% 154.26/23.40  | | ALPHA: (7) implies:
% 154.26/23.40  | |   (8)  op(e2, e3) = e2
% 154.26/23.40  | | 
% 154.26/23.40  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #1181.
% 154.26/23.40  | | 
% 154.26/23.40  | Case 2:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (9)  all_56_3 = e2 & op(e2, e2) = e2
% 154.26/23.40  | | 
% 154.26/23.40  | | ALPHA: (9) implies:
% 154.26/23.40  | |   (10)  op(e2, e2) = e2
% 154.26/23.40  | | 
% 154.26/23.40  | | REF_CLOSE: (1), (2), (4), (10) are inconsistent by sub-proof #1158.
% 154.26/23.40  | | 
% 154.26/23.40  | End of split
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1139 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)  op(e3, e3) = e0
% 154.26/23.40    (2)   ~ (all_14_2 = e0)
% 154.26/23.40    (3)  op(e3, e3) = all_14_2
% 154.26/23.40    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (5)  all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.26/23.40    (6)  all_54_0 = all_14_2
% 154.26/23.40    (7)   ~ (all_14_2 = e2)
% 154.26/23.40    (8)   ~ (all_14_2 = e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | BETA: splitting (5) gives:
% 154.26/23.40  | 
% 154.26/23.40  | Case 1:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (9)  all_54_0 = e3
% 154.26/23.40  | | 
% 154.26/23.40  | | COMBINE_EQS: (6), (9) imply:
% 154.26/23.40  | |   (10)  all_14_2 = e3
% 154.26/23.40  | | 
% 154.26/23.40  | | REDUCE: (2), (10) imply:
% 154.26/23.40  | |   (11)   ~ (e3 = e0)
% 154.26/23.40  | | 
% 154.26/23.40  | | REDUCE: (3), (10) imply:
% 154.26/23.40  | |   (12)  op(e3, e3) = e3
% 154.26/23.40  | | 
% 154.26/23.40  | | REF_CLOSE: (1), (4), (11), (12) are inconsistent by sub-proof #1141.
% 154.26/23.40  | | 
% 154.26/23.40  | Case 2:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (13)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.26/23.40  | | 
% 154.26/23.40  | | REF_CLOSE: (2), (6), (7), (8), (13) are inconsistent by sub-proof #1140.
% 154.26/23.40  | | 
% 154.26/23.40  | End of split
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1140 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)   ~ (all_14_2 = e0)
% 154.26/23.40    (2)  all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 154.26/23.40    (3)  all_54_0 = all_14_2
% 154.26/23.40    (4)   ~ (all_14_2 = e2)
% 154.26/23.40    (5)   ~ (all_14_2 = e1)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.40  | 
% 154.26/23.40  | BETA: splitting (2) gives:
% 154.26/23.40  | 
% 154.26/23.40  | Case 1:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (6)  all_54_0 = e2
% 154.26/23.40  | | 
% 154.26/23.40  | | COMBINE_EQS: (3), (6) imply:
% 154.26/23.40  | |   (7)  all_14_2 = e2
% 154.26/23.40  | | 
% 154.26/23.40  | | REDUCE: (4), (7) imply:
% 154.26/23.40  | |   (8)  $false
% 154.26/23.40  | | 
% 154.26/23.40  | | CLOSE: (8) is inconsistent.
% 154.26/23.40  | | 
% 154.26/23.40  | Case 2:
% 154.26/23.40  | | 
% 154.26/23.40  | |   (9)  all_54_0 = e1 | all_54_0 = e0
% 154.26/23.40  | | 
% 154.26/23.40  | | BETA: splitting (9) gives:
% 154.26/23.40  | | 
% 154.26/23.40  | | Case 1:
% 154.26/23.40  | | | 
% 154.26/23.40  | | |   (10)  all_54_0 = e1
% 154.26/23.40  | | | 
% 154.26/23.40  | | | COMBINE_EQS: (3), (10) imply:
% 154.26/23.40  | | |   (11)  all_14_2 = e1
% 154.26/23.40  | | | 
% 154.26/23.40  | | | REDUCE: (5), (11) imply:
% 154.26/23.40  | | |   (12)  $false
% 154.26/23.40  | | | 
% 154.26/23.40  | | | CLOSE: (12) is inconsistent.
% 154.26/23.40  | | | 
% 154.26/23.40  | | Case 2:
% 154.26/23.40  | | | 
% 154.26/23.40  | | |   (13)  all_54_0 = e0
% 154.26/23.40  | | | 
% 154.26/23.40  | | | COMBINE_EQS: (3), (13) imply:
% 154.26/23.40  | | |   (14)  all_14_2 = e0
% 154.26/23.40  | | | 
% 154.26/23.40  | | | REDUCE: (1), (14) imply:
% 154.26/23.40  | | |   (15)  $false
% 154.26/23.40  | | | 
% 154.26/23.40  | | | CLOSE: (15) is inconsistent.
% 154.26/23.40  | | | 
% 154.26/23.40  | | End of split
% 154.26/23.40  | | 
% 154.26/23.40  | End of split
% 154.26/23.40  | 
% 154.26/23.40  End of proof
% 154.26/23.40  
% 154.26/23.40  Sub-proof #1141 shows that the following formulas are inconsistent:
% 154.26/23.40  ----------------------------------------------------------------
% 154.26/23.40    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.40           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.40    (2)  op(e3, e3) = e3
% 154.26/23.40    (3)  op(e3, e3) = e0
% 154.26/23.40    (4)   ~ (e3 = e0)
% 154.26/23.40  
% 154.26/23.40  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with e0, e3, e3, e3, simplifying with (2), (3)
% 154.26/23.41  |              gives:
% 154.26/23.41  |   (5)  e3 = e0
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1142 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  op(e0, e3) = all_52_3
% 154.26/23.41    (3)  op(e0, e3) = e0
% 154.26/23.41    (4)   ~ (all_52_3 = e0)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with all_52_3, e0, e3, e0, simplifying with
% 154.26/23.41  |              (2), (3) gives:
% 154.26/23.41  |   (5)  all_52_3 = e0
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1143 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  op(e0, e0) = e3
% 154.26/23.41    (3)  op(e0, e0) = e0
% 154.26/23.41    (4)   ~ (e3 = e0)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with e0, e3, e0, e0, simplifying with (2), (3)
% 154.26/23.41  |              gives:
% 154.26/23.41  |   (5)  e3 = e0
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1144 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_56_5 = e0 & op(e2, e1) = e0
% 154.26/23.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (3)  op(e2, e1) = all_52_9
% 154.26/23.41    (4)   ~ (all_52_9 = e0)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | ALPHA: (1) implies:
% 154.26/23.41  |   (5)  op(e2, e1) = e0
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (2) with all_52_9, e0, e1, e2, simplifying with
% 154.26/23.41  |              (3), (5) gives:
% 154.26/23.41  |   (6)  all_52_9 = e0
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (6) imply:
% 154.26/23.41  |   (7)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (7) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1145 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  op(e2, e2) = e2
% 154.26/23.41    (3)  op(e2, e2) = e0
% 154.26/23.41    (4)   ~ (e2 = e0)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with e0, e2, e2, e2, simplifying with (2), (3)
% 154.26/23.41  |              gives:
% 154.26/23.41  |   (5)  e2 = e0
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1146 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  op(e0, e1) = all_52_11
% 154.26/23.41    (2)  all_56_11 = e2
% 154.26/23.41    (3)   ~ (e2 = e0)
% 154.26/23.41    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (5)  all_56_7 = e3
% 154.26/23.41    (6)  all_56_6 = e1
% 154.26/23.41    (7)   ~ (all_52_11 = e3)
% 154.26/23.41    (8)   ~ (e3 = e0)
% 154.26/23.41    (9)  (all_56_8 = e3 & op(e1, e1) = e3) | (all_56_14 = e3 & op(e0, e1) = e3)
% 154.26/23.41    (10)   ~ (e1 = e0)
% 154.26/23.41    (11)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 154.26/23.41          (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | BETA: splitting (9) gives:
% 154.26/23.41  | 
% 154.26/23.41  | Case 1:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (12)  all_56_8 = e3 & op(e1, e1) = e3
% 154.26/23.41  | | 
% 154.26/23.41  | | ALPHA: (12) implies:
% 154.26/23.41  | |   (13)  all_56_8 = e3
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (2), (3), (5), (6), (8), (10), (11), (13) are inconsistent by
% 154.26/23.41  | |            sub-proof #1148.
% 154.26/23.41  | | 
% 154.26/23.41  | Case 2:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (14)  all_56_14 = e3 & op(e0, e1) = e3
% 154.26/23.41  | | 
% 154.26/23.41  | | ALPHA: (14) implies:
% 154.26/23.41  | |   (15)  op(e0, e1) = e3
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (1), (4), (7), (15) are inconsistent by sub-proof #1147.
% 154.26/23.41  | | 
% 154.26/23.41  | End of split
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1147 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  op(e0, e1) = all_52_11
% 154.26/23.41    (3)  op(e0, e1) = e3
% 154.26/23.41    (4)   ~ (all_52_11 = e3)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with all_52_11, e3, e1, e0, simplifying with
% 154.26/23.41  |              (2), (3) gives:
% 154.26/23.41  |   (5)  all_52_11 = e3
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1148 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_56_8 = e3
% 154.26/23.41    (2)  all_56_11 = e2
% 154.26/23.41    (3)   ~ (e2 = e0)
% 154.26/23.41    (4)  all_56_7 = e3
% 154.26/23.41    (5)  all_56_6 = e1
% 154.26/23.41    (6)   ~ (e3 = e0)
% 154.26/23.41    (7)   ~ (e1 = e0)
% 154.26/23.41    (8)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0) |
% 154.26/23.41         (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) = e0)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | BETA: splitting (8) gives:
% 154.26/23.41  | 
% 154.26/23.41  | Case 1:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (9)  (all_56_6 = e0 & op(e1, e3) = e0) | (all_56_7 = e0 & op(e1, e2) = e0)
% 154.26/23.41  | | 
% 154.26/23.41  | | BETA: splitting (9) gives:
% 154.26/23.41  | | 
% 154.26/23.41  | | Case 1:
% 154.26/23.41  | | | 
% 154.26/23.41  | | |   (10)  all_56_6 = e0 & op(e1, e3) = e0
% 154.26/23.41  | | | 
% 154.26/23.41  | | | REF_CLOSE: (5), (7), (10) are inconsistent by sub-proof #1152.
% 154.26/23.41  | | | 
% 154.26/23.41  | | Case 2:
% 154.26/23.41  | | | 
% 154.26/23.41  | | |   (11)  all_56_7 = e0 & op(e1, e2) = e0
% 154.26/23.41  | | | 
% 154.26/23.41  | | | REF_CLOSE: (4), (6), (11) are inconsistent by sub-proof #1151.
% 154.26/23.41  | | | 
% 154.26/23.41  | | End of split
% 154.26/23.41  | | 
% 154.26/23.41  | Case 2:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (12)  (all_56_8 = e0 & op(e1, e1) = e0) | (all_56_11 = e0 & op(e1, e0) =
% 154.26/23.41  | |           e0)
% 154.26/23.41  | | 
% 154.26/23.41  | | BETA: splitting (12) gives:
% 154.26/23.41  | | 
% 154.26/23.41  | | Case 1:
% 154.26/23.41  | | | 
% 154.26/23.41  | | |   (13)  all_56_8 = e0 & op(e1, e1) = e0
% 154.26/23.41  | | | 
% 154.26/23.41  | | | REF_CLOSE: (1), (6), (13) are inconsistent by sub-proof #1150.
% 154.26/23.41  | | | 
% 154.26/23.41  | | Case 2:
% 154.26/23.41  | | | 
% 154.26/23.41  | | |   (14)  all_56_11 = e0 & op(e1, e0) = e0
% 154.26/23.41  | | | 
% 154.26/23.41  | | | REF_CLOSE: (2), (3), (14) are inconsistent by sub-proof #1149.
% 154.26/23.41  | | | 
% 154.26/23.41  | | End of split
% 154.26/23.41  | | 
% 154.26/23.41  | End of split
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1149 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_56_11 = e0 & op(e1, e0) = e0
% 154.26/23.41    (2)  all_56_11 = e2
% 154.26/23.41    (3)   ~ (e2 = e0)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | ALPHA: (1) implies:
% 154.26/23.41  |   (4)  all_56_11 = e0
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.41  |   (5)  e2 = e0
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1150 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_56_8 = e0 & op(e1, e1) = e0
% 154.26/23.41    (2)  all_56_8 = e3
% 154.26/23.41    (3)   ~ (e3 = e0)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | ALPHA: (1) implies:
% 154.26/23.41  |   (4)  all_56_8 = e0
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.41  |   (5)  e3 = e0
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1151 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_56_7 = e0 & op(e1, e2) = e0
% 154.26/23.41    (2)  all_56_7 = e3
% 154.26/23.41    (3)   ~ (e3 = e0)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | ALPHA: (1) implies:
% 154.26/23.41  |   (4)  all_56_7 = e0
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.41  |   (5)  e3 = e0
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1152 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_56_6 = e0 & op(e1, e3) = e0
% 154.26/23.41    (2)  all_56_6 = e1
% 154.26/23.41    (3)   ~ (e1 = e0)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | ALPHA: (1) implies:
% 154.26/23.41  |   (4)  all_56_6 = e0
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.41  |   (5)  e1 = e0
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1153 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_56_5 = e1 & op(e2, e1) = e1
% 154.26/23.41    (2)  all_56_5 = e3
% 154.26/23.41    (3)   ~ (e3 = e1)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | ALPHA: (1) implies:
% 154.26/23.41  |   (4)  all_56_5 = e1
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (2), (4) imply:
% 154.26/23.41  |   (5)  e3 = e1
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1154 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  op(e2, e2) = e1
% 154.26/23.41    (2)   ~ (e2 = e0)
% 154.26/23.41    (3)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) = e2) |
% 154.26/23.41         (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 154.26/23.41    (4)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (5)   ~ (all_52_13 = e2)
% 154.26/23.41    (6)  op(e2, e0) = all_52_13
% 154.26/23.41    (7)   ~ (all_52_9 = e2)
% 154.26/23.41    (8)  op(e2, e1) = all_52_9
% 154.26/23.41    (9)  all_56_2 = e0
% 154.26/23.41    (10)   ~ (e2 = e1)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | BETA: splitting (3) gives:
% 154.26/23.41  | 
% 154.26/23.41  | Case 1:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (11)  (all_56_2 = e2 & op(e2, e3) = e2) | (all_56_3 = e2 & op(e2, e2) =
% 154.26/23.41  | |           e2)
% 154.26/23.41  | | 
% 154.26/23.41  | | BETA: splitting (11) gives:
% 154.26/23.41  | | 
% 154.26/23.41  | | Case 1:
% 154.26/23.41  | | | 
% 154.26/23.41  | | |   (12)  all_56_2 = e2 & op(e2, e3) = e2
% 154.26/23.41  | | | 
% 154.26/23.41  | | | ALPHA: (12) implies:
% 154.26/23.41  | | |   (13)  all_56_2 = e2
% 154.26/23.41  | | | 
% 154.26/23.41  | | | COMBINE_EQS: (9), (13) imply:
% 154.26/23.41  | | |   (14)  e2 = e0
% 154.26/23.41  | | | 
% 154.26/23.41  | | | REDUCE: (2), (14) imply:
% 154.26/23.41  | | |   (15)  $false
% 154.26/23.41  | | | 
% 154.26/23.41  | | | CLOSE: (15) is inconsistent.
% 154.26/23.41  | | | 
% 154.26/23.41  | | Case 2:
% 154.26/23.41  | | | 
% 154.26/23.41  | | |   (16)  all_56_3 = e2 & op(e2, e2) = e2
% 154.26/23.41  | | | 
% 154.26/23.41  | | | ALPHA: (16) implies:
% 154.26/23.41  | | |   (17)  op(e2, e2) = e2
% 154.26/23.41  | | | 
% 154.26/23.41  | | | REF_CLOSE: (1), (4), (10), (17) are inconsistent by sub-proof #1158.
% 154.26/23.41  | | | 
% 154.26/23.41  | | End of split
% 154.26/23.41  | | 
% 154.26/23.41  | Case 2:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (18)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) =
% 154.26/23.41  | |           e2)
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (4), (5), (6), (7), (8), (18) are inconsistent by sub-proof
% 154.26/23.41  | |            #1155.
% 154.26/23.41  | | 
% 154.26/23.41  | End of split
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1155 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  (all_56_5 = e2 & op(e2, e1) = e2) | (all_56_10 = e2 & op(e2, e0) = e2)
% 154.26/23.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (3)   ~ (all_52_13 = e2)
% 154.26/23.41    (4)  op(e2, e0) = all_52_13
% 154.26/23.41    (5)   ~ (all_52_9 = e2)
% 154.26/23.41    (6)  op(e2, e1) = all_52_9
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | BETA: splitting (1) gives:
% 154.26/23.41  | 
% 154.26/23.41  | Case 1:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (7)  all_56_5 = e2 & op(e2, e1) = e2
% 154.26/23.41  | | 
% 154.26/23.41  | | ALPHA: (7) implies:
% 154.26/23.41  | |   (8)  op(e2, e1) = e2
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #1157.
% 154.26/23.41  | | 
% 154.26/23.41  | Case 2:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (9)  all_56_10 = e2 & op(e2, e0) = e2
% 154.26/23.41  | | 
% 154.26/23.41  | | ALPHA: (9) implies:
% 154.26/23.41  | |   (10)  op(e2, e0) = e2
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (2), (3), (4), (10) are inconsistent by sub-proof #1156.
% 154.26/23.41  | | 
% 154.26/23.41  | End of split
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1156 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  op(e2, e0) = all_52_13
% 154.26/23.41    (3)  op(e2, e0) = e2
% 154.26/23.41    (4)   ~ (all_52_13 = e2)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with all_52_13, e2, e0, e2, simplifying with
% 154.26/23.41  |              (2), (3) gives:
% 154.26/23.41  |   (5)  all_52_13 = e2
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1157 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  op(e2, e1) = all_52_9
% 154.26/23.41    (3)  op(e2, e1) = e2
% 154.26/23.41    (4)   ~ (all_52_9 = e2)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with all_52_9, e2, e1, e2, simplifying with
% 154.26/23.41  |              (2), (3) gives:
% 154.26/23.41  |   (5)  all_52_9 = e2
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1158 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  op(e2, e2) = e2
% 154.26/23.41    (3)  op(e2, e2) = e1
% 154.26/23.41    (4)   ~ (e2 = e1)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with e1, e2, e2, e2, simplifying with (2), (3)
% 154.26/23.41  |              gives:
% 154.26/23.41  |   (5)  e2 = e1
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1159 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.26/23.41    (2)  all_56_2 = e1 & op(e2, e3) = e1
% 154.26/23.41    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (4)   ~ (all_52_13 = e0)
% 154.26/23.41    (5)   ~ (all_52_1 = all_52_13)
% 154.26/23.41    (6)   ~ (all_52_13 = e2)
% 154.26/23.41    (7)   ~ (all_52_13 = e3)
% 154.26/23.41    (8)  all_54_7 = all_52_13
% 154.26/23.41    (9)  op(e2, e3) = all_52_1
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | ALPHA: (2) implies:
% 154.26/23.41  |   (10)  op(e2, e3) = e1
% 154.26/23.41  | 
% 154.26/23.41  | BETA: splitting (1) gives:
% 154.26/23.41  | 
% 154.26/23.41  | Case 1:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (11)  all_54_7 = e3
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (7), (8), (11) are inconsistent by sub-proof #1163.
% 154.26/23.41  | | 
% 154.26/23.41  | Case 2:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (12)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (3), (4), (5), (6), (8), (9), (10), (12) are inconsistent by
% 154.26/23.41  | |            sub-proof #1160.
% 154.26/23.41  | | 
% 154.26/23.41  | End of split
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1160 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)   ~ (all_52_13 = e0)
% 154.26/23.41    (3)   ~ (all_52_1 = all_52_13)
% 154.26/23.41    (4)  op(e2, e3) = e1
% 154.26/23.41    (5)   ~ (all_52_13 = e2)
% 154.26/23.41    (6)  all_54_7 = all_52_13
% 154.26/23.41    (7)  all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 154.26/23.41    (8)  op(e2, e3) = all_52_1
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | BETA: splitting (7) gives:
% 154.26/23.41  | 
% 154.26/23.41  | Case 1:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (9)  all_54_7 = e2
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (5), (6), (9) are inconsistent by sub-proof #1162.
% 154.26/23.41  | | 
% 154.26/23.41  | Case 2:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (10)  all_54_7 = e1 | all_54_7 = e0
% 154.26/23.41  | | 
% 154.26/23.41  | | BETA: splitting (10) gives:
% 154.26/23.41  | | 
% 154.26/23.41  | | Case 1:
% 154.26/23.41  | | | 
% 154.26/23.41  | | |   (11)  all_54_7 = e1
% 154.26/23.41  | | | 
% 154.26/23.41  | | | COMBINE_EQS: (6), (11) imply:
% 154.26/23.41  | | |   (12)  all_52_13 = e1
% 154.26/23.41  | | | 
% 154.26/23.41  | | | SIMP: (12) implies:
% 154.26/23.41  | | |   (13)  all_52_13 = e1
% 154.26/23.41  | | | 
% 154.26/23.41  | | | REDUCE: (3), (13) imply:
% 154.26/23.41  | | |   (14)   ~ (all_52_1 = e1)
% 154.26/23.41  | | | 
% 154.26/23.41  | | | REF_CLOSE: (1), (4), (8), (14) are inconsistent by sub-proof #1177.
% 154.26/23.41  | | | 
% 154.26/23.41  | | Case 2:
% 154.26/23.41  | | | 
% 154.26/23.41  | | |   (15)  all_54_7 = e0
% 154.26/23.41  | | | 
% 154.26/23.41  | | | REF_CLOSE: (2), (6), (15) are inconsistent by sub-proof #1161.
% 154.26/23.41  | | | 
% 154.26/23.41  | | End of split
% 154.26/23.41  | | 
% 154.26/23.41  | End of split
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1161 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_54_7 = all_52_13
% 154.26/23.41    (2)  all_54_7 = e0
% 154.26/23.41    (3)   ~ (all_52_13 = e0)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.41  |   (4)  all_52_13 = e0
% 154.26/23.41  | 
% 154.26/23.41  | SIMP: (4) implies:
% 154.26/23.41  |   (5)  all_52_13 = e0
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1162 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_54_7 = all_52_13
% 154.26/23.41    (2)  all_54_7 = e2
% 154.26/23.41    (3)   ~ (all_52_13 = e2)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.41  |   (4)  all_52_13 = e2
% 154.26/23.41  | 
% 154.26/23.41  | SIMP: (4) implies:
% 154.26/23.41  |   (5)  all_52_13 = e2
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1163 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_54_7 = all_52_13
% 154.26/23.41    (2)  all_54_7 = e3
% 154.26/23.41    (3)   ~ (all_52_13 = e3)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.41  |   (4)  all_52_13 = e3
% 154.26/23.41  | 
% 154.26/23.41  | SIMP: (4) implies:
% 154.26/23.41  |   (5)  all_52_13 = e3
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1164 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  op(e3, e1) = all_52_8
% 154.26/23.41    (3)  op(e3, e1) = e3
% 154.26/23.41    (4)   ~ (all_52_8 = e3)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with all_52_8, e3, e1, e3, simplifying with
% 154.26/23.41  |              (2), (3) gives:
% 154.26/23.41  |   (5)  all_52_8 = e3
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1165 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  (all_56_1 = e3 & op(e3, e2) = e3) | (all_56_3 = e3 & op(e2, e2) = e3)
% 154.26/23.41    (2)  op(e3, e2) = all_52_4
% 154.26/23.41    (3)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (4)   ~ (all_52_4 = e3)
% 154.26/23.41    (5)  op(e2, e2) = e2
% 154.26/23.41    (6)   ~ (e3 = e2)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | BETA: splitting (1) gives:
% 154.26/23.41  | 
% 154.26/23.41  | Case 1:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (7)  all_56_1 = e3 & op(e3, e2) = e3
% 154.26/23.41  | | 
% 154.26/23.41  | | ALPHA: (7) implies:
% 154.26/23.41  | |   (8)  op(e3, e2) = e3
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1166.
% 154.26/23.41  | | 
% 154.26/23.41  | Case 2:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (9)  all_56_3 = e3 & op(e2, e2) = e3
% 154.26/23.41  | | 
% 154.26/23.41  | | ALPHA: (9) implies:
% 154.26/23.41  | |   (10)  op(e2, e2) = e3
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1179.
% 154.26/23.41  | | 
% 154.26/23.41  | End of split
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1166 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  op(e3, e2) = all_52_4
% 154.26/23.41    (3)  op(e3, e2) = e3
% 154.26/23.41    (4)   ~ (all_52_4 = e3)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with all_52_4, e3, e2, e3, simplifying with
% 154.26/23.41  |              (2), (3) gives:
% 154.26/23.41  |   (5)  all_52_4 = e3
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1167 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_54_10 = all_4_2
% 154.26/23.41    (2)  all_54_10 = e1
% 154.26/23.41    (3)   ~ (all_4_2 = e1)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.41  |   (4)  all_4_2 = e1
% 154.26/23.41  | 
% 154.26/23.41  | SIMP: (4) implies:
% 154.26/23.41  |   (5)  all_4_2 = e1
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1168 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_54_10 = all_4_2
% 154.26/23.41    (2)  all_54_10 = e2
% 154.26/23.41    (3)   ~ (all_4_2 = e2)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.41  |   (4)  all_4_2 = e2
% 154.26/23.41  | 
% 154.26/23.41  | SIMP: (4) implies:
% 154.26/23.41  |   (5)  all_4_2 = e2
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1169 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  op(e1, e1) = all_4_2
% 154.26/23.41    (3)  op(e1, e1) = e2
% 154.26/23.41    (4)   ~ (all_4_2 = e2)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with all_4_2, e2, e1, e1, simplifying with (2),
% 154.26/23.41  |              (3) gives:
% 154.26/23.41  |   (5)  all_4_2 = e2
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1170 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  all_56_6 = e1
% 154.26/23.41    (3)  (all_56_6 = e2 & op(e1, e3) = e2) | (all_56_7 = e2 & op(e1, e2) = e2)
% 154.26/23.41    (4)  op(e1, e2) = all_52_6
% 154.26/23.41    (5)   ~ (e2 = e1)
% 154.26/23.41    (6)   ~ (all_52_6 = e2)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | BETA: splitting (3) gives:
% 154.26/23.41  | 
% 154.26/23.41  | Case 1:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (7)  all_56_6 = e2 & op(e1, e3) = e2
% 154.26/23.41  | | 
% 154.26/23.41  | | ALPHA: (7) implies:
% 154.26/23.41  | |   (8)  all_56_6 = e2
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #1172.
% 154.26/23.41  | | 
% 154.26/23.41  | Case 2:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (9)  all_56_7 = e2 & op(e1, e2) = e2
% 154.26/23.41  | | 
% 154.26/23.41  | | ALPHA: (9) implies:
% 154.26/23.41  | |   (10)  op(e1, e2) = e2
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #1171.
% 154.26/23.41  | | 
% 154.26/23.41  | End of split
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1171 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (2)  op(e1, e2) = all_52_6
% 154.26/23.41    (3)  op(e1, e2) = e2
% 154.26/23.41    (4)   ~ (all_52_6 = e2)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | GROUND_INST: instantiating (1) with all_52_6, e2, e2, e1, simplifying with
% 154.26/23.41  |              (2), (3) gives:
% 154.26/23.41  |   (5)  all_52_6 = e2
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (4), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1172 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_56_6 = e2
% 154.26/23.41    (2)  all_56_6 = e1
% 154.26/23.41    (3)   ~ (e2 = e1)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.41  |   (4)  e2 = e1
% 154.26/23.41  | 
% 154.26/23.41  | SIMP: (4) implies:
% 154.26/23.41  |   (5)  e2 = e1
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1173 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_54_10 = all_4_2
% 154.26/23.41    (2)  all_54_10 = e3
% 154.26/23.41    (3)   ~ (all_4_2 = e3)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.41  |   (4)  all_4_2 = e3
% 154.26/23.41  | 
% 154.26/23.41  | SIMP: (4) implies:
% 154.26/23.41  |   (5)  all_4_2 = e3
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1174 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_54_4 = all_52_1
% 154.26/23.41    (2)  all_54_4 = e1
% 154.26/23.41    (3)   ~ (all_52_1 = e1)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.41  |   (4)  all_52_1 = e1
% 154.26/23.41  | 
% 154.26/23.41  | SIMP: (4) implies:
% 154.26/23.41  |   (5)  all_52_1 = e1
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1175 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)  all_54_4 = all_52_1
% 154.26/23.41    (2)  all_54_4 = e2
% 154.26/23.41    (3)   ~ (all_52_1 = e2)
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | COMBINE_EQS: (1), (2) imply:
% 154.26/23.41  |   (4)  all_52_1 = e2
% 154.26/23.41  | 
% 154.26/23.41  | SIMP: (4) implies:
% 154.26/23.41  |   (5)  all_52_1 = e2
% 154.26/23.41  | 
% 154.26/23.41  | REDUCE: (3), (5) imply:
% 154.26/23.41  |   (6)  $false
% 154.26/23.41  | 
% 154.26/23.41  | CLOSE: (6) is inconsistent.
% 154.26/23.41  | 
% 154.26/23.41  End of proof
% 154.26/23.41  
% 154.26/23.41  Sub-proof #1176 shows that the following formulas are inconsistent:
% 154.26/23.41  ----------------------------------------------------------------
% 154.26/23.41    (1)   ~ (e3 = e1)
% 154.26/23.41    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.41           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.41    (3)  (all_56_0 = e1 & op(e3, e3) = e1) | (all_56_2 = e1 & op(e2, e3) = e1)
% 154.26/23.41    (4)   ~ (all_52_1 = e1)
% 154.26/23.41    (5)  op(e3, e3) = e3
% 154.26/23.41    (6)  op(e2, e3) = all_52_1
% 154.26/23.41  
% 154.26/23.41  Begin of proof
% 154.26/23.41  | 
% 154.26/23.41  | BETA: splitting (3) gives:
% 154.26/23.41  | 
% 154.26/23.41  | Case 1:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (7)  all_56_0 = e1 & op(e3, e3) = e1
% 154.26/23.41  | | 
% 154.26/23.41  | | ALPHA: (7) implies:
% 154.26/23.41  | |   (8)  op(e3, e3) = e1
% 154.26/23.41  | | 
% 154.26/23.41  | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #1178.
% 154.26/23.41  | | 
% 154.26/23.41  | Case 2:
% 154.26/23.41  | | 
% 154.26/23.41  | |   (9)  all_56_2 = e1 & op(e2, e3) = e1
% 154.26/23.41  | | 
% 154.26/23.41  | | ALPHA: (9) implies:
% 154.26/23.42  | |   (10)  op(e2, e3) = e1
% 154.26/23.42  | | 
% 154.26/23.42  | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #1177.
% 154.26/23.42  | | 
% 154.26/23.42  | End of split
% 154.26/23.42  | 
% 154.26/23.42  End of proof
% 154.26/23.42  
% 154.26/23.42  Sub-proof #1177 shows that the following formulas are inconsistent:
% 154.26/23.42  ----------------------------------------------------------------
% 154.26/23.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.42    (2)  op(e2, e3) = all_52_1
% 154.26/23.42    (3)  op(e2, e3) = e1
% 154.26/23.42    (4)   ~ (all_52_1 = e1)
% 154.26/23.42  
% 154.26/23.42  Begin of proof
% 154.26/23.42  | 
% 154.26/23.42  | GROUND_INST: instantiating (1) with all_52_1, e1, e3, e2, simplifying with
% 154.26/23.42  |              (2), (3) gives:
% 154.26/23.42  |   (5)  all_52_1 = e1
% 154.26/23.42  | 
% 154.26/23.42  | REDUCE: (4), (5) imply:
% 154.26/23.42  |   (6)  $false
% 154.26/23.42  | 
% 154.26/23.42  | CLOSE: (6) is inconsistent.
% 154.26/23.42  | 
% 154.26/23.42  End of proof
% 154.26/23.42  
% 154.26/23.42  Sub-proof #1178 shows that the following formulas are inconsistent:
% 154.26/23.42  ----------------------------------------------------------------
% 154.26/23.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.42    (2)  op(e3, e3) = e3
% 154.26/23.42    (3)  op(e3, e3) = e1
% 154.26/23.42    (4)   ~ (e3 = e1)
% 154.26/23.42  
% 154.26/23.42  Begin of proof
% 154.26/23.42  | 
% 154.26/23.42  | GROUND_INST: instantiating (1) with e1, e3, e3, e3, simplifying with (2), (3)
% 154.26/23.42  |              gives:
% 154.26/23.42  |   (5)  e3 = e1
% 154.26/23.42  | 
% 154.26/23.42  | REDUCE: (4), (5) imply:
% 154.26/23.42  |   (6)  $false
% 154.26/23.42  | 
% 154.26/23.42  | CLOSE: (6) is inconsistent.
% 154.26/23.42  | 
% 154.26/23.42  End of proof
% 154.26/23.42  
% 154.26/23.42  Sub-proof #1179 shows that the following formulas are inconsistent:
% 154.26/23.42  ----------------------------------------------------------------
% 154.26/23.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.26/23.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.26/23.42    (2)  op(e2, e2) = e3
% 154.26/23.42    (3)  op(e2, e2) = e2
% 154.26/23.42    (4)   ~ (e3 = e2)
% 154.26/23.42  
% 154.26/23.42  Begin of proof
% 154.26/23.42  | 
% 154.26/23.42  | GROUND_INST: instantiating (1) with e2, e3, e2, e2, simplifying with (2), (3)
% 154.26/23.42  |              gives:
% 154.26/23.42  |   (5)  e3 = e2
% 154.26/23.42  | 
% 154.26/23.42  | REDUCE: (4), (5) imply:
% 154.26/23.42  |   (6)  $false
% 154.26/23.42  | 
% 154.26/23.42  | CLOSE: (6) is inconsistent.
% 154.26/23.42  | 
% 154.26/23.42  End of proof
% 154.26/23.42  
% 154.26/23.42  Sub-proof #1180 shows that the following formulas are inconsistent:
% 154.26/23.42  ----------------------------------------------------------------
% 154.32/23.42    (1)  (all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 154.32/23.42             e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.32/23.42           all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)) | (all_57_0
% 154.32/23.42           = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 = e3) &
% 154.32/23.42           op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) = all_57_2 &
% 154.32/23.42           op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12))
% 154.32/23.42    (2)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.32/23.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.32/23.42    (3)  op(e2, e3) = all_52_1
% 154.32/23.42    (4)   ~ (all_52_1 = e2)
% 154.32/23.42  
% 154.32/23.42  Begin of proof
% 154.32/23.42  | 
% 154.32/23.42  | BETA: splitting (1) gives:
% 154.32/23.42  | 
% 154.32/23.42  | Case 1:
% 154.32/23.42  | | 
% 154.32/23.42  | |   (5)  all_57_0 = e2 & all_57_14 = e3 &  ~ (all_57_1 = e1) &  ~ (all_57_12 =
% 154.32/23.42  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e1, e3) =
% 154.32/23.42  | |        all_57_1 & op(e1, e1) = e3 & $i(all_57_1) & $i(all_57_12)
% 154.32/23.42  | | 
% 154.32/23.42  | | ALPHA: (5) implies:
% 154.32/23.42  | |   (6)  op(e2, e3) = e2
% 154.32/23.42  | | 
% 154.32/23.42  | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #1181.
% 154.32/23.42  | | 
% 154.32/23.42  | Case 2:
% 154.32/23.42  | | 
% 154.32/23.42  | |   (7)  all_57_0 = e2 & all_57_15 = e3 &  ~ (all_57_2 = e0) &  ~ (all_57_12 =
% 154.32/23.42  | |          e3) & op(e2, e3) = e2 & op(e2, e2) = all_57_12 & op(e0, e3) =
% 154.32/23.42  | |        all_57_2 & op(e0, e0) = e3 & $i(all_57_2) & $i(all_57_12)
% 154.32/23.42  | | 
% 154.32/23.42  | | ALPHA: (7) implies:
% 154.32/23.42  | |   (8)  op(e2, e3) = e2
% 154.32/23.42  | | 
% 154.32/23.42  | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1181.
% 154.32/23.42  | | 
% 154.32/23.42  | End of split
% 154.32/23.42  | 
% 154.32/23.42  End of proof
% 154.32/23.42  
% 154.32/23.42  Sub-proof #1181 shows that the following formulas are inconsistent:
% 154.32/23.42  ----------------------------------------------------------------
% 154.32/23.42    (1)   ! [v0: $i] :  ! [v1: $i] :  ! [v2: $i] :  ! [v3: $i] : (v1 = v0 |  ~
% 154.32/23.42           (op(v3, v2) = v1) |  ~ (op(v3, v2) = v0))
% 154.32/23.42    (2)  op(e2, e3) = all_52_1
% 154.32/23.42    (3)  op(e2, e3) = e2
% 154.32/23.42    (4)   ~ (all_52_1 = e2)
% 154.32/23.42  
% 154.32/23.42  Begin of proof
% 154.32/23.42  | 
% 154.32/23.42  | GROUND_INST: instantiating (1) with all_52_1, e2, e3, e2, simplifying with
% 154.32/23.42  |              (2), (3) gives:
% 154.32/23.42  |   (5)  all_52_1 = e2
% 154.32/23.42  | 
% 154.32/23.42  | REDUCE: (4), (5) imply:
% 154.32/23.42  |   (6)  $false
% 154.32/23.42  | 
% 154.32/23.42  | CLOSE: (6) is inconsistent.
% 154.32/23.42  | 
% 154.32/23.42  End of proof
% 154.32/23.42  % SZS output end Proof for theBenchmark
% 154.32/23.42  
% 154.32/23.42  22822ms
%------------------------------------------------------------------------------